force and shape estimation using fiber bragg grating ... · i would like to thank dr. abhijit lele...
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Force and Shape Estimation using Fiber Bragg Grating
Sensors for Assistance in
Minimally Invasive Diagnostic and Surgical
Procedures
A THE SI S
SUBMITTED FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
IN T HE FA CULTY OF ENGI NEERING
by
Kumar Saurabh
DEPART MENT O F INS TR UMENT ATION AND APP LI ED PHY SI CS
IN DIAN IN STIT UT E O F SCI EN CE
BANGALORE – 560 012
JULY 2017
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Declaration
I declare that the thesis entitled “Force and Shape Estimation using Fiber Bragg Grating
Sensors for Assistance in Minimally Invasive Diagnostic and Surgical Procedures”
submitted by me for the Ph.D. degree of the Indian Institute of Science did not form the subject
matter for any thesis submitted by me for any outside Degree and the original work done by
me and incorporated in the thesis is entirely done at the Indian Institute of Science, Bangalore.
Kumar Saurabh
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Dedicated to my family and my mentors.
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Acknowledgement
Writing this thesis presents me the opportunity to spend some time to think about all the
people who made this journey possible. The External Registration Program at the Indian
Institute of Science provided me the chance to pursue my Ph.D. while still continuing
to work. This allowed me to fulfil my dream which would not have been possible
otherwise.
Throughout this journey, my wife Seema and daughter Surabhi have been extremely
supportive and no words from my side are sufficient to convey my gratitude. Every time
when I was able to conduct experiments till late and night and sleep in the lab leading
to the results I have achieved, they deserved the credit for their patience and
understanding.
The journey started with the head of department of my unit at Robert Bosch Engineering
and Business Solutions Ltd, Dr. Detlef Zerfowski, suggesting that I should pursue a
Ph.D. I had always wanted to do it, but without his support it would never have been
possible to initiate the process. Over the course of the process, I received tremendous
support from Mr. Gaur Dattatreya, Mrs. Pratibha and Mr. Sathyanarayana T.K. in
getting all the approvals.
I have been fortunate to have Prof. Asokan Sundarrajan and Prof. Bharadwaj Amrutur
as my advisers. I have learnt a lot about research, rigor and presentation from them. But
the learning I value most is to be humble and respect everyone I work with. Ph.D. can
be a long journey requiring consistent hard work. Seeing Prof. Asokan and Prof.
Bharadwaj work so hard in the presence of so many challenges has kept me motivated
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to push my limits. I will always remember when I sent a paper for review to Prof.
Bharadwaj at 5:00 A.M. in the morning and got back the review comments within an
hour. I will remember this whenever I know that someone else depends on my response.
Working from FBG sensors requires a lot of skills which can be best learnt from an
expert. I am grateful to my seniors Guruprasad and Sridevi who helped me to learn how
to use all the equipment, especially the sensor fabrication setup.
Designing experiments for interdisciplinary research is both fascinating and
challenging. I would like to thank Dr. Srikanth and Dr. Shanthanu from Dept. of
Mechanical Engineering with whom I collaborated to conduct my experiments. Without
their suggestions, designing some of the experimental setups would not have been
possible. I would also like to thank Prof. G.K. Ananthasuresh for his valuable thought
provoking suggestions. I would also like to thank Dr. Ravi Nayar from C.G.S. Hospital,
Bangalore and Dr. Nageshwar Reddy from Asian Institute of Gastroenterology,
Hyderabad for their valuable suggestions which led to some of the experiments. Being
able to do an endoscopy procedure using a pig model would not have been possible
without Dr. Reddy’s help.
I would like to thank Dr. Abhijit Lele and Mr. Sangeeth Nambiar at Bosch Research
and Technology Centre – India for giving the freedom to pursue my research interests
without being entangled in the administrative complications in the office.
I will cherish forever the time spent with my lab-mates Dr.Srinivas, Dr. Srividya, Dr.
Tamilarasan, Dr. Chandasree, Dr. Sharath and Dr. Sikha. Without a lively group, it
would have been difficult to sustain the motivation over such a long time.
I might have missed some names but I would like to thank all the people at Indian
Institute of Science and Bosch who made it possible for me to pursue my research.
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Abstract
Fiber Bragg Grating (FBG) sensors have become increasingly popular for
applications in biomedical engineering. Amongst these, use of FBGs in ‘smart
instruments’ for minimally invasive diagnostic and surgical procedures look promising
as FBG sensors provide significant advantages compared to other sensing modalities
in terms of size, electromagnetic immunity, and ability to withstand sterilization
procedures.
Minimally invasive procedures provide lower discomfort to the patients and
faster healing time. Procedures based on use of needles as well as flexible medical
instruments like endoscopes form an important part of these procedures. As a natural
progression, there is a growing trend towards robotic and robot-assisted procedures.
Effective sensing of interactions between the instruments and tissues and the state of the
devices plays an important role in this. This thesis showcases the effectiveness of FBG
sensors in the estimation of forces during device-tissue interactions and the shape of
flexible devices through two applications.
The first application demonstrates the feasibility of estimating needle transitions
through tissues using force estimation at the needle tip. Needles with integrated fiber
Bragg grating sensors have been developed for this purpose and experiments have been
conducted using multi-layered Polydimethylsiloxane (PDMS) phantoms. The design has
been extended to handle temperature induced effects and the experiments have also been
performed using heated chicken tissue.
The second application demonstrates the feasibility of estimating the shape of a
flexible medical instrument like endoscope using strain information from fiber Bragg
grating sensors embedded in a polymer filled tube. This overcomes some of the
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constraints of solutions based on sensors bonded on nitinol wires which have been used
earlier. The computation of shape from strain data has been explained.
Widespread use of FBG sensors in such applications is dependent not only on
sensor characteristics but also on the interrogation system. Since the number of sensors
per fiber and the distance between the source and the sensors are small in these
applications, interrogation systems based on linear detector arrays provide a good
option. However, their accuracy depends on the curve fitting method used. For this
purpose, a comparison of accuracies of interrogation systems based on swept tunable
laser and InGaAs linear detector arrays has been performed. The choice and
effectiveness of curve fitting techniques to achieve accuracies similar to tunable laser
based systems have been investigated. The computational feasibility of the algorithm on
embedded hardware has been demonstrated.
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Contents
Chapter 1: Introduction .............................................................. 13
1.1 Minimally Invasive Procedures ...................................................................... 13
1.2 Robotic and Robot Assisted Procedures ........................................................ 15
1.3 Significance of Force and Shape Estimation and Role of Sensors ................ 16
1.4 Thesis Organization........................................................................................ 17
References ................................................................................................................. 19
Chapter 2: Fiber Bragg Gratings as Sensors for Biomedical
Applications ................................................................................ 35
2.1 Fiber Bragg Gratings: evolution and use as sensors ..................................... 35
2.2 Sensor Fabrication .......................................................................................... 37
2.3 Use in Biomedical Application ...................................................................... 38
2.4 Thesis contributions towards novel smart instrument design using FBG
sensors ....................................................................................................................... 40
References ....................................................................................... 42
Chapter 3: Estimating Needle Transitions through Tissue Layers
.................................................................................................... 51
3.1 Introduction .................................................................................................... 51
3.2 Needle and Sensor Characteristics ................................................................. 55
3.3 Needle Insertion Setup ................................................................................... 58
3.4 Polydimethylsiloxane (PDMS) Phantom ....................................................... 60
3.5 Measurements and Results ............................................................................. 60
3.5.2 Sensitivity Determination ....................................................................... 60
3.5.2 Transition through layers with different stiffness ................................... 61
3.6 Temperature Compensation ........................................................................... 69
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3.7 Insertion in heated chicken tissue .................................................................. 71
3.8 Summary ....................................................................................................... 74
References ....................................................................................... 75
Chapter 4: Shape Estimation of Flexible Medical Instruments . 81
4.1 Introduction ................................................................................................... 81
4.2 Need for shape estimation and assistance ..................................................... 83
4.3 Shape Estimation Methods ............................................................................ 86
4.4 Shape Estimation from curvature using beam theory ................................... 88
4.5 Strain estimation using FBG sensors bonded on endoscope and on a nitinol
wire 89
4.6 Shape reconstruction from curvature............................................................. 94
4.7 Curvature estimation using FBG sensors embedded in a PDMS filled highly
flexible tube .............................................................................................................. 97
4.8 Summary ..................................................................................................... 103
References ..................................................................................... 104
Chapter 5: Evaluation of FBG interrogation systems based on
InGaAs linear detector arrays and curve fitting methods using
Gaussian approximation ........................................................... 109
5.1 Introduction ................................................................................................. 109
5.2 Measurement Setup and Data Characteristics ............................................. 115
5.2.1 Setup ..................................................................................................... 115
5.2.2 Data Characteristics ............................................................................. 116
5.3 Bragg Wavelength Estimation ..................................................................... 117
5.3.1 Centroid Algorithm .............................................................................. 118
5.3.2 Gaussian Approximation for the FBG spectrum and least square
estimation of Bragg wavelength ......................................................................... 120
5.3.3 Lower computational cost algorithm utilizing Gaussian Approximation
for the FBG spectrum ......................................................................................... 127
5.4 Summary ..................................................................................................... 130
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References ..................................................................................... 132
Chapter 6: Conclusions and Future Work ................................ 139
Appendix A .............................................................................. 141
FBG sensor fabrication setup .................................................................................. 141
List of Publications ................................................................... 143
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List of Tables Table 3.1 Inner and outer diameters for common needle gauge sizes .......................... 52
Table 4.1 Flexible endoscope types with typical dimensions ....................................... 82
Table 4.2 Estimated Radius of curvature using strains from FBG sensor bonded on the
endoscope .............................................................................................................. 90
Table 4.3 Results of curvature measurements using nitinol wire ................................. 91
Table 5.1 Wavelength shift difference from tunable laser based system using different
number of points for non-linear least squares estimation using Levenberg
Marquardt algorithm ........................................................................................... 125
Table 5.2. Wavelength shift difference from tunable laser based system using
Levenberg Marquardt algorithm and Centroid Algorithm.................................. 126
Table 5.3 Comparison of execution times and difference in estimated wavelength from
tunable laser based system for the three methods ............................................... 130
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List of Figures
Figure 2.1 Reflected peak and transmitted spectrum for a fiber Bragg grating ........... 36
Figure 2.2 Schematic diagram of the phase mask method ........................................... 38
Figure 3.1 (a) Bevel tipped and (b) Franseen needle ................................................... 52
Figure 3.2 Stages of needle insertion: (a) tissue deflection (b) rupture (c) movement
inside tissue ........................................................................................................... 53
Figure 3.3 Simulation configuration with one fixed end ............................................. 55
Figure 3.0.4 Load of 0.1N applied at cutting edge ...................................................... 56
Figure 3.5 Fabrication of two FBG sensors close to each other by translating and pre-
stretching the fiber ................................................................................................ 57
Figure 3.6 Needle with FBG sensors bonded ............................................................. 58
Fig 3.7 Schematic diagram of the needle insertion setup ............................................. 59
Figure 3.8 (a) Complete setup including needle translation stage, controller and data
acquisition setup and (b) Needle being inserted in the phantom with a camera
placed to monitor its progress inside the phantom................................................ 59
Figure 3.9 Strain response of the two FBG sensors .................................................... 61
Figure 3.10 Phantoms with five layers with alternating higher and lower stiffness .... 62
Figure 3.11 Stages during needle insertion in the phantom ......................................... 63
Figure 3.12 Response of the sensors during needle insertion ...................................... 64
Figure 3.13 Gradients of the strains and the force at the needle holder base ............... 65
Figure 3.14 Strains for insertion at 3mm/sec ............................................................... 66
Figure 3.15 Gradients for insertion at 3mm/sec ........................................................... 66
Figure 3.16 Strains measured by the two FBG sensors and force measured at the
needle holder base for insertion in phantom 1 at varying needle insertion rates .. 67
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Figure 3.17 Strains measured by the two FBG sensors and force measured at the
needle holder base for insertion in phantom 2 at varying needle insertion rates . 68
Figure 3.18 Additional hollow needle with FBG sensor used instead of stylet .......... 69
Figure 3.19 Temperature response of actual FBG sensor and the compensation FBG
sensor ................................................................................................................... 70
Figure 3.20 Setup for insertions in heated chicken tissue ........................................... 71
Figure 3.21 Temperature induced wavelength shift during needle insertion .............. 72
Figure 3.22 (a) Response of the sensor bonded to the 18G needle and that of the
inside needle during insertion in heated tissue and (b) the temperature
compensated response of the sensor bonded to the 18G needle .......................... 73
Figure 3.23 Gradients of strain measured by senor 1 bonded on the 18G needle after
temperature compensation ................................................................................... 74
Figure 4.1 (a) Schematic of Endoscope and (b) holding an endoscope for procedure 81
Figure 4.2 Sketch of endoscope looping during colonoscopy ..................................... 84
Figure 4.3 (a) Sketch showing formation of an ‘n’ loop and (b) pushing the scope
further pushes it against the wall of the colon instead of moving it forward ....... 85
Figure 4.4 Simple image showing an endoscopic training system (Image created as
part of ‘Cyber surgery and remote patient care’ project at Robert Bosch Center
for Cyber Physical Systems, Indian Institute of Science which has led to the
startup Mimyk [10]) ............................................................................................. 86
Figure 4.5 Beam deflection ......................................................................................... 88
Figure 4.6 Setup for curvature estimation using FBG sensor bonded on the endoscope
.............................................................................................................................. 89
Figure 4.7 Experimental setup with FBG sensor bonded to a nitinol wire ................. 91
Figure 4.8 (a) spectrum for unstrained sensor and (b) spectrum for sensor at strain of
5500µstrains during bending ................................................................................ 92
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Figure 4.9 radius of curvature for bends during endoscopy ........................................ 93
Figure 4.10 Setup to qualitatively evaluate the impact of the nitinol wire put inside the
endoscope on the flexibility of the endoscope. The left end is fixed while the right
end is translated to change the bending radius of the endoscope. A force sensor
on the right side measures the force at the tip of the endoscope. .......................... 93
Figure 4.11 Estimating shape using curvatures measured by a sensing point close to
the tip moving along the structure ........................................................................ 94
Figure 4.12 Reconstruction using approximate circular segments .............................. 96
Figure 4.13 Cross section of the shape sensing tube .................................................... 97
Figure 4.14 Calibration setup – the inside tube is the sensing tube with FBG sensors
............................................................................................................................... 98
Figure 4.15 Examples of wavelength shifts for varying radii of curvature and
rotational position ................................................................................................. 99
Figure 4.16 Plot showing wavelength shifts for different radii of curvature ............. 100
Figure 4.17 An artificial neural network to perform regression for estimation of radius
of curvature. The shown ANN shows the structure and weights after training
based on data presented in figure 4.16 ................................................................ 101
Figure 4.18 Error plot for tests using the trained neural network .............................. 102
Figure 4.19 Reconstruction of a sample curve using measured wavelength shifts and
estimated radii of curvature using the ANN ....................................................... 103
Figure 5.1 Schematic diagram of interrogation system using edge filter [3] ............. 110
Figure 5.2 (a) Schematic of matched FBGs based interrogation and (b) simultaneous
multiple sensor interrogation [7] [8] ................................................................... 111
Figure 5.3 Schematic diagram of interrogation system using tunable fabry-perot filter
[15] [16] .............................................................................................................. 112
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Figure 5.4 Schematic diagram of an interrogation system with InGaAs linear detector
array [26] ............................................................................................................ 114
Figure 5.5 Setup to generate data samples ................................................................ 116
Figure 5.6 Spectrum obtained from the linear detector array ................................... 117
Figure 5.7 Errors in peak wavelength estimation using the centroid method compared
to measurement using the interrogation system based on swept tunable laser .. 119
Figure 5.8 Plots showing the points around the peak. Each measurement corresponds
to a shift in wavelength due to applied strain. The original and the shifted points
and the estimated peak using centroid algorithm are shown for three different
sensors on the fiber............................................................................................. 120
Figure 5.9 Estimated Bragg wavelengths using different number of pixels around the
peak .................................................................................................................... 122
Figure 5.10 Wavelength shift measured using different number of pixels and
compared to measurement with swept tunable lased based interrogation system.
............................................................................................................................ 123
Figure 5.11 Spectrum for sensor 1 and sensor 2 before and after wavelength shift due
to applied strain .................................................................................................. 124
Figure 5.12 Difference in wavelength shift estimation using Levenberg-Marquardt
algorithm and Gaussian spectrum approximation compared to measurement using
swept tunable laser based interrogation system ................................................. 126
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List of Symbols
λb Bragg wavelength
Δλ Bragg wavelength shift
Λ grating pitch
Λpm phase mask period
pe photo-elastic coefficient of the fiber
αn Thermo-optic coefficient of the fiber
αΛ Thermal expansion coefficient of the fiber
neff effective refractive index
l length
Δl change in length
ε strain
T temperature
ΔT change in temperature
R Radius of curvature
T unit tangent
N unit normal
B unit bi-normal
κ curvature
Ii intensity at ith pixel
λi wavelength corresponding to ith pixel
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Chapter 1 Introduction
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Chapter 1
Introduction
1.1 Minimally Invasive Procedures
The origins of minimally invasive diagnosis can be traced back to a rectal speculum
described by Hippocrates (460-375 B.C.). However, the credit for the first instrument
proposed for being used for diagnosis through a natural orifice goes to Bozzini’s
‘Lichtleiter’ (light conductor) [1]. Even though the idea created controversy and drew
criticism [2], it has laid the foundation for a field which has evolved through the last
two centuries and has significantly impacted the practice of medicine. Several
innovations like the development of flexible fiber-optic endoscope [3], the adoption of
needle biopsies [4], the use of brachytherapy [5] and the introduction of the
laparoscopic cholecystectomy (surgical removal of gall bladder) by Mouret [6], have
been landmarks in the evolution of minimally invasive diagnostic, therapeutic and
surgical procedures. The term ‘minimally invasive surgery’ can be attributed to John
Wicham [7]. His prediction that such techniques will be developed for several types of
surgery has come true [8] [9] [10] [11] [12] [13] [14]. It has even led to extreme
experiments like transatlantic robot assisted tele-surgery [15] and even tele-robotic
procedures in low bandwidth settings [16].
Minimally invasive procedures cover a wide range of diagnostic, therapeutic and
surgical procedures. However, an approach to categorization can be made based on the
type of instrument used which are:
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Chapter 1 Introduction
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i) flexible endoscopes (e.g. through a natural orifice as in gastrointestinal
endoscopy, colonoscopy and bronchoscopy)
ii) laparoscope (e.g. in cholecystectomy)
iii) needles (e.g. in biopsies, ablation, brachytherapy and neurosurgery)
iv) catheters (e.g. in angioplasty and stenting)
Minimally invasive procedures provide several advantages [17] [18] [19] [20] [21] [22]
[23] such as:
Short hospital stay and quick recovery time
Less trauma
Lass scarring
Lower risk of complications
Lower risk of infection
Even though there are several advantages for the patients, minimally invasive
procedures present new challenges and constraints for the doctors. These can be split
into two parts – 1) challenges in performing the procedures, and 2) challenges in
acquiring new skills through training.
The constraints and challenges in performing the procedures are related to [24] [25]
[26]:
constrained operating environment
lack of depth perception
loss of tool orientation and pose
loss of sense of touch and haptic feedback
high effort in maneuvering and risk of perforation
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Chapter 1 Introduction
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The constraints and challenges in skill acquisition are related to [27] [28] [29] [30]:
high initial learning curve
availability of realistic training systems
transfer of skills acquired for one task to other tasks
1.2 Robotic and Robot Assisted Procedures
The motivation for minimally invasive procedures has been to reduce patient discomfort
and the risks associated with the procedure. Over the years, some minimally invasive
procedures in cancer management, cardiac treatments and neurosurgery have become
routine. However, some advanced techniques like Natural Orifice Transluminal Surgery
(NOTES) [31] are still evolving [32] [33] and the efficacy, learning curve [34], role of
new devices [35] [36] and patient benefits are still under discussion [37]. The same is
applicable for robotic and robot assisted procedures [38] [39] [40] [41] with very few
systems like the da Vinci® system available commercially. In such systems, the
motivation has been to help the doctors perform the procedures better by creating
devices with higher degrees of freedom, improved visualization and guidance, and
reducing effects of hand tremors. In its current manifestation, surgical robotics is
restricted to systems which are very constrained in their applications. However, the
consensus document [42] on robotic surgery approved by the Board of Governors of the
Society of American Gastrointestinal and Endoscopic Surgeons (SAGES) suggests that
research in the area should focus on future smart instruments that can provide ‘smart
sensing’ capabilities to provide surgeons with information like blood flow, oxygenation
and tumor margins. It also suggests that future systems can use the knowledge of spatial
coordinates along with preoperative and intra operative imaging providing overlays to
enable identifying danger zones or organ boundaries. Another expectation from future
systems is to overcome the rigidity and size constraints of current systems through the
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Chapter 1 Introduction
16
use of more flexible components. The effects of robotic assistance on learning curves
also have to be addressed [43].
1.3 Significance of Force and Shape Estimation and
Role of Sensors
Minimally invasive procedures create a constrained operating environment leading to
loss of tool orientation and pose and lack of haptic feedback. Both these have attracted
significant research, both in terms of creating improved sensing-enabled devices acting
as ‘smart instruments’ as well as improved visualizations.
Estimating forces as part of tool-tissue interactions is an important aspect of these smart
instruments enabling easier and improved tool manipulation and haptic feedback. These
advantages get amplified when forces cannot be directly transmitted easily to the
operating surgeon’s hand due to device configuration or conversely when the forces
applied at the distal end have to be regulated or the effects of tremors have to be
controlled. Several studies [44] [45] [46] [47] [48] [49] [50] [51] have evaluated the
need and value of estimating these forces and providing feedback. These have led to the
development of novel instruments and end effectors with force measurement
capabilities, such as sensing-enabled endoscopic forceps [52] [53] and graspers [54]
[55] [56] [57], indentation [58] [59] and palpation probes [60] [61], scissor blades [62],
catheters [63] [64] [65], instruments for NOTES [66], neurosurgery [67], and
microsurgery [68] [69]. The choice of sensors plays an important role in development
of these ‘smart instruments’. Several sensor types including Micro Electro Mechanical
Sensors (MEMS) [70] [71], ultrasonic sensors [72] [73], piezoelectric sensors [74] [75]
and optical sensors [76] [77] [78] [79] [80] have been used.
Shape Estimation plays an important role in determining the location and pose of the
end effector as well as the entire instrument. This has higher significance for flexible
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Chapter 1 Introduction
17
instruments where loss of tool orientation during the procedure is more common [37]
or where dynamic shape estimation is important for guidance to effectively reach certain
locations [81]. Similar to force estimation, shape estimation has attracted significant
research. Even though radiological methods like fluoroscopy [82] can be used, it has its
own challenges. There has been effort to reduce the radiation exposure by reducing the
number of X-Ray images required [83]. However, this is still not very suitable for
continuous monitoring. Introduction of robotic and robot assisted procedures has
contributed to additional interest in continuous shape and pose estimation. It has
gathered special significance with recent advances through use of continuum
reconfigurable robots [84] and concentric tube robots [85] [86]. Issues with radiological
procedures have led to development of non-radiological methods including the use of
electromagnetic trackers [87] [88] [89], MEMS [90] [91], optical sensors [92] [93] and
fusion of multiple sensing modalities [94] [95].
1.4 Thesis Organization
In recent years, Fiber Bragg Grating (FBG) sensors have become popular for
applications that require small sensor size, multiplexing and electromagnetic
immunity. This thesis explores the use of FBG sensors in force and shape
estimation for applications in minimally invasive procedures.
Chapter two of the thesis presents an overview of sensing capabilities of Fiber Bragg
Gratings and their use in biomedical applications including medical robotics. The sensor
fabrication method for sensors used in this work is briefly described.
Needles are an important part of several diagnostic, radiological and neurosurgical
procedures. Chapter three presents a method to estimate transition of hollow needles
through tissue layers using force estimation at needle tip using fiber Bragg grating
sensors.
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Chapter 1 Introduction
18
Flexible instruments are an integral part of minimally invasive procedures and more and
more procedures are being done using flexible instruments like endoscopes. A method
to estimate shape for highly flexible instruments is presented in chapter four.
Widespread use of fiber Bragg grating sensor for medical robotic applications depend
not just on sensor characteristics but also on cost effective interrogation systems.
Chapter five provides an analysis of accuracy of interrogation systems based on InGaAs
linear detector arrays and computationally efficient curve fitting algorithm implemented
on embedded hardware for these applications that can enable cost effective interrogation
systems which can be integrated in existing medical setups.
The publications based on the work presented in chapters three, four and five have been
listed at the end of the thesis.
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Chapter 1 Introduction
19
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Chapter 1 Introduction
30
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A. Bossche, "Ultrasonic sensor system for measuring position and
orientation of laproscopic instruments in minimal invasive surgery," in
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EMB Special Topic Conference on, 2002.
[74] C. Li, P.-M. Wu, S. Lee, A. Gorton, M. J. Schulz and C. H. Ahn, "Flexible dome
and bump shape piezoelectric tactile sensors using PVDF-TrFE copolymer,"
Journal of Microelectromechanical Systems, vol. 17, pp. 334-341, 2008.
[75] J. Dargahi, "A piezoelectric tactile sensor with three sensing elements for robotic,
endoscopic and prosthetic applications," Sensors and Actuators A: Physical,
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Chapter 1 Introduction
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[76] P. Puangmali, H. Liu, K. Althoefer and L. D. Seneviratne, "Optical fiber sensor
for soft tissue investigation during minimally invasive surgery," in Robotics
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[77] H. Song, K. Kim and J. Lee, "Development of optical fiber Bragg grating force-
reflection sensor system of medical application for safe minimally invasive
robotic surgery," Review of Scientific Instruments, vol. 82, p. 074301, 2011.
[78] J. Peirs, J. Clijnen, D. Reynaerts, H. Van Brussel, P. Herijgers, B. Corteville and
S. Boone, "A micro optical force sensor for force feedback during minimally
invasive robotic surgery," Sensors and Actuators A: Physical, vol. 115, pp.
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computer assisted radiology and surgery, vol. 4, pp. 383-390, 2009.
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Chapter 1 Introduction
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[82] D. G. Adler, "The role of fluoroscopy in the endoscopic management of luminal
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[83] E. J. Lobaton, J. Fu, L. G. Torres and R. Alterovitz, "Continuous shape estimation
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Chapter 1 Introduction
33
[88] X. Luo and K. Mori, "Robust endoscope motion estimation via an animated
particle filter for electromagnetically navigated endoscopy," IEEE
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Chapter 1 Introduction
34
[94] C. Shi, C. Tercero, X. Wu, S. Ikeda, K. Komori, K. Yamamoto, F. Arai and T.
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Chapter 2 Fiber Bragg Gratings as Sensors for
Biomedical Applications
35
Chapter 2
Fiber Bragg Gratings as Sensors for
Biomedical Applications
2.1 Fiber Bragg Gratings: evolution and use as sensors
The discovery of photosensitivity in optical fibers [1] remained a phenomenon studied
by a small set of researchers for several years [2]. The demonstration of transverse
holographic writing [3] of gratings using two interfering beams external to the fiber
changed this and generated a lot of interest. The extension of this method to fabricate
reflection gratings around 1500nm using an ultraviolet laser [4] made it attractive for
telecommunication applications. Several advances [5] [6] [7] led to improvements in
reflectivity of fiber Bragg gratings paving the way for their widespread use in
telecommunication as wavelength division multiplexer, fiber lasers and dispersion
compensators [8] [9].
The applications of FBGs in sensors was identified quite early for strain and temperature
sensing [10] and for special applications like high pressure [11] and magnetic field [12]
sensing. Even though the initial applications [13] [14] did not gain adoption to the same
extent as in telecommunication, this has changed over the years with applications [15]
[16] [17] where the advantages of fiber Bragg grating sensors can be exploited to the
maximum [18] [19]. Further, the applicability of FBGs in large scale distributed sensing
has been exploited for structural health monitoring [20] while their small size,
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Chapter 2 Fiber Bragg Gratings as Sensors for
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multiplexing capabilities and electromagnetic immunity have led to several applications
in biomedical devices, biomechanics and medical robotics [21].
A fiber Bragg grating (FBG) consists of a periodic modulation of the refractive index in
the core of a single mode optical fiber [22]. Each grating plane scatters light guided
along the core of the fiber. When the Bragg condition is satisfied, reflected light from
each subsequent plane adds constructively to form a back reflected peak. The center
wavelength of the reflected peak is a function of the grating parameters [23].
Figure 2.1 Reflected peak and transmitted spectrum for a fiber Bragg grating
The center wavelength of the reflected peak is given by
λB = 2 neff Λ --- (2.1)
where neff is the effective refractive index of the fiber core and Λ is the grating period.
The simplest sensing principle of fiber Bragg gratings is based on the shift in the Bragg
wavelength due to variation in the periodic spacing between the grating planes and the
effective refractive index in response to an external perturbation such as strain and
temperature changes.
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Chapter 2 Fiber Bragg Gratings as Sensors for
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∆𝜆𝐵 = 2 (𝛬𝜕𝑛𝑒𝑓𝑓
𝜕𝑙+ 𝑛𝑒𝑓𝑓
𝜕𝛬
𝜕𝑙) ∆𝑙 + 2 (𝛬
𝜕𝑛𝑒𝑓𝑓
𝜕𝑇+ 𝑛𝑒𝑓𝑓
𝜕𝛬
𝜕𝑇) ∆𝑇 --- (2.2)
The first term corresponds to the strain response of the sensor and the second term to
the temperature response. Equation (2.2) can be reduced to
∆𝜆𝐵
𝜆𝐵= (1 − 𝑝𝑒)𝜀𝑧 + (𝛼𝑛 + 𝛼Λ)∆𝑇 --- (2.3)
Where 𝑝𝑒 is the effective photo-elastic constant for the optical fiber (≈0.22), 𝛼𝑛 is the
thermo-optic coefficient (≈ 8.6x10-6 for germania doped silica fiber), 𝛼Λ is the thermal
expansion coefficient of the fiber (≈ 0.55x10-6 for germania doped silica fiber) and 𝜀𝑧
is the longitudinal strain.
2.2 Sensor Fabrication
Interferometric methods of fabrication spurred active research in FBGs. However,
it is the phase mask technique of fabrication [24] [25] that has provided an
effective and robust method enabling large scale fabrication of high reflectivity
gratings in a reproducible way. All FBG sensors used in the experiments presented
in this thesis have been fabricated using the phase mask technique.
The phase mask is a periodic surface-relief pattern with period Λpm etched into
fused silica [26] and acts as a diffractive optical element. The profile is selected
such that the zeroth order diffracted beam is suppressed and the ±1 first orders
are maximized. The interference of the ±1 first orders produces a near field fringe
pattern whose period (Λ) is half that of the phase mask.
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Chapter 2 Fiber Bragg Gratings as Sensors for
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Figure 2.2 Schematic diagram of the phase mask method [9]
The details of the setup used for fabrication of sensors used for experiments in this
thesis is available in Appendix A.
2.3 Use in Biomedical Application
FBG sensors have been used for several biomedical applications where their small size,
multiplexing capability, electromagnetic immunity and high sensitivity provide a
significant advantage. The applications can be classified into the following areas based
on application areas:
i) MRI compatible devices
ii) Biomechanics
iii) Biosensors
iv) Smart end effectors for minimally invasive procedures
v) Guidance for minimally invasive procedures
The MRI compatibility of FBG sensors provide them a unique advantage which has
been exploited for monitoring respiration and cardiac activity in an MRI environment
[27] [28]. Different methods have been applied to increase the sensitivity and for signal
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Chapter 2 Fiber Bragg Gratings as Sensors for
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39
analysis based on sensor placement. These have even been extended to create wearable
sensors in the form of smart textiles [29] [30] which could make their use easier in an
MRI environment. FBG sensors have been integrated into needle holders used for
brachytherapy [31] for use in an MRI environment where standard force and torque
sensors cannot be used.
FBG sensors provide a good option for strain measurements in biomechanics and
rehabilitation. Their efficacy during studies involving measurement of tendon and
ligament strains and even detection of ligament deformation has been demonstrated
[32]. They have also been used for measurement of plantar strains and postural stability
[33]. In the area of prosthetics, they have been used for interface pressure measurement
between residual limb and prosthetic socket [34]. Additionally, they have found use in
monitoring decalcification of bones [35] and bone deformation [36]. One of the major
advantages of FBG sensors is the possibility to embed them during processing of
materials. This has been exploited for characterization of bone cement used for
cemented joint arthroplasty [37].
Etched FBG sensors have been used as biosensors by detecting the change in Bragg
wavelength due to refractive index change in the surrounding medium. They can act as
high sensitivity biosensors. This has been used to detect hybridization of DNA [38].
Etched FBG sensors coated with graphene oxide have been used for high sensitivity
detection of C-reactive protein [39] and glucose and glycated hemoglobin [40]. Other
recent applications of bare FBG sensors as biosensors include real time detection of
Escherichia coli [41] and as a biosensor with osteoblast cytocompatibility for possible
in-vivo applications in bone mechanical dynamics [42].
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Chapter 2 Fiber Bragg Gratings as Sensors for
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The application areas which have seen a significant amount of research activity
involving FBG sensors in recent years, apart from structural health monitoring, have
been related to the use of FBG sensors in smart instruments and end effectors with
sensing capabilities for use in medical procedures and in guidance and assistance for
minimally invasive procedures. It is evident that the small size, high multiplexing
capabilities and ability to withstand sterilization procedures provide them a significant
advantage for these applications. They have been integrated into forceps used in
minimally invasive surgery to determine grasping forces [43] and in scissor blades to
determine cutting forces [44]. Their effectiveness for force sensing has been
demonstrated for a complex procedure like vitro-retinal microsurgery [45] [46] [47].
They have been used to monitor temperature and contact force during radiofrequency
ablation [48]. Complex predictions like possibility of perforation during cardiac RF
ablation due to excessive force has also been attempted [49]. Higher acceptance of
minimally invasive procedures and robotic assistance in recent years have been
important factors for increase in research interest in the area. Robot assisted needle
steering [50] has motivated research towards shape estimation of flexible needles made
of nitinol [51] [52] .
2.4 Thesis contributions towards novel smart
instrument design using FBG sensors
Smart biomedical instruments incorporate sensing elements combined with a
computational system to provide improved usability and assistance. Chapter three of
this thesis focusses on the design of a smart needle which can determine the transition
through tissue layers. Most of the prior work in the area of smart needles has been
around solid flexible needles made using nitinol on which FBG sensors have been
bonded [51] [52] [53] [54]. These FBG sensors have been used to determine the needle
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Chapter 2 Fiber Bragg Gratings as Sensors for
Biomedical Applications
41
bending. This can be used for some of the minimally invasive surgical procedures.
However, a range of minimally invasive surgical and diagnostic procedures like
biopsies and radiological procedures use hollow needles. The work presented in this
thesis focusses on hollow needles for such procedures. The benefits of small size and
multiplexing capabilities of FBG sensors have been used to design a smart needle which
can determine the transition through tissue layers to enable better positioning of the
needle tip.
Shape estimation of flexible instruments including endoscopes and needles has been an
active research area in recent years. However, most of the work in this area in recent
years has focused either on using FBG sensors bonded on nitinol wires [51] [52] [53]
or on using FBG sensors fabricated in multi core fibers [55]. Chapter four of this thesis
demonstrates the limitations of using nitinol wires for this purpose. Using multi-core
fibers is promising. However, the sensor fabrication becomes more complex and special
3-D waveguides are required to couple the multi-core fibers to single mode fibers which
can be used with the FBG interrogators. An alternative method based on FBG sensors
embedded in a biocompatible polymer filled tube has been presented in this thesis. This
allows the use of standard phase mask technique for fabricating sensor arrays on single
mode fibers. A computational technique is presented for handling the non-linear
response of the sensors for varying bending radii.
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[33] A. S. G. Prasad, S. N. Omkar, H. N. Vikranth, V. Anil, K. Chethana and S.
Asokan, "Design and development of Fiber Bragg Grating sensing plate for
plantar strain measurement and postural stability analysis," Measurement,
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[34] E. A. Al-Fakih, N. A. A. Osman, F. R. M. Adikan, A. Eshraghi and P. Jahanshahi,
"Development and validation of fiber Bragg grating sensing pad for interface
pressure measurements within prosthetic sockets," IEEE Sensors Journal,
vol. 16, pp. 965-974, 2016.
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Chapter 2 Fiber Bragg Gratings as Sensors for
Biomedical Applications
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[35] V. Mishra, N. Singh, D. V. Rai, U. Tiwari, G. C. Poddar, S. C. Jain, S. K. Mondal
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decalcification," Orthopaedics & Traumatology: Surgery & Research, vol.
96, pp. 646-651, 2010.
[36] T. Fresvig, P. Ludvigsen, H. Steen and O. Reikerås, "Fibre optic Bragg grating
sensors: an alternative method to strain gauges for measuring deformation in
bone," Medical engineering & physics, vol. 30, pp. 104-108, 2008.
[37] C. Frias, O. Frazão, S. Tavares, A. Vieira, A. T. Marques and J. Simões,
"Mechanical characterization of bone cement using fiber Bragg grating
sensors," Materials & Design, vol. 30, pp. 1841-1844, 2009.
[38] A. N. Chryssis, S. S. Saini, S. M. Lee, H. Yi, W. E. Bentley and M. Dagenais,
"Detecting hybridization of DNA by highly sensitive evanescent field etched
core fiber Bragg grating sensors," IEEE Journal of selected topics in
Quantum Electronics, vol. 11, pp. 864-872, 2005.
[39] S. Sridevi, K. S. Vasu, S. Asokan and A. K. Sood, "Sensitive detection of C-
reactive protein using optical fiber Bragg gratings," Biosensors and
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[40] S. Sridevi, K. S. Vasu, S. Sampath, S. Asokan and A. K. Sood, "Optical detection
of glucose and glycated hemoglobin using etched fiber Bragg gratings coated
with functionalized reduced graphene oxide," Journal of biophotonics, 2015.
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Biomedical Applications
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[41] R. Srinivasan, S. Umesh, S. Murali, S. Asokan and S. Siva Gorthi, "Bare fiber
Bragg grating immunosensor for real-time detection of Escherichia coli
bacteria," Journal of biophotonics, 2016.
[42] L. Carvalho, N. J. Alberto, P. S. Gomes, R. N. Nogueira, J. L. Pinto and M. H.
Fernandes, "In the trail of a new bio-sensor for measuring strain in bone:
Osteoblastic biocompatibility," Biosensors and Bioelectronics, vol. 26, pp.
4046-4052, 2011.
[43] S.-C. Lim, H.-K. Lee and J. Park, "Grip force measurement of forceps with fibre
Bragg grating sensors," Electronics Letters, vol. 50, pp. 733-735, 2014.
[44] D. Callaghan, "Force Sensing Surgical Scissor Blades using Fibre Bragg Grating
Sensors," 2013.
[45] I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach and
R. Taylor, "A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic
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computer assisted radiology and surgery, vol. 4, pp. 383-390, 2009.
[46] X. He, M. A. Balicki, J. U. Kang, P. L. Gehlbach, J. T. Handa, R. H. Taylor and
I. I. Iordachita, "Force sensing micro-forceps with integrated fiber bragg
grating for vitreoretinal surgery," in SPIE BiOS, 2012.
[47] B. Gonenc, M. A. Balicki, J. Handa, P. Gehlbach, C. N. Riviere, R. H. Taylor and
I. Iordachita, "Preliminary evaluation of a micro-force sensing handheld
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Chapter 2 Fiber Bragg Gratings as Sensors for
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robot for vitreoretinal surgery," in Intelligent Robots and Systems (IROS),
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[48] D. Tosi, E. G. Macchi, G. Braschi, M. Gallati, A. Cigada, S. Poeggel, G. Leen and
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[49] S. C. M. Ho, M. Razavi, A. Nazeri and G. Song, "FBG sensor for contact level
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[50] K. B. Reed, A. Majewicz, V. Kallem, R. Alterovitz, K. Goldberg, N. J. Cowan
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[51] Y.-L. Park, S. Elayaperumal, B. Daniel, S. C. Ryu, M. Shin, J. Savall, R. J. Black,
B. Moslehi and M. R. Cutkosky, "Real-time estimation of 3-D needle shape
and deflection for MRI-guided interventions," IEEE/ASME Transactions On
Mechatronics, vol. 15, pp. 906-915, 2010.
[52] M. Abayazid, M. Kemp and S. Misra, "3d flexible needle steering in soft-tissue
phantoms using fiber bragg grating sensors," in Robotics and Automation
(ICRA), 2013 IEEE International Conference on, 2013.
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[53] R. J. Roesthuis, M. Kemp, J. J. Dobbelsteen and S. Misra, "Three-dimensional
needle shape reconstruction using an array of fiber bragg grating sensors,"
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[54] K. R. Henken, J. Dankelman, J. J. Dobbelsteen, L. K. Cheng and M. S. Heiden,
"Error analysis of FBG-based shape sensors for medical needle tracking,"
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[55] J. P. Moore and M. D. Rogge, "Shape sensing using multi-core fiber optic cable
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Chapter 3 Estimating Needle Transitions through
Tissue Layers
51
Chapter 3
Estimating Needle Transitions through
Tissue Layers
3.1 Introduction
Needles are used in a variety of medical procedures ranging from simple subcutaneous
and intravenous administration of medicines to complex neurological procedures.
Minimally invasive diagnostic and therapeutic procedures such as biopsies and
radiological seed implantation (brachytherapy) which have had tremendous impact on
cancer management are highly dependent on the use of needles.
Needles are available in a wide variety of geometries. Some of the most common
commercially available needles have variants of bevel shaped cutting tips
(brachytherapy and spinal needles) and symmetrical multi-plane cutting tips (Franseen
needles used in lung biopsy). The tip geometries can be seen in figure 3.1.
Needles also have a wide range of outer diameter. The needle sizes are usually specified
in terms of gauges. The gauge size (G) is inversely related to the needle diameter. For
example, a 26 gauge needle has a smaller diameter than an 18 gauge needle. Table 3.1
provides the nominal inner and outer diameters for common needle gauges.
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Chapter 3 Estimating Needle Transitions through
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(a)
(b)
Figure 3.1 (a) Bevel tipped and (b) Franseen needle
Table 3.1 Inner and outer diameters for common needle gauge sizes
Needle Gauge Nominal Outer Diameter
(mm)
Nominal Inner Diameter
(mm)
14 2.11 1.6
16 1.65 1.19
18 1.27 0.84
20 0.91 0.6
21 0.82 0.51
22 0.72 0.41
24 0.57 0.31
26 0.46 0.26
28 0.36 0.18
30 0.31 0.16
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Chapter 3 Estimating Needle Transitions through
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18G needles are commonly used for brachytherapy and epidural procedures. All
experiments reported in this work have been done using 18G bevel tipped needles
(Quincke) [1].
The advancements in use of robotic and robot-assisted procedures have led to significant
interest in evaluation and modelling of needle tissue interactions [2] [3] [4] [5]. Needle
insertion into tissues is characterized by multiple stages.
(a)
(b)
(c)
Figure 3.2 Stages of needle insertion: (a) tissue deflection (b) rupture (c) movement
inside tissue
ftip
ftip
ftip ffriction
ffriction
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Chapter 3 Estimating Needle Transitions through
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In the first stage as shown in figure 3.2 (a), the tissue undergoes deflection. This is
followed by tissue rupture and the tip enters the tissue as shown in figure 3.2 (b). After
this, the needle tip and the shaft move inside the tissue as shown in figure 3.2 (c).
When the needle moves inside the tissue, it experiences force at the tip as well as
frictional force. There have been several studies to characterize the forces during
deflection as well as the frictional forces. The initial work in the area [6] [7] used
homogeneous linear models for tissues. These have been used to create virtual
simulations for needle insertion. Even though they enable creation of visualizations,
these models have limitations as tissues are inhomogeneous and exhibit nonlinear
viscoelastic behavior. In later work, Okamura et.al. [8] have provided a model using
multiple stages and split the forces into force due to stiffness, frictional forces and
cutting forces. A polynomial model for deflection has been used. However, experiments
with bovine liver has shown high variation in the estimated parameters. This could be
the result of high variations in tissue properties and the presence of vasculature.
In recent years, there has been higher focus on robotic insertion of needles [9] [10] [11]
[12]. These have used measurement of forces at the base of needle holder. Several
experiments have used specially created nitinol (a nickel-titanium alloy) needles which
have high flexibility [13]. The focus has been mostly on needle steering. Several
experiments have used FBG sensors for estimating the shape of these needles [14] [15]
[16] [17] [18]. However, work on hollow needles has been limited [19]. Hollow needles
have different cutting forces due to the tip geometry compared to solid needles.
Estimating forces directly at the needle tip is interesting in this case. This can be used
to avoid modelling the frictional forces which can have high variations. It also allows
their usage in procedures where direct estimation of forces at the base of a large needle
holder is not possible as in the case of NOTES [20] [21] [22].
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Chapter 3 Estimating Needle Transitions through
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3.2 Needle and Sensor Characteristics
The most important parameters to consider for hollow needles are the needle diameter
and needle tip geometry. As indicated before, all experiments presented here have been
carried out using 18G bevel tipped needles.
Before deciding on placement of sensors, FEM simulation has been performed using an
approximate model in COMSOL and applying a fixed load at the cutting edge of the
needle as shown in figures 3.3 and 3.4. This is done to check if the amount of strain that
would be encountered along the axis of the needle can be measured using the sensing
setup.
Figure 3.3 Simulation configuration with one fixed end
In the simulation results, as seen in figure 4, for a load of 0.1N applied axially at the tip,
a strain of approximately 5 micro-strains has been observed at regions 1-2mm away
from the tip along the axis.
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Chapter 3 Estimating Needle Transitions through
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Figure 3.0.4 Load of 0.1N applied at cutting edge
For constant temperature the strain response of FBG sensors can be reduced to
∆ 𝜆𝑏
𝜆𝑏 = (1-𝑝𝑒)𝜀𝑧 = (1-0.213) 𝜀𝑧 = 0.787𝜀𝑧 --- (3.1)
where pe is the photo-elastic constant and 𝜀𝑧 is the longitudinal strain.
The strain of 5 micro-strains for a 0.1N load as seen in the simulation results corresponds
to a wavelength shift of 3.94 pico-meter. This can be detected by the FBG interrogation
systems used for the experiments presented here.
In the present work, FBG sensors have been fabricated in a 125 micron germanosilicate
optical fiber (Nufern) using phase mask method. Phase mask method provides high
repeatability and control on the Bragg wavelength. However, one challenge with the
method is replacement of phase masks for fabricating sensor arrays. Two sensors close
to each other have been fabricated using pre-stretching of the fiber for the second sensor
and translating the fiber as shown in figure 3.5. This allows easy fabrication of sensors
with a Bragg wavelength separation in the range of 1.5-2 nm.
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Chapter 3 Estimating Needle Transitions through
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(a)
(b)
Figure 3.5 Fabrication of two FBG sensors close to each other by translating and pre-
stretching the fiber
The gauge length of each sensor is 3mm and the separation between the two sensors is
about 1.5 cm. The fiber has been bonded inside the needle lumen along the axis as shown
in figure 3.6. The polymer jacket on the fiber has been completely removed in the region
around and between the sensors. This is done to avoid any uneven bonding. During
bonding, the fiber has been maintained in a very slight tension to avoid any bending.
The tip of the fiber beyond the first senor has been cut after the completion of bonding.
UV Beam (248nm)
Translation Stage Fiber Core
Fiber Holder
First Sensor
UV Beam (248nm) Fiber Stretching
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Chapter 3 Estimating Needle Transitions through
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Figure 3.6 Needle with FBG sensors bonded
3.3 Needle Insertion Setup
A test setup has been designed for the controlled needle insertion and to compare forces
measured by the two FBG sensors in correspondence with the forces at the needle holder
base during the needle insertion into tissue-phantoms. It consists of a linear actuation
assembly, a force sensor, a displacement sensor and needle and tissue-phantom holders
as shown schematically in figure 3.7. The linear actuation is controlled manually or
programmed for specific insertion distances at varying speeds through a programmable
logic controller. An S-type strain gauge fixed to the needle holder assembly measures
the forces with a resolution of 1mN with a range of 0-10N. A syringe with the
instrumented needle is rigidly fixed to the holder. A Linear Variable Displacement
Transformer (LVDT) is used as an absolute position sensor. The tissue mimicking
phantoms are contained in a plastic tube rigidly held in the specimen holder. This is
required to prevent the phantom from moving along with the needle during insertion.
Optical Fiber
FBG Sensors To Interrogator
3mm
15mm
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Chapter 3 Estimating Needle Transitions through
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Fig 3.7 Schematic diagram of the needle insertion setup
(a) (b)
Figure 3.8 (a) Complete setup including needle translation stage, controller and data
acquisition setup and (b) Needle being inserted in the phantom with a camera placed
to monitor its progress inside the phantom
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Chapter 3 Estimating Needle Transitions through
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3.4 Polydimethylsiloxane (PDMS) Phantom
Polydimethylsiloxane (PDMS) is a silicone based polymer. It is optically clear which
has led to its usage as tissue mimicking phantom in optical coherence tomography [23]
[24]. Another major advantage is the ability to vary its mechanical properties in a
controlled manner by varying the cross-linking. Hence, it has also been used in studies
related to impact response of biological tissue [25]. The phantom is stable over longer
duration and can be stored easily at room temperature. It can be easily used at
temperatures around 37-40°C which is the usual range of body temperature without
problems related to loss of water and major changes in mechanical properties as
observed with gelatin based phantoms at such temperatures.
Sylgard 184 silicone elastomer kit has been used for preparing the phantoms. It consists
of a base elastomer and a curing agent. For all experiments, phantoms have been
prepared using base polymer to curing agent ratios of 10:0.6 and 10:0.3 and curing at
80°C.
3.5 Measurements and Results
3.5.2 Sensitivity Determination
In order to determine the sensitivity of the instrumented needle to external forces,
calibration has been performed by applying small external loads at the needle tip and
simultaneously measuring the strains measured by the two FBG sensors. The response
obtained is linear as seen in figure 3.9 and the sensitivity of the two sensors is obtained
from the slope of a linear least square fit to the data points.
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Chapter 3 Estimating Needle Transitions through
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Figure 3.9 Strain response of the two FBG sensors
Both loading and unloading experiments have been performed and no hysteresis effects
have been observed. The experiments have been repeated in the limit of 0-1.4N external
forces at the tip and no nonlinear effects are seen. The sensitivity of FBG sensor 1 (closer
to the tip) obtained is 67.3 micro-strains / N and that of FBG sensor 2 is 83.6 micro-
strains / N. The reason for difference in sensitivity is the slight bending at the tip at
higher loads, which acts against compression.
3.5.2 Transition through layers with different
stiffness
Since tumors can have a higher stiffness than healthy tissue [26], one of the goals in
needle penetration estimation is to determine transition from a layer of lower stiffness
to a layer of higher stiffness followed by transition to a layer of lower stiffness. This
includes transition estimation when the needle tip is already surrounded by tissue and
hence the frictional forces are acting on the needle. To analyze the effectiveness of using
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Chapter 3 Estimating Needle Transitions through
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force measurements at the tip for this situation, phantoms with five layers have been
created using PDMS by varying the ratio of base polymer to curing agent as shown in
figure 3.10.
X5 (mm) X4 (mm) X3 (mm) X2 (mm) X1 (mm)
Phantom1 4 7.5 5 8 4
Phantom2 3 8 4 7 4
Figure 3.10 Phantoms with five layers with alternating higher and lower stiffness
The higher stiffness layer is created using a base polymer to curing agent ratio of 10:0.6
and the lower stiffness layer is created using a ratio of 10:0.3. The phantom is created
by adding layers one at a time. The second layer is added after partial curing of first
layer and so on. This method enables creation of multi layered PDMS phantoms without
the need for plasma treatment of layer surfaces. The phantom is prepared inside a plastic
tube with sealing at one end to avoid motion of the phantom during needle insertion.
The needle insertion is made at 1mm/s, 2mm/s, 3mm/s and 4mm/s from the layer with
higher stiffness towards the next layers as shown in figure 3.11 and the strain responses
of the two sensors are recorded along with the needle displacement and force at the
needle holder base. The response of the two FBG sensors during transition through
different layers is shown in figure 3.12.
X1
10:0.3 10:0.6 10:0.3 10:0.6
Needle Insertion
Direction
X2 X3 X4 X5
10:0.6
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Chapter 3 Estimating Needle Transitions through
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(a)
(b)
(c)
(d)
(e)
(f)
Figure 3.11 Stages during needle insertion in the phantom
10:0.3
4mm 1mm 3mm
10:0.6 10:0.3 10:0.6
3mm
10:0.3
4mm 1mm 3mm
10:0.6 10:0.3 10:0.6
3mm
10:0.3
4mm 1mm 3mm
10:0.6 10:0.3 10:0.6
3mm
10:0.3
4mm 1mm 3mm
10:0.6 10:0.3 10:0.6
3mm
10:0.3
4mm 1mm 3mm
10:0.6 10:0.3 10:0.6
3mm
10:0.3
1mm 3mm 4mm
10:0.6 10:0.3 10:0.6
3mm
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An important point to consider is the deformation of the phantoms during insertion. The
presence of alternative layers with higher and lower stiffness also leads to varying
amounts of deformation at different stages of insertion. This is reflected in the graph in
figure 3.12. Hence the points at which transitions occur do not match exact boundaries
as shown in figure 3.11. The deformation of first layer is significantly higher than that
of the third layer. The deformations also vary slightly with insertion velocity.
.
Figure 3.12 Response of the sensors during needle insertion
In order to analyze and use the response, it is required to find the features in the signal
which can be reliably used to determine transitions between layers in spite of variation
in needle insertion speed and depth of insertion. Strain gradients are one such feature.
Figure 3.13 shows the gradient of the strains and the force at the needle holder base
computed using central difference method. The gradients show that sensor one (closer
to the needle tip) responds faster during the transition between layers. Another
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Chapter 3 Estimating Needle Transitions through
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advantage of using the gradient of strains measured by sensor one is the zero crossing
of the gradients. These are the points where the needle tip moves inside the layers with
higher stiffness (points ‘b’ and ‘e’) after rupture leading to a reduction in strains for a
small insertion distance. The effect of deformation is evident by comparing the initial
boundaries of the layers in figure 3.11 and the points ‘b’ and ‘e’ in figure 3.13. Using
the gradient allows the identification of transitions without depending directly on the
knowledge of the thickness of the layers or on the estimation of the deformation and the
subsequent relaxation.
Figure 3.13 Gradients of the strains and the force at the needle holder base
The forces are known to vary even for the same tissues for varying insertion rates.
Hence, it is important to show that the use of gradients is valid for varying needle
insertion rates. The strains and the gradients for insertion at 3mm/s can be seen
respectively in figures 3.14 and 3.15. It can be seen that the gradients of strains measured
by sensor 1 still show a similar pattern and can be used to identify the transitions.
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Figure 3.14 Strains for insertion at 3mm/s
Figure 3.15 Gradients for insertion at 3mm/s
The response of the sensors for all four needle insertion rates and for both phantoms can
be seen in figure 3.16 and 3.17 respectively. The figures show that the nature of response
is similar across needle insertion rates and phantoms with varying thickness of the
layers. The small variations in first transition point based on insertion velocity can also
be seen.
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Figure 3.16 Strains measured by the two FBG sensors and force measured at the
needle holder base for insertion in phantom 1 at varying needle insertion rates
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Figure 3.17 Strains measured by the two FBG sensors and force measured at the
needle holder base for insertion in phantom 2 at varying needle insertion rates
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The measurements show that absolute values of the strains and forces vary across
insertion velocities and phantoms. However, the trends in variation in strains remain the
same. These trends are reflected in the gradients which in turn follow similar patterns
and can be used for transition estimation.
3.6 Temperature Compensation
For experiments using phantoms, there is no temperature change during needle
insertion. However, during insertion in real tissue, there can be slight variations in the
temperature. Hence compensation is required to handle FBG sensor’s cross sensitivity
to temperature. This is achieved by using the configuration as shown in figure 3.18.
Figure 3.18 Additional hollow needle with FBG sensor used instead of stylet
A needle stylet is a solid rod inserted in the needle lumen to prevent any occlusion
during insertion. In the modified design used for temperature compensation, the solid
stylet has been replaced by a hollow needle with sealed tip. Another fiber with an FBG
sensor is bonded close to the tip inside this needle. The outer diameter of this needle is
chosen close to the inner diameter of the actual needle. During insertions, no strain is
induced on this FBG sensor. However, since it is located at the same place as the FBG
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sensor 1, it responds to any temperature changes. This enables the elimination of cross
sensitivity to temperature.
The temperature sensitivity of a 1550nm FBG sensors in a germanium doped silica core
fiber is approximately 14 pm/°C. The temperature response of the two sensors has been
analyzed by placing the needle on a controlled heating plate and applying a step change
from 36°C to 38°C. The temperature of the hot plate rises gradually and then settles
around the final value. The temperature value is chosen close the usual temperature of
human body. The response of the two sensors is as seen in figure 3.19. The slightly
higher settling point for a 2°C change is because of the fact that the final temperature of
the heating plate slightly overshoots 38°C due to inaccuracies in the control method.
Figure 3.19 Temperature response of actual FBG sensor and the compensation FBG
sensor
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During the period where temperature is rising, the maximum error between the actual
sensor on the 18 gauge needle and the compensation sensor in the inside needle is 6pm
and the average error is 3.5pm. Since the wavelength shifts due to strain during needle
insertion are much higher and strain variations are much faster, the compensation can
be used to account for changes in temperature.
3.7 Insertion in heated chicken tissue
To validate that the temperature compensation works in a real tissue, insertions have
been made in a chicken tissue which has been heated using the setup as shown in figure
3.20. The purpose of heating the chicken tissue is to create a temperature gradient.
Figure 3.20 Setup for insertions in heated chicken tissue
The response of senor bonded on the 18-gauge needle is shown in figure 3.21. The effect
of temperature can be clearly seen as the wavelength shift is positive and it continues to
rise because of the temperature till it reaches the settling point. If temperature effect is
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not compensated, it would appear as a response to an axial force causing elongation
instead of compression of the needle during insertion.
Figure 3.21 Temperature induced wavelength shift during needle insertion
The response of the FBG sensor bonded on the measurement needle (18G) and of the
FBG sensor on the inside needle which acts as the stylet can be seen in figure 3.22 (a).
It can be observed that the sensor on the inside needle responds only to the temperature
change. This allows to compensate for temperature induced effects on the measurements
by 18G needle which measures both temperature and strain induced effects during
insertion. This can be done by subtracting the response of the sensor on the inside needle
from that of the sensor on the 18G needle. The compensated response is as shown in
figure 3.22(b).
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(a)
Figure 3.22 (a) Response of the sensor bonded to the 18G needle and that of the
inside needle during insertion in heated tissue and (b) the temperature compensated
response of the sensor bonded to the 18G needle
The gradients of the strain response after applying temperature compensation has been
plotted in figure 3.23 to compare it with those obtained using the insertions in the PDMS
phantoms. The point before needle puncture ‘(a)’ and the point when the needle
punctures the first layer and goes inside tissue ‘(b)’ can be identified in the gradients.
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The movement inside the tissue ‘(c)’ and transition inside the second layer ‘(d)’ can also
be seen.
Figure 3.23 Gradients of strain measured by senor 1 bonded on the 18G needle after
temperature compensation
3.8 Summary
The results from the experiments show that it is possible to detect the different stages
of needle penetration using Fiber Bragg Grating sensors placed close to the needle tip.
The advantages of the small sensor size and high sensitivity are evident. The use of
gradients of the strain measured by sensor 1 in the experiments provides a means to
determine the transitions without use of exact thresholds and slopes. It also overcomes
the challenges posed by the variation in absolute values and the rates of changes of
strains for insertions at varying rates. This would allow its usage in flexible instruments
without the need of force measurements at the needle holder base. This would also
enable developing assistive systems for procedures which involve precise positioning
of needles beyond certain organ or tissue boundaries.
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References
[1] N. Calthorpe, "The history of spinal needles: getting to the point," Anaesthesia,
vol. 59, pp. 1231-1241, 2004.
[2] R. Alterovitz, K. Goldberg, J. Pouliot, R. Taschereau and I.-C. Hsu, "Needle
insertion and radioactive seed implantation in human tissues: Simulation and
sensitivity analysis," in Robotics and Automation, 2003. Proceedings.
ICRA'03. IEEE International Conference on, 2003.
[3] M. Mahvash and P. E. Dupont, "Mechanics of dynamic needle insertion into a
biological material," IEEE Transactions on Biomedical Engineering, vol. 57,
pp. 934-943, 2010.
[4] K. B. Reed, A. Majewicz, V. Kallem, R. Alterovitz, K. Goldberg, N. J. Cowan
and A. M. Okamura, "Robot-assisted needle steering," IEEE robotics \&
automation magazine, vol. 18, pp. 35-46, 2011.
[5] G. Wan, Z. Wei, L. Gardi, D. B. Downey and A. Fenster, "Brachytherapy needle
deflection evaluation and correction," Medical physics, vol. 32, pp. 902-909,
2005.
[6] S. P. DiMaio and S. E. Salcudean, "Needle insertion modeling and simulation,"
IEEE Transactions on robotics and automation, vol. 19, pp. 864-875, 2003.
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[7] S. P. DiMaio and S. E. Salcudean, "Interactive simulation of needle insertion
models," IEEE transactions on biomedical engineering, vol. 52, pp. 1167-
1179, 2005.
[8] A. M. Okamura, C. Simone and M. D. Oĺeary, "Force modeling for needle
insertion into soft tissue," IEEE transactions on biomedical engineering, vol.
51, pp. 1707-1716, 2004.
[9] A. Majewicz, T. R. Wedlick, K. B. Reed and A. M. Okamura, "Evaluation of
robotic needle steering in ex vivo tissue," in Robotics and Automation
(ICRA), 2010 IEEE International Conference on, 2010.
[10] S. Badaan, D. Petrisor, C. Kim, P. Mozer, D. Mazilu, L. Gruionu, A. Patriciu, K.
Cleary and D. Stoianovici, "Does needle rotation improve lesion targeting?,"
The International Journal of Medical Robotics and Computer Assisted
Surgery, vol. 7, pp. 138-147, 2011.
[11] S. E. Salcudean, T. D. Prananta, W. J. Morris and I. Spadinger, "A robotic needle
guide for prostate brachytherapy," in Robotics and Automation, 2008. ICRA
2008. IEEE International Conference on, 2008.
[12] A. Jahya, F. van der Heijden and S. Misra, "Observations of three-dimensional
needle deflection during insertion into soft tissue," in Biomedical Robotics
and Biomechatronics (BioRob), 2012 4th IEEE RAS & EMBS International
Conference on, 2012.
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[13] J. van Gerwen and Dennis, J. Dankelman and J. van den Dobbelsteen and John,
"Needle--tissue interaction forces--A survey of experimental data," Medical
engineering \& physics, vol. 34, pp. 665-680, 2012.
[14] M. Abayazid, M. Kemp and S. Misra, "3d flexible needle steering in soft-tissue
phantoms using fiber bragg grating sensors," in Robotics and Automation
(ICRA), 2013 IEEE International Conference on, 2013.
[15] Y.-L. Park, S. Elayaperumal, B. Daniel, S. C. Ryu, M. Shin, J. Savall, R. J. Black,
B. Moslehi and M. R. Cutkosky, "Real-time estimation of 3-D needle shape
and deflection for MRI-guided interventions," IEEE/ASME Transactions On
Mechatronics, vol. 15, pp. 906-915, 2010.
[16] R. J. Roesthuis, M. Kemp, J. van den Dobbelsteen and John and S. Misra, "Three-
dimensional needle shape reconstruction using an array of fiber bragg grating
sensors," IEEE/ASME Transactions on mechatronics, vol. 19, pp. 1115-
1126, 2014.
[17] H. Sadjadi, K. Hashtrudi-Zaad and G. Fichtinger, "Fusion of electromagnetic
trackers to improve needle deflection estimation: simulation study," IEEE
Transactions on Biomedical Engineering, vol. 60, pp. 2706-2715, 2013.
[18] K. R. Henken, J. Dankelman, J. van den Dobbelsteen and John, L. K. Cheng and
S. van der Heiden and Maurits, "Error analysis of FBG-based shape sensors
for medical needle tracking," IEEE/ASME Transactions on mechatronics,
vol. 19, pp. 1523-1531, 2014.
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[19] J. Z. Moore, "Tissue Cutting in Needle Biopsy," 2011.
[20] I. Halim and A. Tavakkolizadeh, NOTES: The next surgical revolution?, Elsevier,
2008.
[21] S. Gillen, J. Kleeff, M. Kranzfelder, S. V. Shrikhande, H. Friess and H. Feussner,
"Natural orifice transluminal endoscopic surgery in pancreatic diseases,"
World Journal of Gastroenterology: WJG, vol. 16, p. 3859, 2010.
[22] C. F. Granberg, M. T. Gettman and others, "Instrumentation for natural orifice
translumenal endoscopic surgery and laparoendoscopic single-site surgery,"
Indian Journal of Urology, vol. 26, p. 385, 2010.
[23] F. Ayers, A. Grant, D. Kuo, D. J. Cuccia and A. J. Durkin, "Fabrication and
characterization of silicone-based tissue phantoms with tunable optical
properties in the visible and near infrared domain," in Biomedical Optics
(BiOS) 2008, 2008.
[24] G. Lamouche, B. F. Kennedy, K. M. Kennedy, C.-E. Bisaillon, A. Curatolo, G.
Campbell, V. Pazos and D. D. Sampson, "Review of tissue simulating
phantoms with controllable optical, mechanical and structural properties for
use in optical coherence tomography," Biomedical optics express, vol. 3, pp.
1381-1398, 2012.
[25] Z. I. Kalcioglu, R. A. Mrozek, R. Mahmoodian, M. R. VanLandingham, J. L.
Lenhart and V. a. K. J. Vliet, "Tunable mechanical behavior of synthetic
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organogels as biofidelic tissue simulants," Journal of biomechanics, vol. 46,
pp. 1583-1591, 2013.
[26] V. Jalkanen, B. M. Andersson, A. Bergh, B. Ljungberg and O. A. Lindahl,
"Prostate tissue stiffness as measured with a resonance sensor system: a study
on silicone and human prostate tissue in vitro," Medical and Biological
Engineering and Computing, vol. 44, p. 593, 2006.
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Chapter 4 Shape Estimation of Flexible Medical
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Chapter 4
Shape Estimation of Flexible Medical
Instruments
4.1 Introduction
Introduction of flexible medical instruments has provided a new paradigm for diagnosis
and treatment of several medical conditions. Flexible endoscopes are one of the most
prominently used flexible instruments. In general, flexible endoscopes consist of an
insertion tube, a connector section and a control section as shown in figure 4.1 (a). The
doctor typically guides the insertion tube using one hand while controlling knobs using
the other hand as shown in fig 4.1 (b).
(a)
(b)
Figure 4.1 (a) Schematic of Endoscope and (b) holding an endoscope for procedure
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The insertion tube is a flexible tube with working channels that enable passage of
accessories. The tip of the flexible tube is controlled using pull wires attached to it below
the protective sheath. The tube also has a working channel through which accessories
like graspers and needles can be passed and can be seen in the field of view of the
endoscope. The tip can be fixed in a position to perform an investigation on to use the
accessories. The connector provides connection to the electrical system, the light source,
the air and water system and the suction system. The control section has knobs to control
the bending at the distal end. Several types of scopes with varying tube lengths,
diameters and channel sizes are available [1] depending on the type of medical
procedures [2] for which they are used and the supplier. Table 4.1 provides a brief
categorization.
Table 4.1 Flexible endoscope types with typical dimensions
Endoscope Type Procedure
Gastroscope
Viewing: Forward Viewing
Diameter: 4.9-12.8mm
Channel size: 2.0-3.8mm
Insertion tube length: 925-
1100mm
Upper gastrointestinal endoscopy for
esophagus, stomach and duodenum for
detection of Barret’s esophagus, removal
of polyps, biopsy of gastrointestinal
cancers etc.
Colonoscope
Viewing: Forward Viewing
Diameter: 11.1 - 15mm
Channel size: 2.0-4.2mm
Insertion tube length: 1330-
1700mm
Colonoscopy for detection and treatment
of polyps, fissures, colorectal cancer etc.
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Sigmoidoscope
Viewing: Forward Viewing
Diameter: 11.3 – 12.8mm
Channel size: 3.2-4.2mm
Insertion tube length: 700-
790mm
Sigmoidoscopy (for examining the lining
of the rectum and the large intestine) or
detection of polyps, rectal bleeding and
lesions
Duodenoscope
Viewing: Forward Viewing
Diameter: 11.3 – 12.8mm
Channel size: 3.2-4.2mm
Insertion tube length: 700-
790mm
Endoscopic retrograde cholangio-
pancreatography (ERCP) to diagnose and
treat problems of the liver, pancreas and
gallbladder
Enteroscope
Viewing: Forward Viewing
Diameter: 9.2 – 11.6mm
Channel size: 2.2-3.8mm
Insertion tube length: 1520-
2200mm
Enteroscopy (for small intestine) to find
the source of internal bleeding
4.2 Need for shape estimation and assistance
In endoscopic procedures, the surgeon operates with a constrained view of the site as
seen through the tip of the scope. To reach a particular site during colonoscopy or upper
gastrointestinal endoscopy, the scope has to be navigated through a series of complex
bends. This leads to disorientation or ‘getting lost’ effect impeding the performance of
the endoscopist [3]. For example, in colonoscopy, the formation of loops is considered
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as one of the main difficulties related to manipulation of the scope for the endoscopist.
An example is shown in figure 4.2
Figure 4.2 Sketch of endoscope looping during colonoscopy
Typically landmarks are used by the endoscopist to navigate. However, they are not
always easy to identify and there can also be variation from patient to patient. The
endoscopist has to create a mental picture of the orientation of the scope to proceed with
the insertion. This is sometimes difficult [4] even for experienced endoscopists. Several
types of loops can be formed during endoscopy. One of the common ones is an ‘n –
loop’ as shown in fig 4.3 (a). The tip of the endoscope pushes against the colon lining
when pushed further in this situation and does not move forward. Pushing further exerts
force of the wall of the colon as shown in figure 4.3(b). The endoscopist can avoid the
formation of the loop by knowing the trajectory of the scope and the shape it takes. This
can be easily done by straightening the scope when the loop gets formed by pulling it
back and then reinserting it. This can be enabled by estimating the shape of the scope
and assisting the endoscopist through visual feedback.
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(a)
(b)
Figure 4.3 (a) Sketch showing formation of an ‘n’ loop and (b) pushing the scope further
pushes it against the wall of the colon instead of moving it forward
Apart from shape estimations and assistance during in-vivo procedures, training systems
for endoscopy provide another important area where shape estimation can be very
useful. Training on actual patients for endoscopy is a major constraint in practicing the
techniques. Even though ex-vivo and in-vivo training with pig models is possible [5],
this requires special handling at training hospitals. Several training systems for flexible
endoscopy have been developed over the years [6] [7] [8] [9]. These can be used with
real endoscopes and provide haptic feedback as shown in the schematic in figure 4.4.
These provide simulated visualizations as the endoscope is moved forward. However,
rigid systems with only forward insertion do not provide a realistic training
environment. Enabling the detection of bending of endoscopes can allow better
assistance during training through suggestions for pulling back the scope and
reinsertion. This can also help in simulating the effects of the scope pressing against the
colon walls causing stretching.
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Figure 4.4 Simple image showing an endoscopic training system (Image created as
part of ‘Cyber surgery and remote patient care’ project at Robert Bosch Center for
Cyber Physical Systems, Indian Institute of Science which has led to the startup
Mimyk [10])
4.3 Shape Estimation Methods
Direct viewing of the shape of the endoscope is possible using fluoroscopic methods
[11]. However, exposure to radiation leads to constraints in usage. Using it only for the
purpose of shape estimation is difficult to justify unless other benefits are available for
a complex surgical process. Also, it cannot be used continuously creating constraints
for its use in an assistive system.
The two prominent non-radiological methods have been based on the use of
electromagnetic trackers and on shape estimation from curvature measurements.
Systems based on electromagnetic tracking use two components – a field generator and
a magnetic field sensor [12] [13] [14]. The field generator provides a working volume
and the electromagnetic sensor placed within this volume generates an induced voltage
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dependent on the excitation field strength at that location. These systems can provide
high accuracy. However, they are affected by the presence of other ferromagnetic
objects in the operating environment. The accuracy is also dependent on the distance of
the sensor from the field generator. Placing the field generator in the vicinity of the
patient in an already cramped operating environment is a challenge.
The other prominent non-radiological methods are based on estimating the curvature of
the scope. Different sensing modalities including Micro Electro-Mechanical Sensors
[15] [16] and FBG sensors have been use for this purpose. FBG sensors in particular
have become popular for curvature estimation. FBG sensors fabricated in single mode
fibers have mostly been used for shape estimation of flexible solid needles made of
nitinol (a nickel-titanium alloy) [17] [18]. Though a method based on FBG sensors for
endoscope shape estimation has been proposed in earlier work [19], it does not provide
details of measured radii of curvatures and curve reconstruction. Other alternatives to
FBGs in single mode fibers have been recently proposed. These include FBG sensors
fabricated in multi-core fibers [20] and FBG sensors fabricated in no-core fibers using
direct femtosecond laser inscription [21]. These alternatives are interesting. However,
these require complex setups and specialty fibers which make use of standard sensor
fabrication and interrogation techniques more difficult.
One of the main advantages of FBG sensors which differentiate them from other sensors
is the ability to embed them in other materials during the curing process which can be
done at elevated temperatures. In this work, a novel method based on FBG sensors
fabricated in single mode fibers embedded inside a polymer filled tube has been
proposed to estimate the shape based on curvature.
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4.4 Shape Estimation from curvature using beam
theory
Beam theory can be used to determine the curvature of a beam under deflection using
measurements of the strains induced at the surface of the beam due to the deflection as
shown in figure 4.5
Figure 4.5 Beam deflection
Beam theory makes the following assumptions
Plane cross sections, normal to the neutral axis remain plane during bending (no
shear)
Hook’s law is applicable and Young’s modulus for tension and compression are
same
The beam is initially straight and all longitudinal fibers bend into concentric
circular arcs, with radii of curvature that are much larger compared to the cross
sectional dimensions of the beam
Neutral Axis
c d
e f y
R
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Under these assumptions, the strain along the small segment ‘ef’ can be calculated as
𝜀𝑥 = 𝑒𝑓−𝑐𝑑
𝑐𝑑
= (𝑅−𝑦)∆𝜃−𝑅∆𝜃
𝑅∆𝜃= −
𝑦
𝑅 --- (4.1)
Using equation 4.1, and knowing y and the measured strain, it is possible to estimate
the radius of curvature R.
4.5 Strain estimation using FBG sensors bonded on
endoscope and on a nitinol wire
Using the simple bending theory, an experiment has been set up to determine if direct
estimation of radius of curvature is possible from strain measurements using FBG
sensors bonded directly on the endoscope as shown in figure 4.6.
Figure 4.6 Setup for curvature estimation using FBG sensor bonded on the endoscope
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The estimated radius of curvature and the errors are listed in table 4.2. It can be clearly
seen that the errors are almost an order of magnitude higher than the actual radius of
curvature. This can be attributed to the geometry of the endoscope which consists of a
combination of multiple channels, the protective sheath on the endoscope and the
presence of pull wires inside the endoscope.
Table 4.2 Estimated Radius of curvature using strains from FBG sensor bonded on the
endoscope
Actual
Radius of
Curvature
(mm)
Measured strain
(μstrain)
Estimated Radius
of Curvature using
y = 5mm
(mm)
Error
(mm)
164mm 3600 1404 -1240
130mm 4000 1247 -1117
96mm 4900 1012 -916
To overcome the problem, an option is to use a nitinol wire on which FBG sensors can
be bonded and this can be inserted into the working channel of the endoscope. Nitinol
is a nickel-titanium alloy with an elastic modulus of approximately 40 GPa. It is
significantly more flexible compared to stainless steel which has an elastic modulus of
193 GPa. It has been used for medical components like dental implants and stents. The
experimental setup used before has been modified to use a nitinol wire with 1.2mm
diameter on which FBG sensor has been bonded as shown in figure 4.7 and the strains
have been measured.
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Figure 4.7 Experimental setup with FBG sensor bonded to a nitinol wire
Table 4.3 Results of curvature measurements using nitinol wire
Actual Radius of
Curvature
(mm)
Measured
strain
(μstrain)
Calculated Radius of
Curvature using y =
0.605mm
(mm)
Error %
164 3800 158 3.8
154 4100 147 4.7
141 4600 130 8.4
130 4800 125 4
120 5100 118 1.6
108 5800 103 4.8
96 6300 95 1.05
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The results in table 4.3 show that using nitinol wire is feasible for estimation of radius
of curvature. The small errors can be eliminated though calibrations. A three sensor
configuration as used in needle deflection estimation in [17] [18] to handle rotational
invariance can be extended for this application. However, the strains are very high when
the radius of curvature is below 100 mm. This creates three problems – spectrum
distortion, need for large bandwidth allocation to each sensor restricting the extension
of this method to large number of sensing points and frequent sensor breakage.
Even though higher mechanical sensor strength can be obtained for sensors which are
fabricated using draw tower process and immediate recoating, it is still difficult to
achieve radius of curvatures as small as 30mm. The spectrum distortion leads to
difficulty with interrogation as shown in figure 4.8.
(a)
(b)
Figure 4.8 (a) spectrum for unstrained sensor and (b) spectrum for sensor at strain of
6000µstrains during bending
Even for interrogation systems using swept tunable lasers with narrow line-width, this
is a problem as multiple peaks can occur. Such distortion excludes the use of lower cost
interrogation systems based on linear detector arrays and curve fitting using Gaussian
spectrum approximation which can potentially be used when the number of sensors per
fiber is small. During endoscopy it is easily possible to have curvatures up to 30mm for
shapes of endoscope as shown in figure 4.9.
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Figure 4.9 radius of curvature for bends during endoscopy
In order to demonstrate the effect of putting the nitinol wire in the endoscope channel
on the endoscope’s flexibility, forces required for same amount of bending has been
measured. The endoscope has been fixed at one end and the other end has been put in a
fixture with a force sensor. The fixture has been linearly translated and the experiment
has been repeated for two bending positions with and without the nitinol wire inside the
endoscope as shown in figure 4.10.
Figure 4.10 Setup to qualitatively evaluate the impact of the nitinol wire put inside the
endoscope on the flexibility of the endoscope. The left end is fixed while the right end
is translated to change the bending radius of the endoscope. A force sensor on the right
side measures the force at the tip of the endoscope.
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In the measurement, the forces corresponding to bending as seen in figure 4.10 (a) are
1.62 N and 3.02N without and with the nitinol wire respectively. The forces
corresponding to bending as seen in figure 4.10 (b) are 1.95N and 4.02N without and
with the nitinol wire respectively. Thus, putting the nitinol wire inside the scope almost
doubles the force required to achieve the same amount of bending. This significant
adverse effect on the flexibility of the endoscope is undesirable and hence and alternate
approach is required.
4.6 Shape reconstruction from curvature
The shape can be reconstructed from a series of curvature measurements by considering
it to be a curve parameterized by its length ‘s’. When the tip with the sensors moves
along this curve, it measures different strains depending on the curvature and this can
be used to reconstruct the curve as shown in figure 4.11.
Figure 4.11 Estimating shape using curvatures measured by a sensing point close to
the tip moving along the structure
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The Frenet-Serret equations can be written as
�̇�(𝑠) = 𝜅(𝑠) 𝑵(𝑠)
�̇�(𝑠) = −𝜅(𝑠) 𝑻(𝑠) − 𝜏(𝑠) 𝑩(𝑠)
�̇�(𝑠) = 𝜏(𝑠) 𝑵(𝑠)
where T(s) is the unit tangent, N(s) is the unit normal, B(s) is unit binornal, 𝜅(𝑠) is the
curvature at ‘s’ and 𝜏(𝑠) is the torsion at ‘s’. The points on the curve at which
measurements are made can be considered to be equally spaced.
For in-plane bending, 𝜏(𝑠) is zero. Hence the equations can be simplified and written in
matrix notation as
[𝑻(𝑠)̇
𝑵(𝑠)̇] = [
0 𝜅(𝑠)
−𝜅(𝑠) 0] [
𝑻(𝑠)
𝑵(𝑠)] --- (4.2)
Given the starting values T(0), N(0) and 𝜅(0), and strain measurements at regular arc
length of ‘l’, the curvatures 𝜅(1), 𝜅(2),… can be estimated and hence the curve can be
reconstructed using small approximate circular segments with arc lengths l [22] as
shown in figure 4.12.
Given starting coordinate x(0) and T(0), N(0), 𝜅(𝑠) and l
xh(0) = x(0)
T1 = T(0)
N0 = N(0)
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The centre of the circular segment can be obtained as
Cj = 𝒙𝒉(𝑠𝑗) + (1
𝜅(𝑠𝑗)) 𝑵𝑗 --- (4.3)
𝒙𝒉(𝑠𝑗) = 𝒄𝒋 +1
𝜅(𝑠𝑗)[−𝑐𝑜𝑠(𝜅(𝑠𝑗)𝑙)𝑵𝒋 + sin (𝜅(𝑠𝑗)𝑙)𝑻𝑗] --- (4.4)
Figure 4.12 Reconstruction using approximate circular segments
T and N can be updated as
𝑻𝑗+1 = 𝑠𝑖𝑛(𝜅(𝑠𝑗)𝑙)𝑵𝑗 + 𝑐𝑜𝑠(𝜅(𝑠𝑗)𝑙)𝑻𝑗 --- (4.5)
𝑵𝑗+1 = 𝑐𝑜𝑠(𝜅(𝑠𝑗)𝑙)𝑵𝑗 − 𝑠𝑖𝑛(𝜅(𝑠𝑗)𝑙)𝑻𝑗 --- (4.6)
One of the challenges in using this method is that it cannot deal with the change in
direction of the curve after a point where the curvature become zero i.e. where the curve
is almost a straight line. However, when FBG sensors are used, the direction of
curvature is also known as the measured strains also change their sign. Hence the sign
of the normal N can be updated using this information in the software implementation.
xh(s0)
N(s0)
xh(s1)
N(s1)
C0
xh(s2)
N(s2)
C1
)(/1 0s
)(/1 1s
T(s0)
T(s1)
T(s2)
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4.7 Curvature estimation using FBG sensors embedded
in a PDMS filled highly flexible tube
Since FBG sensors can be embedded inside other materials during the curing process,
an alternate device configuration has been created in this work for curvature estimation.
FBG sensors fabricated in a single mode fiber have been embedded in
Polydimethylsiloxane (PDMS) inside a plastic tube as shown in figure 4.13. PDMS has
been chosen because it is biocompatible. Also, it has a very low elastic modulus. The
elastic modulus when base elastomer to curing agent ratio of 10:1 is used is in the range
of 1-9MPa depending on curing temperatures [23]. This makes the sensing tube highly
flexible. The outer diameter of the tube is ~2.1mm and the inner diameter is ~1.2mm.
The fibers are placed under slight strain to avoid bending during the curing process.
After sensors have been placed in the tube which is rigidly held, PDMS with a base to
curing agent ratio of 10:1 has been injected into the tube. Care has been taken that no
bubbles are formed during the injection of PDMS. This has been cured at 70°C for 1
hour. The curing temperature has been restricted to this value to avoid distortion of the
plastic tube shape during curing. The resulting tube is highly flexible and can be bent
up to very small radii of curvature up to 3cm without breaking the sensors.
Figure 4.13 Cross section of the shape sensing tube
Plastic Tube
PDMS
(Base Polymer : Curing
Agent = 10:1)
FBG
Sensors
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The rotation of the tube is another parameter that has to be accounted for. In order to
understand and calibrate the response of the two FBG sensors for different rotations and
radii of curvature, the shape sensing tube has been inserted inside a tube as shown in
figure 4.14. The outer tube has been bent to have different radii of curvature between
3cm and 15cm. Measurements have been taken for six equally spaced rotation angles of
the sensing tube.
Figure 4.14 Calibration setup – the inside tube is the sensing tube with FBG sensors
Estimation of radius of curvature depends on the feasibility of the tube to be used for a
large radius of curvature of 15cm to a small radius of curvature of 3cm for different
rotational position of the sensors with respect to the neutral axis. Figure 4.15 shows the
wavelength shifts for different points during the calibrations. The wavelength shifts are
sufficiently detectable even though the response is not linear for the entire range. The
maximum shift is between +2nm and -2nm. Thus, if the system has to be extended for
multiple sensing points along the tube, the wavelength separation of the sensors has to
be more than 4 nm. The non-linear response requires the estimation of a function to map
the wavelength shifts to the radius of curvature.
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Figure 4.15 Examples of wavelength shifts for varying radii of curvature and
rotational position
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Figure 4.16 Plot showing wavelength shifts for different radii of curvature
In order to estimate the radius of curvature ‘R’ from a measured pair of wavelength shift
for each sensor, it is required to estimate the mapping function corresponding to figure
4.16. Artificial neural networks are good at learning such functions. An Artificial Neural
Network (ANN) in a configuration to perform non-linear regression has been used for
this purpose as shown in figure 4.17. A logistic [24] activation function has been used
for the neural-net nodes in the hidden layers. The two input nodes correspond to the
wavelength shifts corresponding to the bending strain. The output node provides the
radius of curvature. The ‘neuralnet’ package [25] in the statistical analysis software ‘R’
[26] has been used for training the neural network. The training has been performed
using back propagation.
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Figure 4.17 An artificial neural network to perform regression for estimation of radius
of curvature. The shown ANN shows the structure and weights after training based on
data presented in figure 4.16
Generally, for methods based on machine learning, the data is split as 60% for training
and 40% testing. However, having a smaller training set and larger test set ensures better
generalization. For the data generated in this experiment, only 30% of data was used for
training while the rest 70% was used as test set to ensure good generalization over the
different positions. To get reproducible results, the seed for the pseudo random number
generator has been fixed. The results of the tests are shown in figure 4.18. It can be seen
that in general, the median errors are within +/- 10% and on an average are within +/-
5%. The higher errors at some points are due to a few measurement points having high
errors in measured wavelength shifts. This is more for R=15cm as the wavelength shifts
are small and any small measurement error in wavelength shifts leads to large errors in
overall measurements. This is due to manual handling of the shape sensing tube during
the calibration. This method can be improved by using a more controlled calibration
setup and thus seems promising for determination of radius of curvature.
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Figure 4.18 Error plot for tests using the trained neural network
In order to test the accuracy of estimated radii of curvature and the effect of inaccuracies
on the reconstructed shape, the shape sensing tube has been moved along a short sample
curve with each measurement point 0.5mm away corresponding to l=0.5 in equations
4.4 to 4.6. The original shape has been captured using a graph sheet with 1mm markings.
The estimated radii of curvature ‘R’ for each point has been estimated using the trained
ANN shown in figure 4.17. The reconstructed curve has been plotted using the estimated
values of ‘R’ iteratively in equations 4.3 to 4.6 which have been implemented in Python.
Figure 4.18 shows the original and reconstructed curve. Even though the errors are not
small enough for use in exact localization of the tip, the method can be used for
estimation of shape traced by the tip for visualization purposes to assist the surgeons.
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Figure 4.19 Reconstruction of a sample small curve using measured wavelength shifts
and estimated radii of curvature using the ANN
4.8 Summary
The different methods for shape estimation of flexible medical instrument like
endoscopes that have been tried out have been presented in this chapter. Issues in using
FBG sensors bonded on nitinol have been discussed and an alternative methods based
on FBG sensors embedded inside a PDMS filled tube has been presented. This enables
shape estimation for highly flexible instruments up to very small radii of curvature
without having an adverse effect on the flexibility of the instrument. The methods
demonstrated here can determine shapes in a plane. In the current system one sensing
point close to the tip has been used. This is capable of tracing the shape during insertion.
In future, the system can be extended to have multiple sensing points so that better
interpolation can be used for estimating the shape followed during insertion. Handling
of out of plane bending to determine complete 3D shape estimation seems possible and
needs to be studied further.
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[19] L. Zhang, J. Qian, Y. Zhang and L. Shen, "On SDM/WDM FBG sensor net for
shape detection of endoscope," in Mechatronics and Automation, 2005 IEEE
International Conference, 2005.
[20] J. P. Moore and M. D. Rogge, "Shape sensing using multi-core fiber optic cable
and parametric curve solutions," Optics Express, vol. 20, pp. 2967-2973,
2012.
[21] K. K. C. Lee, A. Mariampillai, M. Haque, B. A. Standish, V. X. D. Yang and P.
R. Herman, "Temperature-compensated fiber-optic 3D shape sensor based
on femtosecond laser direct-written Bragg grating waveguides," Optics
express, vol. 21, pp. 24076-24086, 2013.
[22] E. Carlen, Calculus++: Description and prediction of motion, 2013.
[23] I. D. Johnston, D. K. McCluskey, C. K. L. Tan and M. C. Tracey, "Mechanical
characterization of bulk Sylgard 184 for microfluidics and
microengineering," Journal of Micromechanics and Microengineering, vol.
24, no. 3, p. 035017, 2014.
[24] C. M. Bishop, Pattern recognition and machine learning, springer, 2006.
[25] S. Fritsch, F. Guenther, M. Suling and S. M. Mueller, Training of Neural
Networks, CRAN, 2016.
[26] The R Foundation, The R Project for Statistical Computing https://www.r-
project.org/.
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
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Chapter 5
Evaluation of FBG interrogation
systems based on InGaAs linear
detector arrays and curve fitting
methods using Gaussian
approximation
5.1 Introduction
FBG interrogation systems provide the mechanism to measure the Bragg wavelength
shifts. For any application involving FBG sensors, interrogation systems are as
important as sensor characteristics [1]. Successful and widespread adoption of FBG
sensors in biomedical applications is dependent on the availability of cost-effective
interrogation systems meeting the application specific requirements on accuracy and
speed and the possibility of integration with existing measurement systems for real-
world use [2].
Several FBG interrogation systems have been proposed in literature. One of the
simplest, earliest and widely adapted method is based on the use of an edge filter [3] [4]
[5] [6] providing a linear relationship between the wavelength shifts and the output
intensity changes of the filter as shown in figure 5.1.
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Figure 5.1 Schematic diagram of interrogation system using edge filter [3]
The filter can be modeled as
F(λ) = A(λ – λ0)
where A is the filtering slope and F(λ) is zero at λ0.
Assuming back reflected Bragg peak follows a Gaussian profile with center wavelength
λb and spectral width Δλ, the intensity of the reference and the filtered beams can be
represented as
𝐼𝑟𝑒𝑓 = 𝐼0 𝑅 √𝜋
2∆𝜆
𝐼𝑓𝑖𝑙𝑡 = 𝐼0 𝑅 𝐴 √𝜋
2(𝜆𝑏 − 𝜆0 +
Δ𝜆
√𝜋) ∆𝜆
where I0 is the intensity of the light incident on the grating and R is the grating
reflectivity.
Source
Linear Edge Filter F(λ) = A(λ – λ0)
Photodetector Photodetector
Iref Ifilt
Electronics
FBG Sensor
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The ratio of the two outputs is
𝐼𝑓𝑖𝑙𝑡
𝐼𝑟𝑒𝑓= 𝐴 (𝜆𝑏 − 𝜆0 +
Δ𝜆
√𝜋)
The ratio varies linearly as the wavelength λb shifts and is independent of the source
intensity fluctuations. The method has been used with different filtering elements and
even all-fiber approaches have been used to avoid limitations of bulk optic filters. The
technique is cost effective and accuracies can also be improved considering application
specific calibration. However, extending it for use with multiple sensors is difficult as
simultaneous use of several edge filtering components and couplers is not practical.
(a) (b)
Figure 5.2 (a) Schematic of matched FBGs based interrogation and (b) simultaneous
multiple sensor interrogation [7] [8]
A natural simple alternative to this method is to use methods based on matched FBGs
[7] [8] [9] [10] [11] [12] [13] [14]. In its simple form, the concept consists of using a
grating pair of sensing grating (Gs) and receiving grating (Gr) as shown in figure 5.2(a).
The center peak wavelength of both are identical when both experience the same strain
Source G
G
Piezo-stretcher
Photodetector Controller
Source Gs Gs
Gr Gr
Piezo-stretcher
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and temperature. The back-reflected light from Gs is passed through a coupler to Gr
which is mounted on a controlled piezo-stretcher. The back-reflected light is passed to
a photodetector and the intensity is observed which is maximum when the peak
wavelengths match. The peak wavelength of the sensing grating Gs varies in response
to strain or temperature changes. A sweep signal is applied to the piezo-stretcher. The
intensity of back reflected light from Gr is dependent on the matching condition. The
stretching leads to change in intensity at the photodetector.
These methods provide a cost effective mechanism for FBG interrogation. However, it
is difficult to use these for real world applications due to the constraint of using very
closely matched FBGs in both the sensing arm and the receiving arm. Also, the number
of sensors that can be interrogated is pre-determined which is a major constraint.
Figure 5.3 Schematic diagram of interrogation system using tunable fabry-perot filter
[15] [16]
Another interrogation scheme for which several extensions and modifications have been
proposed over the years [15] [16] [17] [18] [19] consists of using a tunable fabry-perot
filter as shown in figure 5.3.
Broadband Source
Fabry-perot filter ∑
Feedback Control
Detector
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The fabry-perot passband is locked to the back reflected signal from the FBG sensor
using a feedback loop. For a fiber fabry perot filter, the tuning can be performed using
piezoelectric adjustment of the cavity spacing at a modulating frequency fm. The output
contains components of the fundamental and harmonics of fm. When the wavelengths of
the fabry-perot filter and the back reflected signal are aligned, the amplitude of the
fundamental is nulled. The tuning constrains the sampling rate and the accuracy of the
system. In recent times high accuracies have been achieved. However, cost effectiveness
still remains a constraint.
Interrogation systems based on narrow linewidth wavelength tunable sources have been
popular in recent years. Different configurations have been used for source. These
include wavelength swept fiber lasers with fabry-perot filter in the cavity to sweep the
laser output wavelength in time [20], wavelength swept fiber lasers with intracavity
acoustooptic tunable filter [21], swept fiber laser based on dispersion tuning technique
which does not require any optical tunable filter in laser cavity [22], Fourier domain
mode locking laser [23] [24] and active mode locking fiber laser [25]. Interrogation
using tunable swept lasers can provide high accuracy. Availability of a high power
budget per sensor enables interrogation of large number of sensors over long distances.
However, at present the cost of swept tunable laser based systems is high. This is
acceptable for applications which require monitoring of large number of sensors
distributed over large distances and also for experimental setups and niche applications.
However, for biomedical applications involving small number of sensor per setup, the
cost is an important factor. The expectation is that technology advancements might
bring down the cost in future.
For several biomedical and robotic applications, only a few FBG sensors per fiber are
required. Meeting application specific requirements for accuracy and resolution along
with required sampling rates and the feasibility of creating systems with integrated
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embedded hardware for real-time computations are sufficient to make widespread
adoption easier. Interrogation systems based on broadband source and InGaAs linear
detector arrays provide an option. Figure 5.4 shows the schematic diagram of an
interrogation system based on transmission grating and linear detector array.
Figure 5.4 Schematic diagram of an interrogation system with InGaAs linear detector
array [26]
The main challenge in using such interrogation systems is achieving the required
resolution. For example, an InGaAs linear photodiode array with 512 pixels with a
wavelength range of 1510nm to 1595 nm provides an FWHM resolution of
approximately 330 pm. This is not sufficient for most applications but curve-fitting
methods [27] [28] have been used to achieve sub-pixel accuracy. However, the effect of
choice of number of pixels around a spectrum peak and the choice of algorithms has a
significant impact on the accuracy and computational efficiency of the curve fitting
algorithm. In this work, a detailed analysis of the effect of the choice of number of pixels
in the region of the peak on the accuracy of the estimated Bragg wavelength and the
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points where errors are highest is provided. This is important because specifications
related to minimum errors are not sufficient for determining usage in several
applications. It is important to choose the algorithms based on the knowledge of
average and maximum errors and the conditions which result in maximum errors.
It is also useful to implement the algorithm on embedded hardware and hence it is
important to consider computational complexity to meet the sampling rate
requirements. Hence experiment has been designed to be able to detect the
maximum errors in the system for multiple sensors and all algorithms have been
evaluated using the data obtained from these measurements.
5.2 Measurement Setup and Data Characteristics
Two commercially available interrogation systems – I-MON 512 USB from Ibsen
Photonics and SM130 from Micron Optics have been used for the work presented in
this thesis. The SM130 is based on a swept tunable laser while the I-MON 512 USB
uses a transmission grating along with an InGaAs linear detector array with 512 pixels.
I-MON 512 has been selected because it allows direct access to the measured intensity
at each pixel and the choice of algorithm for peak estimation is left to the user. The
focus of this work is on the comparison of algorithms and they would be applicable for
any similar system.
5.2.1 Setup
Most sensing applications using FBG sensors are based on measuring the wavelength
shift in response to strain or temperature changes. Hence, for the analysis of the
algorithms, six FBG sensors have been fabricated on a single germanosilicate fiber
using phase mask technique and small incremental strains have been applied using the
setup as shown in figure 5.5. The sensors have been fabricated using three different
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phase masks. For each phase mask, two sensors have been fabricated close to each other
with a separation of approximately 15mm by pre-stretching the fiber and translating it.
The wavelength separation between these two sensors is approximately 1.5nm.
Figure 5.5 Setup to generate data samples
The fiber has been fixed rigidly to both the translation stage and the fixed end. Not
having the fiber bonded to another material avoids any non-linearity or spectrum
distortion arising because of the bonding. Since the strain on each sensor has been
applied thorugh elongation by using the translation stage, and measurements for each
sensor have been made simultaneously, the effect of slight variations in ambient
temperature can be neglected as the temperature variation for all sensors is similar.
5.2.2 Data Characteristics
The translation stage has been linearly moved for 10 steps of 10µm each. At each step,
the data has been acquired using both the interrogation systems and has been logged in
files. The log of data from I-MON 512 consists of the complete spectrum across all
pixels. The log of data from the SM130 consists of the intensity measured at 512 pixels.
There are small variations in the applied strain at each measurement step because of
small inaccuracies in the linear translation stage. However, the variation is not relevant
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for this evaluation as error comparisons have been made for each measurement point.
Figure 5.7 shows the spectrum obtained from the linear detector array for one sample
measurement. In the plot, a linear interpolation has been added between the points to
make visualization of peaks easier.
Figure 5.6 Spectrum obtained from the linear detector array
5.3 Bragg Wavelength Estimation
The linear detector array only provides the intensity at each pixel. Using the pixel with
highest intensity as the one representing peak wavelength would lead to very low
resolution. Hence the peak wavelength has to be estimated using an approximation
algorithm providing sub-pixel resolution.
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5.3.1 Centroid Algorithm
The simplest method to achieve sub-pixel resolution is based on the centroid algorithm
[29] as shown in equation 5.1
𝜆𝑏 =∑ 𝜆𝑖𝐼𝑖
𝑁𝑖=1
∑ 𝜆𝑖𝑁𝑖=1
--- (5.1)
where 𝜆𝑖 are the wavelengths at the pixels around the peak and 𝐼𝑖 are the corresponding
intensity values.
The algorithm has been applied to estimate wavelength shifts for all sensors for the all
the measurements corresponding to incremental strains. The main advantage of the
algorithm is its low computational cost. As is evident from equation 5.1, only a small
number of multiplications and additions and one division are required. The computation
time does not constrain the sampling rates for the overall system even when combined
with a visualization system. The computed values of Bragg wavelength shift using the
centroid algorithm along with that measured using the swept tunable laser based
interrogation system are shown in figure 5.7.
The graphs show the advantage of using the sensor configuration and small incremental
strains for the analysis. For each sensor, there is a corresponding measurement where
the error in measured wavelength shift is very high relative to other measurements. The
absolute value of change in strains for each sensor are not important for this analysis as
only the error in estimation of the same wavelength shift using different techniques is
evaluated.
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Figure 5.7 Errors in peak wavelength estimation using the centroid method compared
to measurement using the interrogation system based on swept tunable laser
The spectrum shift at the points where the deviation is maximum has been analyzed. It
has been found that the deviation is maximum when the spectrum shifts to include a
new pixel. This can be seen in the comparison as shown in figure 5.8.
For wavelength shift due to strain difference between measurement 0 and measurement
1, the spectrum for sensor 1 shifts across pixels. This does not happen for the other
sensors. Similarly, for wavelength shift between measurement 1 and measurement 2,
the spectrum shifts across pixels for sensor 2. The errors in estimation are highest at
these points.
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Figure 5.8 Plots showing the points around the peak. Each measurement corresponds
to a shift in wavelength due to applied strain. The original and the shifted points and
the estimated peak using centroid algorithm are shown for three different sensors on
the fiber.
5.3.2 Gaussian Approximation for the FBG spectrum
and least square estimation of Bragg
wavelength
The FBG spectrum can be approximated as a Gaussian [30] as represented by equation
5.2.
𝐼(𝜆, 𝐴, 𝜆𝑏 , 𝜎)= 𝐴𝑒−
(𝜆−𝜆𝑏)2
2𝜎2 --- (5.2)
where 𝜆𝑏represents the Bragg wavelength.
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Given the wavelengths at the pixels (𝜆𝑖)and the intensities (Ii), from the measurements,
the goal is to estimate the parameters𝜆𝑏, A and 𝜎. This can be done using least squares
estimation. The error function is given by
𝐸 = ∑ (𝐼(𝜆𝑖, 𝐴, 𝜆𝑏 , 𝜎) − 𝐼𝑖)2𝑁𝑖=1 --- (5.3)
has to be minimized with respect to the parameters 𝜆𝑏 , A and 𝜎. Though there are
several methods that can be used to solve this, the Levenberg-Marquard algorithm [31]
[32] has been extensively used and is the default implementation in most libraries (e.g.
the least squares curve fitting function in LabView uses it). In this evaluation, the
implementation in the SciPy [33] library in Python which internally uses the MINPACK
[34] implementation has been used.
To apply, the non-linear least square estimation, it is first required to find the pixels in
the neighborhood of peaks. For extracting these pixels from the data for all the 512
pixels in the spectrum, a simple peak search algorithm has been employed. This first
applies a threshold based on the intensity of the highest intensity peak in the spectrum
to get all possible peak regions. Then the change in gradient of the difference in
intensities has been used to detect all the pixels with highest intensities in a
neighborhood. This method enables handling of sensors with varying reflectivity. The
need for this is evident by observing the spectrum in figure 5.6 where the smallest peak
has an intensity approximately 50% of that of the highest peak. Once all the pixels with
highest intensities has been obtained, the least square method can be employed based
on different number of pixels around the pixel with maximum intensity.
The Levenberg-Marquardt algorithm requires setting of initial values for the parameters
which are being estimated. The wavelength of the pixel with highest intensity and the
intensity at that pixel have been used as the initial values for 𝜆𝑏 and A respectively.
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Figure 5.9 Estimated Bragg wavelengths using different number of pixels around the
peak
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To evaluate the variations in the estimated peak wavelength, the least square estimation
has been performed using four different set of pixels. In the following discussion, peak
refers to the pixel with highest intensity. The first variation uses one pixels to the left
and one to the right of peak, the second uses four pixels with two pixels to the left of
the peak, the third uses four pixels with two pixels to the right of the peak and the fourth
uses five pixels with two pixels on both sides of the peak. Figure 5.9 shows the estimated
wavelengths for all sensors for all measurements.
Since accuracy in measurement of wavelength shift is important, it is analyzed for all
sensors for each measurement point. The comparisons have also been made to the
wavelength shift measured by the interrogator based on swept tunable laser. It has been
found that the accuracy varies with the different number of pixels used in the non-linear
least squares estimation as shown in figure 5.10.
Figure 5.10 Wavelength shift measured using different number of pixels and
compared to measurement with swept tunable lased based interrogation system.
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To find the main source of high variation at certain points, the spectrum shift at these
points has been analyzed. It has been found that similar to the centroid algorithm, the
maximum variation occurs when the spectrum shifts completely one pixel to the left or
right. This is seen in figure 5.11. For the purpose of curve fitting, pixels are assumed as
points (representing the center of the pixel) and the intensities as the values at these
points. In reality, the intensity is spread across the pixels. Hence, when the spectrum
shift corresponding to wavelength shift from one measurement to the next is not limited
to the same set of pixels, the error is higher. Unlike in the case of centroid algorithm,
using five pixels instead of three does not improve the accuracy. It actually reduces it
as the curve fitting works best only when the pixels are within the Full Width at Half
Maximum (FWHM) range.
Figure 5.11 Spectrum for sensor 1 and sensor 2 before and after wavelength shift due
to applied strain
Since all measurements have been done by applying increasing strain, the wavelength
shift is in the same direction. This is direction towards left in terms of pixels in the linear
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detector array as pixel number one represents the maximum wavelength limit of
1595nm. Hence, at the error points, the impact is highest on the peak estimation using
four points where the two points are to the left of the pixel with highest intensity as there
is a high asymmetry around the peak after the shift.
Figure 5.11 clearly shows that the variation between the estimated wavelength shifts is
very small for the different number of pixels for sensor 2 because the spectrum does not
shift across the pixels. However, the estimated wavelength shift vary significantly for
sensor 1 because of the shift in spectrum by one pixel to the left. Figure 5.12 shows the
plot for the difference between the estimated wavelength shifts using the Gaussian
approximation and that measured using the swept tunable laser based interrogation
system for all six sensors for the eight wavelength shift measurements. The results have
been summarized in table 5.1.
Table 5.1 Wavelength shift difference from tunable laser based system using different
number of points for non-linear least squares estimation using Levenberg Marquardt
algorithm
3
Points
4 points
(peak - 2 to
peak + 1)
4 points
(peak - 1 to
peak + 2)
5 points
Maximum wavelength
shift difference (pm)
6 32 12 14
Median wavelength shift
difference (pm)
0.3 1.7 0.8 0.8
Even though the median difference between the estimated values and those measured
using tunable laser based systems are less than 1 pm, the maximum errors are much
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higher when using 4 points and 5 points as compared to 3 points. This is attributed to
the measurements when the spectrum shifts across the pixels.
Figure 5.12 Difference in wavelength shift estimation using Levenberg-Marquardt
algorithm and Gaussian spectrum approximation compared to measurement using
swept tunable laser based interrogation system
Table 5.2. Wavelength shift difference from tunable laser based system using
Levenberg Marquardt algorithm and Centroid Algorithm
Lev-Mar 3
Points
Centroid 3
Points
Centroid 5 points
Maximum wavelength
shift difference (pm)
6 102 70
Median wavelength
shift difference (pm)
0.3 14.4 9.6
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Comparison of errors using curve fitting with Lev-Mar method and using centroid
algorithm highlights the specific advantage of using the Lev-Mar specifically to reduce
the maximum errors. The maximum error using centroid fit can be up to 102 pm using
3 points and 70 pm using 5 points while that with Lev-Mar and 3 points is limited to 6
pm. The median error is also significantly reduced from close to 15pm for centroid with
3 points to less than 1 pm for Lev-Mar with 3 points as summarized in table 5.2.
5.3.3 Lower computational cost algorithm utilizing
Gaussian Approximation for the FBG spectrum
In the previous section, it has been shown that Bragg wavelength estimation using non-
linear least square estimation and Gaussian approximation for interrogation systems
based on InGaAs linear detector arrays can achieve accuracy very close to those
achieved by interrogation systems based on swept tunable laser. The errors are lowest
when using three pixels for the least square estimation such that the center pixel is the
one with the highest intensity. However, the computational cost of non-linear least
square estimation is high in spite of using the Levenberg-Marquard algorithm. To
overcome this, Caruana’s algorithm [35] [36] has been evaluated which is specific to
curve fitting for Gaussian function and does not require any iterative method. Caruana’s
algorithm reduces the estimation to solving simultaneous linear equations which can be
done efficiently using matrix manipulation methods.
Taking natural logarithm on both sides for equation (5.2)
ln 𝐼 = ln 𝐴 −(𝜆−𝜆𝑏)2
2𝜎2 --- (5.4)
= ln 𝐴 −𝜆2
2𝜎2 +2𝜆𝑏𝜆
2𝜎2 −𝜆𝑏
2
2𝜎2 --- (5.5)
= 𝑎 + 𝑏𝜆 + 𝑐𝜆2 --- (5.6)
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
128
where 𝑎 = ln 𝐴 − 𝜆𝑏
2
2𝜎2 , 𝑏 = 𝜆𝑏
𝜎2 , 𝑐 = −1
2𝜎2
For measured intensities Ii at pixels with wavelengths λi, this is equivalent to fitting a
parabola to the points. Formulating it as a least squares estimation problem, the error
term to be minimized can be written as
𝐸 = ∑ (ln 𝐼𝑖 − 𝑎 − 𝑏𝜆𝑖 − 𝑐𝜆𝑖2)
2𝑁𝑖=1 --- (5.7)
Minimization can be done by solving
𝜕𝐸
𝜕𝑎= 0 --- (5.8)
𝜕𝐸
𝜕𝑏= 0 --- (5.9)
𝜕𝐸
𝜕𝑐= 0 --- (5.10)
Solving (7), (8) and (9) respectively,
∑ ln 𝐼𝑖𝑁𝑖=1 − 𝑎𝑁 − 𝑏 ∑ 𝜆𝑖
𝑁𝑖=1 − 𝑐 ∑ 𝜆𝑖
2𝑁𝑖=1 = 0 --- (5.11)
∑ 𝜆𝑖ln 𝐼𝑖𝑁𝑖=1 − 𝑎 ∑ 𝜆𝑖
𝑁𝑖=1 − 𝑏 ∑ 𝜆𝑖
2𝑁𝑖=1 − 𝑐 ∑ 𝜆𝑖
3𝑁𝑖=1 = 0 --- (5.12)
∑ 𝜆𝑖2ln 𝐼𝑖
𝑁𝑖=1 − 𝑎 ∑ 𝜆𝑖
2𝑁𝑖=1 − 𝑏 ∑ 𝜆𝑖
3𝑁𝑖=1 − 𝑐 ∑ 𝜆𝑖
4𝑁𝑖=1 = 0 --- (5.13)
[
𝑁 ∑ 𝜆𝑖𝑁𝑖=1 ∑ 𝜆𝑖
2𝑁𝑖=1
∑ 𝜆𝑖𝑁𝑖=1 ∑ 𝜆𝑖
2𝑁𝑖=1 ∑ 𝜆𝑖
3𝑁𝑖=1
∑ 𝜆𝑖2𝑁
𝑖=1 ∑ 𝜆𝑖3𝑁
𝑖=1 ∑ 𝜆𝑖4𝑁
𝑖=1
] [𝑎𝑏𝑐
] = [
∑ ln 𝐼𝑖𝑁𝑖=1
∑ 𝜆𝑖ln 𝐼𝑖𝑁𝑖=1
∑ 𝜆𝑖2ln 𝐼𝑖
𝑁𝑖=1
] ---
(5.14)
𝜆𝑏 = −𝑏
2𝑐 --- (5.15)
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
129
This is in the standard form Ax = b. The terms with higher powers in A can be computed
efficiently by using vector representations for data points and dot products. Since, for
the purpose of this evaluation, all implementations have been done in Python, these can
be very efficiently done. In order, to estimate the gain in efficiency, the Bragg
wavelength estimation has been done both with the non-linear least squares estimation
using Levenberg- Marquardt algorithm and Caruana’s algorithm in comparison to
Centroid algorithm. The execution time has been measured on a Raspberry Pi 2 model
B board with a 900MHz quad core ARM Cortex – A7 CPU and 1GB of RAM and
running Rasbian operating system which is based on Debian operating system. The
method for timing estimate has been done using the standard recommended method in
Python using the timeit library.
The results have been summarized in Table 5.3. As can be seen, the execution time is
significantly lower for Caruana’s algorithm as compared to Levenberg Marquardt
algorithm. It has been observed that using Caruana’s algorithm provides an average
speed up of approximately 6.5 times. Using Levenberg Marquard algorithm with the
used setup reduces the maximum sampling frequency to around 30Hz. However, using
Caruana’s algorithm allows a sampling rate around 200Hz. The estimated values for
Bragg wavelength have also been compared. The difference between Caruana’s
algorithm and Lev-Mar is less than 0.01pm which is sufficient to recommend the use of
Caruana’s algorithm over non-linear least square estimation using Levenberg-
Marquardt algorithm with three pixels on embedded hardware.
There is another advantage of using Caruana’s algorithm. When the strain changes
slowly compared to the sampling rate and the pixels for each peak do not change, there
is no need to recalculate the matrix A. This would further reduce the required
computation for each sample. However, this was not used in the computation time
evaluation here to avoid any dependency on specific data.
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
130
Table 5.3 Comparison of execution times and difference in estimated wavelength
from tunable laser based system for the three methods
Centroid 3
points
Lev-Mar 3
Points
Caruana 3
Points
Median Normalized
Execution time
1x 64x 10x
Maximum wavelength
shift difference from
tunable laser based
system (pm)
100 6 6
Median wavelength shift
difference from tunable
laser based system
(pm)
15 0.3 0.3
5.4 Summary
This evaluation has shown that FBG interrogation systems based on InGaAs linear
detector arrays combined with curve fitting methods utilizing Gaussian approximation
of the FBG spectrum can achieve accuracy close to that achieved by interrogation
systems based on swept tunable laser. This is useful for interrogation systems for
biomedical and robotic applications where the number of sensors and distance between
the sensors and the interrogation system is small and benefits other than high accuracy
of a swept laser baser system are not required. It has been shown that the choice of
number of pixels around the peak has a significant impact on the maximum errors when
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
131
using the non-linear least square estimation based on Levenberg-Marquardt algorithm.
It has also been shown that Caruana’s algorithm provides the same accuracy as
Levenberg-Marquardt algorithm while being significantly computationally faster. This
has been demonstrated through implementation on an embedded hardware platforms
which can be packaged with the linear detector array and the transmission gratings.
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
132
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based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
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Chapter 5 Evaluation of FBG interrogation systems
based on InGaAs linear detector arrays and curve fitting
methods using Gaussian approximation
138
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Chapter 6 Conclusions and Future Work
139
Chapter 6
Conclusions and Future Work
This thesis studies the applications of FBG sensors for force and shape estimation for
flexible medical instruments.
A method to estimate the forces at the tip of a hollow needle has been presented in
chapter 3. It has been shown that this can be used to estimate the transition of needle
through tissue layers of varying stiffness. The analysis shows that gradients of the strains
measured by the sensor close to the tip can be used to determine the transition without
the need to depend on the absolute values of the strains. In future, the method can be
extended to also determine the compression of the tissue during needle insertion.
Need for shape estimation of flexible instruments and methods to do it have been
explored in chapter 4. Curvature estimation using FBG sensors bonded to a nitinol wire
have been found to significantly reduce the flexibility of the assembly. A new alternative
based on FBG sensors embedded in a PDMS filled tube has been presented. The
tolerance of FBG sensors to the curing process has enabled their use for the fabrication
of the shape sensing tube. However, the setup leads to a non-determinism of rotation
angle. It has been shown that an Artificial Neural Network based calibration can be used
to estimate the radius of curvature and hence aid in the reconstruction of shape for in-
plane bending. In future, the method can be extended to include estimation for out-of
plane bending as well and hence can enable complete 3D shape reconstruction.
Cost effective interrogation systems are as important as sensor characteristics for
widespread commercial use of FBG sensors in biomedical applications. This thesis has
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Chapter 6 Conclusions and Future Work
140
shown that interrogation systems based on InGaAs linear detector arrays in combination
with computationally efficient curve fitting techniques can achieve good accuracies to
enable their usage for biomedical applications. In future, the system can be extended
with an approach to enable dynamic trade-offs of wavelength range versus resolution.
The benefits of small size and multiplexing of FBG sensors can enable the creation of a
unified setup as shown in figure 6.1 where shape sensing can be used in conjunction
with force sensing for aiding surgeons in complex procedures like Natural Orifice
Transluminal Endoscopy.
Fig 6.1 Proposed future device with integrated shape sensing tube and force sensing
needle
Flexible scope with shape sensing
Working Channel Needle with FBG
sensors
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141
Appendix A
FBG sensor fabrication setup
Figure A.1: Setup used for fabricating FBG sensors
The beam from KrF excimer laser (Braggstar industrial) is focused on the fiber using a
cylindrical lens. The phase mask is aligned perpendicular to the laser beam. The fiber is
mounted on a translation stage with a motion controller of resolution 0.1µm and speed
of 20mm/sec. The phase mask is mounted on a stage which has x, y and z translation,
tilt and rotation adjustments. This enables very precise alignment. The alignment is
Phase Mask
KrF Laser
Linear Motion Stage
Motion Controller Camera
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142
monitored using a camera mounted on top of the setup. During fabrication, the fiber is
placed in very close proximity to the phase mask. The entire setup is placed on a
vibration isolation optical table.
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List of Publications
Kumar Saurabh, Venkoba Shrikanth, Bharadwaj Amrutur, Sundarrajan Asokan, M.S.
Bobji, “Detecting stages of needle penetration into tissues through force estimation
at needle tip using fiber bragg grating sensors”, J. Biomed. Opt., 21(12), 2016
Kumar Saurabh, V Shrikanth, Bharadwaj Amrutur, Sundarrajan Asokan, M.S. Bobji,
“Estimating needle-tissue interaction forces for hollow needles using fiber Bragg
grating sensors”, Proc. of. SPIE 9702, Mar 2016
Kumar Saurabh, Shanthanu Chakravarthy, G. K. Ananthasuresh, Bharadwaj Amrutur,
Asokan Sundarrajan, “Shape Estimation for Flexible Medical Instruments - An
Approach Based on FBG Sensors Embedded in a Biocompatible Polymer Filled
Tube”, IEEE/RSJ IROS Workshop on Navigation and Actuation of Flexible Instruments
for Medical Applications (NAFIMA), Hamburg, Oct 2015
Ananya, Shanthanu Chakravarthy, Kumar Saurabh and G. K. Ananthasuresh, “Shape
Estimation and Prediction of Locations of the Force on a Flexible Tube using
Strains at a Few Points”, 2nd International and 17th National Conference on
Machines and Mechanisms, 2015
Kumar, Saurabh, Bharadwaj Amrutur, and Sundarrajan Asokan. "Evaluation of fiber
Bragg grating sensor interrogation using InGaAs linear detector arrays and
Gaussian approximation on embedded hardware" Review of Scientific Instruments,
89.2 (2018)
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An experiment is a question which science poses to Nature, and a
measurement is the recording of Nature's answer.
- Max Planck