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ARTICLE IN PRESS Model

JBE-2090; No. of Pages 9

Medical Engineering & Physics xxx (2012) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Medical Engineering & Physics

jou rna l h omepa g e: www.elsev ier .com/ locate /medengphy

oninvasive induction implant heating: An approach for contactless altering ofechanical properties of shape memory implants

onny Pfeifera,∗, Michael Hustedta, Volker Weslinga, Christoph Hurschlerb, Gavin Olenderb,artin Machc, Thomas Göslingd, Christian W. Müllerd

Laser Zentrum Hannover e.V., Hollerithallee 8, 30419 Hannover, GermanyLaboratory for Biomechanics and Biomaterials, Department of Orthopaedics, Hannover Medical School (MHH), Anna-von-Borries-Str. 1-7, 30625 Hannover, GermanyInstitute of Electrotechnology, Leibniz University Hannover, Wilhelm-Busch-Str. 4, 30167 Hannover, GermanyTrauma Department, Hannover Medical School (MHH), Carl-Neuberg-Str. 1, 30625 Hannover, Germany

r t i c l e i n f o

rticle history:eceived 1 August 2011eceived in revised form 29 February 2012ccepted 21 March 2012

a b s t r a c t

This article shows an approach to change the properties of an orthopaedic shape memory implant withinbiological tissue, using contactless induction heating. Due to inducing the one way-memory effect, trig-gered by the rise of temperature within the implant, the geometry and hence the mechanical propertiesof the implant itself, are altered. The power uptake of the implant, depending on the induction param-eters as well as on its position within the induction coil, is shown. Thermographic measurements are

eywords:nduction heatinghape memory alloy (SMA)iTiitinol

mplant

carried out in order to determine the surface temperature distribution of the implant. In order to sim-ulate biological tissue, the implant was embedded in agarose gel. Suitable heating parameters, in termsof a short heating process in combination with a reduced heat impact on the surrounding environment,were determined.

© 2012 IPEM. Published by Elsevier Ltd. All rights reserved.
tiffness
. Introduction

Apart from biological aspects, e.g. local blood supply, hormonesnd growth factors, the healing of bone fractures is influenced byechanical stimuli [1]. In particular, the stiffness on the stabiliz-

ng implant, e.g. an internal osteosynthetic plate, directly affectinghe local strain allocation within the fracture gap, has a big impactn the bone healing process [2]. To this date, the “ideal” stiffnessf an internal implant has not yet been entirely clarified. Further-ore, the alternation of mechanical properties, e.g. stiffness, over

he course of healing is still a topic of research. However, with thexception of a fixateur externe, i.e. an external fixation of the boner biodegradable implants, today, any necessary alteration of theechanical properties of an implant results in further surgery.This article shows an approach to modify the stiffness of a

etallic shape memory implant within the human body, usingontactless induction heating. In general, this principle could offerifferent possibilities in regard to compression or expanding,nchoring or altering further mechanical properties of implants.

Please cite this article in press as: Pfeifer R, et al. Noninvasive induction iproperties of shape memory implants. Med Eng Phys (2012), http://dx.doi.

∗ Corresponding author. Tel.: +49 511 2788 161; fax: +49 511 2788 100.E-mail address: [email protected] (R. Pfeifer).

350-4533/$ – see front matter © 2012 IPEM. Published by Elsevier Ltd. All rights reservettp://dx.doi.org/10.1016/j.medengphy.2012.03.010

1.1. One-way shape memory effect

The shape memory effect is based on a reversible martensiticphase transformation (Fig. 1). By cooling the parent phase austen-ite to a critical temperature Ms (martensite start temperature),the monocrystalline structure changes into twinned martensite.This transformation is finished by reaching the martensite finishtemperature (Mf). In this state, the martensite can be deformedmechanically. The maximum reversible strain (ε), depending onthe structure and its thermomechanical treatment, is about 6–8%(6.7% for polycrystalline NiTi [3], 8% for nanocrystalline NiTi [4] fornickel–titanium (NiTi) shape memory alloys (SMA) [5,6]. By raisingthe temperature above the austenite finish temperature (Af), themartensite completely converts into austenite again and the SMAreturns to its initial predetermined state, exhibiting the so-calledone-way shape memory effect (SME) [5]. It should be noted thatthe Young’s modulus of NiTi nearly doubles when converting frommartensite into austenite (cf. Table 1).

1.2. Shape memory alloys for medical applications

mplant heating: An approach for contactless altering of mechanicalorg/10.1016/j.medengphy.2012.03.010

Since their first description in 1932, SMAs have been of increas-ing interest in the industrial and scientific field [5,7]. To this date,several metallic alloys offering the SME are known, whereby Cu-based (CuAlNi, CuZnAl), Fe-based and NiTi-based alloy systems are

d.

dx.doi.org/10.1016/j.medengphy.2012.03.010


http://www.sciencedirect.com/science/journal/13504533

http://www.elsevier.com/locate/medengphy

mailto:[email protected]


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JJBE-2090; No. of Pages 9

2 R. Pfeifer et al. / Medical Engineering & Physics xxx (2012) xxx– xxx

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Fig. 1. Macroscopic (left) and microscopic (righ

f commercial importance [8]. In addition, several polymers (SMP)hich offer the SME, have been investigated as well throughout

he last 20 years [8–11]. Furthermore, the combination of SMAs orMPs with other materials, resulting in shape memory compositesSMC) or shape memory hybrids (SMH), offer further options toealize different phenomena and features [8].

Due to their outstanding properties, the most common SMAsoday are the NiTi-SMAs. They contain a nearly equiatomic inter-

etallic compound of 54–60 wt% Ni, rest Ti. Compared to otherMAs, NiTi-SMAs offer the most pronounced one- and two-wayME and the pseudoplasticity, i.e. the ability to recover an appar-ntly plastic strain on loading. Additionally, they show a highechanical strength and a high efficiency in converting thermal

nto mechanical energy. Due to its resistant inert oxide layer,iTi-SMAs are characterized by an excellent biocompatibility andorrosion resistance [12,13]. Table 1 shows typical physical proper-ies of different SMAs and illustrates the benefits of NiTi comparedo other SMAs.

Hence, NiTi-SMAs are widely used within the medical field.oday, they are applied for stents in vascular surgery and gas-roenterology [14], guide wires for catheters [7], microgrippers andaskets [15], inferior vena cava filters, brackets, wires and files forrthodontic applications [16,17]. NiTi SMAs are further applied astaples for foot surgery [18] or as porous NiTi implants for inter-ertebral body fusion [12].

Please cite this article in press as: Pfeifer R, et al. Noninvasive induction iproperties of shape memory implants. Med Eng Phys (2012), http://dx.doi

Whilst most clinical applications exploit the pseudoplasticityf NiTi-SMAs, only a few clinical applications are based on thene-way shape-memory effect, e.g. NiTi staples [5,18], such as sur-ical fixators in minimal access surgery (experimental) [19] or vena

able 1hysical and mechanical properties of NiTi-SMA [25–27]. Several parameters are depicte

Properties Unit

Fusion point ◦C

Density g/cm3

Thermal conductivity at 20 ◦C (A; M) W/m K

Specific heat J/kg K

Dilatation coefficient (A; M) �m/K

Young’s modulus (A; M) GPa

Yield strength MPa

Tensile strength MPa

Max. reversible strain (one-way m. effect) N = 1 %

Max. reversible strain (two-way m. effect) N = 1 %

Hysteresis K

Electric resistivity at 20 ◦C (A; M) �� m

Magnetic susceptibility

Relative permeability

Corrosion resistance

Biocompatibility

he “o” means average, given the following ranking: very good: ++, good: +, average: o, p

cription of the one-way shape memory effect.

cava filters to treat pulmonary embolism [20]. However, severalexperimental studies, especially in the orthopaedic field, have beencarried out in order to take account of a heat-induced shape modi-fication. For example, NiTi SMAs have been used in order to exert aconstant force on the bone after a fracture [21], for the correction ofscoliosis by applying bending forces on the growing spine [22,23]and on long bones [24].

In most cases, the body temperature itself or the temperatureincrease due to electrical heating is used to heat the implant aboveAf, hence triggering the SME. That means, the SME is initiated duringor shortly after implantation. In contrast, using an “external heatsource”, e.g. inductive heating, offers the possibility to induce theSME to an arbitrary date after implantation.

1.3. Inductive heating of shape memory devices

Contactless inductive heating generally can be used to increasethe temperature of any conductive workpiece, triggering highlydifferent effects when using NiTi-SMAs. So far, a few experimen-tal applications are shown in literature. Giroux et al. used radio(f = 28 MHz) and low frequency heating (f = 8 kHz) to heat NiTi wiresas an active part of a linear translator for leg lengthening [25].External heating of stents by radio waves (f = 253 kHz) to inhibithyperplasia, i.e. an exceeding proliferation of cells, was shownby Levitt et al. [28]. Floren et al. showed inductive stent heat-

mplant heating: An approach for contactless altering of mechanical.org/10.1016/j.medengphy.2012.03.010

ing (f = 200 kHz) to prevent instent restenosis [29]. The inductiveheating of SMPs (f = 12.2 MHz) was shown by Buckley et al. by theexperimental use of a shape-memory polymer for an endovascu-lar thrombectomy device for stroke treatment and an expandable

d for both states of the SMA, the martensitic (M) and the austenitic state (A).

NiTi CuZnAl CuAlNi

1250 1050 10206.4–6.5 7.5–8.0 7.1–7.28.6; 18 84; 120 30; 75490 440 39011; 6.7 17; – 18; –70–83; 23–41 80–100 70–100100–130 70 40875 800 7006–8 4–6 4–63.2 1 0.82–50 5–20 20–400.5; 1.1 0.07; 0.12 0.1; 0.143 × 106 2.9 2.91.002 1.002 1.001++ + o++ − −

oor: −, very poor: − −.




R. Pfeifer et al. / Medical Engineering & Physics xxx (2012) xxx– xxx 3

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the diameter of the material to be heated and the skin depth, i.e.the depth of penetration of the eddy currents.

ig. 2. Left: shows the CAD design of an experimental implant sample in its initial anhe one-way SME by inductive heating. Altering the geometry affects the mechanic

MP foam for aneurysm embolization [9]. Similar experimentsere shown by Mohr et al. as they used the inductive heating

f = 258 kHz) of magnetic nanoparticles in thermoplastic polymers10]. Short time heating of cylindrically NiTi-SMAs in biologicalissue (f = 250 kHz), has been shown by Müller et al. [30].

General problems of this method can be seen in the directxposition of living tissue to high-frequency fields resulting in annintended heating of the tissue (e.g. as it is exploited for regionalyperthermia [31]) and the damage of the surrounding tissue dueo heat conduction from the implant device. The direct impact ofhe HF field to the tissue can be reduced using a suitable inductionrequency and low strength of the magnetic field. However, thendirect heating of the tissue due to conduction, depends on theemperature slope and the maximum temperature of the implant,s well as on the physical properties of the implant and the sur-ounding tissue.

. Materials and methods

.1. SMA implant samples

Straight annealed, polycrystalline NiTi sheets (Alloy M,f = 55–65 ◦C, Memry GmbH, Germany) with thicknesses of d = 0.5nd 1.0 mm were used to manufacture the implant samples. Theaterial used was NiTi (49.8–50.0 at.% Ni, rest Ti) prepared by

acuum induction melting (VIM) or vacuum arc melting (VAR),espectively. After cold rolling, the sheets were flat annealed using aot press. In order to remove oxides, the sheets were etched chem-

cally, resulting in a blank metallic surface. DSC measurementsTmin = −20 ◦C, Tmax = 110 ◦C, heating/cooling rate of 10 K/min) of thesed material showed an As = 50.8 ◦C, and an Ap = 58.0 ◦C (austeniteeak temperature) and an Af = 63.0 ◦C. The implant samples (length:3 mm, width: 6 mm, height: 4 mm) were generated by laser cut-ing of different implant segments [32] followed by joining thearts using pulsed laser welding [33]. Fig. 2 shows an experimentaliTi implant sample before and after inducing the one-way effect.anual deformation of the outer sheets (Fig. 2, left) results in aaximum strain of 4.1%, i.e. within the range of the max. reversible

train of polycrystalline NiTi (max. def. Strain: 6.8% [3]). Due tohe heating process, the two outer sheets in the middle part of themplant were straightened, resulting in an increase of the second

oment of area. Due to both, the shape alteration and the poten-ial microstructural change, e.g. a remaining portion of austenitexhibiting an increased Young’s modulus after the cooling process,he mechanical properties of the implant (here: the increase ofending stiffness) can be adapted to specific requirements [34].

.2. Induction heating


Compared to other heating methods, contactless induction heat-ng is one of the most effective ways to heat any electricallyonducting material [35,36]. A high frequency (HF) magnetic field,

nal state. Right: illustrates the manufactured NiTi implant before and after inducingperties of the implant, i.e. the bending stiffness is increased.

generated in a coil, is used to induce a voltage in the workpiece,resulting in an alternating current (Fig. 3).

Due to conductivity, these currents are bypassed (eddy currents)and start circulating basically on the surface of the used mate-rial (skin effect). The skin depth ı (m) can be calculated using thefollowing equation [35]:

ı = 12�

(�107

f�r

)0.5

= 503(

�

f�r

)0.5(1)

Here, � (� m) is the electric resistivity, �r is the relative permeabil-ity of the used material, and f (Hz) is the frequency of the magneticfield. Using the values for NiTi (shown in Table 1) and an inductionfrequency of f = 250 kHz, a skin depth of ı = 1.05 mm is achieved.The ohmic resistance of the workpiece results in the heating of thematerial. Due to heat conduction, the workpiece if finally heatedin volume. The thermal penetration � (m) depends on the heatingtime t (s) and the thermal diffusivity coefficient ̨ (m2/s) and canbe calculated using the following formula [25]:

� = 4(˛t)0.5 (2)

In general, the heating of the workpiece depends on the intensityof the magnetic field, on the distance between the workpiece andinductor as well as on the properties of the material used. Especiallyfor ferromagnetic materials, additional heating (up to the Curietemperature) occurs, caused by the change in magnetization dueto the continuously alternating field. For any cylindrical configura-tion, the efficiency of the process also depends on the ratio between


Fig. 3. Principle of induction heating.Adapted from [35]





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ig. 4. Experimental calorimeter setup with specifications of the inductive coil andrue to scale.

.3. Inductive heating device

The induction device used was a water-cooled generator withn adjustable power output (PO) between 0.1 and 10 kW. Thenduction coil used was made of 3 copper windings with an inneriameter of 150 mm (Fig. 4). It was enclosed by a PMMA hous-

ng, limiting the usable diameter within the coil to 125 mm. Thendividual water cooled windings had a rectangular cross section

ith a dimension of 20 mm × 10 mm. An induction frequency of = 250 kHz was used.

.4. Calorimetry

The calorimeter was made by drilling a hole (∅ = 10 mm,epth = 70 mm) in a 50 mm diameter styrofoam cylinder, accom-odating a thin 10 mm diameter teflon tube (Fig. 4). The tubeas filled with double-distilled deionized water and the implantas embedded in a fixed position. The temperature of the wateras measured using a fiber-optic probe. The heat capacity of the

alorimeter (ccal = 8 J/K) was determined experimentally and con-idered for all calculations. The convective heat-transfer coefficient

of the calorimeter with free air convection was calculated to = 4.53 W/m2 K. In relation to the power uptake and the achievedemperatures (cf. Fig. 6), this results in a negligible heat loss to thenvironment.

.5. Temperature measurements

To measure the temperature (TW) of the water within thealorimeter and the temperature of the implant sample itselfTIMP), fiber-optic probes (probe TS5, TS1, FoTemp 1/4, OPTOCon,ermany) were used. Thus, the temperature was determined byetecting a temperature-dependent shift within the optical banddge of a GaAs-crystal embedded in the tip of the probe. Thisethod is unimpaired in an environment with electromagnetic

nterference. Furthermore, due to both, the small heat dissipationnd the small heat capacity, this method offers an accurate tem-erature measurement (minimal accuracy ±1 ◦C, resolution 0.1 ◦C).

n order to measure the surface temperature of the implant, the


ip of the probe was put in contact with the implant’s surface. Amall teflon ring was used to fix the probe. It should be noted thathe temperature measurements were performed on undeformedmplants.

atic illustration of the different positions of the implant. Depicted illustrations are

Further experiments were performed using thermocouples(Type K), which were laser-welded onto the implant’s surface. Thetemperature was read out using a custom-made Labview® pro-gram.

2.6. Thermographic measurements

The heat distribution was determined using an infrared thermocamera (FLIR SC 1000). As in general thermographic measurementsof blank, metallic surfaces are difficult due to reflections and thelow emission coefficient, the implant’s surface was colored blackusing graphite. This leads to a high emissivity (ε ≈ 1), allowing for ameasurement of the spatial and temporal temperature distributionat the surface of the implant during the induction process.

3. Results

First experiments were performed to determine the generalenergy uptake of the SMA implant. Therefore, the implant wasembedded within the calorimeter. The increase of the water tem-perature due to induction heating of the implant was determined.

3.1. Impact of induction parameters

Calorimetric tests were performed at different power settingsand exposure times (texp). Fig. 5 shows the temperature rise of thewater within the calorimeter, depending on the exposure time andthe power output for two different positions of the implant withinthe induction coil (position 1 (centre): y = 0 mm, x = 0 mm; position3 (next to the coil): y = 47 mm, x = 0 mm).

A linear behaviour of the temperature increase, depending onboth, the exposure time and the power output, is observable. Inboth cases, the impact of the implant’s position is clearly observ-able, as the achieved temperature increase �TW is always lowerfor the centre position (position 1) compared to the outer position(position 3), independent of PO and texp.

Fig. 6 illustrates the simulated density of the field lines (Fig. 6A)and the flux density of the alternating magnetic field (Fig. 6B) for across section of the induction coil (f = 250 kHz, PO = 1 kW). In orderto determine the impact of the altering field strength within the


coil on the heating process, the position of the implant was subse-quently altered in small steps in y-direction (cf. Fig. 4). Thereby, thex-position was kept constant. Fig. 6 (right) shows PIMP, dependingon both, the power output PO and the y-position of the implant.





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20

30

40

50

60

70

80

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temperature

(K)

WΔT

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20

30

40

50

60

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output powe r (kW )PO

i ncrease

temperature

(K)

WΔTy

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F sure ti

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ig. 5. Temperature increase of the water within the calorimeter against the expomplant.

s implied by Fig. 5, the power uptake of the implant is more pro-ounced if the implant is positioned closer to the coil. Keeping POonstant, PIMP increases up to 40% between the middle (position 1)nd the outer position (position 4).

For all following experiments, the position of the implant wasept fixed at position 2 (x = 0 mm, y = 25 mm).

.2. Surface temperature distribution of the SMA implant

In order to get an impression regarding the heat distributionithin or on the surface of the implant, an infrared thermo cam-

ra was used to determine the surface temperature during theeating process. These measurements were performed in an airnvironment, as the infrared radiation ( = 3.4–5 �m) detected byhe camera is entirely absorbed by any kind of water containing

aterial.As illustrated in Fig. 7, the surface temperature is nearly

onstant across the whole implant, except for the edges andhe boundary of the middle, active part of the implant and


he middle part itself (cf. Fig. 7, texp = 10.0 s). In this case,he determined difference of the temperature between theifferent points does not exceed 5 K, resulting in a compa-ably homogeneous temperature distribution. However, further

ig. 6. Left: Schematic illustration of the density of field lines (A) and the flux density of

ight: Power uptake of the implant (PIMP) depending on the power output (PO) of the indu

ime (left) and the power output (right) for two different positions (1 and 3) of the

experiments showed that the inhomogeneity is more pronouncedwhen increasing PO.

3.3. Heating process within a biological tissue model

In order to simulate the heating process in biological tissue,additional experiments were performed during embedding of theimplant in agarose gel (polysaccharide which congeals whilst cool-ing down). The volume ratio between implant and gel was 1:30.Agarose gel basically offers the physical properties of water. How-ever, it eliminates any convection-driven flows during the heatingexperiments.

As any optical temperature measurement was not possiblewhen embedding the implant within a water-containing material, afiber-optic measurement system was used. To prove the reliabilityof the contact-temperature measurement of the implant’s surface,comparative measurements were performed using thermocouples.A maximum difference of 0.5 K between both measuring methodswas determined, confirming the reliability of the optical measure-ment. In order to avoid measurement errors due to shape alteration,


the implant was undeformed (“final state”), i.e. the outer sheetswere kept straight.

Depending on the thermographic measurements and on pre-liminary tests (cf. Section 3.2 and Fig. 7), the temperatures were

the magnetic field (B) within the coil (lighter colors indicate a higher flux density).ction device and the y-position of the implant within the coil (see Fig. 4).





Fig. 7. Surface temperature distribution of the NiTi implant during the induction heating process (PO = 1 kW, texp = 10 s, position 3).

mltiftPm

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the water temperature whilst keeping the position of the implant

easured at the surface position with the highest (P1) and theowest (P2, active part) expected temperature increase. The surfaceemperature was determined using different output powers of thenduction device. Fig. 8 shows the resulting surface temperatureor a temperature increase of �T = 30 K. Within the linear range,he slope differs from 0.5 K/s (PO = 1 kW, P2) to 4.2 K/s (PO = 5 kW,1). As indicated in Fig. 7, the temperature difference between theiddle (active) and the massive part increases when enhancing PO.Compared to a high temperature slope within the implant, a

ow slope strongly increases the time to induce the one-way SME,ut allows to control the resulting temperature, e.g. in terms ofverheating. However, the resulting temperature within the sur-ounding tissue may be disadvantageous when using a low powerutput, taking into account the cumulative energy loss duringhe induction process. In order to prove this assumption, furtheremperature measurements were performed directly within thegarose gel, next to the implant.

Fig. 9 depicts the temperature increase of the agarose gelepending on both, PO and the measuring position (P3 and P4).ased on the different slopes, the exposure time to induce the SMEeaches from texp = 160 s (PO = 1 kW) to texp = 26 s (PO = 3 kW) andexp = 14 s (PO = 5 kW).


As expected, the slope of temperature increase within thegarose gel directly depends on PO (cf. Fig. 8). However, as assumed,ue to the increased texp when decreasing PO, the resulting

ig. 8. Typical surface temperature increase of the implant for a (PO = 1, 3 and 5 kW,nvironment: agarose gel, position 2).

temperature of the surrounding tissue strongly increases whendecreasing PO.

3.4. Inducing the shape memory effect within agarose gel

Fig. 10 shows the one-way SME of an SMA implant embeddedin agarose gel. According to the results described in Section 3.3, anoutput power of PO = 3 kW was used. Depending on texp, i.e. on thetemperature increase, the return of the implants to its original state(straightened), hence altering its mechanical properties, was initi-ated. Measurements of the bending stiffness showed a maximumincrease up to 74% [34].

4. Discussion

This article shows the impact of different induction and pro-cess parameters on the heating process of a metallic orthopaedicshape-memory implant. To determine the impact of the outputpower, exposure time and position of the implant on heating pro-cess, calorimetric measurements were performed. As expected,increasing texp (PO respectively) leads to a proportional increase of


constant (Fig. 5). The strength of the magnetic field is directly influ-enced by the power output of the induction device, hence, theenergy or the power uptake (PIMP) of the implant increases directly

Fig. 9. Temperature increase of the surrounding agarose gel during the heating pro-cess (environment: agarose gel, position 2). The heating process started at t = 10 s,the starting temperature was T = 20 ◦C. The distance between the probe and theSMA-implant was 4 mm.





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ig. 10. Inducing the one-way shape memory effect in the active part of the implans recovering its original shape, hence altering its mechanical properties.

roportional to PO. PIMP was calculated using the following formulahere the heat loss to the environment was neglected):

IMP = (mwatercp,water + mimplantcp,implant + ccal)�T (3)

IMP = EIMP

texp(4)

ere, cp is the specific heat capacity of the respective materialcp,water = 4184 J/K kg, cp,implant = 490 J/K kg), ccal is the heat capac-ty of the calorimeter (ccal = 8 J/K), m is the mass of the materialmwater = 3.2 g, mimplant = 6.68 g) and �TW (K) is the maximumncrease of the water temperature. It should be noted that PIMP doesot consider any temperature distribution within the SMA implant,ut its overall power uptake.

Fig. 6 illustrates the dependence of the resulting power uptaken the y-position of the implant. Additionally, the magnetic fieldines and the amplitude were simulated (Fig. 6A and B). The den-ity of the magnetic field lines, i.e. the strength of the magneticeld (Fig. 6A), is varying in y direction whilst it is comparativelyomogeneous in x direction. The amplitude of the magnetic field

s rather homogeneous within the coil, with the exception of theirect vicinity of the coil windings (Fig. 6B). Thus, as depicted inig. 6 (right), the power uptake PIMP of the implant is more pro-ounced (increase of 40%) in vicinity of the coil windings due tohe inhomogeneous magnetic field strength.

Using these results, the efficiency ind of the heating process,.e. the ratio between the power uptake of the implant PIMP and theower output of the induction device PO, was determined using theollowing equation:

ind = PIMP

PO(5)

Depending on the position of the implant, the heating efficiencyanges from ind = 1.2% (position 1, centre) to ind = 1.5% (position 4,ext to the coil winding). In contrast to the high energy efficiencyf the inductive heating process in general, only a small amount ofhe output power is converted into heat here. This is mainly causedy small geometric dimensions of the SMA implant compared tohe diameter of the experimental induction coil (cf. Section 2.2).

The previous measurements using the calorimeter setup onlyonsider the cumulative power- and energy uptake. In order toetermine the temperature distribution on the implant’s surface,


he infrared radiation was measured. Although 86% [35] of the over-ll energy is converted to heat within the skin depth ı, the surfaceemperature does not necessarily reflect the temperature withinhe implant. However, as the implant’s surface is in direct contact to

edded in agarose gel (position 2). Due to short-time induction heating, the implant

the surrounding tissue, the surface temperature is one of the mostinteresting values to be determined. As shown in Fig. 7, the heatingprocess leads to a different temperature of the implant’s surface, tosome extent. Cooling the implant leads to an equal distribution ofthe temperature, due to heat conduction. As the density of the eddycurrents is normally equally distributed, any change of the volumeor the surface causes redistribution and concentration of the cur-rents. This leads to a different temperature in certain parts of theimplant. Furthermore, the surface-to-volume ratio differs over theimplant’s geometry, resulting in different temperatures (cf. Fig. 8).

To explore the heating process in biological tissue, i.e. using asuitable rate of heat- and heat convection, the surface temperaturewas determined during embedding of the implant in agarose gel(99.0 wt% water). Due to the high viscosity of agarose gel, primaryheat conduction is responsible for the heat loss to the environment.

As biological tissue in general consists of water (k = 0.604 W/m Kfor T = 20 ◦C) for the most part, water represents a good model forbiological tissue [37]. It was shown by Valvano et al. [38,39] thatthe thermal properties of agarose gel (99.0 wt% water) equal thoseof water. The heat conductivity k of water is convenient for theheat conductivity of biological tissue (k = 0.509 W/m K for T = 37 ◦C)determined by Valvano et al. [39] or the heat conductivity forhuman muscle (k = 0.46 W/m K) determined by Hensel and Bock[40]. However, especially for the simulation of muscle tissue, k issignificantly affected by blood flow [39,40]. It should be noted that,compared to soft tissue, the heat conductivity within hard tissue(e.g. k = 0.16–0.34 W/m K for human femora [41]), is substantiallylower, hence resulting in a different heat dissipation and in differ-ent temperatures of the surrounding tissue. In future experiments,as an alternative to agarose gel, a mineralized synthetic hydrogelcould be used in order to simulate the bone.

The measured surface temperature is shown in Fig. 8. The resultsare convenient to Figs. 5 and 7, in terms of the direct impact of PO,resulting in a higher slope and a temperature drop in middle partof the implant. As this part has to be heated to the Af-temperaturein order to induce the SME, a higher thermal exposure of the tis-sue, which is in contact with the massive parts of the implant, isassumed.

As this effect will be more pronounced when increasing theheating rate, it should be considered in the choice of an appro-priate heating rate, i.e. output power, allowing an equalization ofthe temperature within the implant. Additionally, this effect could


be minimized by modification of the implant’s design in order toequalize the temperature. Further experiments were performed todetermine the effect of the heating process on the ambient tissue.The aim was to determine the optimum PO in terms of the thermal


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oad of the surrounding tissue (Fig. 9). Therefore, the temperature ofhe agarose gel, enclosing the implant, was determined at a distancef approximately 4 mm to the implant. The maximum tempera-ure decreases when increasing PO and decreasing the necessaryxposure time texp, respectively. A low power output results in aigher temperature of the surrounding tissue, and the cumulatednergy loss increases. The energy input can approximately be cal-ulated to EIMP = 160 kJ (PO = 1 kW) to EIMP = 78 kJ (PO = 3 kW) and toIMP = 70 kJ (PO = 5 kW). Therefore, apart from the lower tempera-ure impact on the surrounding tissue, a high power output is alsoeneficial from the energetic point of view. However, a high powerutput increases the surface temperature difference and may alsoncrease the risk of overheating due to the high slope.

Fig. 10 shows the contactless triggering of the SME within anmplant sample embedded in agarose gel. PO was set to 3 kW. Thisalue seems to be a compromise between a good temperatureontrol (e.g. moderate temperature slope), an equal temperatureistribution and a fast increase of the implant temperature, i.e. ahort heating period and minor heat transfer to the environment.

ithin texp = 26 s, the transition temperature is reached, hence trig-ering the straightening of the outer NiTi sheets. Here, increasinghe second moment of inertia of the implant’s middle part resultsn enhancing the bending stiffness up to 74% [34].

It is shown in [4,6] that the functional properties of NiTi, e.g.ecovery strain or reversible deformation, strongly depend on thelloy structure resulting from thermomechanical treatment, i.e. theanufacturing process. As indicated in [42], the transition temper-

ture range can be altered (increased) depending on internal stress,.e. due to deformation.

Here, the time required to straighten the outer sheets (Fig. 10),ndicates a minimum temperature increase of 35 K (cf. Fig. 8) i.e. a

inimum temperature of 55 ◦C at the middle part of the implant.s this value is between As und Af of the used NiTi alloy, the alter-tion of the transition temperature range does not seem to be veryronounced. Possibly, one reason could be the relatively low strainf the outer sheets (4.1%) compared to the maximum reversibletrain for polycrystalline NiTi-SMA.

However, due to the facts mentioned above, the temperatureand therefore the power PO and time texp of the induction process)equired to induce the full one-way SME should be tested for everymplant design, as the deformation i.e. the strain may alter.

. Conclusions

The feasibility of contactless triggering of the one-way SMEithin a metallic orthopaedic NiTi-SMA implant sample, due to

nduction heating, was presented. The geometric change of theiddle part of the implant leads to an alteration of the bending

tiffness.Besides the proportional influence of the output power and the

xposure time, the impact of the implant’s position on the heatingrocess, was determined. Due to the distribution of the magneticeld, the power uptake during the heating process differs up to 40%,epending on the implant’s position.

In order to simulate the heating process within soft biologicalissue, the implant was embedded in agarose gel offering similarhermal properties. The temperature difference on the implant’surface increases whilst increasing the temperature slope. A loweating rate reduces both, the inhomogeneity of the implant’surface temperature and the risk of overheating, due to its control-ability. However, a reduced heating rate results in an increased


xposure time in order to reach Af and to induce the SME. Hence,he temperature load of the surrounding tissue increases.

With further optimization, inductive heating of SMA implantsay provide an effective method, in order to use the shape memory

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PRESS & Physics xxx (2012) xxx– xxx

effect in the medical field of application. Using a custom-made NiTiSMA, with As and Af, next to the body temperature in combinationwith suitable induction parameters, would further alleviate the riskof overheating.

This is one step in the development of new orthopaedic implantsin which stiffness or rigidity can be modified after implantationwithout additional invasive procedures. Thus, the optimization ofbone-healing could be facilitated. In general, this method offers thepossibility to change the properties of implanted SMA devices atan arbitrary time. Currently, different designs that are offering thepossibility to decrease the stiffness (e.g. to decrease stress shieldingeffects) due to inducing the one-way SME, are tested. Further stepsto determine both, the effect of the induction heating on the tissueand the effect of the stiffness alteration regarding the bone-healingprocess in vivo are planned.

Acknowledgements

This work is funded by the “Deutsche Forschungsgemeinschaft(DFG)” (SFB 599, TPD10). The authors would like to thank the DFGfor their support. Furthermore, the authors would like to thankTim Hösel, Andreas Gehringer and Antonio Castellanos for electricaldischarge machining and their experimental support.

Conflict of interest statement

The authors have no conflicts of interest.

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