measurement and simulation of the distribution of tc-maa ... · 1.2 function, bloodflow and anatomy...

Measurement and simulation of the

distribution of 99mTc-MAA and 90Y

microspheres in radionuclide

therapy of hepatic tumours

A master’s thesis

by

Jens Hemmingsson

Supervisors

Peter Bernhardt, Professor

Emma Wikberg, M.Sc.

Department of Radiation Physics

University of Gothenburg

Sweden, June 2015

CONTENTS ABBREVIATIONS AND ACRONYMS ................................................................................................. 1

ABSTRACT .............................................................................................................................................. 2

1. THEORY .......................................................................................................................................... 4

1.1 RADIOEMBOLIZATION ........................................................................................................ 4

1.2 FUNCTION, BLOODFLOW AND ANATOMY OF THE LIVER ......................................... 5

1.3 TUMORAL BLOODFLOW .................................................................................................... 6

1.4 HEPATIC CANCER ............................................................................................................... 7

1.5 PATIENT SELECTION ............................................................................................................. 7

1.6 SIDE EFFECTS FROM RADIOEMBOLIZATION .................................................................. 8

1.7 SIMULATION .......................................................................................................................... 8

1.8 IMAGING MODALITIES ..................................................................................................... 10

2. MATERIAL AND METHODS ....................................................................................................... 11

2.1 PATIENTS .................................................................................................................................... 11

2.2 EXTRACTING DATA FROM DIAGNOSTIC IMAGING ....................................................... 12

2.3 SIMULATION ............................................................................................................................. 14

2.3.1 SIMULATIONS – Method 1 – Curve Fitting ................................................................. 15

2.3.2 SIMULATIONS – Method 2 – Compartment ............................................................. 16

2.4 PHANTOM MEASUREMENTS ................................................................................................. 17

3. RESULTS ........................................................................................................................................ 19

3.1 PATIENT HISTOGRAMS ........................................................................................................... 19

3.2 SIMULATIONS – Method 1 – Curve Fitting ........................................................................ 21

3.2 SIMULATIONS – Method 2 – Compartment..................................................................... 22


4. DISCUSSION ................................................................................................................................ 25

4.1 nNUFTI AND THRESHOLD INDEX .......................................................................................... 25

4.2 PATIENT HISTOGRAMS 99mTc-MAA and 90Y ...................................................................... 26


4.4 SIMULATIONS – Method 1 – Curve Fitting ........................................................................ 27

4.5 SIMULATIONS – Method 2 – Compartment..................................................................... 27

5. CONCLUSIONS .......................................................................................................................... 28

6. FUTURE ASPECTS ........................................................................................................................ 28

ACKNOWLEDGEMENT ..................................................................................................................... 28

7. REFERENCES ............................................................................................................................... 29

1

ABBREVIATIONS AND ACRONYMS

β particle - Electron or positron

166Ho - 166 - Holmium

90Y - 90 - Yttrium

99mTc - 99m - Technetium

CSDA - Continuous slowing down approximation

CT - Computed tomography

eV - Electronvolt

HCC - Hepatocellular carcinoma

LS - Lung shunt

MAA - MacroAggregate Albumin

mCPV - Mean counts per voxel

MRI - Magnetic resonance imaging

Node - Point of vessel branching

nNUFTI - Number of normalized uptake foci VS threshold index

PET - Positron emission tomography

PFSD - Relative standard deviation of the flow

RE - Radioembolization

REILD - Radioembolization-induced liver disease

ROI - Region of interest

SPECT - Single-photon emission computed tomography

TNC - Tumour-to-normal tissue activity concentration ratio

VOI - Volume of interest

2

ABSTRACT

Background

Radioembolization (RE) is a treatment option for patients with unresectable malignancies in

the liver. The utility of external beam radiotherapy (EBRT) is limited because of the high

absorbed doses delivered to the radiosensitive hepatic parenchyma (1). RE is performed by

injecting 90Y microspheres of resin or glass into the hepatic artery causing them to mainly reach

tumour tissue. Prior to the RE a treatment simulation is performed by injecting 99mTc bound to

MacroAggregate Albumin (MAA). This is to supply information about extra-hepatic spread

of activity as well as provide a foundation for the therapeutic absorbed dose determination,

which is based on uptake and absorbed dose limitations of normal liver tissue.

However, the accuracy of the treatment simulation with 99mTc-MAA is under scrutiny (2).

Mainly because the assumption might be wrong that 99mTc-MAA distributes in a similar

manner as 90Y microspheres inside the arterial structure of the liver. The MAA particles differ

from the microspheres in quantity, shape and size (3). Therefore, the information provided by

the simulation might not be as valuable as originally thought and may need reevaluation. An

accurate description and understanding of the distribution of 99mTc-MAA in the normal tissue

of the liver is a step towards more accurate absorbed dose calculations.

Comparing single-photon emission computed tomography (SPECT) images of 99mTc and 90Y

can provide information on similarities and differences in distribution patterns between MAA

and microspheres. Unfortunately it is difficult due to the low quality of 90Y-bremsstrahlung

images. An alternative is to produce an inter-therapeutic positron emission tomography (PET)

image on 90Y microsphere distributions, allowing for comparison with 99mTc-MAA-SPECT. The

resulting images are possibly higher quality than 99mTc-MAA but suffer from far more noise

(4).

Accurate individualized treatment planning is a promising way to improve existing

treatments and is an objective in several fields within medical physics. This requires a deep

understanding of the processes involved in the treatment as well as inter-patient differences.

Computer simulations are useful tools when working with large amounts of data, as is the

case with studies of the human anatomy, and might be necessary to individualize

radioembolization and make the treatment more effective.

Aims

Develop a method for characterizing the macroscopic non-uniformity from activity

histograms

Construct a model for simulation of macroscopic non-uniformities of activity

Provide a macroscopic study of 99mTc-MAA distribution in healthy liver tissue.

3

Material and Methods

6 patients were chosen for the study, all of which had undergone both simulation and

treatment. Initially, normal tissue was separated from tumour tissue whilst studying

SPECT/CT examinations in the image processing tool RONSO. Data was then evaluated and

used in MATLAB®-based simulations of the arterial structure with the aim of creating similar

distributions as the ones observed in the SPECT/CT.

Results & Discussion

Ranging between 0.04 and 0.34, the standard deviation of the flow in the simulations was

determined through comparison with patient data. Dividing the patient histograms into

compartments, between 9 and 37 compartments are needed to approximate the distributions

included this study. The phantom measurements needs to be verified using Monte Carlo

simulations and a different phantom.

Conclusion

The simulation model of bifurcations can to some extent be used to create histograms of

microsphere distributions similar to that of a patient. Further development is necessary to

completely mimic the macroscopic activity distribution in a patient.

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1. THEORY

1.1 RADIOEMBOLIZATION

Radionuclides that are suitable for use in radioembolization should emit particles with

energies allowing a reasonable range in tissue to enable high absorbed tumour doses while

sparing surrounding healthy tissue. These characteristics are displayed by beta emitters,

particularly 90Y although other radionuclides are under development such as 166Ho (3).

The range of a charged particle is dependent on its kinetic energy along with its mass and

charge and the properties of the medium it is penetrating. Electrons and positrons are

considered to be light charged particles that lose kinetic energy (Ek) through ionizing collisions

(Scol) and through production of bremsstrahlung (Srad) when interacting with the atomic

nucleus. For positrons an additional mode of energy loss is in-flight annihilation causing the

release of two photons that are not collinear (included in Srad). Because of the low mass

electrons and positrons can be scattered in large angles and lose a high energy fraction per

interaction, making accurate range calculations more imprecise than for heavier particles.

Several definitions of range are available, from the continuous slowing down approximation

(CSDA) to practical length and maximum range. CSDA range is based on the fact that if a

particle is travelling through an absorber losing small fractions of energy along its trajectory,

its range should be well defined and can be calculated with equation I. While accurate for

heavy charged particles, the CSDA range for β particles differs 10-15 % in low Z absorbers

such as liver tissue (5). In medical physics the ranges R80 and R50 are in common use meaning

the depth at which 80 and 50 percent of the maximum dose is delivered in a certain absorber

(6).

𝑅𝐶𝑆𝐷𝐴 = ∫𝑑𝐸

𝑆𝑡𝑜𝑡(𝐸)

(𝐸𝑘)0

0

[I]

Stot (E) is the energy dependent sum of collision stopping power (Scol) and radiative stopping power

(Srad)

Ek (0) is the initial kinetic energy of the charged particle.

5

Unlike α decay, which emits particles of a given energy, both β- and β+ decay with energies

within a continuous spectrum giving an effective energy at roughly a third of the maximum,

equation II (6).

(𝐸𝛽)𝑒𝑓𝑓 ≈

1

3(𝐸𝛽)𝑚𝑎𝑥

[II]

With a half-life of 64, 2 hours 90Y is a pure beta emitter with an average decay energy of 0,936

MeV (max 2,280 MeV) and a tissue range at maximum 11 mm with a mean range of 2, 5 mm

(7). Microspheres of either resin or glass contain 90Y and are injected into the liver. Depending

on its material the activity per sphere will vary along with the number injected and the spheres

individual size (table 1).

Table 1. Properties of two different types of spheres used in radioembolization (8).

MICROSPHERE MATERIAL RESIN GLASS

Mean particle size [µm] 32.5 ± 2.5 25 ± 5 Number of spheres per GBq [106] 20 0.4

Activity per sphere [Bq] 50 2500

1.2 FUNCTION, BLOODFLOW AND ANATOMY OF THE LIVER

Well protected by the rib cage and located below the diaphragm on the right side of the body,

the liver (latin: hepar) is the largest gland in the human body weighing roughly 1.5 kg in

adults(9). Amongst several other functions the liver plays a vital part in the body’s

detoxification, immune system and provides storage for nutrients as well as glycogen (10). The

liver can be divided into two lobes, left and right, which in turn can be divided into 8 segments

according to the Couinaud classification seen in figure 1 (11).

Figure 1. The internal structure of the liver allows for it to be divided into eight segments, according to the Couinaud classification. The hepatic artery branches out, eventually reaching all segments.

6

On a microscopic scale the liver is constructed in a network of lobules consisting of portal

tracts (portal vein, small artery and bile duct) surrounding a central vein. The regular

hexagonal shape of the lobules usually portrayed in textbooks (figure 2) are infrequent.

Instead, a pattern of varying shape and size emerges when studying a biopsy, with the number

of vessels in each portal tract differing (12).

Figure 2. Lobules in a liver vary greatly in shape and size as well as in the number of portal tracts attributed to each lobule. Portal vein, artery and bile duct in blue, red and green respectively (image from sirtex.com).

The portal tracts connect with the central vein through small blood vessels called sinusoids

through which both arterial and venous blood flow (10). Lining the sinusoids is the livers

functional tissue called hepatocytes. The hepatocytes form the radiosensitive parenchyma,

setting dose limitations for treatments. The livers venous blood flow is full of nutrients and

arrive after passing through the spleen and the gastrointestinal tract while the oxygenated

blood is supplied by the hepatic artery.

1.3 TUMORAL BLOODFLOW

In radioembolization of inoperable hepatic malignancies the dual blood supply of the liver is

one of the corner stones for successful therapy. Normal hepatic tissue derive most of its blood

from the portal vein while both primary and secondary malignancies receive most of their

blood circulation from the hepatic artery (13). Also, metastatic lesions have roughly 3 times

the density of arterial vessels than normal tissue (14). Injections made into specific segments

of the liver through the hepatic artery will therefore mainly reach malignant parts of the liver.

The tumour-to-normal tissue activity concentration ratio (TNC) will roughly be about 4 but

can assume values as high as 25 (15, 16).

7

1.4 HEPATIC CANCER

Cancers of the liver are divided into primary and secondary malignancies. If the malignant

cells origins from the liver tissue the hepatic cancer is considered primary and when

disseminated from another organ of the body, through the bloodstream or lymph system, the

cancer is referred to as secondary. Hepatocellular carcinoma (HCC) and cholangiocarcinoma

are two types of primary cancer occurring in the liver. HCC is the third most common cause

of cancer related mortality and the sixth most common of all cancers and studies predict that

up to 25 % of all cancer patients will develop metastases in the liver (17, 18). Risk factors for

developing hepatic cancer include hepatitis B and C viruses and alcohol and tobacco

consumption (17).

1.5 PATIENT SELECTION

For a patient to be eligible for radioembolization the primary or metastatic hepatic disease

should be unresectable, the tumour burden liver dominant and the patient’s life expectancy

more than 3 months (1). Further limitations in the patient’s eligibility include a large extra-

hepatic deposition of activity such as a shunt of microspheres to the radiosensitive lungs or

gastrointestinal tract. In a patient with a large lung shunt (LS) a significant number of

microspheres will pass through the hepatic arteries to the arteries of the lung, increasing the

risk of developing radiation pneumonitis, a deteriorating and potentially lethal condition.

Lung shunting is controlled prior to the treatment by injecting the gamma emitting nuclide 99mTc bound to macro-aggregated albumin (MAA) in a manner similar to the injection of 90Y-

microspheres. The size of the MAA particles diameter range between 10 – 90 µm, never

exceeding 150 µm (19). Shortly after injection the amount of 99mTc-MAA in the lungs can be

quantified and compared to the total activity injected in the liver using planar images from a

gamma camera. Both lungs and the part of the liver to be treated are encased in regions of

interest (ROI) on anterior and posterior images and the LS-fraction is calculated according to

equation III (20). LS-fractions between 10 – 20 % results in a reduced therapeutic dose of 90Y

and if above 20 %, radioembolization is not performed (3).

𝐿𝑆 − 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 [%] =

𝑅𝑂𝐼 𝐿𝑢𝑛𝑔 𝑐𝑜𝑢𝑛𝑡𝑠

𝑅𝑂𝐼 𝐿𝑢𝑛𝑔 𝑐𝑜𝑢𝑛𝑡𝑠 + 𝑅𝑂𝐼 𝐿𝑖𝑣𝑒𝑟 𝑐𝑜𝑢𝑛𝑡𝑠∙ 100

[III]

8

1.6 SIDE EFFECTS FROM RADIOEMBOLIZATION

Radioembolization enables local delivery of high absorbed tumour doses. Unfortunately, as

with all forms of radiation therapy, normal tissue will receive significant absorbed doses.

Potential hazards of RE includes RE-induced liver disease (REILD) and toxic hepatitis,

especially in patients with liver dysfunction such as cirrhosis, a state not uncommon in patients

diagnosed with HCC (21). REILD was first described as ascites and jaundice in non-cirrhotic

patients, possibly caused by damage to functional liver tissue as well as non-parenchymal cells

(20).

Reasons behind REILD is under investigation but the minor embolic effect noticed in resin

sphere treatments seems not to be the cause of REILD, instead the major influence on REILD

are believed to be derived from radiation (22). Between 0 – 4 % of patients treated with 90Y RE

develop REILD (23). The induction of toxic hepatitis in cirrhotic livers could be due to

microvascular changes that occur when liver tissue is replaced by fibrosis and nodules altering

the distribution of microspheres and possibly causing higher absorbed doses to normal liver

tissue (20). Toxic hepatitis may lead to liver failure and can be potentially fatal. However, if

patients are selected carefully and the injection of microspheres is successfully executed risks

are acceptable (8).

1.7 SIMULATION

If eligible for RE, a vital step in the treatment planning is dosimetry. The aim is, of course, to

expose tumour tissue to high absorbed doses while sparing the surrounding liver parenchyma.

The condition of the liver varies from patient to patient along with the tumour burden and

several other factors, making it difficult to perform accurate absorbed dose calculations. Using

computers to simulate liver structures is one way of understanding the transport of

microspheres and might be a step towards improved individualized treatment planning.

Recently, Walrand et al. constructed a simulation model of the microspheres transport through

the arteries in the liver’s vasculature. This model is a simplistic artery tree model as can be

seen in figure 3. The model consists of bifurcations, i.e. a parent vessel branch into two smaller

daughter vessels with the branching point being called a node.

Earlier simulations of Kennedy et al. (2009) and Basciano et al. (2010) produced results that

indicated a difference in the distribution of microspheres between two daughter vessels. This

led Walrand et al. to set a fixed 60-40 % difference between the blood flows of two daughter

vessels (24). The size of the simulated arterial structure was based on approximations of the

number of lobules in a liver and the amount of arteries inside each lobule. This rendered a

structure with 21 nodes and 221 portal tracts, each node with number of vessels (25).

9

Figure 3. The concept behind the bifurcation model of the hepatic arterial structure. Every time a vessel branches, two daughter vessels are created, this branching point is called a node. For a tree made of 21 nodes this eventually creates 221 vessels.

Debbaut et al. used vascular corrosion casting and micro CT-scanning to map the hepatic

vasculature. Results pointed to a structure far larger and more complex than the bifurcations

model (26). However, Högberg et al. (27) used this simplified model to simulate that

inhomogeneities in microsphere distributions increase with an increasing amount of

microspheres in contrast to what has previously been assumed. The results of Högberg et al.

are valid for small scales but can be applied to larger volumes through manipulation of the

bifurcations model. Hopefully, the simulations conducted in this study can be used in a similar

approach to analyze the activity distributions from a larger scale such as SPECT down to the

small scales in the results of Högberg et al.

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1.8 IMAGING MODALITIES

Depending on the gamma camera system´s components, the object being imaged and the

source to collimator distance the detail and sharpness of the image will vary. This is referred

to as spatial resolution and determines what size an object must have to stand out from its

environment i.e. be detectable to the human eye studying the image.

Different imaging settings and protocols are used depending on the radionuclide distribution

being imaged and the information needed from the examination. When producing a SPECT-

image of the 99mTc-MAA distribution in the liver or the shunt to lungs and gastro a ±10 %

energy window centered around 140 keV is applied. This provides an image of the activity

distribution on a macroscopic scale, which is combined with a CT-scan to create reference

points for the uptake.

Depicting the distribution of a beta-emitting source such as 90Y requires a much larger energy

window (67 %) than for 99mTc (28). This is due to the fact that the electrons release

bremsstrahlung photons with energies within a large spectrum making the sensitivity very

low for a narrow energy window. Furthermore, the electron usually travels a distance before

the release of bremsstrahlung making it difficult to determine its origin, resulting in smearing

of the signal.

Spatial resolution is therefore lower in a 90Y-SPECT than in a 99mTc-MAA-SPECT image where

unscattered photons all have energies close to 140 keV. Measurements performed by a research

group here at Sahlgrenska University hospital show that the spatial resolution is

approximately 15 mm and 18 mm for 99mTc-MAA and 90Y, respectively. Low spatial resolution

is a problem since the inter-therapeutic imaging is an important part of evaluating the success

of the procedure.

An inter-therapeutic alternative or compliment to 90Y-SPECT is positron emission tomography

(PET). This is made possible by a small branch (32∙10-6) of the 90Y β- particles decaying into the

first excited state (0+) of the stable isotope 90Zr. At 1, 76 MeV the energy demand of 1,022 MeV

is fulfilled and internal pair production is a mode of decay (29).

The amount of information that can be found by studying a SPECT/CT image is limited by the

resolution of the SPECT image. In addition there is smearing of the signal causing information

to be divided between voxels. When converting the distribution of activity in a SPECT image

to a histogram, all spatial information is lost.

In a study of the liver’s vasculature Debbaut et al. (26) concludes that the macrocirculation

ends when the radius of the arterial vessels are smaller than 0.65 mm. The voxel size in the

SPECT images of this study is 4,423 mm (≈ 86 mm3) and as the spatial resolution exceeds 15

mm the data available in this study is suitable for a macroscopic study.

11

2. MATERIAL AND METHODS

The focus of this study has been the normal tissue of the liver. 99mTc-MAA SPECT/CT-images

of 6 patients have been analyzed and evaluated with the in house image processing tool

RONSO and MATLAB®. The clinical data has then been applied to a MATLAB® based

simulation of the arterial structure with the aim of producing similar distributions and thereby

validating the model.

2.1 PATIENTS

The patients used in this study have all undergone at least one Tc99m-MAA examination and

eventually also radioembolization. Depending on resection and tumour burden the amount of

healthy tissue available for analysis will differ significantly. Preferably, a large part of the liver

should be tumour free to supply as much information as possible from each patient. As a

method to minimize exposure of healthy liver tissue, microspheres with Y90 are usually

injected selectively to parts of the liver with tumour tissue.

In recent years 99mTc-MAA is also injected selectively (figure 4 B) for patients at Sahlgrenska

University Hospital. As the segmentation of normal tissue is difficult to begin with, the

decision was made to base this study on patients were Tc99m-MAA was injected into the entire

liver (figure 4 A). This allowed for a larger margin when drawing the line between tumour

and normal tissue, hopefully making the extracted data more consistent when not containing

tumour tissue.

Figure 4. Tc99m-MAA-SPECT/CT of two patients. To the left Tc99m has been injected into the entire liver while patient number two has hade Tc99m-MAA injected selectively into the left lobe.

12

2.2 EXTRACTING DATA FROM DIAGNOSTIC IMAGING

The 99mTc-MAA distribution produced in the SPECT is placed over the CT image to enable

segmentation of the liver, one cross section at a time. Once the entire liver was placed inside a

volume of interest (VOI), data such as distribution of voxel values and liver volume could be

extracted (figure 5). Normal tissue was separated from tumour (figure 6) by a region growing

algorithm in RONSO (nNUFTI = Number of normalized uptake foci VS threshold index).

Figure 6. A segmented liver containing Tc99m-MAA marked with a VOI. The central part of the VOI is considered tumour tissue and is excluded in this study.

Figure 5. The blue plot contains the entire segmented liver from above. When removing the contribution from high uptake tumour tissue, the red plot is the remaining signal.

13

The algorithm calculated 125 equidistant values (thresholds) between the highest and lowest

voxel value within the VOI (figure 7 B). Starting at the highest voxel value in the segmented

liver the region (or regions) increased in size until a certain threshold was reached, creating a

volume within the original VOI (figure 7 A). The threshold set for this study has been a

radiologist’s measurement of the tumour size in a CT or MRI. The segmented tumour volume

was then removed to create a VOI filled with only normal tissue.

Figure 7. nNUFTI analysis of a liver. A small step to the right with the red line is equivalent to a large volume in the liver to the left.

Voxel data, i.e. counts per voxel, from a VOI in RONSO was extracted in the form of a

histogram with bin width 1 and transferred to MATLAB®. Single voxels in the beginning and

end of the patient’s histogram might be random events or small tumour residues and was

removed for statistical reasons. This can be seen in the red line of figure 7 B showing the normal

tissue of patient 6 were the few voxels containing more than 600 counts were removed before

the histogram was analyzed.

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2.3 SIMULATION

Using the method of Högberg et. al (27) for simulating microsphere transport in the liver´s

arterial tree, the simulations of this study were aimed at creating similar distributions as the

ones obtained from the SPECT/CT exams.

Figure 8. Delineation of the arterial tree used in the simulations of this study. At each node (6 in this simplification) a flow is calculated using equation IV.

The simulation moves one microsphere at a time from injection into the artery through a

bifurcating vasculature seen in figure 8. Unlike the simulations of Walrand et al. (24) the flow

through each of the two sister vessels was initially 50-50. The path was altered by a varying

standard deviation at each node causing certain paths to be favored. When the terminal artery

is reached the path ends and different sized clusters formed. Being a macroscopic study, the

size of the arterial tree was set to 8 nodes instead of the 21 used by Walrand et al.

If setting the relative standard deviation of the flow (PFSD) to zero the probability of a

microsphere going through either of the daughter vessels is 0.5. When plotting a histogram of

the clusters they will form a normal distribution in the terminal arteries (figure 9). Slowly

increasing the PFSD will shift the normal distribution towards lognormal. For each branch,

consisting of two daughter vessels, the flow was determined by producing a normally

distributed random number (randn command in MATLAB®) and multiplying it by the

standard deviation PFSD according to equation IV. This produces a set of unique probabilities

that will determine which way a microsphere travels.

𝐹𝑙𝑜𝑤 = 0.5 + 𝑟𝑎𝑛𝑑𝑛 ∙ 𝑃𝐹𝑆𝐷 IV

15

Figure 9. Simulating 8 nodes creates an arterial tree with 256 arteries at the end. The image on the left contain the distribution of microspheres in these 256 arteries. The image on the right is the same distribution portrayed in a histogram of bin width 4.

Arterial density is another variable in the simulations, meaning the number of arteries per

lobule. This will vary greatly in patients since the perfect hexagonal shape that is used to

illustrate the liver’s structure rarely exists. As the simulation is set to end when a threshold

dose is reached the arterial density is closely related to the number of microspheres simulated.

This is because a uniform dose is easier to achieve with fewer microspheres if we have a dense

arterial system. While Walrand et al. used the arterial density 2.4 in their simulations, 6.4 was

suggested as a suitable starting point for these simulations (24).

2.3.1 SIMULATIONS – Method 1 – Curve Fitting

Initially, the simulations were aimed at finding the best parameters for each patient through

the method of least squares. Each run-through of the simulation was performed with a 0.5

probability of a microsphere going into one of two daughter vessels but with a changing

standard deviation of the flow or changing arterial density.

Firstly, a large range of standard deviations was used to pin point good fits and then the range

was tightened around these values. Because the simulation is a random process according to

equation IV, every PFSD was simulated five times to achieve better statistics. This produced a

number of varying distributions to be compared with each patient’s data. The comparison was

made by producing the cumulative distribution for each dataset, both for the patient’s

SPECT/CT and the simulation (figure 10), and then calculating the R2 value according to

equation V.

16

𝑅2 = 1 −

∑ (𝑦𝑖 − 𝑓𝑖)2𝑖

∑ (𝑦𝑖 − �̅�)2𝑖

= 1 − 𝑆𝑆𝑟𝑒𝑠

𝑆𝑆𝑡𝑜𝑡

V

Where yi is the patient dataset and fi is the dataset produced in the simulation.

Figure 10. Cumulative distribution of simulations with different PFSD and a patient. Each of the blue lines represent a unique standard deviation for the flow. The red line is the cumulative distribution of a patient’s histogram.

2.3.2 SIMULATIONS – Method 2 – Compartment

A second method of determining plausible simulation parameters was to estimate it from a

patient’s unique distribution of activity from the Tc99m-MAA- and 90Y-SPECT/CT examination.

The distribution was divided into a number of compartments ranging from 1 to 512 and for

each compartment the mean number of counts per voxel (mCPV) was calculated. For every

voxel in the current compartment a normally distributed random number is produced and

multiplied by the compartments standard deviation as seen in equation VI. The number of

compartments needed to mimic a specific histogram (figure 11) was determined by calculating

the integral of the two functions and comparing the area between the curves.

Compartment i = 𝑚𝐶𝑃𝑉 + 𝑟𝑎𝑛𝑑𝑛 ∙ √𝑚𝐶𝑃𝑉 VI This calculation is performed for each of the i compartments

17

Figure 11. Three attempts to mimic the histogram of Pat 6 starting with only one compartment, then 7 and lastly 18. It is clear that neither A or B provide a particularly good fit while C is much more similar.

2.4 PHANTOM MEASUREMENTS

As a method of controlling the data extraction from RONSO, phantom measurements using

NEMA/IEC 2001 PET Phantom (figure 12) from A. Hermansson’s master’s thesis in 2013 were

used (30). The phantom in these measurements consists of a hollow case of acrylic glass with

six hollow spheres inside it, down the middle runs a hollow rod filled with plastic beads used

to approximate the attenuation in lungs when performing a CT scan.

The spheres have radii between 0.5 – 1.85 cm and can be filled with a fluid from the outside of

the acrylic glass case. The volume surrounding the spheres can be filled with a substance to

produce a background in the measurements, either water or a solution containing activity. A

Tc99m-solution was used to fill both the background and the spheres.

In the measurement used here the background (Bg) as well as the spheres were filled with 20

kBq/ml. The spheres inside the phantom were treated as tumours and the surroundings were

considered to be normal tissue. Two volumes of interest were created inside the phantom, one

close to the edges and the other one with a margin (figure 13). Both with the spheres (tumours)

excluded to be as similar to the patient measurements as possible.

18

Figure 12. Phantom used in the measurements contain six hollow spheres (tumours) to be filled with a different concentration of activity for each of the three measurements. The volume surrounding the spheres was also filled with activity

Figure 13. A SPECT/CT of the phantom filled with a Tc99m solution. The green lines represent two different volumes of interest. The spheres are excluded from the volume of interest as it is supposed to represent normal tissue without tumours. In this SPECT the concentration of activity was 4 times larger in the spheres than the rest of the phantom.

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3. RESULTS

3.1 PATIENT HISTOGRAMS

The VOI corresponding normal tissue in each patient was transferred from RONSO to

MATLAB® for analysis of the histograms. High levels of counts in a voxel will push it to the

right in the histogram and when many voxels share similar number of counts the histogram

will grow in the positive y-direction. In figures 14 A-C below, each patient’s 99mTc-MAA and 90Y distribution are displayed.

Figure 14 A. Histograms of the activity distribution in normal tissue from the 99mTc-MAA- and 90Y-SPECT examinations. Patients 6 and 8.

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Figure 14 B. Histograms of the activity distribution in normal tissue from the 99mTc-MAA- and 90Y-SPECT examinations. Patients 9 and 10.

Figure 14 C. Histograms of the activity distribution in normal tissue from the 99mTc-MAA- and 90Y-SPECT examinations. Patients 11 and 12.

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3.2 SIMULATIONS – Method 1 – Curve Fitting

If initially using 0.5 as the probability of a microsphere going through one of the two sister

vessels and then slowly increasing the standard deviation (PFSD) from 0 to 0.5 the best PFSD

for each patient can be calculated through the R2-value (equation V). The arterial density was

set to 6.4 meaning that the same number of microspheres were simulated each time. The R2-

value closest to 1 and the corresponding PFSD can be seen in table 2.

Table 2. Initial simulations to create microsphere distributions corresponding to each patient’s histogram as well as the phantom measurements. The standard deviation was slowly increased and stopped at the highest R2 value. P-1 is referring to the phantom measure.

PATIENT PFSD AT THE BEST FIT R2 - VALUE

6 0.06 0.981

8 0.06 0.992

9 0.34 0.972

10 0.04 0.997

11 0.10 0.999

12 0.24 0.976

P – 1 0.18 0.922

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3.2 SIMULATIONS – Method 2 – Compartment

For each patient the compartment method was applied to both the 99mTc-MAA and the 90Y

distributions. On the right side in figures 15 A-B below are the original histograms together

with the calculated approximations. The left side of the figures show the sum of the area

between the curves calculated for each compartment size; a small value equals a good fit.

Figure 15 A. The best fit achieved for patient 6 is the green/red line to the right with the blue line being the original distribution. The figures on the left show the area between the original histogram and the approximation, with a unique value for every compartment size.

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Figure 15 B. The best fit achieved for patient 11 is the green/red line to the right with the blue line being the original distribution. The figures on the left show the sum of the area between the two curves on the right (y-axis) for a certain number of compartments.

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The number of compartments needed to produce a good fit can be seen in table 3 and was

determined at the first point after the large initial fluctuation, i.e. where the plateau was

reached. If the result was oscillating heavily (figure 15 A, bottom left corner), no best fit was

determined.

Table 3. The best fit between the patient’s histogram and the calculated approximation varied amongst patients and was reached at these number of compartments. A dash indicates an oscillating number of compartments and therefore no best fit was determined.

PATIENT NUMBER OF COMPARTMENTS

99mTc-MAA 90Y

6 18 -

8 9 11

9 37 12

10 15 -

11 30 17

12 22 17

P - 1 - -


The phantom measurements were treated and segmented in RONSO in the same manner as

the patients. This provided the different histograms seen in figure 16 depending on which

volume of interest was used (figure 13).

Figure 16. The histograms resulting from the VOI's in figure 13. The distribution to the left derives from the VOI with a large

margin to the edges of the phantom. In the figure to the right the VOI approaches the edges of the phantom as well as the

center.

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A profile of the activity in a cross section of the phantom was extracted from RONSO (figure

17). The profile was made up of a thousand points of measurement.

Figure 17. The green line in image A displays where the activity profile of the phantom measurement was drawn. Image B is the number of counts in every pixel of the activity profile.

4. DISCUSSION

The spatial resolution of the SPECT/CT is a limiting factor in this study in the sense that

microscopic information is lost. Instead of studying the images directly, focus lies on extracting

suitable data in the form of histograms. These histograms contain the distribution of activity

throughout the liver but provide no information regarding the position of the uptake.

However, if processed correctly, information concerning the hepatic structure and segments

might be made available.

4.1 nNUFTI AND THRESHOLD INDEX

The delineation of tumour from surrounding normal tissue (figure 4-7) involves a certain

measure of approximation. High activity regions in the images rarely have sharp edges and at

some point a line has to be drawn to separate the two types of tissue. It is particularly difficult

in a smeared bremsstrahlung SPECT where a small step for the region growing algorithm can

result in a large volume change as the curve usually is quite steep.

Using a radiologist’s measurements of liver/tumour volume has been helpful in some

instances and difficult in others. Therefore a solid margin has been applied to suspected

tumour areas when possible.

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4.2 PATIENT HISTOGRAMS 99mTc-MAA and 90Y

Comparing medical images of soft tissue from different imaging sessions is especially difficult

when involved with growing tumours. Organ positions will shift slightly, tumour

vascularization may alter the technique used for imaging and the overall position and

condition of the patient will vary. For the patients in this study the time between 99mTc-MAA-

injection and the injection of 90Y microspheres is two weeks to a month.

Therefore, differences between the histograms containing activity distribution of 99mTc-MAA

and 90Y microspheres were expected (figure 14 A-C). In addition, the volumes of interest had

to be remade for each patient and imaging modality, introducing another uncertainty when

comparing them.

In patient 9 and 12 the similarities between 99mTc- and 90Y-histograms are easy to identify. This

is due to a single, large uptake of activity remaining in roughly the same position in both

images, resulting in a consistent distribution and similar histograms for both imaging

techniques.

The reverse situation occurs for patient 8, 10 and 11. Several tumours throughout the liver and

varying uptake of 99mTc-MAA and 90Y result in dissimilar histograms. Furthermore, the signal

is very high and almost constant in large parts of the liver making the separation of normal

tissue difficult. For patient 10 the injection of 99mTc-MAA has been selective to the right lobe

while 90Y is found in both lobes, this give rise to different volumes of interest and in the end

different histograms.

Although patient 6 has had 99mTc-MAA injected into the entire liver, parts of the liver have

very little signal. For the 90Y microspheres the signal is almost homogenous throughout the

normal tissue.


The differences between a large VOI without margins and a small VOI far from the edges of

the phantom are quite clear. If assuming that the activity is homogenously distributed within

the phantom the histogram of the small VOI might not come as a surprise. Since the spheres,

representing tumours, are removed in both large and small VOI the differences in the

distributions might be attributed to edge effects.

A possible explanation is that photons travelling the full length of the phantom lose energy

along the way and are therefore scattered in large angles close to the edge, giving rise to the

smaller peaks in the histogram. Monte Carlo simulations in SIMIND® could provide answers

for this speculation.

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However, looking at the activity profile in figure 17 B, it is clear that the activity is not

homogenously distributed, possibly due to the 99mTc sticking to the acrylic glass surface.

Therefore, the phantom might be unsuitable for measurements such as this one. Further

measurements are required.

4.4 SIMULATIONS – Method 1 – Curve Fitting

For all 99mTc-MAA examinations the least square method generated R2 values above 0.98

meaning a reasonably good fit between simulation and patient-based data. For the phantom

measurements the fit was worse, reaching only 0.92. Ideally, PFSD = 0 should provide a good

fit for a phantom with a homogenous activity distribution. The flow parameters (PFSD) found

through this method of analysis ranged between 0.04 – 0.336 (table 2).

If applying the calculated standard deviation to the simulation it is possible to generate

microsphere distributions resembling the patient’s. However, the resulting distribution do not

carry specific traits from the patients, such as multiple peaks. To acquire further resemblance

it is necessary to include more flow parameters in the simulation, possibly a unique value for

every branching.

4.5 SIMULATIONS – Method 2 – Compartment

Depending on the complexity or irregularity of the histogram from the 99mTc-MAA- or 90Y-

SPECT/CT, the number of compartments needed to produce a good fit will vary. Considering

the fact that the liver contain 8 segments (figure 1), a qualified guess might be that a minimum

of 8 compartments is needed. Furthermore, if assuming that the model can provide good

correlation between patient distributions and distributions calculated by the mean counts per

voxel model, it is reasonable to believe that the fit will not improve much after a certain

number of compartments.

A large initial fluctuation in all patients shows that a few number of compartments is not

enough to mimic any distribution (figure 15 A-B, table 3). For most patients, a plateau is

reached when increasing the number of compartments above 20-30. After this point there is

little gain in increasing the numbers further. However, for shapes similar to that of a normal

distribution the fit will improve periodically and reach a maximum when approaching 512

compartments.

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5. CONCLUSIONS

Further measurements with a different phantom are required to rule out uncertainties

regarding the phantom used in this study.

Using a constant standard deviation of the flow, the simulation model based on bifurcations

works well to produce normal and lognormal histograms of microsphere distributions.

However, when histograms of uptake in patients adopts a more complex appearance the

simulation fails to mimic this.

The number of compartments needed to imitate a patients histogram is initially increasing but

levels out quickly. After this point, increasing the number of compartments does little to

improve the approximation.

6. FUTURE ASPECTS

The next step in the simulations is to calculate unique flow parameters for each node starting

from a patient’s distribution of activity from the Tc99m-MAA- and 90Y-SPECT/CT examination.

This could prove to be the step necessary to accurately simulate patient histograms and

connect the macroscopic information of this thesis with the small scale studies of Högberg et

al. If performed successfully, this would provide a more comprehensive view of the processes

involved in radioembolization, from injection of microspheres to formation of clusters.

ACKNOWLEDGEMENT

Thanks to my supervisors Peter Bernhardt and Emma Wikberg for great support and

encouragement. Also thanks to Johanna Svensson, Tobias Magnander and Jonas Högberg for

answering a lot of questions and for including me in the (irrelevant) discussions in the hallway.

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