Initial development of voxel dose kernel dosimetry in MATLAB

for alpha particles using Alpha Camera

imaging of tissue samples

M.Sc. Thesis

Besart Rexhaj

besartrexhaj@hotmail.com

Supervisors:

Tom Bäck

Stig Palm

Department of Radiation Physics University of Gothenburg

Gothenburg, Sweden May 2013

1

Abstract Targeted alpha therapy (TAT), where alpha-particle emitting radionuclides are used is a

promising treatment of metastatic cancers. By using an alpha emitter attached to a targeting

molecule , one can obtain high absorbed dose to very small tumors (micro tumors), while

dose to normal tissues can be kept low. This is due to the short range of alpha particles and

high LET. Alpha Camera imaging is a new method for ex-vivo imaging of alpha particles, the

method can be used to study how the tumor-targeting molecules labeled with alpha

emitters is distributed in tumors and organs. Due to the short range of alpha particles the

dose distribution can be non-uniform and making it difficult to assess the effect of treatment

and side effects. Alpha Camera Imaging is a quantitative method with such high resolution

that activity distribution can be studied at the cellular level. The method is based on tissue

samples that are harvested and then analyzed after freeze sectioning (cryosectioning). Alpha

Camera imaging can be used as a tool for small scale dosimetry, which is needed for the

continued development of internal radiation therapy with alpha emitters.

This work aimed at developing an initial method, using Alpha Camera images and MATLAB

programming, to calculate the absorbed dose and its distribution of the alpha emitter (211At).

By using the activity images from the Alpha Camera, these images can be processed with a

kernel (VDK-method), and an energy-spread image is obtained, which can be used to

calculate the dose and its distribution.

The mean absorbed dose-rate with the VDK-method was for the central section of the two

series; 0.0814 and 0.1005 mGy/s/MBq. The mean absorbed dose rate calculated without

using the VDK-method was 0.1052 and 0.1267 mGy/s/MBq. Results show that the tumor

receives an inhomogeneous dose distribution; about 80% of the tumor volume receives a

level of 60% of the mean absorbed dose rate.

2

Acknowledgements I would especially like to thank my two supervisors, Tom Bäck and Stig Palm. You've meant a

lot to me during the last months, without your support and help, this project would have

been even more difficult.

I also want to thank my family and friends for their understanding and support. Finally, I

want to thank my dearest Pamela, you're my Everything.

Furthermore, I want to share a quote to the reader that is worth remembering; “The more I

learn, the more I learn how little I know”-Socrates.

3

Abbreviations and Acronyms

TAT Targeted alpha therapy

LET Linear energy transfer

Ex-vivo Experimentations done in an artificial environment outside the

organism with the minimum change of natural condition.

At-211 Astatine 211

VDK-method Voxel dose kernel- method

α-RIT Alpha- radioimmunotherapy

FWHM Full width at half maximum

3D Three-dimensional

Voxel Three-dimensional pixel, volume element

Gy Gray (Joule/kg)

RBE Relative biological effect

MIRD Medical Internal Radiation Dose, (Committee of the Society of Nuclear Medicine)

CCD-detector Charged couple device-detector

Bq Becquerel (number of decays per second)

TPI Total pixel intensity

Floor-command Round toward negative infinity

MeV Mega electron volt

ROI Region of interest

4

Table of Contents Abstract ...................................................................................................................................... 1

Acknowledgements .................................................................................................................... 2

Abbreviations and Acronyms ..................................................................................................... 3

Introduction ................................................................................................................................ 5

Purpose/Aim ........................................................................................................................... 6

Theory ......................................................................................................................................... 6

Astatine-211 ........................................................................................................................... 6

MATLAB .................................................................................................................................. 7

Digital image ........................................................................................................................... 7

Registering an image .............................................................................................................. 7

Alpha dosimetry ...................................................................................................................... 8

Alpha Camera imaging ............................................................................................................ 8

Principle of voxel dose kernel dosimetry ............................................................................. 10

Linear Filtering and the Imfilter function ............................................................................. 11

Monte Carlo method ............................................................................................................ 13

Prework .................................................................................................................................... 13

Materials and methods ............................................................................................................ 15

Alpha camera images............................................................................................................ 15

Generating the VDKs - Monte Carlo simulation for the dose distribution ........................... 17

Calculation of the absorbed dose rate using a VDK-method ............................................... 18

Calculation of absorbed dose rate without using a VDK-method ........................................ 19

Validation of the method ..................................................................................................... 19

Results ...................................................................................................................................... 20

Results of the validation ....................................................................................................... 24

Discussion ................................................................................................................................. 26

Conclusion ................................................................................................................................ 29

References ................................................................................................................................ 30

Appendix ................................................................................................................................... 31

General code ......................................................................................................................... 31

5

Introduction Targeted alpha therapy (TAT), where alpha-particle emitting radionuclides are used is a

promising treatment of metastatic cancers, such as ovarian cancer and prostate cancer. By

attaching an alpha emitting radionuclide to a targeting molecule, which is specific to tumor

cells, high absorbed doses can be obtained to very small tumors (micro tumors), while doses

to normal, healthy, tissues can be kept low. This is due to the short range in tissue (<100 µm)

and the high LET, Linear Energy Transfer (~100 keV/µm) of alpha particles. Alpha-

radioimmunotherapy (α-RIT) provides most promise for the therapy against single tumor

cells up to small tumor clusters. Treatment could be for cancer localized in the circulation

system (e.g. lymphoma and leukemia), micro metastases and minimal residual diseases, and

small malignances growing freely on the compartment walls. By using alpha particles, the

targeted tumor cells could be highly irradiated, while avoiding toxicity to nearby normal

tissue. In Gothenburg, research has shown that α-RIT with 211At-MX35-F(ab’)2 is promising

for the treatment of ovarian cancer, and a Phase I clinical trial of 12 women has been

completed [1].

The clinical Phase I study was performed in order to evaluate the toxicity and dosimetry of

the compound. Results showed that there were no major toxicities at the activity level that

should be therapeutic for the micrometastases [1]. This treatment is so far conducted as a

loco-regional treatment; i.e. 211At-MX35-F(ab’)2 is not administered systemically (in the blood

stream) but in this case intra-peritoneally (in the peritoneal cavity).

Despite the promising experimental results with TAT, several challenges still remain. For

example, improved small-scale dosimetry is needed to predict the biological outcome. This

will be of special importance in systemic treatments.

Due to the short range of alpha particles, the dose distribution can become non-uniform,

leading to an aggravation of the evaluation of TAT treatments and side effects. The Alpha

Camera is a new technique for ex-vivo imaging of alpha particles. The method has been

developed in Gothenburg with the purpose to study in detail how the tumor-targeting

molecules labeled with alpha emitters distribute within tumors and various organs [2]. Alpha

Camera imaging is a quantitative method with high spatial resolution (FWHM 35 ±11 µm).

6

Purpose/Aim

This work aimed at developing an initial method, using Alpha Camera images and MATLAB

programming, to calculate the absorbed dose and its spatial distribution due to decay of the

alpha emitter At-211 on a small scale. Absorbed dose rates were calculated from existing

images. Based on these, the dose distribution was calculated and determined for each

corresponding volume element (voxel). Series of consecutive cryosections previously imaged

with the Alpha Camera were used, and the corresponding dose-rate in the three-

dimensional volumes (voxels) was determined. Image intensity in each image pixel was

recalculated to the corresponding number of 211At decays and used as input for the

calculation of the absorbed dose rates in the central section of the series (sampled tissues)

at a certain time after start of TAT (injection of 211At-MX35-F(ab’)2 ).

Theory

Astatine-211

Astatine-211 is produced by accelerating α-particles to high energies (~28 MeV) in a

cyclotron and bombarding a 209Bi-target. The nuclear reaction is thus 209Bi(α,2n)211At.

The half-life, T1/2, of 211At is 7.21 h and its decay has two branches. In one, with a probability

of 41.7% it decays to form the daughter nuclide 207Bi. This daughter nuclide has a half-life of

38 years and decays to form 207Pb.

In the other branch, with a probability of 58.3%, it first decays to form a daughter nuclide

(211Po) with a half-life of 0.52 s. The decay of 211At to 211Po is by electron capturing and

involves the emission of X-ray photons (77-92 keV). This daughter nuclide then decays to

form 207Pb.

The 41.7% branch is described by the simplified scheme:

t 211 i

2 e2 α e

The second branch is described by the scheme:

t 211 o

211 b 22 e2

α e

oth branches involves the emission of an α-particle. Each decay of 211At thus leads to the

emission of one α-particle.

7

MATLAB

MATLAB is a software package for scientific and engineering calculations [3]. MATLAB has

various built-in functions for solving various types of calculations, as well as so called

toolboxes for different applications areas, such as image processing, statistics and signal

processing. These toolboxes contain a variety of useful special commands. MATLAB is

commonly used in various fields such as industry, education and research.

Digital image

A digital image is a matrix consisting of a set number of rows and columns. A pixel in the

image, image element or a position in the matrix has a finite value that represents the

intensity. Digital images may have different bit depth; the intensity of a pixel in a 16-bit

image has a gray scale value between 0 and 65535.

When two or more digital images/matrices are added together in a 3-dimensional matrix,

the pixels are extended into volume elements, also called voxels.

Registering an image

The process of aligning two or more images is called image registration. One of the images is

considered the reference to which the other images, called input images, are compared.

There may be different reasons for the need of aligning the images. One could be that the

object in the image has moved, stretched or twisted slightly differently for one section than

for the others in the series. This is possible to correct by using image registration. By

applying a spatial transformation to the input image, the input image will be aligned with the

base image. The key to a successful image registration process is to determine the

parameters of the spatial transformation needed to bring the images into alignment [4].

Two different transformation principles that are worth mentioning are rigid and non-rigid

transformations. In the rigid transformation, the image cannot be scaled or stretched, it is

treated as a rigid body, which can rotate and transform [4].

The second transformation method allows elastic or non-rigid transformations. In order to align the input images with the reference image this transformation allows bending and twisting locally in the images [4].

8

Alpha dosimetry

Compared to electrons, alpha-particles deposit a very high amount of energy in the close

vicinity (~100 m) of the position for the decay of the alpha-emitting radionuclide. The

specific energy deposited in a cell nucleus following the traversal of a single alpha-particle is

on the order of 0.2 Gy. Together with a relative biological effect (RBE) of around 5 for cell

inactivation, it follows that only a few alpha-particle events are required to reach a high

probability for cell death. Such low numbers of events, together with a heterogeneous

distribution of the radionuclide, makes the use of (mean) absorbed dose to entire organs or

tumors limited for understanding the biological effects of alpha-particle irradiation.

Ideally, one would want information on both the actual microdistribution of the

radionuclide, and also the energy deposited along each alpha-particle track. Such detailed

information is needed for a proper microdosimetric analysis of the radiation effect. In this

work, we combine small-scale information on the spatial distribution of the radionuclide

using the Alpha Camera technique, together with Monte Carlo-based microdosimetry for

evaluating the biological effect of 211At irradiation.

Alpha Camera imaging

Alpha-particles may contribute to a non-uniform dose distribution, because the required

dose is often generated by only a few events from the alpha radionuclide. Therefore, use of

small-scale or microdosimetry is needed. Alpha camera imaging is a quantitative method

with such a high resolution that the activity distribution can be studied at the cellular level [2]. Tissue samples (radioactive) are dissected, frozen and sectioned. The sections are placed

in the Alpha Camera and images are acquired.

The principle of Alpha Camera was described in detail previously [2], but the general principle

is shown in Figure 1. The tissue sample (A) is radioactive and the alpha particles emitted

upon decay interact with a scintillation layer (B). This layer consists of ZnS (Ag) scintillation

phosphor that generates scintillation photons with maximum emission wave length of 450

nm. These photons are detected through an optical system by a cooled high-resolution CCD-

detector. The pixel intensity in the acquired images is proportional to the activity of 211At in

the imaged samples, see Figure 2.

9

Figure 1. Schematic figure of the alpha camera setup for Alpha Camera Imaging. Cryosections (A) are added directly to

the scintillation layer (B). The scintillation layer is coated on a polyester layer (C). The solid black arrows represents alpha

particles, which are emitted from the tissue sample, and interacts with the scintillation layer. Scintillation photons are

generated (blue dotted arrows) which traverse through the tissue layer before being imaged. Adopted from a publication

and used with permission [2].

10

Figure 2. Pixel intensity in Alpha Camera images of kidneys cryosections is plotted as a function of the measured 211

At

activity (using gamma counter) in the corresponding sample. Adopted from a publication and used with permission [2].

Principle of voxel dose kernel dosimetry

There are currently three different methods for performing internal dosimetry at the voxel

level [5]. The first one uses direct Monte Carlo radiation transport, the second is a MIRD

approach that use S-values at the voxel level, while the third one uses the 'superposition

principle' and is currently the most used [6]. When the radioactivity represented in the image

is known, the resulting dose distribution can be determined by transforming the activity

distribution from the image to absorbed radiation energy using an appropriate kernel [6]. The

kernel transfers an activity distribution to an absorbed energy distribution by weighing the

energy deposition of the particles over its range. This is referred to as voxel dose kernel

(VDK) dosimetry. The VDK method is widely used today, particularly for the more commonly

used radionuclides that emit beta, auger electrons and photons. Today, only a few research

groups present experimental data on the small-scale distribution of alpha-emitting

radionuclides. In this work, we use Alpha Camera images of tissues harvested from mice that

have been injected with an alpha-particle emitting compound. This method is unique since it

was developed locally and is not commercially available.

11

An example can illustrate the principle of the voxel dose kernel dosimetry. Start with a 3D

image (stack of image slices) with pixel values representing the number of decays. Since the

total number of decays is known from gamma-well counting, an approximate mean

absorbed dose can be calculated for a slice. It's very important to know at what time the

image was acquired, and the length of exposure. This is needed for correction for long

acquisition time, and in order to correct for physical decay to any desired time.

To transform the activity distribution in the image to represent energy deposition, we use an

energy kernel.

This kernel can be acquired using Monte Carlo programming in e.g. Matlab for a desired

radionuclide, in this case 211At. The kernel contains information on how the radiation energy

resulting from one decay is spatially deposited. An energy deposition image is obtained by

applying the kernel to the original image through a filtering process. Each voxel assigns

energy (J or MeV) and by dividing it with the mass of the voxel, we generate a specific

energy, or absorbed dose (Gy) in each voxel of the image. The values in this specific energy

(or dose) image can then be used to generate a dose-volume histogram, which presents the

volume (or a percentage of the volume) that receives some dose in a given range of dose

levels.

Linear Filtering and the Imfilter function

One technique of modifying an image is by filtering [4]. Linear filtering is a neighborhood

operation. The pixel’s neighborhood is a set of pixels which is defined by their locations

relative to that pixel. By applying some algorithm to the values of the pixels in the

neighborhood of the given pixel in the input image, the value of any given pixel in the output

image is determined. Figure 3 shows an example, using our own kernel, on how to compute

the (2,3) output pixel of the correlation of the image matrix A. Matrix A and the correlation

kernel (or filter) h contains samples of experimental data that was used in this study. The

method is using these steps:

Slide the correlation filter so that the center of the filter lies on top of the (2,3)

element of A.

Each weight of the correlation kernel is multiplied with the pixel values in A

underneath.

Sum the individual products.

The output pixel (2,3) from correlation is:

12

Figure 3. Description of how the correlations method works, the image matrix is A and the correlation kernel is h. The output pixel is computed to 14.33 MeV.

Linear filtering is a filtering where the value of an output pixel is a linear combination of the

values of the pixels in the input pixel’s neighborhood. Linear filtering can be accomplished

through two different operations called convolution and correlation. The two operations are

neighborhood operations in which each output pixel is the weighted sum of neighboring

input pixels. The matrix of weights is called a kernel or filter [4].

Imfilter is a built-in function in MATLAB that filters a matrix with a kernel, the matrix and the

kernel can also be multidimensional. The kernel is usually off the edge of the image when

computing an output pixel at the boundary of an image, therefore imfilter has boundary

padding options. By assuming that the off-the-edge image pixels are zero the imfilter

function normally fills in these with 0. This is called zero-padding [4].

13

Monte Carlo method

Monte Carlo methods are based on a variety of algorithms and are used to simulate various

physical and mathematical systems. The method is stochastic, i.e., non-deterministic, that is,

by relying on random number generators. Monte Carlos iterative algorithms and the large

amount of calculations, makes the method suitable for computer simulations [7].

Prework The available data for this work was two series of Alpha Camera images of an ovarian cancer

tumor. The tumor was established as a xenograft in nude mice, by injecting tumor cells

(human ovarian cancer cell line OVCAR-3) under the skin (subcutaneously, s.c.). After 2

weeks of growth, when the tumor had reached a diameter of 5-7 mm, the mouse was

injected intravenously with the tumor-specific antibody MX35-F(ab’)2, radiolabeled with 211At. The injected activity was 5.41 MBq. After 4.1 hours, the mouse was sacrificed and the

tumor was excised. After dissection, the tumor was snap-frozen in liquid nitrogen and

sectioned into 12 µm thick sections. Two series of sections was taken from the same tumor –

each representing a continuous series of 12 sections. Thus, each series represent a 144 µm

thick tissue-sample of the tumor. All sections in both series were used for Alpha Camera

imaging. After imaging, the tissue sections were also measured for activity using a gamma

well counter.

This mouse model of s.c. ovarian cancer has been used in a previous biodistribution study [8].

In that study, the tumor uptake was measured at different times after injection of 211At -

MX35-F(ab’)2 (Fig. 4). The tumor uptake was also used to calculate the total mean absorbed

dose to tumor, which in that study was estimated to be 4.1 Gy/MBq. The same data on

tumor uptake was also used to estimate the dose rate to the tumor at different times after

injection (Fig.5). These data from the previous study was used for comparison with the data

derived in the current work.

A more precise description of the steps from cryosectioning to Alpha Camera imaging was described previously [2].

14

Figure 4. The uptake in tumor after injection of 211

At -MX35-F(ab’)2 plotted as a function of time after injection. The

tumor uptake is expressed as percentage of injected activity per gram tissue (%IA/g).

Figure 5. The mean absorbed dose rate in tumor after injection of 211

At -MX35-F(ab’)2 plotted as a function of time after

injection. The dotted curve represents a polynomial fit of the plotted data.

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 10 20 30 40 50

Up

take

in

tu

mo

r (%

IA

/g)

Time after injection (h)

0,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,10

0 50000 100000 150000 200000

Ab

sorb

ed

do

se r

ate

(m

Gy

· s-1

· MB

q-1

)

Time after injection (s)

Dose rate per MBq (mGy s-1 MBq-1)

y = axb * exp(cx)

15

Materials and methods

Alpha camera images

The images used needed to be registered (aligned) because the tumor tissue was elastic, and

could be stretched and placed differently for different sections in the series. The images

were registered (aligned) using a semi manual method. A first rough alignment was done

using Photoshop CS. Registration of the images was then performed automatically in ImageJ

(Fiji version) using the plug-in StackReg (by rigid affined transformation). The images were

also calibrated (background- and geometry corrected) so that the total pixel intensity (TPI)

was proportional to the total number of decays. The pictures were taken from a mouse

tumor [as described under ‘Prework’]. All slices in serie 1 were exposed at the same time,

but in three different alpha camera systems. The exposure time for the first set of serie

images was 6600 seconds. The exposure time for the second set of serie images was 36000

seconds for slice number 1,2,3,4,10,11 and 12 and 28800 seconds for slice number 5,6 and 7.

The ninth slice in serie 2 contained artifacts due to tissue folds and therefore couldn’t be

used. However, a ninth slice was created by averaging the two neighboring slices, i.e. eighth

and tenth slice. The eight and tenth slice TPI-values was divided by the respective exposure

time, thus, the unit value was in TPI/seconds. Therefore, the exposure time for the created

slice could be chosen. The exposure time for the ninth slice was chosen to 28800 seconds.

The total activity in the entire section was determined with great accuracy by immersing it

into a 3" NaI(TI) gamma-well detector and measure for the characteristic X-ray photons (77-

92 keV) that are emitted in the 211At decay chain.

In the alpha-camera system, the alpha particles emitted through 211At and 211Po decays

interact with the scintillation layer to generate optical photons, which are then detected by

the Alpha Camera. The number of emitted alpha particles corresponds to the numerical

values of the images. Thus, the sum of all numerical values in all pixels of the image, i.e. the

total pixel intensity (TPI), represents the total number of decays during the image acquisition

time.

This way, a calibration factor was calculated separately for each image slice, i.e. by dividing

the number of 211At decays, N (or ) during the image acquisition with the resulting TPI-

value,

Where N represents the total number of decays [Bqs]; c is a calibration factor [Bqs / TPI];

and TPI is the sum of all numerical values of all pixels in the resulting image.

16

Physical decay of 211At was accounted for both during the often long, up to 10 hours, image

acquisition time, as well as for the difference in time from the harvesting of the sample from

the mouse to the start of the image acquisition. In this work we have used samples that

were dissected 4.1 hours post injection (hpi) of 211At into the mouse.

The correction for the long image acquisition time was made by first solving for the number

of 211At decays (N or cumulated activity, ) during the acquisition time, eq 2.

The solution to equation 2 is described in equation 3,

Where [Bqs] is the cumulated activity during t seconds of exposure time, Ab [Bq]

represents the activity at the beginning of the exposure time, t [sec] is the exposure time.

is the decay constant and it is defined by equation 4,

T1/2 [sec] is the half-life for 211At.

The number of decays during the acquisition time is the one generating the images.

Since this number correlates to Ab, a simple decay correction can then be made to any time

before or after this time. Since we are interested in the time for tissue harvesting, i.e. 4.1

hpi, we used

Where A0 [Bq] represents the activity at 4.1 hpi after the injection time and t [sec] is the time

from 4.1 hpi to the start of the image acquisition.

The intensity value in each pixel was converted to a corresponding number of decays, using

factor c from eq. 1. This number of decays was then used for assigning a certain amount of

17

radioactivity at a certain time to the volume (voxel) represented by this image pixel. Physical

decay were corrected for to the time of tissue harvesting, i.e. 4.1 hpi of the mouse.

Following the above steps, each pixel intensity value in the original image was converted to a

corresponding amount of activity (Bq) at the time for dissecting the mouse, i.e. 4.1 hours

post-injection.

A Monte Carlo program was then designed to simulate the energy deposition of alpha

particles generated within the volume elements represented by each pixel. In other words,

where is the radiation energy deposited for 211At decays occurring in such small volume

elements? It is important to stress that the simulation will generate the dose-rate (Gy/s) at a

certain time point, e.g. the time for mouse dissection. The actual dose rate to the tumor

during the prolonged irradiation of TAT, will vary depending on the changing biological

processes and the physical decay of the radionuclide used.

Generating the VDKs - Monte Carlo simulation for the dose distribution

By generating a multidimensional kernel, using Monte Carlo simulation, the distribution of

absorbed dose in each voxel was calculated.

The code simulates 1’ ’ alpha-particles. The coordinate system was centered at x = y =

z = 0. A zero matrix was predefined in order to save simulation time [3], this was done using

the zeros-command in Matlab. The locations of the astatine-211 decays were randomly

distributed in a homogeneous pattern within the central voxel. An initial direction of the

particle was randomized. Then the code executed a random test to decide which decay

branch should be considered. For the polonium branch, the maximum range was defined,

i.e. 72 µm. The code stepped 1 µm at a time while the initial direction still was in force

(natural physical behavior for α-particles). The energy losses were collected using Stopping

Power [9] values of alpha particles in water. These values were placed in each respective

voxel along its track. The voxel size (µm) was predefined but the program allow the use of

any voxel size from 12 µm and upwards. A 12 µm voxel size was used in this work because

the image slices were 12 µm thick. If the voxel size is changed, the dimensions of the matrix

will be adjusted so that it fits in the original coordinate system. A kernel was built by adding

to the voxel values the energy deposition values for the current alpha-particle track for each

1 µm track length. The code used separate stopping-power values for the At-branch decay,

with the maximum range set to 50 µm. The kernel values were then scaled to represent the

energy deposited from one decay of an 211At atom. This was done by dividing the kernel

values with the number of simulated particles.

The unit values in the kernel were in MeV. In order to convert this into dose rate (mGy/s) at

a certain time following some activity injected into the mouse (MBq), we used two steps.

First the mass of the cubic voxel was calculated by assuming the density of the tissue is the

18

same as for water, i.e. 1 g/(cm)3. The calculated mass was then used in equation 6 for

converting MeV to mGy.

Where D is the absorbed dose [mGy], H is the values in the kernel [MeV], m is the mass [kg]

of the voxel and 1.6022e-13 is the conversion factor (from MeV to Joule). Each kernel value

now represents the absorbed dose (or specific energy) (mGy) to that voxel element due to

one 211At disintegration occurring in the central voxel.

When the kernel has been applied to the corrected images (now representing the activity

(Bq) at 4.1 hpi, equations 1-5), the resulting values in each voxel then represent the dose-

rate (mGy/s) at 4.1 hpi.

Finally, in order to harmonize the resulting dose-rate with standard nomenclature for

radiopharmaceuticals, the values were divided by the total amount of radioactivity injected

into the mouse, Ainj. The original alpha-camera images had then been converted to voxel

values of the dose-rate (mGy/s) in this voxel at 4.1 hpi due to an injected amount of Ainj

(MBq) into the mouse. The final unit of the voxel values in the resulting matrix is thus

(mGy/s)/MBq.

The Imfilter function was used to distribute the energy in the multidimensional array (stack

of images) according to the simulated kernel. The imfilter-function was operating according

to 'default'-values, i.e. with zero-padding boundary. This situation exists for our tumor

images. There is no data for decays at the surroundings of the tumor and therefore, this is

set to zero. We thus choose to neglect any contribution originating from outside the tumor

area.

After the image processing was done, dose-histograms and dose-volume histograms of the

central image slice were plotted using Excel.

Calculation of the absorbed dose rate using a VDK-method

The images were imported into MATLAB and assembled into a multidimensional array. The

images were also converted to double precision (needed for image manipulation). Because

the images were calibrated in the sense that the pixel intensity was proportional to the

number of decays, these unit values could be converted to total number of decays. This

included also a correction for long measurement time and decay correction to the time 4.1

19

hpi. These calculations were done in MATLAB using equations 1-5 defined above. In this way

the activity (Bq) at 4.1 hpi were obtained in each voxel of the multidimensional array.

After the image was processed with the kernel, the mean absorbed dose-rate (at 4.1 hpi)

was calculated by taking the mean value of the dose rates in each voxel of the central image

slice, i.e. slice nr 7.

Calculation of absorbed dose rate without using a VDK-method

An approximation of the mean absorbed dose-rate (for a certain amount of time, i.e. 4.1hpi,

per injected activity) was also calculated directly from the central image slice, without using

the VDK-method, i.e. without processing the image with the kernel. The assumption for this

calculation was that all alpha-particles generated in the slice deposits all their energy within

the slice and that there are no energy contribution from neighboring slices, i.e. the absorbed

fraction was one. The result is thus erroneous but can serve to illustrate the importance of

using a more correct energy distribution kernel. This was done using Equation 7.

Where is the mean absorbed dose rate [mGy/s] per injected activity into mouse [MBq].

A0 is the sum of the corrected activity [Bq] in each voxel of the slice and is the mass of

the tissue slice, assuming that the density of the tumor is the same as for water. The factor,

represents mean energy emitted per 211At [Joule/number of decays] and this

energy is only for the α-particles. Note that the contribution from photons and electrons is

assumed negligible. Ainj is the injected activity which was 5.41 MBq.

The mean absorbed dose rate calculated this way, was compared with the calculated mean

absorbed dose rate using the VDK-method.

Validation of the method

The Monte Carlo program had previously been tested in several ways. One was to compare

the analytically solved mean chord length of traversals of a centric inner sphere of tracks

originating from an outside sphere [10] with that given by the Monte Carlo calculations.

Another was to calculate the mean absorbed dose to a larger volume and compare it with

that found from a large number of individual hits.

The mean absorbed dose was also compared with previously measured data from a

biodistribution study, this for further confirmation that the code works.

20

The resulting kernel was controlled so that the values were symmetrically distributed.

The energy distribution was verified by using the kernel on a 3D-image consisting of just one

decay occuring at the centre of the 3D-image. In this way, the energy distribution of this

single decay can be observed in all slices. The 3D-image was constructed from 12 slices and

the seventh slice was chosen to be the central one. When the image was processed with the

kernel, the distribution from the single decay was observed. The decay should be isotropic

and therefore spread symmetrically around the central axes. This could be verified by

observing the next adjacent slice (sixth or eighth); the central voxel value must have the

same value as the value adjacent to the central voxel value at the central slice. The central

voxel value of the fourth slice should have the same value as the adjacent central voxel in

the fifth slice, and so on.

Results A general description of the code is given in the appendix. The general code is self-

explanatory by the inserted comments. The code begins by importing the images (the

images must be registered in beforehand), and then a 3D image is created. The activity and

the cumulative activity for the entire image stack are calculated. Then the mean absorbed

dose rate is calculated for the unprocessed central image. Volume, density and mass are also

calculated for the central slice. The code performs a Monte Carlo simulation and thus a

corresponded kernel is created. The voxel size, step length and number of simulated

particles can be chosen. Then the image is processed with the kernel. Mean absorbed dose

rate for the center image is calculated. The code saves the processed image into a text-file,

which can then be used for plotting various graphs.

The results are shown in the command window. A figure is also plotted, see Figure 6 and 7.

Figure 6 shows the various results produced by the code. Figure 7 shows an example of what

the code plots from the results; the first sub-image labeled at top, illustrates the dose

distribution for the calculated image slice, the second sub-image at lower left shows the

unprocessed image, and the sub-image at lower right shows the energy-distribution image

for the central section of the image stack, i.e. in this case, the seventh slice.

21

Figure 7. An example of the figure that the code generates. The image at top shows the distribution of the dose, lower left is an example of an unprocessed image, the lower right image is the corresponded energy distribution image.

Figure 6. Results from the code, which are shown on the command window.

22

The kernel is visualized in figure 8. The first image visualizes the kernel in voxel-level, the

energy distribution is voxel-divided. The second image shows how the kernel looks like

without being voxel divided, i.e. a continuous energy distribution. The third image is a

combination of the two.

Figure 8. Visualization of the kernel in various ways. The first is voxel-divided, the second is a continuous image and the

third is a combination of the two images.

The results of the dose distribution and the dose rates for both series are presented in Figure

9 and 10. The figures contain four sub images each, the first in the figure at the top left

shows the central section, unprocessed, i.e. an activity image. The second image at the top

right is the scattered energy image of the center slice. The figure at the bottom left shows

the distribution of voxel values, dose rate relative to the mean dose rate for the center slice.

The image on the bottom right is a DVH-histogram showing how much of the tumor [%] that

receives a certain relative dose rate [%], relative to the mean absorbed dose rate.

The mean absorbed dose rate for the central section of the Series 1 was 0.0814 mGy/s/MBq

and 0.1005 mGy/s/MBq for Series 2. The calculated mean absorbed dose without using the

VDK-method was calculated to 0.1052 mGy/s/MBq for serie 1 and 0.1267 mGy/s/MBq for

serie 2 of the images.

23

Figure 9. Results for serie 1 images. a)Activity image on seventh slice, b) Energy spread image, c)Dose distribution relative to mean dose rate, d)DVH-histogram showing the dose distribution within the tumor.

24

Results of the validation

The calculated mean absorbed dose rates; 0.0814 and 0.1005 mGy/s/MBq at the time of

4.51 hpi is close to the value that was calculated from the biodistribution study, see fig 11.

By looking at the values in the adjacent kernel slice, the central value in the adjacent section

is similar to the values just next to the central value in the central kernel. The energy spread

is symmetrically distributed around the central axes. See figure 12.

Figure 10 .Results for serie 1 images. a)Activity image on seventh slice, b) Energy spread image, c)Dose distribution relative to mean dose rate, d)DVH-histogram showing the dose distribution within the tumor.

25

Figure 11. The mean absorbed dose rate in tumor after injection of 211

At -MX35-F(ab’)2 plotted as a function of time after injection. The dotted curve represents a polynomial fit of the plotted data. Results of Series 1 and Series 2 are also

included and these are very similar to the results from the biodistribution study (blue dots).

-

0,020

0,040

0,060

0,080

0,100

0,120

0 50000 100000 150000 200000

Ab

sorb

ed

do

se r

ate

(m

Gy .

s-1

. MB

q-1

)

Time after injection (s)

Dose rate per MBq (mGy s-1 MBq-1)

y = a(x^b) * exp(cx)

Serie 1

Serie 2

26

Figure 12. Energy deposition is isotropic. The yellow highlighted elements should be similar.

Discussion The central section of the 12 image slices is not the chosen seventh slice. A central slice

would lie between the sixth and seventh slice. It should not matter which of these 2 slices

we choose as the central section, since the contributions from the sections furthest away

hardly contributes to these slices. Therefore, we do not expect a large difference in results

between using the sixth or the seventh slice.

From the dose-histograms, we see that a large amount of the voxels had a very low dose-

rate compared to the mean absorbed dose rate, and therefore a large volume of the tumor

should receive relatively low dose rates. As revealed in the DVH-diagrams, the distribution of

the dose was not homogeneous. A large part, about 80% of the tumor volume receives a

relatively low dose, approximately 60% of the mean absorbed dose. This result tells us that

there is a risk of insufficient cell kill for a population of the tumor cells, due to low absorbed

radiation dose.

27

The registration of the images might have been better if another registration method was

chosen, e.g. a non-rigid method. The series 2 was taken at a later time than series 1,

meaning that those tissue slices contained less radioactivity, which in turn influence the

registration procedure. Certain contours and anatomical formations, used in the registration,

can be seen more clearly when the images contain more radioactivity.

Furthermore, there was a missing section in the serie. True contribution from this slice could

therefore not be accounted for. This lacking slice could also contain important information

on trends in the images and aid in the progress of registration. Instead, we assumed a

distribution and interpolated an image based on the two adjacent slices. This way, we could

account for an assumed contribution of energy from this missing section. Obviously, the real

missing image could contain more or less activity which would impact the other slices.

Another problem is that experimental information about the anatomy and trends were

missing.

The images were corrected for background, i.e. electronic noise mainly due to heating in the

detector. The images in this study were acquired with three different Alpha Camera systems,

each having different calibration factors converting pixel intensity to number of decays.

However, in this study we derived a unique calibration factor for each imaged section, by

measuring each section for activity in a gamma counter after imaging.

The voxels were limited in geometry, i.e. could only be cubic, because they could only then

fit into the coordinate system of the simulation kernel. Future work may include

modifications so that other geometries can be used. The code can also be further developed,

for example by directly generating DVH-histograms which can save the user time. Other

features can also be further developed, for example, choice of radionuclide.

The voxel size does matter, a voxel with a 12x12x12 um size was chosen because it matched

both the thickness of the imaged tissue sections, i.e. 12 um, and also the picture scale (each

pixel in the acquired images corresponded to an actual distance of 12 m in the tissue). If

the voxel size changes, e.g. increases the “resolution” of the dosimetry would be less good

A large voxel size is not desirable in alpha particle dosimetry.

The step length at the Monte Carlo simulation was changed during the study, we changed

the step length to 0.01 µm, and simulated 50 million particles, but the results were about

the same, the energy distribution became a bit finer, but it took about 5 days for the code to

execute, compared for 1 million particles simulated with 1 µm step length, which took about

150 seconds. Due to the simulation time, we decided to present the results for 1 µm step

length with 1 million particles simulated.

At the validation of the kernel, we saw that it was distributed as we expected, i.e.

homogeneously. It might be expected that the highest values of the kernel should occur at

28

some distance, corresponding to the Bragg Peak from the origin of the alpha particles. This

is, however, not the case, since millions of particles were simulated in different directions,

and since the distribution is isotropic, the result will be a larger average deposition of energy

closer to the origin. This was also was noticed during the validation.

The Imfilter function was run with "zero-padding" option, since this situation was assumed

to be valid for our images of subcutaneous tumors. If we had used other images where the

tumor tissue overlapped with other tissue, it had not been easy to choose the boundary

options. One had instead been forced to assume any value outside the tumor. That could

introduce errors due to boundary effects.

Since the alpha particles have such short ranges and high LET, and the absorbed dose levels

in TAT can be the result of only a few events, the dose distribution can become very non-

uniform. The VDK-method, used at a suitable voxel level, is one strategy to perform small-

scale dosimetry. In our case with 211At, the contribution from electrons and photons was

almost negligible, in comparison to the dose from the alpha particles. In this study, we

compared the mean absorbed dose rate obtained from the energy distribution image of the

central tumor slice (VDK-method), with that of the unprocessed original image. It is

interesting to compare these because the VDK-method also takes into account the

contributions from the surrounding tissues while the mean absorbed dose from the original

image assumes that all energy was deposited within the central the slice. We see this clearly

in the results; the mean absorbed dose rate with the VDK-method for series 1 was 0.0814

mGy/s/MBq which can be compared with the calculated mean absorbed dose without the

VDK-method, 0.1052 mGy/s/MBq.

The calculated mean absorbed dose rates using the VDK method was found to be

comparable to the dose rates estimated from a previous biodistribution study of the same

tumor model. Although this can be seen as an indirect validation, a more formal validation is

indeed needed. This will be one of the important steps for the future work with this method.

Other important steps will be to relate morphological structures in the image to the dose

distribution variations. This can provide further insight about the biological effects of alpha

particles in TAT.

29

Conclusion In this study, we have shown that small-scale dosimetry based on experimental data was

feasible and relevant, revealing important information on variations in absorbed dose on a

near-cellular scale. This was achieved by Alpha Camera imaging of serial tissue sections, in

combination with microdosimetry simulations. After being complemented with necessary

validations, we believe that this image-based small-scale dosimetry will help to improve the

understanding and development of targeted alpha therapy.

30

References 1. Andersson, H., et al., Intraperitoneal alpha particle radioimmunotherapy of ovarian

cancer patients: pharmacokinetics and dosimetry of (211)At-MX35 F(ab’)2—a phase I study. J Nucl Med, 2009. 50(7): p.1153-60.

2. Bäck T, Jacobsson L. The Alpha-Camera: A Quantitative Digital Autoradiography Technique Using a Charge-Coupled Device for Ex Vivo High-Resolution Bioimaging of {alpha}-Particles. J Nucl Med. Sep 16 2010.

3. Jönsson P: MATLAB-beräkningar inom teknik och naturvetenskap-med symbolisk matematik. Art nr 31130, ISBN 978-91-44-01780 Upplaga 2:3, Studentlitteratur 2004, 2006.

4. The Matworks, Inc:Image Proceccing Toolbox 5 User’s Guide, ©Copyright 1993-2005, Octboder 2004.

5. A. C. Traino, S. Marcatili, C. Avigo, M. Sollini, P. A. Erba, and G. Mariani: Dosimetry for nonuniform activity distributions: A method for the calculation of 3D absorbed-dose distribution without the use of voxel S-values, point kernels, or Monte Carlo simulations. Med. Phys. 40, 042505 (2013);

6. Lidia Strigari, Enrico Menghi, Marco D’Andrea, and Marcello Benassi: Monte Carlo dose voxel kernel calculations of beta-emitting and Auger-emitting radionuclides for internal dosimetry: A comparison between EGSnrcMP and EGS4. Med Phys. 2006 Sep;33(9):3383-9.

7. Zaidi and Sgouros - Therapeutic Applications of Monte Carlo Calculations in Nuclear Medicine H. Zaidi (Editor), G Sgouros (Editor) Institute of Physics, Taylor and Francis, UK, 2002.

8. Bäck T, Andersson H, Divgi CR, Hultborn R, Jensen H, Lindegren S, Palm S, Jacobsson

L. 211At radioimmunotherapy of subcutaneous human ovarian cancer xenografts:

evaluation of relative biologic effectiveness of an alpha-emitter in vivo. J Nucl Med.

Dec 2005;46(12):2061-2067

9. Stopping Powers and Ranges for Protons and Alpha Particles.Publication 49.

Bethesda, MD: International Commission on Radiation Units and Measurements; 1993.

10. Humm JL., A microdosimetric model of astatine-211 labeled antibodies for radioimmunotherapy. Int J Radiat Oncol Biol Phys. 1987 Nov;13(11):1767-73.

31

Appendix

General code %Calculates the absorbed dose from At-211 with sectional images, also the %dose distribution. %Copyright 2013, Stig Palm, Tom Bäck & Besart Rexhaj %E-mail:stig.palm@radfys.gu.se, tom.back@radfys.gu.se,

besartrexhaj@hotmail.com

clear all; format longE %Display format for output values in''long scientific

notation'' tic %Measure time %-------Import image sections----------------------------------------------

------ A1 = imread ('filename of the image'); A2 = imread ('filename of the image'); A3 = imread ('filename of the image'); A4 = imread ('filename of the image'); A5 = imread ('filename of the image'); A6 = imread ('filename of the image'); A7 = imread ('filename of the image'); A8 = imread ('filename of the image'); A9 = imread ('filename of the image'); A10 = imread ('filename of the image'); A11 = imread ('filename of the image'); A12 = imread ('filename of the image');

%--Convert to double precision, needed for image manipulating--

A1=double(A1); A2=double(A2); A3=double(A3); A4=double(A4); A5=double(A5); A6=double(A6); A7=double(A7); A8=double(A8); A9=double(A9); A10=double(A10); A11=double(A11); A12=double(A12);

%------------From TPI value to Bqs (number of decays)------------- %Use your own calibration factor. (Aktivity/TPI value) A1=A1*'factor'; A2=A2*'factor'; A3=A3*'factor'; A4=A4*'factor'; A5=A5*'factor'; A6=A6*'factor'; A7=A7*'factor'; A8=A8*'factor'; A9=A9*'factor'; A10=A10*'factor'; A11=A11*'factor'; A12=A12*'factor';

32

%--------------Make into a multidimensional array--------------------------

-

A=cat(3,A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11,A12);

%------------The sum of all the matrix values gives cumulated activity-----

B = sum(sum(sum(A7))); Btot=B/6600; %From Bqs to Bq.

%------------The sum of all the matrix values gives cumulated activity----- A_7=A7/6600; %Values in slice nr 7 in Bq. x=find(A_7(:)); %Number of elements above 0 in vector form. vx=length(x); %Number of voxels in slice nr 7.

%--------The volume of the central slice (cubic) in m^3 --------- V=(12*10^-6)^3; %12x12x12 um voxel, volume in m^3. m_1=V*1000; %density of water is 1000 kg/m^3 %m1 is the mass of one voxel.

m1 = vx*m_1; % The mass of the tumor in slice nr 7 (kg).

%---------------Calculate the mean absorbed dose rate for the whole

multidimensional array------- D_at_po=(1.02e-12*(B/m1))/6600*1000/5.41376365245306; %Mean absorbed

dose rate. 1.02e-12 is a mean average energyfactor for both alpha particles

disp('Total number of decays (Bqs) in the 3D-image') disp(B) disp('Total activity in the 3D-image (Bq)') disp(Btot) disp('The mass of the tumor in slice nr 7 (kg)') disp(m1) disp('Mean absorbed dose from At-211 in mGy/s/MBq (unprocessed image)') disp(D_at_po)

%-If you would like to have the 3D matrix as a text file. Opens with Excel- %dlmwrite('3Dmatris.txt',A,'\t');

%-------------Monte Carlo simulation of a multidimensional kernel---------- rng shuffle %Random clock.

%Input for the kernel v='voxel size';%(input a number); %Enter the size of the voxel, for

example 12x12x12 then enter the number 12, (v = 12) um='step length'; %Type in the desired step length in

um. %1=um, simulation step is i 1 um. %10=um, simulation step is in 0,1 um. %100=um, simulation step is in 0,01 um. w=ceil((142/v)+1); %Rounds to the nearest whole number up. For the

matrix that will fit in the original coordinate system.

noe = 1000000; % Number of particles simulated (decays) l = 0; k = 0; H = zeros(w,w,w); % Defines the array, zero in all elements

33

for a = 0:noe xo = rand()*v - (v/2); % Puts randomly in VxVxV um inner cell yo = rand()*v - (v/2); % homogeneously distributed. zo = rand()*v - (v/2); phi = 2*pi*rand(); % Randomizing initial direction for alpha theta = acos(1-2*rand()); ab = rand(); % Test for Po or At branching decay

if ab < 0.583 % Po branching fraction decay k = k+1; % Counter, test for Po branching decay for b = 1:(72*um) % step up to 72 um.

x = xo + (b/um)*sin(theta)*cos(phi); % 1 um at a time y = yo + (b/um)*sin(theta)*sin(phi); % Maintain the same

direction z = zo + (b/um)*cos(theta); m = (b/um);

po_energy = (0.079202831114 - 0.013487426752*m +

0.0043324922135*m^2 - 0.00060194480247*m^3 +... 4.4612300977e-05*m^4 - 1.9145593371e-06*m^5 + 4.9069434535e-

08*m^6 -... 7.3981665427e-10*m^7 + 6.0466212661e-12*m^8 - 2.0646549817e-

14*m^9) * 1.0; % MeV per um, 9 degree polynomial, a describing of the

stoppin power for Po.

if po_energy < 0; % Erases negative stopping power values

??if they exist. po_energy = 0; end %---Placement to respective voxel------------------------------ voxelx = floor(((w*v/2)+x)/v + 1); % x-voxel from 1 to w; v um

width, floor = rounded voxely = floor(((w*v/2)+y)/v + 1); % y-voxel from 1 to w; v um

width voxelz = floor(((w*v/2)+z)/v + 1); % z-voxel from 1 to w; v um

width H(voxelx, voxely, voxelz) = H(voxelx, voxely, voxelz) +

po_energy; %MeV deposited in the last 1 um track length. end %-------The same for At branching decay------- else l = l + 1; % Counter, test for At branching decay

for b = 1:(50*um) % Step up to 50 um

x = xo + (b/um)*sin(theta)*cos(phi); % Maintain the same

direction y = yo + (b/um)*sin(theta)*sin(phi); z = zo + (b/um)*cos(theta); n = (b/um);

at_energy = (0.069799772772 + 0.011434492859*n -

0.0040772931278*n^2 + 0.00070220775416*n^3 -... 6.3643167323e-05*n^4 + 3.2776709344e-06*n^5 - 9.7634472878e-

08*n^6 +... 1.6246132894e-09*n^7 - 1.3371049389e-11*n^8 + 3.7740449708e-

14*n^9) * 1.0; % MeV per um

34

if at_energy < 0; % Erases negative stopping power values

??if they exist. at_energy = 0; end

voxelx = floor(((w*v/2)+x)/v + 1); % x-voxel from 1 to w; v um

width, floor = avrundat voxely = floor(((w*v/2)+y)/v + 1); % y-voxel from 1 to w; v um

width voxelz = floor(((w*v/2)+z)/v + 1); % z-voxel from 1 to w; v um

width H(voxelx, voxely, voxelz) = H(voxelx, voxely, voxelz) +

at_energy; % MeV deposited in the last 1 um track length. end end end I = sum(sum(sum(H))); %The sum of the energy

deposition fprintf('number of events = %u\n', noe) fprintf('Po decay = %u\n', k) fprintf('At decay = %u\n', l) fprintf('SumA = %8.4f\n', I)

%--If you would like to have the kernel as a text file, open with Excel---- %dlmwrite('energimatris.txt',H,'\t');

%------------------------Kernel values from MeV to mGy/s/MBq---------------

----

V1=(v*10^-6)^3; %12x12x12 um voxel, volume in m^3. m12=V1*1000; %density of water is 1000 kg/m^3

H=((H*1.6022e-13/m12)/6600*1000)/5.41376365245306; %From MeV to mGy/s/MBq.

%-----Spread the energy from the multidimensional array with the kernel---- G=H/1000000; %Normalization of the kernel to one decay. C = imfilter(A,G,'corr'); %A type of 3D-convolution, The multidimensional

array(A) with the multidimensional kernel (G) %Zero-padding and correlation as default.

C(C==0)=NaN; %Replace all "0" to NaN. Cmean=nanmean(nanmean(nanmean('central slice'))); %Mean absorbed dose rate Cmax=nanmax(nanmax(nanmax('central slice'))); Cmin=nanmin(nanmin(nanmin('central slice'))); Ccent='central slice'; B2=Ccent(:); %Convert from matrix to vector B2=B2/Cmean; %Relate the dose rate to mean dose rate.

disp('Step length used for kernel simulation (um)') disp(um)

disp('Voxel dimensions V x V x V (um)') disp(v)

disp('The mass of the cubic voxel (kg)') disp(m12)

disp('Mean absorbed dose rate in central section in mGy/s/MBq. (processed

image)')

35

disp(Cmean)

disp('Max absorbed dose rate in central section in mGy/s/MBq.') disp(Cmax)

disp('Min absorbed dose rate in central section in mGy/s/MBq.') disp(Cmin)

Cimage=mat2gray(Ccent); %From matrix to grayscale image. Cuimage=mat2gray(A7); subplot(2,2,1:2), hist(B2,20) %Plot histogram of the dose distribution. title('Data for the slice labeled at the center of the image stack') xlabel('Dose rate relative to mean absorbed dose rate') %Normalized to the

max dose rate. ylabel('Number of voxels') subplot(2,2,3), imshow(Cuimage) title('Activity image (Unproccecced image)') subplot(2,2,4), imshow(Cimage) title('Energy spread image')

dlmwrite('energymatris.txt','central slice','\t'); %proccessed central

image saved as a text file. %disp('Proccessed image values in mGy/s /MBq') toc