Development of a Monte Carlo cell model for ionizing radiation

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Development of a Monte Carlo cell model for ionizing
radiation microdosimetric track structure simulations
1,2Michael
Douglass, 1,2Eva Bezak, 2Scott Penfold
1-University of Adelaide – School of Chemistry and Physics
2-Royal Adelaide Hospital – Department of Medical Physics
•  Talk
Outline
• What are we developing?
• Why are we developing it?
• Structure of the Cell
Design in Geant 4
• Ellipsoidal Cell Generation Code
Code Design
Optimization
Code Processing Times
Preliminary Results
• Physics List and the Prediction of Cell Death
• Current Work
• Future Work
• What are we developing?
• 
Physically, chemically and biologically accurate model of a cell
• 
Physically and chemically – Represents realistic interaction of ionization
radiation on microscopic scale
• 
Biologically –Ultimately allow for assessment of individual cell damage
due to ionizing radiation leading to multiple cell death pathways.
• Why are we developing it?
• 
All Previous and most current works assume a cell is
killed only through DSB and SSB in the nucleus
• 
Typical Assumption: 2 Damages within 10 BP will kill the cell
There are many other channels of cell death:
• 
Many pixel based cell death models.
• 
Traditional Models
Voxellised Water Phantom
Voronoi Polygons Cell Representation (M.Partridge et.
al, 2008) –1 Target
• Why are we developing it?
Nucleus – DNA
Damage
Cellular Communication
Nucleolus –
Nucleus
Membrane
Damage
-Cell Death without radiation
damage
-Cells release proteins after
being irradiated which is
received by surrounding cells
(Bystander Effect)
Membrane –
Flow of organic
fluids I/O of cell,
cellular expand
& Burst
Cytoplasm
Damage
Organelles –
Mitochondria
Damage etc.
• What can it be used for?
• 
We wish to better understand how a cell is destroyed by
ionizing radiation for the following purposes (but not
limited to):
• 
• 
• 
• 
Microbeam Therapy
Gold Nano-Particle Therapy
Auger Electron Therapy
Heavy Ion Therapy
We need an accurate cell model to
represent a realistic cell!
Cellular Membrane
• Geant 4 Cellular Model
Elliptical Cells of Various Sizes, shapes and
chemically accurate composition
Endoplasmic Reticulum
Cytoplasm
Nucleolus
Nucleus Size = 2 microns
Membrane Size = 5 nm
Nucleus
Cell Size = 7-30 microns
• Cellular Chemical Composition
Membrane:
44.4% H, 22.2% O, 11.2% Carbon, 22.2% N
Nucleus:
10.6% H, 74.5% O, 9% C, 3% N, 2% P
Cytoplasm:
59% H, 24.2% O, 11.1% C, 4% N, 1% P
“Simulation of ion propagation in the
microbeam line of CENBG using Geant 4”
S.Incerti et. al. 2003
• Cell Structure !Cell Matrix
• 
• 
We have developed a physically and chemically realistic cell in
Geant4
We now need a cell distribution
• 
• 
Large distribution of randomized ellipsoidal cells in
space, size and rotation to form a macroscopic tumor
structure
~109 Cells
We need an algorithm to randomly place
ellipsoid cells in a volume without
overlapping
• Ellipsoidal Cell Distribution Code
• 
Ellipsoidal Cells Positions, Rotations and Sizes Randomized
• 
Internal components of cell arranged based on outer cell (membrane)
geometry
• 
We have developed an efficient algorithm for placing randomized
microscopic ellipsoidal cells to form a macroscopic tumor phantom.
• 
Biggest Challenge
• 
Randomly Distributing Ellipsoidal Cells without Overlap
• 
Minimizing Processing Time (Checking 109 Cells)
• 
Minimizing RAM Usage (9 Properties with 109 Cells) – Huge Matrix!
•  Preliminary
1
2
Code Structure
• Randomises Cell Position, Size and Rotation to Fill a
Box of Specified Size
• Begins Check for Intersection
3
• If Cells are separated by more than the sum of the
semi major axes then cell checking ceases
4
• If cell centres are within this distance, overlapping is
determined by an eigenvalue method
5
• If cells are overlapping then that cell is deleted
Future Work: When Cell deleted, Re-Randomise Cell
-Extra Processing Times
•  Eigenvalue
• 
Solution – 4D Matrix
Aerospace Based Collision Detection– (A Simple Mathematical Approach for Determining Intersection of
Quadratic Surfaces, Chan et. al, 2001)
Ellipsoid Centered at Origin
Rotation Matrices
Translated Ellipsoid – General Form
Final Matrices
Solve Eigenvalue Problem
•  Eigenvalue
Separated
Solution – 3 Cases
Touching
Two Acceptable Cases
Delete in all other cases
Overlap
•  Final
• 
Result
Randomized Cell Geometry
Cells are Individual Entities
• 
• 
• 
No two ellipsoids overlap
Each ellipsoidal cell contains
full cell structure with accurate
chemical materials
Cells surrounded by water
Box is Filled with Cells
•  Problems
• 
Encountered:
We are trying to simulate a
tumor composed of individual
cells
• 
• 
• 
We need a large number of cells
(~109 Cells for a 1x1x1 cm3 tumor)
!Large processing times and large
amounts of RAM required
!Optimize to obtain reasonable
processing times (~1-5 days)
•  Optimization
• 
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• 
• 
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• 
• 
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• 
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• 
<B(7M(]]@[(@NH(
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•  Optimization
• 
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^&%P1:$Y(
• 
_-'$%(5&'$-12(+'&:-,%&:(%1('&`#-'&((a)CCC(F&/'$(!!1#":(P/5&(M&&2(/(5&'F("12T(QP]b(
• 
_#'%P&'(1+0^-$/012(M'1#TP%(%P-$(:1S2(%1(IC(:/F$(3(Q/'/""&"(Q'1,&$$-2T(/2:(Q'&c
/""1,/012(1W(/''/F$(-2(@NH(
• 
J1S('#2$(-2(#2:&'(<B(P1#'$(dZ)CI(,&""$(-2(/()L)L)(,^[(M1Le(3(*"-,&:(f1"#^&(
• 
82,'&/$&$(%1([(:/F$(W1'(/([L[L[(,^[(M1L(
•  Optimization
• 
• 
– Slicing of Cells into Layers
@/%P&'(%P/2(,P&,A-2T(&/,P(,&""(/T/-2$%(%P&('&^/-2-2T(,&""$g($+"-%(-2%1("/F&'$(
hL+12&20/"(]&,'&/$&(-2(Q'1,&$$-2T(>-^&(
•  Optimization
Number of Cells vs Processing Time (seconds) - For Slice thickness
1 cm - 0.001 cm
Processing Time (Seconds)
1E+09
Slice Thickness = 1 cm
Slice Thickness = 0.5 cm
Slice Thickness = 0.2 cm
Slice Thickness = 0.1 cm
1000000
Slice Thickness = 0.02 cm
Slice Thickness = 0.01
100000
Slice Thickness = 0.001 cm
100000000
10000000
10000
1000
100
19 Hours
10
1
10000
0.1
100000
1000000
10000000
100000000
1E+09
Number of Cells (Total = # of Cells/Slices x # of Slices)
Exponential Decrease in Processing Time
Should be an optimal number of slices: More boundary checking
• 
• 
• 
• 
Randomized Geometry –
Last Slice: 445,000 Cells - Total # of Cells = 445 x 106 Cells
Cell Major Axes between 7 – 30 microns
•  Geant4
– Cell Code
• 
7&/2%(B(@&/:$(-2(!*f(_-"&(S-%P(ig(jg(k(Q1$-012g(H/l1'(NL&$(Ng(Gg(!(/2:(@1%/012$(mg(
ng(o(
• 
>P&$&(Q'1+&'0&$(W1'^(%P&(p#%&'(H&^M'/2&(K/F&'(
• 
N""(82%&'2/"(*%'#,%#'&$($,/"&:(MF(H&^M'/2&(Q'1+&'0&$Y(!F%1+"/$^g(J#,"&#$g(
J#,"&1"#$g(h2:1+"/$^-,(@&0,#"#^(
• 
N""(!&""#"/'(!1^+12&2%$(!12%/-2(!P&^-,/""F(N,,#'/%&(H/%&'-/"$(
• 
!&""$(*#''1#2:&:(MF(q/%&'(H&:-#^(
• 
_-'&(7/^^/$g(h"&,%'12$g(Q'1%12$(/2:(E&/5F(812$(
•  Sample
Result
Randomized Cell Geometry
Geant 4 Visualization Example – 1x1x1 cm3 3x107 Cells
•  Example: Firing Alpha Particles into Cells
• 
• 
• 
• 
Randomized Cell Geometry in air
1 MeV Alpha Particles
Score Ionization Event Histories from Radiation
Predict Cell Death
Blue: Position of ionization events
from alpha particles in cells
•  Predict
Cell Death
In order to predict cell death we need to simulate ionization events to
small scales (<10 nm)
Geant 4 has several physics lists available for photon, electron, proton
and alpha particles at low energy.
Information Output:
• 
• 
• 
What Particle? (photon, electron etc.), Event Type? (Ionization, photo effect), Which Cell?
(Cell copy #), Where in the cell? (Membrane etc.)
• 
• 
Electrons
• 
• 
• 
• 
Photons
• 
• 
• 
Livermore
Penelope
DNA
Livermore
Penelope
Protons
• 
• 
Low Energy
DNA
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/data/G4EMLOW6.19/dna
/data/G4EMLOW6.19/phot
/data/G4EMLOW6.19/penelope
/data/G4EMLOW6.19/ioni
/01#&-2#)$&'33)3#$%+'(3)4'&)567&'2#()-(7)8-%#&9)
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Livermore >100 eV
)
Penelope > 250 eV
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(%[email protected],+.
DNA > 11
0111111
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!(#&26)/#:9)
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•  What's
Next?
• 
Extrapolate or add new cross sections to allow simulation to 0.1 nm
• 
Once ionizations can be recorded on a DNA level! Develop Cellular
model to simulate cell death due to radiation damage via different
processes
• 
Estimate how many cells will die
• 
Starting to confirm simulation results using a alpha emitting radioisotope
(Thorium 227) with cellular spheroids
•  Future
• 
Work
We can vary composition and therefore model cellular
hypoxia
• 
Introduce Free Radical Formation and Cellular
Communication into a program which will predict the
various methods of cell death
• 
Gold Nano Particles in Cellular Membrane
Thank you for your Attention
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