LCSC - 01 Monte Carlo Simulation of Radiation Transport, for Stereotactic Radio Surgery Per Kjäll Elekta Instrument AB

LCSC - 01 Agenda:Background Leksell GammaKnife Monte-Carlo Simulation Parallel approaches

LCSC - 01 Photon tracks

LCSC - 01

(the dose at any point in  V)  E = Expectation Value of energy imparted in the volume  V  m = Mass in the volume  V The dose is distributed and deposited by the electrons Definition of Dose D =  E/  m [Gy  J/kg]

LCSC - 01 Thermal effect: A dose of 10 Gy absorbed in tissue is equivalent to a temperature increase of approximately degrees C The effects of Radiation Clinical effect: LD50 for whole body irradiation is 10 Gy.

LCSC - 01 Direct Action Path lengths for electrons in the range MeV in water is mm - 4 mm. diameter of a cell  0.01 mm diameter of cell nucleus  mm Action must occur within the DNA. Increased dose = increased likelihood of interaction with the DNA. LET = Linear Energy Transfer

LCSC - 01 Order of Events 1. Diagnosis 2. Acquiring diagnostical/anatomical images 3. Determining the required dose 4. Simulation of dose delivery 5. Dose delivery 6. Dose verification

LCSC - 01 Simulation of dose delivery (Measurement in vivo is difficult/impossible) Models Empirical / Semiempirical / Phenomenological Analytical Stochastic simulation Accuracy = f( time, clinical information needed, clinical reality, …)

LCSC - 01 Ideal situation after dose delivery

LCSC - 01 Real situation

LCSC - 01 Strategies: I A few, highly shaped (dynamical) beams

LCSC - 01 Strategies: II Multiple, narrow, converging simple beams

LCSC - 01 Total Accuracy Discrepancy dependent on Positioning / movement Radiation delivery Equipment (status) Simulation of treatment Clinical data Radiation modality used

LCSC - 01 The Clinical Balance Tumourcidal Effect Damage to healthy tissue

LCSC - 01 Leksell Gamma Knife

LCSC - 01 Leksell Gamma Knife Helmet supports Automatic Positioning System Treatment couch with mattress Protection panels Shielding doors Shielding Helmet with collimators Helmet in treatment position Cobalt-60 sources Beam channel Plastic cover

LCSC - 01 Leksell Gamma Knife

LCSC narrow beams intersecting in one point Patient rigidly (invasively) fixed to the treatment unit Sources (Co-60) fixed, i.e. not moving. 4 different collimators (helmets): 4,8,14 & 18 mm

LCSC - 01

Dose Simulation (revisited) Dose is a function of: Tissue in, and around, the beam path and the target Location of target Type of radiation (spectrum) Intensity Irradiation Time Ideal Simulation Characteristics: Fast, accurate, simple and requiring a minimum of clinical data.

LCSC - 01 Monte Carlo Simulation The tracks are stocastically generated: i.e.the path lengths, the types and the details of the interactions undergone are all sampled from the physical models (distributions) describing these interactions. One history is the sum total of all effects caused by one photon; such as generation of secondary particles and their energy deposition. A “good” random number generator is needed. My PC: 250 histories/s Real source: photons/s

LCSC - 01 Random Number Generators, some remarks Or, rather “Pseudo” Random Number Generators, since the computer algorithms generating the sequences are strictly deterministic. The same seed will genrate the same sequence of “random” numbers. An important “quality” of a Generator is a small correlation between the values in the sequence. Two radiation transport runs with the same seeds and the same number of particles will produce two sets of identical histories. The sequence of numbers generated by a random number generator is periodic. The longer the period, the better. For example, the RAND-function in FORTRAN 77 produces 32-bit floating point numbers uniformly distributed between 0 and 1, and with a period of the order of Running the random number generator through a sequence longer than its period will duplicate histories. No new information is obtained.

LCSC - 01 What will we use MCS for? Treatment planning Radiation protection/safety Dose to other parts of the body (radiation milieu) Design of effective beam shaping “Dynamical” dose delivery

LCSC - 01 Treatment Planning Phase-space information: Energy, direction, type, history

LCSC - 01 Treatment Planning And then some numbers: Loading the phase space file with 10 million particles per channel (100 days on my PC !), and using 28 bytes per particle, results in a phase space file of approx GB. The clinical data set (MR / Voxels): 100 slices x 0.5MB/slice => 50 MB. “Releasing” the particles in the phase space file is estimated to require approx. 100 days on my PC. Desired calculation time …. 1 second/shot !

LCSC - 01 Design of effective beam shaping Requirement: A final dose distribution with a set of desired characteristics. Approx. Calculation time on my PC is 3 weeks. Size of data set, < 50 MB.

LCSC - 01 Radiation milieu Phase space surfaces Effects due to changes to shielding? Dose to various parts of the body ? Data set size can be huge! Calc. time,..,?

LCSC - 01 Parallel computation Random number generators for parallel computation (the Leapfrog Method). Cluster architecture: Using available PC-network Dedicated cluster Buying computer time (NSC)