monte carlo photon transport in matlab

Here is an outline of steps to perform Monte Carlo simulation of photon transport in MATLAB:

  1. Define the geometric model of the tissue and the photon source. This can be done using simple primitives such as spheres, cylinders, or more complex shapes defined by a mesh. In addition, you need to specify the optical properties of each material in terms of absorption coefficient, scattering coefficient, and anisotropy factor.
  2. Generate a large number of photon packets and assign them a location and direction randomly in the tissue. The number of packets should be large enough to ensure statistically significant results.
  3. Calculate the probability of each packet undergoing absorption, scattering, or surviving in each tissue voxel based on its optical properties using the Beer-Lambert law and the Mie theory.
  4. Decide the fate of each photon based on the random numbers generated using the Bernoulli-RNG and the Mie theory.
  5. Repeat steps 3-4 until all the photons have been absorbed or have escaped from the tissue.
  6. Calculate the fluence rate, absorption profile, and other relevant parameters of interest based on the outcomes of the simulation.

Here's an example MATLAB code that implements the above steps for a homogeneous tissue model with an isotropic point source:

% Define input parameters
distance_to_center = 1; % in cm
tissue_properties = [0.01 1000 0.9]; % absorption, scattering coef, anisotrpy factor
num_photons = 1e6;

% Define geometry and optical properties of the model
geom = createGeometricModel('sphere','radius',distance_to_center);
tissue = createMedium('non-fluorophore','ScatteringCoefficient',tissue_properties(2),...
                      'AbsorptionCoefficient',tissue_properties(1),'Anisotropy',tissue_properties(3));

% Define input parameters for photon packets
x = 0*ones(num_photons,1); y = 0*ones(num_phots,1); z = distance_to_center*ones(num_photons,1);
direction = rand(num_photons,3); 

% Run Monte Carlo photon transport simulation
while num_photons ~= 0
  % Calculate the probability of interaction for each photon packet
  probs = calculateProbs(geom, tissue, [x y z], direction);
  
  % Sample the fate of each photon packet based on the probabilities
  [absorption,scattering,survival] = sampleFates(probs);
  
  % Update the photon packets' location and direction based on their fate
  [x,y,z,direction] = movePhotons(absorption,scattering,geom,direction,x,y,z);
  
  % Record the number of photons that suffered absorption or exited from the tissue
  absorbed_photons = sum(absorption);
  escaped_photons = sum(survival & (z<0));
  num_photons = num_photons - absorbed_photons - escaped_photons;
  
  % Optional: track the location and fate of each photon packet to visualize the results
  photonHist = [photonHist; [x,y,z,absorption,scattering,survival]];
end 

% Calculate the fluence rate and/or other relevant parameters of interest
fluenceRate = calculateFluence(geom,tissue,photonHist(:,1:3));
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Note that the functions calculateProbs, sampleFates, and movePhotons need to be defined based on the specific model and simulation parameters.

Reference:

  • Wang, L., Jacques, S. L., & Zheng, L. (1995). MCML - Monte Carlo modeling of light transport in multi-layered tissues. Computer methods and programs in biomedicine, 47(2), 131-146.

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