Monte Carlo Photon Transport in a Tissue Slab

A Monte Carlo photon-transport playground. Photons normally incident on a water slab are followed history by history: a free path is sampled as $-\ln(U)/\mu$, the interaction type is drawn from the photoelectric, Compton and Rayleigh cross sections, Compton scattering is sampled from the Klein-Nishina distribution by Kahn's method, and the released electron energy is deposited over a forward CSDA range, which produces the depth-dose build-up before the exponential falloff. Panel A shows the photon histories coloured by interaction type, Panel B the depth dose and the 2D dose map, Panel C the interaction fractions versus energy and the energy balance. The sampled mean free path follows $1/\mu$, the photoelectric-to-Compton dominance crosses over with energy, energy is conserved history by history, and the depth dose shows the build-up before the Beer-Lambert falloff.

Figure 1. Monoenergetic photons enter a water slab and are tracked by Monte Carlo: each is transported a sampled free path 1/mu, then absorbed (photoelectric), Compton-scattered or Rayleigh-scattered by the energy-dependent cross sections. The released electrons deposit dose a short distance forward, giving the characteristic build-up before the exponential falloff. Method: seeded Monte Carlo with Klein-Nishina Compton sampling; Canvas2D, deterministic.

photon energy (keV)1000

slab thickness (cm)15

histories (x1000)8

WHAT TO TRY

Raise the photon energy: the interaction mix shifts from photoelectric (steep low-energy) toward Compton, the attenuation coefficient mu drops, and photons penetrate deeper into the slab.
Thicken the slab: more histories deposit their energy inside and the transmitted fraction falls. The depth-dose curve shows the buildup then exponential attenuation.
Add histories (x1000): the depth-dose curve and the interaction-fraction estimates get smoother, the 1/sqrt(N) convergence that is the cost of Monte Carlo transport.