Physics Processes Simulations

Markov Chain Monte Carlo (MCMC)

MCMC: It provides a way to sample from a Bayesian posterior without explicitly calculating its normalization:

P(λ | D) ∝ P(D | λ) · P(λ).

Metropolis–Hastings

MH: is one of the particular MCMC algorithms.

Starting from the current parameter point (\lambda_t), the algorithm proposes a new point (\lambda^*) using a proposal distribution.

q(λ* | λₜ)

What does the simulation show?

The simulation visualizes this process in a two-dimensional parameter space:

Start from an initial parameter point.
Propose a new point near the current position.
Evaluate its relative posterior probability.
Accept or reject the proposal according to the Metropolis–Hastings rule.
Repeat the process many times.
After convergence, the distribution of the samples approximates the target posterior.

Topas is a user-friendly GEANT4 wrapper simulator. It enables a text-based parameter control system for advanced and flexible modelling of physics processes.

Key capabilities:

Models x-ray, proton, and ion therapy treatment heads and nozzles.
Imports patient geometry directly from CT images to score radiation doses and particle fluence.
Supports fully four-dimensional (4D) simulations to account for moving geometry, such as patient breathing during treatment.

Normalized depth-dose distribution comparison in water for Proton (150 MeV), Carbon-12 (300 MeV/u), Helium-4 (150 MeV/u), and Electron (10 MeV) beams, highlighting the characteristic Bragg peaks of heavy charged particles.

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