Transport in turbid media

Solving radiative transport in thin systems

Simulated trajectories in a multilayer slab
Simulated trajectories in a multilayer slab

Numerous areas of science employ Monte Carlo (MC) methods to simulate complex processes. Light propagation in random media, often referred to as photon migration, is an area of physics in which such methods are of great importance. Prime examples include radiative transfer in highly scattering materials such as biological tissues, clouds, and pharmaceuticals. There, MC simulation is generally considered the gold standard of modeling and is used to investigate complex systems and processes, to validate simpler models, as well as to evaluate data.

Given the complexity of the radiative transfer equation (RTE) – a widely used analytical model for light diffusion through turbid media – approximations such as the diffusion approximation (DA) are most often used. However these simplifications do not perform equally well in every situation and they have their shortcomings. On the other hand the RTE directly follows from energy conservation. With the computing power available nowadays, it is possible to implement a Monte Carlo method to find exact solutions to the RTE, the only approximation being that the number of simulated photons is finite. This is especially true because this kind of simulations have an inherently parallel nature and so they can leverage nowadays multi-threading CPUs and GPUs.

We have developed a flexible and modular Monte Carlo platform, named MCPlusPlus, that we employ to study light transport in optically thin systems where existing approximations are known to be defective. MCPlusPlus comes with a Python interface that makes it possible to script simulations very easily. Go to the software project page.

Recent work

With the developed software, we performed an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation [1]. We completely characterize the so-called ballistic-to-diffusive transition, notably in terms of the spatial variance of the transmitted/reflected profile. We also test the validity of the prediction cast by diffusion theory, that the spatial variance should grow independently of absorption and, to a first approximation, of the sample thickness and refractive index contrast. Based on a large set of simulated data, we build a freely available look-up table routine allowing reliable and precise determination of the microscopic transport parameters starting from robust observables which are independent of absolute intensity measurements.

In a second work we show that, after a short transient, the mean square width of the transmitted intensity still exhibits a simple linear increase with time as predicted by diffusion theory, even at optical thickness as low as one [2]. Light diffusion is usually associated with thick, opaque media. Nonetheless, at long enough times, transport in an infinite thin slab is still determined by a multiple scattering process whose complete characterization is lacking. Interestingly, the linear growth is predicted not to depend neither on the slab thickness nor on its refractive index contrast, yet the accuracy of this simple approximation in the ballistic-to-diffusive regime hasn't been investigated so far. By means of Monte Carlo simulations, we find clear evidence that boundary conditions play an active role in redefining the very asymptotic value of the diffusion coefficient by directly modifying the statistical distributions underlying light transport in such media. In this respect, we demonstrate the need to distinguish between a set of intrinsic and effective transport parameters, whose relation and interplay with boundary conditions remains to be fully understood.

Diffusion in a scattering medium
Diffusion in a scattering medium

Publications

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