5. Conclusions

Figures 5 and 6 show that our new importance sampling technique reduces the computational cost for obtaining the Class I diffuse reflectance by approximately three orders of magnitude when compared to the standard Monte Carlo method. This algorithm is optimum when the additional bias probability is equal to p = 0.5. Since only half of the back-scatterings are biased, this choice contributes toward enabling an optimum number of Class II photons to be collected by the tip of the

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

We note that the results obtained with the MCML have confidence intervals that are noticeably larger than those of the results obtained with importance sampling shown in Figure 6, even though the standard Monte Carlo simulations have a computational cost 113 times larger than those obtained with importance sampling. In Figure 6, we also note that our importance sampling technique reduces the computational cost of calculating the Class II reflectance by more than two orders of

In Figure 7 we show the relationship between the relative error in calculating Class I and the Class II reflectances at two different depths: 400 and 670 μm and the bias coefficient a for p = 0.5. The depths at 400 and 670 μm correspond to tissue regions near the second and third regions with high local reflectance due to the higher local scattering coefficient. The relative variation in the results is the ratio between the square root of the variance, shown in Eq. (4), and the reflectance

We note that Class I reflectance has a minimum relative error at 400 μm with a = 0.925, but the minimum error at 670 μm occurs at a = 0.95 μm at 670 μm. The deeper the tissue region, the stronger the required bias because of the increase in the number of scatterings with the depth. However, as the bias coefficient is increased toward 1, larger variations in the likelihood ratio lead to an increase in the relative error. We also note that Class II reflectance has its minimum relative error at 400 μm with a = 0.91, while its minimum relative error at 670 μm increased to only about a = 0.925 μm. The optimum amount of bias required by the Classs II diffusive

reflectance in both wavelengths is lower than the optimum bias coefficient

The relative error in calculated reflectance using importance sampling as a function of bias coefficient a.

Reprinted with permission from [15] © The Optical Society of America.

observed in the Class I reflectance because the number of ballistic and quasi-ballistic photons increases with the bias, which leads to a decrease in the number of collected photon packets that undergo multiple scatterings. Figure 7 also shows that there is a range for the bias parameter a between 0.9 and 0.95 that enables fast calculation of

optical fiber.

magnitude.

in Eq. (3).

Figure 7.

14

We described two importance sampling techniques for a standard Monte Carlo (MC) method that could enable fast simulation of signals from optical coherence tomography (OCT) imaging systems. These OCT signals are generated due to diffusive reflections from either multilayered or arbitrarily shaped, turbid media, for example, tissue. Such signals typically consist of ballistic and quasi-ballistic components, of scattered photons inside the medium, in addition to photons that undergo multiple scattering. We showed that MC simulation of these OCT signals using our importance sampling reduced its computation time on a serial processor by up to three orders of magnitude compared to its corresponding standard implementation. Therefore, our importance sampling techniques enable practical simulation of OCT B-scans of turbid media, for example, tissue, using commonly available workstations.
