A novel Monte-Carlo based method of calculating mean transit time through voxelized biological organs

Abstract

Capillary transit time, defined as the time required for blood to traverse the microvascular network, is a cornerstone parameter in the study of hemodynamics. The study of capillary transit time, the foundation of which was laid by August Krogh in his seminal 1919 work, has come a long way since its advent. At present, capillary transit time analysis is being used to assess microvascular function and tissue oxygenation in conditions like stroke, tumors, and neurodegenerative diseases, guiding treatment strategies in radiotherapy and thrombolysis. It also helps optimize drug delivery by revealing how blood flow heterogeneity affects therapeutic agent distribution and retention in target tissues. With the advancement of blood flow simulation using computational human phantoms (CHP), a potential novel use of capillary transit time analysis in the field of internal and external dosimetry has arisen, where it may be used to predict the distribution of dose imparted by the radiophermaceuticals and the distribution of irradiated white blood cells in tumors. Various experimental and mathematical methods have been developed over the years to measure and predict capillary transit time. However, these models lack applicability in particle tracing applications. On the other hand, existing Monte-Carlo particle tracing codes lack the functionality of tracing particles inside vasculatures. Hence, the aim of the present work is to develop a path tracing algorithm that follows blood flow in the vasculature, including the capillary bed, using the principles of Monte-Carlo simulation and existing blood flow framework found in contemporary literature (The VoM-PhyS framework) to facilitate the calculation of mean transit time. One of the main challenges in developing a path tracing framework is finding a suitable probability distribution of possible next steps, based on which each step of the random walk of the particles is chosen. In the present study, this probability distribution is derived based on the outgoing flow rate at a particular node. Flow rate is calculated from governing equations, including Hagen-Poiseuille and Darcy’s equation of porous media, depending on particle location in the network. Using this probability distribution, random particle tracks are generated for increasing particle numbers and the associated elapsed-times are calculated. Variability of the elapsed time resulting from variation in the particle’s velocity considering its position with respect to the centerline of arterial and venous vessels is accommodated in this framework, as well. In the VoM-PhyS model, blood takes an instantaneous jump from the terminal of the segmentable vessels to a nearby tissue voxel within a specified sphere of influence. A method of estimating the time elapsed in this jump was also developed and implemented. The transit time distributions and the mean transit times were derived from these data. It was found that the distribution of mean transit time follows a gamma-variate distribution, which flattens with increasing sphere of influence, i.e., the variation in times increases. It was also found that the peak of the distributions shifts to increasing time values and the mean transit time increases with increasing sphere of influence. Finally, results of various statistical tests are presented to verify the statistical significance of the data generated using the proposed framework.