Stochastic Growth Modeling of Vascular Plaque Dynamics and Derivation of Optimal Dosing Curves

Targeted drug delivery offers a promising approach for personalized medicine in treating vascular stenosis. However, biomechanical constraints, such as drug washout by high-velocity central blood flow and unintended absorption by healthy vascular walls, complicate the determination of optimal dosing locations. Conventional three-dimensional computational fluid dynamics (CFD) provides precise flow analysis but incurs prohibitive computational costs, making long-term tracking of plaque growth and reverse-engineering of optimal delivery highly inefficient. In this study, we propose a pseudo-3D stochastic growth model that dramatically reduces computational load while capturing the essential dynamics of plaque progression and regression. By modeling the advection-diffusion of lipid and drug particles as a discrete Markov process within a Stokes flow field, we simulate the morphological evolution of plaques under continuous and interrupted targeted therapies. Furthermore, by formulating the drug transport process as an absorbing Markov chain with boundaries at the healthy walls and vessel outlet, we calculate the exact reaching probability and mean first passage time (MFPT) to the plaque. Based on these probability distributions, we discover continuous "Optimal Dosing Curves", which indicate the most effective spatial coordinates for catheter-based drug release to maximize therapeutic efficacy. This mathematical framework not only elucidates the stochastic nature of vascular plaque dynamics but also provides a scalable, computationally efficient foundation for optimizing targeted drug delivery in personalized medicine.