Graph-Based Pharmacokinetic-Pharmadynamic Modeling for Large Scale Systems: Nanoparticles Case

Pharmaceutical nanoparticles (NPs) carrying molecular payloads are used for medical purposes such as diagnosis and medical treatment. They are designed to modify the pharmacokinetics-pharmacodynamics (PKPD) of their associated payloads, to obtain better clinical results. Currently, the research process of discovering the PKPD properties of new candidates for efficient clinical treatment is complicated and time-consuming. In silico experiments are known to be powerful tools for studying biological and clinical processes and therefore can significantly improve the process of developing new and optimizing current NPs-based drugs. However, the current PKPD models are limited by the number of parameters they can take into consideration and the ability to solve large-scale in vivo settings, thus providing relatively large errors in predicting treatment outcomes. In this study, we present a novel mathematical graph-based model for PKPD of NPs-based drugs. The proposed model is based on a population of NPs performing a directed walk on a graph describing the blood vessels and organs, taking into consideration the interactions between the NPs and their environment. In addition, we define a mechanism to perform different prediction queries on the proposed model to analyze two in vivo experiments with eight different NPs, done on mice, obtaining a fitting of 0.84 {+/-} 0.01 and 0.66 {+/-} 0.01 (mean {+/-} standard deviation), respectively, comparing the in vivo values and the in silico results.