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

Abstract

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.

Generic Purpose Pharmacokinetics-Pharmacodynamics Mathematical Model For Nanomedicine Targeted Drug Delivery: Mouse Model

“…In the case of two blood vessels, the proposed flow dynamics improve significantly -0.59 compared to 0.35 simulator's fidelity, after 48 simulated hours. In a similar manner, for three blood vessels, the proposed flow dynamics obtain 0.35 fidelity compared to 0.2 obtained by the model proposed by Lazebnik et al [46].…”

“…Furthermore, to evaluate the flow dynamics influence for the entire mouse model rather than in the scale of a few blood vessels, we compute the in silico results of the model proposed by Lazebnik et al [46] but replace the flow dynamics (see Eq. ( 1) in [46]) with the proposed flow dynamics (see Section 4.2.1) and compared with the original model. The comparison was conducted over five in vivo experiments as described in Table 2 and evaluate in several points in time, according to the reported in vivo values of each experiment.…”

“…5 such that the x-axis is the time in hours from the beginning of the treatment and the y-axis is the simulator's fidelity compared to SimVascular [72]. Similarly, a comparison between the proposed flow dynamics with the proposed by Lazebnik et al [46] for two blood vessels such that the flow is circulating between the first and second blood vessels, as shown in Fig. 6, where the x-axis is the time in hours from the beginning of the treatment and the y-axis is the simulator's fidelity compared to SimVascular [72].…”

“…One approach to model PKPD nanoparticles (NP) based dynamics for drug delivery is using a graph-based model [46]. While the graph-based PKPD model produces a relatively accurate prediction of the biodistribution of the NP-based drug in the body compared to other PKPD mathematical models, it involves several simplifications of the biological systems and the bioclinical properties of the introduced drug giving rise to large errors in the forecast of the corresponding in vivo experiments:…”

“…A comparison between the flow dynamics algorithm in[46] and the proposed algorithm on five different in vivo experiments. The results are shown as the mean of n = 70 repetitions and the mean of all the NPs in each in vivo experiment.…”