Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles

Abstract

Nanoparticles (NP) are being increasingly explored as vehicles for targeted drug delivery because they can overcome free therapeutic limitations by drug encapsulation, thereby increasing solubility and transport across cell membranes. However, a translational gap exists from animal to human studies resulting in only several NP having FDA approval. Because of this, researchers have begun to turn toward physiologically based pharmacokinetic (PBPK) models to guide in vivo NP experimentation. However, typical PBPK models use an empirically derived framework that cannot be universally applied to varying NP constructs and experimental settings. The purpose of this study was to develop a physics-based multiscale PBPK compartmental model for determining continuous NP biodistribution. We successfully developed two versions of a physics-based compartmental model, models A and B, and validated the models with experimental data. The more physiologically relevant model (model B) had an output that more closely resembled experimental data as determined by normalized root mean squared deviation (NRMSD) analysis. A branched model was developed to enable the model to account for varying NP sizes. With the help of the branched model, we were able to show that branching in vasculature causes enhanced uptake of NP in the organ tissue. The models were solved using two of the most popular computational platforms, MATLAB and Julia. Our experimentation with the two suggests the highly optimized ODE solver package DifferentialEquations.jl in Julia outperforms MATLAB when solving a stiff system of ordinary differential equations (\textbf{ODEs}). We experimented with solving our PBPK model with a neural network using Julia's Flux.jl package. We were able to demonstrate that a neural network can learn to solve a system of ODEs when the system can be made non-stiff via quasi-steady-state approximation (QSSA). In the future, this model will incorporate modules that account for varying NP surface chemistries, multiscale vascular hydrodynamic effects, and effects of the immune system to create a more comprehensive and modular model for predicting NP biodistribution in a variety of NP constructs.

Physiologically Based Pharmacokinetic Modeling of Nanoparticle Biodistribution: A Review of Existing Models, Simulation Software, and Data Analysis Tools

“…In the case of PBPK models and related PBPK analyses, intermediate to advanced programming skills are required, which present a considerable disadvantage for its widespread use in the field [ 69 ]. MATLAB provides a range of mathematical and numerical methods for solving PBPK model equations, parameter estimation, and sensitivity analysis [ 53 , 54 , 55 , 56 , 61 , 70 , 71 , 72 , 73 , 74 , 75 , 76 ]. In particular, several MATLAB toolkits can be used for modeling, simulating, and analyzing PBPK systems, namely SimBiology [ 57 , 77 , 78 , 79 , 80 ], PottersWheel [ 81 , 82 ], and IntiQuan IQM Tools [ 70 ].…”

“…Julia [ 128 ] is a flexible dynamic programming language appropriate for scientific and numerical computing. It has been shown that in the context of PBPK models, a DifferentialEquations.jl package outperforms MATLAB in solving a stiff system of ordinary differential equations [ 72 ].…”

“…It works with a wide variety of charts ( x - y , histograms, polar, ternary, maps, etc.) and can be used to digitize experimental data on the biodistribution of NPs published as graphs [ 50 , 60 , 72 , 102 ].…”