Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles
Authors: Glass Emma , Kulkarni Sahil , Eng Christina , Feng Shurui , Malavia Avishi , Radhakrishnan Ravi 
Published: March 2022

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 (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.

Author summary

Nanoparticles (NP) have been used in various drug delivery contexts because they can target specific locations in the body. However, there is a translational gap between animals and humans, so researchers have begun toward computational models to guide in vivo NP experimentation. Here, we present several versions of physics-based multiscale physiologically based pharmacokinetic models (PBPK) for determining NP biodistribution. We successfully developed two versions of ODE-based compartmental models (models A and B) and an ODE-based branched vascular model implemented in MATLAB and Julia and validated models with experimental data. Additionally, we demonstrated using a neural network to solve our ODE system. In the future, this model can integrate different NP surface chemistries, immune system effects, multiscale vascular hydrodynamic effects, which will enhance the ability of this model to guide a variety of in vivo experiments.