Multiphysics pharmacokinetic model for targeted nanoparticles

Emma M Glass; Sahil Kulkarni; Christina Eng; Shurui Feng; Avishi Malaviya; Ravi Radhakrishnan

doi:10.3389/fmedt.2022.934015

Multiphysics pharmacokinetic model for targeted nanoparticles

Front Med Technol. 2022 Jul 15:4:934015. doi: 10.3389/fmedt.2022.934015. eCollection 2022.

Authors

Emma M Glass^{1

2}, Sahil Kulkarni³, Christina Eng³, Shurui Feng⁴, Avishi Malaviya⁵, Ravi Radhakrishnan^{3

4}

Affiliations

¹ Department of Computational Applied Mathematics and Statistics, College of William and Mary, Williamsburg, VA, United States.
² Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, United States.
³ Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, United States.
⁴ Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, United States.
⁵ Department of Bioengineering, Carnegie Mellon University, Pittsburgh, PA, United States.

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 (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). Our model incorporates 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.

Keywords: biodistribution; neural network; physiologically based pharmacokinetic; quasi steady-state approximation; vascular branching.