Nelum S. S. M. Hapuhinna

arXiv2026

TumorPred: A Computational Framework Implemented via an R/Shiny Web Application for Parameter Estimation and Sensitivity Analysis in Compartmental Brain Modeling

It is difficult or infeasible to directly measure how much of a drug actually enters the human brain and a brain tumor, how long it remains there, and to estimate drug-specific or patient-specific parameters, as well as how changes in these parameters influence model outputs and pharmacokinetic characteristics. Compartmental modeling offers a powerful mathematical approach to describe drug distribution and elimination in the body using systems of differential equations. This study introduces TumorPred, an R/Shiny-based web application designed for model simulation, sensitivity analysis, and pharmacokinetic parameter calculation in a permeability-limited four-compartment brain model. The model closely mimics human brain functionality for drug delivery and aims to predict the pharmacokinetics of drugs in the brain blood, brain mass, and cranial and spinal cerebrospinal fluid (CSF) of the human brain. The app provides real-time output updates in response to input modifications and allows users to visualize and download simulated plots and data tables. The computational accuracy of TumorPred is validated against results from the Simcyp Simulator (Certara Inc.). TumorPred is freely accessible and serves as an invaluable computational tool and data-driven resource for advancing drug development and optimizing treatment strategies for more effective brain cancer therapy.

math.DS↗

arXiv2026

PBPK-iPINNs: Inverse Physics-Informed Neural Networks for Physiologically Based Pharmacokinetic Brain Models

Physics-Informed Neural Networks (PINNs) integrate machine learning with differential equations to solve forward and inverse problems while ensuring that predictions adhere to physical laws. Physiologically based pharmacokinetic (PBPK) modeling advances beyond classical compartmental approaches by employing a mechanistic, physiology-focused framework. Such models involve many unknown parameters that are difficult to measure directly in humans due to ethical and practical constraints. PBPK models are constructed as systems of ordinary differential equations (ODEs) and these parametric ODEs are often stiff, and traditional numerical and statistical methods frequently fail to converge. In this study, we consider a permeability-limited, four-compartment PBPK brain model that mimics human brain functionality in drug delivery. We introduce PBPK-iPINN, a method for estimating drug-specific or patient-specific parameters and drug concentration profiles using inverse PINNs. We also conducted parameter identifiability analysis to determines whether the parameters can be uniquely and reliably estimated from the available data. We demonstrate that, for the inverse problem to converge to the correct solution, the components of the loss function (data loss, initial condition loss, and residual loss) must be appropriately weighted, and the hyperparameters including the number of layers and neurons, activation functions, learning rate, optimizer, and collocation points must be carefully tuned. The performance of the PBPK-iPINN approach is then compared with established numerical and statistical methods. Accurate parameter estimation yields precise drug concentration-time profiles, which in turn enable the calculation of pharmacokinetic metrics. These metrics support drug developers and clinicians in designing and optimizing therapies for brain cancer.

stat.ML↗