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.

翻译：物理信息神经网络（PINNs）将机器学习与微分方程相结合，以求解正问题和反问题，同时确保预测结果遵循物理定律。基于生理的药代动力学（PBPK）建模通过采用一种机制性的、以生理学为中心的框架，超越了经典的房室建模方法。此类模型涉及许多未知参数，由于伦理和实际限制，这些参数难以在人体中直接测量。PBPK模型构建为常微分方程（ODEs）系统，这些参数化常微分方程通常是刚性的，传统的数值和统计方法常常无法收敛。在本研究中，我们考虑一个模拟人脑在药物递送中功能的、渗透性受限的四房室PBPK脑模型。我们引入了PBPK-iPINN方法，该方法利用反演PINNs来估计药物特异性或患者特异性参数以及药物浓度分布。我们还进行了参数可识别性分析，以确定是否可以从现有数据中唯一且可靠地估计这些参数。我们证明，为了使反问题收敛到正确解，损失函数的组成部分（数据损失、初始条件损失和残差损失）必须适当加权，并且包括层数和神经元数、激活函数、学习率、优化器和配置点在内的超参数必须仔细调整。随后，将PBPK-iPINN方法的性能与成熟的数值和统计方法进行了比较。准确的参数估计可产生精确的药物浓度-时间分布，进而能够计算药代动力学指标。这些指标有助于药物开发人员和临床医生设计和优化脑癌治疗方案。