Deep learning approach to parameter optimization for physiological models

Inferring nonlinear dynamics and parameters in biological data modeling is challenging. Standard parameter optimization methods are difficult to constrain to biological ranges, especially for nonlinear models. We propose a novel method to evaluate and improve putative models using neural networks to simultaneously address biological modeling, parametrization, and parameter inference. As an example, utilizing data from clinical frequently sampled intravenous glucose tolerance testing, we introduce two physiological lipolysis models of glucose, insulin, and free fatty acids dynamics. Parameter values are obtained via optimization from the limited clinical data. We then generate simulated data from the model by sampling parameters within physiological ranges while ensuring that the joint parameter distributions are physiologically appropriate. A convolutional neural network is trained to take the simulated glucose, insulin, and free fatty acids time courses as input and output the model parameters. We evaluate the performance of the trained neural network for both parameter inference and trajectory reconstruction using a testing dataset, optimized model-fitting curves, and real physiological data, and show that it enables accurate inference across all three settings. The trained neural network produces consistently high R-squared values and low p-values across different feature engineering strategies and training dataset sizes. We assess the impact of feature engineering choices and training dataset size on inference performance, demonstrating that appropriately designed feature transformations and specific activation function choices improve accuracy. Our results establish a deep learning framework for parameter inference in mathematical models, which can be adapted to various physiological systems.