Physiological Modeling and Parameter Inference with Deep Learning: A Lipolysis Example

Authors

• X Duan
• M Aggarwal
• V Periwal

Abstract

Inference of nonlinear dynamics and parameters within biological modeling has been challenging. Conventional methodologies, based on hypothetical underlying mechanisms, complicate inference because standard parameter optimization methods are difficult to constrain to physiological ranges. Here, we propose a novel method using neural networks for physiological modeling, parametrization, and parameter inference simultaneously. Utilizing data from frequently sampled intravenous glucose tolerance testing, we construct a physiological lipolysis model of glucose, insulin, and free fatty acid dynamics. Parameter values are obtained via optimization, involving parameter sampling and model integration to generate simulated data. Gaussian process regression filters out data with undesirable shapes in the simulated dataset. A convolutional neural network is trained to output the model parameters, evaluated for both parameter inference and trajectory reconstruction over a test dataset. In addition to hyperparameter fine-tuning, we enhance modeling techniques through: (1) evaluating network performance across various parametrizations to ascertain identifiability, and (2) feature engineering by incorporating more nonlinear terms of state variables as inputs to the network. These strategies yield small width-at-half-maximum values for the distribution of errors in parameter inference and trajectory reconstruction over the test dataset. We apply the Kolmogorov-Smirnov test to compare different feature engineering scenarios, identifying the smallest error scenario, involving the concatenation of convolutional layer outputs and original data. Our research demonstrates how to establish a robust deep learning methodology for both model and parameter inference. Such a trained neural network could be used as a black box by clinicians directly to find the physiological parameters underlying their data.

Scientific Focus Area: Computational Biology

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