Huxley muscle model surrogates for high-speed multi-scale simulations of cardiac contraction

The computational requirements of the Huxley-type muscle models are substantially higher than those of Hill-type models, making large-scale simulations impractical or even impossible to use. We constructed a data-driven surrogate model that operates similarly to the original Huxley muscle model but consumes less computational time and memory to enable efficient usage in multiscale simulations of the cardiac cycle. The data was collected from numerical simulations to train deep neural networks so that the neural networks' behavior resembles that of the Huxley model. Since the Huxley muscle model is history-dependent, time series analysis is required to take the previous states of the muscle model into account. Recurrent and temporal convolutional neural networks are typically used for time series analysis. These networks were trained to produce stress and instantaneous stiffness. Once the networks have been trained, we compared the similarity of the produced stresses and achieved speed-up to the original Huxley model, which indicates the potential of the surrogate model to replace the model efficiently. We presented the creation procedure of the surrogate model and integration of the surrogate model into the finite element solver. Based on similarities between the surrogate model and the original model in several types of numerical experiments, and also achieved speed-up of an order of magnitude, it can be concluded that the surrogate model has the potential to replace the original model within multiscale simulations. Finally, we used our surrogate model to simulate a full cardiac cycle in order to demonstrate the application of the surrogate model in larger-scale problems.