Automated model discovery for human cardiac tissue

Discovering the best model and parameters

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For more than half a century, scientists have developed mathematical models to understand the behavior of the human heart. Today, we have dozens of heart tissue models to choose from, but selecting the best model is limited to expert professionals, prone to user bias, and vulnerable to human error. Here we take the human out of the loop and automate the process of model discovery. Towards this goal, we establish a novel incompressible orthotropic constitutive neural network to simultaneously discover both, model and parameters, that best explain human cardiac tissue. Notably, our network features 32 individual terms, 8 isotropic and 24 anisotropic, and fully autonomously selects the best model, out of more than 4 billion possible combinations of terms. We demonstrate that we can successfully train the network with triaxial shear and biaxial extension tests and systematically sparsify the parameter vector with L1-regularization. Strikingly, we robustly discover a four-term model that features a quadratic term in the second invariant I2, and exponential quadratic terms in the fourth and eighth invariants I4f, I4n, and I8fs. Importantly, our discovered model is interpretable by design and has parameters with well-defined physical units. We show that it outperforms popular existing myocardium models and generalizes well, from homogeneous laboratory tests to heterogeneous whole heart simulations. This is made possible by a new universal material subroutine that directly takes the discovered network weights as input. Automating the process of model discovery has the potential to democratize cardiac modeling, broaden participation in scientific discovery, and accelerate the development of innovative treatments for cardiovascular disease. Our source code, data, and examples are available at