Democratizing biomedical simulation through automated model discovery and a universal material subroutine

Abstract

Personalized computational simulations have emerged as a vital tool to understand the biomechanical factors of a disease, predict disease progression, and design personalized intervention. Material modeling is critical for realistic biomedical simulations, and poor model selection can have life-threatening consequences for the patient. However, selecting the best model requires a profound domain knowledge and is limited to a few highly specialized experts in the field. Here we explore the feasibility of eliminating user involvement and automate the process of material modeling in finite element analyses. We leverage recent developments in constitutive neural networks, machine learning, and artificial intelligence to discover the best constitutive model from thousands of possible combinations of a few functional building blocks. We integrate all discoverable models into the finite element workflow by creating a universal material subroutine that contains more than 60,000 models, made up of 16 individual terms. We prototype this workflow using biaxial extension tests from healthy human arteries as input and stress and stretch profiles across the human aortic arch as output. Our results suggest that constitutive neural networks can robustly discover various flavors of arterial models from data, feed these models directly into a finite element simulation, and predict stress and strain profiles that compare favorably to the classical Holzapfel model. Replacing dozens of individual material subroutines by a single universal material subroutine–populated directly via automated model discovery–will make finite element simulations more user-friendly, more robust, and less vulnerable to human error. Democratizing finite element simulation by automating model selection could induce a paradigm shift in physics-based modeling, broaden access to simulation technologies, and empower individuals with varying levels of expertise and diverse backgrounds to actively participate in scientific discovery and push the boundaries of biomedical simulation.

On sparse regression, Lp‐regularization, and automated model discovery

“…Instead, running L 0 regularization for all possible one-and two-term models provides a quick first insight into the nature and hierarchy of the best-in-class models. 22 From this initial first glimpse, we can proceed by successively adding terms. In addition, from the best-in-class one-term models, we can use the discovered weights w i,L 0 to initialize the weights for higher order runs and to normalize the weights in the regularization term, 𝛼 || 𝜽 ||…”

“…) discrete models, in our case 8, 28, 56, or 70. 22 Out of all possible discovery algorithms, this is the most honest, unbiased, and transparent approach.…”

Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics

“…Constitutive neural networks use physics-informed insights about constitutive models as well as powerful deep learning methods to simultaneously discover the function form of the constitutive model and learn its appropriate parameters [19]. While the first family of constitutive neural networks only discovered isotropic models for materials such as rubber [19], brain [20] or plant-based meat [37], more recent networks can now discover transversely isotropic models for skin [21] or arteries [35]. Here we explore how to expand constitutive neural networks to discover more complex anistropic constitutive models from biaxial extension data.…”

“…For the isotropic terms ψ(I 1 ) and ψ(I 2 ), we adapt an isotropic constitutive neural network initially designed for rubber-like materials [19]. For the anisotropic terms ψ(I 4w ) and ψ(I 4s ), we adapt an anisotropic constitutive neural network initially designed for arteries [35], with the additional constraint that the linear and exponential linear terms in the warp direction, −w 9 w * ) − 1], are not independent but share the same weights [51]. The free energy function for the two-fiber network takes the following explicit form,…”