Hyperelasticity of blood clots: Bridging the gap between microscopic and continuum scales

The biomechanical properties of blood clots, which are dictated by their compositions and microstructures, play a critical role in determining their fates, i.e., occlusion, persistency, or embolization in the human circulatory system. While numerous constitutive models have emerged to describe the biomechanics of blood clots, most of these models have primarily focused on the macroscopic deformation of the clots and the resultant strain-stress correlations without depicting the microscopic contributions from their structural components, such as fibrin fibers, fibrin network and red blood cells. This work addresses the gap in current scientific understanding by quantifying how changes in the microstructure of blood clots affect its mechanical responses under different external stresses. We leverage our previous published work to develop a hyperelastic potential model for blood clots, which incorporates six distinct strain-energy components to describe the alignment of fibers, the entropic and enthalpic stretching of fibrin fibers, the buckling of these fibers, clot densification, and clot jamming. These strain-energy components are represented by a combination of simple harmonic oscillators, one-sided harmonic potentials, and a Gaussian potential. The proposed model, which is $C^0,C^1$ , and $C^2$ continuous with a total of 13 parameters, has been validated against three datasets: 1) fibrin clot in tension, 2) blood clot in compression, and 3) blood clots in shear, demonstrating its robustness. Subsequent simulations of a microscopic blood clot model are performed to uncover mechanistic correlations for a majority of the hyperelastic potential's stiffness/strain parameters. Our results show that only one proposed term concerning fiber buckling needs further refinement, while the remaining five strain-energy terms appear to describe precisely what they were intended to. In summary, the proposed model provides insight into the behavior of thromboembolisms and assistance in computer-aided design of surgical tools and interventions such as thrombectomy.