State-of-the-art and tomorrow’s challenges and opportunities in constitutive modeling of soft biological tissues with a focus on arterial, cardiac and brain biomechanics

The aim of this paper is to provide an up-to-date overview of the constitutive modeling of soft biological tissues, both from a simulation and experimental perspective by taking into account different length scales. After providing some essential ingredients on continuum mechanics, especially nonlinear elasticity, the focus is on mechanical and structural modeling of fiber-reinforced materials, including the features of soft tissues such as collagen fiber dispersion, and residual stresses. Materials testing and data acquisition for constitutive modeling of soft tissue are also discussed, with emphasis on measuring strain fields using imaging techniques and digital image correlation. The topics are illustrated for three tissues. First, applications to arteries are illustrated and the effects of vascular adaptation in diseases such as aneurysms and aortic dissections are discussed. The second application includes cardiac biomechanical modeling, touching on the nonlinear anisotropic and viscoelastic nature of the myocardium, the synthesis and integration of these concepts into whole-organ models, and the assimilation of image-based data for patient-specific modeling. The third focus is on brain mechanics, including the unusual response of brain tissues and axons under loads, the formation of the brain and skull during development, and the study of brain trauma and diseases. The important area of machine learning for discovering constitutive models and parameter identification is also covered. To show how constitutive models can be selected, a model discovery approach is reviewed. Because the mechanical properties of soft tissues may vary with age, sex, health and disease an account of uncertainty quantification in the model assumptions and measurement errors is provided. Future directions and challenges for research in multiscale biomechanics and mechanobiology are identified involving mechanical, biological, electrical and fluid-structure interactions. Statement of Significance: This review provides a state-of-the art summary of the importance of constitutive modeling, simulations and their experimental basis of soft biological tissues. A focus is put on applications to materials testing and data acquisition, artery and cardiac biomechanics and mechanobiology at different length scales and the biomechanics of brain at the cell, tissue and organ levels. In addition, novel approaches to constitutive modeling and parameter identification of soft biological tissues based on machine learning, model discovery and data mining are highlighted. Finally, open problems are summarized and recent and future directions and challenges for research in multiscale biomechanics and mechanobiology are identified, particularly involving mechanical, biological, electrical and fluid-structure interactions.