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Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1–10 mm) stress-strain response and the deformation of the mesoscale (10–1000 µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. 

Embryonic development is a complex phenomenon that integrates genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogens guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes the morphogen patterns in three-dimensional (3D) space, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo, nor how the patterns are controlled over time. Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP-mediated DV patterning. The layer of epithelial cells begins to thin as they spread toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members through advection. We developed a Finite Element Model (FEM) that incorporates all stages of zebrafish embryonic development data and solves the advection-diffusion-reaction Partial Differential Equations (PDE) in a growing domain. We use the model to investigate mechanisms in underlying BMP-driven DV patterning during epiboly. Solving the PDE is computationally expensive for parameter exploration. To overcome this obstacle, we developed a Neural Network (NN) metamodel of the 3D embryo that is accurate and fast and provided a nonlinear map between high-dimensional input and output that replaces the direct numerical simulation of the PDEs. From the modeling and acceleration by the NN metamodels, we identified the impact of advection on patterning and the influence of the dynamic expression level of regulators on the BMP signaling network. 

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. This review serves as introduction to a special issue on Uncertainty Quantification, Machine Learning, and Data-Driven Modeling of Biological Systems that will help identify current roadblocks and areas where computational mechanics, as a discipline, can play a significant role. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.