Steel and bone: Mesoscale modeling and middle-out strategies in physics and biology

Mesoscale modeling is often considered merely as a practical strategy used when information on lower-scale details is lacking, or when there is a need to make models cognitively or computationally tractable. Without dismissing the importance of practical constraints for modeling choices, we argue that mesoscale models should not just be considered as abbreviations or placeholders for more “complete” models. Because many systems exhibit different behaviors at various spatial and temporal scales, bottom-up approaches are almost always doomed to fail. Mesoscale models capture aspects of multi-scale systems that cannot be parameterized by simple averaging of lower-scale details. To understand the behavior of multi-scale systems, it is essential to identify mesoscale parameters that “code for” lower-scale details in a way that relate phenomena intermediate between microscopic and macroscopic features. We illustrate this point using examples of modeling of multi-scale systems in materials science (steel) and biology (bone), where identification of material parameters such as stiffness or strain is a central step. The examples illustrate important aspects of a so-called “middle-out” modeling strategy. Rather than attempting to model the system bottom-up, one starts at intermediate (mesoscopic) scales where systems exhibit behaviors distinct from those at the atomic and continuum scales. One then seeks to upscale and downscale to gain a more complete understanding of the multi-scale systems. The cases highlight how parameterization of lower-scale details not only enables tractable modeling but is also central to understanding functional and organizational features of multi-scale systems

Constitutive modelling of skin ageing

The objective of this chapter is to review the main biomechanical and structural aspects associated with both intrinsic and extrinsic skin ageing, and to present potential research avenues to account for these effects in mathematical and computational models of the skin. This will be illustrated through recent work of the authors which provides a basis to those interested in developing mechanistic constitutive models capturing the mechanobiology of skin across the life course

In silico assessment of biomedical products: the conundrum of rare but not so rare events in two case studies

In silico clinical trials, defined as “The use of individualized computer simulation in the development or regulatory evaluation of a medicinal product, medical device, or medical intervention,” have been proposed as a possible strategy to reduce the regulatory costs of innovation and the time to market for biomedical products. We review some of the the literature on this topic, focusing in particular on those applications where the current practice is recognized as inadequate, as for example, the detection of unexpected severe adverse events too rare to be detected in a clinical trial, but still likely enough to be of concern. We then describe with more details two case studies, two successful applications of in silico clinical trial approaches, one relative to the University of Virginia/Padova simulator that the Food and Drug Administration has accepted as possible replacement for animal testing in the preclinical assessment of artificial pancreas technologies, and the second, an investigation of the probability of cardiac lead fracture, where a Bayesian network was used to combine in vivo and in silico observations, suggesting a whole new strategy of in silico-augmented clinical trials, to be used to increase the numerosity where recruitment is impossible, or to explore patients’ phenotypes that are unlikely to appear in the trial cohort, but are still frequent enough to be of concern

Mechanical behaviour of curvilinear elastic fibers: An energy approach

An energy approach for the analysis of the mechanical response of three-dimensional elastic curvilinear fibers is proposed. Equivalent tangent stiffnesses and compliances are defined relating generalized displacements with applied loads in terms of both direct and mutual moduli. Many numerical applications are developed in order to investigate about the influence of fiber geometric parameters, addressing also large-displacement cases by means of an incremental formulation. Finally, considering planar fibers, explicit relationships for tangent and secant equivalent along-the-chord elastic moduli are deduced, leading to useful and direct expressions for the analysis and the design of composite materials reinforced by curvilinear elastic fibers

Convex analysis and ideal tensegrities

A theoretical framework based on convex analysis is formulated and developed to study tensegrity structures under steady-state loads. Many classical results for ideal tensegrities are rationally deduced from subdifferentiable models in a novel mechanical perspective. Novel energy-based criteria for rigidity and pre-stressability are provided, allowing to formulate numerical algorithms for computations

An insight on multiscale tendon modeling in muscle-tendon integrated behavior

This paper aims to highlight the need for a refined tendon model to reproduce the main mechanical features of the integrated muscle-tendon unit (MTU). Elastic non-linearities of the tendon, both at the nano and microscale, are modeled by a multiscale approach, accounting for the hierarchical arrangement (from molecules up to the fibers) of the collagen structures within the tissue. This model accounts also for the variation of tendon stiffness due to physical activity. Since the proposed tendon model is based on tissue structured histology, the training-driven adaptation laws are directly formulated starting from histological evidences. Such a tendon description is integrated into a viscoelastic Hill-type model of the whole MTU. A fixed-end contraction test is numerically simulated, and results based on both linear and non-linear tendon elastic model are compared. Sound and effective time-histories of muscle contractile force and fiber length are obtained only accounting for tendon elastic non-linearities, which allow to quantitatively recover some experimental data. Finally, proposed numerical results give clear indications towards a rational explanation of the influence of tendon remodeling induced by physical activity on muscular contractile force