Abstract
More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space–time continuum. We are forced to consider multiple space–time continua, each representing the phenomenon of interest at a characteristic space–time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: ‘causal confirmation,’ where multiscale models are used as materializations of the causation theories; ‘predictive accuracy,’ where multiscale modeling is aimed to improve the predictive accuracy; and ‘determination of effect,’ where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space–time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375For further resources related to this article, please visit the WIREs website.
Highlights
As per March 2016, PubMed indexed 2180 papers including the word ‘multiscale’ in the title, and 5457 anywhere in the PubMed record
Of all possible angles we could use to structure this review, we chose that of the modeling intent, organizing all reviewed papers around three distinct operational motivations: ‘Causal confirmation,’ ‘Predictive accuracy,’ and ‘Determination of effect.’
The first represents the most ‘humble’ intent, among the three. In these papers multiscale modeling is used to merely show that a complex set of observations is ‘compatible’ with a mechanistic theory embodied by the multiscale model; ‘compatible’ does not mean ‘true,’ and even less ‘accurate.’ The papers that fall in the predictive accuracy category are driven by the necessity to improve predictive accuracy over systems where the assumption of scale separation applies poorly
Summary
As per March 2016, PubMed indexed 2180 papers including the word ‘multiscale’ in the title, and 5457 anywhere in the PubMed record. The microscale architecture of the muscle and the process of force generation in the muscle (active/passive) are reasonably well understood, the mechanosensitivity of the muscular remodeling process is largely phenomenologically defined.[27,28] Zöllner et al.[29] obtained causal confirmation for a multiscale model that predicted the shortening of the gastrocnemius muscle as a result of remodeling induced by highheeled footwear use In their model, the apparent scale muscle length was a function of cellular scale sarcomere number. At the same time, considering the inclusions in the bone composite to possess a given distribution of orientations, Fritsch et al successfully assessed the predictive accuracy of the model with respect to tissue scale elastic anisotropy, directly answering the problem MSK_PA1 posed earlier. Tendon tissue mechanics: A multiscale model that predicts better than a single-scale model the stiffness tensor of a tendon tissue
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