A systematic approach to the scale separation problem in the development of multiscale models

Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such 'multiscale' problems, that of defining a 'scale' remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.

Musculoskeletal modelling of the human cervical spine for the investigation of injury mechanisms during axial impacts

Head collisions in sport can result in catastrophic injuries to the cervical spine. Musculoskeletal modelling can help analyse the relationship between motion, external forces and internal loads that lead to injury. However, impact specific musculoskeletal models are lacking as current viscoelastic values used to describe cervical spine joint dynamics have been obtained from unrepresentative quasi-static or static experiments. The aim of this study was to develop and validate a cervical spine musculoskeletal model for use in axial impacts. Cervical spine specimens (C2-C6) were tested under measured sub-catastrophic loads and the resulting 3D motion of the vertebrae was measured. Specimen specific musculoskeletal models were then created and used to estimate the axial and shear viscoelastic (stiffness and damping) properties of the joints through an optimisation algorithm that minimised tracking errors between measured and simulated kinematics. A five-fold cross validation and a Monte Carlo sensitivity analysis were conducted to assess the performance of the newly estimated parameters. The impact-specific parameters were integrated in a population specific musculoskeletal model and used to assess cervical spine loads measured from Rugby union impacts compared to available models. Results of the optimisation showed a larger increase of axial joint stiffness compared to axial damping and shear viscoelastic parameters for all models. The sensitivity analysis revealed that lower values of axial stiffness and shear damping reduced the models performance considerably compared to other degrees of freedom. The impact-specific parameters integrated in the population specific model estimated more appropriate joint displacements for axial head impacts compared to available models and are therefore more suited for injury mechanism analysis.

Multiscale modeling methods in biomechanics

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.1375 For further resources related to this article, please visit the WIREs website.

Osteoarthritis year in review 2015: mechanics

Motivated by the conceptual framework of multi-scale biomechanics, this narrative review highlights recent major advances with a focus on gait and joint kinematics, then tissue-level mechanics, cell mechanics and mechanotransduction, matrix mechanics, and finally the nanoscale mechanics of matrix macromolecules. A literature review was conducted from January 2014 to April 2015 using PubMed to identify major developments in mechanics related to osteoarthritis (OA). Studies of knee adduction, flexion, rotation, and contact mechanics have extended our understanding of medial compartment loading. In turn, advances in measurement methodologies have shown how injuries to both the meniscus and ligaments, together, can alter joint kinematics. At the tissue scale, novel findings have emerged regarding the mechanics of the meniscus as well as cartilage superficial zone. Moving to the cell level, poroelastic and poro-viscoelastic mechanisms underlying chondrocyte deformation have been reported, along with the response to osmotic stress. Further developments have emerged on the role of calcium signaling in chondrocyte mechanobiology, including exciting findings on the function of mechanically activated cation channels newly found to be expressed in chondrocytes. Finally, AFM-based nano-rheology systems have enabled studies of thin murine tissues and brush layers of matrix molecules over a wide range of loading rates including high rates corresponding to impact injury. With OA acknowledged to be a disease of the joint as an organ, understanding mechanical behavior at each length scale helps to elucidate the connections between cell biology, matrix biochemistry and tissue structure/function that may play a role in the pathomechanics of OA.