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Annual Review of Biomedical Engineering

Volume 19, 2017

Multiscale Modeling of Muscular-Skeletal Systems

Abstract

Multiscale modeling of muscular-skeletal systems—the materials and structures that help organisms support themselves and move—is a rapidly growing field of study that has contributed key elements to the understanding of these systems, especially from a multiscale perspective. The systems, including materials such as bone and muscle, have hierarchical structures ranging from the nano- to the macroscale, and it is difficult to understand their macroscopic behaviors, both physiological and pathological, without knowledge of their hierarchical structures and properties. In this review, we discuss the methods of multiscale modeling. Through a series of case studies about key materials in muscular-skeletal systems, we describe how different methods can bridge the gap between hierarchical structures and their roles in the systems’ mechanical properties. In particular, we emphasize the importance of the quality of minerals in bone. Finally, we discuss biomimetic material designs facilitated by additive manufacturing technology.

Keyword(s): 3D printing design, collagen, elastin, hydroxyapatite, multiscale modeling, muscular-skeletal systems
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2017-06-21
2025-06-19
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Multiscale Modeling of Muscular-Skeletal Systems
Annual Review of Biomedical Engineering 19, 435 (2017); https://doi.org/10.1146/annurev-bioeng-071516-044555
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Supplementary Data

  • Download all Supplemental Figures as a single PDF, or see below.

    Supplemental Figure 1. Multiscale dynamics of water molecules. The various dynamics govern different properties at the different time and length scales, which can be solved with independent methods. Image of water and electron cloud adopted from (1) licensed under CC BY-SA. Image of water splash adopted from Reference (2) licensed under CC BY-SA. Image of river adopted from Reference (3) licensed under CC BY-SA 2.0. Image of iceberg is adopted from Reference (4) licensed under CC BY-SA 4.0.

    Supplemental Figure 2. The basic term of the classical MD and the concept of the bond orders in the reactive MD (5). (a) The classical potential of molecular dynamics commonly has terms for torsion, bond stretching, angle and non-bonded interactions. (b) Based on the distance bond-order allow to distinguish single, double, triple bonds of carbons. The potential energy between carbon atoms changes and goes to zero when it reaches bonds’ breaking points.

    Supplemental Figure 3. Concepts of the continuum theories (a) Elongation of a homogenous bar (length: L) under a tensile force F is given as Δu (b) Brittle and ductile materials show different stress-strain behaviors. (c) Griffith criterion and energy release rate in a homogenous materials with a crack are given by the equation in the panel. (d) The basic concept of a cohesive zone model: The deformation in the region I is reversible without damages. Once stress reaches the Tmax, the element gets damaged and the elastic behavior changes to red arrow. When the extension reaches δf , the element totally breaks and the required energy is the total area of the triangle, characterized as the critical energy release rate.

    Supplemental Figure 4. The concept of the replica exchange molecular dynamics (REMD). Each replica is equilibrated at the slightly different temperatures. Every set number of steps, each replica tries to exchange the temperature with the neighboring replicas based on the Metropolis Monte Carlo criterion. At every pre-determined number of steps, each replica attempts a temperature exchange with the neighboring replica based on the Metropolis Monte Carlo criterion. High temperatures prevent trapping of the system at a local minimum and low temperatures help to determine minimum energy configurations.

    Supplemental Figure 5. Simulations of tri-peptide aggregations based on the MARTINI FF. The different sequences show different aggregation patterns. Image reprinted with permission from Macmillan Publishers Ltd: Reference (6).

    Supplemental Figure 6. Full atomistic model of a tropocollagen molecule for MD and corresponding bead-spring model for CGMD with MARTINI FF.

    Supplemental Figure 7. Deformation of CG model of mineralized collagen fibrils with 35% mineral density. Image reprinted with permission from Reference (7). Copyright © 2015 Elsevier.

    Supplemental Figure 8. The effects of including heterogeneity (contour of osteon) or holes (Haversian canals) of the osteon model under compression in FEM.  The microstructures with holes indicate that the stress fields are delocalized. The stress-fields are Image adopted with permission from Reference (8). Copyright © 2012 Wiley.

    Supplemental Figure 9. Mineralized collagen-like composite design from additive manufacturing technique. Two main toughening mechanisms of the composite under tensile loadings have been confirmed: (1) delocalization of stress concentration due to micro-crack formation and (2) distinct crack deflection. Figure reprinted with permission from Reference (9) Copyright © 2013 Wiley.

    Supplemental Figure 10. Osteon-like design with magnetic nanoparticles. The circular reinforcement (reinforcement angle = all) shows fracture resistance to tensile loading in all directions. Figure adopted from Reference (10) under a Creative Commons Attribution-Noncommercial license.

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