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Multi-scale Structural Modeling of Soft Tissues Mechanics and Mechanobiology

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Abstract

Soft tissues account for a major fraction of the body volume and mass. They are present in all non-skeletal organs, being responsible for protecting the body, maintaining internal homeostasis, and allowing for mobility. Their function in different organs is highly diverse, as are their properties which are optimally suited for their specific tasks. From a mechanical perspective, specificity of structure and properties is acquired via evolutionary adaptation of the tissue composition and multi-scale structure. In modeling tissue mechanics and mechano-biology, it is thus natural to seek the structural determinants of tissues and their evolution (the “structural approach”). Earlier models were exclusively phenomenological, based either on the general principles of non-linear continuum mechanics or alternatively, on empirical mathematical expressions that fit specific response patterns. In the late 1970’s, structural models were introduced to tissue mechanics (Lanir in J. Biomechanics 12(6): 423–436, 1979; Lanir in J. Biomechanics 16(1): 1–12, 1983). Ever since, a gradually increasing number of structural models have been developed for different types of tissues, and today, it is the method of choice (Cowin and Humphrey in J. Elasticity 61: ix–xii, 2000). The structural approach was recently extended to incorporate a mechanistic formulation of mechano-biological pathways by which tissue structures remodel during growth (Lanir in Biomech Model Mechanobiol, 14(2): 245–266, 2015). Here, the characteristic features of soft tissue structures and their constitutive modeling are reviewed. The presentation starts with a brief survey of the multi-scale and multi-phasic soft tissues structure. The global mechanical characteristics of soft tissues and of their constituents are then briefly reviewed. These two aspects form the basis for structural constitutive formulation via the multi-scale structure-function link. Based on established criteria for model validity, predictions of the formulated theory are contrasted against measured response characteristics. Using this structure-function relationship, the evolutionary pathway by which tissue structure and mechanics remodel during growth to adapt to their physiological function, is laid down. The review concludes with an account of the state of the art, the big picture, and future research challenges in tissue mechanobiological modeling.

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Notes

  1. The integration limits must account for the orientation symmetry since each fiber has two opposite orientations. One possibility for limits is \(0 \le \varPhi \le \pi\), \(0 \le \varTheta \le \pi\), another one is \(0 \le \varPhi \le \pi /2\), \(0 \le \varTheta \le 2\pi\).

  2. For example, in an isotropic network \(\mathbb{R}(\varPhi,\varTheta ) = \sin\varPhi /2\pi\).

  3. The Prony series in Eq. (3.5) is not related to the underlying mechanisms which give rise to the fiber’s viscoelasticity. These mechanisms are insufficiently known. In common with other phenomenological VE models, this Prony representation is not unique.

  4. The beta function was preferred over the normal one since it is physically more realistic and more general: it is bounded, can be symmetric and non-symmetric, and can assume different shapes.

  5. \(D(q,t)\) has the same physical meaning at a given growth time \(t\) as the function \(D(q,\mathbf{N})\) in Eq. (2.5) in a uniaxial fiber network (no dependence on \(\mathbf{N}\)).

Abbreviations

CSK:

Cytoskeleton

CVS:

Cardiovascular system

ECM:

Extra-cellular matrix

G&R:

Growth and remodeling

GAG:

Glycosaminoglycans

LM:

Light microscopy

LVE:

Linear viscoelasticity

LV:

Left ventricle

OA:

Opening angle

PC:

Preconditioning

PG:

Proteoglycans

QLV:

Quasilinear viscoelasticity

REV:

Representative elementary volume

RPC:

Recruitment preconditioning

RS:

Residual stress

RVE:

Recruitment viscoelasticity

SEM:

Scanning electron microscopy

VE:

Viscoelasticity

1D, 2D, 3D:

One-, two-, and three-dimensional

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Acknowledgement

The comments and advice of Prof. David Durban are gratefully acknowledged. This research was supported by the National Institutes of Health (grant NIH R01 HL117990).

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    Yoram Lanir

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Lanir, Y. Multi-scale Structural Modeling of Soft Tissues Mechanics and Mechanobiology. J Elast 129, 7–48 (2017). https://doi.org/10.1007/s10659-016-9607-0

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