Computational modeling of bone density profiles in response to gait: a subject-specific approach

Pang, Henry; Shiwalkar, Abhishek P.; Madormo, Chris M.; Taylor, R. E.; Andriacchi, Thomas P.; Kuhl, Ellen

doi:10.1007/s10237-011-0318-y

Cited by 14 publications

(27 citation statements)

References 37 publications

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“…We know why dental implants loosen over time in response to bone remodeling. We know that osteoporosis is associated with a local bone loss, which can be correlated to gait profiles [91]. And we know why high-performance athletes in asymmetric sports, such as tennis players or baseball pitchers, have a significantly stronger dominant arm, in which they might develop chronic pain [104].…”

Section: A Brief History Of Growth and Remodelingmentioning

confidence: 99%

Frontiers in growth and remodeling

Menzel

Kuhl

2012

Mechanics Research Communications

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189

140

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Unlike common engineering materials, living matter can autonomously respond to environmental changes. Living structures can grow stronger, weaker, larger, or smaller within months, weeks, or days as a result of a continuous microstructural turnover and renewal. Hard tissues can adapt by increasing their density and grow strong. Soft tissues can adapt by increasing their volume and grow large. For more than three decades, the mechanics community has actively contributed to understand the phenomena of growth and remodeling from a mechanistic point of view. However, to date, there is no single, unified characterization of growth, which is equally accepted by all scientists in the field. Here we shed light on the continuum modeling of growth and remodeling of living matter, and give a comprehensive overview of historical developments and trends. We provide a state-of-the-art review of current research highlights, and discuss challenges and potential future directions. Using the example of volumetric growth, we illustrate how we can establish and utilize growth theories to characterize the functional adaptation of soft living matter. We anticipate this review to be the starting point for critical discussions and future research in growth and remodeling, with a potential impact on life science and medicine.

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Section: A Brief History Of Growth and Remodelingmentioning

confidence: 99%

Frontiers in growth and remodeling

Menzel

Kuhl

2012

Mechanics Research Communications

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189

140

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“…The balance of mass for open systems balances its rate of change ρ̇ 0 with a possible in- or outflux of mass R and mass source ℛ 0 [51, 64].

{\overset{ρ}{true}}_{0} = Div (R) {+ ℛ}_{0}

…”

Section: Continuum Modeling Of Area Growthmentioning

confidence: 99%

Growing skin: A computational model for skin expansion in reconstructive surgery

Tepole

Ploch

Wong

et al. 2011

Journal of the Mechanics and Physics of Solids

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113

106

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The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

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“…The second keep the volume constant, while the density changes. Pang et al (2011) presented these concepts for isotropic growth andMenzel (2004, 2007) for anisotropic growth. The kinematics of these approximations were first described by Skalak et al (1982) and Rodriguez et al (1994).…”

Section: Motivationmentioning

confidence: 99%

Mathematical modeling of collagen turnover in biological tissue

et al. 2012

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We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-β and tissue inhibitors of metalloproteinases TIMP. While the upregulation of the former increases the collagen density, the upregulation of the latter increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.

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Computational modeling of bone density profiles in response to gait: a subject-specific approach

Cited by 14 publications

References 37 publications

Frontiers in growth and remodeling

Frontiers in growth and remodeling

Growing skin: A computational model for skin expansion in reconstructive surgery

Mathematical modeling of collagen turnover in biological tissue

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