Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

Köry, J.; Hill, N. A.; Luo, X. Y.; Stewart, P. S.

doi:10.1098/rspa.2023.0611

Cited by 3 publications

(1 citation statement)

References 68 publications

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“…The strip is fixed at both ends to the limbus, as a segment of a cylindrical annulus in plane-strain configuration, loaded with the IOP on the posterior surface. Aiming at a rational continuum description of the stroma, we use discrete-to-continuum upscaling to obtain the corresponding strain-energy density [ 33 , 34 ], which will provide the stress and the local stiffness of the tissue. We use this framework to model the onset and progression of keratoconus, by imposing a reduction in the stiffness of the stromal components localized at the central portion of the cornea, and compute the resulting displacement field and the corresponding stress and strain distributions.…”

Section: Introductionmentioning

confidence: 99%

A discrete-to-continuum model for the human cornea with application to keratoconus

Köry,

Stewart,

Hill

et al. 2024

R. Soc. Open Sci.

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We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue. We demonstrate that, for physiological values of the IOP, the predictions of the discrete model converge to those of the continuum model. We use the continuum model to simulate the progression of the degenerative disease known as keratoconus, characterized by a localized bulging of the corneal shell. We assign a spatial distribution of damage (i.e. reduction of the stiffness) to the mechanical properties of the structural elements and predict the resulting macroscopic shape of the cornea, showing that a large reduction in the element stiffness results in substantial corneal thinning and a significant increase in the curvature of both the anterior and posterior surfaces.

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Section: Introductionmentioning

confidence: 99%

A discrete-to-continuum model for the human cornea with application to keratoconus

Köry,

Stewart,

Hill

et al. 2024

R. Soc. Open Sci.

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Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Thekkethil,

Köry,

Guo

et al. 2024

Biomech Model Mechanobiol

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Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes.

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Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

Köry,

Hill,

Luo

et al. 2024

Proc. R. Soc. A.

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We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at cross-links to form a network. Assuming that the inter-cross-link distance is much shorter than the length scale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterizing the cell rheology through the force–displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.

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Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

Cited by 3 publications

References 68 publications

A discrete-to-continuum model for the human cornea with application to keratoconus

A discrete-to-continuum model for the human cornea with application to keratoconus

Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

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