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Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells.

ABSTRACT: Hemodynamic forces applied at the apical surface of vascular endothelial cells may be redistributed to and amplified at remote intracellular organelles and protein complexes where they are transduced to biochemical signals. In this study we sought to quantify the effects of cellular material inhomogeneities and discrete attachment points on intracellular stresses resulting from physiological fluid flow. Steady-state shear- and magnetic bead-induced stress, strain, and displacement distributions were determined from finite-element stress analysis of a cell-specific, multicomponent elastic continuum model developed from multimodal fluorescence images of confluent endothelial cell (EC) monolayers and their nuclei. Focal adhesion locations and areas were determined from quantitative total internal reflection fluorescence microscopy and verified using green fluorescence protein-focal adhesion kinase (GFP-FAK). The model predicts that shear stress induces small heterogeneous deformations of the endothelial cell cytoplasm on the order of <100 nm. However, strain and stress were amplified 10-100-fold over apical values in and around the high-modulus nucleus and near focal adhesions (FAs) and stress distributions depended on flow direction. The presence of a 0.4 microm glycocalyx was predicted to increase intracellular stresses by approximately 2-fold. The model of magnetic bead twisting rheometry also predicted heterogeneous stress, strain, and displacement fields resulting from material heterogeneities and FAs. Thus, large differences in moduli between the nucleus and cytoplasm and the juxtaposition of constrained regions (e.g. FAs) and unattached regions provide two mechanisms of stress amplification in sheared endothelial cells. Such phenomena may play a role in subcellular localization of early mechanotransduction events.

SUBMITTER: Ferko MC

PROVIDER: S-EPMC3251212 | biostudies-literature | 2007 Feb

REPOSITORIES: biostudies-literature

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Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells.

Ferko Michael C MC Bhatnagar Amit A Garcia Mariana B MB Butler Peter J PJ

Annals of biomedical engineering 20061212 2

Hemodynamic forces applied at the apical surface of vascular endothelial cells may be redistributed to and amplified at remote intracellular organelles and protein complexes where they are transduced to biochemical signals. In this study we sought to quantify the effects of cellular material inhomogeneities and discrete attachment points on intracellular stresses resulting from physiological fluid flow. Steady-state shear- and magnetic bead-induced stress, strain, and displacement distributions ...[more]

PMID: 17160699

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Project description:PurposeThe study presents an averaged anterior eye geometry model combined with a localised material model that is straightforward, appropriate and amenable for implementation in finite element (FE) modelling.MethodsBoth right and left eye profile data of 118 subjects (63 females and 55 males) aged 22-67 years (38.5 ± 7.6) were used to build an averaged geometry model. Parametric representation of the averaged geometry model was achieved through two polynomials dividing the eye into three smoothly connected volumes. This study utilised the collagen microstructure x-ray data of 6 ex-vivo healthy human eyes, 3 right eyes and 3 left eyes in pairs from 3 donors, 1 male and 2 females aged between 60 and 80 years, to build a localised element-specific material model for the eye.ResultsFitting the cornea and the posterior sclera sections to a 5th-order Zernike polynomial resulted in 21 coefficients. The averaged anterior eye geometry model recorded a limbus tangent angle of 37° at a radius of 6.6 mm from the corneal apex. In terms of material models, the difference between the stresses generated in the inflation simulation up to 15 mmHg in the ring-segmented material model and localised element-specific material model were significantly different (p < 0.001) with the ring-segmented material model recording average Von-Mises stress 0.0168 ± 0.0046 MPa and the localised element-specific material model recording average Von-Mises stress 0.0144 ± 0.0025 MPa.ConclusionsThe study illustrates an averaged geometry model of the anterior human eye that is easy to generate through two parametric equations. This model is combined with a localised material model that can be used either parametrically through a Zernike fitted polynomial or non-parametrically as a function of the azimuth angle and the elevation angle of the eye globe. Both averaged geometry and localised material models were built in a way that makes them easy to implement in FE analysis without additional computation cost compared to the limbal discontinuity so-called idealised eye geometry model or ring-segmented material model.

Project description:BACKGROUND: Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan. METHODS: A Galerkin-based finite element model was developed and implemented to solve a system of two coupled partial differential equations governing biomolecule transport and reaction in live cells. The simulator was coupled, in the framework of an inverse modeling strategy, with an optimization algorithm and an experimental time series, obtained by the Fluorescence Recovery after Photobleaching (FRAP) technique, to estimate biomolecule mass transport and reaction rate parameters. In the inverse algorithm, an adaptive method was implemented to calculate sensitivity matrix. A multi-criteria termination rule was developed to stop the inverse code at the solution. The applicability of the model was illustrated by simulating the mobility and binding of GFP-tagged glucocorticoid receptor in the nucleoplasm of mouse adenocarcinoma. RESULTS: The numerical simulator shows excellent agreement with the analytic solutions and experimental FRAP data. Detailed residual analysis indicates that residuals have zero mean and constant variance and are normally distributed and uncorrelated. Therefore, the necessary and sufficient criteria for least square parameter optimization, which was used in this study, were met. CONCLUSION: The developed strategy is an efficient approach to extract as much physiochemical information from the FRAP protocol as possible. Well-posedness analysis of the inverse problem, however, indicates that the FRAP protocol provides insufficient information for unique simultaneous estimation of diffusion coefficient and binding rate parameters. Care should be exercised in drawing inferences, from FRAP data, regarding concentrations of free and bound proteins, average binding and diffusion times, and protein mobility unless they are confirmed by long-range Markov Chain-Monte Carlo (MCMC) methods and experimental observations.

Project description:Isolating the role(s) of microstructural pathological features in affecting diastolic filling is important in developing targeted treatments for heart diseases. We developed a microstructure-based constitutive model of the myocardium and implemented it in an efficient open-source finite element modeling framework to simulate passive inflation of the left ventricle (LV) in a representative 3D geometry based on experimentally measured muscle fiber architecture. The constitutive model was calibrated using previous tissue-level biaxial mechanical test data derived from the canine heart and validated with independent sets of measurements made at both the isolated constituent and organ level. Using the validated model, we investigated the load taken up by each tissue constituent and their effects on LV passive inflation. The model predicts that the LV compliance is sensitive to the collagen ultrastructure, specifically, the collagen fiber azimuthal angle with respect to the local muscle fiber direction and its waviness. The model also predicts that most of the load in the sub-epicardial and sub-endocardial regions is taken up, respectively, by the muscle fibers and collagen fiber network. This result suggests that normalizing LV passive stiffness by altering the collagen fiber network and myocyte stiffness is most effective when applied to the sub-endocardial and sub-epicardial regions, respectively. This finding may have implication for the development of new pharmaceutical treatments targeting individual cardiac tissue constituents to normalize LV filling function in heart diseases. STATEMENT OF SIGNIFICANCE: Current constitutive models describing the tissue mechanical behavior of the myocardium are largely phenomenological. While able to represent the bulk tissue mechanical behavior, these models cannot distinguish the contribution of the tissue constituents and their ultrastructure to heart function. Although microstructure-based constitutive models can be used to isolate the role of tissue ultrastructure, they have not been implemented in a computational framework that can accommodate realistic 3D organ geometry. The present study addresses these issues by developing and validating a microstructure-based computational modeling framework, which is used to investigate the role of tissue constituents and their ultrastructure in affecting heart function.

Dataset Information

Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells.

Publications

Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells.

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