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Research Papers

A Finite Element Model of Cell-Matrix Interactions to Study the Differential Effect of Scaffold Composition on Chondrogenic Response to Mechanical Stimulation

[+] Author and Article Information
Taly P. Appelman, Joseph Mizrahi

Faculty of Biomedical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel

Dror Seliktar1

Faculty of Biomedical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israeldror@bm.technion.ac.il

1

Corresponding author.

J Biomech Eng 133(4), 041010 (Mar 23, 2011) (12 pages) doi:10.1115/1.4003314 History: Received March 30, 2010; Revised December 14, 2010; Posted December 22, 2010; Published March 23, 2011; Online March 23, 2011

Mechanically induced cell deformations have been shown to influence chondrocyte response in 3D culture. However, the relationship between the mechanical stimulation and cell response is not yet fully understood. In this study a finite element model was developed to investigate cell-matrix interactions under unconfined compression conditions, using a tissue engineered encapsulating hydrogel seeded with chondrocytes. Model predictions of stress and strain distributions within the cell and on the cell boundary were shown to exhibit space-dependent responses that varied with scaffold mechanical properties, the presence of a pericellular matrix (PCM), and the cell size. The simulations predicted that when the cells were initially encapsulated into the hydrogel scaffolds, the cell size hardly affected the magnitude of the stresses and strains that were reaching the encapsulated cells. However, with the inclusion of a PCM layer, larger cells experienced enhanced stresses and strains resulting from the mechanical stimulation. It was also noted that the PCM had a stress shielding effect on the cells in that the peak stresses experienced within the cells during loading were significantly reduced. On the other hand, the PCM caused the stresses at the cell-matrix interface to increase. Based on the model predictions, the PCM modified the spatial stress distribution within and around the encapsulated cells by redirecting the maximum stresses from the periphery of the cells to the cell nucleus. In a tissue engineered cartilage exposed to mechanical loading, the formation of a neo-PCM by encapsulated chondrocytes appears to protect them from initially excessive mechanical loading. Predictive models can thus shed important insight into how chondrocytes remodel their local environment in order to redistribute mechanical signals in tissue engineered constructs.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Histological cross-sections of hydrogel constructs stained for proteoglycans with Safranin O: (a) after 24 h, ((b) and (c)) after 28 days with stimulation in two different types of hydrogels, and ((d) and (e)) examples of sections including different cells subjected to the same mechanical stimulation but resulting in different quantities of PCM secretion. Scale bars: 10 μm.

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Figure 2

2D meshes used in the axisymmetry simulation in the case of cell radii of (a)5 μm, (b) 7.5 μm, and (c) 10 μm. The coordinate system used in the simulations can be found in (c).

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Figure 3

Modification of the neo-Hookean model for the scaffold subdomain. The modification of the neo-Hookean model (squares versus circles) produced a better fit to the experimental behavior (plain line) observed in the compression experiments. The experimental trend line was based on modulus values taken directly from the true stress-strain curves of the scaffold under compression, as measured by an Instron testing machine (14).

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Figure 4

Scaffold modulus effects on the von Mises stresses with deformations: ((a) and (d)) with PCM and ((b) and (c)) without PCM, for scaffold modulus of ((a) and (b)) 2 kPa and ((c) and (d)) 10 kPa. Each set of matching figures have the same scale and color bar to simplify comparison. PCM parameters are E=40 kPa, ν=0.04, cell parameters are E=3.2 kPa, ν=0.4.

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Figure 5

Von Mises stresses within the cell space ((a) and (d)) with and ((b) and (c)) without PCM for the cases that the scaffold modulus was ((a) and (b)) 10 kPa and ((c) and (d)) 2 kPa. Changes can be noted in both spatial distribution and magnitude.

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Figure 6

Maximum von Mises stresses in the ((a) and (b)) cell subdomain and ((c) and (d)) on the cell-matrix boundary as a function of scaffold modulus in the case of three different cell sizes, before and after the PCM was created

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Figure 7

The effect of scaffold modulus on the relative cell radius change (RRC), defined as the deformed radius divided by the initial radius, in the z and r directions, with and without PCM, for three cell sizes

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Figure 8

The effect of different modeling techniques on the maximum von Mises stress in the different subdomains as a function of scaffold modulus, with and without PCM. Cell radius was taken as 5 μm.

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Figure 9

The effect of different constitutive models on the maximum von Mises stress at the cell-matrix boundary as a function of scaffold modulus, with and without PCM. Cell radius was taken as 5 μm.

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Figure 10

The effect of different constitutive models on the relative cell radius change (RRC), defined as the deformed radius divided by the initial radius, in the z and r directions as a function of scaffold modulus, with and without PCM. The initial cell radius was taken as 5 μm.

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Figure 11

The effect of cell modulus on (b) maximum von Mises stresses in the subdomains, (c) relative cell radius change, defined as the deformed radius divided by the initial radius, in the z direction, (d) relative cell radius change. In the r direction, and (e) maximum von Mises stress at the cell-PCM boundary (parameters used are summarized in (a)). The spatial von Mises stresses and deformation are demonstrated for the case of cell modulus of (f) 0.35 kPa and (g) 4 kPa.

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Figure 12

PCM secretion effects on (a) the maximum von Mises stresses in the different subdomains and (b) the von Mises stresses on the cell-matrix boundary plotted according to the arc length

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