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Research Papers

# Parametric Finite Element Analysis of Physical Stimuli Resulting From Mechanical Stimulation of Tissue Engineered Cartilage

[+] Author and Article Information
Omotunde M. Babalola

Department of Biomedical Engineering, Cornell University, 151 Weill Hall, Ithaca, NY 14853omb3@cornell.edu

Lawrence J. Bonassar1

Department of Biomedical Engineering and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853lb244@cornell.edu

1

Corresponding author.

J Biomech Eng 131(6), 061014 (May 11, 2009) (7 pages) doi:10.1115/1.3128672 History: Received November 18, 2008; Revised March 12, 2009; Published May 11, 2009

## Abstract

While mechanical stimulation of cells seeded within scaffolds is widely thought to be beneficial, the amount of benefit observed is highly variable between experimental systems. Although studies have investigated specific experimental loading protocols thought to be advantageous for cartilage growth, less is known about the physical stimuli (e.g., pressures, velocities, and local strains) cells experience during these experiments. This study used results of a literature survey, which looked for patterns in the efficacy of mechanical stimulation of chondrocyte seeded scaffolds, to inform the modeling of spatial patterns of physical stimuli present in mechanically stimulated constructs. The literature survey revealed a large variation in conditions used in mechanical loading studies, with a peak to peak strain of 10% (i.e., the maximum amount of deformation experienced by the scaffold) at 1 Hz on agarose scaffolds being the most frequently studied parameters and scaffold. This loading frequency was then used as the basis for simulation in the finite element analyses. 2D axisymmetric finite element models of $2×4 mm2$ scaffolds with 360 modulus/permeability combinations were constructed using COMSOL MULTIPHYSICS software. A time dependent coupled pore pressure/effective stress analysis was used to model fluid/solid interactions in the scaffolds upon loading. Loading was simulated using an impermeable frictionless loader on the top boundary with fluid and solid displacement confined to the radial axis. As expected, all scaffold materials exhibited classic poro-elastic behavior having pressurized cores with low fluid flow and edges with high radial fluid velocities. Under the simulation parameters of this study, PEG scaffolds had the highest pressure and radial fluid velocity but also the lowest shear stress and radial strain. Chitosan and KLD-12 simulated scaffold materials had the lowest radial strains and fluid velocities, with collagen scaffolds having the lowest pressures. Parametric analysis showed maximum peak pressures within the scaffold to be more dependent on scaffold modulus than on permeability and velocities to depend on both scaffold properties similarly. The dependence of radial strain on permeability or modulus was more complex; maximum strains occurred at lower permeabilities and moduli, and the lowest strain occurred at the stiffest most permeable scaffold. Shear stresses within all scaffolds were negligible. These results give insight into the large variations in metabolic response seen in studies involving mechanical stimulation of cell-seeded constructs, where the same loading conditions produce very different results due to the differences in material properties.

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## Figures

Figure 5

Schematic of the device geometry commonly used for mechanical stimulation studies and the resultant free body diagram of the dynamic compression of an axisymmetric model of a scaffold used in such a device

Figure 6

Map of scaffold materials depicting the range of modulus (horizontal) and hydraulic permeability (vertical) used in cartilage tissue engineering studies

Figure 7

Surface plots of pressure (Pa) and radial velocity (arrows) of dynamically loaded cartilage (a), polyethylene glycol (PEG) (b), alginate (c), and collagen models at steady state (t=299.75 s) and their assumed modulus (kPa) and permeability (m4/N s)

Figure 8

Maximum peak pressure and radial fluid velocity as a function of permeability and modulus, showing sample scaffolds with related material properties with labels for scaffolds superimposed over appropriate regions of material properties

Figure 1

Flow chart of experimental approaches used to study mechanical influences on cartilage or chondrocyte metabolism

Figure 2

Results of the survey of the strain amplitudes and frequencies used for the cyclic axial compression of chondrocytes-seeded scaffolds displaying the wide range of strains and frequencies studied to date

Figure 3

Compilation of the data from surveyed studies demonstrating the effect of loading parameters (frequency (a) and % peak to peak strain (b)) on GAG synthesis

Figure 4

Compilation of data from surveyed studies showing the effect of scaffold properties (modulus (a) and porosity (b)) on GAG synthesis.

Figure 9

Plots of maximum (a) shear stress and (b) radial strain as a function of permeability and modulus, showing sample scaffolds with related material properties with labels for scaffold materials superimposed over appropriate regions of materials

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