Simulation of Artificial Cartilage
The Tribology Group in the Department of Orthopedic Surgery at Rush University Medical Center investigates the physical principles of friction, wear, and lubrication of natural and artificial joints. In a team effort with the Institute of Mechanics at the Chemnitz University of Technology ( Germany), theoretical solutions regarding contact problems with hyperelastic materials are sought. When cartilage, an elastic, biphasic material covering the surfaces of joints (such as the knee joint) wears out, it is painful and may require surgical intervention to replace the worn area. An attractive treatment option would be to replace the worn tissue with artificially grown cartilage.
Over the past several years, the evolving field of "functional tissue engineering" has become increasingly popular. In functional tissue engineering, controlled mechanical loads are applied to cartilage cells seeded in a scaffold in an attempt to stimulate the growth of cartilage that will be able to withstand the loads placed on it when it is implanted in the human body. In the development of a functional tissue engineering protocol, it is essential to understand how mechanical forces stimulate the desired response. The optimal loading protocols for the functional development of joint cartilage, however, remain to be identified. To help predict the type and magnitude of mechanical stimuli that are most beneficial for developing artificial tissue, we have turned to computer models. Theoretical modeling, predicting flow and stress fields, for example, are used in synergy with biological experiments to predict how tissue level loading will influence cell behavior and tissue development. Figure 1 shows a potential strategy map. The plan carries the underlying assumption that the mechanical cell stimuli for tissue engineering should be close to what occurs naturally in the joint. Therefore, the strategy plan includes a comparison between tissue engineered constructs and joint cartilage regarding the spatial patterns of mechanical field variables.
Figure 1: Possible Strategy Map
We use MSC software as a platform to simulate cell-seeded implants using finite element analysis (FEA). Subroutines are incorporated to model the complex material behavior and allow for the inclusion of an evolution equation. The evolutional equation allows for time dependent simulation of growing extracellular matrix. A multiscale FEA-approach has been chosen (Figure 2). Starting with a FEM-macromodel of the cartilage cell-scaffold construct, the local load history of a selected element of the FE macro-mesh provides the boundary conditions for a FE-micromodel with a single cell and its neighborhood.
The engineered cartilage tissue can be considered a mixture of two immiscible components, and it is generally accepted that it can be modeled as a saturated porous medium. The poroelastic features of MSC.Marc have been used to account for this biphasic material behavior of the artificial cartilage construct (cartilage cells embedded in a porous polyurethane scaffold). The viscoelastic effects of the scaffold itself were implemented using a newly developed non-linear, bimodular hyperelastic function with a special structural tensor, which modeled the anisotropic behavior of the solid phase.
Figure 2: Macromodel (above) of a cell-scaffold construct and micromodel (right) of a single cell and its neighborhood.
It has been well-established that mechanical loading regulates the anabolic and catabolic metabolism of cells. In particular, anabolic mechanisms are of vital importance for tissue engineering. Within this context, cells seeded and cultured in appropriate constructs have to be stimulated to produce and structure contents of the extracellular tissue matrix.
An incorporated stochastic "tissue growth function" helps to determine the time course as well as the spatial distribution of matrix development.
Since the identification and control of mechanical stimuli driving biological activities represent the crucial link between the experimental and the numerical approach, a coupled experimental-numerical procedure to simulate the spatial distribution (localization) of biological activities has been developed. Once fine tuned, the procedure can be used to reduce the nearly infinite number of combinations of possible loading-scaffold- cell-growth factor to a reasonable set of the most promising conditions that can be evaluated experimentally.