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Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis.

ABSTRACT: The feasibility of determining biphasic material properties using a finite element model of stress relaxation coupled with two types of constrained optimization to match measured data was investigated. Comparison of these two approaches, a zero-order method and a gradient-based algorithm, validated the predicted material properties. Optimizations were started from multiple different initial guesses of material properties (design variables) to establish the robustness of the optimization. Overall, the optimal values are close to those found by Cohen et al. (1998) but these small differences produced a marked improvement in the fit to the measured stress relaxation. Despite the greater deviation in the optimized values obtained from the zero-order method, both optimization procedures produced material properties that gave equally good overall fits to the measured data. Furthermore, optimized values were all within the expected range of material properties. Modeling stress relaxation using the optimized material properties showed an excellent fit to the entire time history of the measured data.

SUBMITTER: Chung CY

PROVIDER: S-EPMC4286505 | biostudies-literature | 2015 Feb

REPOSITORIES: biostudies-literature

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Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis.

Chung Chen-Yuan CY Mansour Joseph M JM

Journal of the mechanical behavior of biomedical materials 20141028

The feasibility of determining biphasic material properties using a finite element model of stress relaxation coupled with two types of constrained optimization to match measured data was investigated. Comparison of these two approaches, a zero-order method and a gradient-based algorithm, validated the predicted material properties. Optimizations were started from multiple different initial guesses of material properties (design variables) to establish the robustness of the optimization. Overall ...[more]

PMID: 25460921

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Project description:Osteoarthrosis is a debilitating disease affecting millions, yet engineering materials for cartilage regeneration has proven difficult because of the complex microstructure of this tissue. Articular cartilage, like many biological tissues, produces a time-dependent response to mechanical load that is critical to cell's physiological function in part due to solid and fluid phase interactions and property variations across multiple length scales. Recreating the time-dependent strain and fluid flow may be critical for successfully engineering replacement tissues but thus far has largely been neglected. Here, microindentation is used to accomplish three objectives: (1) quantify a material's time-dependent mechanical response, (2) map material properties at a cellular relevant length scale throughout zonal articular cartilage and (3) elucidate the underlying viscoelastic, poroelastic, and nonlinear poroelastic causes of deformation in articular cartilage. Untreated and trypsin-treated cartilage was sectioned perpendicular to the articular surface and indentation was used to evaluate properties throughout zonal cartilage on the cut surface. The experimental results demonstrated that within all cartilage zones, the mechanical response was well represented by a model assuming nonlinear biphasic behavior and did not follow conventional viscoelastic or linear poroelastic models. Additionally, 10% (w/w) agarose was tested and, as anticipated, behaved as a linear poroelastic material. The approach outlined here provides a method, applicable to many tissues and biomaterials, which reveals and quantifies the underlying causes of time-dependent deformation, elucidates key aspects of material structure and function, and that can be used to provide important inputs for computational models and targets for tissue engineering. STATEMENT OF SIGNIFICANCE:Elucidating the time-dependent mechanical behavior of cartilage, and other biological materials, is critical to adequately recapitulate native mechanosensory cues for cells. We used microindentation to map the time-dependent properties of untreated and trypsin treated cartilage throughout each cartilage zone. Unlike conventional approaches that combine viscoelastic and poroelastic behaviors into a single framework, we deconvoluted the mechanical response into separate contributions to time-dependent behavior. Poroelastic effects in all cartilage zones dominated the time-dependent behavior of articular cartilage, and a model that incorporates tension-compression nonlinearity best represented cartilage mechanical behavior. These results can be used to assess the success of regeneration and repair approaches, as design targets for tissue engineering, and for development of accurate computational models.

Project description:Over the past two decades, the increase in prevalence of cardiovascular diseases and the limited availability of autologous blood vessels and saphenous vein grafts have motivated the development of tissue-engineered vascular grafts (TEVGs). However, compliance mismatch and poor mechanical properties of the TEVGs remain as two major issues that need to be addressed. Researchers have investigated the role of various culture conditions and mechanical conditioning in deposition and orientation of collagen fibers, which are the key structural components in the vascular wall; however, the intrinsic complexity of mechanobiological interactions demands implementing new engineering approaches that allow researchers to investigate various scenarios more efficiently. In this study, we utilized a coupled agent-based finite element analysis (AB-FEA) modeling approach to study the effect of various loading modes (uniaxial, biaxial, and equibiaxial), boundary conditions, stretch magnitudes, and growth factor concentrations on growth and remodeling of smooth muscle cell-populated TEVGs, with specific focus on collagen deposition and orientation. Our simulations (12 weeks of culture) showed that biaxial cyclic loading (and not uniaxial or equibiaxial) leads to alignment of collagen fibers in the physiological directions. Moreover, axial boundary conditions of the TEVG act as determinants of fiber orientations. Decreasing the serum concentration, from 10% to 5% or 1%, significantly decreased the growth and remodeling speed, but only affected the fiber orientation in the 1% serum case. In conclusion, in silico tissue engineering has the potential to evolve the future of tissue engineering, as it will allow researchers to conceptualize various interactions and investigate numerous scenarios with great speed. In this study, we were able to predict the orientation of collagen fibers in TEVGs using a coupled AB-FEA model in less than 8?h. Impact Statement Tissue-engineered vascular grafts (TEVGs) hold potential to replace the current gold standard of vascular grafting, saphenous vein grafts. However, developing TEVGs that mimic the mechanical performance of the native tissue remains a challenging task. We developed a computational model of the grafts' remodeling processes and studied the effects of various loading mechanisms and culture conditions on collagen fiber orientation, which is a key factor in mechanical performance of the grafts. We were able to predict the fiber orientations accurately and show that biaxial loading and axial boundary conditions are important factors in collagen fiber organization.

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Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis.

Publications

Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis.

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