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1.  Evaluation of a Post-Processing Approach for Multiscale Analysis of Biphasic Mechanics of Chondrocytes 
Understanding the mechanical behavior of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue level deformations drive cell level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of 1st and 2nd order data passing to predict chondrocyte mechanics by analyzing cartilage deformations obtained for varying complexity of loading scenarios. A tissue scale model with a sub-region incorporating representation of chondron size and distribution served as control. The postprocessing approach first required solution of a homogeneous tissue level model, results of which were used to drive a separate cell level model (same characteristics as the subregion of control model). The 1st data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, e.g., change in aspect ratio. The 2nd order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries were considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, e.g., mass exchange rate. Nonetheless, employing higher-order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.
PMCID: PMC4157590  PMID: 23809004
multiscale; computational modeling; finite element; cartilage; chondrocyte; poroelastic; biphasic; tissue mechanics; cell mechanics; homogenization
2.  A Computational Model of In Vitro Angiogenesis based on Extracellular Matrix Fiber Orientation 
Recent interest in the process of vascularization within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remain poorly understood. In vitro methods for studying angiogenesis exist, however measurements available using such techniques often suffer from limited spatial and temporal resolution. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This manuscript outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching, and orientation morphometrics collected from vascularized tissue constructs. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modeling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.
PMCID: PMC3459304  PMID: 22515707
Angiogenesis; computational model; tissue engineering; extracellular matrix; fiber orientation; matrix anisotropy
3.  Chondrocyte Deformations as a Function of Tibiofemoral Joint Loading Predicted by a Generalized High-Throughput Pipeline of Multi-Scale Simulations 
PLoS ONE  2012;7(5):e37538.
Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 μm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method’s generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.
PMCID: PMC3359292  PMID: 22649535
4.  Angiogenesis in a Microvascular Construct for Transplantation Depends on the Method of Chamber Circulation 
Tissue Engineering. Part A  2009;16(3):795-805.
Effective tissue prevascularization depends on new vessel growth and subsequent progression of neovessels into a stable microcirculation. Isolated microvessel fragments in a collagen-based microvascular construct (MVC) spontaneously undergo angiogenesis in static conditions in vitro but form a new microcirculation only when implanted in vivo. We have designed a bioreactor, the dynamic in vitro perfusion (DIP) chamber, to culture MVCs in vitro with perfusion. By altering bioreactor circulation, microvessel fragments in the DIP chamber either maintained stable, nonsprouting, patent vessel morphologies or sprouted endothelial neovessels that extended out into the surrounding collagen matrix (i.e., angiogenesis), yielding networks of neovessels within the MVC. Neovessels formed in regions of the construct predicted by simulation models to have the steepest gradients in oxygen levels and expressed hypoxia inducible factor-1α. By altering circulation conditions in the DIP chamber, we can control, possibly by modulating hypoxic stress, prevascularizing activity in vitro.
PMCID: PMC2862615  PMID: 19778185

Results 1-4 (4)