NC STATE UNIVERSITY
Orthopaedic Biomaterials Group
Participants
Faculty Leader Mansoor Haider
Postdoctoral Fellows

Zhengzheng Hu

Graduate Students

Mandy Smith

Undergraduate Students

Tim Wessler

Alumni Brandy Benedict (PhD 2008)
(Assistant Professor, Dept. of Mathematics, Merrimack College)
Sarah Olson (PhD 2008)
(VIGRE Postdoc, Mathematics Dept.,Tulane University)
Eunjung Kim (PhD 2009)
(Research Associate, Moffitt Cancer Center & Research Institute)
Janine Haugh (PhD 2010)
(Assistant Professor, Dept. of Mathematics, UNC-Asheville)
Research Highlights
1. Modeling cartilage regeneration in the extracellular enviroment of a cell-seeded hydrogel
(Janine Haugh, PhD 2010)
Articular cartilage is a connective tissue lining the surfaces of bones in diarthrodial joints such as hips, knees, and shoulders. As a natural biomaterial, cartilage is important for load support, energy distribution, and lubrication of joints, but can become damaged due to injury or osteoarthritis. Cartilage has a limited capacity for repair and growth that is regulated by cells, called chondrocytes, that are sparsely distributed throughout the tissue’s extracellular matrix (ECM).   In recent years, the potential use of nutrient-rich hydrogels seeded with cartilage cells as biomaterials for tissue regeneration and repair has seen wide interest. In this study, we develop mathematical models for cartilage regeneration in the local environment of a single cell seeded in a hydrogel scaffold. A spherical geometry is employed with three concentric regions: the cell, its extracellular matrix and the hydrogel.  Radially symmetric reaction-diffusion equations are used to describe the coupling of nutrient [left] and synthesized (unlinked) matrix concentrations [right] in the region. Several models are considered to describe the process by which unlinked matrix proteins react with the hydrogel to form linked extracellular matrix.  Numerical solutions are based on finite difference methods and capture motion of the evolving gel-tissue interface.  The resulting models are used to conduct a parametric analysis that quantifies tissue regeneration times in terms of underlying biophysical parameters in the models.
2. Axisymmetric boundary integral model for in situ estimation of cartilage pericellar matrix elastic properties
(Eunjung Kim, PhD 2009)
The pericellular matrix (PCM) is a narrow tissue region completely surrounding chondrocytes in articular cartilage, which together with the enclosed cell is termed a chondron. The PCM is defined primarily by the presence of type VI collagen, in contrast to the extracellular matrix (ECM) which contains type II collagen. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the mechanical environment of the chondrocyte. A multiscale boundary integral model was developed to determine the elastic properties of the PCM via inverse analysis of in situ confocal microscopy data from the three-dimensional morphological changes of the chondron under unconfined compression. The microscale cartilage environment was represented as a three-zone equilibrated biphasic region [left] consisting of an ellipsoidal chondrocyte with encapsulating PCM that was embedded in a spherical ECM subjected to unconfined compressive loading boundary conditions. Accuracy of the three-zone boundary integral model was evaluated and compared to analytical solutions and finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder-Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data [right]. This study represents the first application of a computational model to estimate material properties of the PCM in situ, i.e. withing the native ECM of cartilage.