Session B-2
Wound healing (1:30 - 3:30)

1:30 - 2:00 : Xue, chuan (Mathematical Biosciences Institute, Ohio State University)
-Title: Modeling Ischemic Cutaneous Wounds
Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia, primarily caused by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this talk, we present a mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model equations involve the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how ischemic conditions may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings.

2:00 - 2:30 : Lee, Pilhwa (Wolgemuth lab, Department of Cell Biology, University of Connecticut Health Center, Courant Institute, New York University)
-Title: Toward wound healing of MDCK tissue : model and experiments
The migration of crawling cells is considered in their behavior of wound closure. The talk is focused on the mechanical contribution of crawling cells, i.e. dipole stress, and the stress dynamics derived from Lacker-Peskin model. In our model, actomyosin driven purse-strings or biochemical signaling of Rho family do not involve directly. In simplified one-dimensional formulations, velocity profiles for healing are explored in terms of turn-over rate and cell-to-cell viscosity mediated by Cadherin proteins. For the circular wound assay, we show a transition from closure to non-closure behavior with the dead cell zone in the epithelial layers, which supports the hypothesis that a crawling cell's dipole can close wounds without purse strings or signaling. In a rigorous two-dimensional model, we observe the healing speed is dependent on the assay width. There are long-range correlations in the scale of 100 micron from streaming and circulating cells. All of them are consistent with experimental data from MDCK assay. Interestingly, a bundle of tissue parameters applied in the one-dimensional approximation is a good precursor for the parameter exploration on two-dimensional simulation.

2:30 - 3:00 : Arciero, Julia (Mathematics, University of Pittsburgh)
-Title: Simulating wound healing with a two dimensional continuum mechanical model
Collective cell migration is an important mode of cell movement during wound healing. We have developed a two-dimensional continuum mechanical model that is used to simulate cell sheet migration and that captures the mechanical coupling between cells in the layer, the adhesion of cells to the substrate, the forces generated by lamellipodia at the cell edge and within the layer, and the proliferation and apoptosis of cells in the layer. The governing equations are solved numerically using a level set method. The model is calibrated by comparing the predicted density of the layer with experimentally observed cell density. Model results show good agreement with experimental observations of the dependence of the rate of wound closure on time.

3:00 - 3:30 : Kao, Chiu-Yen (Mathematics, Ohio State University)
Authors: Anastasios Matzavinos,Chiu-Yen Kao, J. Edward F. Green, Alok Sutradhar, Michael Miller and Avner Friedman
-Title: Modeling oxygen transport in surgical tissue transfer
Reconstructive microsurgery is a clinical technique used to transfer large amounts of a patient's tissue from one location used to another in order to restore physical deformities caused by trauma, tumors, or congenital abnormalities. The trend in this field is to transfer tissue using increasingly smaller blood vessels, which decreases problems associated with tissue harvest but increases the possibility that blood supply to the transferred tissue may not be adequate for healing. It would thus be helpful to surgeons to understand the relationship between the tissue volume and blood vessel diameter to ensure success in these operations. As a first step towards addressing this question, we present a simple mathematical model that might be used to predict successful tissue transfer based on blood vessel diameter, tissue volume, and oxygen delivery.