During dermal wound healing, platelet-derived growth factor (PDGF) serves as both a chemoattractant and mitogen for fibroblasts, potently stimulating their invasion of the fibrin clot across mm to cm length scales over a period of days to weeks. A continuum model of this process is presented, which integrates the pertinent details of PDGF gradient sensing through intracellular PDGF receptor/phosphoinositide (PI) 3-kinase-mediated signal transduction. Analysis of the model suggests that PDGF receptor-mediated endocytosis and degradation of PDGF allows a constant PDGF concentration profile to be maintained at the leading front of the fibroblast density profile as it propagates, at a constant rate, into the clot. Thus, the constant PDGF gradient can span the optimal concentration range for asymmetric PI 3-kinase signaling and fibroblast chemotaxis, with near-maximal invasion rates elicited over a relatively broad range of PDGF secretion rates. A somewhat surprising finding was that extremely sharp PDGF gradients do not necessarily stimulate faster progression through the clot, because maintaining such a gradient through PDGF consumption is a potentially rate-limiting process. We have recently supplemented the continuum results with probabilistic simulations of discrete cells, which show that cell-to-cell variability in receptor expression levels can enhance the rate of wound invasion by widening the range of PDGF concentrations that elicit effective gradient sensing. This analysis links signal transduction at the single cell level to the dynamic progression of wound invasion at the cell population level.