The effects of tumor growth factors on the growth rate of cell cultures

AbstractA mathematical model of growth control in a cell culture in which Tumor Growth Factors (TGF) diffuse through intercellular spaces and act locally is constructed

Mathematical Models of Prevascular Tumor Growth by Diffusion

A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest. The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption on the prevascular tissue growth are examined. The concentrations of nutrients and growth inhibitor are governed by diffusion processes, and thus the equations are of diffusion type in spherically symmetric geometries. Since a key characteristic of cancerous diseases is uncontrolled growth, the sensitivity of a model to the nature of different mitotic control functions is examined and the stability of subsequent tissue growth is discussed. A limiting size for the stable tissue growth is provided, and in related models the time-evolution of the tissue prior to that limiting state is described via a growth (integro-differential) equation for the different phases of tumor growth; the kernel of which depends on the solutions of the spherically symmetric diffusion equations for the concentration of nutrient and growth inhibitor within the tumor. Conditions on the existence and uniqueness of solutions to two classes of non-linear time-independent diffusion equations, which arise in tumor growth models, are also examined. A detailed study of theoretical models of the type constructed here provides useful insight into the basic biological mechanisms of tumor growth, and therefore may offer possibilities for optimization of cancer therapy (e.g. chemo- or radio-therapy)

Everybody Counts or Nobody Counts

Like most campuses, we constantly deal with change at RIT, ranging from policy to climate. We believe everyone needs to feel valued - “Everybody Counts or Nobody Counts, and are attempting to build a supportive culture that includes individual and group mentoring, funding opportunities, and recognition

Eden Model Simulation of Re-Epithelialization and Angiogenesis of an Epidermal Wound

Among the vital processes of cutaneous wound healing are epithelialization and angiogenesis. The former leads to the successful closure of the wound while the latter ensures that nutrients are delivered to the wound region during and after healing is completed. These processes are regulated by various cytokines and growth factors that subtend their proliferation and migration into the wound region until full healing is attained. Wound epithelialization can be enhanced by the administration of epidermal stem cells (ESC) or impaired by the presence of an infection. This paper uses the Eden model of a growing cluster to independently simulate the processes of epithelialization and angiogenesis in a cutaneous wound for different geometries. Further, simulations illustrating bacterial infection are provided. Our simulation results demonstrate contraction and closure for any wound geometry due to a collective migration of epidermal cells from the wound edge in fractal form and the diffusion of capillary sprouts with the laying down of capillary blocks behind moving tips into the wound area