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

A review of mathematical models for the formation of vascular networks

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyse these phenomena. In this article, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA

Computational modelling of wound healing insights to develop new treatments

About 1% of the population will suffer a severe wound during their life. Thus, it is really important to develop new techniques in order to properly treat these injuries due to the high socioeconomically impact they suppose. Skin substitutes and pressure based therapies are currently the most promising techniques to heal these injuries. Nevertheless, we are still far from finding a definitive skin substitute for the treatment of all chronic wounds. As a first step in developing new tissue engineering tools and treatment techniques for wound healing, in silico models could help in understanding the mechanisms and factors implicated in wound healing. Here, we review mathematical models of wound healing. These models include different tissue and cell types involved in healing, as well as biochemical and mechanical factors which determine this process. Special attention is paid to the contraction mechanism of cells as an answer to the tissue mechanical state. Other cell processes such as differentiation and proliferation are also included in the models together with extracellular matrix production. The results obtained show the dependency of the success of wound healing on tissue composition and the importance of the different biomechanical and biochemical factors. This could help to individuate the adequate concentration of growth factors to accelerate healing and also the best mechanical properties of the new skin substitute depending on the wound location in the body and its size and shape. Thus, the feedback loop of computational models, experimental works and tissue engineering could help to identify the key features in the design of new treatments to heal severe wounds

The Effect of Bacteria on Epidermal Wound Healing

Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage-derived growth factors. We express the model as a system of reaction-diffusion equations, and we present results of computations for a version of the model with one spatial dimension