BIOMAT. MATHEMATICAL MODELS AND METHODS IN BIOLOGY AND MEDICINE.

In recent years the use of quantitative methods in Biology and Medicine has considerably increased. In this Programme we intend to focus on some particular research lines where this type of techniques shows particularly promising prospects. More precisely, we shall deal with following issues.

1.- Vasculogenesis.

The vascular system is the first functional system which becomes fully operational in vertebrates. As a matter of fact, its functioning is required to ensure nutrients inflow, and waste disposal, to the developing organs of the embryo. The vascular system is made up of blood vessels, which are formed according to two basic mechanisms. The first of these is vasculogenesis, which gives raise to formation of vessels of different sizes and widths, starting from isolated precursors (angioblasts), thus yielding the basic layout of the vascular net of adult organisms. A second process, termed as angiogenesis, is used to remodel an already pre-existent vasculature, both in homeostatic and pathological circumstances. Angiogenesis consistently produces small vessels only, in sharp contrast with the broad range of sizes attained by vasculogenesis. Our main interest in this area consists in deriving and analysing mathematical models of vasculogenesis that provide information about the time and space scales in the formation of the primordial vascular net. To this end use will be made of data obtained from experimental studies conducted on chick embryos.

2.- Models of blood coagulation.

Blood coagulation is a robust security mechanisms of human vascular system, which in particular prevents bleeding from minor injuries to occur. Any alteration in its correct performance may thus have serious consequences. While the biochemical cascade regulating such process is reasonably well understood by now, nay aspects of the dynamics of blood coagulation remain to be ascertained as yet. For instance, our current knowledge about the immunological reaction appearing in many hemophylia patients upon infusion of coagulating factors remains incomplete. On the other hand, the mechanisms of thrombi, or blood clots, formation are only beginning to be elucidated nowadays. We intend to address precise aspects of the aforementioned questions. In particular, we are interested in modelling the pathological immune response often seen in hemophylia A patients. Of concern will also be a precise description of the early stages of microthrombi formation in blood, and its subsequent evolution into pathological situations.

3.- Quantitative aspects of tumour growth.

Tumour diseases are a serious health problem, whose importance is well known. Among the manifold techniques designed to check these processes, the design of models that could afford for quantitative, and reliable, predictions of tumour growth is being increasingly used during the last years. Examples of such techniques are the selection of suitable chemotherapy protocols, or the precise description of the mechanisms that facilitate tumour invasion. Our goals here include: i) The derivation of theoretical models allowing to uncover links among the morphological properties of a tumour and its growth dynamics, ii) The comparison among pathological invasive processes (as tumour growth) and homeostatic invasive ones (as the formation of bone tissue starting from a cartilage template), and iii) The design of optimal chemotherapy and radiotherapy protocols based in keeping undesired side effects under control.