Biomedical subjects
Publications and source records attributed to C P Calderón.
Theoretical and empirical arguments are used to support the growth kinetics of disseminated tumors. Employing viable hypotheses, it is established that Gompertzian growth of disseminated cancer cells can be derived from a number of theoretical considerations. Empirical methods are used to validate and confirm the theoretical assertions with the use of available data.
Biomathematical models describing acute leukemia are introduced. These models are used to show some of the possible ways in which the normal cell population declines in the presence of malignant cells in acute leukemia. They also described situations in which normal cell inhibition by the malignant clone contributes to and supports leukemic development. The progression of acute leukemia is quantified both analytically and numerically by considering the steady-state and dynamic properties of the models. The studies and investigations indicate that as long as malignant cells are present in acute leukemia, normal cell growth or regrowth capabilities will be very reduced and diminished. As biomedicine becomes more quantitative, studies that involve the employment and use of various mathematical methods and techniques also become more relevant. In this regard, the models could be useful in predicting the quantitative and qualitative behavior of cell population in certain acute leukemias as the search for more effective therapeutic strategies continues.
The meaning and limitations of certain mathematical models of tumor growth are discussed, and some new derivations of the existing models are given. A theoretical justification for Gompertz's law of growth for tumors is presented. An age-dependent Von Bertalanffy's equation and diffusion models are introduced, and existence and uniqueness problems are addressed.
We consider the problem of finding the probability density for the location of an untrapped pest satisfying a diffusion equation with the scaled Laplacian. Then by taking the initial data to the diffusion process to be in some Lp spaces, we establish the existence and uniqueness of local solutions in these spaces and the existence and uniqueness of weak global solutions in Lp,q; p,q greater than 3. The interest of this method relies on the fact that it is by successive approximations and hence amenable to numerical treatment.