Some perspectives on modeling leukemia

Diverse Ideas on the Growth Kinetics of Disseminated Cancer Cells

“…We note that for moderate to large values of t a representation of m(t) could be obtained from equation (18) (see Section 3) by choosing m(t) to be approximately equal to L(t), which exhibits Gompertzian behavior. At this juncture, it is important to mention that in the case of the disseminated cancers being discussed here, the scientific evidence (Schrier, 1994;Afenya and Calderón, 1996;Afenya and Bentil, 1998) reveals that there is an ultimate packing and clogging of the bone marrow, which is the focus of our studies, by malignant cells in the untreated disease state. Such a situation may arise long after the appearance of the first malignant cell.…”

“…In recent modeling activities (Afenya, 1996(Afenya, , 1998Afenya and Calderón, 1996;Afenya and Bentil, 1998), we used assumptions of the Gompertzian growth of leukemia cells to arrive at some biological conjectures about the disease that could have useful implications for treatment. The models predicted certain behaviors that are observed in leukemia.…”

Mathematical Models of Cancer and Their Relevant Insights

“…This may mean that in the malignant state normal cell survival cannot occur unless this state is itself disrupted by an external agent, in this case, a drug (Spinolo, 1994). These predictions and the ensuing simulations in Afenya and Bentil (1998) show, in what follows, that (4) There may be accumulations of cells at certain sites and depletions at other sites and through such processes malignant cells may occupy sites of the normal cells as the propagation of spatial heterogeneities occur. As a result, it may be suggested that the positions occupied by the leukemic cells as they expand may be very fertile areas that are rich in nutrients needed for hematopoiesis.…”

“…The models (Afenya, 1996;Afenya and Calderón, 1996) also include the notion of Gompertzian growth of normal and malignant cells but do not include cell cycle descriptions since the cells are lumped together into single co-existing cell populations. Such lumping constitutes a limitation on the models from a cell cycle oriented viewpoint but they provide some important insights that were built upon in the work of Afenya and Bentil (1998).…”

Optimal control applied to drug administration in cancer chemotherapy: the case of several toxicity constraints

“…In our analysis, we adopt the model from [ 1,2]. Though this model was invented to describe the human acute leukemia, the assumptions underlying it are so general that it can be employed in analysis of a wider variety of cancers.…”