Use of real time leukaemia data to validate model predictions based on analyses and computer simulations.

Predictions arising out of a mathematical model that describes the expansion of leukaemia from a diffusion-orientated perspective are critiqued and validated by employing available real time data. Based on agreements found between model predictions and the data, but mindful of the limitations it presents, it is concluded that the model could be used to describe the dynamics of normal and abnormal cells in leukaemia. It is suggested that further studies of the behaviour of certain normal cell types in contrast to abnormal cells during leukaemic development could engender additional insights into leukaemia and its treatment.

Recovery of normal hemopoiesis in disseminated cancer therapy--a model.

The strategy of normal cell regeneration with recombinant hematopoietic growth factors during cancer chemotherapy is investigated by superimposing a treatment protocol on a simple model that describes an expanding malignant cell population that is coexisting with and inhibiting the population of normal cells. The model predictions suggest that the strategy of normal cell stimulation, possibly with growth factors, and possibly carried out within an intensive treatment framework may be a worthwhile chemotherapeutic option. Under this protocol, the model also predicts a minimum time interval for active treatment, a time to discontinue treatment, and a rest period during treatment in order to guarantee patient safety and recovery. Consequently, by relating and comparing model predictions to patient data, model simulations forecast that treatment could be shortened by 1-2 weeks if organized over or in the neighborhood of a predicted optimal time interval. Following this, it is conjectured that such an approach engendered by the model could produce outcomes that may have an edge over outcomes arising from therapeutic strategies that are executed over time frames that are relatively longer or significantly shorter than the predicted optimal time.

Diverse ideas on the growth kinetics of disseminated cancer cells.

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.

Some perspectives on modeling leukemia.

A diffusion model of leukemia is presented. The space-occupying effects of leukemic cells during leukemic expansion is investigated. The analyses and simulations of the model suggest that acute leukemia is a state in which positions inhabited by colonies of normal cells are invaded by emerging colonies of abnormal cells. Normal cells are then driven to a state of extinction as leukemic cells evolve toward high and dominant steady state levels.

Normal cell decline and inhibition in acute leukemia: a biomathematical modeling approach.

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.