The research planning activities will involve studies and investigations of leukemia from a biomathematical viewpoint. The project will focus on preliminary explorations of the following: a) Construction of mathematical models that quantitatively and qualitatively describe and characterize leukemia; b) Contributions to the understanding of leukemia cell kinetics; c) Construction of models that describe treatment schemes and protocols for leukemia; d) Studies and comparison of various treatment protocols through the use of mathematical models; e) Treatment optimization models; f) Suggestion of ways to improve the treatment of leukemia; g) Development of analytical and numerical techniques that aid in the solution of model equations that involve nonlinear ordinary and partial differential equations; h) Interpretation of model results and predictions within the context of the biomedical situation; i) Studies of leukemia data as it pertains to insights and predictions obtained from models; j) Development of collaborative activities with physicians, biomedical researchers, and other mathematicians and scientists interested in this endeavor; and k) Extensions of the studies to include other cancers.
Specifics of the preliminary studies and investigations will include biomathematical descriptions of leukemogenesis; studies of models of normal and leukemic cells considered as interacting cell populations; investigations of normal and leukemic cell behavior in the bone marrow, blood, and the active and resting phases of the cell cycle; studies of the inherent effects of time lags in leukemic development; explorations of leukemia from diffusion-oriented perspectives; considerations of bone marrow transplantation models and chemotherapeutic and radiotherapeutic treatment models for leukemia. Exploratory mathematical models will be used to investigate treatment schemes and protocols. Mathematical techniques for the development, analysis, and solution of models will be explored. Particular attention will be paid to gathering of leukemia data from various sources and statistical analysis of such data will be pursued. Numerical and analytical techniques for solving large model systems of coupled ordinary and partial differential equations, differential-difference equations, and delay differential equations will also be explored and studied.
It is envisioned that the research planning activities
will lead to a comprehensive biomathematical research project that will
advance knowledge in understanding cancer cell dynamics, mathematically
and biomedically, and will aid the biomedical community in its search for
better therapeutic strategies.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.