Modeling and optimal regulation of erythropoiesis subject to benzene intoxication - H. T. Banks; Cammey E. Cole; Paul M. Schlosser; Hien T. Tran (Mathematical Biosciences and Engineering)
Benzene (C6H6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, andindustrial processes. Benzene increases the incidence of leukemia in humanswhen they are exposed to high doses for extended periods; however, leukemiarisks in humans subjected to low exposures are uncertain. The exposure-dose-response relationship of benzene in humans is expected to be nonlinear becausebenzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic effects on the bonemarrow. &nbsp Since benzene is a known human leukemogen, the toxicity of benzene in thebone marrow is of most importance. And because blood cells are producedin the bone marrow, we investigated the effects of benzene on hematopoiesis(blood cell production and development). An age-structured model was usedto examine the process of erythropoiesis, the development of red blood cells.This investigation proved the existence and uniqueness of the solution of thesystem of coupled partial and ordinary differential equations. In addition, weformulated an optimal control problem for the control of erythropoiesis andperformed numerical simulations to compare the performance of the optimalfeedback law and another feedback function based on the Hill function.