Benzene and its effect on erythropoiesis: Models, optimal controls, and analyses

Benzene (C₆H₆) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain.; We developed a physiologically based pharmacokinetic model for the uptake and elimination of benzene in mice to relate the concentration of inhaled and orally administered benzene to the tissue doses of benzene and its key metabolites. Analysis was done to examine the existence and uniqueness of solutions of the system. We formulated an inverse problem to obtain estimates for the unknown parameters; data from multiple independent experiments were used.; The model was then revised to take into account the zonal distribution of enzymes and metabolisms in the liver, rather than assuming the liver is one homogeneous compartment, and extrahepatic metabolisms were also considered. Despite the sources of variability, the multicompartment metabolism model simulations matched the data reasonably well in most cases and improved results from the original model.; Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis. An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. Again, the existence and uniqueness of the solution of the system was proven. The system was then written in weak form and reduced from an infinite dimensional system to a system of ordinary differential equations by employing a finite element formulation. The control of this process is governed by a hormone. The form of the feedback of this hormone is unknown. Although a Hill function has previously been used to represent this feedback, it has no physiological basis, so an optimal control problem was formulated in order to find the optimal form of the feedback function and to track the total number of mature cells. Numerical results for both forms of the feedback function are presented.