A model of isoniazid treatment of tuberculosis

A mathematical model is presented of the growth and death of bacilli in a granuloma. The granuloma is treated with isoniazid (INH), a drug that inhibits the synthesis of mycolic acids (MA). Since MA is an essential component of cell walls, the organisms fail to reach maturity if deficient in MA. Cell wall turnover is a well-known feature of bacteria, at the exterior surface material sloughs off to foil attacks by hosts or other organisms, simultaneously synthesizing products for new cell wall assembly. Thus cell wall thickness is maintained in a dynamic equilibrium (Doyle et al., 1988). Presumably cell death is a result of loss in cell wall due to autolysis in combination with stinted replenishing. The mathematical model presented here uses differential equations to predict the effects of intracellular INH on cell wall thickness and cell viability. This analysis purposely distinguishes intracellular INH concentration from the concentration in the plasma. The concentration in the plasma depends only on the dosing. The intracellular INH concentration, however, depends on diffusion through the cell walls of the bacteria. This paper addresses the complex interactions between intracellular INH, cell wall thickness, and the rate of cell wall synthesis.