A Mathematical Model of fiber Carcinogenicity and Fibrosis in Inhalation and Intraperitoneal Experiments in Rats

Abstract

A hypothesis is presented that predicts the incidence of tumors and fibrosis in rats exposed to various types of rapidly dissolving fibers in an inhalation study or in an intraperitoneal (ip) injection experiment, for which the response to durable fibers has been determined. The model takes into account the fiber diameter and the dissolution rate of fibers longer than 20 μm in the lung, and it predicts the measured tumor and fibrosis incidence to within approximately the precision of the measurements. The basic concept of the model is that a rapidly dissolving long fiber has the same response in an animal bioassay as a much smaller dose of a durable fiber. Long, durable fibers are considered to have special significance since no effective mechanism is known by which these fibers may be removed. In particular, the hypothesis is that the effective dose of a dissolving long fiber scales as the residence time of that fiber in the extracellular fluid. For example, a certain dose of a fiber that dissolves in 1 yr acts like half that dose of a fiber that requires 2 yr to dissolve. The residence time of a fiber is estimated directly from the average fiber diameter, its density, and the fiber dissolution rate as measured in simulated lung fluid at neutral pH. The incidence of fibrosis in a recent series of chronic inhalation tests at the Research and Consulting Company (RCC) in Geneva, Switzerland, is predicted well by the mathematical model. The observed lung tumor rates in these studies are consistent with this model. The model also predicts the incidence of mesothelioma in the ip model of Pott and colleagues. The model allows one to predict, for an inhalation or ip experiment, what residence time and dissolution rate are required for an acceptably small tumorigenic or fibrotic response to a given fiber dose. For an inhalation test in rats at the maximum tolerated dose (MTD), such as the ones completed at RCC, the model suggests that less than 10% incidence of fibrosis would be obtained at the maximum tolerated dose of 1 μm diameter fibers if the dissolution rate were greater than 80 ng/cm²/h. The dissolution rate that would give no detectable lung tumors in such an inhalation test in rats is much smaller. Thus a fiber with a dissolution rate of 100 ng/cm²/h has an insignificant chance of producing either fibrosis or tumors by inhalation in rats, even at the maximum tolerated dose used in the RCC study.