Review article : Computer simulation of the progression of an acute myelocytic leukemia in the brown norway rat

Abstract

Reduction and extrapolation of experimental data concerning both the perturbed and unperturbed growth characteristics of a malignant population was the reason for developing a simple descriptive mathematical model. Data were obtained by inoculating BN/Rij rats i.v. with 10 7 viable cells of a transplantable myelocytic leukemia (BNML). At various time points the tumor load in the bone marrow was determined by means of a clonogenic stemcell (LCFU-S) assay or by a dose–survival time bioassay (SVL). By fitting hypothetical growth curves to the LCFU-S datapoints, using a non-linear least squares computer algorithm, an optimal functional relationship between the BNML population size, N, and time after inoculation, t, was found. The unperturbed data are best explained by a curve that consists of an exponential part which, at a transition point, changes into a Gompertz curve to account for a steady state plateau phase. Chemotherapy applied for perturbation purposes consisted of a single dose (100 mg/kg) of cyclophosphamide (CY) given i.p. at day 13. The effect of the drug was modelled as either pulse-shaped or as a more gradual event. In the former case an instantaneous tumor load reduction occurs, after which regrowth can be modelled in a way similar to unperturbed growth. Different parameter values apply, resulting in slower population size increase and a lower level plateau phase. Statistical significance is rather poor though, owing to uncertainty in the observations. The tumor load reduction is somewhat larger than can be deduced from dose–response experiments (6.0 and 5.5 decades, respectively). Correction is possible, without changing the goodness of fit, by introducing a time delay in the early exponential phase. To model gradual drug influence various functions were tested, i.e. a constant level during some time, an exponentially decreasing level, parabolic increase and decrease, and a combination of the first two categories. This last one, when superimposed on the function for unperturbed growth, yielded the best fit to the observed LCFU-S datapoints. Taking the total correlation coefficient, TCC, as measure of goodness of fit (TCC tends to 1 with improving fit) it must be concluded that the instantaneous drug effect model is only slight better than the gradual model (TCC = 0.80253 and 0.84915, respectively). The SVL datapoints also indicate instaneous rather than gradual drug effect.