906 Mathematical and Computer Modelling Reports

One of the model’s variables represents the chromatin condensation/replication cycle. The second variable is related to the cell’s ability to grow: the number of fibrillar centers in the cell’s nucleoli, in excess of the minimum number found in quiescent cells. The number of these centers is assumed to increase and decrease at random, with transition rates that are functions of the growth conditions. The chromatin variable is postulated to increase at a rate proportional to the nucleolar variable (through a mechanism involving ubiquitin), so that the cell’s generation time will also be random. The number of fibrillar centers in a mitotic mother cell persists in newly-formed daughter cells, providing a mechanism for positive correlation between sibling and motherdaughter cell generation times.

Expressions for the following quantities are provided as a function of the model’s parameters: the average, variance and higher moments of the intermitotic time, the distribution of the number of fibrillar centers, the joint distribution of sibling, mother and daughter cell intermitotic times, the Malthusian parameter of exponential population growth, numbers that describe the damped oscillation of a perturbed population and the entropy of a cell population.

Compuf. Math. Applic. Vol. 14, No. 9-12, pp. 741-749. 1987

MODELLING OF THE INFLUENCE OF ‘HTdR KINETICS IN MOUSE EPIDERMIS

H. FRANKE and H. E. WICHMANN

ON CELL

Abt. Biostatistik, Med. Institut fur Umwelthygiene an der Universitlt Dusseldorf, Gurlittstr. 53, D-4000 Dusseldorf, West Germany

C. S. POITEN and L. TODD

Paterson Laboratories, Christie Hospital and Holt Radium Institute, Withington, Manchester M20 9BX, England

Abstract-Fluctuations occur in the labelling index (Ll) of mouse epidermis over the first two days after application of tritiated thymidine CHTdR) for which there has in the past been no explanation. Similarly, there has been no adequate explanation for the fluctuations in the percent labelled mitoses (PLM) data seen immediately after the first peak. Here we propose a model which provides an explanation for both these features. The hypothesis suggested is that some cells are killed by the 3HTdR either immediately when they are still in the S phase or later when they have reached G, . In both cases the labelled precursor is released from the cell and may be incorporated into other S phase cells after an appropriate delay. The model has been formulated into a computer programme which can derive the appropriate LI or PLM curves and fit curves to the relevant data. The resulting curves fit the data well suggesting that such cytotoxic and reutilization processes may in fact occur.

Cornput. Math. Applic. Vol. 14, No. 9-12, pp. 751-761, 1987

COMPUTER SIMULATION OF THE PROGRESSION OF AN ACUTE MYELOCYTIC LEUKEMIA IN THE

BROWN NORWAY RAT

F. W. SCHULTZ,’ A. C. M. MARTENS’ and A. HAGENBEEK’~~

’ Radiobiological Institute TNO, P.O. Box 5815, 2280 HV Rijswijk, The Netherlands ZThe Dr Daniel den Hoed Cancer Center, Department of Hematology,

P.O. Box 5201, 3008 AE Rotterdam, The Netherlands

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’ 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).