A mathematical model for predicting likely levels of the 6-mercaptopurine (6MP) effective metabolite during maintenance chemotherapy treatment for childhood acute lymphoblastic leukemia (ALL) using information already commonly taken during a patient's regular check-ups is presented. In the treatment of childhood ALL, 6 months of aggressive therapy is followed by a 2-3 year period of less strenuous maintenance chemotherapy. Daily 6-mercaptopurine is the major of this maintenance chemotherapy where maintaining the effective metabolite level within a desired window (Chrzanowska et al. 1999) is correlated with the rate of disease-free survival. Since the 5 year remission rate of childhood ALL has improved from under 20% before 1972 to 86% in 2000 (Felix et al. 2000), the identification of patients who are not receiving sufficient effective doses may represent a significant fraction of those patients who come out of remission. In light of this improved remission rate, expensive metabolite assays are not as feasible and a more cost-effective alternative has been sought. The mean corpuscular volume (MCV) of peripheral red blood cells (RBCs) provides the necessary surrogate marker.

We have observed that the MCV of RBCs of clinical patients increases when undergoing 6MP therapies and decreases once taken off the medication. In addition, the extent of this increase depends upon the prescribed MCV dosage. The fact that the MCV increase occurs steadily over a 4-6 months before stabilizing (so long as the treatment remains stable) implies that the peripheral blood can be modeled as a surge tank where older cells are replaced by fresh cells from the bone marrow. Our aim is to develop a quantitative description of the volume distribution of RBCs in the bone marrow and periphery as a function of 6MP metabolism which can be used to determine the likely 6MP levels for an individual patient given their MCV history.

A volume- and age- structured population balance model is developed where; beginning with the earliest committed erythroid lineage, the number densities for discrete maturation stages (distinguishable cytometrically) is modeled. Cells will continually divide, grow, mature, and die at stage specific volume and age structured rates which incorporate the effects of the active metabolite. We show how the model, which couples peripheral dynamics to its bone marrow source of cells, captures the MCV trends observed clinically during 6MP chemotherapy. We also show how these peripheral observations are related to the drug metabolite level and, assuming a stable metabolite level, that these observations yield drug metabolite concentration distributions.

References:

Chrzanowska M, Kolecki P, Duczmal-Cichocka B, and Fiet J. ”Metabolites of mercaptopurine in red blood cells: A relationship between 6-thioguanine nucleotides and 6-methylmercaptorpurine metabolite concentrations in children with lymphoblastic leukemia.” European Journal of Pharmaceutical Sciences, 8: 329-334, 1999.

Felix CA, Lange BJ, and Chessells JM. “Pediatric acute lymphoblastic leukemia: Challenges and controversies in 2000.” Hematology: American Society of Hematology Education Program Book, 2000.