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Relapse in Chronic Myeloid Leukemia after Bone Marrow Transplantation: Biomathematical Modeling as a New Approach to Understanding Pathogenesis

^a The Kanematsu Laboratories, Royal Prince Alfred Hospital, Camperdown, Australia;
^b Department of Clinical Physiology, Occupational and Social Medicine;
^c Department of Measurement, Control and Microtechnology, University of Ulm, Ulm, Germany

Key Words. Biomathematical modeling • Chronic myeloid leukemia • Relapse • Ph-chromosome • Bone marrow transplantation

Prof. Dr. med. Dr. h.c. mult. Theodor M. Fliedner, Radiation Medicine Research Group, Medical Center of the University of Ulm, Helmholtzstrasse 20, D-89081 Ulm, Germany.

A biomathematical model was developed to simulate relapse development in patients with chronic myeloid leukemia (CML) following bone marrow transplantation (BMT). The purpose of this study was to better understand the pathophysiology of the time evolution of CML relapse and to provide means whereby the outcomes of patients with CML relapse can be projected and treatment modified accordingly. The model consists of three parallel series of catenated compartments representing granulopoiesis in normal (donor) cells from the marrow, in CML cells from the marrow, and in CML cells from extramedullary sites. It was assumed that CML stem cells were resistant to feedback control and that CML-derived neutrophils, as well as normal neutrophils, exercised feedback regulation of normal stem cells. The known longer generation times for CML neutrophil precursors compared with normal neutrophil precursors were used, and it was assumed that 10⁷ pluripotential stem cells were infused with BMT.

The model was evaluated for its ability to simulate the reappearance of CML (Philadelphia chromosome positive) metaphases in the marrow and the recovery pattern in the blood neutrophil count in six patients who had relapsed following BMT (allogeneic in three patients, allogeneic with T-cell depletion in two patients, and syngeneic in one patient). The variables tested included the site of origin of the CML stem cells responsible for relapse (marrow alone versus marrow and extramedullary sites), the minimum number of CML stem cells responsible for relapse, and the time delay between BMT and the onset of relapse.

Model profiles based on the observed values were obtained in each case. The simulations pointed to the fact that relapse began from a small number of CML cells in medullary and extramedullary sites. The time delay between BMT and the onset of relapse varied from 15 to 240 days.

We suggest that this biomathematical model should be further investigated as a possible means of predicting outcome and guiding the treatment for patients with CML relapsing after BMT.