An Extended Mathematical Model of Pathophysiology and Response to Treatment in Chronic Myelogenous Leukemia
Authors: Nannya Yasuhito , Imai Yoichi , Hangaishi Akira , Kurokawa Mineo 
Published: April 2020

Abstract
Chronic myelogenous leukemia (CML) is a malignant clonal disorder of hematopoietic stem cells that results in increase in myeloid, erythroid cells, and platelets in the peripheral blood and marked myeloid hyperplasia in the bone marrow. This disorder is characterized by the specific cytogenetic abnormality, the Philadelphia (Ph) chromosome, which results from a balanced translocation between the long arms of chromosomes 9 and 22, generating the bcr/abl chimeric gene that expresses an abnormal fusion protein with altered tyrosine kinase activity. Imatinib mesylate (IM, Gleevec, Novartis, Basel, Switzerland), is a potent and selective competitive inhibitor of the BCR-ABL protein tyrosine kinase and has shown to induce a high rate of cytogenetic and hematologic response in patients with chronic phase (CP) CML both as initial therapy and as secondary therapy after previous interferon therapy failed. Because the pathophysiology of CML and the mechanism for the clinical effects by IM is relatively uniform among patients, simplification and generalization with mathematical models have been proposed and they have excellently simulated the regression of leukemic cells by IM therapy and the regrowth of CML cells after appearance of IM-resistant clones. These models are based on the assumption that the transition rate of leukemic stem cells or precursor cells to more differentiated fractions are profoundly diminished by the administration of IM. This assumption is sufficient to explain the response as long as the observation period is short. In contrast, the issue regarding the influence of IM on the self-reproduction rate of leukemic stem cells was not focused on in these models because this issue had little effect on short-term outcomes with IM. After a decade since the appearance of IM, accumulated observations of CML patients treated with IM revealed long-term effectiveness; novel transformations to accelerate phase or blastic crisis are rarely observed in patients who continue to receive 400mg/day of IM for five or six years. Our aim is to clarify the effect of IM on leukemic stem cell fractions by extending and modifying the existing models so that they are compatible with actual long-term outcomes of IM therapy. First, we demonstrated that sustained effectiveness of IM for over six years cannot be achieved unless a stem cell fraction of CML is decremented by IM. In order to estimate the degree of stem cell attack by IM, we computed the rate of novel generation of IM-resistant clones before and after IM administration. In this model, we presumed that this rate is proportional to the accumulated number of self-duplication of leukemic stem cells. In order to simulate the actual observation that the clonal evolution decrease annually after IM administration, we illustrated that the rate of self duplication is depleted to at one fourth or less with IM compared to without IM. With this simulation, we show that the tyrosine kinase inhibitors can eradicate malignant cells thus leading to the radical cure of the disease. We also showed that the achievement of major molecular response (MMR; defined as at least three-log reduction of bcr/abl positive clones in the peripheral blood) at the 18th month of IM therapy is roughly associated with the absence of resistant clones at the moment of IM administration, and is obviously linked to successful therapy of CML after IM therapy is launched. This provides the supportive evidence of the previously reported observation that MMR at 18th month is associated with long-term effectiveness. Our model underscores the significance of prompt elimination of leukemic stem cells in order to diminish the generation of novel resistant clones and accomplish complete cure of CML. Development of the evaluation system to quantify residual leukemic stem cells would verify this hypothesis and pursuit to maximal response including early administration of second-generation tyrosine kinase inhibitors would be justified.