A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Abstract

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Stability Analysis of Equilibria for a Model of Maintenance Therapy in Acute Lymphoblastic Leukemia

“…In Figure 3, the equilibrium point Ẽ1 is clearly unstable. By checking Condition (11), we obtain the same result: the condition does not hold, and the equilibrium point is unstable. The equilibrium point Ẽ2 corresponds to a healthy state of the patient.…”

“…For more information about hematopoiesis and its underlying processes, please see [2,3,10,11], pp. 1-18. Acute lymphoblastic leukemia (ALL) is a type of cancer that affects white blood cells [4].…”

Mathematical Biology: Modeling, Analysis, and Simulations

“…The present volume contains the 12 articles accepted and published in 2021 in the Special Issue, "Mathematical Biology: Modeling, Analysis, and Simulations" of the MDPI Mathematics journal, which covers a wide range of topics connected to the mathematical modeling of different biologically inspired and motivated problems. These topics include, among others, elements from processes in developmental biology [1]; equilibria and bifurcations in cardiac [2], tumoral [3] and regulatory cell [4] models; complexity in human pupillary light reflexes [5] and visual disorders [6]; a descriptive geometrical method as a model for motion [7]; statistical analysis applied to lactation model fitting [8]; DNA microarray experiments [9]; the transmission dynamics of HIV [10]; and mathematical models of the phosphorylation of glucose [11] and the transmission of tuberculosis [12].…”

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

“…Given the complexity of the processes involved in the survival and development of drug resistance in LCs, computational and mathematical modeling have been crucial to the understanding of leukemias and the improvement of patient prognosis [ 27 ]. The majority of mathematical models that have been developed for acute leukemias are simplistic compartmental cellular-level models to study leukemogenesis and cellular population dynamics and differentiation [ 28 – 39 ]. Other simplistic compartmental models have focused on treatment dynamics [ 40 – 47 ] and predicting patient relapse risk and outcome [ 48 – 53 ].…”