Abstract
Chlorambucil (Chl), Melphalan (Mel), and Cytarabine (Cyt) are recognized drugs used in the chemotherapy of patients with advanced Chronic Lymphocytic Leukemia (CLL). The optimal treatment schedule and timing of Chl, Mel, and Cyt administration remains unknown and has traditionally been decided empirically and independently of preclinical in vitro efficacy studies. As a first step toward mathematical prediction of in vivo drug efficacy from in vitro cytotoxicity studies, we used murine A20 leukemic cells as a test case of CLL. We first found that logistic growth best described the proliferation of the cells in vitro. Then, we tested in vitro the cytotoxic efficacy of Chl, Mel, and Cyt against A20 cells. On the basis of these experimental data, we found the parameters for cancer cell death rates that were dependent on the concentration of the respective drugs and developed a mathematical model involving nonlinear ordinary differential equations. For the proposed mathematical model, three equilibrium states were analyzed using the general method of Lyapunov, with only one equilibrium being stable. We obtained a very good symmetry between the experimental results and numerical simulations of the model. Our novel model can be used as a general tool to study the cytotoxic activity of various drugs with different doses and modes of action by appropriate adjustment of the values for the selected parameters.
Highlights
Chronic Lymphocytic Leukemia (CLL) is the most common leukemia in adults and is characterized by the uncontrolled growth of mature B lymphocytes (B cells) [1]
Reference [19] used a compartmental model to separate circulating CLL cells from those in lymphoid tissues. This model tracked the production of new CLL cells and showed that the growth rate and death rate of CLL cells are similar
The model described in our work was based on that used by [23], who employed a system of Ordinary Differential Equations (ODE) to study chemotherapy and immunotherapy in CLL, but we introduced modifications and focused on the effect of chemotherapy on CLL cell growth
Summary
CLL is the most common leukemia in adults and is characterized by the uncontrolled growth of mature B lymphocytes (B cells) [1]. With special regard to CLL, several studies [15,16,17] have modeled the interaction between peripheral blood lymphocytes and CLL cells These studies produced dynamic systems and identified parameters that describe the growth rate of cancer cells. Reference [19] used a compartmental model to separate circulating CLL cells from those in lymphoid tissues This model tracked the production of new CLL cells and showed that the growth rate and death rate of CLL cells are similar. A major limitation of these quantitative models is that they are not based on real-life experimental data These models depict the relationship between CLL growth and the immune response to it, but they do not describe or predict the optimal use of drugs for this disease
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