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.

Immunotherapy with bacillus Calmette–Guérin (BCG) is a classic treatment for superficial bladder cancer. Although BCG instillation is a well-established protocol, some patients do not respond to this treatment. To model improvement of this protocol, Bunimovich-Mendrazitsky (B-M) et al. provided a platform for in silico testing of modified protocols of BCG instillation and combination with IL-2. The purpose of this work is to improve and further develop this BCG model describing the tumor–immune interactions occurring in the bladder in response to BCG and IL-2 therapies, based on novel clinical data.To validate this BCG model, we used the results of BCG treatment of 10 patients with bladder cancer 3-5 years ago. Individual data for each patient was entered to simulate the model. As a result, a treatment protocol was obtained which coincided with the protocol assigned by the doctor. In addition, cancer cell growth graphs were obtained from the model simulations, which coincided with the clinical conclusions of the patient’s treatment outcome. Moreover, the program provides a more optimal treatment protocol for each patient.We show that calculated protocols from the model can prevent excess side effects of immunotherapy and even of unnecessary death for some patients, informing the clinical potential of our model.

In recent years, mathematical models have developed into an important tool for cancer research, combining quantitative analysis and natural processes. We have focused on Chronic Lymphocytic Leukemia (CLL), since it is one of the most common adult leukemias, which remains incurable. As the first step toward the mathematical prediction of in vivo drug efficacy, we first found that logistic growth best described the proliferation of fluorescently labeled murine A20 leukemic cells injected in immunocompetent Balb/c mice. Then, we tested the cytotoxic efficacy of Ibrutinib (Ibr) and Cytarabine (Cyt) in A20-bearing mice. The results afforded calculation of the killing rate of the A20 cells as a function of therapy. The experimental data were compared with the simulation model to validate the latter’s applicability. On the basis of these results, we developed a new ordinary differential equations (ODEs) model and provided its sensitivity and stability analysis. There was excellent accordance between numerical simulations of the model and results from in vivo experiments. We found that simulations of our model could predict that the combination of Cyt and Ibr would lead to approximately 95% killing of A20 cells. In its current format, the model can be used as a tool for mathematical prediction of in vivo drug efficacy, and could form the basis of software for prediction of personalized chemotherapy.

This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and experimental cytotoxicity of two Federal Drug Administration (FDA)-approved anticancer drugs, Cytarabine (Cyt) and Ibrutinib (Ibr) in an in vitro model system of Chronic Lymphocytic Leukemia (CLL). Maximum growth inhibition with Cyt (95%) was reached at an 8-fold lower drug concentration (6.25 μM) than for Ibr (97%, 50 μM). For the proposed ordinary differential equations (ODE) model, a multistep strategy was used to estimate the parameters relevant to the analysis of in vitro experiments testing the effects of different drug concentrations. The simulation results demonstrate that our model correctly predicts the effects of drugs on leukemic cells. To assess the closeness of the fit between the simulations and experimental data, RMSEs for both drugs were calculated (both RMSEs < 0.1). The numerical solutions of the model show a symmetrical dynamical evolution for two drugs with different modes of action. Simulations of the combinatorial effect of Cyt and Ibr showed that their synergism enhanced the cytotoxic effect by 40%. We suggest that this model could predict a more personalized drug dose based on the growth rate of an individual’s cancer cells.

Finding synergistic drug combinations is an important area of cancer research. Here, we sought to rationally design synergistic drug combinations with an inhibitor of BTK kinase, ibrutinib, which is used for the treatment of several types of leukemia. We (a) used a pooled shRNA screen to identify genes that protect cells from the drug, (b) identified protective pathways via bioinformatics analysis of these gene sets, and (c) identified drugs that inhibit these pathways. Based on this analysis, we established that inhibitors of proteasome and mTORC1 could synergize with ibrutinib both in vitro and in vivo. We suggest that FDA-approved inhibitors of these pathways could be effectively combined with ibrutinib for the treatment of chronic lymphocytic leukemia (CLL).