Mathematical modeling of cyclic treatments of chronic myeloid leukemia

Rotating between ponatinib and imatinib temporarily increases the efficacy of imatinib as shown in a chronic myeloid leukaemia model

Targeted therapies for chronic myeloid leukaemia (CML) are effective, but rarely curative. Patients typically require treatment indefinitely, which gives ample time for drug resistance to evolve. Drug resistance issues are one of the main causes of death owing to CML, thus any means of preventing resistance are of importance. Drug rotations, wherein treatment is switched periodically between different drugs are one such option, and have been theorized to delay the onset of resistance. In vitro testing of drug rotation therapy is a first step towards applying it in animal or human trials. We developed a method for testing drug rotation protocols in CML cell lines based around culturing cells with a moderate amount of inhibitors interspersed with washing procedures and drug swaps. Drug rotations of imatinib and ponatinib were evaluated in a CML specific cell line, KCL-22. The growth of KCL-22 cells was initially reduced by a drug rotation, but the cells eventually adapted to the protocol. Our results show that ponatinib in a drug rotation temporarily sensitizes the cells to imatinib, but the effect is short-lived and is eventually lost after a few treatment cycles. Possible explanations for this observation are discussed.

A systematic review of modeling and simulation approaches in designing targeted treatment technologies for Leukemia Cancer in low and middle income countries

Virtual experimentation is a widely used approach for predicting systems behaviour especially in situations where resources for physical experiments are very limited. For example, targeted treatment inside the human body is particularly challenging, and as such, modeling and simulation is utilised to aid planning before a specific treatment is administered. In such approaches, precise treatment, as it is the case in radiotherapy, is used to administer a maximum dose to the infected regions while minimizing the effect on normal tissue. Complicated cancers such as leukemia present even greater challenges due to their presentation in liquid form and not being localised in one area. As such, science has led to the development of targeted drug delivery, where the infected cells can be specifically targeted anywhere in the body. Despite the great prospects and advances of these modeling and simulation tools in the design and delivery of targeted drugs, their use by Low and Middle Income Countries (LMICs) researchers and clinicians is still very limited. This paper therefore reviews the modeling and simulation approaches for leukemia treatment using nanoparticles as an example for virtual experimentation. A systematic review from various databases was carried out for studies that involved cancer treatment approaches through modeling and simulation with emphasis to data collected from LMICs. Results indicated that whereas there is an increasing trend in the use of modeling and simulation approaches, their uptake in LMICs is still limited. According to the review data collected, there is a clear need to employ these tools as key approaches for the planning of targeted drug treatment approaches.

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

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.

Optimization of combination therapy for chronic myeloid leukemia with dosing constraints

In this work, we demonstrate a mathematical technique for optimizing combination regimens with constraints. We apply the technique to a mathematical model for treatment of patients with chronic myeloid leukemia. The in-host model includes leukemic cell and immune system dynamics during treatment with tyrosine kinase inhibitors and immunomodulatory compounds. The model is minimal (semi-mechanistic) with just enough detail that all relevant therapeutic effects can be represented. The regimens are optimized to yield the highest possible reduction in disease burden, taking into account dosing constraints and side effect risks due to drug exposure. We compare the following three types of regimens: (1) regimens that are restricted to certain discrete dose levels, which can only change every three months; (2) optimal regimens determined using optimal control; and (3) regimens that are piecewise-constant like the first type of regimen, but are obtained as approximations to the optimal control regimens. All three types of regimens result in similar outcomes, but the last one is easy to compute in addition to being clinically feasible.

How to mathematically optimize drug regimens using optimal control

This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Dynamics of resistance development to imatinib under increasing selection pressure: a combination of mathematical models and in vitro data

In the last decade, cancer research has been a highly active and rapidly evolving scientific area. The ultimate goal of all efforts is a better understanding of the mechanisms that discriminate malignant from normal cell biology in order to allow the design of molecular targeted treatment strategies. In individual cases of malignant model diseases addicted to a specific, ideally single oncogene, e.g. Chronic myeloid leukemia (CML), specific tyrosine kinase inhibitors (TKI) have indeed been able to convert the disease from a ultimately life-threatening into a chronic disease with individual patients staying in remission even without treatment suggestive of operational cure. These developments have been raising hopes to transfer this concept to other cancer types. Unfortunately, cancer cells tend to develop both primary and secondary resistance to targeted drugs in a substantially higher frequency often leading to a failure of treatment clinically. Therefore, a detailed understanding of how cells can bypass targeted inhibition of signaling cascades crucial for malignant growths is necessary. Here, we have performed an in vitro experiment that investigates kinetics and mechanisms underlying resistance development in former drug sensitive cancer cells over time in vitro. We show that the dynamics observed in these experiments can be described by a simple mathematical model. By comparing these experimental data with the mathematical model, important parameters such as mutation rates, cellular fitness and the impact of individual drugs on these processes can be assessed. Excitingly, the experiment and the model suggest two fundamentally different ways of resistance evolution, i.e. acquisition of mutations and phenotype switching, each subject to different parameters. Most importantly, this complementary approach allows to assess the risk of resistance development in the different phases of treatment and thus helps to identify the critical periods where resistance development is most likely to occur.