Past Event: Oden Institute Seminar

Using Fixed Point Techniques to Design Optimal Low-Dose Metronomic Therapy for Cancer Patients

Lois Okereke, Postdoctoral Fellow, Oden Institute

Abstract

Low-dose metronomic therapy (LDMT) is an emerging philosophy in oncology that advocates for the frequent administration of cytotoxic drugs at low doses over prolonged periods without extended breaks. The rationale is to minimize treatment-induced toxicity and overcome tumor resistance while keeping tumor growth in check within well-defined boundaries. Although LDMT could significantly improve overall patients’ survival, the empiricism currently associated with its design undermines its advantages.

In this talk, I will discuss a systematic approach for optimal LDMT design. The approach involves stratifying patients who would benefit from LDMT and then designing a personalized optimal therapeutic regimen for those patients. The approach relies on mathematical operators that map tumor growth and drug delivery mechanisms to treatment response and toxicity. A mathematical description of the temporal dynamics of the processes is captured by coupled systems of autonomous and non-autonomous nonlinear ordinary differential equations (ODEs), whose parameters are directly measurable in the clinics. 

Using fixed point techniques to rigorously analyze the equilibrium behaviors of the dynamical systems used to describe tumor growth and response to treatment allows one to theoretically identify personalized treatment regimens that effectively maintain tumor stability (in the sense of the Response Evaluation Criteria in Solid Tumors; i.e., the standard for assessing treatment response within clinical trial) and constrain treatment-associated toxicity below a desired threshold. An admissibility condition characterized by inequalities expressed in terms of model parameters establishes a patient-specific criterion for determining the feasibility of a dosing schedule that is both effective and safe. Patients whose model parameters satisfy the admissibility condition are deemed to benefit from LDMT. Further findings indicate that tumor stability can be achieved with minimally toxic regimens. Overall, LDMT requires lower steady-state drug concentration when compared to regimens designed for tumor eradication. More specifically, for tumors with a pre-treatment volume to carrying capacity ratio (i.e., the proliferation saturation index) between 0.10 and 0.25, tumor stability can be achieved with a total dose up to 43.2% less than the conventional total dose. 

This study generates intriguing hypotheses for treatment scheduling that can be directly tested in experimental settings, thereby providing a systematic approach for designing effective, minimally toxic LDMT regimens for tumor experiments. Moreover, the fixed point technique utilized in the mathematical analysis of the non-autonomous systems contributes further to the mathematical aspects of examining such systems.

Biography

Lois Okereke is a postdoctoral fellow at the Oden Institute's Center for Computational Oncology.  She received her Ph.D. in Pure and Applied Mathematics from the African University of Science and Technology, (AUST) Abuja, Nigeria in November 2022, after completing a split-site Ph.D. carried out between the Mathematics Institute at AUST, Abuja, and the Institute of Systems Molecular and Integrative Biology at the University of Liverpool, United Kingdom. During this time, she had extended research visits to the Computational Biology and Integrative Genomics laboratory at Oxford and the Statistical Modelling Laboratory at Gaston Berger University, Senegal.

Her research focuses on the use of mathematical approaches (including modeling, algorithm development, rigorous analysis, and data analytics)  to study and characterize cancer development and progression to optimize cancer therapies on a patient-specific basis. Lois Okereke is a 2021 laureate of the L'Oreal-UNESCO For Women in Science Young Talent Award sub-Saharan Africa, a former Mwalimu Nyerere African Union scholar, and an alumna of the United Kingdom's Commonwealth Scholarship. She is a Provost Early Career Fellow at UT Austin and one of the one hundred promising young researchers in Mathematics invited to interact with the winners of the biggest prizes in Mathematics and Computer Science at the 11th Heidelberg Laureate Forum in Germany.