Optimal control of multiplicative control systems arising from cancer therapy

Optimal radiation fractionation for low-grade gliomas: Insights from a mathematical model

“…the pioneering paper of Bahrami and Kim [1] and also the book of Wheldon [42] for early survey). Most available papers on mathematical modeling of gliomas have considered specific aspects of radiation therapy for high-grade gliomas [2,5,12,13,31].…”

Personalized drug administration for cancer treatment using Model Reference Adaptive Control

“…Therefore, obtaining the optimal drug delivery scenario for a patient not only prevents squandering monetary resources but also restrains the toxicity of healthy tissues and other side effects, and increases the survival chance of the cancer patient. Several optimal control based methods have been proposed for the treatment of cancer patients via chemotherapy by different researchers (Bahrami and Kim, 1975;Swan and Vincent, 1977;Swan, 1990;dePillis andRadunskaya, 2001, 2003;dePillis et al, 2007;Itik et al, 2009;Chen et al, 2012;Batmani and Khaloozadeh, 2013;Rao et al, 2010;Madhavi et al, 2013;Shi et al, 2011).…”

“…Researches by Bahrami and Kim (1975) and Swan and Vincent (1977) are the first steps in extending optimal control theories to chemotherapy for cancer treatment. Subsequently, other researchers have extended the optimal control techniques for determining optimal treatment plans including drug dosage, administration period and frequency.…”

Modeling Tumor Clonal Evolution for Drug Combinations Design

“…Specifically, with dynamical systems modeled using deterministic differential equations, we can apply many concepts from optimal control theory in engineering to study the stability and control of cancer – with the goal of maximizing tumor kill and minimizing drug toxicity. Bahrami and Kim 115 first reported applications of optimal control theory to minimize tumor growth (and used an example with vincristine against murine AKR leukemia). Swan and Vincent 116 subsequently studied optimal control of chemotherapy in human IgG multiple myeloma.…”