Analysis and comparison of multimodal cancer treatments

Abstract

We analyze the sequence in which the three most commonly prescribed cancer treatments -surgery (S), chemotherapy (C) and radiotherapy (R) -should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the interrelationship between the primary tumor and the distant metastatic tumors, including primary tumor shedding and the primary tumor's effect on the rate of angiogenesis in the metastatic tumors.Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e., SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally-timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e., highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumors.

Scheduling the adjuvant endocrine therapy for early stage breast cancer

“…Operations research (OR) methods have been applied extensively to problems related to various aspects of cancer treatment, such as the detailed scheduling of radiotherapy and chemotherapy (Beil and Wein 2001). For example, a common optimization problem arising in radiotherapy is to determine the number, positioning and the intensity of radiation beams so that the maximum number of cancer cells in a tumor are eliminated, while constraining the dosage of radiation obtained by healthy tissues around the targeted tumor (see, e.g., Brahme 2001;Hamacher and Küfer 2002;Lee et al 2003;Ferris et al 2003;Romeijn et al 2006).…”

“…Beil and Wein (2001) propose an optimization model for determining a sequence in which surgery (S), chemotherapy (C) and radiotherapy (R) should be administered. The problem is modeled using a system of ordinary differential equations that captures various local and systemic effects of each of these therapies.…”

“…The objective is to maximize the cancer cure probability subject to toxicity constraints. Beil and Wein (2001) analytically show that SRCR and RSCR are two best-performing schedules among the eight considered variants, which also included the six permutations of S, C and R.…”

Scheduling the adjuvant endocrine therapy for early stage breast cancer

“…Operations research (OR) methods have been applied extensively to problems related to various aspects of cancer treatment, such as the detailed scheduling of radiotherapy and chemotherapy (Beil and Wein 2001). For example, a common optimization problem arising in radiotherapy is to determine the number, positioning and the intensity of radiation beams so that the maximum number of cancer cells in a tumor are eliminated, while constraining the dosage of radiation obtained by healthy tissues around the targeted tumor (see, e.g., Brahme 2001;Hamacher and Küfer 2002;Lee et al 2003;Ferris et al 2003;Romeijn et al 2006).…”

“…Beil and Wein (2001) propose an optimization model for determining a sequence in which surgery (S), chemotherapy (C) and radiotherapy (R) should be administered. The problem is modeled using a system of ordinary differential equations that captures various local and systemic effects of each of these therapies.…”

“…The objective is to maximize the cancer cure probability subject to toxicity constraints. Beil and Wein (2001) analytically show that SRCR and RSCR are two best-performing schedules among the eight considered variants, which also included the six permutations of S, C and R.…”

The dynamics of war between benign cells, malignant cells, and killer agents

“……”

Scheduling the adjuvant endocrine therapy for early stage breast cancer

“…Operations research (OR) methods have been applied extensively to problems related to various aspects of cancer treatment, such as the detailed scheduling of radiotherapy and chemotherapy (Beil and Wein 2001). For example, a common optimization problem arising in radiotherapy is to determine the number, positioning and the intensity of radiation beams so that the maximum number of cancer cells in a tumor are eliminated, while constraining the dosage of radiation obtained by healthy tissues around the targeted tumor (see, e.g., Brahme 2001;Hamacher and Küfer 2002;Lee et al 2003;Ferris et al 2003;Romeijn et al 2006).…”

“…Beil and Wein (2001) propose an optimization model for determining a sequence in which surgery (S), chemotherapy (C) and radiotherapy (R) should be administered. The problem is modeled using a system of ordinary differential equations that captures various local and systemic effects of each of these therapies.…”

“…The objective is to maximize the cancer cure probability subject to toxicity constraints. Beil and Wein (2001) analytically show that SRCR and RSCR are two best-performing schedules among the eight considered variants, which also included the six permutations of S, C and R.…”

The dynamics of war between benign cells, malignant cells, and killer agents

“……”

Scheduling the adjuvant endocrine therapy for early stage breast cancer

“…Operations research (OR) methods have been applied extensively to problems related to various aspects of cancer treatment, such as the detailed scheduling of radiotherapy and chemotherapy (Beil and Wein 2001). For example, a common optimization problem arising in radiotherapy is to determine the number, positioning and the intensity of radiation beams so that the maximum number of cancer cells in a tumor are eliminated, while constraining the dosage of radiation obtained by healthy tissues around the targeted tumor (see, e.g., Brahme 2001;Hamacher and Küfer 2002;Lee et al 2003;Ferris et al 2003;Romeijn et al 2006).…”

“…Beil and Wein (2001) propose an optimization model for determining a sequence in which surgery (S), chemotherapy (C) and radiotherapy (R) should be administered. The problem is modeled using a system of ordinary differential equations that captures various local and systemic effects of each of these therapies.…”

“…The objective is to maximize the cancer cure probability subject to toxicity constraints. Beil and Wein (2001) analytically show that SRCR and RSCR are two best-performing schedules among the eight considered variants, which also included the six permutations of S, C and R.…”

The dynamics of war between benign cells, malignant cells, and killer agents

“……”