Mathematical Oncology

Do mechanisms matter?

Behind the paper

Written by Fred Adler - July 29, 2021

Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives

Cassidy K. Buhler, Rebecca S. Terry, Kathryn G. Link, Frederick R. Adler

Read the paper
I have long been concerned that the models that buttress the intuitive argument for adaptive therapy had not been sufficiently explored, although recent papers have made important contributions ("A theoretical analysis of tumour containment" by Yannick Viossat & Robert Noble, Nature Ecology & Evolution 5:826–835, 2021). I was fortunate to work with an outstanding undergraduate student, Cassie Buhler, and two redoubtable graduate students, Becky Terry and Katie Link, to take on this problem ("Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives", Mathematical Biosciences and Engineering, 18:6205-6327, 2021).

Adaptive therapy depends on three key assumptions: resistance is costly, resistant cells can be suppressed by competition with sensitive cells, and therapy reduces the population of sensitive cells (although Viossat & Noble show that the first of these assumptions is not essential). However, what happens when these assumptions are tested against a wider set of ecological backgrounds? We expanded on the original work by Zhang et al ("Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer", Nature Communications, 8:1816, 2017) to investigate four extensions of a basic competition model: 1) competition with healthy cells, 2) inclusion of resource dynamics, 3) an immune response, and 4) an Allee effect. We tested how a comprehensive set of intermittent and adaptive therapies balance two types of treatment failure (the time when resistant cells exceed some threshold and the time when the total cell population exceeds a different threshold) and two costs: average cell population and total treatment burden.

We found three key results. First, with the exception of models that include a strong Allee effect, all models closely follow a tradeoff curve between cancer cell burden and time to emergence of resistant cells. The Allee effect, meaning that cancer cell populations decline if they fall below some threshold, adds an additional type of control of resistant cells, and breaks this relationship. Second, again with the exception of models with an Allee effect, the tradeoff among time to total cancer cell number escape, average cancer cell burden, and total treatment, is similar but not identical over a range of intermittent and adaptive therapies. In most cases, some adaptive therapies do delay tumor growth, but at the cost of higher average cell populations. With the Allee effect, some adaptive therapies perform quite poorly because the threshold for stopping therapy is above the Allee threshold. Third, and most importantly, no therapeutic choice robustly breaks the three-way tradeoff among delaying emergence of resistance, delaying cancer growth, and minimizing treatment.

Is it time to move beyond these simple models? They have a few idealized dimensions, no explicit evolution, no spatial interactions, and investigate strategies without feedback from the responses of individual patients to mention just a few missing elements. Nonetheless, we think these models are valuable in showing general principles, like the tradeoffs we quantify, and in pointing the way toward integration with fuller data sets that include measurements of additional factors like resources, signals, healthy cells and immune cells. Given the necessarily limited information we have on any individual patient, these models provide links to the whole population that increase our power to leverage that information most effectively.
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