Limiting the Development of Anti-Cancer Drug Resistance in a Spatial Model of Micrometastases

Abstract

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.

Microenvironmental Niches and Sanctuaries: A Route to Acquired Resistance

“…If the microenvironment is incorporated, it is typically treated as a homogeneous medium. Some excellent overviews of such methods can be found in [7,13,29,30,34,54], and in our previous publications [16,59]. There are only a few mathematical models that deal with microenvironmental heterogeneity in the context of chemotherapy and drug resistance, using either agent-based approaches [42,52,53,61] or continuous equations [22,26,35,37].…”

A mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment

“…For instance, nitrogen mustards can induce base substitutions and chromosomal rearrangements, topoisomerase II inhibitors can induce chromosomal translocations, and antimetabolites can induce double stranded breaks and chromosomal aberrations [73]. Such drug-induced genomic alterations would generally be non-reversible, and a handful of mathematical models have considered this type of drug-induced resistance [29,49,68,1,20]. Drug resistance can also be induced at the epigenetic level via DNA methylation and histone modification [62,65].…”

“…Cancer models have also been utilized to assess how various underlying mechanisms contribute to the resistant phenotype [80,13,59,18,20], and to calculate the probability that drug resistance emerges within a specified time frame, be it before or during cancer treatment [39,40,58,24,3,26,59]. The question of how frequently, and at what dose, a single cancer drug should be administered given the presence of (or risk of developing) resistant cells has also been explored through mathematical modeling [37,23,24,33,46,49,68,1,9]. When multiple drugs are available, mathematical models have been used to determine the drug schedule (number of drugs to use, dose, sequence, timing) that best controls tumor progression in spite of drug resistance [39,47,70,16,60,63,4,51,10].…”

“…Mathematical modeling studies in particular have been used to explore both broad and detailed aspects of cancer drug resistance, as reviewed in [43,7,25]. The fundamental question of how the presence of drug resistant cells influences tumor dynamics and treatment outcomes has been thoroughly explored in mathematical models under a wide variety of assumptions [14,37,39,47,58,40,23,24,70,16,45,60,63,4,22,33,44,52,65,3,32,80,13,26,29,46,49,51,57,59,77,18,68,1,9,10,20]. Cancer models have also been utilized to assess how various underlying mechanisms contribute to the resistant phenotype [80,13,59,18,20], and to calculate the probability that drug resistance emerges within a specified time frame, be it before or during cancer treatment …”

“…As examples, pre-existing BCR-ABL kinase domain mutations confer resistance to the tyrosine kinase inhibitor imatinib in chronic myeloid leukemia patients [66,36], and pre-existing MEK1 mutations confer resistance to BRAF inhibitors in melanoma patients [8]. Many mathematical models have considered how the presence of preexisting resistant cells impact cancer progression and treatment [37,39,58,40,23,24,70,16,60,63,4,22,44,3,32,80,29,49,57,59,77,68,9,10].On the other hand, acquired drug resistance broadly describes the case in which drug resistance develops during the course of therapy from a population of cells that were initially drug sensitive [34]. The term "acquired resistance" is really an umbrella term for two distinct phenomena, which complicates the study of acquired resistance.…”