There is increasing interest in identifying therapeutic regimens capable of maintaining tumor burden within well-defined size boundaries with constraints on the amount and frequency of drugs on a patient-specific basis. We have developed coupled systems of ordinary differential equations (ODEs) capturing the temporal dynamics of tumor burden, treatment effects due to cytotoxic drugs, and neurotoxicity. The models account for tumor cell proliferation and phenotypic heterogeneity, drug availability due to continuous or impulsive drug delivery, drug-induced apoptosis and microglia activation. We utilize nullclines of the system to derive effective dose ranges that stabilize tumor burden and mitigate neurotoxicity. Our results generate bounded treatment regimens that can be validated in the experimental setting. We found that for tumors with a proliferation saturation index (i.e., pre-treatment volume to carrying capacity ratio) between 0.10 and 0.30, containing the tumor in the sense of RECIST can yield up to a 51.8% reduction in drug concentration when compared with regimens designed for tumor eradication. In silico experiments using data from a breast cancer study demonstrate that the nullcline-derived treatments maintained stable disease in the tumors with neurotoxicity maintained below the desired threshold. The methodology developed in this study provides a theoretical formalism to potentially explain several preclinical and clinical observations indicating that low dose therapy can stabilize tumor growth and result in an enhanced quality of life. Importantly, our model identified quantitative biologic indices that can offer practical guidance to the design of personalized regimens that balance treatment efficacy and toxicity.
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