Multiple myeloma remains treatable but incurable. Despite a growing armamentarium of effective agents, choice of therapy, especially in relapse, still relies almost exclusively on clinical acumen. We have developed a system, Mathematical Myeloma Advisor (EMMA), consisting of patient-specific mathematical models parameterized by an assay that reverse engineers the intensity and heterogeneity of chemosensitivity of primary cells from multiple myeloma patients, allowing us to predict clinical response to up to 31 drugs within 5 days after bone marrow biopsy. From a cohort of 52 multiple myeloma patients, EMMA correctly classified 96% as responders/nonresponders and correctly classified 79% according to International Myeloma Working Group stratification of level of response. We also observed a significant correlation between predicted and actual tumor burden measurements (Pearson = 0.5658, < 0.0001). Preliminary estimates indicate that, among the patients enrolled in this study, 60% were treated with at least one ineffective agent from their therapy combination regimen, whereas 30% would have responded better if treated with another available drug or combination. Two clinical trials with experimental agents ricolinostat and venetoclax, in a cohort of 19 multiple myeloma patient samples, yielded consistent results with recent phase I/II trials, suggesting that EMMA is a feasible platform for estimating clinical efficacy of drugs and inclusion criteria screening. This unique platform, specifically designed to predict therapeutic response in multiple myeloma patients within a clinically actionable time frame, has shown high predictive accuracy in patients treated with combinations of different classes of drugs. The accuracy, reproducibility, short turnaround time, and high-throughput potential of this platform demonstrate EMMA's promise as a decision support system for therapeutic management of multiple myeloma..

Recent data have demonstrated that cancer drug resistance reflects complex biological factors including tumor heterogeneity, varying growth, differentiation, apoptosis pathways, and cell density. As a result, there is a need to find new ways to incorporate these complexities in the mathematical modeling of multidrug resistance. Here, we derive a novel structured population model that describes the behavior of cancer cells under selection with cytotoxic drugs. Our model is designed to estimate intratumoral heterogeneity as a function of the resistance level and time. This updated model of the multidrug resistance problem integrates both genetic and epigenetic changes, density-dependence, and intratumoral heterogeneity. Our results suggest that treatment acts as a selection process, while genetic/epigenetic alterations rates act as a diffusion process. Application of our model to cancer treatment suggests that reducing alteration rates as a first step in treatment causes a reduction in tumor heterogeneity, and may improve targeted therapy. The new insight provided by this model could help to dramatically change the ability of clinical oncologists to design new treatment protocols and analyze the response of patients to therapy. Major Findings We suggest that chemotherapeutic treatment acts as a selection process in the effective drug concentrations range, while genetic/epigenetic alterations act as a diffusion process that results in trait spread based on different stress signals. Application of our model to cancer treatment suggests that reducing the alteration rate as a first step in treatment causes a reduction in tumor heterogeneity, and may improve targeted therapy.

In this paper we develop a mathematical framework for describing multidrug resistance in cancer. To reflect the complexity of the underlying interplay between cancer cells and the therapeutic agent, we assume that the resistance level is a continuous parameter. Our model is written as a system of integro-differential equations that are parametrized by the resistance level. This model incorporates the cell-density and mutation dependence. Analysis and simulations of the model demonstrate how the dynamics evolves to a selection of one or more traits corresponding to different levels of resistance. The emerging limit distribution with nonzero variance is the desirable modeling outcome as it represents tumor heterogeneity.

PurposeDrug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols.Materials and MethodsTo better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance.ResultsOur model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment’s propensity to induce resistance.

Highlights A novel mathematical model of COVID-19 explicitly includes social-distancing. Short delay of distancing mandates has no appreciable effects on flattening the curve. Effect of periodic relaxation of distancing is highly sensitive to timing. Rate of gradual relaxation determines presence of a second wave, and its severity.