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.
Resistance to chemotherapy is a major impediment to the successful treatment of cancer. Classically, resistance has been thought to arise primarily through random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that the progression to drug resistance need not occur randomly, but instead may be induced by the therapeutic agent itself. This process of resistance induction can be a result of genetic changes, or can occur through epigenetic alterations that cause otherwise drug-sensitive cancer cells to undergo phenotype switching. This relatively novel notion of resistance further complicates the already challenging task of designing treatment protocols that minimize the risk of developing drug resistance. In an effort to better understand resistance to treatment, we have developed a mathematical modeling framework that incorporates both random and drug-induced resistance. Our model demonstrates that the ability (or lack thereof) of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. The importance of induced resistance in treatment response led us to ask if, in our model, one can determine the resistance induction rate of a drug for a given treatment protocol. Not only could we prove that the induction parameter in our model is theoretically identifiable, we have also proposed a possible in vitro protocol which could potentially be used to determine a treatment's propensity to induce resistance. (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/235150 doi: bioRxiv preprint first posted online Dec. 15, 2017; Tumor resistance to chemotherapy and targeted drugs is a major cause of treatment failure. Both molecular and microenvironmental factors have been implicated in the development of drug resistance [34]. As an example of molecular resistance, the upregulation of drug efflux transporters can prevent sufficiently high intracellular drug accumulation, limiting treatment efficacy [31]. Other molecular causes of drug resistance include modification of drug targets, enhanced DNA damage repair mechanisms, dysregulation of apoptotic pathways, and the presence of cancer stem cells [31,17,34,78,81]. The irregular tumor vasculature which results in inconsistent drug distribution and hypoxia is an example of a microenvironmental factor that impacts drug resistance [76]. Other characteristics of the tumor microenvironment that influence drug resistance include regions of acidity, immune cell infiltration and activation, and the tumor stroma [27,76,56,15,34,55].Research continues to shed light on the multitude of factors that contribute to cancer drug resistance. 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 ques...
Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multi-drug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level.
Motivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic "socially distant" populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied. One of the striking features of this model is the existence of a critical implementation delay in issuing separation mandates: while a delay of about four weeks does not have an appreciable effect, issuing mandates after this critical time results in a far greater incidence of infection. In other words, there is a nontrivial but tight "window of opportunity" for commencing social distancing. Different relaxation strategies are also simulated, with surprising results. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule's frequency. Further, we considered the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines, if not carefully designed. 0 These authors (listed alphabetically) contributed equally.
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