Modelling chemotherapy resistance in palliation and failed cure

The goal of palliative cancer chemotherapy treatment is to prolong survival and improve quality of life when tumour eradication is not feasible. Chemotherapy protocol design is considered in this context using a simple, robust, model of advanced tumour growth with Gompertzian dynamics, taking into account the effects of drug resistance. It is predicted that reduced chemotherapy protocols can readily lead to improved survival times due to the effects of competition between resistant and sensitive tumour cells. Very early palliation is also predicted to quickly yield near total tumour resistance and thus decrease survival duration. Finally, our simulations indicate that failed curative attempts using dose densification, a common protocol escalation strategy, can reduce survival times

A theoretical study of the response of vascular tumours to different types of chemotherapy

In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs

Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics

One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity. Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on cancer progression, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and virus replication rate, can lead to complex, time-dependent behaviors of the tumor. Thus, irregular, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus. The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

: Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents' pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system

Mathematical Models of Chemotherapy

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens. The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling specific chemotherapeutic processes, and drug resistance. By studying the models we can obtain a better understanding of the dynamics of the chemotherapeutic drugs and how better to implement them. The mathematical methods used are mostly in the area of dynamical systems in particular Floquet Theory. These methods are used on either a single equation or a system of periodic ordinary differential equations which model the chemotherapeutic process. These are reduced to difference equations that describe the state of the cancer at the beginning of each period. By studying the characteristic multipliers, we are able to determine the bifurcation between successful and unsuccessful regimens, if existing drug regimens seem reasonable from a mathematical model standpoint, and suggest ways to better implement the existing chemotherapeutic drugs

Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model

Cancer is a proliferation disease affecting a genetically unstable cell population, in which molecular alterations can be somatically inherited by genetic, epigenetic or extragenetic transmission processes, leading to a cooperation of neoplastic cells within tumoral tissue. The efflux protein P-glycoprotein (P gp) is overexpressed in many cancer cells and has known capacity to confer multidrug resistance to cytotoxic therapies. Recently, cell-to-cell P-gp transfers have been shown. Herein, we combine experimental evidence and a mathematical model to examine the consequences of an intercellular P-gp trafficking in the extragenetic transfer of multidrug resistance from resistant to sensitive cell subpopulations. We report cell-to-cell transfers of functional P-gp in co-cultures of a P-gp overexpressing human breast cancer MCF-7 cell variant, selected for its resistance towards doxorubicin, with the parental sensitive cell line. We found that P-gp as well as efflux activity distribution are progressively reorganized over time in co-cultures analyzed by flow cytometry. A mathematical model based on a Boltzmann type integro-partial differential equation structured by a continuum variable corresponding to P-gp activity describes the cell populations in co-culture. The mathematical model elucidates the population elements in the experimental data, specifically, the initial proportions, the proliferative growth rates, and the transfer rates of P-gp in the sensitive and resistant subpopulations. We confirmed cell-to-cell transfer of functional P-gp. The transfer process depends on the gradient of P-gp expression in the donor-recipient cell interactions, as they evolve over time. Extragenetically acquired drug resistance is an additional aptitude of neoplastic cells which has implications in the diagnostic value of P-gp expression and in the design of chemotherapy regimensComment: 13 pages, 8 figures, 1 tabl

The role of copper in disulfiram-induced toxicity and radiosensitization of cancer cells

<p>Disulfiram has been used for several decades in the treatment of alcoholism. It now shows promise as an anti-cancer drug and radiosensitizer. Proposed mechanisms of action include the induction of oxidative stress and inhibition of proteasome activity. Our purpose was to determine the potential of disulfiram to enhance the anti-tumor efficacy of external beam ϒ-irradiation and 131I-metaiodobenzylguanidine (131I-MIBG), a radiopharmaceutical used for the therapy of neuroendocrine tumors.</p> <p>Methods: The role of copper in disulfiram-induced toxicity was investigated by clonogenic assay after treatment of human SK-N-BE(2c) neuroblastoma and UVW/NAT glioma cells. Synergistic interaction between disulfiram and radiotherapy was evaluated by combination index analysis. Tumor growth delay was determined in vitro using multicellular tumor spheroids and in vivo using human tumor xenografts in athymic mice.</p> <p>Results: Escalating disulfiram dosage caused a biphasic reduction in the surviving fraction of clonogens. Clonogenic cell kill after treatment with disulfiram concentrations less than 4 μM was copper-dependent, whereas cytotoxicity at concentrations greater than 10 μM was caused by oxidative stress. The cytotoxic effect of disulfiram was maximal when administered with equimolar copper. Likewise, disulfiram’s radiosensitization of tumor cells was copper-dependent. Furthermore, disulfiram treatment enhanced the toxicity of 131I-MIBG to spheroids and xenografts expressing the noradrenaline transporter.</p> <p>Conclusions: The results demonstrate that (i) the cytotoxicity of disulfiram was copper-dependent; (ii) molar excess of disulfiram relative to copper resulted in attenuation of disulfiram-mediated cytotoxicity; (iii) copper was required for the radiosensitizing activity of disulfiram and (iv) copper-complexed disulfiram enhanced the efficacy not only of external beam radiation but also of targeted radionuclide therapy in the form of 131I-MIBG. Therefore disulfiram may have anti-cancer potential in combination with radiotherapy.</p&gt