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Lung cancer is the most common type of cancer across the world. There are known two main types of lung cancer non-small cell lung (NSCLC) and small cell one (SCLC). Here, we focus on NSCLC that is known to disseminate to distant organs such as the brain or bones. What is more, the death of a patient with this type of cancer is caused usually by metastases. It justifies tackling the problem of the emergence of metastases in NSLC in this paper. Here, we investigated which mathematical parameters affect the emergence of metastases using the mathematical oncology approach. We developed a mathematical model of lung cancer growth and metastasis dissemination by taking into account stochasticity in the process. We incorporated into the model two paths of metastasis dissemination through lymphatic and blood vessels. We performed a global sensitivity analysis to identify parameters that affect the model output (metastasis-free survival) the most. We discover that four model parameters have dominating effect on the output and two of them are controllable - the growth rate of primary tumor cells (through the administration of chemotherapeutic agents) and carrying capacity (through the administration of angio-therapy). In conclusion, a mathematical oncology approach could be applied to investigate which treatment modalities in cancer could delay the emergence of metastases.

We developed a computational platform including machine learning and a mechanistic mathematical model to find the optimal protocol for administration of platinum-doublet chemotherapy in a palliative setting. The platform has been applied to advanced metastatic non-small cell lung cancer (NSCLC). The 42 NSCLC patients treated with palliative intent at Maria Sklodowska-Curie National Research Institute of Oncology, Gliwice Branch, were collected from a retrospective cohort of patients diagnosed in 2004–2014. Patients were followed-up, for three years. Clinical data collected include complete information about the clinical course of the patients including treatment schedule, response according to RECIST classification, and survival. The core of the platform is the mathematical model, in the form of a system of ordinary differential equations, describing dynamics of platinum-sensitive and platinum-resistant cancer cells and interactions reflecting competition for space and resources. The model is simulated stochastically by sampling the parameter values from a joint probability distribution function. The machine learning model is applied to calibrate the mathematical model and to fit it to the overall survival curve. The model simulations faithfully reproduce the clinical cohort at three levels long-term response (OS), the initial response (according to RECIST criteria), and the relationship between the number of chemotherapy cycles and time between two consecutive chemotherapy cycles. In addition, we investigated the relationship between initial and long-term response. We showed that those two variables do not correlate which means that we cannot predict patient survival solely based on the initial response. We also tested several chemotherapy schedules to find the best one for patients treated with palliative intent. We found that the optimal treatment schedule depends, among others, on the strength of competition among various subclones in a tumor. The computational platform developed allows optimizing chemotherapy protocols, within admissible limits of toxicity, for palliative treatment of metastatic NSCLC. The simplicity of the method allows its application to chemotherapy optimization in different cancers., Author summary Lung cancer is usually diagnosed at an advanced stage because of non-specific symptoms. The most common subtype of lung cancer is non-small cell lung cancer, which constitutes 80% of lung cancer cases. Here, we developed the methodology for finding the optimal treatment schedule for patients treated with palliative intent. The goal is not to cure the patients who are at an advanced stage but to prolong their survival by the administration of platinum-based chemotherapy. The method is based on the mathematical model describing the growth of tumors and its response to chemotherapy which is calibrated using real clinical data.

A major issue in oncology is the high failure rate of translating preclinical results in successful clinical trials. Using a virtual clinical trial simulations approach, we present a mathematical framework to estimate the added value of combinatorial treatments in ovarian cancer. This approach was applied to identify effective targeted therapies that can be combined with the platinum-taxane regimen and overcome platinum resistance in high-grade serous ovarian cancer. We modeled and evaluated the effectiveness of three drugs that target the main platinum resistance mechanisms, which have shown promising efficacy in vitro, in vivo, and early clinical trials. Our results show that drugs resensitizing chemoresistant cells are superior to those aimed at triggering apoptosis or increasing the bioavailability of platinum. Our results further show that the benefit of using biomarker stratification in clinical trials is dependent on the efficacy of the drug and tumor composition. The mathematical framework presented herein is suitable for systematically testing various drug combinations and clinical trial designs in solid cancers.

A major issue in oncology is the high failure rate of translating preclinical results in successful clinical trials. Using a virtual clinical trial simulations approach, we present a mathematical framework to estimate the added value of combinatorial treatments in ovarian cancer. This approach was applied to identify effective targeted therapies that can be combined with the platinum-taxane regimen and overcome platinum resistance in high-grade serous ovarian cancer. We modeled and evaluated the effectiveness of three drugs that target the main platinum resistance mechanisms, which have shown promising efficacy in vitro, in vivo, and early clinical trials. Our results show that drugs resensitizing chemoresistant cells are superior to those aimed at triggering apoptosis or increasing the bioavailability of platinum. Our results further show that the benefit of using biomarker stratification in clinical trials is dependent on the efficacy of the drug and tumor composition. The mathematical framework presented herein is suitable for systematically testing various drug combinations and clinical trial designs in solid cancers.

Many diseases with a genetic background such as some types of cancer are caused by damage in the p53 signaling pathway. The damage changes the system dynamics providing cancer cells with resistance to therapy such as radiation therapy. The change can be observed as the difference in bifurcation diagrams and equilibria type and location between normal and damaged cells, and summarized as the changes of the mathematical model parameters and following changes of the eigenvalues of Jacobian matrix. Therefore a change in other model parameters, such as mRNA degradation rates, may restore the proper eigenvalues and by that proper system dynamics. From the biological point of view, the change of mRNA degradation rate can be achieved by application of the small interfering RNA (siRNA). Here, we propose a general mathematical framework based on the bifurcation theory and siRNA-based control signal in order to study how to restore the proper response of cells with damaged p53 signaling pathway to therapy by using ionizing radiation (IR) therapy as an example. We show the difference between the cells with normal p53 signaling pathway and cells with abnormalities in the negative (as observed in SJSA-1 cell line) or positive (as observed in MCF-7 or PNT1a cell lines) feedback loop. Then we show how the dynamics of these cells can be restored to normal cell dynamics by using selected siRNA.

Platinum-based chemotherapy constitutes the backbone of clinical care in advanced solid cancers such as high-grade serous ovarian cancer (HGSOC) and has prolonged survival of millions of patients with cancer. Most of these patients, however, become resistant to chemotherapy, which generally leads to a fatal refractory disease. We present a comprehensive stochastic mathematical model and simulator approach to describe platinum resistance and standard-of-care (SOC) therapy in HGSOC. We used pre- and posttreatment clinical data, including 18F-FDG-PET/CT images, to reliably estimate the model parameters and simulate “virtual patients with HGSOC.” Treatment responses of the virtual patients generated by our mathematical model were indistinguishable from real-life patients with HGSOC. We demonstrated the utility of our approach by evaluating the survival benefit of combination therapies that contain up to six drugs targeting platinum resistance mechanisms. Several resistance mechanisms were already active at diagnosis, but combining SOC with a drug that targets the most dominant resistance subpopulation resulted in a significant survival benefit. This work provides a theoretical basis for a cancer treatment paradigm in which maximizing platinum's killing effect on cancer cells requires overcoming resistance mechanisms with targeted drugs. This freely available mathematical model and simulation framework enable rapid and rigorous evaluation of the benefit of a targeted drug or combination therapy in virtual patients before clinical trials, which facilitates translating preclinical findings into clinical practice. Significance: These findings present a comprehensive mathematical model for platinum resistance and standard-of-care therapy in a solid cancer, allowing virtual evaluation of novel therapy regimens. Cancer Res; 78(14); 4036–44. ©2018 AACR.