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Clinical data for calibration and validation cohorts.

Detailed description of mathematical model and parameter estimation.

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.

BackgroundNon-small cell lung cancer (NSCLC) is the most common type of lung cancer, and the median overall survival is approximately 2-3 years among patients with stage III disease. Furthermore, it is one of the deadliest types of cancer globally due to non-specific symptoms and the lack of a biomarker for early detection. The most important decision that clinicians need to make after a lung cancer diagnosis is the selection of a treatment schedule. This decision is based on, among others factors, the risk of developing metastasis.MethodsA cohort of 115 NSCLC patients treated using chemotherapy and radiotherapy with curative intent was retrospectively collated and included patients for whom positron emission tomogra-phy/computed tomography (PET/CT) images, acquired before radiotherapy, were available. The PET/CT images were used to compute radiomic features extracted from a region of interest, the primary tumor. Radiomic and clinical features were then classified to stratify the patients into short and long time to metastasis, and regression analysis was used to predict the risk of metastasis.ResultsClassification based on binarized metastasis-free survival (MFS) was applied with moderate success. Indeed, an accuracy of 0.73 was obtained for the selection of features based on the Wilcoxon test and logistic regression model. However, the Cox regression model for metastasis risk prediction performed very well, with a concordance index (c-index) score equal to 0.84.ConclusionsIt is possible to accurately predict the risk of metastasis in NSCLC patients based on radiomic features. The results demonstrate the potential use of features extracted from cancer imaging in predicting the risk of metastasis.

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.

The aim of this study was to determine changes in the quality of lamb meat (Longissimus thoracis et lumborum), which was vacuum-packaged and freezer-stored (-26°C) for 6 and 12 months. The experiment was performed on 12 male lambs of the Kamieniec Longwool breed, raised to 106 days of age. In comparison with fresh meat, thawed meat was characterized by lower ash content, higher pH, greater natural drip loss and cooking loss, and lower scores for taste intensity. Vacuum packaging and low-temperature storage protected lamb meat against oxidative changes, and alleviated the adverse effects of oxidation on the color, aroma and taste of meat. It can be concluded that freezer storage (-26°C) of vacuum-packaged meat can help meet consumer demand for lamb meat products in periods when fresh meat is unavailable. However, it should be noted that long-term frozen storage induces undesirable changes in meat quality, including a decrease in water-holding capacity and taste intensity.

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.

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Purpose: We introduce here the most comprehensive mathematical model to date for high-grade serous ovarian cancer patient treatment response and use it to predict the effect of novel combination therapies. Introduction: Platinum-based chemotherapy constitutes the backbone for clinical care of advanced solid cancers, such as high-grade serous ovarian cancer (HGSOC). The vast majority of patients, however, become resistant to platinum, which eventually leads to generally fatal refractory disease. As HGSOC tumors are heterogeneous, cancer cells often have activated many resistant mechanisms, and targeting a single mechanism at a time is unlikely to result in significant improvement in survival rates. A systems biology approach, where resistance mechanisms are comprehensively considered, is required in efforts to overcome platinum resistance. Methods: Platinum resistance is a multifactorial process and the most important resistance mechanisms are: 1) reduced intake or increased efflux leading to reduced platinum bioavailability in a cell, 2) DNA repair mechanisms that overcome platinum-induced DNA adducts, and 3) dysfunctional apoptosis machinery. The herein established mathematical model is based on three major resistance mechanisms and it models tumor growth and evolution as a deterministic continuous time, multitype branching process. Importantly, we have used comprehensive pre- and postoperative clinical data, including high-resolution 18F-fluorodeoxyglucose positron emission tomography/computed tomography images, from a HGSOC patient cohort. This allows accurate calibration of the model parameters, which ensures that the model is able to capture clinical course of HGSOC patients. In addition to quantifying the effect of a platinum-taxane to tumor burden of an HGSOC patient, we have modeled the impact of debulking surgery. This enables us to use the mathematical model in simulating “virtual HGSOC patients” who undergo standard-of-care (SOC) therapy, i.e., debulking surgery and platinum-taxane therapy. Results: Our model-generated virtual patients show almost identical treatment responses with two validation HGSOC cohorts that together contain data from 105 HGSOC patients. The average virtual HGSOC patient has platinum-free interval (PFI) of six months, which is identical to the mean PFI in the training and independent validation cohorts. The ability to create in silico HGSOC patients whose responses correspond to real-life HGSOC cohorts was supported statistically by the Kolmogorov-Smirnov test. As our model can capture the heterogeneous responses of individual HGSOC patients, we utilized it to evaluate the added value of combining novel targeted therapies to the current first-line SOC therapy. The results from the virtual clinical trials with selected targeted agents are in line with the results from early-phase clinical trials and pinpoint the most effective combination strategies. Further, our results show that targeting the three most important platinum-resistant mechanisms simultaneously with clinically available agents provides a significant survival advance to HGSOC patients. Conclusions: High failure rate in translating preclinical results to successful clinical trials is a major issue in oncology. The herein introduced mathematical framework enables creating virtual patient cohorts that capture the response variation in real-life patient cohorts. This allows for rapid and reliable estimate of the added value of the novel therapy in comparison to SOC therapy to optimize clinical trial design. Here we focused on overcoming platinum resistance in HGSOC and our results show substantial added value of combining three early-phase clinical trial agents, which target the three major resistant mechanisms and have been individually combined with SOC. Citation Format: Sampsa Hautaniemi, Emilia Kozlowska, Anniina Färkkilä, Tuulia Vallius, Olli Carpen, Seija Grenman, Rainer Lehtonen, Johanna Hynninen, Sakari Hietanen. Mathematical model quantifies the effect of novel combination therapies in high-grade serous ovarian cancer. [abstract]. In: Proceedings of the AACR Conference: Addressing Critical Questions in Ovarian Cancer Research and Treatment; Oct 1-4, 2017; Pittsburgh, PA. Philadelphia (PA): AACR; Clin Cancer Res 2018;24(15_Suppl):Abstract nr B70.

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.