Mathematical Model of Intrinsic Drug Resistance in Lung Cancer.

Drug resistance is a bottleneck in cancer treatment. Commonly, a molecular treatment for cancer leads to the emergence of drug resistance in the long term. Thus, some drugs, despite their initial excellent response, are withdrawn from the market. Lung cancer is one of the most mutated cancers, leading to dozens of targeted therapeutics available against it. Here, we have developed a mechanistic mathematical model describing sensitization to nine groups of targeted therapeutics and the emergence of intrinsic drug resistance. As we focus only on intrinsic drug resistance, we perform the computer simulations of the model only until clinical diagnosis. We have utilized, for model calibration, the whole-exome sequencing data combined with clinical information from over 1000 non-small-cell lung cancer patients. Next, the model has been applied to find an answer to the following questions: When does intrinsic drug resistance emerge? And how long does it take for early-stage lung cancer to grow to an advanced stage? The results show that drug resistance is inevitable at diagnosis but not always detectable and that the time interval between early and advanced-stage tumors depends on the selection advantage of cancer cells.

Mathematical model predicts response to chemotherapy in advanced non-resectable non-small cell lung cancer patients treated with platinum-based doublet.

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.

Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings.

BACKGROUND: Examination of physiological processes and the influences of the drugs on them can be efficiently supported by mathematical modeling. One of the biggest problems is related to the exact fitting of the parameters of a model. Conditions inside the organism change dynamically, so the rates of processes are very difficult to estimate. Perturbations in the model parameters influence the steady state so a desired therapeutic goal may not be reached. Here we investigate the effect of parameter deviation on the steady state in three simple models of the influence of a therapeutic drug on its target protein. Two types of changes in the model parameters are taken into account: small perturbations in the system parameter values, and changes in the switching time of a specific parameter. Additionally, we examine the systems response in case of a drug concentration decreasing with time. RESULTS: The models which we analyze are simplified, because we want to avoid influences of complex dynamics on the results. A system with a negative feedback loop is the most robust and the most rapid, so it requires the largest drug dose but the effects are observed very quickly. On the other hand a system with positive feedback is very sensitive to changes, so small drug doses are sufficient to reach a therapeutic target. In systems without feedback or with positive feedback, perturbations in the model parameters have a bigger influence on the reachability of the therapeutic target than in systems with negative feedback. Drug degradation or inactivation in biological systems enforces multiple drug applications to maintain the level of a drug's target under the desired threshold. The frequency of drug application should be fitted to the system dynamics, because the response velocity is tightly related to the therapeutic effectiveness and the time for achieving the goal. CONCLUSIONS: Systems with different types of regulation vary in their dynamics and characteristic features. Depending on the feedback loop, different types of therapy may be the most appropriate, and deviations in the model parameters have different influences on the reachability of the therapeutic target.

Gene signature of the post-Chernobyl papillary thyroid cancer.

PURPOSE: Following the nuclear accidents in Chernobyl and later in Fukushima, the nuclear community has been faced with important issues concerning how to search for and diagnose biological consequences of low-dose internal radiation contamination. Although after the Chernobyl accident an increase in childhood papillary thyroid cancer (PTC) was observed, it is still not clear whether the molecular biology of PTCs associated with low-dose radiation exposure differs from that of sporadic PTC. METHODS: We investigated tissue samples from 65 children/young adults with PTC using DNA microarray (Affymetrix, Human Genome U133 2.0 Plus) with the aim of identifying molecular differences between radiation-induced (exposed to Chernobyl radiation, ECR) and sporadic PTC. All participants were resident in the same region so that confounding factors related to genetics or environment were minimized. RESULTS: There were small but significant differences in the gene expression profiles between ECR and non-ECR PTC (global test, p < 0.01), with 300 differently expressed probe sets (p < 0.001) corresponding to 239 genes. Multifactorial analysis of variance showed that besides radiation exposure history, the BRAF mutation exhibited independent effects on the PTC expression profile; the histological subset and patient age at diagnosis had negligible effects. Ten genes (PPME1, HDAC11, SOCS7, CIC, THRA, ERBB2, PPP1R9A, HDGF, RAD51AP1, and CDK1) from the 19 investigated with quantitative RT-PCR were confirmed as being associated with radiation exposure in an independent, validation set of samples. CONCLUSION: Significant, but subtle, differences in gene expression in the post-Chernobyl PTC are associated with previous low-dose radiation exposure.

Development of a population of cancer cells: Observation and modeling by a Mixed Spatial Evolutionary Games approach.

Living cells, like whole living organisms during evolution, communicate with their neighbors, interact with the environment, divide, change their phenotypes, and eventually die. The development of specific ways of communication (through signaling molecules and receptors) allows some cellular subpopulations to survive better, to coordinate their physiological status, and during embryonal development to create tissues and organs or in some conditions to become tumors. Populations of cells cultured in vitro interact similarly, also competing for space and nutrients and stimulating each other to better survive or to die. The results of these intercellular interactions of different types seem to be good examples of biological evolutionary games, and have been the subjects of simulations by the methods of evolutionary game theory where individual cells are treated as players. Here we present examples of intercellular contacts in a population of living human cancer HeLa cells cultured in vitro and propose an evolutionary game theory approach to model the development of such populations. We propose a new technique termed Mixed Spatial Evolutionary Games (MSEG) which are played on multiple lattices corresponding to the possible cellular phenotypes which gives the possibility of simulating and investigating the effects of heterogeneity at the cellular level in addition to the population level. Analyses performed with MSEG suggested different ways in which cellular populations develop in the case of cells communicating directly and through factors released to the environment.

Value of computed tomography radiomics combined with inflammation indices in predicting the efficacy of immunotherapy in patients with locally advanced and metastatic non-small cell lung cancer.

Background: Although immunotherapy has revolutionized the treatment landscape of lung cancer and improved the prognosis of this malignancy, many patients with lung cancer still are not able to benefit from it because of many different reasons. The expression of programmed death ligand-1 (PD-L1) in tumor cells has been approved for the prediction of immunotherapy efficacy; however, its clinical application has been limited by the invasiveness of PD-L1 determination and the heterogeneity of tumor cells. As a promising technology, radiomics has made significant progress in the diagnosis and treatment of lung cancer. Thus, we constructed a noninvasive predictive model which based on radiomics to predict the immunotherapy efficacy of lung caner patients. Methods: Data of 82 patients with stage IIIa/IVb NSCLC who received immunotherapy at the First Affiliated Hospital of Soochow University from December 2019 to January 2023 were retrospectively collected. These patients were followed up for durable clinical benefit (DCB), as defined by whether progression-free survival (PFS) reached 12 months. The least absolute shrinkage and selection operator (LASSO) algorithm was used to screen for the radiomic features in the training set, and a radiomics score (Rad-score) was calculated. The clinical baseline data were analyzed, and the peripheral blood inflammation indices were calculated. Univariate and multivariate analyses were performed to identify the applicable indices, which were combined with the Rad-score to create a comprehensive forecasting model (CFM) and nomograms. Internal validation was performed in the validation set. Results: Up to the last follow-up time, 48 of 82 patients had a PFS of more than 12 months. The area under the receiver operating characteristic (ROC) curve (AUC) of the Rad-score was 0.858 and 0.812, respectively, in the training set and validation set. A systemic immune-inflammation index (SII) score of <500.88 after two cycles of immunotherapy was a protective factor for PFS >12 months [odds ratio (OR) 0.054; P=0.003]. The CFM had an AUC of 0.930 and 0.922, respectively, in the training and validation sets. The calibration curves and decision curve analysis (DCA) demonstrated the reliability and clinical applicability of the model, respectively. Conclusions: The radiomics model performed well in predicting whether patients with locally advanced or metastatic NSCLC can achieve DCB after receiving immunotherapy. The CFM had good predictive performance and reliability.

Radiomic signature accurately predicts the risk of metastatic dissemination in late-stage non-small cell lung cancer.

Background: Non-small cell lung cancer (NSCLC) is the most common type of lung cancer, and the median overall survival (OS) 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. Methods: A cohort of 115 NSCLC patients treated using chemotherapy and radiotherapy (RT) with curative intent was retrospectively collated and included patients for whom positron emission tomography/computed tomography (PET/CT) images, acquired before RT, were available. The PET/CT images were used to compute radiomic features extracted from a region of interest (ROI), 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. Results: Classification 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. Conclusions: It 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.

Non-parametric MRI Brain Atlas for the Polish Population.

Introduction: The application of magnetic resonance imaging (MRI) to acquire detailed descriptions of the brain morphology in vivo is a driving force in brain mapping research. Most atlases are based on parametric statistics, however, the empirical results indicate that the population brain tissue distributions do not exhibit exactly a Gaussian shape. Our aim was to verify the population voxel-wise distribution of three main tissue classes: gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), and to construct the brain templates for the Polish (Upper Silesian) healthy population with the associated non-parametric tissue probability maps (TPMs) taking into account the sex and age influence. Material and Methods: The voxel-wise distributions of these tissues were analyzed using the Shapiro-Wilk test. The non-parametric atlases were generated from 96 brains of the ethnically homogeneous, neurologically healthy, and radiologically verified group examined in a 3-Tesla MRI system. The standard parametric tissue proportion maps were also calculated for the sake of comparison. The maps were compared using the Wilcoxon signed-rank test and Kolmogorov-Smirnov test. The volumetric results segmented with the parametric and non-parametric templates were also analyzed. Results: The results confirmed that in each brain structure (regardless of the studied sub-population) the data distribution is skewed and apparently not Gaussian. The determined non-parametric and parametric templates were statistically compared, and significant differences were found between the maps obtained using both measures (the maps of GM, WM, and CSF). The impacts of applying the parametric and non-parametric TPMs on the segmentation process were also compared. The GM volumes are significantly greater when using the non-parametric atlas in the segmentation procedure, while the CSF volumes are smaller. Discussion and Conclusion: To determine the population atlases the parametric measures are uncritically and widely used. However, our findings suggest that the mean and parametric measures of such skewed distribution may not be the most appropriate summary statistic to find the best spatial representations of the structures in a standard space. The non-parametric methodology is more relevant and universal than the parametric approach in constructing the MRI brain atlases.

Whole Brain and Cranial Size Adjustments in Volumetric Brain Analyses of Sex- and Age-Related Trends.

Our goal was to determine the influence of sex, age and the head/brain size on the compartmental brain volumes in the radiologically verified healthy population (96 subjects; 54 women and 42 men) from the Upper Silesia region in Poland. The MRI examinations were done using 3T Philips Achieva with the same T1-weighted and T2-weighted protocols. The image segmentation procedures were performed with SPM (Statistical Parameter Mapping) and FSL-FIRST software. The volumes of 14 subcortical structures for the left and right hemispheres and 4 overall volumes were calculated. The General Linear Models (GLM) analysis was used with and without the Total Brain Volume (TBV) and Intracranial Volume (ICV) parameters as the covariates to study the regional vs. global brain atrophy. After the ICV/TBV adjustments, the majority of sex differences in the specific volumes of interest (VOIs) revealed to be linked to the difference in the head/brain size parameters. The analysis also confirmed the significant effect of the aging process on the brain loss. After the TBV adjustment, the age- and sex-related volumetric trends for the gray and white matter volumes were observed: the negative age dependence of the gray matter volume is more pronounced in the males, while in case of the white matter the positive age-related trend in the female group is weaker. The local losses of the left caudate nucleus and the right thalamus are more advanced than the global brain atrophy. Different head-size correction strategies are not interchangeable and may yield various volumetric results, but when used together, facilitate studies on the regional dependencies inherent to a healthy, but aging, brain.

A multi-gene approach to differentiate papillary thyroid carcinoma from benign lesions: gene selection using support vector machines with bootstrapping.

Selection of novel molecular markers is an important goal of cancer genomics studies. The aim of our analysis was to apply the multivariate bioinformatical tools to rank the genes - potential markers of papillary thyroid cancer (PTC) according to their diagnostic usefulness. We also assessed the accuracy of benign/malignant classification, based on gene expression profiling, for PTC. We analyzed a 180-array dataset (90 HG-U95A and 90 HG-U133A oligonucleotide arrays), which included a collection of 57 PTCs, 61 benign thyroid tumors, and 62 apparently normal tissues. Gene selection was carried out by the support vector machines method with bootstrapping, which allowed us 1) ranking the genes that were most important for classification quality and appeared most frequently in the classifiers (bootstrap-based feature ranking, BBFR); 2) ranking the samples, and thus detecting cases that were most difficult to classify (bootstrap-based outlier detection). The accuracy of PTC diagnosis was 98.5% for a 20-gene classifier, its 95% confidence interval (CI) was 95.9-100%, with the lower limit of CI exceeding 95% already for five genes. Only 5 of 180 samples (2.8%) were misclassified in more than 10% of bootstrap iterations. We specified 43 genes which are most suitable as molecular markers of PTC, among them some well-known PTC markers (MET, fibronectin 1, dipeptidylpeptidase 4, or adenosine A1 receptor) and potential new ones (UDP-galactose-4-epimerase, cadherin 16, gap junction protein 3, sushi, nidogen, and EGF-like domains 1, inhibitor of DNA binding 3, RUNX1, leiomodin 1, F-box protein 9, and tripartite motif-containing 58). The highest ranking gene, metallophosphoesterase domain-containing protein 2, achieved 96.7% of the maximum BBFR score.

Adjoint systems for models of cell signaling pathways and their application to parameter fitting.

The paper concerns the problem of fitting mathematical models of cell signaling pathways. Such models frequently take the form of sets of nonlinear ordinary differential equations. While the model is continuous in time, the performance index used in the fitting procedure, involves measurements taken at discrete time moments. Adjoint sensitivity analysis is a tool, which can be used for finding the gradient of a performance index in the space of parameters of the model. In the paper a structural formulation of adjoint sensitivity analysis called the Generalized Backpropagation Through Time (GBPTT) is used. The method is especially suited for hybrid, continuous-discrete time systems. As an example we use the mathematical model of the NF-kB regulatory module, which plays a major role in the innate immune response in animals.

Gene expression profile of papillary thyroid cancer: sources of variability and diagnostic implications.

The study looked for an optimal set of genes differentiating between papillary thyroid cancer (PTC) and normal thyroid tissue and assessed the sources of variability in gene expression profiles. The analysis was done by oligonucleotide microarrays (GeneChip HG-U133A) in 50 tissue samples taken intraoperatively from 33 patients (23 PTC patients and 10 patients with other thyroid disease). In the initial group of 16 PTC and 16 normal samples, we assessed the sources of variability in the gene expression profile by singular value decomposition which specified three major patterns of variability. The first and the most distinct mode grouped transcripts differentiating between tumor and normal tissues. Two consecutive modes contained a large proportion of immunity-related genes. To generate a multigene classifier for tumor-normal difference, we used support vector machines-based technique (recursive feature replacement). It included the following 19 genes: DPP4, GJB3, ST14, SERPINA1, LRP4, MET, EVA1, SPUVE, LGALS3, HBB, MKRN2, MRC2, IGSF1, KIAA0830, RXRG, P4HA2, CDH3, IL13RA1, and MTMR4, and correctly discriminated 17 of 18 additional PTC/normal thyroid samples and all 16 samples published in a previous microarray study. Selected novel genes (LRP4, EVA1, TMPRSS4, QPCT, and SLC34A2) were confirmed by Q-PCR. Our results prove that the gene expression signal of PTC is easily detectable even when cancer cells do not prevail over tumor stroma. We indicate and separate the confounding variability related to the immune response. Finally, we propose a potent molecular classifier able to discriminate between PTC and nonmalignant thyroid in more than 90% of investigated samples.

Local controllability and optimal control for a model of combined anticancer therapy with control delays.

We study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from these models. The control delays are related to PK/PD effects and some clinical recommendations, e.g., normalization of the vascular network. The optimized protocols of the combined therapy for the model, considered as solutions to an optimal control problem with delays in control, are found using necessary conditions of optimality and numerical computations. Our numerical approach uses dicretization and nonlinear programming methods as well as the direct optimization of switching times. The structural sensitivity of the considered control properties and optimal solutions is also discussed.

Meta- and reanalysis of gene expression profiles of hot and cold thyroid nodules and papillary thyroid carcinoma for gene groups.

CONTEXT: There are an increasing number of studies analyzing gene expression profiles in various benign and malignant thyroid tumors. This creates the opportunity to validate results obtained from one microarray study with those from other data sets. This process requires rigorous methods for accurate comparison. OBJECTIVE: The ability to compare data sets derived from different Affymetrix GeneChip generations and the influence of intra- and interindividual comparisons of gene expression data were evaluated to build multigene classifiers of benign thyroid nodules to verify a previously proposed papillary thyroid carcinoma (PTC) classifier and to look for molecular pathways essential for PTC oncogenesis. METHODS: Gene expression profile data sets from autonomously functioning and cold thyroid nodules and from PTC were analyzed by support vector machines. GenMAPP analysis was used for PTC data analysis to examine the expression patterns of biologically relevant gene sets. RESULTS: Only intraindividual reference samples allowed the identification of subtle changes in the expression patterns of relevant signaling cascades, such as the MAPK pathway in PTC. Using an artificial intelligence approach, the autonomously functioning and cold thyroid nodule multigene classifiers were derived and evaluated by cross-comparisons. CONCLUSION: We recommend defining classifiers within one generation of gene chips and subsequently checking them across different array generations. Using this approach, we have demonstrated the specificity of a previously reported PTC classifier on an independent collection of benign tumors. Moreover, we propose multigene classifiers for different types of benign thyroid nodules.

Multidimensional extended spatial evolutionary games.

The goal of this paper is to study the classical hawk-dove model using mixed spatial evolutionary games (MSEG). In these games, played on a lattice, an additional spatial layer is introduced for dependence on more complex parameters and simulation of changes in the environment. Furthermore, diverse polymorphic equilibrium points dependent on cell reproduction, model parameters, and their simulation are discussed. Our analysis demonstrates the sensitivity properties of MSEGs and possibilities for further development. We discuss applications of MSEGs, particularly algorithms for modelling cell interactions during the development of tumours.

Cancer heterogeneity and multilayer spatial evolutionary games.

BACKGROUND: Evolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. Our model contains four main phenotypes. Moreover, in a standard approach only heterogeneity of populations is studied, while cancer cells remain homogeneous. A multilayer approach proposed in this paper enables to study heterogeneity of single cells. METHOD: In the extended model presented in this paper we consider four strategies (phenotypes) that can arise by mutations. We propose multilayer spatial evolutionary games (MSEG) played on multiple 2D lattices corresponding to the possible phenotypes. It enables simulation and investigation of heterogeneity on the player-level in addition to the population-level. Moreover, it allows to model interactions between arbitrary many phenotypes resulting from the mixture of basic traits. RESULTS: Different equilibrium points and scenarios (monomorphic and polymorphic populations) have been achieved depending on model parameters and the type of played game. However, there is a possibility of stable quadromorphic population in MSEG games for the same set of parameters like for the mean-field game. CONCLUSION: The model assumes an existence of four possible phenotypes (strategies) in the population of cells that make up tumour. Various parameters and relations between cells lead to complex analysis of this model and give diverse results. One of them is a possibility of stable coexistence of different tumour cells within the population, representing almost arbitrary mixture of the basic phenotypes. REVIEWERS: This article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.

How fast is repopulation of tumor cells during the treatment gap?

PURPOSE/OBJECTIVE: Our goal was to analyze the repopulation of surviving tumor cells during a treatment gap in radiotherapy for head-and-neck cancer. METHODS AND MATERIALS: Clinical material is based on the records of 1502 patients treated by radiotherapy alone in Maria Sklodowska-Curie Memorial Institute in Gliwice during the period between1980 and 1989. All patients had histologically confirmed squamous cell carcinoma of the larynx or pharynx. The mean gap duration was 9 days. Only 10% of patients were treated without gaps. The dose per fraction was in the range of 1.5 to 2.5 Gy. Patient data were fitted directly to the mixed linear-quadratic model using maximum-likelihood estimation. Tumor stage or tumor localization was introduced into the equation as a categorical variable. Tumor proliferation was estimated by dividing the treatment gaps into three groups: the first 2 weeks, second 2 weeks, and the period after 4 weeks of irradiation. RESULTS: Tumor control probability was significantly correlated with radiation dose, tumor progression (according to TNM), overall treatment time, and gap duration. Laryngeal cancers had a better prognosis than cancers of the oro- and nasopharynx. Significant tumor repopulation was found after the first 2 weeks of radiotherapy. During the treatment gap, the proliferation rate was equal to 0.75 Gy/day. During the days with irradiation, repopulation was slower and equal to 0.2 Gy/day. CONCLUSION: The repopulation of tumor cells is faster during a gap than during the normal days of irradiation. Accelerated repopulation probably starts soon after 2 weeks of irradiation.

Radiation-induced micronucleus frequency in peripheral blood lymphocytes is correlated with normal tissue damage in patients with cervical carcinoma undergoing radiotherapy.

In an effort to find a test to predict the response of normal tissue to radiotherapy, the lymphocyte micronucleus assay was used on blood samples from patients with cervical carcinoma. Peripheral blood samples from 55 patients with advanced-stage (II B-IV B) cervical carcinoma were obtained before radiotherapy. The patients were treated with external-beam radiotherapy followed by high-dose-rate brachytherapy. Acute and late normal tissue reactions were scored and correlated with the micronucleus frequency in lymphocytes after irradiation with 4 Gy in vitro. Great interindividual variability was observed in the radiation-induced lymphocyte micronucleus frequency, especially at 4 Gy. The mean number of micronuclei per 100 binucleated cells in cells irradiated with 4 Gy in vitro was significantly higher in samples from patients who suffered from acute and/or late normal tissue reactions than in those from patients with no reactions (51.0 +/- 17.7 and 29.6 +/- 10.1, respectively). A significant correlation was also found between the micronucleus frequency at 4 Gy and the severity of acute reactions and late reactions. However, the overlap between the micronucleus frequencies of patients with high-grade late normal tissue reactions and low-grade reactions is too great to recommend the micronucleus assay in its present form for routine clinical application.

Comparison of simple models of periodic protocols for combined anticancer therapy.

Several simple ordinary differential equation (ODE) models of tumor growth taking into account the development of its vascular network are discussed. Different biological aspects are considered from the simplest model of Hahnfeldt et al. proposed in 1999 to a model which includes drug resistance of cancer cells to chemotherapy. Some of these models can be used in clinical oncology to optimize antiangiogenic and cytostatic drugs delivery so as to ensure maximum efficacy. Simple models of continuous and periodic protocols of combined therapy are implemented. Discussion on the dynamics of the models and their complexity is presented.

Application of evolutionary games to modeling carcinogenesis.

We review a quite large volume of literature concerning mathematical modelling of processes related to carcinogenesis and the growth of cancer cell populations based on the theory of evolutionary games. This review, although partly idiosyncratic, covers such major areas of cancer-related phenomena as production of cytotoxins, avoidance of apoptosis, production of growth factors, motility and invasion, and intra- and extracellular signaling. We discuss the results of other authors and append to them some additional results of our own simulations dealing with the possible dynamics and/or spatial distribution of the processes discussed.