Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Cancer cell cycle heterogeneity as a critical determinant of therapeutic resistance

Intra-tumor heterogeneity is now arguably one of the most-studied topics in tumor biology, as it represents a major obstacle to effective cancer treatment. Since tumor cells are highly diverse at genetic, epigenetic, and phenotypic levels, intra-tumor heterogeneity can be assumed as an important contributing factor to the nullification of chemotherapeutic effects, and recurrence of the tumor. Based on the role of heterogeneous subpopulations of cancer cells with varying cell-cycle dynamics and behavior during cancer progression and treatment; herein, we aim to establish a comprehensive definition for adaptation of neoplastic cells against therapy. We discuss two parallel and yet distinct subpopulations of tumor cells that play pivotal roles in reducing the effects of chemotherapy: "resistant" and "tolerant" populations. Furthermore, this review also highlights the impact of the quiescent phase of the cell cycle as a survival mechanism for cancer cells. Beyond understanding the mechanisms underlying the quiescence, it provides an insightful perspective on cancer stem cells (CSCs) and their dual and intertwined functions based on their cell cycle state in response to treatment. Moreover, CSCs, epithelial-mesenchymal transformed cells, circulating tumor cells (CTCs), and disseminated tumor cells (DTCs), which are mostly in a quiescent state of the cell cycle are proved to have multiple biological links and can be implicated in our viewpoint of cell cycle heterogeneity in tumors. Overall, increasing our knowledge of cell cycle heterogeneity is a key to identifying new therapeutic solutions, and this emerging concept may provide us with new opportunities to prevent the dreadful cancer recurrence.

A Mathematical Model to Investigate the Effects of Ceralasertib and Olaparib in Targeting the Cellular DNA Damage Response Pathway

The ataxia-telangiectasia and Rad3-related (ATR) inhibitor ceralasertib and the poly (ADP-ribose) polymerase (PARP) inhibitor olaparib have shown synergistic activity, in vitro, in the FaDu ATM-knockout cell line. It was found that combining these drugs with lower doses and for shorter treatment periods induced greater or equal toxicity in cancer cells than using either as a single agent. Here, we developed a biologically motivated mathematical model governed by a set of ordinary differential equations, considering the cell cycle-specific interactions of olaparib and ceralasertib. By exploring a range of different possible drug mechanisms, we have studied the effects of their combination as well as which drug interactions are the most prominent. After careful model selection, the model was calibrated and compared with relevant experimental data. We have used this developed model further to investigate other doses of olaparib and ceralasertib in combination, which can be potentially helpful in exploring optimized dosage and delivery. SIGNIFICANCE STATEMENT: Drugs that target cellular DNA damage repair pathways are now being used as a new way to maximize the effect of multimodality treatments such as radiotherapy. Here, we develop a mathematical model to investigate the effects of ceralasertib and olaparib, two drugs that target DNA damage response pathways.

Predicting the Tumour Response to Radiation by Modelling the Five Rs of Radiotherapy Using PET Images

Despite the intensive use of radiotherapy in clinical practice, its effectiveness depends on several factors. Several studies showed that the tumour response to radiation differs from one patient to another. The non-uniform response of the tumour is mainly caused by multiple interactions between the tumour microenvironment and healthy cells. To understand these interactions, five major biologic concepts called the "5 Rs" have emerged. These concepts include reoxygenation, DNA damage repair, cell cycle redistribution, cellular radiosensitivity and cellular repopulation. In this study, we used a multi-scale model, which included the five Rs of radiotherapy, to predict the effects of radiation on tumour growth. In this model, the oxygen level was varied in both time and space. When radiotherapy was given, the sensitivity of cells depending on their location in the cell cycle was taken in account. This model also considered the repair of cells by giving a different probability of survival after radiation for tumour and normal cells. Here, we developed four fractionation protocol schemes. We used simulated and positron emission tomography (PET) imaging with the hypoxia tracer 18F-flortanidazole (18F-HX4) images as input data of our model. In addition, tumour control probability curves were simulated. The result showed the evolution of tumours and normal cells. The increase in the cell number after radiation was seen in both normal and malignant cells, which proves that repopulation was included in this model. The proposed model predicts the tumour response to radiation and forms the basis for a more patient-specific clinical tool where related biological data will be included.

Evaluation of entropy and fractal dimension as biomarkers for tumor growth and treatment response using cellular automata

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study cancer therapies' effects, which are often designed to disrupt single-cell dynamics. In this work, we propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which a time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination. At the same time, entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the prognostic value of the proposed biomarkers could vary considerably with time. Thus, it is essential to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells scattered along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Risk modeling of single-cell transcriptomes reveals the heterogeneity of immune infiltration in hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is one of the most common primary hepatic malignancies. E2F transcription factors play an important role in the tumorigenesis and progression of HCC, mainly through the RB/E2F pathway. Prognostic models for HCC based on gene signatures have been developed rapidly in recent years; however, their discriminating ability at the single-cell level remains elusive, which could reflect the underlying mechanisms driving the sample bifurcation. In this study, we constructed and validated a predictive model based on E2F expression, successfully stratifying patients with HCC into two groups with different survival risks. Then we used a single-cell dataset to test the discriminating ability of the predictive model on infiltrating T cells, demonstrating remarkable cellular heterogeneity as well as altered cell fates. We identified distinct cell subpopulations with diverse molecular characteristics. We also found that the distribution of cell subpopulations varied considerably across onset stages among patients, providing a fundamental basis for patient-oriented precision evaluation. Moreover, single-sample gene set enrichment analysis revealed that subsets of CD8⁺ T cells with significantly different cell adhesion levels could be associated with different patterns of tumor cell dissemination. Therefore, our findings linked the conventional prognostic gene signature to the immune microenvironment and cellular heterogeneity at the single-cell level, thus providing deeper insights into the understanding of HCC tumorigenesis.

Predicting and elucidating the post-printing behavior of 3D printed cancer cells in hydrogel structures by integrating in-vitro and in-silico experiments

A key feature distinguishing 3D bioprinting from other 3D cell culture techniques is its precise control over created structures. This property allows for the high-resolution fabrication of biomimetic structures with controlled structural and mechanical properties such as porosity, permeability, and stiffness. However, analyzing post-printing cellular dynamics and optimizing their functions within the 3D fabricated environment is only possible through trial and error and replicating several experiments. This issue motivated the development of a cellular automata model for the first time to simulate post-printing cell behaviour within the 3D bioprinted construct. To improve our model, we bioprinted a 3D construct using MDA-MB-231 cell-laden hydrogel and evaluated cellular functions, including viability and proliferation in 11 days. The results showed that our model successfully simulated the 3D bioprinted structure and captured in-vitro observations. We demonstrated that in-silico model could predict and elucidate post-printing biological functions for different initial cell numbers in bioink and different bioink formulations with gelatine and alginate, without replicating several costly and time-consuming in-vitro measurements. We believe such a computational framework will substantially impact 3D bioprinting's future application. We hope this study inspires researchers to further realize how an in-silico model might be utilized to advance in-vitro 3D bioprinting research.

Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell Populations

Evolutionary dynamics allows us to understand many changes happening in a broad variety of biological systems, ranging from individuals to complete ecosystems. It is also behind a number of remarkable organizational changes that happen during the natural history of cancers. These reflect tumour heterogeneity, which is present at all cellular levels, including the genome, proteome and phenome, shaping its development and interrelation with its environment. An intriguing observation in different cohorts of oncological patients is that tumours exhibit an increased proliferation as the disease progresses, while the timescales involved are apparently too short for the fixation of sufficient driver mutations to promote explosive growth. Here, we discuss how phenotypic plasticity, emerging from a single genotype, may play a key role and provide a ground for a continuous acceleration of the proliferation rate of clonal populations with time. We address this question by combining the analysis of real-time growth of non-small-cell lung carcinoma cells (N-H460) together with stochastic and deterministic mathematical models that capture proliferation trait heterogeneity in clonal populations to elucidate the contribution of phenotypic transitions on tumour growth dynamics.

Understanding the mechanisms of HPV-related carcinogenesis: Implications for cell cycle dynamics

The role of human papillomavirus (HPV) as a causative agent for epithelial cancers is well-known, but many open questions remain regarding the downstream gene regulatory effects of viral proteins E6 and E7 on the cell cycle. Here, we extend a cell cycle model originally presented by Gérard and Goldbeter (2009) in order to capture the effects of E6 and E7 on key actors in the cell cycle. Results suggest that E6 is sufficient to reverse p53-induced quiescence, while E7 is sufficient to reverse p16INK4a-induced quiescence; both E6 and E7 are necessary when p53 and p16INK4a are both active. Moreover, E7 appears to play a role as a "growth factor substitute", inducing cell division in the absence of growth factor. Low levels of E7 may permit regular cell division, but the results suggest that higher levels of E7 dysregulate the cell cycle in ways that may destabilize the cellular genome. The mechanisms explored here provide opportunities for developing new treatment targets that take advantage of the cell cycle regulatory system to prevent HPV-related cancer effects.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Classical mathematical models for prediction of response to chemotherapy and immunotherapy

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

Mathematical oncology uses quantitative models for prediction of tumor growth and treatment response. The theoretical foundation of mathematical oncology is provided by six classical mathematical models: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. These models have been introduced decades ago, have been used in thousands of scientific articles and are part of textbooks and curricula in mathematical oncology. However, these models have not been systematically tested in clinical data from actual patients. In this study, we have collected quantitative tumor volume measurements from thousands of patients in five large clinical trials of cancer immunotherapy. We use this dataset to systematically investigate how accurately mathematical models can describe tumor growth, showing that there are pronounced differences between models. In addition, we show that two of these models can predict tumor response to immunotherapy and chemotherapy at later time points when trained on early tumor growth dynamics. Thus, our article closes a conceptual gap in the literature and at the same time provides a simple tool to predict response to chemotherapy and immunotherapy on the level of individual patients.

A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy

Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models with continuous models using hybrid cellular automata (CA) is a powerful approach for mimicking biological complexity and describing the dynamical exchange of information across different scales. However, when clinically relevant cancer portions are taken into account, such models become computationally very expensive. While efficient parallelization techniques for continuous models exist, their coupling with discrete models, particularly CA, necessitates more elaborate solutions. Building upon FEniCS, a popular and powerful scientific computing platform for solving partial differential equations, we developed parallel algorithms to link stochastic CA with differential equations (https://bitbucket.org/HTasken/cansim). The algorithms minimize the communication between processes that share CA neighborhood values while also allowing for reproducibility during stochastic updates. We demonstrated the potential of our solution on a complex hybrid cellular automaton model of breast cancer treated with combination chemotherapy. On a single-core processor, we obtained nearly linear scaling with an increasing problem size, whereas weak parallel scaling showed moderate growth in solving time relative to increase in problem size. Finally, we applied the algorithm to a problem that is 500 times larger than previous work, allowing us to run personalized therapy simulations based on heterogeneous cell density and tumor perfusion conditions estimated from magnetic resonance imaging data on an unprecedented scale.

Effect of energy requirements in the growth of brain tumor: a theoretical approach

A malignant tumor is an uncontrolled growth of tissues receiving energy in form of the nutrients provided by the microvascular networks. It is proposed that the supplied energy to a tumor is used for three purposes: the creation of new cells, maintenance of tumor cells, and tumor volume expansion by overcoming external pressure. A mathematical model studying the effects of energy required for maintenance and overcoming external pressure, the energy required creating a single cell, death rate, and tumor cell density on tumor development has been formulated. Including a term, residual energy for tumor growth in the tumor growth equation, the well-known logistic equation has been re-derived for tumors. Analytical solutions have been developed, and numerical analysis for the growth in brain tumors with the variation of parameters related to energy supply, the energy required for maintenance, and expansion of tumor has been performed. Expressions for the tumor growth rate(r) and carrying capacity(C) of the tumor are formulated in terms of the parameters used in the model. The range of 'r', estimated using our model is found within the ranges of tumor growth rates in gliomas reported by the other researchers. Selecting the model parameters precisely for a particular individual, the tumor growth rate and carrying capacity could be estimated accurately. Our study indicates that the actual growth rate and carrying capacity of a tumor reduce and tumor saturation time increases with the increase of death rate, the energy required for a single cell division, and energy requirement for the tumor cell maintenance.

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.

HDAC Inhibitors: Dissecting Mechanisms of Action to Counter Tumor Heterogeneity

Intra-tumoral heterogeneity presents a major obstacle to cancer therapeutics, including conventional chemotherapy, immunotherapy, and targeted therapies. Stochastic events such as mutations, chromosomal aberrations, and epigenetic dysregulation, as well as micro-environmental selection pressures related to nutrient and oxygen availability, immune infiltration, and immunoediting processes can drive immense phenotypic variability in tumor cells. Here, we discuss how histone deacetylase inhibitors, a prominent class of epigenetic drugs, can be leveraged to counter tumor heterogeneity. We examine their effects on cellular processes that contribute to heterogeneity and provide insights on their mechanisms of action that could assist in the development of future therapeutic approaches.

A neuro evolutionary algorithm for patient calibrated prediction of survival in Glioblastoma patients

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is the most common and malignant type of primary brain tumors. Radiation therapy (RT) plus concomitant and adjuvant Temozolomide (TMZ) constitute standard treatment of GBM. Existing models for GBM growth do not consider the effect of different schedules on tumor growth and patient survival. However, clinical trials show that treatment schedule and drug dosage significantly affect patient survival. The goal is to provide a patient calibrated model for predicting survival according to the treatment schedule.

METHODS

We propose a top-down method based on artificial neural networks (ANN) and genetic algorithm (GA) to predict survival of GBM patients. A feed forward undercomplete Autoencoder network is integrated with the neuro-evolutionary (NE) algorithm in order to extract a compressed representation of input clinical data. The proposed NE algorithm uses GA to obtain optimal architecture of a multi-layer perceptron (MLP). Taguchi L₁₆ orthogonal design of experiments is used to tune parameters of the proposed NE algorithm. Finally, the optimal MLP is used to predict survival of GBM patients.

RESULTS

Data from 8 related clinical trials have been collected and integrated to train the model. From 847 evaluable cases, 719 were used for train and validation and the remaining 128 cases were used to test the model. Mean absolute error of the predictions on the test data is 0.087 months which shows excellent performance of the proposed model in predicting survival of the patients. Also, the results show that the proposed NE algorithm is superior to other existing models in both the mean and variability of the prediction error.

Modeling How Heterogeneity in Cell Cycle Length Affects Cancer Cell Growth Dynamics in Response to Treatment

Tumors are complex, dynamic, and adaptive biological systems characterized by high heterogeneity at genetic, epigenetic, phenotypic, as well as tissue microenvironmental level. In this work, utilizing cellular automata methods, we focus on intrinsic heterogeneity with respect to cell cycle duration and explore whether and to what extent this heterogeneity affects cancer cell growth dynamics when cytotoxic treatment is applied. We assume that treatment acts on cancer cells specifically during mitosis and compare it with a (cell cycle-non-specific) cytotoxic treatment that acts randomly regardless of the cell cycle phase. We simulate the spatiotemporal evolution of tumor cells with different initial spatial configurations and different cell length probability distributions. We observed that in heterogeneous populations, strong selection forces act on cancer cells favoring the faster cells, when the death rates are lower than the proliferation rates. However, at higher mitotic death rates, selection of the slower proliferative cells is favored, leading to slower post-treatment regrowth rates, as compared to untreated growth. Of note, random cell death progressively eliminates the slower proliferative cells, consistently, favoring highly proliferative phenotypes. Interestingly, compared to the monoclonal populations that exhibit complete response at high random death rates, emergent resistance arises naturally in heterogeneous populations during treatment. As divergent selection forces may act on a heterogeneous cancer cell population, we argue that treatment plan selection can considerably alter the post-treatment tumor dynamics, cell survival, and emergence of resistance, proving its significant biological and therapeutic impact.

Reinforcement learning for optimal scheduling of Glioblastoma treatment with Temozolomide

BACKGROUND

Glioblastoma multiforme (GBM) is the most frequent primary brain tumor in adults and Temozolomide (TMZ) is an effective chemotherapeutic agent for its treatment. In Silico models of GBM growth provide an appropriate foundation for analysis and comparison of different regimens. We propose a mathematical frame for patient specific design of optimal chemotherapy regimens for GBM patients.

METHODS

The proposed frame includes online interaction of a virtual GBM with an optimizing agent. Spatiotemporal dynamics of GBM growth and its response to TMZ are simulated with a three dimensional hybrid cellular automaton. Q learning is tailored to the virtual GBM for treatment optimization aimed at minimizing tumor size at the end of treatment course. Q learning consists of a learning agent that interacts with the virtual GBM. System state is affected by the agent decisions and the obtained rewards guide Q learning to the optimal schedule.

RESULTS

Computational results confirm that the optimal chemotherapy schedule depends on some patient specific parameters including body weight, tumor size and its position in the brain. Furthermore, the algorithm is used for scheduling 2100 mg of TMZ on a virtual GBM and the obtained schedule is to administer150 mg of TMZ every other day. The obtained schedule is compared to the standard 7/14 regimen and the results show that it is superior to the 7/14 regimen in minimizing tumor size.

CONCLUSION

The proposed frame is an appropriate decision support system for patient specific design of TMZ administration regimens on GBM patients. Also, since the obtained optimal schedule outperforms the standard 7/14 regimen, it is worthy of further clinical testing.

Combining hypoxia-activated prodrugs and radiotherapy in silico: Impact of treatment scheduling and the intra-tumoural oxygen landscape

Hypoxia-activated prodrugs (HAPs) present a conceptually elegant approach to not only overcome, but better yet, exploit intra-tumoural hypoxia. Despite being successful in vitro and in vivo, HAPs are yet to achieve successful results in clinical settings. It has been hypothesised that this lack of clinical success can, in part, be explained by the insufficiently stringent clinical screening selection of determining which tumours are suitable for HAP treatments. Taking a mathematical modelling approach, we investigate how tumour properties and HAP-radiation scheduling influence treatment outcomes in simulated tumours. The following key results are demonstrated in silico: (i) HAP and ionising radiation (IR) monotherapies may attack tumours in dissimilar, and complementary, ways. (ii) HAP-IR scheduling may impact treatment efficacy. (iii) HAPs may function as IR treatment intensifiers. (iv) The spatio-temporal intra-tumoural oxygen landscape may impact HAP efficacy. Our in silico framework is based on an on-lattice, hybrid, multiscale cellular automaton spanning three spatial dimensions. The mathematical model for tumour spheroid growth is parameterised by multicellular tumour spheroid (MCTS) data.

Collective invasion of glioma cells through OCT1 signalling and interaction with reactive astrocytes after surgery

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. miR-451 and its downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can play a significant role in tumour dynamics. In this work, we develop a multi-scale mathematical model of miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling and individual cell dynamics of the tumour and reactive astrocytes after surgery. We show how the effects of fluctuating glucose on tumour cells need to be reprogrammed by taking into account the recent history of glucose variations and an AMPK/miR-451 reciprocal feedback loop. The model shows how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line-specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making.

Executable cancer models: successes and challenges

Making decisions on how best to treat cancer patients requires the integration of different data sets, including genomic profiles, tumour histopathology, radiological images, proteomic analysis and more. This wealth of biological information calls for novel strategies to integrate such information in a meaningful, predictive and experimentally verifiable way. In this Perspective we explain how executable computational models meet this need. Such models provide a means for comprehensive data integration, can be experimentally validated, are readily interpreted both biologically and clinically, and have the potential to predict effective therapies for different cancer types and subtypes. We explain what executable models are and how they can be used to represent the dynamic biological behaviours inherent in cancer, and demonstrate how such models, when coupled with automated reasoning, facilitate our understanding of the mechanisms by which oncogenic signalling pathways regulate tumours. We explore how executable models have impacted the field of cancer research and argue that extending them to represent a tumour in a specific patient (that is, an avatar) will pave the way for improved personalized treatments and precision medicine. Finally, we highlight some of the ongoing challenges in developing executable models and stress that effective cross-disciplinary efforts are key to forward progress in the field.

Estimation of drug and tumor properties using novel hybrid meta-heuristic methods

One of the major drawbacks in mathematical modeling of the drug delivery in living species is application of a common value for a specific property such as diffusion coefficient of drug in tissue, while this property is unique for each person or species. Therefore, knowledge on the species-specific values of these properties can improve the process of drug delivery and treatment. Inverse problem methods can achieve these unique properties for each specimen. Estimation of the individual-specific drug and tumor parameters requires the evaluation of the drug concentration (the concentration of medical images) within the tumor tissue. Accordingly, in this paper, first, the drug transport equation in tumor is determined. Then, the sensitivity analysis is conducted to determine the appropriate area for selecting the drug concentration to estimate the drug and tumor parameters. Finally, the parameters estimated by meta-heuristic and hybrid meta-heuristic methods are compared. To enhance the validity of the methods, two different drug transport models are examined. The results indicate that the hybrid methods gave rise to more precise estimations, especially the hybrid particle swarm optimization (PSO) method with whale optimization algorithm (WOA) which offer more appropriate responses in the parameters estimation of two models.

Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to

The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735-1741, 1977; Norton in Can Res 48:7067-7071, 1988; Hahnfeldt et al. in Can Res 59:4770-4775, 1999; Anderson et al. in Comput Math Methods Med 2:129-154, 2000. https://doi.org/10.1080/10273660008833042 ; Michor et al. in Nature 435:1267-1270, 2005. https://doi.org/10.1038/nature03669 ; Anderson et al. in Cell 127:905-915, 2006. https://doi.org/10.1016/j.cell.2006.09.042 ; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800 ). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.

Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation

AIM

The negative impact of tumour hypoxia on cancer treatment outcome has been long-known, yet there has been little success combating it. This paper investigates the potential role of in silico modelling to help test emerging hypoxia-targeting treatments in cancer therapy.

METHODS

A Medline search was undertaken on the current landscape of in silico models that simulate cancer therapy and evaluate their ability to test hypoxia-targeting treatments. Techniques and treatments to combat tumour hypoxia and their current challenges are also presented.

RESULTS

Hypoxia-targeting treatments include tumour reoxygenation, hypoxic cell radiosensitization with nitroimidazoles, hypoxia-activated prodrugs and molecular targeting. Their main challenges are toxicity and not achieving adequate delivery to hypoxic regions of the tumour. There is promising research toward combining two or more of these techniques. Different types of in silico therapy models have been developed ranging from temporal to spatial and from stochastic to deterministic models. Numerous models have compared the effectiveness of different radiotherapy fractionation schedules for controlling hypoxic tumours. Similarly, models could help identify and optimize new treatments for overcoming hypoxia that utilize novel hypoxia-targeting technology.

CONCLUSION

Current therapy models should attempt to incorporate more sophisticated modelling of tumour angiogenesis/vasculature and vessel perfusion in order to become more useful for testing hypoxia-targeting treatments, which typically rely upon the tumour vasculature for delivery of additional oxygen, (pro)drugs and nanoparticles.

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer. To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner-a multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix-degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs such as MMP-2.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451–AMPK–mTOR–cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.

pH as a potential therapeutic target to improve temozolomide antitumor efficacy : A mechanistic modeling study

Despite intensive treatments including temozolomide (TMZ) administration, glioblastoma patient prognosis remains dismal and innovative therapeutic strategies are urgently needed. A systems pharmacology approach was undertaken to investigate TMZ pharmacokinetics-pharmacodynamics (PK-PD) incorporating the effect of local pH, tumor spatial configuration and micro-environment. A hybrid mathematical framework was designed coupling ordinary differential equations describing the intracellular reactions, with a spatial cellular automaton to individualize the cells. A differential drug impact on tumor and healthy cells at constant extracellular pH was computationally demonstrated as TMZ-induced DNA damage was larger in tumor cells as compared to normal cells due to less acidic intracellular pH in cancer cells. Optimality of TMZ efficacy defined as maximum difference between damage in tumor and healthy cells was reached for extracellular pH between 6.8 and 7.5. Next, TMZ PK-PD in a solid tumor was demonstrated to highly depend on its spatial configuration as spread cancer cells or fragmented tumors presented higher TMZ-induced damage as compared to compact tumor spheroid. Simulations highlighted that smaller tumors were less acidic than bigger ones allowing for faster TMZ activation and their closer distance to blood capillaries allowed for better drug penetration. For model parameters corresponding to U87 glioma cells, inter-cell variability in TMZ uptake play no role regarding the mean drug-induced damage in the whole cell population whereas this quantity was increased by inter-cell variability in TMZ efflux which was thus a disadvantage in terms of drug resistance. Overall, this study revealed pH as a new potential target to significantly improve TMZ antitumor efficacy.

The many faces of mathematical modelling in oncology

The application of modelling to solve problems in biology and medicine, and specifically in oncology and radiation therapy, is increasingly established and holds big promise. We provide an overview of the basic concepts of the field and its current state, along with new tools available and future directions for research. We will outline radiobiology models, examples of other anticancer therapy models, multiscale modelling, and we will discuss mechanistic and phenomenological approaches to modelling.

Integrating in vitro experiments with in silico approaches for Glioblastoma invasion: the role of cell-to-cell adhesion heterogeneity

Glioblastoma cells adopt migration strategies to invade into the brain parenchyma ranging from individual to collective mechanisms, whose role and dynamics are not yet fully understood. In this work, we explore Glioblastoma heterogeneity and recapitulate its invasive patterns both in vitro, by utilizing primary cells along with the U87MG cell line, and in silico, by adopting discrete, individual cell-based mathematics. Glioblastoma cells are cultured three-dimensionally in an ECM-like substrate. The primary Glioblastoma spheroids adopt a novel cohesive pattern, mimicking perivascular invasion in the brain, while the U87MG adopt a typical, starburst invasive pattern under the same experimental setup. Mathematically, we focus on the role of the intrinsic heterogeneity with respect to cell-to-cell adhesion. Our proposed mathematical approach mimics the invasive morphologies observed in vitro and predicts the dynamics of tumour expansion. The role of the proliferation and migration is also explored showing that their effect on tumour morphology is different per cell type. The proposed model suggests that allowing cell-to-cell adhesive heterogeneity within the tumour population is sufficient for variable invasive morphologies to emerge which remain originally undetectable by conventional imaging, indicating that exploration in pathological samples is needed to improve our understanding and reveal potential patient-specific therapeutic targets.

Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations indicate that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.

An agent-based model for drug-radiation interactions in the tumour microenvironment: Hypoxia-activated prodrug SN30000 in multicellular tumour spheroids

Multicellular tumour spheroids capture many characteristics of human tumour microenvironments, including hypoxia, and represent an experimentally tractable in vitro model for studying interactions between radiotherapy and anticancer drugs. However, interpreting spheroid data is challenging because of limited ability to observe cell fate within spheroids dynamically. To overcome this limitation, we have developed a hybrid continuum/agent-based model (ABM) for HCT116 tumour spheroids, parameterised using experimental models (monolayers and multilayers) in which reaction and diffusion can be measured directly. In the ABM, cell fate is simulated as a function of local oxygen, glucose and drug concentrations, determined by solving diffusion equations and intracellular reactions. The model is lattice-based, with cells occupying discrete locations on a 3D grid embedded within a coarser grid that encompasses the culture medium; separate solvers are employed for each grid. The generated concentration fields account for depletion in the medium and specify concentration-time profiles within the spheroid. Cell growth and survival are determined by intracellular oxygen and glucose concentrations, the latter based on direct measurement of glucose diffusion/reaction (in multilayers) for the first time. The ABM reproduces known features of spheroids including overall growth rate, its oxygen and glucose dependence, peripheral cell proliferation, central hypoxia and necrosis. We extended the ABM to describe in detail the hypoxia-dependent interaction between ionising radiation and a hypoxia-activated prodrug (SN30000), again using experimentally determined parameters; the model accurately simulated clonogenic cell killing in spheroids, while inclusion of reversible cell cycle delay was required to account for the marked spheroid growth delay after combined radiation and SN30000. This ABM of spheroid growth and response exemplifies the utility of integrating computational and experimental tools for investigating radiation/drug interactions, and highlights the critical importance of understanding oxygen, glucose and drug concentration gradients in interpreting activity of therapeutic agents in spheroid models.

Studies in 3D cultures, notably multicellular tumour spheroids that mimic many features of solid tumours, have great potential for speeding up anticancer drug development. However the increased complexity of 3D cultures makes interpretation of experiments more difficult. We have developed a hybrid continuum/agent-based mathematical model, validated by experiments, to aid interpretation of spheroid experiments in developing drugs designed to eliminate radiation-resistant hypoxic cells. This model includes key features of the tumour microenvironment including oxygen and glucose transport and regions of hypoxia where the cells are resistant to radiation, but sensitive to hypoxia-activated prodrugs such as SN30000. This enables us to predict the growth and cell response in untreated spheroids and compare the results to spheroids treated with radiation and SN30000. We demonstrate good prediction of cellular responses in spheroids treated with radiation and SN30000 and good agreement with spheroid regrowth after treatment when additional effects of cellular growth delay are added. This demonstrates that the modelling approach has potential to improve interpretation of experimental investigations of drug and radiation combinations.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

The invasion speed of cell migration models with realistic cell cycle time distributions

Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells' average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.

Anti-angiogenic drug scheduling optimisation with application to colorectal cancer

Bevacizumab (bvz) is a first choice anti-angiogenic drug in oncology and is primarily administered in combination with chemotherapy. It has been hypothesized that anti-angiogenic drugs enhance efficacy of cytotoxic drugs by "normalizing" abnormal tumor vessels and improving drug penetration. Nevertheless, the clinical relevance of this phenomenon is still unclear with several studies over recent years suggesting an opposing relationship. Herein, we sought to develop a new computational tool to interrogate anti-angiogenic drug scheduling with particular application in the setting of colorectal cancer (CRC). Specifically, we have employed a mathematical model of vascular tumour growth which interrogates the impact of anti-angiogenic treatment and chemotherapeutic treatment on tumour volume. Model predictions were validated using CRC xenografts which underwent treatment with a clinically relevant combinatorial anti-angiogenic regimen. Bayesian model selection revealed the most appropriate term for capturing the effect of treatments on the tumour size, and provided insights into a switch-like dependence of FOLFOX delivery on the tumour vasculature. Our experimental data and mathematical model suggest that delivering chemotherapy prior to bvz may be optimal in the colorectal cancer setting.

Modelling the effects of bacterial cell state and spatial location on tuberculosis treatment: Insights from a hybrid multiscale cellular automaton model

If improvements are to be made in tuberculosis (TB) treatment, an increased understanding of disease in the lung is needed. Studies have shown that bacteria in a less metabolically active state, associated with the presence of lipid bodies, are less susceptible to antibiotics, and recent results have highlighted the disparity in concentration of different compounds into lesions. Treatment success therefore depends critically on the responses of the individual bacteria that constitute the infection. We propose a hybrid, individual-based approach that analyses spatio-temporal dynamics at the cellular level, linking the behaviour of individual bacteria and host cells with the macroscopic behaviour of the microenvironment. The individual elements (bacteria, macrophages and T cells) are modelled using cellular automaton (CA) rules, and the evolution of oxygen, drugs and chemokine dynamics are incorporated in order to study the effects of the microenvironment in the pathological lesion. We allow bacteria to switch states depending on oxygen concentration, which affects how they respond to treatment. This is the first multiscale model of its type to consider both oxygen-driven phenotypic switching of the Mycobacterium tuberculosis and antibiotic treatment. Using this model, we investigate the role of bacterial cell state and of initial bacterial location on treatment outcome. We demonstrate that when bacteria are located further away from blood vessels, less favourable outcomes are more likely, i.e. longer time before infection is contained/cleared, treatment failure or later relapse. We also show that in cases where bacteria remain at the end of simulations, the organisms tend to be slower-growing and are often located within granulomas, surrounded by caseous material.

The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

Genome-wide transcriptional analysis of BRD4-regulated genes and pathways in human glioma U251 cells

Bromodomain containing 4 (BRD4), a member of the bromodomain and extra-terminal family, has become a promising drug target for numerous types of cancer. BRD4 has been reported to be deregulated in gliomas; however, the precise molecular pathways regulated by BRD4 remained elusive. In the present study, BRD4 expression was silenced in the glioma cell line U251 and the results demonstrated that BRD4 knockdown attenuated cell proliferation and promoted cell apoptosis. A genome-wide analysis of BRD4-regulated transcripts in U251 cells was performed using microarray to reveal the possible molecular mechanism. A total of 3,529 differentially expressed genes were identified; 1,648 of these genes were upregulated and 1,881 were downregulated. The results of the gene ontology analysis revealed that these genes were mainly involved in membrane organization, mitotic cell cycle, cell division and DNA replication. Pathway analysis revealed that the pathways altered following BRD4 knockdown included multiple cellular processes, such as cell cycle and apoptosis. Candidate genes were identified through global signal transduction network analysis and were validated using reverse transcription-quantitative polymerase chain reaction and western blot analyses. The results demonstrated that BRD4 knockdown decreased the expression of KRAS proto-oncogene GTPase (KRAS). Downregulated KRAS expression in U251 cells restrained cell proliferation and promoted cell apoptosis, suggesting that the effect of BRD4 on glioma cells might occur through the Ras pathway. In conclusion, the present results confirmed the role of BRD4 in glioma and provided information for further exploration of the molecular mechanism of BRD4 in glioma development and progression.

Agent-Based Modeling of Cancer Stem Cell Driven Solid Tumor Growth

Computational modeling of tumor growth has become an invaluable tool to simulate complex cell-cell interactions and emerging population-level dynamics. Agent-based models are commonly used to describe the behavior and interaction of individual cells in different environments. Behavioral rules can be informed and calibrated by in vitro assays, and emerging population-level dynamics may be validated with both in vitro and in vivo experiments. Here, we describe the design and implementation of a lattice-based agent-based model of cancer stem cell driven tumor growth.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

Blood vessel tortuosity selects against evolution of aggressive tumor cells in confined tissue environments: A modeling approach

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype of each cell determines its success. Selection in this process is imposed by both the microenvironment (neighboring cells, extracellular matrix, and diffusing substances), and the whole of the organism through for example the blood supply. In this view, the development of tumor cells is in close interaction with their increasingly changing environment: the more cells can change, the more their environment will change. Furthermore, instabilities are also introduced on the organism level: blood supply can be blocked by increased tissue pressure or the tortuosity of the tumor-neovascular vessels. This coupling between cell, microenvironment, and organism results in behavior that is hard to predict. Here we introduce a cell-based computational model to study the effect of blood flow obstruction on the micro-evolution of cells within a cancerous tissue. We demonstrate that stages of tumor development emerge naturally, without the need for sequential mutation of specific genes. Secondly, we show that instabilities in blood supply can impact the overall development of tumors and lead to the extinction of the dominant aggressive phenotype, showing a clear distinction between the fitness at the cell level and survival of the population. This provides new insights into potential side effects of recent tumor vasculature normalization approaches.

Significance of Inactivated Genes in Leukemia: Pathogenesis and Prognosis

Epigenetic and genetic alterations are two mechanisms participating in leukemia, which can inactivate genes involved in leukemia pathogenesis or progression. The purpose of this review was to introduce various inactivated genes and evaluate their possible role in leukemia pathogenesis and prognosis. By searching the mesh words "Gene, Silencing AND Leukemia" in PubMed website, relevant English articles dealt with human subjects as of 2000 were included in this study. Gene inactivation in leukemia is largely mediated by promoter's hypermethylation of gene involving in cellular functions such as cell cycle, apoptosis, and gene transcription. Inactivated genes, such as ASPP1, TP53, IKZF1 and P15, may correlate with poor prognosis in acute lymphoid leukemia (ALL), chronic lymphoid leukemia (CLL), chronic myelogenous leukemia (CML) and acute myeloid leukemia (AML), respectively. Gene inactivation may play a considerable role in leukemia pathogenesis and prognosis, which can be considered as complementary diagnostic tests to differentiate different leukemia types, determine leukemia prognosis, and also detect response to therapy. In general, this review showed some genes inactivated only in leukemia (with differences between B-ALL, T-ALL, CLL, AML and CML). These differences could be of interest as an additional tool to better categorize leukemia types. Furthermore; based on inactivated genes, a diverse classification of Leukemias could represent a powerful method to address a targeted therapy of the patients, in order to minimize side effects of conventional therapies and to enhance new drug strategies.

The role of myosin II in glioma invasion: A mathematical model

Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.