Spatial Metrics of Tumour Vascular Organisation Predict Radiation Efficacy in a Computational Model. PLoS Comput Biol. 2016;12:e1004712. [PMID: 26800503 PMCID: PMC4723304 DOI: 10.1371/journal.pcbi.1004712]

Predicting Individual Tumor Response Dynamics in Locally Advanced Non-Small Cell Lung Cancer Radiation Therapy: A Mathematical Modelling Study

PURPOSE

To predict individual tumor responses to radiation therapy (RT) in non-small cell lung cancer.

MATERIALS AND METHODS

The proliferation saturation index (PSI) model, which models tumor dynamics in response to RT as an instantaneous reduction in tumor volume, was fit to n = 162 patients with 4 distinct dose fractionation schedules (30-32 fractions × 2 Gy, 23-24 fractions × 2.75 Gy, 32-42 fractions × 1.8 Gy, and 30 fractions × 1.5 Gy Bidaily, followed by 5-12 fractions × 2 Gy daily). Following initial training, the predictive power of the model was tested using only the first 3 tumor volume measurements as measured on daily imaging. The remainder of tumor volume regression during RT was simulated using the PSI model. Comparisons of the measured to the simulated volumes were made using scatter plots, coefficient of determination (R2), and Pearson correlation coefficient values.

RESULTS

The PSI model predicted tumor volume regression during RT with a high degree of accuracy. Comparison of the measured versus predicted volumes resulted in R2 values of 0.968, 0.954, 0.968, and 0.937, and Pearson correlation coefficient values of 0.984, 0.977, 0.984, and 0.968 in the 2 Gy, 1.8 Gy, 2.75 Gy, and Bidaily groups, respectively.

CONCLUSION

The proliferation saturation model can predict, with a high degree of accuracy, non-small cell lung cancer tumor volume regression in response to RT in 4 distinct dose fractionation schedules.

Cell-cell fusion in cancer: The next cancer hallmark?

In this review, we consider the role of cell-cell fusion in cancer development and progression through an evolutionary lens. We begin by summarizing the origins of fusion proteins (fusogens), of which there are many distinct classes that have evolved through convergent evolution. We then use an evolutionary framework to highlight how the persistence of fusion over generations and across different organisms can be attributed to traits that increase fitness secondary to fusion; these traits map well to the expanded hallmarks of cancer. By studying the tumor microenvironment, we can begin to identify the key selective pressures that may favor higher rates of fusion compared to healthy tissues. The paper concludes by discussing the increasing number of research questions surrounding fusion, recommendations for how to answer them, and the need for a greater interest in exploring cell fusion and evolutionary principles in oncology moving forward.

Modeling hypoxia-induced radiation resistance and the impact of radiation sources

Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30×2GyRBE). Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success. On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT. Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N * 2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy.

Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis

Drug resistance is a prominent impediment to the efficacy of targeted therapies across various cancer types, including glioblastoma (GBM). However, comprehending the intricate intracellular and extracellular mechanisms underlying drug resistance remains elusive. Empirical investigations have elucidated that genetic aberrations, such as gene mutations, along with microenvironmental adaptation, notably angiogenesis, act as pivotal drivers of tumor progression and drug resistance. Nonetheless, mathematical models frequently compartmentalize these factors in isolation. In this study, we present a multiscale agent-based model of GBM, encompassing cellular dynamics, intricate signaling pathways, gene mutations, angiogenesis, and therapeutic interventions. This integrative framework facilitates an exploration of the interplay between genetic mutations and the vascular microenvironment in shaping the dynamic evolution of tumors during treatment with tyrosine kinase inhibitor. Our simulations unveil that mutations influencing the migration and proliferation of tumor cells expedite the emergence of phenotype heterogeneity, thereby exacerbating tumor invasion under both treated and untreated conditions. Moreover, angiogenesis proximate to the tumor fosters a protumoral milieu, augmenting mutation-induced drug resistance by increasing the survival rate of tumor cells. Collectively, our findings underscore the dual roles of intrinsic genetic mutations and extrinsic microenvironmental adaptations in steering tumor growth and drug resistance. Finally, we substantiate our model predictions concerning the impact of gene mutations and angiogenesis on the responsiveness of targeted therapies by integrating single-cell RNA-seq, spatial transcriptomics, bulk RNA-seq, and clinical data from GBM patients. The multidimensional approach enhances our understanding of the complexities governing drug resistance in glioma and offers insights into potential therapeutic strategies.

HtrA3: a promising prognostic biomarker and therapeutic target for head and neck squamous cell carcinoma

Objective

The dysregulation of the human high-temperature requirement A (HtrA) family of serine proteases is associated with many malignancies. However, there are few reports on HtrAs in head and neck squamous cell carcinoma (HNSCC). The aim of this study was to investigate the expression, prognostic value, and biological functions of HtrAs in HNSCC.

Methods

The RNA-sequencing data and clinical data of HNSCC were downloaded from The Cancer Genome Atlas (TCGA) database. The GSE30784 and GSE31056 datasets from the Gene Expression Omnibus (GEO) database were used for further verification. This study explored the differential expression of HtrAs and assessed their potential impact on the prognosis of HNSCC patients using a survival module. Correlations between clinical characteristics and HtrA expression levels were then explored using a Wilcoxon rank sum test. A Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG), and Gene Set Enrichment Analysis (GSEA) were performed using "clusterProfile" in the R software. A Pearson/Spearman correlation test was applied to analyze the relationship between HtrAs and immune infiltration level/checkpoint genes. Validation of HtrA expression levels were carried out by RT-PCR and western blot in human squamous carcinoma cell lines (Fadu and Cal-27) and human non-tumorigenic bronchial epithelium cells (BEAS-2B). Finally, through cell transfection, CCK-8, Ki-67 immunofluorescence, and flow cytometry assays, the effect of HtrA3 knockdown on the malignant biological behavior of HNSCC cells was explored.

Results

The gene expression levels of HtrAs were significantly upregulated and associated with patient age, TNM stage, clinical stage, and TP53 mutation status in the TCGA-HNSCC cohort. High expressions of HtrA1/3 were associated with shorter overall survival, shorter progress-free interval, and lower disease-specific survival in HNSCC. A nomogram for HtrAs was constructed and validated. HtrA-related genes were significantly enriched in the immune response and cell apoptosis pathway. In addition, the expression of HtrAs showed significant correlations with B cells, M cells, DC cell infiltration, and immune infiltration checkpoint (CD276, TNFRSF14). Validation of HtrA expression was carried out by RT-PCR and western blot. Results of in vitro experiments indicated that HtrA3 gene knockdown inhibits the proliferation of FaDu and Cal-27 cells while concurrently promoting apoptosis.

Conclusions

HtrA3 shows significant potential as both a prognostic marker and a promising therapeutic target for HNSCC, highlighting its relevance and importance in future research and potential clinical applications.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N*2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more accurately reflect the selection fo drug resistant genotypes. Furthermore, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Radio-immune response modelling for spatially fractionated radiotherapy

Objective.Radiation-induced cell death is a complex process influenced by physical, chemical and biological phenomena. Although consensus on the nature and the mechanism of the bystander effect were not yet made, the immune process presumably plays an important role in many aspects of the radiotherapy including the bystander effect. A mathematical model of immune response during and after radiation therapy is presented.Approach.Immune response of host body and immune suppression of tumor cells are modelled with four compartments in this study; viable tumor cells, T cell lymphocytes, immune triggering cells, and doomed cells. The growth of tumor was analyzed in two distinctive modes of tumor status (immune limited and immune escape) and its bifurcation condition.Main results.Tumors in the immune limited mode can grow only up to a finite size, named as terminal tumor volume analytically calculated from the model. The dynamics of the tumor growth in the immune escape mode is much more complex than the tumors in the immune limited mode especially when the status of tumor is close to the bifurcation condition. Radiation can kill tumor cells not only by radiation damage but also by boosting immune reaction.Significance.The model demonstrated that the highly heterogeneous dose distribution in spatially fractionated radiotherapy (SFRT) can make a drastic difference in tumor cell killing compared to the homogeneous dose distribution. SFRT cannot only enhance but also moderate the cell killing depending on the immune response triggered by many factors such as dose prescription parameters, tumor volume at the time of treatment and tumor characteristics. The model was applied to the lifted data of 67NR tumors on mice and a sarcoma patient treated multiple times over 1200 days for the treatment of tumor recurrence as a demonstration.

Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions

We introduce a new spatial statistic, the weighted pair correlation function (wPCF). The wPCF extends the existing pair correlation function (PCF) and cross-PCF to describe spatial relationships between points marked with combinations of discrete and continuous labels. We validate its use through application to a new agent-based model (ABM) which simulates interactions between macrophages and tumour cells. These interactions are influenced by the spatial positions of the cells and by macrophage phenotype, a continuous variable that ranges from anti-tumour to pro-tumour. By varying model parameters that regulate macrophage phenotype, we show that the ABM exhibits behaviours which resemble the 'three Es of cancer immunoediting': Equilibrium, Escape, and Elimination. We use the wPCF to analyse synthetic images generated by the ABM. We show that the wPCF generates a 'human readable' statistical summary of where macrophages with different phenotypes are located relative to both blood vessels and tumour cells. We also define a distinct 'PCF signature' that characterises each of the three Es of immunoediting, by combining wPCF measurements with the cross-PCF describing interactions between vessels and tumour cells. By applying dimension reduction techniques to this signature, we identify its key features and train a support vector machine classifier to distinguish between simulation outputs based on their PCF signature. This proof-of-concept study shows how multiple spatial statistics can be combined to analyse the complex spatial features that the ABM generates, and to partition them into interpretable groups. The intricate spatial features produced by the ABM are similar to those generated by state-of-the-art multiplex imaging techniques which distinguish the spatial distribution and intensity of multiple biomarkers in biological tissue regions. Applying methods such as the wPCF to multiplex imaging data would exploit the continuous variation in biomarker intensities and generate more detailed characterisation of the spatial and phenotypic heterogeneity in tissue samples.

A simulation of parental and glycolytic tumor phenotype competition predicts observed responses to pH changes and increased glycolysis after anti-VEGF therapy

Clinical cancers are typically spatially and temporally heterogeneous, containing multiple microenvironmental habitats and diverse phenotypes and/or genotypes, which can interact through resource competition and direct or indirect interference. A common intratumoral evolutionary pathway, probably initiated as adaptation to hypoxia, leads to the "Warburg phenotype" which maintains high glycolytic rates and acid production, even in normoxic conditions. Since individual cancer cells are the unit of Darwinian selection, intraspecific competition dominates intratumoral evolution. Thus, elements of the Warburg phenotype become key "strategies" in competition with cancer cell populations that retain the metabolism of the parental normal cells. Here we model the complex interactions of cell populations with Warburg and parental phenotypes as they compete for access to vasculature, while subject to direct interference by Warburg-related acidosis. In this competitive environment, vasculature delivers nutrients, removes acid and necrotic detritus, and responds to signaling molecules (VEGF and TNF-α). The model is built in a nested fashion and growth parameters are derived from monolayer, spheroid, and xenograft experiments on prostate cancer. The resulting model of in vivo tumor growth reaches a steady state, displaying linear growth and coexistence of both glycolytic and parental phenotypes consistent with experimental observations. The model predicts that increasing tumor pH sufficiently early can arrest the development of the glycolytic phenotype, while decreasing tumor pH accelerates this evolution and increases VEGF production. The model's predicted dual effects of VEGF blockers in decreasing tumor growth while increasing the glycolytic fraction of tumor cells has potential implications for optimizing angiogenic inhibitors.

Translation of Precision Medicine Research Into Biomarker-Informed Care in Radiation Oncology

The reach of personalized medicine in radiation oncology has expanded greatly over the past few decades as technical precision has improved the delivery of radiation to each patient's unique anatomy. Yet, the consideration of biological heterogeneity between patients has largely not been translated to clinical care. There are innumerable promising advancements in the discovery and validation of biomarkers, which could be used to alter radiation therapy directly or indirectly. Directly, biomarker-informed care may alter treatment dose or identify patients who would benefit most from radiation therapy and who could safely avoid more aggressive care. Indirectly, a variety of biomarkers could assist with choosing the best radiosensitizing chemotherapies. The translation of these advancements into clinical practice will bring radiation oncology even further into the era of precision medicine, treating patients according to their unique anatomical and biological differences.

Theoretical modeling of collaterally sensitive drug cycles: shaping heterogeneity to allow adaptive therapy

In previous work, we focused on the optimal therapeutic strategy with a pair of drugs which are collaterally sensitive to each other, that is, a situation in which evolution of resistance to one drug induces sensitivity to the other, and vice versa. Yoona (Bull Math Biol 8:1-34,Yoon et al. 2018) Here, we have extended this exploration to the optimal strategy with a collaterally sensitive drug sequence of an arbitrary length, N. To explore this, we have developed a dynamical model of sequential drug therapies with N drugs. In this model, tumor cells are classified as one of N subpopulations represented as [Formula: see text]. Each subpopulation, [Formula: see text], is resistant to '[Formula: see text]' and each subpopulation, [Formula: see text] (or [Formula: see text], if [Formula: see text]), is sensitive to it, so that [Formula: see text] increases under '[Formula: see text]' as it is resistant to it, and after drug-switching, decreases under '[Formula: see text]' as it is sensitive to that drug(s). Similar to our previous work examining optimal therapy with two drugs, we found that there is an initial period of time in which the tumor is 'shaped' into a specific makeup of each subpopulation, at which time all the drugs are equally effective ([Formula: see text]). After this shaping period, all the drugs are quickly switched with duration relative to their efficacy in order to maintain each subpopulation, consistent with the ideas underlying adaptive therapy. West(Canver Res 80(7):578-589Gatenby et al. 2009) and Gatenby (Cancer Res 67(11):4894-4903West et al. 2020). Additionally, we have developed methodologies to administer the optimal regimen under clinical or experimental situations in which no drug parameters and limited information of trackable populations data (all the subpopulations or only total population) are known. The therapy simulation based on these methodologies showed consistency with the theoretical effect of optimal therapy .

Revisiting a Null Hypothesis: Exploring the Parameters of Oligometastasis Treatment

PURPOSE

In the treatment of patients with metastatic cancer, the current paradigm states that metastasis-directed therapy does not prolong life. This paradigm forms the basis of clinical trial null hypotheses, where trials are built to test the null hypothesis that patients garner no overall survival benefit from targeting metastatic lesions. However, with advancing imaging technology and increasingly precise techniques for targeting lesions, a much larger proportion of metastatic disease can be treated. As a result, the life-extending benefit of targeting metastatic disease is becoming increasingly clear.

METHODS AND MATERIALS

In this work, we suggest shifting this qualitative null hypothesis and describe a mathematical model that can be used to frame a new, quantitative null. We begin with a very simple formulation of tumor growth, an exponential function, and illustrate how the same intervention (removing a given number of cells from the tumor) at different times affects survival. Additionally, we postulate where recent clinical trials fit into this parameter space and discuss the implications of clinical trial design in changing these quantitative parameters.

RESULTS

Our model shows that although any amount of cell kill will extend survival, in many cases the extent is so small as to be unnoticeable in a clinical context or is outweighed by factors related to toxicity and treatment time.

CONCLUSIONS

Recasting the null in these quantitative terms will allow trialists to design trials specifically to increase understanding of the circumstances (patient selection, disease burden, tumor growth kinetics) that can lead to improved overall survival when targeting metastatic lesions, rather than whether targeting metastases extends survival for patients with (oligo-) metastatic disease.

Personalizing Radiotherapy Prescription Dose Using Genomic Markers of Radiosensitivity and Normal Tissue Toxicity in NSCLC

INTRODUCTION

Cancer sequencing efforts have revealed that cancer is the most complex and heterogeneous disease that affects humans. However, radiation therapy (RT), one of the most common cancer treatments, is prescribed on the basis of an empirical one-size-fits-all approach. We propose that the field of radiation oncology is operating under an outdated null hypothesis: that all patients are biologically similar and should uniformly respond to the same dose of radiation.

METHODS

We have previously developed the genomic-adjusted radiation dose, a method that accounts for biological heterogeneity and can be used to predict optimal RT dose for an individual patient. In this article, we use genomic-adjusted radiation dose to characterize the biological imprecision of one-size-fits-all RT dosing schemes that result in both over- and under-dosing for most patients treated with RT. To elucidate this inefficiency, and therefore the opportunity for improvement using a personalized dosing scheme, we develop a patient-specific competing hazards style mathematical model combining the canonical equations for tumor control probability and normal tissue complication probability. This model simultaneously optimizes tumor control and toxicity by personalizing RT dose using patient-specific genomics.

RESULTS

Using data from two prospectively collected cohorts of patients with NSCLC, we validate the competing hazards model by revealing that it predicts the results of RTOG 0617. We report how the failure of RTOG 0617 can be explained by the biological imprecision of empirical uniform dose escalation which results in 80% of patients being overexposed to normal tissue toxicity without potential tumor control benefit.

CONCLUSIONS

Our data reveal a tapestry of radiosensitivity heterogeneity, provide a biological framework that explains the failure of empirical RT dose escalation, and quantify the opportunity to improve clinical outcomes in lung cancer by incorporating genomics into RT.

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].

Evidence for hypoxia increasing the tempo of evolution in glioblastoma

BACKGROUND

Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear.

METHODS

We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity.

RESULTS

Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results.

CONCLUSIONS

Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.

Abnormal morphology biases hematocrit distribution in tumor vasculature and contributes to heterogeneity in tissue oxygenation

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal tumor vascular structure. We investigate the role that anomalies in red blood cell transport plays in establishing oxygen heterogeneity in tumor tissue. We introduce a metric to characterize tumor vasculature (mean vessel length-to-diameter ratio, λ) and demonstrate how it predicts tissue-oxygen heterogeneity. We also report an increase in λ following treatment with the antiangiogenic agent DC101. Together, we propose λ as an effective way of monitoring the action of antiangiogenic agents and a proxy measure of oxygen heterogeneity in tumor tissue. Unraveling the causal relationship between tumor vascular structure and tissue oxygenation will pave the way for new personalized therapeutic approaches.

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal vascular structure of the tumor, but the precise mechanisms linking abnormal structure and compromised oxygen transport are only partially understood. In this paper, we investigate the role that red blood cell (RBC) transport plays in establishing oxygen heterogeneity in tumor tissue. We focus on heterogeneity driven by network effects, which are challenging to observe experimentally due to the reduced fields of view typically considered. Motivated by our findings of abnormal vascular patterns linked to deviations from current RBC transport theory, we calculated average vessel lengths L¯ and diameters d¯ from tumor allografts of three cancer cell lines and observed a substantial reduction in the ratio λ=L¯/d¯ compared to physiological conditions. Mathematical modeling reveals that small values of the ratio λ (i.e., λ<6) can bias hematocrit distribution in tumor vascular networks and drive heterogeneous oxygenation of tumor tissue. Finally, we show an increase in the value of λ in tumor vascular networks following treatment with the antiangiogenic cancer agent DC101. Based on our findings, we propose λ as an effective way of monitoring the efficacy of antiangiogenic agents and as a proxy measure of perfusion and oxygenation in tumor tissue undergoing antiangiogenic treatment.

Toward Engineering Biosystems With Emergent Collective Functions

Many complex behaviors in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans many length-scales. Here, we present a perspective on how some of these challenges could be overcome by using multi-agent modeling as a design framework within synthetic biology. Using case studies covering the construction of synthetic ecologies to biological computation and synthetic cellularity, we show how multi-agent modeling can capture the core features of complex multi-scale systems and provide novel insights into the underlying mechanisms which guide emergent functionalities across scales. The ability to unravel design rules underpinning these behaviors offers a means to take synthetic biology beyond single molecules or cells and toward the creation of systems with functions that can only emerge from collectives at multiple scales.

Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma

Microvascular proliferation in glioblastoma multiforme is a biological key mechanism to facilitate tumor growth and infiltration and a main target for treatment interventions. The vascular architecture can be obtained by Single Plane Illumination Microscopy (SPIM) to evaluate vascular heterogeneity in tumorous tissue. We make use of the Gibbs point field model to quantify the order of regularity in capillary distributions found in the U87 glioblastoma model in a murine model and to compare tumorous and healthy brain tissue. A single model parameter Γ was assigned that is linked to tissue-specific vascular topology through Monte-Carlo simulations. Distributions of the model parameter Γ differ significantly between glioblastoma tissue with mean 〈Γ_G〉=2.1±0.4, as compared to healthy brain tissue with mean 〈Γ_H〉=4.9±0.4, suggesting that the average Γ-value allows for tissue differentiation. These results may be used for diagnostic magnetic resonance imaging, where it has been shown recently that Γ is linked to tissue-inherent relaxation parameters.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

Illuminating the Numbers: Integrating Mathematical Models to Optimize Photomedicine Dosimetry and Combination Therapies

Cancer photomedicine offers unique mechanisms for inducing local tumor damage with the potential to stimulate local and systemic anti-tumor immunity. Optically-active nanomedicine offers these features as well as spatiotemporal control of tumor-focused drug release to realize synergistic combination therapies. Achieving quantitative dosimetry is a major challenge, and dosimetry is fundamental to photomedicine for personalizing and tailoring therapeutic regimens to specific patients and anatomical locations. The challenge of dosimetry is perhaps greater for photomedicine than many standard therapies given the complexity of light delivery and light-tissue interactions as well as the resulting photochemistry responsible for tumor damage and drug-release, in addition to the usual intricacies of therapeutic agent delivery. An emerging multidisciplinary approach in oncology utilizes mathematical and computational models to iteratively and quantitively analyze complex dosimetry, and biological response parameters. These models are parameterized by preclinical and clinical observations and then tested against previously unseen data. Such calibrated and validated models can be deployed to simulate treatment doses, protocols, and combinations that have not yet been experimentally or clinically evaluated and can provide testable optimal treatment outcomes in a practical workflow. Here, we foresee the utility of these computational approaches to guide adaptive therapy, and how mathematical models might be further developed and integrated as a novel methodology to guide precision photomedicine.

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.

Modeling triple-negative breast cancer heterogeneity: Effects of stromal macrophages, fibroblasts and tumor vasculature

A hallmark of breast tumors is its spatial heterogeneity that includes its distribution of cancer stem cells and progenitor cells, but also heterogeneity in the tumor microenvironment. In this study we focus on the contributions of stromal cells, specifically macrophages, fibroblasts, and endothelial cells on tumor progression. We develop a computational model of triple-negative breast cancer based on our previous work and expand it to include macrophage infiltration, fibroblasts, and angiogenesis. In vitro studies have shown that the secretomes of tumor-educated macrophages and fibroblasts increase both the migration and proliferation rates of triple-negative breast cancer cells. In vivo studies also demonstrated that blocking signaling of selected secreted factors inhibits tumor growth and metastasis in mouse xenograft models. We investigate the influences of increased migration and proliferation rates on tumor growth, the effect of the presence on fibroblasts or macrophages on growth and morphology, and the contributions of macrophage infiltration on tumor growth. We find that while the presence of macrophages increases overall tumor growth, the increase in macrophage infiltration does not substantially increase tumor growth and can even stifle tumor growth at excessive rates.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Multiscale Modeling of Inflammation-Induced Tumorigenesis Reveals Competing Oncogenic and Oncoprotective Roles for Inflammation

Chronic inflammation is a serious risk factor for cancer; however, the routes from inflammation to cancer are poorly understood. On the basis of the processes implicated by frequently mutated genes associated with inflammation and cancer in three organs (stomach, colon, and liver) extracted from the Gene Expression Omnibus, The Cancer Genome Atlas, and Gene Ontology databases, we present a multiscale model of the long-term evolutionary dynamics leading from inflammation to tumorigenesis. The model incorporates cross-talk among interactions on several scales, including responses to DNA damage, gene mutation, cell-cycle behavior, population dynamics, inflammation, and metabolism-immune balance. Model simulations revealed two stages of inflammation-induced tumorigenesis: a precancerous state and tumorigenesis. The precancerous state was mainly caused by mutations in the cell proliferation pathway; the transition from the precancerous to tumorigenic states was induced by mutations in pathways associated with apoptosis, differentiation, and metabolism-immune balance. We identified opposing effects of inflammation on tumorigenesis. Mild inflammation removed cells with DNA damage through DNA damage-induced cell death, whereas severe inflammation accelerated accumulation of mutations and hence promoted tumorigenesis. These results provide insight into the evolutionary dynamics of inflammation-induced tumorigenesis and highlight the combinatorial effects of inflammation and metabolism-immune balance. This approach establishes methods for quantifying cancer risk, for the discovery of driver pathways in inflammation-induced tumorigenesis, and has direct relevance for early detection and prevention and development of new treatment regimes. Cancer Res; 77(22); 6429-41. ©2017 AACR.

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.

The proportion of cancer-related entries in PubMed has increased considerably; is cancer truly "The Emperor of All Maladies"?

In this work, the public database of biomedical literature PubMed was mined using queries with combinations of keywords and year restrictions. It was found that the proportion of Cancer-related entries per year in PubMed has risen from around 6% in 1950 to more than 16% in 2016. This increase is not shared by other conditions such as AIDS, Malaria, Tuberculosis, Diabetes, Cardiovascular, Stroke and Infection some of which have, on the contrary, decreased as a proportion of the total entries per year. Organ-related queries were performed to analyse the variation of some specific cancers. A series of queries related to incidence, funding, and relationship with DNA, Computing and Mathematics, were performed to test correlation between the keywords, with the hope of elucidating the cause behind the rise of Cancer in PubMed. Interestingly, the proportion of Cancer-related entries that contain “DNA”, “Computational” or “Mathematical” have increased, which suggests that the impact of these scientific advances on Cancer has been stronger than in other conditions. It is important to highlight that the results obtained with the data mining approach here presented are limited to the presence or absence of the keywords on a single, yet extensive, database. Therefore, results should be observed with caution. All the data used for this work is publicly available through PubMed and the UK’s Office for National Statistics. All queries and figures were generated with the software platform Matlab and the files are available as supplementary material.

Predicting the Influence of Microvascular Structure On Tumor Response to Radiotherapy

OBJECTIVE

The purpose of this study is to investigate how theoretical predictions of tumor response to radiotherapy (RT) depend on the morphology and spatial representation of the microvascular network.

METHODS

A hybrid multiscale model, which couples a cellular automaton model of tumor growth with a model for oxygen transport from blood vessels, is used to predict the viable fraction of cells following one week of simulated RT. Both artificial and biologically derived three-dimensional (3-D) vessel networks of well vascularized tumors are considered and predictions compared with 2-D descriptions.

RESULTS

For literature-derived values of the cellular oxygen consumption rate there is little difference in predicted viable fraction when 3-D network representations of biological or artificial vessel networks are employed. Different 2-D representations are shown to either over- or under-estimate viable fractions relative to the 3-D cases, with predictions based on point-wise descriptions shown to have greater sensitivity to vessel network morphology.

CONCLUSION

The predicted RT response is relatively insensitive to the morphology of the microvessel network when 3-D representations are adopted, however, sensitivity is greater in certain 2-D representations.

SIGNIFICANCE

By using realistic 3-D vessel network geometries this study shows that real and artificial network descriptions and assumptions of spatially uniform oxygen distributions lead to similar RT response predictions in relatively small tissue volumes. This suggests that either a more detailed description of oxygen transport in the microvasculature is required or that the oxygen enhancement ratio used in the well known linear-quadratic RT response model is relatively insensitive to microvascular structure.

Role of mathematical medicine in gastrointestinal carcinoma: Current status and perspectives

Mathematical medicine has already played an important role in clinical and basic research as a major interdisciplinary branch of medicine. Mathematical medicine has an important role not only in imaging diagnosis, image storage and transmission in gastrointestinal (GI) cancer, but also in tumor precision therapy. Specifically, in the field of minimally invasive treatment such as precise ablation, 3-dimension modeling, navigation, and surgical simulation significantly improve the therapeutic safety and efficiency in GI cancer. In addition, in the era of big data, data analysis and individualized therapy using mathematical medicine will become a trend in the future, offering an effective method for diagnosing and treating GI cancer and promoting clinical and scientific research.

Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.