Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics

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.

CONCLUSIONS

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.

Biopsy location and tumor-associated macrophages in predicting malignant glioma recurrence using an in-silico model

Predicting the biological behavior and time to recurrence (TTR) of high-grade diffuse gliomas (HGG) after maximum safe neurosurgical resection and combined radiation and chemotherapy plays a pivotal role in planning clinical follow-up, selecting potentially necessary second-line treatment and improving the quality of life for patients diagnosed with a malignant brain tumor. The current standard-of-care (SoC) for HGG includes follow-up neuroradiological imaging to detect recurrence as early as possible and relies on several clinical, neuropathological, and radiological prognostic factors, which have limited accuracy in predicting TTR. In this study, using an in-silico analysis, we aim to improve predictive power for TTR by considering the role of (i) prognostically relevant information available through diagnostics used in the current SoC, (ii) advanced image-based information not currently part of the standard diagnostic workup, such as tumor-normal tissue interface (edge) features and quantitative data specific to biopsy positions within the tumor, and (iii) information on tumor-associated macrophages. In particular, we introduced a state-of-the-art spatio-temporal model of tumor-immune interactions, emphasizing the interplay between macrophages and glioma cells. This model serves as a synthetic reality for assessing the predictive value of various features. We generated a cohort of virtual patients based on our mathematical model. Each patient's dataset includes simulated T1Gd and Fluid-attenuated inversion recovery (FLAIR) MRI volumes. T1-weighted imaging highlights anatomical structures with high contrast, providing clear detail on brain morphology, whereas FLAIR suppresses fluid signals, improving the visualization of lesions near fluid-filled spaces, which is particularly helpful for identifying peritumoral edema. Additionally, we simulated results on macrophage density and proliferative activity, either in a specified part of the tumor, namely the tumor core or edge ("localized"), or unspecified ("non-localized"). To enhance the realism of our synthetic data, we imposed different levels of noise. Our findings reveal that macrophage density at the tumor edge contributed to a high predictive value of feature importance for the selected regression model. Moreover, there are lower MSE values for the "localized" biopsy in prediction accuracy toward recurrence post-resection compared with "non-localized" specimens in the noisy data. In conclusion, the results show that localized biopsies provided more information about tumor behavior, especially at the interface of tumor and normal tissue (Edge).

Mathematical modeling of microtube-driven regrowth of gliomas after local resection

Recently, glioblastoma tumors were shown to form tumor microtubes, which are thin, long protrusions that help the tumor grow and spread. Follow-up experiments were conducted on mice in order to test what impact the tumor microtubes have on tumor regrowth after the partial removal of a tumor region. The surgery was performed in isolation and along with growth-inhibiting treatments such as a tumor microtube-inhibiting treatment and an anti-inflammatory treatment. Here, we have proposed a partial differential equation model applicable to describe the microtube-driven regrowth of the cancer in the lesion. We found that the model is able to replicate the main trends seen in the experiments such as fast regrowth, larger cancer density in the lesion, and further spread into healthy tissue. The model indicates that the dominant mechanisms of re-growth are growth-inducing wound-healing mechanisms and the proliferative advantage from the tumor microtubes. In addition, tumor microtubes provide orientational guidance from the untreated tissue into the lesion.

Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth

Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition. We discuss how our approach enables the introduction of effective bio-mechanical interactions in a CA framework for future studies.

Phagocytosis Checkpoints in Glioblastoma: CD47 and Beyond

Glioblastoma multiforme (GBM) is one of the deadliest human cancers with very limited treatment options available. The malignant behavior of GBM is manifested in a tumor which is highly invasive, resistant to standard cytotoxic chemotherapy, and strongly immunosuppressive. Immune checkpoint inhibitors have recently been introduced in the clinic and have yielded promising results in certain cancers. GBM, however, is largely refractory to these treatments. The immune checkpoint CD47 has recently gained attention as a potential target for intervention as it conveys a "don't eat me" signal to tumor-associated macrophages (TAMs) via the inhibitory SIRP alpha protein. In preclinical models, the administration of anti-CD47 monoclonal antibodies has shown impressive results with GBM and other tumor models. Several well-characterized oncogenic pathways have recently been shown to regulate CD47 expression in GBM cells and glioma stem cells (GSCs) including Epidermal Growth Factor Receptor (EGFR) beta catenin. Other macrophage pathways involved in regulating phagocytosis including TREM2 and glycan binding proteins are discussed as well. Finally, chimeric antigen receptor macrophages (CAR-Ms) could be leveraged for greatly enhancing the phagocytosis of GBM and repolarization of the microenvironment in general. Here, we comprehensively review the mechanisms that regulate the macrophage phagocytosis of GBM cells.

The dopamine receptor D1 inhibitor, SKF83566, suppresses GBM stemness and invasion through the DRD1-c-Myc-UHRF1 interactions

BACKGROUND

Extensive local invasion of glioblastoma (GBM) cells within the central nervous system (CNS) is one factor that severely limits current treatments. The aim of this study was to uncover genes involved in the invasion process, which could also serve as therapeutic targets. For the isolation of invasive GBM cells from non-invasive cells, we used a three-dimensional organotypic co-culture system where glioma stem cell (GSC) spheres were confronted with brain organoids (BOs). Using ultra-low input RNA sequencing (ui-RNA Seq), an invasive gene signature was obtained that was exploited in a therapeutic context.

METHODS

GFP-labeled tumor cells were sorted from invasive and non-invasive regions within co-cultures. Ui-RNA sequencing analysis was performed to find a gene cluster up-regulated in the invasive compartment. This gene cluster was further analyzed using the Connectivity MAP (CMap) database. This led to the identification of SKF83566, an antagonist of the D1 dopamine receptor (DRD1), as a candidate therapeutic molecule. Knockdown and overexpression experiments were performed to find molecular pathways responsible for the therapeutic effects of SKF83566. Finally, the effects of SKF83566 were validated in orthotopic xenograft models in vivo.

RESULTS

Ui-RNA seq analysis of three GSC cell models (P3, BG5 and BG7) yielded a set of 27 differentially expressed genes between invasive and non-invasive cells. Using CMap analysis, SKF83566 was identified as a selective inhibitor targeting both DRD1 and DRD5. In vitro studies demonstrated that SKF83566 inhibited tumor cell proliferation, GSC sphere formation, and invasion. RNA sequencing analysis of SKF83566-treated P3, BG5, BG7, and control cell populations yielded a total of 32 differentially expressed genes, that were predicted to be regulated by c-Myc. Of these, the UHRF1 gene emerged as the most downregulated gene following treatment, and ChIP experiments revealed that c-Myc binds to its promoter region. Finally, SKF83566, or stable DRD1 knockdown, inhibited the growth of orthotopic GSC (BG5) derived xenografts in nude mice.

CONCLUSIONS

DRD1 contributes to GBM invasion and progression by regulating c-Myc entry into the nucleus that affects the transcription of the UHRF1 gene. SKF83566 inhibits the transmembrane protein DRD1, and as such represents a candidate small therapeutic molecule for GBMs.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

Effects of a differentiating therapy on cancer-stem-cell-driven tumors

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter adif. To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of adif the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For microchamber-grown tumorspheres, there is a threshold in therapy strength below which both subpopulations survive, while high values of adif lead to the complete elimination of the CSC phenotype. For tumorspheres grown on hard and soft agar and in the presence of growth factors, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment.

A stochastic hierarchical model for low grade glioma evolution

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker-Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.

Cancer stem cells: an insight into the development of metastatic tumors and therapy resistance

The term "cancer stem cells" (CSCs) refers to cancer cells that exhibit traits parallel to normal stem cells, namely the potential to give rise to every type of cell identified in a tumor microenvironment. It has been found that CSCs usually develops from other neoplastic cells or non-cancerous somatic cells by acquiring stemness and malignant characteristics through particular genetic modifications. A trivial number of CSCs, identified in solid and liquid cancer, can give rise to an entire tumor population with aggressive anticancer drug resistance, metastasis, and invasiveness. Besides, cancer stem cells manipulate their intrinsic and extrinsic features, regulate the metabolic pattern of the cell, adjust efflux-influx efficiency, modulate different signaling pathways, block apoptotic signals, and cause genetic and epigenetic alterations to retain their pluripotency and ability of self-renewal. Notably, to keep the cancer stem cells' ability to become malignant cells, mesenchymal stem cells, tumor-associated fibroblasts, immune cells, etc., interact with one another. Furthermore, CSCs are characterized by the expression of particular molecular markers that carry significant diagnostic and prognostic significance. Because of this, scientific research on CSCs is becoming increasingly imperative, intending to understand the traits and behavior of cancer stem cells and create more potent anticancer therapeutics to fight cancer at the CSC level. In this review, we aimed to elucidate the critical role of CSCs in the onset and spread of cancer and the characteristics of CSCs that promote severe resistance to targeted therapy.

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.

Effects of Fractionated Radiation Exposure on Vimentin Expression in Cervical Cancers: Analysis of Association with Cancer Stem Cell Response and Short-Term Prognosis

Elucidation of the mechanisms for the response of cancer stem cells (CSCs) to radiation exposure is of considerable interest for further improvement of radio- and chemoradiotherapy of cervical cancer (CC). The aim of this work is to evaluate the effects of fractionated radiation exposure on the expression of vimentin, which is one of the end-stage markers of epithelial-mesenchymal transition (EMT), and analyze its association with CSC radiation response and short-term prognosis of CC patients. The level of vimentin expression was determined in HeLa, SiHa cell lines, and scrapings from the cervix of 46 CC patients before treatment and after irradiation at a total dose of 10 Gy using real-time polymerase chain reaction (PCR) assay, flow cytometry, and fluorescence microscopy. The number of CSCs was assessed using flow cytometry. Significant correlations were shown between vimentin expression and postradiation changes in CSC numbers in both cell lines (R = 0.88, p = 0.04 for HeLa and R = 0.91, p = 0.01 for SiHa) and cervical scrapings (R = 0.45, p = 0.008). Associations were found at the level of tendency between postradiation increase in vimentin expression and unfavorable clinical outcome 3-6 months after treatment. The results clarify some of the relationships between EMT, CSCs, and therapeutic resistance that are needed to develop new strategies for cancer treatment.

The Tumor Invasion Paradox in Cancer Stem Cell-Driven Solid Tumors

Cancer stem cells (CSCs) are key in understanding tumor growth and tumor progression. A counterintuitive effect of CSCs is the so-called tumor growth paradox: the effect where a tumor with a higher death rate may grow larger than a tumor with a lower death rate. Here we extend the modeling of the tumor growth paradox by including spatial structure and considering cancer invasion. Using agent-based modeling and a corresponding partial differential equation model, we demonstrate and prove mathematically a tumor invasion paradox: a larger cell death rate can lead to a faster invasion speed. We test this result on a generic hypothetical cancer with typical growth rates and typical treatment sensitivities. We find that the tumor invasion paradox may play a role for continuous and intermittent treatments, while it does not seem to be essential in fractionated treatments. It should be noted that no attempt was made to fit the model to a specific cancer, thus, our results are generic and theoretical.

The Network of Tumor Microtubes: An Improperly Reactivated Neural Cell Network With Stemness Feature for Resistance and Recurrence in Gliomas

Gliomas are known as an incurable brain tumor for the poor prognosis and robust recurrence. In recent years, a cellular subpopulation with tumor microtubes (TMs) was identified in brain tumors, which may provide a new angle to explain the invasion, resistance, recurrence, and heterogeneity of gliomas. Recently, it was demonstrated that the cell subpopulation also expresses neural stem cell markers and shares a lot of features with both immature neurons and cancer stem cells and may be seen as an improperly reactivated neural cell network with a stemness feature at later time points of life. TMs may also provide a new angle to understand the resistance and recurrence mechanisms of glioma stem cells. In this review, we innovatively focus on the common features between TMs and sprouting axons in morphology, formation, and function. Additionally, we summarized the recent progress in the resistance and recurrence mechanisms of gliomas with TMs and explained the incurability and heterogeneity in gliomas with TMs. Moreover, we discussed the recently discovered overlap between cancer stem cells and TM-positive glioma cells, which may contribute to the understanding of resistant glioma cell subpopulation and the exploration of the new potential therapeutic target for gliomas.

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.

MATHEMATICAL MODELING OF PANCREATIC CANCER TREATMENT WITH CANCER STEM CELLS

Of all cancers, pancreatic cancer has a significantly low rate of survival, mostly due to lack of early screening. Thus, once detected, pancreatic cancer is usually in later stages, reducing the likelihood of full recovery. The most common treatment strategy is chemotherapy, although several immunotherapeutic drugs show promising results in extending the patient’s lifespan. In this paper, we provide a validated mathematical model for the pancreatic cancer after fitting the parameter values, such as tumor growth rate, inverse carrying capacity, activation and decay rate of pancreatic stellate cells, with the use of the experimental data presented by Cioffi et al. cioffi2015inhibition For treatments with the chemotherapeutic drugs, Abraxane and Gemcitabine, and the immunotherapeutic drug, Anti-CD47, we modified the model accurately and compared the simulation results with the experimental data not only to model pancreatic cancer treatment correctly but also to move forward with other drug trials. Then, we include the cancer stem cells, which are known to initiate tumors and cause a relapse post-chemotherapy, per cancer stem cell hypothesis so that cancer progression can be assessed based on this phenomenon. In addition, we investigate optimal drug protocols. We find out that the most effective treatment is dual therapy due to extending survival time when compared to other drugs. Moreover, this study reveals that drug dose is more effectual than frequency of drug injection on account of different treatment scheduling with the same dose over a week. The model could be a starting point to investigate pancreatic cancer progression based on cancer stem cell hypothesis and shed light on novel drug discoveries.

Intraoperative radiotherapy for glioblastoma: A systematic review of techniques and outcomes

BACKGROUND

Despite multimodality treatment, the prognosis of glioblastoma (GBM) has remained poor. Intraoperative radiation therapy (IORT) offers additional local control by directly applying a radiation source to the resection margin, where most recurrences occur.

METHODS

We performed a systematic review on the oncologic outcomes and toxicities of IORT for GBM in the era of modern external beam radiation therapy (EBRT) and chemotherapy with temozolamide.

RESULTS

Four studies representing 123 patients were included. Majority (81%) were newly diagnosed, and gross total resection was reported in 13-80% of cases. IORT modalities included electrons from a linear accelerator (LINAC) and photons from a 50-kV x-ray device. Median doses were from 12.5 to 20 Gy for electron-based studies and 10-25 Gy for photon-based studies. Adjuvant treatment consisted of 46-60 Gy post-operative EBRT in electron-based studies and the Stupp protocol in photon-based studies. Complications included radiation necrosis (2.8-33%), infection, hematoma, perilesional edema, and wound dehiscence. Median time to local recurrence was 9.9-16 months and the reported overall progression-free survival was 11.2-12.2 months. Median overall survival was 13-14.2 months for the electron-based studies and 13.8-18 months for the photon-based studies.

CONCLUSION

IORT resulted in improved local control and comparable overall survival rates with the Stupp protocol. Although photon-based IORT had better results than electron IORT, this may be due to improvements in other forms of adjuvant treatment rather than the IORT modality itself. The overall effect of IORT on GBM treatment is still inconclusive due to the small number of patients and heterogeneous reporting of data.

Tumor-immune ecosystem dynamics define an individual Radiation Immune Score to predict pan-cancer radiocurability

Radiotherapy efficacy is the result of radiation-mediated cytotoxicity coupled with stimulation of antitumor immune responses. We develop an in silico 3-dimensional agent-based model of diverse tumor-immune ecosystems (TIES) represented as anti- or pro-tumor immune phenotypes. We validate the model in 10,469 patients across 31 tumor types by demonstrating that clinically detected tumors have pro-tumor TIES. We then quantify the likelihood radiation induces antitumor TIES shifts toward immune-mediated tumor elimination by developing the individual Radiation Immune Score (iRIS). We show iRIS distribution across 31 tumor types is consistent with the clinical effectiveness of radiotherapy, and in combination with a molecular radiosensitivity index (RSI) combines to predict pan-cancer radiocurability. We show that iRIS correlates with local control and survival in a separate cohort of 59 lung cancer patients treated with radiation. In combination, iRIS and RSI predict radiation-induced TIES shifts in individual patients and identify candidates for radiation de-escalation and treatment escalation. This is the first clinically and biologically validated computational model to simulate and predict pan-cancer response and outcomes via the perturbation of the TIES by radiotherapy.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

A phase I/II trial of 5-fraction stereotactic radiosurgery with 5-mm margins with concurrent temozolomide in newly diagnosed glioblastoma: primary outcomes

BACKGROUND

We sought to determine the maximum tolerated dose (MTD) of 5-fraction stereotactic radiosurgery (SRS) with 5-mm margins delivered with concurrent temozolomide in newly diagnosed glioblastoma (GBM).

METHODS

We enrolled adult patients with newly diagnosed glioblastoma to 5 days of SRS in a 3 + 3 design on 4 escalating dose levels: 25, 30, 35, and 40 Gy. Dose limiting toxicity (DLT) was defined as Common Terminology Criteria for Adverse Events grades 3-5 acute or late CNS toxicity, including adverse radiation effect (ARE), the imaging correlate of radiation necrosis.

RESULTS

From 2010 to 2015, thirty patients were enrolled. The median age was 66 years (range, 51-86 y). The median target volume was 60 cm3 (range, 14.7-137.3 cm3). DLT occurred in 2 patients: one for posttreatment cerebral edema and progressive disease at 3 weeks (grade 4, dose 40 Gy); another patient died 1.5 weeks following SRS from postoperative complications (grade 5, dose 40 Gy). Late grades 1-2 ARE occurred in 8 patients at a median of 7.6 months (range 3.2-12.6 mo). No grades 3-5 ARE occurred. With a median follow-up of 13.8 months (range 1.7-64.4 mo), the median survival times were: progression-free survival, 8.2 months (95% CI: 4.6-10.5); overall survival, 14.8 months (95% CI: 10.9-19.9); O6-methylguanine-DNA methyltransferase hypermethylated, 19.9 months (95% CI: 10.5-33.5) versus 11.3 months (95% CI: 8.9-17.6) for no/unknown hypermethylation (P = 0.03), and 27.2 months (95% CI: 11.2-48.3) if late ARE occurred versus 11.7 months (95% CI: 8.9-17.6) for no ARE (P = 0.08).

CONCLUSIONS

The per-protocol MTD of 5-fraction SRS with 5-mm margins with concurrent temozolomide was 40 Gy in 5 fractions. ARE was limited to grades 1-2 and did not statistically impact survival.

MATHEMATICAL CHARACTERIZATION OF HETEROGENEITY IN A CANCER STEM CELL DRIVEN TUMOR GROWTH MODEL WITH NONLINEAR SELF-RENEWAL

The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie cellular expansion under the hierarchical guidelines of the cancer stem cell (CSC) hypothesis. Important features of the model include (i) a nonlinear probability of CSC self-renewal that reflects the fact that this key type of stem cell division can be regulated by extrinsic and intrinsic chemical signaling as well as environmental (niche) constraints and (ii) an amplification factor that captures the transient amplifying divisions that are a defining characteristic of progenitor cells. We present a thorough mathematical analysis of the model and highlight the conditions required for tumors to evolve toward either bounded or exponential growth. Numerical simulations further illustrate the impact of the various parameters on the tumor growth rate and on the heterogeneous cellular composition, which varies during progression.

Radiation Response of Cervical Cancer Stem Cells Is Associated with Pretreatment Proportion of These Cells and Physical Status of HPV DNA

Radio- and chemoresistance of cancer stem cells (CSCs) is considered as one of the possible causes of adverse results of chemoradiotherapy for various malignancies, including cervical cancer. However, little is known about quantitative changes in the CSC subpopulation in the course of treatment and mechanisms for individual response of CSCs to therapy. The purpose of the study was to evaluate the association of radiation response of cervical CSCs with clinical and morphological parameters of disease and features of human papillomavirus (HPV) infection. The proportion of CD44⁺CD24^low CSCs was determined by flow cytometry in cervical scrapings from 55 patients with squamous cell carcinoma of uterine cervix before treatment and after fractionated irradiation at a total dose of 10 Gy. Real-time PCR assay was used to evaluate molecular parameters of HPV DNA. Post-radiation increase in the CSC proportion was found in 47.3% of patients. Clinical and morphological parameters (stage, status of lymph node involvement, and histological type) were not significantly correlated with radiation changes in the CSC proportion. Single- and multifactor analyses revealed two independent indicators affecting the radiation response of CSCs: initial proportion of CSCs and physical status of HPV DNA (R = 0.86, p = 0.001 for the multiple regression model in the whole).

Psychological Stress Up-Regulates CD147 Expression Through Beta-Arrestin1/ERK to Promote Proliferation and Invasiveness of Glioma Cells

Psychological stress is closely related to the occurrence and prognosis of various malignant tumors, but the underlying mechanisms are not well studied. CD147 has been reported to be expressed in glioma and other malignant tumors. CD147 not only participates in lactic acid transport, but it also plays an important role in the invasion and metastasis of malignant tumor cells by stimulating the production of numerous matrix metalloproteinases (MMPs) and vascular endothelial growth factor by fibroblasts, and could also act as an autocrine factor stimulating MMPs production in metastatic tumor cells. Here, we found that silencing CD147 in chronically stressed nude mice not only inhibited the proliferation of xenografts but also decreased matrix metalloproteinase-2, 9 expression and lactic acid content in tumor tissues. Furthermore, norepinephrine (NE) was significantly increased in the serum of nude mice in glioma stress model. To determine the underlying cellular mechanism, we added exogenous NE into LN229 and U87 cells to simulate the stress environment in vitro. The invasiveness of the glioma cells was subsequently examined using a Matrigel invasion assay. We demonstrated that knockdown of CD147 inhibited glioma invasiveness and metastasis with norepinephrine stimulation. Luciferase reporter gene experiments further demonstrated that the expression of CD147 is up-regulated primarily by norepinephrine via the β-Adrenalin receptor (βAR)-β-arrestin1-ERK1/2-Sp1 pathway. High expression of CD147 promoted the secretion of MMP-2 and the increment of lactic acid, which accelerated the augmented invasion and metastasis of glioma induced by psychological stress. Taken together, these results suggest that psychological stress promotes glioma proliferation and invasiveness by up-regulating CD147 expression. Thus, CD147 might be a potential target site in the treatment of glioma progression induced by chronic psychological stress.

Radiotherapy targeting cancer stem cells "awakens" them to induce tumour relapse and metastasis in oral cancer

Radiotherapy is one of the most common treatments for oral cancer. However, in the clinic, recurrence and metastasis of oral cancer occur after radiotherapy, and the underlying mechanism remains unclear. Cancer stem cells (CSCs), considered the “seeds” of cancer, have been confirmed to be in a quiescent state in most established tumours, with their innate radioresistance helping them survive more easily when exposed to radiation than differentiated cancer cells. There is increasing evidence that CSCs play an important role in recurrence and metastasis post-radiotherapy in many cancers. However, little is known about how oral CSCs cause tumour recurrence and metastasis post-radiotherapy. In this review article, we will first summarise methods for the identification of oral CSCs and then focus on the characteristics of a CSC subpopulation induced by radiation, hereafter referred to as “awakened” CSCs, to highlight their response to radiotherapy and potential role in tumour recurrence and metastasis post-radiotherapy as well as potential therapeutics targeting CSCs. In addition, we explore potential therapeutic strategies targeting these “awakened” CSCs to solve the serious clinical challenges of recurrence and metastasis in oral cancer after radiotherapy.

Analysis of influencing factors of no/low response to preoperative concurrent chemoradiotherapy in locally advanced rectal cancer

The aim of this study is to investigate the influencing factors associated with no/low response to preoperative concurrent chemoradiotherapy (CCRT) for locally advanced rectal cancer (LARC) patients. A total of 79 patients were included in this prospective study. Fifteen factors that might affect the resistance to CCRT were included in this logistic regression analysis, these factors include the general clinical data of patients, the expression status of tumor stem cell marker CD44v6 and the volumetric imaging parameters of primary tumor lesions. We found that the no/low response status to preoperative CCRT was positively correlated with the real tumor volume (RTV), the total surface area of tumor (TSA), and CD44v6 expression, whereas negatively correlated with the tumor compactness (TC). According to the results of logistic regression analysis, two formulas that could predict whether or not no/low response to preoperative CCRT were established. The Area Under Curve (AUC) of the two formulas and those significant measurement data (RTV, TC, TSA) were 0.900, 0.858, 0.771, 0.754, 0.859, the sensitivity were 95.8%, 79.17%, 62.50%, 95.83%, 62.5%, the specificity were 70.9%, 74.55%, 83.64%,47.27%, 96.36%, the positive predictive values were 58.96%, 57.58%, 62.51%,44.23%, 88.23%, the negative predictive values were 97.48%, 89.13%, 83.64%, 96.29%, and 85.48%, respectively.

Development of transient radioresistance during fractionated irradiation in vitro

BACKGROUND AND PURPOSE

Effective combination treatments with fractionated radiotherapy rely on a proper understanding of the dynamic responses that occur during treatment. We explored the effect of clinical fractionated radiotherapy on the development and timing of radioresistance in tumor cells.

METHODS AND MATERIALS

Different colon (HT29/HCT116/COLO320/SW480/RKO) and high-grade astrocytoma (D384/U-251MG) cancer cell lines were treated for 6 weeks with daily fractions of 2 Gy, 5 days per week. Clonogenic survival was determined throughout the treatment period. In addition, the radiosensitivity of irradiated and non-irradiated was compared. Finally, the effect of different dose fractions on the development of radioresistance was determined.

RESULTS

All cell lines developed radioresistance within 2-3 weeks during fractionated radiotherapy. This was characterized by the occurrence of a steady state phase of clonogenic survival. In U-251MG cells this was accompanied by increased cell senescence and stemness. After recovering from six weeks of treatment, the radiosensitivity of fractionally irradiated and non-irradiated cells was similar. Including transient radioresistance, described as (α/β)^-(d+1), as a factor in the classic LQ model resulted in a perfect fit with the experimental data observed during fractionated radiotherapy. This was confirmed when different dose fractions were applied.

CONCLUSIONS

Fractionated irradiation of cancer cells in vitro following clinical radiation schedules induces a reversible radioresistance response. This adaptive response can be included in the LQ model as a function of the dose fraction and the alpha/beta-ratio of a given cell line. These findings warrant further investigation of the mechanisms and clinical relevance of adaptive radioresistance.

Personalizing Gastric Cancer Screening With Predictive Modeling of Disease Progression Biomarkers

Gastric cancer (GC) remains the third most common cause of cancer-related death worldwide. Infection with Helicobacter pylori is responsible for over 70% of GC incidence; colonization induces chronic inflammation, which can facilitate progression to intestinal metaplasia, dysplasia, and GC (Correa pathway). Although H. pylori eradication is a necessary first step in GC prevention, some patients continue to progress to advanced stage disease if substantial tissue damage has occurred or inflammation persists. This progression is often asymptomatic until cancer reaches stage IV, yet efficient, cost-effective screening protocols for patients who present with early stages of the Correa pathway do not exist. Given the high interpatient heterogeneity in progression time through this pathway, such screening protocols must necessarily be personalized. This requires the identification of reliable and longitudinally assessable biomarkers of patient-specific progression. Several gastric stem cell (GSC) markers including CD44, CD133, and Lgr5 are upregulated in GC. Here we show a significant stepwise increase in immunohistochemical staining for these markers in biopsies at different stages of the Correa pathway, suggesting GSC fraction to be a promising candidate biomarker for early detection of malignant transformation. We present a mathematical model capable of both simulating clinically observed increases in GSC fraction in longitudinal biopsy samples of individual patients, and forecasting patient-specific disease progression trajectories based only on characteristics identified from immunohistochemistry at initial presentation. From these forecasts, personalized screening schedules may be identified that would allow early stratification of high-risk patients, and potentially earlier detection of dysplasia or early-stage GC.

Mathematical oncology and it's application in non melanoma skin cancer - A primer for radiation oncology professionals

Cancers of the skin (the majority of which are basal and squamous cell skin carcinomas, but also include the rarer Merkel cell carcinoma) are overwhelmingly the most common of all types of cancer. Most of these are treated surgically, with radiation reserved for those patients with high risk features or anatomical locations less suitable for surgery. Given the high incidence of both basal and squamous cell carcinomas, as well as the relatively poor outcome for Merkel cell carcinoma, it is useful to investigate the role of other disciplines regarding their diagnosis, staging and treatment. Mathematical modelling is one such area of investigation. The use of mathematical modelling is a relatively recent addition to the armamentarium of cancer treatment. It has long been recognised that tumour growth and treatment response is a complex, non-linear biological phenomenon with many mechanisms yet to be understood. Despite decades of research, including clinical, population and basic science approaches, we continue to be challenged by the complexity, heterogeneity and adaptability of tumours, both in individual patients in the oncology clinic and across wider patient populations. Prospective clinical trials predominantly focus on average outcome, with little understanding as to why individual patients may or may not respond. The use of mathematical models may lead to a greater understanding of tumour initiation, growth dynamics and treatment response.

Influence of the human papillomavirus on the radio-responsiveness of cancer stem cells in head and neck cancers

A growing proportion of head and neck cancers (HNC) result from HPV infection. Between HNC aetiological groups (HPV positive and HPV negative) clinical evidence demonstrates significantly better treatment response among HPV positive cancers. Cancer stem cells (CSCs) are identified in HNC tumour populations as agents of treatment resistance and a target for tumour control. This study examines dynamic responses in populations of a CSC phenotype in HNC cell lines following X-irradiation at therapeutic levels, and comparing between HPV statuses. Variations in CSC density between HPV groups showed no correlation with better clinical outcomes seen in the HPV positive status. CSC populations in HPV positive cell lines ranged from 1.9 to 4.8%, and 2.6 to 9.9% for HPV negative. Following 4 Gy X- irradiation however, HPV negative cell lines demonstrated more frequent and significantly greater escalation in CSC proportions, being 3-fold that of the HPV positive group at 72 hours post irradiation. CSC proportions of tumour populations are not fixed but subject to change in response to radiation at therapeutic dose levels. These findings imply a potential effect of aetiology on radio-responsiveness in CSCs, illustrating that clonogen treatment response may be more informative of therapy outcomes than inherent population density alone.

Emerging intersections between neuroscience and glioma biology

The establishment of neuronal and glial networks in the brain depends on the activities of neural progenitors, which are influenced by cell-intrinsic mechanisms, interactions with the local microenvironment and long-range signaling. Progress in neuroscience has helped identify key factors in CNS development. In parallel, studies in recent years have increased our understanding of molecular and cellular factors in the development and growth of primary brain tumors. To thrive, glioma cells exploit pathways that are active in normal CNS progenitor cells, as well as in normal neurotransmitter signaling. Furthermore, tumor cells of incurable gliomas integrate into communicating multicellular networks, where they are interconnected through neurite-like cellular protrusions. In this Review, we discuss evidence that CNS development, organization and function share a number of common features with glioma progression and malignancy. These include mechanisms used by cells to proliferate and migrate, interact with their microenvironment and integrate into multicellular networks. The emerging intersections between the fields of neuroscience and neuro-oncology considered in this review point to new research directions and novel therapeutic opportunities.

Mathematical Models of Organoid Cultures

Organoids are engineered three-dimensional tissue cultures derived from stem cells and capable of self-renewal and self-organization into a variety of progenitors and differentiated cell types. An organoid resembles the cellular structure of an organ and retains some of its functionality, while still being amenable to in vitro experimental study. Compared with two-dimensional cultures, the three-dimensional structure of organoids provides a more realistic environment and structural organization of in vivo organs. Similarly, organoids are better suited to reproduce signaling pathway dynamics in vitro, due to a more realistic physiological environment. As such, organoids are a valuable tool to explore the dynamics of organogenesis and offer routes to personalized preclinical trials of cancer progression, invasion, and drug response. Complementary to experiments, mathematical and computational models are valuable instruments in the description of spatiotemporal dynamics of organoids. Simulations of mathematical models allow the study of multiscale dynamics of organoids, at both the intracellular and intercellular levels. Mathematical models also enable us to understand the underlying mechanisms responsible for phenotypic variation and the response to external stimulation in a cost- and time-effective manner. Many recent studies have developed laboratory protocols to grow organoids resembling different organs such as the intestine, brain, liver, pancreas, and mammary glands. However, the development of mathematical models specific to organoids remains comparatively underdeveloped. Here, we review the mathematical and computational approaches proposed so far to describe and predict organoid dynamics, reporting the simulation frameworks used and the models’ strengths and limitations.

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.

Integrating Mathematical Modeling into the Roadmap for Personalized Adaptive Radiation Therapy

In current radiation oncology practice, treatment protocols are prescribed based on the average outcomes of large clinical trials, with limited personalization and without adaptations of dose or dose fractionation to individual patients based on their individual clinical responses. Predicting tumor responses to radiation and comparing predictions against observed responses offers an opportunity for novel treatment evaluation. These analyses can lead to protocol adaptation aimed at the improvement of patient outcomes with better therapeutic ratios. We foresee the integration of mathematical models into radiation oncology to simulate individual patient tumor growth and predict treatment response as dynamic biomarkers for personalized adaptive radiation therapy (RT).

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.

Proliferation saturation index in an adaptive Bayesian approach to predict patient-specific radiotherapy responses

Purpose: Radiotherapy prescription dose and dose fractionation protocols vary little between individual patients having the same tumor grade and stage. To personalize radiotherapy a predictive model is needed to simulate radiation response. Previous modeling attempts with multiple variables and parameters have been shown to yield excellent data fits at the cost of non-identifiability and clinically unrealistic results. Materials and methods: We develop a mathematical model based on a proliferation saturation index (PSI) that is a measurement of pre-treatment tumor volume-to-carrying capacity ratio that modulates intrinsic tumor growth and radiation response rates. In an adaptive Bayesian approach, we utilize an increasing number of data points for individual patients to predict patient-specific responses to subsequent radiation doses. Results: Model analysis shows that using PSI as the only patient-specific parameter, model simulations can fit longitudinal clinical data with high accuracy (R²=0.84). By analyzing tumor response to radiation using daily CT scans early in the treatment, response to the remaining treatment fractions can be predicted after two weeks with high accuracy (c-index = 0.89). Conclusion: The PSI model may be suited to forecast treatment response for individual patients and offers actionable decision points for mid-treatment protocol adaptation. The presented work provides an actionable image-derived biomarker prior to and during therapy to personalize and adapt radiotherapy.

Diversity of cancer stem cells in head and neck carcinomas: The role of HPV in cancer stem cell heterogeneity, plasticity and treatment response

Head and neck squamous cell carcinomas (HNSCC) resulting from oncogenic transformations following human papillomavirus (HPV) infection consistently demonstrate better treatment outcomes than HNSCC from other aetiologies. Squamous cell carcinoma of the oropharynx (OPSCC) shows the highest prevalence of HPV involvement at around 70-80%. While strongly prognostic, HPV status alone is not sufficient to predict therapy response or any potential dose de-escalation. Cancer stem cell (CSC) populations within these tumour types represent the most therapy-resistant cells and are the source of recurrence and metastases, setting a benchmark for tumour control. This review examines clinical and preclinical evidence of differences in response to treatment by the HPV statuses of HNSCC and the role played by CSCs in treatment resistance and their repopulation from non-CSCs. Evidence was collated from literature searches of PubMed, Scopus and Ovid for differential treatment response by HPV status and contribution by critical biomarkers including CSC fractions and chemo-radiosensitivity. While HPV and CSC are yet to fulfil promise as biomarkers of treatment response, understanding how HPV positive and negative aetiologies affect CSC response to treatment and tumour plasticity will facilitate their use for greater treatment individualisation.

A Review of Cell-Based Computational Modeling in Cancer Biology

Cancer biology involves complex, dynamic interactions between cancer cells and their tissue microenvironments. Single-cell effects are critical drivers of clinical progression. Chemical and mechanical communication between tumor and stromal cells can co-opt normal physiologic processes to promote growth and invasion. Cancer cell heterogeneity increases cancer's ability to test strategies to adapt to microenvironmental stresses. Hypoxia and treatment can select for cancer stem cells and drive invasion and resistance. Cell-based computational models (also known as discrete models, agent-based models, or individual-based models) simulate individual cells as they interact in virtual tissues, which allows us to explore how single-cell behaviors lead to the dynamics we observe and work to control in cancer systems. In this review, we introduce the broad range of techniques available for cell-based computational modeling. The approaches can range from highly detailed models of just a few cells and their morphologies to millions of simpler cells in three-dimensional tissues. Modeling individual cells allows us to directly translate biologic observations into simulation rules. In many cases, individual cell agents include molecular-scale models. Most models also simulate the transport of oxygen, drugs, and growth factors, which allow us to link cancer development to microenvironmental conditions. We illustrate these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance. An ecosystem of interoperable cell-based simulation tools is emerging at a time when cloud computing resources make software easier to access and supercomputing resources make large-scale simulation studies possible. As the field develops, we anticipate that high-throughput simulation studies will allow us to rapidly explore the space of biologic possibilities, prescreen new therapeutic strategies, and even re-engineer tumor and stromal cells to bring cancer systems under control.

Polydatin Increases Radiosensitivity by Inducing Apoptosis of Stem Cells in Colorectal Cancer

This study aimed to investigate the radiosensitizing effect of polydatin (PD) on colorectal cancer (CRC) and its underlying mechanism. The C57BL/6 mouse model of CRC was induced by treatment with azoxymethane (AOM)/dextran sodium sulfate (DSS) and then divided into four groups: control, PD alone, IR alone, and combination of PD and IR. Radiation therapy (200 cGy/min, 10Gy) was performed in mice in the experimental groups for once a week with a total of four times. Thirty minutes before IR, mice were intraperitoneally injected with PD at the dose of 25mg/kg. The number and volume of CRC xenografts were calculated. Immunohistochemical staining was performed to detect the expression of Ki67 and cleaved caspase-3 in tumor tissues samples. The effects of PD on proliferation and apoptosis were evaluated in CT26 and HCT116 colon tumor cells. Leucine-rich repeat-containing G-protein coupled receptor 5 positive (Lgr5⁺) cancer stem cells (CSCs) were sorted from CT26 cells and the effects of PD on their proliferation and apoptosis were observed to elucidate the radiosensitizing mechanism of PD in CRC cells. Combined therapy with PD and IR significantly decreased tumor volume, inhibited proliferation and induced apoptosis of tumor cells in the mouse model of CRC compared to other three groups. Compared to the IR group, in vitro assay showed that PD combined with IR inhibited proliferation and promoted apoptosis of CT26 and HCT116 colon tumor cells as well as Lgr5⁺ CSCs. However, addition of the bone morphogenetic protein (BMP) type I receptor inhibitor K02288 (6.4nM) dramatically increased proliferation of Lgr5⁺ CSCs and abolished the cytotoxic effect of PD combined with IR on Lgr5⁺ CSCs. The in vivo and in vitro experiments demonstrated that IR combined treatment with PD could inhibit proliferation and promote apoptosis of CRC cells and Lgr5⁺ CSCs, and BMP signaling pathway was involved in the radiosensitizing effect of PD.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth

We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.

HIF1α regulates single differentiated glioma cell dedifferentiation to stem-like cell phenotypes with high tumorigenic potential under hypoxia

The standard treatment for Glioblastoma multiforme (GBM) is surgical resection and subsequent radiotherapy and chemotherapy. Surgical resection of GBM is typically restricted because of its invasive growth, which results in residual tumor cells including glioma stem cells (GSCs) and differentiated cells. Recurrence has been previously thought to occur as a result of these GSCs, and hypoxic microenvironment maintains the GSCs stemness also plays an important role. Summarizing traditional studies and we find many researchers ignored the influence of hypoxia on differentiated cells. We hypothesized that the residual differentiated cells may be dedifferentiated to GSC-like cells under hypoxia and play a crucial role in the rapid, high-frequency recurrence of GBM. Therefore, isolated CD133-CD15-NESTIN- cells were prepared as single-cell culture and treated with hypoxia. More than 95% of the surviving single differentiated CD133-CD15-NESTIN- cell dedifferentiated into tumorigenic CD133+CD15+NESTIN+ GSCs, and this process was regulated by hypoxia inducible factor-1α. Moreover, the serum also played an important role in this dedifferentiation. These findings challenge the traditional glioma cell heterogeneity model, cell division model and glioma malignancy development model. Our study also highlights the mechanism of GBM recurrence and the importance of anti-hypoxia therapy. In addition to GSCs, residual differentiated tumor cells also substantially contribute to treatment resistance and the rapid, high recurrence of GBM.

A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment

Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth.

A small population of cancer stem cells that share many of the biological characteristics of normal adult stem cells are believed to initiate and sustain tumor growth for a wide variety of malignancies. Growth and survival of these cancer stem cells is highly influenced by tumor micro-environmental factors and molecular signaling initiated by cytokines and growth factors. This work focuses on quantifying the influence of IL-6, a pleiotropic cytokine secreted by a variety of cell types, on cancer stem cell self-renewal and survival. We present a mathematical model for IL-6 mediated, cancer stem cell driven tumor growth that operates at the following levels: (1) the molecular level—capturing cell surface dynamics of receptor-ligand binding and receptor activation that lead to intra-cellular signal transduction cascades; and (2) the cellular level—describing tumor growth, cellular composition, and response to treatments targeted against IL-6.

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.

Mathematical Modeling of the Effects of Tumor Heterogeneity on the Efficiency of Radiation Treatment Schedule

Radiotherapy uses high doses of energy to eradicate cancer cells and control tumors. Various treatment schedules have been developed and tried in clinical trials, yet significant obstacles remain to improving the radiotherapy fractionation. Genetic and non-genetic cellular diversity within tumors can lead to different radiosensitivity among cancer cells that can affect radiation treatment outcome. We propose a minimal mathematical model to study the effect of tumor heterogeneity and repair in different radiation treatment schedules. We perform stochastic and deterministic simulations to estimate model parameters using available experimental data. Our results suggest that gross tumor volume reduction is insufficient to control the disease if a fraction of radioresistant cells survives therapy. If cure cannot be achieved, protocols should balance volume reduction with minimal selection for radioresistant cells. We show that the most efficient treatment schedule is dependent on biology and model parameter values and, therefore, emphasize the need for careful tumor-specific model calibration before clinically actionable conclusions can be drawn.