Estimating dose painting effects in radiotherapy: a mathematical model

Modeling of chemo-radiotherapy targeting growing vascular tumors: A continuum-level approach

The aim of this study is to demonstrate the enhanced efficiency of combined therapeutic strategies for the treatment of growing tumors, based on computational experiments of a continuous-level modeling framework. In particular, the tumor growth is simulated within a host tissue and treated as a multiphase fluid, with each cellular species considered as a distinct fluid phase. Our model integrates the impact of chemical species on tumor dynamics, and we model -through reaction-diffusion equations- the spatio-temporal evolution of oxygen, vascular endothelial growth factor (VEGF) and chemotherapeutic agents. Simulations of a growing tumor exposed to external radiation showcase the rapid impact of radiotherapy on tumor suppression, however this effect diminishes over time. To enhance the therapeutic efficiency of radiotherapy, we investigate the combination of external radiation with the anti-VEGF drug bevacizumab and the cytotoxic drug docetaxel. Our simulations demonstrate that this synergistic approach integrates the immediate effectiveness of radiation therapy with the enduring tumor-suppressive capabilities of chemotherapy.

Rethinking the potential role of dose painting in personalized ultra-fractionated stereotactic adaptive radiotherapy

Fractionated radiotherapy was established in the 1920s based upon two principles: (1) delivering daily treatments of equal quantity, unless the clinical situation requires adjustment, and (2) defining a specific treatment period to deliver a total dosage. Modern fractionated radiotherapy continues to adhere to these century-old principles, despite significant advancements in our understanding of radiobiology. At UT Southwestern, we are exploring a novel treatment approach called PULSAR (Personalized Ultra-Fractionated Stereotactic Adaptive Radiotherapy). This method involves administering tumoricidal doses in a pulse mode with extended intervals, typically spanning weeks or even a month. Extended intervals permit substantial recovery of normal tissues and afford the tumor and tumor microenvironment ample time to undergo significant changes, enabling more meaningful adaptation in response to the evolving characteristics of the tumor. The notion of dose painting in the realm of radiation therapy has long been a subject of contention. The debate primarily revolves around its clinical effectiveness and optimal methods of implementation. In this perspective, we discuss two facets concerning the potential integration of dose painting with PULSAR, along with several practical considerations. If successful, the combination of the two may not only provide another level of personal adaptation ("adaptive dose painting"), but also contribute to the establishment of a timely feedback loop throughout the treatment process. To substantiate our perspective, we conducted a fundamental modeling study focusing on PET-guided dose painting, incorporating tumor heterogeneity and tumor control probability (TCP).

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.

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.

Investigating the Influence of Growth Arrest Mechanisms on Tumour Responses to Radiotherapy

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific treatment design. In this paper, we investigate how two different mechanisms for growth control may affect tumour cell responses to fractionated radiotherapy (RT) by extending an existing ordinary differential equation model of tumour growth. In the absence of treatment, this model distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes: nutrient limited, space limited (SL) and bistable (BS), where both mechanisms for growth arrest coexist. We study the effect of RT for tumours in each regime, finding that tumours in the SL regime typically respond best to RT, while tumours in the BS regime typically respond worst to RT. For tumours in each regime, we also identify the biological processes that may explain positive and negative treatment outcomes and the dosing regimen which maximises the reduction in tumour burden.

Cancer Therapy Assessment Accounting for Heterogeneity Using q-Rung Picture Fuzzy Dynamic Aggregation Approach

Due to the fact that there is no symmetry in the division of cancer cells, it is important to consider this asymmetrical behavior. Because of this heterogeneity during any therapy, not every cancer cell that is killed only is abolished, which is sensitive to the particular treatment chosen. Mathematical models that describe these pathways are critical for predicting cancer cell proliferation behavior. The literature on the mathematical modeling of cancer onset, growth, and metastasis is extensive. Both deterministic and stochastic factors were used to develop mathematical models to mimic the development rate of cancer cells. We focus on the cell’s heterogeneity in our model so that the cells generally responsible for spreading cancer, which are called stem cells, can be killed. Aggregation operators (AOs) play an important role in decision making, especially when there are several competing factors. A key issue in the case of uncertain data is to develop appropriate solutions for the aggregation process. We presented two novel Einstein AOs: q-rung picture fuzzy dynamic Einstein weighted averaging (q-RPFDEWA) operator and q-rung picture fuzzy dynamic Einstein weighted geometric (q-RPFDEWG) operator. Several enticing aspects of these AOs are thoroughly discussed. Furthermore, we provide a method for dealing with multi-period decision-making (MPDM) issues by applying optimal solutions. A numerical example is presented to explain how the recommended technique can be used in cancer therapy assessment. Authenticity analysis is also presented to demonstrate the efficacy of the proposed technique. The suggested AOs and decision-making methodologies are generally applicable in real-world multi-stage and dynamic decision analysis.

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.

Reciprocal interactions between tumour cell populations enhance growth and reduce radiation sensitivity in prostate cancer

Intratumoural heterogeneity (ITH) contributes to local recurrence following radiotherapy in prostate cancer. Recent studies also show that ecological interactions between heterogeneous tumour cell populations can lead to resistance in chemotherapy. Here, we evaluated whether interactions between heterogenous populations could impact growth and response to radiotherapy in prostate cancer. Using mixed 3D cultures of parental and radioresistant populations from two prostate cancer cell lines and a predator-prey mathematical model to investigate various types of ecological interactions, we show that reciprocal interactions between heterogeneous populations enhance overall growth and reduce radiation sensitivity. The type of interaction influences the time of regrowth after radiation, and, at the population level, alters the survival and cell cycle of each population without eliminating either one. These interactions can arise from oxygen constraints and from cellular cross-talk that alter the tumour microenvironment. These findings suggest that ecological-type interactions are important in radiation response and could be targeted to reduce local recurrence.

Small Animal IMRT Using 3D-Printed Compensators

PURPOSE

Preclinical radiation replicating clinical intensity modulated radiation therapy (IMRT) techniques can provide data translatable to clinical practice. For this work, treatment plans were created for oxygen-guided dose-painting in small animals using inverse-planned IMRT. Spatially varying beam intensities were achieved using 3-dimensional (3D)-printed compensators.

METHODS AND MATERIALS

Optimized beam fluence from arbitrary gantry angles was determined using a verified model of the XRAD225Cx treatment beam. Compensators were 3D-printed with varied thickness to provide desired attenuation using copper/polylactic-acid. Spatial resolution capabilities were investigated using printed test-patterns. Following American Association of Physicists in Medicine TG119, a 5-beam IMRT plan was created for a miniaturized (∼1/8th scale) C-shape target. Electron paramagnetic resonance imaging of murine tumor oxygenation guided simultaneous integrated boost (SIB) plans conformally treating tumor to a base dose (Rx₁) with boost (Rx₂) based on tumor oxygenation. The 3D-printed compensator intensity modulation accuracy and precision was evaluated by individually delivering each field to a phantom containing radiochromic film and subsequent per-field gamma analysis. The methodology was validated end-to-end with composite delivery (incorporating 3D-printed tungsten/polylactic-acid beam trimmers to reduce out-of-field leakage) of the oxygen-guided SIB plan to a phantom containing film and subsequent gamma analysis.

RESULTS

Resolution test-patterns demonstrate practical printer resolution of ∼0.7 mm, corresponding to 1.0 mm bixels at the isocenter. The miniaturized C-shape plan provides planning target volume coverage (V_95% = 95%) with organ sparing (organs at risk D_max < 50%). The SIB plan to hypoxic tumor demonstrates the utility of this approach (hypoxic tumor V_95%,Rx2 = 91.6%, normoxic tumor V_95%,Rx1 = 95.7%, normal tissue V_100%,Rx1 = 7.1%). The more challenging SIB plan to boost the normoxic tumor rim achieved normoxic tumor V_95%,Rx2 = 90.9%, hypoxic tumor V_95%,Rx1 = 62.7%, and normal tissue V_100%,Rx2 = 5.3%. Average per-field gamma passing rates using 3%/1.0 mm, 3%/0.7 mm, and 3%/0.5 mm criteria were 98.8% ± 2.8%, 96.6% ± 4.1%, and 90.6% ± 5.9%, respectively. Composite delivery of the hypoxia boost plan and gamma analysis (3%/1 mm) gave passing results of 95.3% and 98.1% for the 2 measured orthogonal dose planes.

CONCLUSIONS

This simple and cost-effective approach using 3D-printed compensators for small-animal IMRT provides a methodology enabling preclinical studies that can be readily translated into the clinic. The presented oxygen-guided dose-painting demonstrates that this methodology will facilitate studies driving much needed biologic personalization of radiation therapy for improvements in patient outcomes.

Immunologic Consequences of Sequencing Cancer Radiotherapy and Surgery

PURPOSE

Early-stage cancers are routinely treated with surgery followed by radiotherapy (SR). Radiotherapy before surgery (RS) has been widely ignored for some cancers. We evaluate overall survival (OS) and disease-free survival (DFS) with SR and RS for different cancer types and simulate the plausibility of RS- and SR-induced antitumor immunity contributing to outcomes.

MATERIALS AND METHODS

We analyzed a SEER data set of early-stage cancers treated with SR or RS. OS and DFS were calculated for cancers with sufficient numbers for statistical power (cancers of lung and bronchus, esophagus, rectum, cervix uteri, corpus uteri, and breast). We simulated the immunologic consequences of SR, RS, and radiotherapy alone in a mathematical model of tumor-immune interactions.

RESULTS

RS improved OS for cancers with low 20-year survival rates (lung: hazard ratio [HR], 0.88; P = .046) and improved DFS for cancers with higher survival (breast: HR = 0.64; P < .001). For rectal cancer, with intermediate 20-year survival, RS improved both OS (HR = 0.89; P = .006) and DFS (HR = 0.86; P = .04). Model simulations suggested that RS could increase OS by eliminating cancer for a broader range of model parameters and radiotherapy-induced antitumor immunity compared with SR for selected parameter combinations. This could create an immune memory that may explain increased DFS after RS for certain cancers.

CONCLUSION

Study results suggest plausibility that radiation to the bulk of the tumor could induce a more robust immune response and better harness the synergy of radiotherapy and antitumor immunity than postsurgical radiation to the tumor bed. This exploratory study provides motivation for prospective evaluation of immune activation of RS versus SR in controlled clinical studies.

On the Immunological Consequences of Conventionally Fractionated Radiotherapy

Emerging evidence demonstrates that radiotherapy induces immunogenic death on tumor cells that emit immunostimulating signals resulting in tumor-specific immune responses. However, the impact of tumor features and microenvironmental factors on the efficacy of radiation-induced immunity remains to be elucidated. Herein, we use a calibrated model of tumor-effector cell interactions to investigate the potential benefits and immunological consequences of radiotherapy. Simulations analysis suggests that radiotherapy success depends on the functional tumor vascularity extent and reveals that the pre-treatment tumor size is not a consistent determinant of treatment outcomes. The one-size-fits-all approach of conventionally fractionated radiotherapy is predicted to result in some overtreated patients. In addition, model simulations also suggest that an arbitrary increase in treatment duration does not necessarily result in better tumor control. This study highlights the potential benefits of tumor-immune ecosystem profiling during treatment planning to better harness the immunogenic potential of radiotherapy.

•

Radiotherapy success depends on radiation-induced tumor-specific immune responses

•

Pre-treatment tumor size is not a consistent determinant of radiotherapy outcomes

•

Increase in treatment duration does not necessarily result in better tumor control

•

Tumor vascularity impacts antitumor efficacy of radiation-induced immune responses

A minimal modeling framework of radiation and immune system synergy to assist radiotherapy planning

Recent evidence indicates the ability of radiotherapy to induce local and systemic tumor-specific immune responses as a result of immunogenic cell death. However, fractionation regimes routinely used in clinical practice typically ignore the synergy between radiation and the immune system, and instead attempt to completely eradicate tumors by the direct lethal effect of radiation on cancer cells. This paradigm is expected to change in the near future due to the potential benefits of considering radiation-induced antitumor immunity during treatment planning. Towards this goal, we propose a minimal modeling framework based on key aspects of the tumor-immune system interplay to simulate the effects of radiation on tumors and the immunological consequences of radiotherapy. The impacts of tumor-associated vasculature and intratumoral oxygen-mediated heterogeneity on treatment outcomes are ininvestigated. The model provides estimates of the minimum radiation doses required for tumor eradication given a certain number of treatment fractions. Moreover, estimates of treatment duration for disease control given predetermined fractional radiation doses can be also obtained. Although theoretical in nature, this study motivates the development and establishment of immune-based decision-support tools in radiotherapy planning.

Towards Multidrug Adaptive Therapy

A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

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.

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

Modeling the effect of intratumoral heterogeneity of radiosensitivity on tumor response over the course of fractionated radiation therapy

Background

Standard radiobiology theory of radiation response assumes a uniform innate radiosensitivity of tumors. However, experimental data show that there is significant intratumoral heterogeneity of radiosensitivity. Therefore, a model with heterogeneity was developed and tested using existing experimental data to show the potential effects from the presence of an intratumoral distribution of radiosensitivity on radiation therapy response over a protracted radiation therapy treatment course.

Methods

The standard radiation response curve was modified to account for a distribution of radiosensitivity, and for variations in the repopulation rates of the tumor cell subpopulations. Experimental data from the literature were incorporated to determine the boundaries of the model. The proposed model was then used to show the changes in radiosensitivity of the tumor during treatment, and the effects of fraction size, α/β ratio and variation of the repopulation rates of tumor cells.

Results

In the presence of an intratumoral distribution of radiosensitivity, there is rapid selection of radiation-resistant cells over a course of fractionated radiation therapy. Standard treatment fractionation regimes result in the near-complete replacement of the initial population of sensitive cells with a population of more resistant cells. Further, as treatment progresses, the tumor becomes more resistant to further radiation treatment, making each fractional dose less efficacious. A wider initial distribution induces increased radiation resistance. Hypofractionation is more efficient in a heterogeneous tumor, with increased cell kill for biologically equivalent doses, while inducing less resistance. The model also shows that a higher growth rate in resistant cells can account for the accelerated repopulation that is seen during the clinical treatment of patients.

Conclusions

Modeling of tumor cell survival with radiosensitivity heterogeneity alters the predicted tumor response, and explains the induction of radiation resistance by radiation treatment, the development of accelerated repopulation, and the potential beneficial effects of hypofractionation. Tumor response to treatment may be better predicted by assaying for the distribution of radiosensitivity, or the extreme of the radiosensitivity, rather than measuring the initial, general radiation sensitivity of the untreated tumor.

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.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

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.

Radiomics in Nuclear Medicine Applied to Radiation Therapy: Methods, Pitfalls, and Challenges

Radiomics is a recent area of research in precision medicine and is based on the extraction of a large variety of features from medical images. In the field of radiation oncology, comprehensive image analysis is crucial to personalization of treatments. A better characterization of local heterogeneity and the shape of the tumor, depicting individual cancer aggressiveness, could guide dose planning and suggest volumes in which a higher dose is needed for better tumor control. In addition, noninvasive imaging features that could predict treatment outcome from baseline scans could help the radiation oncologist to determine the best treatment strategies and to stratify patients as at low risk or high risk of recurrence. Nuclear medicine molecular imaging reflects information regarding biological processes in the tumor thanks to a wide range of radiotracers. Many studies involving ¹⁸F-fluorodeoxyglucose positron emission tomography suggest an added value of radiomics compared with the use of conventional PET metrics such as standardized uptake value for both tumor diagnosis and prediction of recurrence or treatment outcome. However, these promising results should not hide technical difficulties that still currently prevent the approach from being widely studied or clinically used. These difficulties mostly pertain to the variability of the imaging features as a function of the acquisition device and protocol, the robustness of the models with respect to that variability, and the interpretation of the radiomic models. Addressing the impact of the variability in acquisition and reconstruction protocols is needed, as is harmonizing the radiomic feature calculation methods, to ensure the reproducibility of studies in a multicenter context and their implementation in a clinical workflow. In this review, we explain the potential impact of positron emission tomography radiomics for radiation therapy and underline the various aspects that need to be carefully addressed to make the most of this promising approach.

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.

Homeostasis Back and Forth: An Ecoevolutionary Perspective of Cancer

The role of genetic mutations in cancer is indisputable: They are a key source of tumor heterogeneity and drive its evolution to malignancy. But, the success of these new mutant cells relies on their ability to disrupt the homeostasis that characterizes healthy tissues. Mutated clones unable to break free from intrinsic and extrinsic homeostatic controls will fail to establish a tumor. Here, we will discuss, through the lens of mathematical and computational modeling, why an evolutionary view of cancer needs to be complemented by an ecological perspective to understand why cancer cells invade and subsequently transform their environment during progression. Importantly, this ecological perspective needs to account for tissue homeostasis in the organs that tumors invade, because they perturb the normal regulatory dynamics of these tissues, often coopting them for its own gain. Furthermore, given our current lack of success in treating advanced metastatic cancers through tumor-centric therapeutic strategies, we propose that treatments that aim to restore homeostasis could become a promising venue of clinical research. This ecoevolutionary view of cancer requires mechanistic mathematical models to both integrate clinical with biological data from different scales but also to detangle the dynamic feedback between the tumor and its environment. Importantly, for these models to be useful, they need to embrace a higher degree of complexity than many mathematical modelers are traditionally comfortable with.

Therapeutic Potential of Bacteria against Solid Tumors

Intentional bacterial infections can produce efficacious antitumor responses in mice, rats, dogs, and humans. However, low overall success rates and intense side effects prevent such approaches from being employed clinically. In this work, we titered bacteria and/or the proinflammatory cytokine TNFα in a set of established murine models of cancer. To interpret the experiments conducted, we considered and calibrated a tumor-effector cell recruitment model under the influence of functional tumor-associated vasculature. In this model, bacterial infections and TNFα enhanced immune activity and altered vascularization in the tumor bed. Information to predict bacterial therapy outcomes was provided by pretreatment tumor size and the underlying immune recruitment dynamics. Notably, increasing bacterial loads did not necessarily produce better long-term tumor control, suggesting that tumor sizes affected optimal bacterial loads. Short-term treatment responses were favored by high concentrations of effector cells postinjection, such as induced by higher bacterial loads, but in the longer term did not correlate with an effective restoration of immune surveillance. Overall, our findings suggested that a combination of intermediate bacterial loads with low levels TNFα administration could enable more favorable outcomes elicited by bacterial infections in tumor-bearing subjects. Cancer Res; 77(7); 1553-63. ©2017 AACR.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

Cancer therapeutic potential of combinatorial immuno- and vasomodulatory interventions

Currently, most of the basic mechanisms governing tumour-immune system interactions, in combination with modulations of tumour-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumour growth, where the main novelty is the modelling of the interplay between functional tumour vasculature and effector cell recruitment dynamics. Parameters are calibrated on the basis of different in vivo immunocompromised Rag1(-/-) and wild-type (WT) BALB/c murine tumour growth experiments. The model analysis supports that tumour vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immunostimulations. We find that improved levels of functional tumour vasculature, potentially mediated by normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumour burden reduction and growth control. Normalization of tumour blood vessels opens a therapeutic window of opportunity to augment the antitumour immune responses, as well as to reduce intratumoral immunosuppression and induced hypoxia due to vascular abnormalities. The potential success of normalizing tumour-associated vasculature closely depends on the effector cell recruitment dynamics and tumour sizes. Furthermore, an arbitrary increase in the initial effector cell concentration does not necessarily imply better tumour control. We evidence the existence of an optimal concentration range of effector cells for tumour shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immuno- and vasomodulatory interventions.

Variations in target volume definition and dose to normal tissue using anatomic versus biological imaging (18 F-FDG-PET) in the treatment of bone metastases: results from a 3-arm randomized phase II trial

INTRODUCTION

To report the impact on target volume delineation and dose to normal tissue using anatomic versus biological imaging (¹⁸ F-FDG-PET) for bone metastases.

METHODS

Patients with uncomplicated painful bone metastases were randomized (1:1:1) and blinded to receive either 8 Gy in a single fraction with conventionally planned radiotherapy (ConvRT-8 Gy) or 8 Gy in a single fraction with dose-painting-by-numbers (DPBN) dose range between 6 and 10 Gy) (DPBN-8 Gy) or 16 Gy in a single fraction with DPBN (dose range between 14 and 18 Gy) (DPBN-16 Gy). The primary endpoint was overall pain response at 1 month. Volumes of the gross tumour volume (GTV) - both biological (GTV_PET ) and anatomical (GTV_CT ) -, planning target volume (PTV), dose to the normal tissue and maximum standardized-uptake values (SUV_MAX ) were analysed (secondary endpoint).

RESULTS

Sixty-three percent of the GTV_CT volume did not show ¹⁸ F-FDG-uptake. On average, 20% of the GTV_PET volume was outside GTV_CT . The volume of normal tissue receiving 4 Gy, 6 Gy and 8 Gy was at least 3×, 6× and 13× smaller in DPBN-8 Gy compared to ConvRT-8 Gy and DPBN-16 Gy (P < 0.05).

CONCLUSION

Positron emitting tomography-information potentially changes the target volume for bone metastases. DPBN between 6 and 10 Gy significantly decreases dose to the normal tissue compared to conventional radiotherapy.

Monitoring cancer stem cells: insights into clinical oncology

Cancer stem cells (CSCs) are a small, characteristically distinctive subset of tumor cells responsible for tumor initiation and progression. Several treatment modalities, such as surgery, glycolytic inhibition, driving CSC proliferation, immunotherapy, and hypofractionated radiotherapy, may have the potential to eradicate CSCs. We propose that monitoring CSCs is important in clinical oncology as CSC populations may reflect true treatment response and assist with managing treatment strategies, such as defining optimal chemotherapy cycles, permitting pretreatment cancer surveillance, conducting a comprehensive treatment plan, modifying radiation treatment, and deploying rechallenge chemotherapy. Then, we describe methods for monitoring CSCs.

Artificial Life in Quantum Technologies

We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies.

Spatial Metrics of Tumour Vascular Organisation Predict Radiation Efficacy in a Computational Model

Intratumoural heterogeneity is known to contribute to poor therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the underlying variations in oxygen tension. We seek to determine whether histologic scale measures of the erratic distribution of blood vessels within a tumour can be used to predict differing radiation response. Using a two-dimensional hybrid cellular automaton model of tumour growth, we evaluate the effect of vessel distribution on cell survival outcomes of simulated radiation therapy. Using the standard equations for the oxygen enhancement ratio for cell survival probability under differing oxygen tensions, we calculate average radiation effect over a range of different vessel densities and organisations. We go on to quantify the vessel distribution heterogeneity and measure spatial organization using Ripley’s L function, a measure designed to detect deviations from complete spatial randomness. We find that under differing regimes of vessel density the correlation coefficient between the measure of spatial organization and radiation effect changes sign. This provides not only a useful way to understand the differences seen in radiation effect for tissues based on vessel architecture, but also an alternate explanation for the vessel normalization hypothesis.

In this paper we use a mathematical model, called a hybrid cellular automaton, to study the effect of different vessel distributions on radiation therapy outcomes at the cellular level. We show that the correlation between radiation outcome and spatial organization of vessels changes signs between relatively low and high vessel density. Specifically, that for relatively low vessel density, radiation efficacy is decreased when vessels are more homogeneously distributed, and the opposite is true, that radiation efficacy is improved, when vessel organisation is normalised in high densities. This result suggests an alteration to the vessel normalization hypothesis which states that normalisation of vascular beds should improve radio- and chemo-therapeutic response, but has failed to be validated in clinical studies. In this alteration, we show that Ripley’s L function allows discrimination between vascular architectures in different density regimes in which the standard hypothesis holds and does not hold. Further, we find that this information can be used to augment quantitative histologic analysis of tumours to aid radiation dose personalisation.

A dose-volume histogram based decision-support system for dosimetric comparison of radiotherapy treatment plans

Background

The choice of any radiotherapy treatment plan is usually made after the evaluation of a few preliminary isodose distributions obtained from different beam configurations. Despite considerable advances in planning techniques, such final decision remains a challenging task that would greatly benefit from efficient and reliable assessment tools.

Methods

For any dosimetric plan considered, data on dose-volume histograms supplied by treatment planning systems are used to provide estimates on planning target coverage as well as on sparing of organs at risk and the remaining healthy tissue. These partial metrics are then combined into a dose distribution index (DDI), which provides a unified, easy-to-read score for each competing radiotherapy plan. To assess the performance of the proposed scoring system, DDI figures for fifty brain cancer patients were retrospectively evaluated. Patients were divided in three groups depending on tumor location and malignancy. For each patient, three tentative plans were designed and recorded during planning, one of which was eventually selected for treatment. We thus were able to compare the plans with better DDI scores and those actually delivered.

Results

When planning target coverage and organs at risk sparing are considered as equally important, the tentative plan with the highest DDI score is shown to coincide with that actually delivered in 32 of the 50 patients considered. In 15 (respectively 3) of the remaining 18 cases, the plan with highest DDI value still coincides with that actually selected, provided that organs at risk sparing is given higher priority (respectively, lower priority) than target coverage.

Conclusions

DDI provides a straightforward and non-subjective tool for dosimetric comparison of tentative radiotherapy plans. In particular, DDI readily quantifies differences among competing plans with similar-looking dose-volume histograms and can be easily implemented for any tumor type and localization, irrespective of the planning system and irradiation technique considered. Moreover, DDI permits to estimate the dosimetry impact of different priorities being assigned to sparing of organs at risk or to better target coverage.

Cancer Stem Cell Plasticity as Tumor Growth Promoter and Catalyst of Population Collapse

It is increasingly argued that cancer stem cells are not a cellular phenotype but rather a transient state that cells can acquire, either through intrinsic signaling cascades or in response to environmental cues. While cancer stem cell plasticity is generally associated with increased aggressiveness and treatment resistance, we set out to thoroughly investigate the impact of different rates of plasticity on early and late tumor growth dynamics and the response to therapy. We develop an agent-based model of cancer stem cell driven tumor growth, in which plasticity is defined as a spontaneous transition between stem and nonstem cancer cell states. Simulations of the model show that plasticity can substantially increase tumor growth rate and invasion. At high rates of plasticity, however, the cells get exhausted and the tumor will undergo spontaneous remission in the long term. In a series of in silico trials, we show that such remission can be facilitated through radiotherapy. The presented study suggests that stem cell plasticity has rather complex, nonintuitive implications on tumor growth and treatment response. Further theoretical, experimental, and integrated studies are needed to fully decipher cancer stem cell plasticity and how it can be harnessed for novel therapeutic approaches.

Spatio-Temporal Dynamics of Hypoxia during Radiotherapy

Tumour hypoxia plays a pivotal role in cancer therapy for most therapeutic approaches from radiotherapy to immunotherapy. The detailed and accurate knowledge of the oxygen distribution in a tumour is necessary in order to determine the right treatment strategy. Still, due to the limited spatial and temporal resolution of imaging methods as well as lacking fundamental understanding of internal oxygenation dynamics in tumours, the precise oxygen distribution map is rarely available for treatment planing. We employ an agent-based in silico tumour spheroid model in order to study the complex, localized and fast oxygen dynamics in tumour micro-regions which are induced by radiotherapy. A lattice-free, 3D, agent-based approach for cell representation is coupled with a high-resolution diffusion solver that includes a tissue density-dependent diffusion coefficient. This allows us to assess the space- and time-resolved reoxygenation response of a small subvolume of tumour tissue in response to radiotherapy. In response to irradiation the tumour nodule exhibits characteristic reoxygenation and re-depletion dynamics which we resolve with high spatio-temporal resolution. The reoxygenation follows specific timings, which should be respected in treatment in order to maximise the use of the oxygen enhancement effects. Oxygen dynamics within the tumour create windows of opportunity for the use of adjuvant chemotherapeutica and hypoxia-activated drugs. Overall, we show that by using modelling it is possible to follow the oxygenation dynamics beyond common resolution limits and predict beneficial strategies for therapy and in vitro verification. Models of cell cycle and oxygen dynamics in tumours should in the future be combined with imaging techniques, to allow for a systematic experimental study of possible improved schedules and to ultimately extend the reach of oxygenation monitoring available in clinical treatment.

Cancer stem cells: small subpopulation or evolving fraction?

This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.

A matter of timing: identifying significant multi-dose radiotherapy improvements by numerical simulation and genetic algorithm search

Multi-dose radiotherapy protocols (fraction dose and timing) currently used in the clinic are the product of human selection based on habit, received wisdom, physician experience and intra-day patient timetabling. However, due to combinatorial considerations, the potential treatment protocol space for a given total dose or treatment length is enormous, even for relatively coarse search; well beyond the capacity of traditional in-vitro methods. In constrast, high fidelity numerical simulation of tumor development is well suited to the challenge. Building on our previous single-dose numerical simulation model of EMT6/Ro spheroids, a multi-dose irradiation response module is added and calibrated to the effective dose arising from 18 independent multi-dose treatment programs available in the experimental literature. With the developed model a constrained, non-linear, search for better performing cadidate protocols is conducted within the vicinity of two benchmarks by genetic algorithm (GA) techniques. After evaluating less than 0.01% of the potential benchmark protocol space, candidate protocols were identified by the GA which conferred an average of 9.4% (max benefit 16.5%) and 7.1% (13.3%) improvement (reduction) on tumour cell count compared to the two benchmarks, respectively. Noticing that a convergent phenomenon of the top performing protocols was their temporal synchronicity, a further series of numerical experiments was conducted with periodic time-gap protocols (10 h to 23 h), leading to the discovery that the performance of the GA search candidates could be replicated by 17-18 h periodic candidates. Further dynamic irradiation-response cell-phase analysis revealed that such periodicity cohered with latent EMT6/Ro cell-phase temporal patterning. Taken together, this study provides powerful evidence towards the hypothesis that even simple inter-fraction timing variations for a given fractional dose program may present a facile, and highly cost-effecitive means of significantly improving clinical efficacy.