Modelling tumour oxygenation, reoxygenation and implications on treatment outcome

Deciphering oxygen distribution and hypoxia profiles in the tumor microenvironment: a data-driven mechanistic modeling approach

Objective. The distribution of hypoxia within tissues plays a critical role in tumor diagnosis and prognosis. Recognizing the significance of tumor oxygenation and hypoxia gradients, we introduce mathematical frameworks grounded in mechanistic modeling approaches for their quantitative assessment within a tumor microenvironment. By utilizing known blood vasculature, we aim to predict hypoxia levels across different tumor types.Approach. Our approach offers a computational method to measure and predict hypoxia using known blood vasculature. By formulating a reaction-diffusion model for oxygen distribution, we derive the corresponding hypoxia profile.Main results. The framework successfully replicates observed inter- and intra-tumor heterogeneity in experimentally obtained hypoxia profiles across various tumor types (breast, ovarian, pancreatic). Additionally, we propose a data-driven method to deduce partial differential equation models with spatially dependent parameters, which allows us to comprehend the variability of hypoxia profiles within tissues. The versatility of our framework lies in capturing diverse and dynamic behaviors of tumor oxygenation, as well as categorizing states of vascularization based on the dynamics of oxygen molecules, as identified by the model parameters.Significance. The proposed data-informed mechanistic method quantitatively assesses hypoxia in the tumor microenvironment by integrating diverse histopathological data and making predictions across different types of data. The framework provides valuable insights from both modeling and biological perspectives, advancing our comprehension of spatio-temporal dynamics of tumor oxygenation.

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

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

Hypoxia dose painting in SBRT - the virtual clinical trial approach

BACKGROUND

Treating hypoxic tumours remains a challenge in radiotherapy as hypoxia leads to enhanced tumour aggressiveness and resistance to radiation. As escalating the doses is rarely feasible within the healthy tissue constraints, dose-painting strategies have been explored. Consensus about the best of care for hypoxic tumours has however not been reached because, among other reasons, the limits of current functional in-vivo imaging systems in resolving the details and dynamics of oxygen transport in tissue. Computational modelling of the tumour microenvironment enables the design and conduction of virtual clinical trials by providing relationships between biological features and treatment outcomes. This study presents a framework for assessing the therapeutic influence of the individual characteristics of the vasculature and the resulting oxygenation of hypoxic tumours in a virtual clinical trial on dose painting in stereotactic body radiotherapy (SBRT) circumventing the limitations of the imaging systems.

MATERIAL AND METHODS

The homogeneous doses required to overcome hypoxia in simulated SBRT treatments of 1, 3 or 5 fractions were calculated for tumours with heterogeneous oxygenation derived from virtual vascular networks. The tumour control probability (TCP) was calculated for different scenarios for oxygenation dynamics resulting on cellular reoxygenation.

RESULTS

A three-fractions SBRT treatment delivering 41.9 Gy (SD 2.8) and 26.5 Gy (SD 0.1) achieved only 21% (SD 12) and 48% (SD 17) control in the hypoxic and normoxic subvolumes, respectively whereas fast reoxygenation improved the control by 30% to 50%. TCP values for the individual tumours with similar characteristics, however, might differ substantially, highlighting the crucial role of the magnitude and time evolution of hypoxia at the microscale.

CONCLUSION

The results show that local microvascular heterogeneities may affect the predicted outcome in the hypoxic core despite escalated doses, emphasizing the role of theoretical modelling in understanding of and accounting for the dominant factors of the tumour microenvironment.

The Impact of Heterogeneous Cell Density in Hypoxic Tumors Treated with Radiotherapy

Hypoxia is frequently found in solid tumors and is known to increase the resistance to several kinds of treatment modalities including radiation therapy. Besides, the treatment response is also largely determined by the total number of clonogenic cells, i.e., cells with unlimited proliferative capacity. Depending on the duration of hypoxia, the rate of proliferation and hence also the clonogen density could be expected to differ in hypoxic compartments. The combination at the microscale between heterogeneous tumor oxygenation and clonogen density could therefore be crucial with respect to the outcome of a radiotherapy treatment. In this study it was investigated the impact of heterogeneous clonogen density on the outcome of stereotactic radiotherapy treatments of hypoxic tumors. A recently developed three-dimensional model for tissue vasculature and oxygenation was used to create realistic in silico tumors with heterogeneous oxygenation. Stereotactic radiotherapy treatments were simulated, and cell survival was calculated on a voxel-level accounting for the oxygenation. For a tumor with a diameter of 1 cm and a baseline clonogenic density of 107/cm3 for the normoxic subvolume, when the relative density for the hypoxic cells drops by a factor of 10 the tumor control probability (TCP) decreases by about 10% when relatively small hypoxic volumes and few fractions are considered; longer treatments tend to level out the results. With increasing size of the hypoxic subvolume, the TCP decreased overall as expected, and the difference in TCP between a homogeneous and a heterogeneous distribution of cells increased. The results demonstrate a delicate interplay between the heterogeneous distribution of tumor oxygenation and clonogenic cells that could significantly impact on the treatment outcome of radiotherapy.

Perfusion-Limited Hypoxia Determines the Outcome of Radiation Therapy of Hypoxic Tumours

Despite advancements in functional imaging, the resolution of modern techniques is still limited with respect to the tumour microenvironment. Radiotherapy strategies to counteract e.g., tumour hypoxia based on functional imaging therefore carry an inherent uncertainty that could compromise the outcome of the treatment. It was the aim of this study to investigate the impact of variations in the radiosensitivity of hypoxic tumours in small regions in comparison to the resolution of current imaging techniques on the probability of obtaining tumour control. A novel in silico model of three-dimensional tumour vasculature and oxygenation was used to model three tumours with different combinations of diffusion-limited, perfusion-limited and anaemic hypoxia. Specifically, cells in the transition region from a tumour core with diffusion-limited hypoxia to the well-oxygenated tumour rim were considered with respect to their differential radiosensitivity depending on the character of the hypoxia. The results showed that if the cells in the transition region were under perfusion-limited hypoxia, the tumour control probability was substantially lower in comparison to the case when the cells were anaemic (or under diffusion-limited hypoxia). This study therefore demonstrates the importance of differentiating between different forms of hypoxia on a scale currently unattainable to functional imaging techniques, lending support to the use and importance of radiobiological modelling of the cellular radiosensitivity and response at microscale.

Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue

In this paper we introduce a system of partial differential equations that is capable of modeling a variety of dynamic processes in soft tissue cellular populations and their microenvironments. The model is designed to be general enough to simulate such processes as tissue regeneration, tumor growth, immune response, and many more. It also has built-in flexibility to include multiple chemical fields and/or sub-populations of cells, interstitial fluid and/or extracellular matrix. The model is derived from the conservation laws for mass and linear momentum and therefore can be classified as a continuum multi-phase model. A careful choice of state variables provides stability in solving the system of discretized equations defining advective flux terms. A concept of deviation from normal allows us to use simplified constitutive relations for stresses. We also present an algorithm for computing numerical approximations to the solutions of the system and discuss properties of these approximations. We demonstrate several examples of applications of the model. Numerical simulations show a significant potential of the model for simulating a variety of processes in soft tissues.

Radiobiological Evaluation of Combined Gamma Knife Radiosurgery and Hyperthermia for Pediatric Neuro-Oncology

Simple Summary

This study proposes a novel strategy in brain cancer management. Stereotactic radiosurgery delivered by the Gamma Knife was combined with hyperthermia. For the radiobiological modelling of this synergistic treatment modality, we used the linear-quadratic model with temperature-dependent parameters to assess the potential enhancement of the therapeutic outcome. The results indicate that focused intracranial heating can be used to boost the dose to the target. Alternatively, one can conclude that for the same therapeutic effect, hyperthermia can help to minimize the dose undesirably delivered to healthy tissues. This study is also the first to advocate a combination of stereotactic radiosurgery with focused heating and motivates the future development of hyperthermia systems for brain cancer treatment.

Abstract

Combining radiotherapy (RT) with hyperthermia (HT) has been proven effective in the treatment of a wide range of tumours, but the combination of externally delivered, focused heat and stereotactic radiosurgery has never been investigated. We explore the potential of such treatment enhancement via radiobiological modelling, specifically via the linear-quadratic (LQ) model adapted to thermoradiotherapy through modulating the radiosensitivity of temperature-dependent parameters. We extend this well-established model by incorporating oxygenation effects. To illustrate the methodology, we present a clinically relevant application in pediatric oncology, which is novel in two ways. First, it deals with medulloblastoma, the most common malignant brain tumour in children, a type of brain tumour not previously reported in the literature of thermoradiotherapy studies. Second, it makes use of the Gamma Knife for the radiotherapy part, thereby being the first of its kind in this context. Quantitative metrics like the biologically effective dose (BED) and the tumour control probability (TCP) are used to assess the efficacy of the combined plan.

Molecular and functional imaging insights into the role of hypoxia in cancer aggression

Hypoxia in cancers has evoked significant interest since 1955 when Thomlinson and Gray postulated the presence of hypoxia in human lung cancers, based on the observation of necrosis occurring at the diffusion limit of oxygen from the nearest blood vessel, and identified the implication of these observations for radiation therapy. Coupled with discoveries in 1953 by Gray and others that anoxic cells were resistant to radiation damage, these observations have led to an entire field of research focused on exploiting oxygenation and hypoxia to improve the outcome of radiation therapy. Almost 65 years later, tumor heterogeneity of nearly every parameter measured including tumor oxygenation, and the dynamic landscape of cancers and their microenvironments are clearly evident, providing a strong rationale for cancer personalized medicine. Since hypoxia is a major cause of extracellular acidosis in tumors, here, we have focused on the applications of imaging to understand the effects of hypoxia in tumors and to target hypoxia in theranostic strategies. Molecular and functional imaging have critically important roles to play in personalized medicine through the detection of hypoxia, both spatially and temporally, and by providing new understanding of the role of hypoxia in cancer aggressiveness. With the discovery of the hypoxia-inducible factor (HIF), the intervening years have also seen significant progress in understanding the transcriptional regulation of hypoxia-induced genes. These advances have provided the ability to silence HIF and understand the associated molecular and functional consequences to expand our understanding of hypoxia and its role in cancer aggressiveness. Most recently, the development of hypoxia-based theranostic strategies that combine detection and therapy are further establishing imaging-based treatment strategies for precision medicine of cancer.

Simulation of hypoxia PET-tracer uptake in tumours: Dependence of clinical uptake-values on transport parameters and arterial input function

Poor radiotherapy outcome is in many cases related to hypoxia, due to the increased radioresistance of hypoxic tumour cells. Positron emission tomography may be used to non-invasively assess the oxygenation status of the tumour using hypoxia-specific radiotracers. Quantification and interpretation of these images remains challenging, since radiotracer binding and oxygen tension are not uniquely related. Computer simulation is a useful tool to improve the understanding of tracer dynamics and its relation to clinical uptake parameters currently used to quantify hypoxia. In this study, a model for simulating oxygen and radiotracer distribution in tumours was implemented to analyse the impact of physiological transport parameters and of the arterial input function (AIF) on: oxygenation histograms, time-activity curves, tracer binding and clinical uptake-values (tissue-to-blood ratio, TBR, and a composed hypoxia-perfusion metric, FHP). Results were obtained for parallel and orthogonal vessel architectures and for vascular fractions (VFs) of 1% and 3%. The most sensitive parameters were the AIF and the maximum binding rate (K_max). TBR allowed discriminating VF for different AIF, and FHP for different K_max, but neither TBR nor FHP were unbiased in all cases. Biases may especially occur in the comparison of TBR- or FHP-values between different tumours, where the relation between measured and actual AIF may vary. Thus, these parameters represent only surrogates rather than absolute measurements of hypoxia in tumours.

The Survival Benefit of Combination Therapy With Mild Temperature Hyperthermia and an Herbal Prescription of Gun-Chil-Jung in 54 Cancer Patients Treated With Chemotherapy or Radiation Therapy: A Retrospective Study

Background: The combination of herbal medicine with conventional treatment increases the survival rate of cancer patients, but the effect is not great. Hyperthermia may have a synergistic effect with herbal medicine alongside conventional medicine. Objective: To monitor the efficacy of hyperthermia together with Gun-Chil-Jung (GCJ) capsule for event-free survival (EFS) and overall survival (OS) for the treatment of various cancers. Methods: We collected data retrospectively on 54 cancer patients of all stages. They were divided into 4 groups according to each hyperthermia or GCJ treatment period. Hyperthermia with 0.46 MHz radiofrequency wave was applied a power of 50 to 100 W for 70 minutes. GCJ capsules were administered orally 3 times a day. Results: The median follow-up was 13.4 months, and 25 (55.6%) patients showed disease-related events. Hyperthermia with GCJ treatment was administered in combination group (n = 36, 66.7%) and traditional Korean medicine-only group (n = 17, 31.5%). The median EFS was 190 days, and the median OS was 390 days. The group of hyperthermia 7 times or fewer and GCJ more than 28 days showed longer EFS and OS. The analysis of superiority between hyperthermia and GCJ showed no significant difference (EFS, P = .55; OS, P = .364). Conclusions: The combination of hyperthermia 1 to 2 times a week with GCJ treatment may improve survival of cancer patients treated or being treated with conventional cancer therapies.

Impact of SBRT fractionation in hypoxia dose painting - Accounting for heterogeneous and dynamic tumor oxygenation

PURPOSE

Tumor hypoxia, often found in nonsmall cell lung cancer (NSCLC), implies an increased resistance to radiotherapy. Pretreatment assessment of tumor oxygenation is, therefore, warranted in these patients, as functional imaging of hypoxia could be used as a basis for dose painting. This study aimed at investigating the feasibility of using a method for calculating the dose required in hypoxic subvolumes segmented on ¹⁸ F-HX4 positron emission tomography (PET) imaging of NSCLC.

METHODS

Positron emission tomography imaging data based on the hypoxia tracer ¹⁸ F-HX4 of 19 NSCLC patients were included in the study. Normalized tracer uptake was converted to oxygen partial pressure (pO₂ ) and hypoxic target volumes (HTVs) were segmented using a threshold of 10 mmHg. Uniform doses required to overcome the hypoxic resistance in the target volumes were calculated based on a previously proposed method taking into account the effect of interfraction reoxygenation, for fractionation schedules ranging from extremely hypofractionated stereotactic body radiotherapy (SBRT) to conventionally fractionated radiotherapy.

RESULTS

Gross target volumes ranged between 6.2 and 859.6 cm³ , and the hypoxic fraction < 10 mmHg between 1.2% and 72.4%. The calculated doses for overcoming the resistance of cells in the HTVs were comparable to those currently prescribed in clinical practice as well as those previously tested in feasibility studies on dose escalation in NSCLC. Depending on the size of the HTV and the distribution of pO₂ , HTV doses were calculated as 43.6-48.4 Gy for a three-fraction schedule, 51.7-57.6 Gy for five fractions, and 59.5-66.4 Gy for eight fractions. For patients in whom the HTV pO₂ distribution was more favorable, a lower dose was required despite a bigger volume. Tumor control probability was lower for single-fraction schedules, while higher levels of tumor control probability were found for schedules employing several fractions.

CONCLUSIONS

The method to account for heterogeneous and dynamic hypoxia in target volume segmentation and dose prescription based on ¹⁸ F-HX4-PET imaging appears feasible in NSCLC patients. The distribution of oxygen partial pressure within HTV could impact the required prescribed dose more than the size of the volume.

Hypoxia Patterns in Primary and Metastatic Prostate Cancer Environments

Metastatic dissemination continues to be a major cause of prostate cancer (PCa) mortality, creating a compelling need to understand factors that play a role in the metastatic cascade. Since hypoxia plays an important role in PCa aggressiveness, we characterized patterns of hypoxia in the primary tumor and metastatic environments of a human PCa xenograft. We previously developed and characterized an imaging strategy based on the hypoxia response element (HRE)-driven expression of long-lived enhanced green fluorescent protein (EGFP) and short-lived luciferase (luc) fused to the oxygen-dependent degradation domain in human PCa PC-3 cells. Both reporter proteins were placed under the transcriptional control of a five-tandem repeat HRE sequence. PC-3 cells also constitutively expressed the tdTomato red fluorescent protein, allowing cancer cell detection in vivo. This "timer" strategy can provide information on the temporal evolution of HIF activity and hypoxia in tumors. Here, for the first time, we performed in vivo and ex vivo imaging of this dual HIF reporter system in PC-3 metastatic tumors implanted orthotopically in the prostate and PC-3 nonmetastatic tumors implanted subcutaneously. We observed distinct patterns of EGFP and luc expression in subcutaneous and orthotopic tumors, and in metastatic nodules, that provide new insights into the presence of hypoxia at primary and metastatic tumor sites, and of the role of hypoxia in metastasis.

Accounting for Two Forms of Hypoxia for Predicting Tumour Control Probability in Radiotherapy: An In Silico Study

The progress in functional imaging and dose delivery has opened the possibility of targeting tumour hypoxia with radiotherapy. Advanced approaches apply quantitative information on tumour oxygenation retrieved from imaging in dose prescription. These do not, however, take into account the potential difference in radiosensitivity of chronically and acutely hypoxic cells. It was the aim of this study to evaluate the implications of assuming the same or different sensitivities for the hypoxic cells. An in silico 3D-model of a hypoxic tumour with heterogeneous oxygenation was used to model the probabilities of tumour control with different radiotherapy regimens. The results show that by taking into account the potential lower radioresistance of chronically hypoxic cells deprived of oxygen and nutrients, the total dose required to achieve a certain level of control is substantially reduced for a given fractionation scheme in comparison to the case when chronically and acutely hypoxic cells are assumed to have similar features. The results also suggest that the presence of chronic hypoxia could explain the success of radiotherapy for some hypoxic tumours. Given the implications for clinical dose escalation trials, further exploration of the influence of the different forms of hypoxia on treatment outcome is therefore warranted.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

Hypoxia imaging and radiotherapy: bridging the resolution gap

Oxygen distribution is a major determinant of treatment success in radiotherapy, with well-oxygenated tumour regions responding by up to a factor of three relative to anoxic volumes. Conversely, tumour hypoxia is associated with treatment resistance and negative prognosis. Tumour oxygenation is highly heterogeneous and difficult to measure directly. The recent advent of functional hypoxia imaging modalities such as fluorine-18 fluoromisonidazole positron emission tomography have shown promise in non-invasively determining regions of low oxygen tension. This raises the prospect of selectively increasing dose to hypoxic subvolumes, a concept known as dose painting. Yet while this is a promising approach, oxygen-mediated radioresistance is inherently a multiscale problem, and there are still a number of substantial challenges that must be overcome if hypoxia dose painting is to be successfully implemented. Current imaging modalities are limited by the physics of such systems to have resolutions in the millimetre regime, whereas oxygen distribution varies over a micron scale, and treatment delivery is typically modulated on a centimetre scale. In this review, we examine the mechanistic basis and implications of the radiobiological oxygen effect, the factors influencing microscopic heterogeneity in tumour oxygenation and the consequent challenges in the interpretation of clinical hypoxia imaging (in particular fluorine-18 fluoromisonidazole positron emission tomography). We also discuss dose-painting approaches and outline challenges that must be addressed to improve this treatment paradigm.

How tumour-induced vascular changes alter angiogenesis: Insights from a computational model

A computational model was developed to describe experimentally observed vascular changes induced by the introduction of a tumour on a mouse equipped with a dorsal skinfold chamber. The vascular structure of the host tissue was segmented from in vivo images and transposed into the computational framework. Simulations of tumour-induced vascular changes were performed and include the destabilizing effects of the growth factor VEGF on the integrity of the vessels walls. The integration of those effects, that include alteration of the vessel wall elasticity and wall breaching, were required to realistically reproduce the experimental observations. The model was then used to investigate the importance of the vascular changes for oxygen delivery and tumour development. To that end, we compared simulations obtained with a dynamic vasculature with those obtained with a static one. The results showed that the tumour growth was strongly impeded by the constant vascular changes. More precisely, it is the angiogenic process itself that was affected by vascular changes occurring in bigger upstream vessels and resulting in a less efficient angiogenic network for oxygen delivery. As a consequence, tumour cells are mostly kept in a non-proliferative hypoxic state. Tumour dormancy thus appears as one potential consequence of the intense vascular changes in the host tissue.

The role of necrosis, acute hypoxia and chronic hypoxia in 18F-FMISO PET image contrast: a computational modelling study

Positron emission tomography (PET) using 18F-fluoromisonidazole (FMISO) is a promising technique for imaging tumour hypoxia, and a potential target for radiotherapy dose-painting. However, the relationship between FMISO uptake and oxygen partial pressure ([Formula: see text]) is yet to be quantified fully. Tissue oxygenation varies over distances much smaller than clinical PET resolution (<100 μm versus  ∼4 mm), and cyclic variations in tumour perfusion have been observed on timescales shorter than typical FMISO PET studies (∼20 min versus a few hours). Furthermore, tracer uptake may be decreased in voxels containing some degree of necrosis. This work develops a computational model of FMISO uptake in millimetre-scale tumour regions. Coupled partial differential equations govern the evolution of oxygen and FMISO distributions, and a dynamic vascular source map represents temporal variations in perfusion. Local FMISO binding capacity is modulated by the necrotic fraction. Outputs include spatiotemporal maps of [Formula: see text] and tracer accumulation, enabling calculation of tissue-to-blood ratios (TBRs) and time-activity curves (TACs) as a function of mean tissue oxygenation. The model is characterised using experimental data, finding half-maximal FMISO binding at local [Formula: see text] of 1.4 mmHg (95% CI: 0.3-2.6 mmHg) and half-maximal necrosis at 1.2 mmHg (0.1-4.9 mmHg). Simulations predict a non-linear non-monotonic relationship between FMISO activity (4 hr post-injection) and mean tissue [Formula: see text] : tracer uptake rises sharply from negligible levels in avascular tissue, peaking at  ∼5 mmHg and declining towards blood activity in well-oxygenated conditions. Greater temporal variation in perfusion increases peak TBRs (range 2.20-5.27) as a result of smaller predicted necrotic fraction, rather than fundamental differences in FMISO accumulation under acute hypoxia. Identical late FMISO uptake can occur in regions with differing [Formula: see text] and necrotic fraction, but simulated TACs indicate that additional early-phase information may allow discrimination of hypoxic and necrotic signals. We conclude that a robust approach to FMISO interpretation (and dose-painting prescription) is likely to be based on dynamic PET analysis.

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.

Optimal fractionation in radiotherapy for non-small cell lung cancer--a modelling approach

BACKGROUND

Conventionally fractionated radiotherapy (CFRT) has proven ineffective in treating non-small cell lung cancer while more promising results have been obtained with stereotactic body radiotherapy (SBRT). Hypoxic tumours, however, might present a challenge to extremely hypofractionated schedules due to the decreased possibility for inter-fraction fast reoxygenation. A potentially successful compromise might be found in schedules employing several fractions of varying fractional doses. In this modelling study, a wide range of fractionation schedules from single-fraction treatments to heterogeneous, multifraction schedules taking into account repair, repopulation, reoxygenation and radiosensitivity of the tumour cells, has been explored with respect to the probability of controlling lung tumours.

MATERIAL AND METHODS

The response to radiation of tumours with heterogeneous spatial and temporal oxygenation was simulated including the effects of accelerated repopulation and intra-fraction repair. Various treatments with respect to time, dose and fractionation were considered and the outcome was estimated as Poisson-based tumour control probability for local control.

RESULTS

For well oxygenated tumours, heterogeneous fractionation could increase local control while hypoxic tumours are not efficiently targeted by such treatments despite reoxygenation. For hypofractionated treatments employing large doses per fraction, a synergistic effect was observed between intra-fraction repair and inter-fraction fast reoxygenation of the hypoxic cells as demonstrated by a reduction in D50 from 53.3 Gy for 2 fractions to 52.7 Gy for 5 fractions.

CONCLUSIONS

For well oxygenated tumours, heterogeneous fractionation schedules could increase local control rates substantially compared to CFRT. For hypoxic tumours, SBRT-like hypofractionated schedules might be optimal despite the increased risk of intra-fraction repair due to a synergistic effect with inter-fraction reoxygenation.

Relative clinical effectiveness of carbon ion radiotherapy: theoretical modelling for H&N tumours

Comparison of the efficiency of photon and carbon ion radiotherapy (RT) administered with the same number of fractions might be of limited clinical interest, since a wide range of fractionation patterns are used clinically today. Due to advanced photon treatment techniques, hypofractionation is becoming increasingly accepted for prostate and lung tumours, whereas patients with head and neck tumours still benefit from hyperfractionated treatments. In general, the number of fractions is considerably lower in carbon ion RT. A clinically relevant comparison would be between fractionation schedules that are optimal within each treatment modality category. In this in silico study, the relative clinical effectiveness (RCE) of carbon ions was investigated for human salivary gland tumours, assuming various radiation sensitivities related to their oxygenation. The results indicate that, for hypoxic tumours in the absence of reoxygenation, the RCE (defined as the ratio of D(50) for photons to carbon ions) ranges from 3.5 to 5.7, corresponding to carbon ion treatments given in 36 and 3 fractions, respectively, and 30 fractions for photons. Assuming that interfraction local oxygenation changes take place, results for RCE are lower than that for an oxic tumour if only a few fractions of carbon ions are used. If the carbon ion treatment is given in more than 12 fractions, the RCE is larger for the hypoxic than for the well-oxygenated tumour. In conclusion, this study showed that in silico modelling enables the study of a wide range of factors in the clinical considerations and could be an important step towards individualisation of RT treatments.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

Survival and tumour control probability in tumours with heterogeneous oxygenation: a comparison between the linear-quadratic and the universal survival curve models for high doses

BACKGROUND

The validity of the linear-quadratic (LQ) model at high doses has been questioned due to a decreasing agreement between predicted survival and experimental cell survival data. A frequently proposed alternative is the universal survival curve (USC) model, thought to provide a better fit in the high-dose region. The comparison between the predictions of the models has mostly been performed for uniform populations of cells with respect to sensitivity to radiation. This study aimed to compare the two models in terms of cell survival and tumour control probability (TCP) for cell populations with mixed sensitivities related to their oxygenation.

METHODS

The study was performed in two parts. For the first part, cell survival curves were calculated with both models assuming various homogeneous populations of cells irradiated with uniform doses. For the second part, a realistic three-dimensional (3D) model of complex tumour oxygenation was used to study the impact of the differences in cell survival on the modelled TCP. Cellular response was assessed with the LQ and USC models at voxel level and a Poisson TCP model at tumour level.

RESULTS

For hypoxic tumours, the disputed continuous bend of the LQ survival curve was counteracted by the increased radioresistance of the hypoxic cells and the survival curves started to diverge only at much higher doses than for oxic tumours. This was also reflected by the TCP curves for hypoxic tumours for which the difference in D50 values for the LQ and USC models was reduced from 5.4 to 0.2 Gy for 1 and 3 fractions, respectively, in a tumour with only 1.1% hypoxia and from 9.5 to 0.4 Gy in a tumour with 11.1% hypoxia.

CONCLUSIONS

For a large range of fractional doses including hypofractionated schemes, the difference in predicted survival and TCP between the LQ and USC models for tumours with heterogeneous oxygenation was found to be negligible.

Treatment fractionation for stereotactic radiotherapy of lung tumours: a modelling study of the influence of chronic and acute hypoxia on tumour control probability

Background

Stereotactic body radiotherapy (SBRT) for non-small-cell lung cancer (NSCLC) has led to promising local control and overall survival for fractionation schemes with increasingly high fractional doses. A point has however been reached where the number of fractions used might be too low to allow efficient local inter-fraction reoxygenation of the hypoxic cells residing in the tumour. It was therefore the purpose of this study to investigate the impact of hypoxia and extreme hypofractionation on the tumour control probability (TCP) from SBRT.

Methods

A three-dimensional model of tumour oxygenation able to simulate oxygenation changes on the microscale was used. The TCP was determined for clinically relevant SBRT fractionation schedules of 1, 3 and 5 fractions assuming either static tumour oxygenation or that the oxygenation changes locally between fractions due to fast reoxygenation of acute hypoxia without an overall reduction in chronic hypoxia.

Results

For the schedules applying three or five fractions the doses required to achieve satisfying levels of TCP were considerably lower when local oxygenation changes were assumed compared to the case of static oxygenation; a decrease in D₅₀ of 17.7 Gy was observed for a five-fractions schedule applied to a 20% hypoxic tumour when fast reoxygenation was modelled. Assuming local oxygenation changes, the total doses required for a tumor control probability of 50% were of similar size for one, three and five fractions.

Conclusions

Although attractive from a practical point of view, extreme hypofractionation using just one single fraction may result in impaired local control of hypoxic tumours, as it eliminates the possibility for any kind of reoxygenation.

A systems biology view of blood vessel growth and remodelling

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.