A model to simulate the oxygen distribution in hypoxic tumors for different vascular architectures

Effects of intra-tumoral cellular heterogeneity of oxygen partial pressure on biological effectiveness of hydrogen-, helium-, carbon-, oxygen-, and neon-ion beams

Objective.The tumor microenvironment characterized by heterogeneously organized vasculatures causes intra-tumoral heterogeneity of oxygen partial pressurepat the cellular level, which cannot be measured by current imaging techniques. The intra-tumoral cellularpheterogeneity may lead to a reduction of therapeutic effects of radiation. The purpose of this study was to investigate the effects of the heterogeneity on biological effectiveness of H-, He-, C-, O-, and Ne-ion beams for different oxygenation levels, prescribed dose levels, and cell types.Approach.The intra-tumoral cellularpdistributions were simulated with a numerical tumor model for average oxygen pressuresp¯tranging from 2.5 to 15 mmHg. The relative biological effectiveness (RBE)-weighted dose distributions of 3-15 Gy prescribed doses were planned for a cuboid target with the five ion species for constantp¯tvalues. Radiosensitivities of human salivary gland tumor (HSG) and Chinese hamster ovary (CHO) cells were investigated. The planned dose distributions were then recalculated by taking thepheterogeneity into account.Main results.Asp¯tdecreased and prescribed dose increased, the biological effectiveness of the ion beams decreased due to thepheterogeneity. The reduction in biological effectiveness was pronounced for lighter H- and He-ion beams compared to heavier C-, O-, and Ne-ion beams. The RBE-weighted dose in the target for HSG (CHO) cells decreased by 41.2% (44.3%) for the H-ion beam, while it decreased by 16.7% (14.7%) for the Ne-ion beam at a prescribed dose of 15 Gy under ap¯tof 2.5 mmHg.Significance.The intra-tumoral cellularpheterogeneity causes a significant reduction in biological effectiveness of ion beams. These effects should be considered in estimation of therapeutic outcomes.

AMBER: A Modular Model for Tumor Growth, Vasculature and Radiation Response

Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.

An in-silico study of conventional and FLASH radiotherapy iso-effectiveness: potential impact of radiolytic oxygen depletion on tumor growth curves and tumor control probability

Objective. This work aims to investigate the iso-effectiveness of conventional and FLASH radiotherapy on tumors through in-silico mathematical models. We focused on the role of radiolytic oxygen depletion (ROD), which has been argued as a possible factor to explain the FLASH effect.Approach. We used a spatiotemporal reaction-diffusion model, including ROD, to simulate tumor oxygenation and response. From those oxygen distributions we obtained surviving fractions (SFs) using the linear-quadratic (LQ) model with the oxygen enhancement ratios (OERs). We then employed the calculated SFs to describe the evolution of preclinical tumor volumes through a mathematical model of tumor response, and we also extrapolated those results to calculate tumor control probabilities (TCPs) using the Poisson-LQ approach.Main results. Our study suggests that the ROD effect may cause differences in SF between FLASH and conventional radiotherapy, especially in lowα/βandpoorly oxygenatedcells. However, a statistical analysis showed that these changes in SF generally do not result in significant differences in the evolution of preclinical tumor growth curves when the sample size is small, because such differences in SF may not be noticeable in the heterogeneity of the population of animals. Nonetheless, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH radiotherapy). When analyzing the response of tumors with heterogeneous oxygenations, differences in TCP are more important forwell oxygenatedtumors. This apparent contradiction with the results obtained for homogeneously oxygenated cells is explained by the complex interplay between the heterogeneity of tumor oxygenation, the OER effect, and the ROD effect.Significance. This study supports the experimentally observed iso-effectiveness of FLASH and conventional radiotherapy when analyzing the volume evolution of preclinical tumors (that are far from control). However, this study also hints that tumor growth curves may be less sensitive to small variations in SF than tumor control probability: ROD may lead to increased SF in FLASH radiotherapy, which while not large enough to cause significant differences in tumor growth curves, could lead to important differences in clinical TCPs. Nonetheless, it cannot be discarded that other effects not modeled in this work, like radiation-induced immune effects, can contribute to tumor control and maintain the iso-effectiveness of FLASH radiotherapy. The study of tumor growth curves may not be the ideal experiment to test the iso-effectiveness of FLASH, and experiments reporting TCP orD50may be preferred.

Biological dose optimization incorporating intra-tumoural cellular radiosensitivity heterogeneity in ion-beam therapy treatment planning

Objective.Treatment plans of ion-beam therapy have been made under an assumption that all cancer cells within a tumour equally respond to a given radiation dose. However, an intra-tumoural cellular radiosensitivity heterogeneity clearly exists, and it may lead to an overestimation of therapeutic effects of the radiation. The purpose of this study is to develop a biological model that can incorporate the radiosensitivity heterogeneity into biological optimization for ion-beam therapy treatment planning.Approach.The radiosensitivity heterogeneity was modeled as the variability of a cell-line specific parameter in the microdosimetric kinetic model following the gamma distribution. To validate the developed intra-tumoural-radiosensitivity-heterogeneity-incorporated microdosimetric kinetic (HMK) model, a treatment plan with H-ion beams was made for a chordoma case, assuming a radiosensitivity heterogeneous region within the tumour. To investigate the effects of the radiosensitivity heterogeneity on the biological effectiveness of H-, He-, C-, O-, and Ne-ion beams, the relative biological effectiveness (RBE)-weighted dose distributions were planned for a cuboid target with the stated ion beams without considering the heterogeneity. The planned dose distributions were then recalculated by taking the heterogeneity into account.Main results. The cell survival fraction and corresponding RBE-weighted dose were formulated based on the HMK model. The first derivative of the RBE-weighted dose distribution was also derived, which is needed for fast biological optimization. For the patient plan, the biological optimization increased the dose to the radiosensitivity heterogeneous region to compensate for the heterogeneity-induced reduction in biological effectiveness of the H-ion beams. The reduction in biological effectiveness due to the heterogeneity was pronounced for low linear energy transfer (LET) beams but moderate for high-LET beams. The RBE-weighted dose in the cuboid target decreased by 7.6% for the H-ion beam, while it decreased by just 1.4% for the Ne-ion beam.Significance.Optimal treatment plans that consider intra-tumoural cellular radiosensitivity heterogeneity can be devised using the HMK model.

Modeling of the resensitization effect on carbon-ion radiotherapy for stage I non-small cell lung cancer

Objective. To investigate the effect of redistribution and reoxygenation on the 3-year tumor control probability (TCP) of patients with stage I non-small cell lung cancer (NSCLC) treated with carbon-ion radiotherapy.Approach. A meta-analysis of published clinical data of 233 NSCLC patients treated by carbon-ion radiotherapy under 18-, 9-, 4-, and single-fraction schedules was conducted. The linear-quadratic (LQ)-based cell-survival model incorporating the radiobiological 5Rs, radiosensitivity, repopulation, repair, redistribution, and reoxygenation, was developed to reproduce the clinical TCP data. Redistribution and reoxygenation were regarded together as a single phenomenon and termed 'resensitization' in the model. The optimum interval time between fractions was investigated for each fraction schedule using the determined model parameters.Main results.The clinical TCP data for 18-, 9-, and 4-fraction schedules were reasonably reproduced by the model without the resensitization effect, whereas its incorporation was essential to reproduce the TCP data for all fraction schedules including the single fraction. The curative dose for the single-fraction schedule was estimated to be 49.0 Gy (RBE), which corresponds to the clinically adopted dose prescription of 50.0 Gy (RBE). For 18-, 9-, and 4-fraction schedules, a 2-to-3-day interval is required to maximize the resensitization effect during the time interval. In contrast, the single-fraction schedule cannot benefit from the resensitization effect, and the shorter treatment time is preferable to reduce the effect of sub-lethal damage repair during the treatment.Significance.The LQ-based cell-survival model incorporating the radiobiological 5Rs was developed and used to evaluate the effect of the resensitization on clinical results of NSCLC patients treated with hypo-fractionated carbon-ion radiotherapy. The incorporation of the resensitization into the cell-survival model improves the reproducibility to the clinical TCP data. A shorter treatment time is preferable in the single-fraction schedule, while a 2-to-3-day interval between fractions is preferable in the multi-fraction schedules for effective treatments.

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.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

The dose-related plateau effect of surviving fraction in normal tissue during the ultra-high-dose-rate radiotherapy

Objective.Ultra-high-dose-rate radiotherapy, referred to as FLASH therapy, has been demonstrated to reduce the damage of normal tissue as well as inhibiting tumor growth compared with conventional dose-rate radiotherapy. The transient hypoxia may be a vital explanation for sparing the normal tissue. The heterogeneity of oxygen distribution for different doses and dose rates in the different radiotherapy schemes are analyzed. With these results, the influence of doses and dose rates on cell survival are evaluated in this work.Approach.The two-dimensional reaction-diffusion equations are used to describe the heterogeneity of the oxygen distribution in capillaries and tissue. A modified linear quadratic model is employed to characterize the surviving fraction at different doses and dose rates.Main results.The reduction of the damage to the normal tissue can be observed if the doses exceeds a minimum dose threshold under the ultra-high-dose-rate radiation. Also, the surviving fraction exhibits the 'plateau effect' under the ultra-high dose rates radiation, which signifies that within a specific range of doses, the surviving fraction either exhibits minimal variation or increases with the dose. For a given dose, the surviving fraction increases with the dose rate until tending to a stable value, which means that the protection in normal tissue reaches saturation.Significance.The emergence of the 'plateau effect' allows delivering the higher doses while minimizing damage to normal tissue. It is necessary to develop appropriate program of doses and dose rates for different irradiated tissue to achieve more efficient protection.

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

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

Development of a coupled modeling for tumor growth, angiogenesis, oxygen delivery, and phenotypic heterogeneity

Analysis of the evolution and growth dynamics of tumors is crucial for understanding cancer and the development of individually optimized therapies. During tumor growth, a hypoxic microenvironment around cancer cells caused by excessive non-vascular tumor growth induces tumor angiogenesis that plays a key role in the ensuing tumor growth and its progression into higher stages. Various mathematical simulation models have been introduced to simulate these biologically and physically complex hallmarks of cancer. Here, we developed a hybrid two-dimensional computational model that integrates spatiotemporally different components of the tumor system to investigate both angiogenesis and tumor growth/proliferation. This spatiotemporal evolution is based on partial diffusion equations, the cellular automation method, transition and probabilistic rules, and biological assumptions. The new vascular network provided by angiogenesis affects tumor microenvironmental conditions and drives individual cells to adapt themselves to spatiotemporal conditions. Furthermore, some stochastic rules are involved besides microenvironmental conditions. Overall, the conditions promote some commonly observed cellular states, i.e., proliferative, migrative, quiescent, and cell death, depending on the condition of each cell. Altogether, our results offer a theoretical basis for the biological evidence that regions of the tumor tissue near blood vessels are densely populated by proliferative phenotypic variants, while poorly oxygenated regions are sparsely populated by hypoxic phenotypic variants.

A phenomenological model of proton FLASH oxygen depletion effects depending on tissue vasculature and oxygen supply

Introduction

Radiation-induced oxygen depletion in tissue is assumed as a contributor to the FLASH sparing effects. In this study, we simulated the heterogeneous oxygen depletion in the tissue surrounding the vessels and calculated the proton FLASH effective-dose-modifying factor (FEDMF), which could be used for biology-based treatment planning.

Methods

The dose and dose-weighted linear energy transfer (LET) of a small animal proton irradiator was simulated with Monte Carlo simulation. We deployed a parabolic partial differential equation to account for the generalized radiation oxygen depletion, tissue oxygen diffusion, and metabolic processes to investigate oxygen distribution in 1D, 2D, and 3D solution space. Dose and dose rates, particle LET, vasculature spacing, and blood oxygen supplies were considered. Using a similar framework for the hypoxic reduction factor (HRF) developed previously, the FEDMF was derived as the ratio of the cumulative normoxic-equivalent dose (CNED) between CONV and UHDR deliveries.

Results

Dynamic equilibrium between oxygen diffusion and tissue metabolism can result in tissue hypoxia. The hypoxic region displayed enhanced radio-resistance and resulted in lower CNED under UHDR deliveries. In 1D solution, comparing 15 Gy proton dose delivered at CONV 0.5 and UHDR 125 Gy/s, 61.5% of the tissue exhibited ≥20% FEDMF at 175 μm vasculature spacing and 18.9 μM boundary condition. This percentage reduced to 34.5% and 0% for 8 and 2 Gy deliveries, respectively. Similar trends were observed in the 3D solution space. The FLASH versus CONV differential effect remained at larger vasculature spacings. A higher FLASH dose rate showed an increased region with ≥20% FEDMF. A higher LET near the proton Bragg peak region did not appear to alter the FLASH effect.

Conclusion

We developed 1D, 2D, and 3D oxygen depletion simulation process to obtain the dynamic HRF and derive the proton FEDMF related to the dose delivery parameters and the local tissue vasculature information. The phenomenological model can be used to simulate or predict FLASH effects based on tissue vasculature and oxygen concentration data obtained from other experiments.

Modulating Nucleus Oxygen Concentration by Altering Intramembrane Cholesterol Levels: Creating Hypoxic Nucleus in Oxic Conditions

We propose a novel mechanism by which cancer cells can modulate the oxygen concentration within the nucleus, potentially creating low nuclear oxygen conditions without the need of an hypoxic micro-environment and suited for allowing cancer cells to resist chemo- and radio-therapy. The cells ability to alter intra-cellular oxygen conditions depends on the amount of cholesterol present within the cellular membranes, where high levels of cholesterol can yield rigid membranes that slow oxygen diffusion. The proposed mechanism centers on the competition between (1) the diffusion of oxygen within the cell and across cellular membranes that replenishes any consumed oxygen and (2) the consumption of oxygen in the mitochondria, peroxisomes, endoplasmic reticulum (ER), etc. The novelty of our work centers around the assumption that the cholesterol content of a membrane can affect the oxygen diffusion across the membrane, reducing the cell ability to replenish the oxygen consumed within the cell. For these conditions, the effective diffusion rate of oxygen becomes of the same order as the oxygen consumption rate, allowing the cell to reduce the oxygen concentration of the nucleus, with implications to the Warburg Effect. The cellular and nucleus oxygen content is indirectly evaluated experimentally for bladder (T24) cancer cells and during the cell cycle, where the cells are initially synchronized using hydroxeaurea (HU) at the late G1-phase/early S-phase. The analysis of cellular and nucleus oxygen concentration during cell cycle is performed via (i) RT-qPCR gene analysis of hypoxia inducible transcription factors (HIF) and prolyl hydroxylases (PHD) and (ii) radiation clonogenic assay every 2 h, after release from synchronization. The HIF/PHD genes allowed us to correlate cellular oxygen with oxygen concentration in the nucleus that is obtained from the cells radiation response, where the amount DNA damage due to radiation is directly related to the amount of oxygen present in the nucleus. We demonstrate that during the S-phase cells can become hypoxic in the late S-phase/early G2-phase and therefore the radiation resistance increases 2- to 3-fold.

Estimation of pO2 distribution in EPR oximetry

Electron paramagnetic resonance (EPR) oximetry, using oxygen-sensing implant such as OxyChip, is capable of measuring oxygen concentration in vivo - a critical tissue information required for successful medical treatment such as cancer, wound healing and diabetes. Typically, EPR oximetry produces one value of the oxygen concentration, expressed as pO2 at the site of implant. However, it is well recognized that in vivo one deals with a distribution of oxygen concentration and therefore reporting just one number is not representative_a long-standing critique of EPR oximetry. Indeed, when it comes to the assessment of radiation efficacy one should be guided not by the mean or median but the proportion of oxygenated cancer cells which can be estimated only when the whole oxygen distribution in the tumor is known. Although there is a handful of papers attempting estimation of the oxygen distribution they suffer from the problem of negative frequencies and no theoretical justification and no biomedical interpretation. The goal of this work is to suggest a novel method using the empirical Bayesian approach realized via nonlinear mixed modeling with a priori distribution of oxygen following a two-parameter lognormal distribution with parameters estimated from the multi-implant single component EPR scan. Unlike previous work, the result of our estimation is the distribution with positive values for the frequency and the associated pO2 value. Our algorithm based on nonlinear regression is illustrated with EPR measurements on OxyChips equilibrated with gas mixtures containing four values of pO2 and computation of the proportion of volume with pO2 greater than any given threshold. This approach may become crucial for application of the EPR oximetry in clinical setting when the sucsess of the treatment depends of the proportion of tissue oxygenated.

Towards a Reduced In Silico Model Predicting Biochemical Recurrence After Radiotherapy in Prostate Cancer

OBJECTIVE

Purposes of this work were i) to develop an in silico model of tumor response to radiotherapy, ii) to perform an exhaustive sensitivity analysis in order to iii) propose a simplified version and iv) to predict biochemical recurrence with both the comprehensive and the reduced model.

METHODS

A multiscale computational model of tumor response to radiotherapy was developed. It integrated the following radiobiological mechanisms: oxygenation, including hypoxic death; division of tumor cells; VEGF diffusion driving angiogenesis; division of healthy cells and oxygen-dependent response to irradiation, considering, cycle arrest and mitotic catastrophe. A thorough sensitivity analysis using the Morris screening method was performed on 21 prostate computational tissues. Tumor control probability (TCP) curves of the comprehensive model and 15 reduced versions were compared. Logistic regression was performed to predict biochemical recurrence after radiotherapy on 76 localized prostate cancer patients using an output of the comprehensive and the reduced models.

RESULTS

No significant difference was found between the TCP curves of the comprehensive and a simplified version which only considered oxygenation, division of tumor cells and their response to irradiation. Biochemical recurrence predictions using the comprehensive and the reduced models improved those made from pre-treatment imaging parameters (AUC = 0.81 ± 0.02 and 0.82 ± 0.02 vs. 0.75 ± 0.03, respectively).

CONCLUSION

A reduced model of tumor response to radiotherapy able to predict biochemical recurrence in prostate cancer was obtained.

SIGNIFICANCE

This reduced model may be used in the future to optimize personalized fractionation schedules.

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.

A Model of Indirect Cell Death Caused by Tumor Vascular Damage after High-Dose Radiotherapy

There is increasing evidence that high doses of radiotherapy, like those delivered in stereotactic body radiotherapy (SBRT), trigger indirect mechanisms of cell death. Such effect seems to be two-fold. High doses may trigger an immune response and may cause vascular damage, leading to cell starvation and death. Development of mathematical response models, including indirect death, may help clinicians to design SBRT optimal schedules. Despite increasing experimental literature on indirect tumor cell death caused by vascular damage, efforts on modeling this effect have been limited. In this work, we present a biomathematical model of this effect. In our model, tumor oxygenation is obtained by solving the reaction-diffusion equation; radiotherapy kills tumor cells according to the linear-quadratic model, and also endothelial cells (EC), which can trigger loss of functionality of capillaries. Capillary death will affect tumor oxygenation, driving nearby tumor cells into severe hypoxia. Capillaries can recover functionality due to EC proliferation. Tumor cells entering a predetermined severe hypoxia status die according to a hypoxia-death model. This model fits recently published experimental data showing the effect of vascular damage on surviving fractions. It fits surviving fraction curves and qualitatively reproduces experimental values of percentages of functional capillaries 48 hours postirradiation, and hypoxic cells pre- and 48 hours postirradiation. This model is useful for exploring aspects of tumor and EC response to radiotherapy and constitutes a stepping stone toward modeling indirect tumor cell death caused by vascular damage and accounting for this effect during SBRT planning. SIGNIFICANCE: A novel biomathematical model of indirect tumor cell death caused by vascular radiation damage could potentially help clinicians interpret experimental data and design better radiotherapy schedules.

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

AIM

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

METHODS

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

RESULTS

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

CONCLUSION

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

Impact of different biologically-adapted radiotherapy strategies on tumor control evaluated with a tumor response model

Motivated by the capabilities of modern radiotherapy techniques and by the recent developments of functional imaging techniques, dose painting by numbers (DPBN) was proposed to treat tumors with heterogeneous biological characteristics. This work studies different DPBN optimization techniques for virtual head and neck tumors assessing tumor response in terms of cell survival and tumor control probability with a previously published tumor response model (TRM). Uniform doses of 2 Gy are redistributed according to the microscopic oxygen distribution and the density distribution of tumor cells in four virtual tumors with different biological characteristics. In addition, two different optimization objective functions are investigated, which: i) minimize tumor cell survival (OF_surv) or; ii) maximize the homogeneity of the density of surviving tumor cells (OF_std). Several adaptive schemes, ranging from single to daily dose optimization, are studied and the treatment response is compared to that of the uniform dose. The results show that the benefit of DPBN treatments depends on the tumor reoxygenation capability, which strongly differed among the set of virtual tumors investigated. The difference between daily (fraction by fraction) and three weekly optimizations (at the beginning of weeks 1, 3 and 4) was found to be small, and higher benefit was observed for the treatments optimized using OF_surv. This in silico study corroborates the hypothesis that DPBN may be beneficial for treatments of tumors which show reoxygenation during treatment, and that a few optimizations may be sufficient to achieve this therapeutic benefit.

Matching the reaction-diffusion simulation to dynamic [18F]FMISO PET measurements in tumors: extension to a flow-limited oxygen-dependent model

Positron-emission tomography (PET) with hypoxia specific tracers provides a noninvasive method to assess the tumor oxygenation status. Reaction-diffusion models have advantages in revealing the quantitative relation between in vivo imaging and the tumor microenvironment. However, there is no quantitative comparison of the simulation results with the real PET measurements yet. The lack of experimental support hampers further applications of computational simulation models. This study aims to compare the simulation results with a preclinical [¹⁸F]FMISO PET study and to optimize the reaction-diffusion model accordingly. Nude mice with xenografted human squamous cell carcinomas (CAL33) were investigated with a 2 h dynamic [¹⁸F]FMISO PET followed by immunofluorescence staining using the hypoxia marker pimonidazole and the endothelium marker CD 31. A large data pool of tumor time-activity curves (TAC) was simulated for each mouse by feeding the arterial input function (AIF) extracted from experiments into the model with different configurations of the tumor microenvironment. A measured TAC was considered to match a simulated TAC when the difference metric was below a certain, noise-dependent threshold. As an extension to the well-established Kelly model, a flow-limited oxygen-dependent (FLOD) model was developed to improve the matching between measurements and simulations. The matching rate between the simulated TACs of the Kelly model and the mouse PET data ranged from 0 to 28.1% (on average 9.8%). By modifying the Kelly model to an FLOD model, the matching rate between the simulation and the PET measurements could be improved to 41.2-84.8% (on average 64.4%). Using a simulation data pool and a matching strategy, we were able to compare the simulated temporal course of dynamic PET with in vivo measurements. By modifying the Kelly model to a FLOD model, the computational simulation was able to approach the dynamic [¹⁸F]FMISO measurements in the investigated tumors.

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.

Oxygen Distributions-Evaluation of Computational Methods, Using a Stochastic Model for Large Tumour Vasculature, to Elucidate the Importance of Considering a Complete Vascular Network

PURPOSE

To develop a general model that utilises a stochastic method to generate a vessel tree based on experimental data, and an associated irregular, macroscopic tumour. These will be used to evaluate two different methods for computing oxygen distribution.

METHODS

A vessel tree structure, and an associated tumour of 127 cm3, were generated, using a stochastic method and Bresenham's line algorithm to develop trees on two different scales and fusing them together. The vessel dimensions were adjusted through convolution and thresholding and each vessel voxel was assigned an oxygen value. Diffusion and consumption were modelled using a Green's function approach together with Michaelis-Menten kinetics. The computations were performed using a combined tree method (CTM) and an individual tree method (ITM). Five tumour sub-sections were compared, to evaluate the methods.

RESULTS

The oxygen distributions of the same tissue samples, using different methods of computation, were considerably less similar (root mean square deviation, RMSD≈0.02) than the distributions of different samples using CTM (0.001< RMSD<0.01). The deviations of ITM from CTM increase with lower oxygen values, resulting in ITM severely underestimating the level of hypoxia in the tumour. Kolmogorov Smirnov (KS) tests showed that millimetre-scale samples may not represent the whole.

CONCLUSIONS

The stochastic model managed to capture the heterogeneous nature of hypoxic fractions and, even though the simplified computation did not considerably alter the oxygen distribution, it leads to an evident underestimation of tumour hypoxia, and thereby radioresistance. For a trustworthy computation of tumour oxygenation, the interaction between adjacent microvessel trees must not be neglected, why evaluation should be made using high resolution and the CTM, applied to the entire tumour.

Computational Model for Tumor Oxygenation Applied to Clinical Data on Breast Tumor Hemoglobin Concentrations Suggests Vascular Dilatation and Compression

We present a computational model for trans-vascular oxygen transport in synthetic tumor and host tissue blood vessel networks, aiming at qualitatively explaining published data of optical mammography, which were obtained from 87 breast cancer patients. The data generally show average hemoglobin concentration to be higher in tumors versus host tissue whereas average oxy-to total hemoglobin concentration (vascular segment RBC-volume-weighted blood oxygenation) can be above or below normal. Starting from a synthetic arterio-venous initial network the tumor vasculature was generated by processes involving cooption, angiogenesis, and vessel regression. Calculations of spatially resolved blood flow, hematocrit, oxy- and total hemoglobin concentrations, blood and tissue oxygenation were carried out for ninety tumor and associated normal vessel networks starting from various assumed geometries of feeding arteries and draining veins. Spatial heterogeneity in the extra-vascular partial oxygen pressure distribution can be related to various tumor compartments characterized by varying capillary densities and blood flow characteristics. The reported higher average hemoglobin concentration of tumors is explained by growth and dilatation of tumor blood vessels. Even assuming sixfold metabolic rate of oxygen consumption in tumorous versus host tissue, the predicted oxygen hemoglobin concentrations are above normal. Such tumors are likely associated with high tumor blood flow caused by high-caliber blood vessels crossing the tumor volume and hence oxygen supply exceeding oxygen demand. Tumor oxy- to total hemoglobin concentration below normal could only be achieved by reducing tumor vessel radii during growth by a randomly selected factor, simulating compression caused by intra-tumoral solid stress due to proliferation of cells and extracellular matrix. Since compression of blood vessels will impede chemotherapy we conclude that tumors with oxy- to total hemoglobin concentration below normal are less likely to respond to chemotherapy. Such behavior was recently reported for neo-adjuvant chemotherapy of locally advanced breast tumors.

Correlation of FMISO simulations with pimonidazole-stained tumor xenografts: A question of O2 consumption?

PURPOSE

To compare a dedicated simulation model for hypoxia PET against tumor microsections stained for different parameters of the tumor microenvironment. The model can readily be adapted to a variety of conditions, such as different human head and neck squamous cell carcinoma (HNSCC) xenograft tumors.

METHODS

Nine different HNSCC tumor models were transplanted subcutaneously into nude mice. Tumors were excised and immunoflourescently labeled with pimonidazole, Hoechst 33342, and CD31, providing information on hypoxia, perfusion, and vessel distribution, respectively. Hoechst and CD31 images were used to generate maps of perfused blood vessels on which tissue oxygenation and the accumulation of the hypoxia tracer FMISO were mathematically simulated. The model includes a Michaelis-Menten relation to describe the oxygen consumption inside tissue. The maximum oxygen consumption rate M0 was chosen as the parameter for a tumor-specific optimization as it strongly influences tracer distribution. M0 was optimized on each tumor slice to reach optimum correlations between FMISO concentration 4 h postinjection and pimonidazole staining intensity.

RESULTS

After optimization, high pixel-based correlations up to R(2) = 0.85 were found for individual tissue sections. Experimental pimonidazole images and FMISO simulations showed good visual agreement, confirming the validity of the approach. Median correlations per tumor model varied significantly (p < 0.05), with R(2) ranging from 0.20 to 0.54. The optimum maximum oxygen consumption rate M0 differed significantly (p < 0.05) between tumor models, ranging from 2.4 to 5.2 mm Hg/s.

CONCLUSIONS

It is feasible to simulate FMISO distributions that match the pimonidazole retention patterns observed in vivo. Good agreement was obtained for multiple tumor models by optimizing the oxygen consumption rate, M0, whose optimum value differed significantly between tumor models.

Glycolysis determines dichotomous regulation of T cell subsets in hypoxia

Hypoxia occurs in many pathological conditions, including chronic inflammation and tumors, and is considered to be an inhibitor of T cell function. However, robust T cell responses occur at many hypoxic inflammatory sites, suggesting that functions of some subsets are stimulated under low oxygen conditions. Here, we investigated how hypoxic conditions influence human T cell functions and found that, in contrast to naive and central memory T cells (TN and TCM), hypoxia enhances the proliferation, viability, and cytotoxic action of effector memory T cells (TEM). Enhanced TEM expansion in hypoxia corresponded to high hypoxia-inducible factor 1α (HIF1α) expression and glycolytic activity compared with that observed in TN and TCM. We determined that the glycolytic enzyme GAPDH negatively regulates HIF1A expression by binding to adenylate-uridylate-rich elements in the 3'-UTR region of HIF1A mRNA in glycolytically inactive TN and TCM. Conversely, active glycolysis with decreased GAPDH availability in TEM resulted in elevated HIF1α expression. Furthermore, GAPDH overexpression reduced HIF1α expression and impaired proliferation and survival of T cells in hypoxia, indicating that high glycolytic metabolism drives increases in HIF1α to enhance TEM function during hypoxia. This work demonstrates that glycolytic metabolism regulates the translation of HIF1A to determine T cell responses to hypoxia and implicates GAPDH as a potential mechanism for controlling T cell function in peripheral tissue.

Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such as oxygen or glucose, is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature. Integrative models, based on detailed experimental data and physical laws, implement, in silico, the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. This chapter provides an overview over the current status of computer simulations of vascular remodeling during tumor growth including interstitial fluid flow, drug delivery, and oxygen supply within the tumor. The model predictions are compared with experimental and clinical data and a number of longstanding physiological paradigms about tumor vasculature and intratumoral solute transport are critically scrutinized.

Comparison of [18F]-FMISO, [18F]-FAZA and [18F]-HX4 for PET imaging of hypoxia--a simulation study

BACKGROUND

To investigate the effect of hypoxia tracer properties on positron emission tomography (PET) image quality for three tracers [18F]-fluoromisonidazole (FMISO), [18F]-fluoroazomycinarabinoside (FAZA) and [18F]-flortanidazole (HX4), using mathematical simulations based on microscopic tumor tissue sections.

MATERIAL AND METHODS

Oxygen distribution and tracer binding was mathematically simulated on immunohistochemically stained cross-sections of tumor xenografts. Tracer diffusion properties were determined based on available literature. Blood activity and clearance over a four-hour period post-injection (p.i.) were derived from clinical dynamic PET scans of patients suffering from head and neck or bronchial cancer. Simulations were performed both for average patient blood activities and for individual patients, and image contrast between normoxic and hypoxic tissue areas was determined over this four-hour period p.i.

RESULTS

On average, HX4 showed a six-fold higher clearance than FMISO and an almost three-fold higher clearance than FAZA based on the clinical PET data. The absolute variation in clearance was significantly higher for HX4 than for FMISO (standard deviations of 5.75 *10-5 s-1 vs. 1.55 *10-5 s-1). The absolute tracer activity in these scans at four hours p.i. was highest for FMISO and lowest for HX4. Simulated contrast at four hours p.i. was highest for HX4 (2.39), while FMISO and FAZA were comparable (1.67 and 1.75, respectively). Variations in contrast of 7-11% were observed for each tracer depending on the vascularization patterns of the chosen tissue. Higher variations in clearance for HX4 resulted in an increased inter-patient variance in simulated contrast at four hours p.i.

CONCLUSIONS

In line with recent experimental and clinical data, the results suggest that HX4 is a promising new tracer that provides high image contrast four hours p.i., though inter-patient variance can be very high. Nevertheless, the widely used tracer FMISO provides a robust and reproducible signal four hours p.i., but with a lower contrast. The simulations revealed tracer clearance to be the key factor in determining image contrast.

A voxel-based multiscale model to simulate the radiation response of hypoxic tumors

PURPOSE

In radiotherapy, it is important to predict the response of tumors to irradiation prior to the treatment. This is especially important for hypoxic tumors, which are known to be highly radioresistant. Mathematical modeling based on the dose distribution, biological parameters, and medical images may help to improve this prediction and to optimize the treatment plan.

METHODS

A voxel-based multiscale tumor response model for simulating the radiation response of hypoxic tumors was developed. It considers viable and dead tumor cells, capillary and normal cells, as well as the most relevant biological processes such as (i) proliferation of tumor cells, (ii) hypoxia-induced angiogenesis, (iii) spatial exchange of cells leading to tumor growth, (iv) oxygen-dependent cell survival after irradiation, (v) resorption of dead cells, and (vi) spatial exchange of cells leading to tumor shrinkage. Oxygenation is described on a microscopic scale using a previously published tumor oxygenation model, which calculates the oxygen distribution for each voxel using the vascular fraction as the most important input parameter. To demonstrate the capabilities of the model, the dependence of the oxygen distribution on tumor growth and radiation-induced shrinkage is investigated. In addition, the impact of three different reoxygenation processes is compared and tumor control probability (TCP) curves for a squamous cells carcinoma of the head and neck (HNSSC) are simulated under normoxic and hypoxic conditions.

RESULTS

The model describes the spatiotemporal behavior of the tumor on three different scales: (i) on the macroscopic scale, it describes tumor growth and shrinkage during radiation treatment, (ii) on a mesoscopic scale, it provides the cell density and vascular fraction for each voxel, and (iii) on the microscopic scale, the oxygen distribution may be obtained in terms of oxygen histograms. With increasing tumor size, the simulated tumors develop a hypoxic core. Within the model, tumor shrinkage was found to be significantly more important for reoxygenation than angiogenesis or decreased oxygen consumption due to an increased fraction of dead cells. In the studied HNSSC-case, the TCD50 values (dose at 50% TCP) decreased from 71.0 Gy under hypoxic to 53.6 Gy under the oxic condition.

CONCLUSIONS

The results obtained with the developed multiscale model are in accordance with expectations based on radiobiological principles and clinical experience. As the model is voxel-based, radiological imaging methods may help to provide the required 3D-characterization of the tumor prior to irradiation. For clinical application, the model has to be further validated with experimental and clinical data. If this is achieved, the model may be used to optimize fractionation schedules and dose distributions for the treatment of hypoxic tumors.

The impact of including spatially longitudinal heterogeneities of vessel oxygen content and vascular fraction in 3D tumor oxygenation models on predicted radiation sensitivity

PURPOSE

Oxygen distribution models have been used to analyze the influences of oxygen tensions on tissue response after radiotherapy. These distributions are often generated assuming constant oxygen tension in the blood vessels. However, as red blood cells progress through the vessels, oxygen is continuously released into the plasma and the surrounding tissue, resulting in longitudinally varying oxygen levels in the blood vessels. In the present study, the authors investigated whether a tumor oxygenation model that incorporated longitudinally varying oxygen levels would provide different predictions of necrotic fractions and radiosensitivity compared to commonly used models with a constant oxygen pressure.

METHODS

Our models simulated oxygen diffusion based on a Green's function approach and oxygen consumption according to the Michaelis-Menten equation. The authors constructed tumor models with different vascular fractions (VFs), from which they generated depth oxygenation curves and a look-up table of oxygen pressure gradients. The authors evaluated models of spherical tumors of various sizes, from 1 to 10(4) mg. The authors compared the results from a model with constant vessel oxygen (CVO) pressure to those from models with longitudinal variations in oxygen saturation and either a constant VF (CVF) or variable VF (VVF) within the tumor tissue. The authors monitored the necrotic fractions, defined as tumor regions with an oxygen pressure below 1 mmHg. Tumor radiation sensitivity was expressed as D99, the homogeneous radiation dose required for a tumor control probability of 0.99.

RESULTS

In the CVO saturation model, no necrosis was observed, and decreasing the VF could only decrease the D99 by up to 10%. Furthermore, the D99 vs VF dependence was similar for different tumor masses. Compared to the CVO model, the extended CVF and VVF models provided clearly different results, including pronounced effects of VF and tumor size on the necrotic fraction and D99, necrotic fractions ranging from 0% to 97%, and a maximal D99 increment of 57%. Only minor differences were observed between different vessel architectures, i.e., CVF vs VVF. In the smallest tumor with a low necrotic fraction, the D99 strictly decreased with increasing blood velocity. Increasing blood velocity also decreased the necrotic fraction in all tumor sizes. VF had the most profound influence on both the necrotic fraction and on D99.

CONCLUSIONS

Our present analysis of necrotic formation and the impact of tumor oxygenation on D99 demonstrated the importance of including longitudinal variations in vessel oxygen content in tumor models. For small tumors, radiosensitivity was particularly dependent on VF and slightly dependent on the blood velocity and vessel arrangement. These dependences decreased with increasing tumor size, because the necrotic fraction also increased, thereby decreasing the number of viable tumor cells that required sterilization. The authors anticipate that the present model will be useful for estimating tumor oxygenation and radiation response in future detailed studies.