The effects of hypoxia on the theoretical modelling of tumour control probability

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.

A simple mathematical model of cyclic hypoxia and its impact on hypofractionated radiotherapy

PURPOSE

There is evidence that the population of cells that experience fluctuating oxygen levels ("acute," or, "cyclic" hypoxia) are more radioresistant than chronically hypoxic ones and hence, this population may determine radiotherapy (RT) response, in particular for hypofractionated RT, where reoxygenation may not be as prominent. A considerable effort has been devoted to examining the impact of hypoxia on hypofractionated RT; however, much less attention has been paid to cyclic hypoxia specifically and the role its kinetics may play in determining the efficacy of these treatments. Here, a simple mathematical model of cyclic hypoxia and fractionation effects was worked out to quantify this.

METHODS

Cancer clonogen survival fraction was estimated using the linear quadratic model, modified to account for oxygen enhancement effects. An analytic approximation for oxygen transport away from a random network of capillaries with fluctuating oxygen levels was used to model inter-fraction tissue oxygen kinetics. The resulting survival fraction formula was used to derive an expression for the iso-survival biologically effective dose (BED), BED_iso-SF . These were computed for some common extra-cranial hypofractionated RT regimens.

RESULTS

Using relevant literature parameter values, inter-fraction fluctuations in oxygenation were found to result in an added 1-2 logs of clonogen survival fraction in going from five fractions to one for the same nominal BED (i.e., excluding the effects of oxygen levels on radiosensitivity). BED_iso-SF 's for most ultra-hypofractionated (five or fewer fractions) regimens in a given tumor site are similar in magnitude, suggesting iso-efficacy for common fractionation schedules.

CONCLUSIONS

Although significant, the loss of cell-killing with increasing hypofractionation is not nearly as large as previous estimates based on the assumption of complete reoxygenation between fractions. Most ultra-hypofractionated regimens currently in place offer sufficiently high doses to counter this loss of cell killing, although care should be taken in implementing single-fraction regimens.

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

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

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

Hypoxia dynamics on FMISO-PET in combination with PD-1/PD-L1 expression has an impact on the clinical outcome of patients with Head-and-neck Squamous Cell Carcinoma undergoing Chemoradiation

Tumor-associated hypoxia influences the radiation response of head-and-neck cancer (HNSCC) patients, and a lack of early hypoxia resolution during treatment considerably deteriorates outcomes. As the detrimental effects of hypoxia are partly related to the induction of an immunosuppressive microenvironment, we investigated the interaction between tumor hypoxia dynamics and the PD-1/PD-L1 axis in HNSCC patients undergoing chemoradiation and its relevance for patient outcomes in a prospective trial.

Methods: 49 patients treated with definitive chemoradiation for locally advanced HNSCC were enrolled in this trial and received longitudinal hypoxia PET imaging using fluorine-18 misonidazole ([¹⁸F]FMISO) at weeks 0, 2 and 5 during treatment. Pre-therapeutic tumor biopsies were immunohistochemically analyzed regarding the PD-1/PD-L1 expression both on immune cells and on tumor cells, and potential correlations between the PD-1/PD-L1 axis and tumor hypoxia dynamics during chemoradiation were assessed using Spearman's rank correlations. Hypoxia dynamics during treatment were quantified by subtracting the standardized uptake value (SUV) index at baseline from the SUV values at weeks 2 or 5, whereby SUV index was defined as ratio of maximum tumor [¹⁸F]FMISO SUV to mean SUV in the contralateral sternocleidomastoid muscle (i.e. tumor-to-muscle ratio). The impact of the PD-1/PD-L1 expression alone and in combination with persistent tumor hypoxia on locoregional control (LRC), progression-free survival (PFS) and overall survival (OS) was examined using log-rank tests and Cox proportional hazards models.

Results: Neither PD-L1 nor PD-1 expression levels on tumor-infiltrating immune cells influenced LRC (HR = 0.734; p = 0.480 for PD-L1, HR = 0.991; p = 0.989 for PD-1), PFS (HR = 0.813; p = 0.597 for PD-L1, HR = 0.796; p = 0.713 for PD-1) or OS (HR = 0.698; p = 0.405 for PD-L1, HR = 0.315; p = 0.265 for PD-1). However, patients with no hypoxia resolution between weeks 0 and 2 and PD-L1 expression on tumor cells, quantified by a tumor proportional score (TPS) of at least 1%, showed significantly worse LRC (HR = 3.374, p = 0.022) and a trend towards reduced PFS (HR = 2.752, p = 0.052). In the multivariate Cox regression analysis, the combination of absent tumor hypoxia resolution and high tumoral PD-L1 expression remained a significant prognosticator for impaired LRC (HR = 3.374, p = 0.022). On the other side, tumoral PD-L1 expression did not compromise the outcomes of patients whose tumor-associated hypoxia declined between week 0 and 2 during chemoradiation (LRC: HR = 1.186, p = 0.772, PFS: HR = 0.846, p = 0.766).

Conclusion: In this exploratory analysis, we showed for the first time that patients with both persistent tumor-associated hypoxia during treatment and PD-L1 expression on tumor cells exhibited a worse outcome, while the tumor cells' PD-L1 expression did not influence the outcomes of patients with early tumor hypoxia resolution. While the results have to be validated in an independent cohort, these findings form a foundation to investigate the combination of hypoxic modification and immune checkpoint inhibitors for the unfavorable subgroup, moving forward towards personalized radiation oncology treatment.

Modeling Cellular Response in Large-Scale Radiogenomic Databases to Advance Precision Radiotherapy

Radiotherapy is integral to the care of a majority of patients with cancer. Despite differences in tumor responses to radiation (radioresponse), dose prescriptions are not currently tailored to individual patients. Recent large-scale cancer cell line databases hold the promise of unravelling the complex molecular arrangements underlying cellular response to radiation, which is critical for novel predictive biomarker discovery. Here, we present RadioGx, a computational platform for integrative analyses of radioresponse using radiogenomic databases. We fit the dose-response data within RadioGx to the linear-quadratic model. The imputed survival across a range of dose levels (AUC) was a robust radioresponse indicator that correlated with biological processes known to underpin the cellular response to radiation. Using AUC as a metric for further investigations, we found that radiation sensitivity was significantly associated with disruptive mutations in genes related to nonhomologous end joining. Next, by simulating the effects of different oxygen levels, we identified putative genes that may influence radioresponse specifically under hypoxic conditions. Furthermore, using transcriptomic data, we found evidence for tissue-specific determinants of radioresponse, suggesting that tumor type could influence the validity of putative predictive biomarkers of radioresponse. Finally, integrating radioresponse with drug response data, we found that drug classes impacting the cytoskeleton, DNA replication, and mitosis display similar therapeutic effects to ionizing radiation on cancer cell lines. In summary, RadioGx provides a unique computational toolbox for hypothesis generation to advance preclinical research for radiation oncology and precision medicine. SIGNIFICANCE: The RadioGx computational platform enables integrative analyses of cellular response to radiation with drug responses and genome-wide molecular data. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/79/24/6227/F1.large.jpg.See related commentary by Spratt and Speers, p. 6076.

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.

Predicting the Influence of Microvascular Structure On Tumor Response to Radiotherapy

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSION

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

SIGNIFICANCE

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

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.

Monte-Carlo model development for evaluation of current clinical target volume definition for heterogeneous and hypoxic glioblastoma

Clinical target volume (CTV) determination may be complex and subjective. In this work a microscopic-scale tumour model was developed to evaluate current CTV practices in glioblastoma multiforme (GBM) external radiotherapy. Previously, a Geant4 cell-based dosimetry model was developed to calculate the dose deposited in individual GBM cells. Microscopic extension probability (MEP) models were then developed using Matlab-2012a. The results of the cell-based dosimetry model and MEP models were combined to calculate survival fractions (SF) for CTV margins of 2.0 and 2.5 cm. In the current work, oxygenation and heterogeneous radiosensitivity profiles were incorporated into the GBM model. The genetic heterogeneity was modelled using a range of α/β values (linear-quadratic model parameters) associated with different GBM cell lines. These values were distributed among the cells randomly, taken from a Gaussian-weighted sample of α/β values. Cellular oxygen pressure was distributed randomly taken from a sample weighted to profiles obtained from literature. Three types of GBM models were analysed: homogeneous-normoxic, heterogeneous-normoxic, and heterogeneous-hypoxic. The SF in different regions of the tumour model and the effect of the CTV margin extension from 2.0-2.5 cm on SFs were investigated for three MEP models. The SF within the beam was increased by up to three and two orders of magnitude following incorporation of heterogeneous radiosensitivities and hypoxia, respectively, in the GBM model. However, the total SF was shown to be overdominated by the presence of tumour cells in the penumbra region and to a lesser extent by genetic heterogeneity and hypoxia. CTV extension by 0.5 cm reduced the SF by a maximum of 78.6  ±  3.3%, 78.5  ±  3.3%, and 77.7  ±  3.1% for homogeneous and heterogeneous-normoxic, and heterogeneous hypoxic GBMs, respectively. Monte-Carlo model was developed to quantitatively evaluate SF for genetically heterogeneous and hypoxic GBM with two CTV margins and three MEP distributions. The results suggest that photon therapy may not provide cure for hypoxic and genetically heterogeneous GBM. However, the extension of the CTV margin by 0.5 cm could be beneficial to delay the recurrence time for this tumour type due to significant increase in tumour cell irradiation.

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.

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.

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.

Efficacy of dose escalation on TCP, recurrence and second cancer risks: a mathematical study

OBJECTIVE

We investigated the effects of conventional and hypofractionation protocols by modelling tumour control probability (TCP) and tumour recurrence time, and examined their impact on second cancer risks. The main objectives of this study include the following: (a) incorporate tumour recurrence time and second cancer risks into the TCP framework and analyse the effects of variable doses and (b) investigate an efficient protocol to reduce the risk of a secondary malignancy while maximizing disease-free survival and tumour control.

METHODS

A generalized mathematical formalism was developed that incorporated recurrence and second cancer risk models into the TCP dynamics.

RESULTS

Our results suggest that TCP and relapse time are almost identical for conventional and hypofractionated regimens; however, second cancer risks resulting from hypofractionation were reduced by 22% when compared with the second cancer risk associated with a conventional protocol. The hypofractionated regimen appears to be sensitive to dose escalation and the corresponding impact on tumour recurrence time and reduction in second cancer risks. The reduction in second cancer risks is approximately 20% when the dose is increased from 60 to 72 Gy in a hypofractionated protocol.

CONCLUSION

Our results suggest that hypofractionation may be a more efficient regimen in the context of TCP, relapse time and second cancer risks. Overall, our study demonstrates the importance of including a second cancer risk model in designing an efficient radiation regimen.

ADVANCES IN KNOWLEDGE

The impact of various fractionation protocols on TCP and relapse in conjunction with second cancer risks is an important clinical question that is as yet unexplored.

Clinical oxygen enhancement ratio of tumors in carbon ion radiotherapy: the influence of local oxygenation changes

The effect of carbon ion radiotherapy on hypoxic tumors has recently been questioned because of low linear energy transfer (LET) values in the spread-out Bragg peak (SOBP). The aim of this study was to investigate the role of hypoxia and local oxygenation changes (LOCs) in fractionated carbon ion radiotherapy. Three-dimensional tumors with hypoxic subvolumes were simulated assuming interfraction LOCs. Different fractionations were applied using a clinically relevant treatment plan with a known LET distribution. The surviving fraction was calculated, taking oxygen tension, dose and LET into account, using the repairable-conditionally repairable (RCR) damage model with parameters for human salivary gland tumor cells. The clinical oxygen enhancement ratio (OER) was defined as the ratio of doses required for a tumor control probability of 50% for hypoxic and well-oxygenated tumors. The resulting OER was well above unity for all fractionations. For the hypoxic tumor, the tumor control probability was considerably higher if LOCs were assumed, rather than static oxygenation. The beneficial effect of LOCs increased with the number of fractions. However, for very low fraction doses, the improvement related to LOCs did not compensate for the increase in total dose required for tumor control. In conclusion, our results suggest that hypoxia can influence the outcome of carbon ion radiotherapy because of the non-negligible oxygen effect at the low LETs in the SOBP. However, if LOCs occur, a relatively high level of tumor control probability is achievable with a large range of fractionation schedules for tumors with hypoxic subvolumes, but both hyperfractionation and hypofractionation should be pursued with caution.

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.

Tumour control probability in cancer stem cells hypothesis

The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCP_S as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer or CD133 for glioma, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCP_CD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations parameterized for the case of gliomas, to compare the theoretical TCP_S and the measurable TCP_CD+. We also use the measurable TCP to compare the effect of various radiation protocols.

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

PURPOSE

As hypoxic cells are more resistant to photon radiation, it is desirable to obtain information about the oxygen distribution in tumors prior to the radiation treatment. Noninvasive techniques are currently not able to provide reliable oxygenation maps with sufficient spatial resolution; therefore mathematical models may help to simulate microvascular architectures and the resulting oxygen distributions in the surrounding tissue. Here, the authors present a new computer model, which uses the vascular fraction of tumor voxels, in principle measurable noninvasively in vivo, as input parameter for simulating realistic PO2 histograms in tumors, assuming certain 3D vascular architectures.

METHODS

Oxygen distributions were calculated by solving a reaction-diffusion equation in a reference volume using the particle strength exchange method. Different types of vessel architectures as well as different degrees of vascular heterogeneities are considered. Two types of acute hypoxia (ischemic and hypoxemic) occurring additionally to diffusion-limited (chronic) hypoxia were implemented as well.

RESULTS

No statistically significant differences were observed when comparing 2D- and 3D-vessel architectures (p>0.79 in all cases) and highly heterogeneously distributed linear vessels show good agreement, when comparing with published experimental intervessel distance distributions and PO2 histograms. It could be shown that, if information about additional acute hypoxia is available, its contribution to the hypoxic fraction (HF) can be simulated as well. Increases of 128% and 168% in the HF were obtained when representative cases of ischemic and hypoxemic acute hypoxia, respectively, were considered in the simulations.

CONCLUSIONS

The presented model is able to simulate realistic microscopic oxygen distributions in tumors assuming reasonable vessel architectures and using the vascular fraction as macroscopic input parameter. The model may be used to generate PO2 histograms, which are needed as input in models predicting the radiation response of hypoxic tumors.

Predictive value of modelled tumour control probability based on individual measurements of in vitro radiosensitivity and potential doubling time

OBJECTIVE

The aim of this study was to compare patient-specific radiobiological parameters with population averages in predicting the clinical outcome after radiotherapy (RT) using a tumour control probability (TCP) model based on the biological effective dose (BED).

METHODS

A previously published study of 46 head and neck carcinomas with individually identified radiobiological parameters, radiosensitivity and potential doubling time (Tpot), and known tumour size was investigated. These patients had all been treated with external beam RT, and the majority had also received brachytherapy. The TCP for each individual based on the BED using patient-specific radiobiological parameters was compared with the TCP based on the BED using average radiobiological parameters (α=0.3 Gy(-1), Tpot=3 days).

RESULTS

43 patients remained in the final analysis. There was only a weak trend for increasing local tumour control with increasing BED in both groups. However, when the TCP was calculated, the use of patient-specific parameters was better for identifying local control correctly. The sensitivity and specificity for tumour-specific parameters were 63% and 80%, respectively. The corresponding values for population-based averages were 0% and 91%, respectively. The positive predictive value was 92% when tumour-specific parameters were used compared with 0% for population-based averages. A receiver operating characteristic curve confirmed the superiority of patient-specific parameters over population averages in predicting local control.

CONCLUSION

Individual radiobiological parameters are better than population-derived averages when used in a mathematical model to predict TCP after curative RT in head and neck carcinomas.

ADVANCES IN KNOWLEDGE

TCP based on individual radiobiological parameters is better than TCP based on population-based averages for identifying local control correctly.

Altered fractionation outcomes for hypoxic head and neck cancer using the HYP-RT Monte Carlo model

OBJECTIVE

Altered fractionation radiotherapy is simulated on a set of virtual tumours to assess the total doses required for tumour control compared with clinical head and neck data and the doses required to control hypoxic vs well-oxygenated tumours with different radiobiological properties.

METHODS

The HYP-RT model is utilised to explore the impact of tumour oxygenation and the onset times of accelerated repopulation (AR) and reoxygenation (ROx) during radiotherapy. A biological effective dose analysis is used to rank the schedules based on their relative normal tissue toxicities.

RESULTS

Altering the onset times of AR and ROx has a large impact on the doses required to achieve tumour control. Immediate onset of ROx and 2-week onset time of AR produce results closely predicting average human outcomes in terms of the total prescription doses in clinical trials. Modifying oxygen enhancement ratio curves based on dose/fraction significantly reduces the dose (5-10 Gy) required for tumour control for hyperfractionated schedules. HYP-RT predicts 10×1.1 Gy per week to be most beneficial, whereas the conventional schedule is predicted as beneficial for early toxicity but has average-poor late toxicity.

CONCLUSION

HYP-RT predicts that altered radiotherapy schedules increase the therapeutic ratio and may be used to make predictions about the prescription doses required to achieve tumour control for tumours with different oxygenation levels and treatment responses.

ADVANCES IN KNOWLEDGE

Oxic and hypoxic tumours have large differences in total radiation dose requirements, affected by AR and ROx onset times by up to 15-25 Gy for the same fractionation schedule.

In silico modelling of treatment-induced tumour cell kill: developments and advances

Mathematical and stochastic computer (in silico) models of tumour growth and treatment response of the past and current eras are presented, outlining the aims of the models, model methodology, the key parameters used to describe the tumour system, and treatment modality applied, as well as reported outcomes from simulations. Fractionated radiotherapy, chemotherapy, and combined therapies are reviewed, providing a comprehensive overview of the modelling literature for current modellers and radiobiologists to ignite the interest of other computational scientists and health professionals of the ever evolving and clinically relevant field of tumour modelling.

Modeling the spatial distribution of chronic tumor hypoxia: implications for experimental and clinical studies

Tumor oxygenation status is considered one of the important prognostic markers in cancer since it strongly influences the response of cancer cells to various treatments; in particular, to radiation therapy. Thus, a proper and accurate assessment of tumor oxygen distribution before the treatment may highly affect the outcome of the treatment. The heterogeneous nature of tumor hypoxia, mainly influenced by the complex tumor microenvironment, often makes its quantification very difficult. The usual methods used to measure tumor hypoxia are biomarkers and the polarographic needle electrode. Although these techniques may provide an acceptable assessment of hypoxia, they are invasive and may not always give a spatial distribution of hypoxia, which is very useful for treatment planning. An alternative method to quantify the tumor hypoxia is to use theoretical simulations with the knowledge of tumor vasculature. The purpose of this paper is to model tumor hypoxia using a known spatial distribution of tumor vasculature obtained from image data, to analyze the accuracy of polarographic needle electrode measurements in quantifying hypoxia, to quantify the optimum number of measurements required to satisfactorily evaluate the tumor oxygenation status, and to study the effects of hypoxia on radiation response. Our results indicate that the model successfully generated an accurate oxygenation map for tumor cross-sections with known vascular distribution. The method developed here provides a way to estimate tumor hypoxia and provides guidance in planning accurate and effective therapeutic strategies and invasive estimation techniques. Our results agree with the previous findings that the needle electrode technique gives a good estimate of tumor hypoxia if the sampling is done in a uniform way with 5-6 tracks of 20–30 measurements each. Moreover, the analysis indicates that the accurate measurement of oxygen profile can be very useful in determining right radiation doses to the patients.

Efficient Monte Carlo modelling of individual tumour cell propagation for hypoxic head and neck cancer

A Monte Carlo tumour model has been developed to simulate tumour cell propagation for head and neck squamous cell carcinoma. The model aims to eventually provide a radiobiological tool for radiation oncology clinicians to plan patient treatment schedules based on properties of the individual tumour. The inclusion of an oxygen distribution amongst the tumour cells enables the model to incorporate hypoxia and other associated parameters, which affect tumour growth. The object oriented program FORTRAN 95 has been used to create the model algorithm, with Monte Carlo methods being employed to randomly assign many of the cell parameters from probability distributions. Hypoxia has been implemented through random assignment of partial oxygen pressure values to individual cells during tumour growth, based on in vivo Eppendorf probe experimental data. The accumulation of up to 10 million virtual tumour cells in 15 min of computer running time has been achieved. The stem cell percentage and the degree of hypoxia are the parameters which most influence the final tumour growth rate. For a tumour with a doubling time of 40 days, the final stem cell percentage is approximately 1% of the total cell population. The effect of hypoxia on the tumour growth rate is significant. Using a hypoxia induced cell quiescence limit which affects 50% of cells with and oxygen levels less than 1 mm Hg, the tumour doubling time increases to over 200 days and the time of tumour growth for a clinically detectable tumour (10(9) cells) increases from 3 to 8 years. A biologically plausible Monte Carlo model of hypoxic head and neck squamous cell carcinoma tumour growth has been developed for real time assessment of the effects of multiple biological parameters which impact upon the response of the individual patient to fractionated radiotherapy.

The influence of output measurement time interval and tolerance on treatment dose deviation in photon external beam radiotherapy

A method was developed to estimate the spread of treatment doses due to a given output measurement, time interval and action level in external photon beam radiotherapy. The method exploits empirical or simulated data of both output stability and the reproducibility of the absolute output measurements and relative constancy checks. The spread of an output and the probability that an output is outside the predefined tolerance limits were estimated for different quality control procedures of the output. The use of internationally recommended output measurement intervals of 3, 1 and 0.25 months together with an action level of +/-2% results in the out-of-tolerance probability up to 49%, 26% and 3%, respectively, while the output is kept within up to +/-5.5%, +/-4.0% and +/-2.0%, respectively. It was also found that the action level has more prominent relative influence than the measurement interval. The results suggest that similar treatment quality can be achieved by doubling the output measurement time interval and lowering the action level from +/-2% to +/-1.5% and the constancy check action level from +/-3% to +/-2%.