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

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.

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.

Radiobiology

New understandings of the biology of radiosurgery are considered. Differences from the radiobiology of fractionated radiotherapy are outlined. It is noted DNA damage alone is insufficient to account for the tissue changes which occur. Changes in blood vessels and immunological mechanisms are also involved. Tissue repair is more rapid than previously thought so that dose rate (the rate of delivery of radiation to the tissues) has been seen to be more important. The value of fractionation is examined. The effect of radiosurgery on normal brain (so called functional radiosurgery) is considered. The desired effects may be achieved by a focal stable destruction of brain from a high radiation dose. They may also be achieved using a lower dose which acts through the mechanism known as radiosurgical neuromodulation.

Development of generalized time-dependent TCP model and the investigation of the effect of repopulation and weekend breaks in fractionated external beam therapy

We developed a tumor control probability (TCP) model that incorporates variable time intervals between fractions and a kick-off time (T_k) for radiation-induced accelerated tumor proliferation. The resulting Lee-Rosen model, TCP_LR, was used to compute TCPs for treatment courses with and without weekend treatment for tumors with different proliferation rates - slow (prostate), moderate (breast), and rapid (head and neck). TCPs were computed using ideal uniform dose distributions and actual patient plans. The doses for the uniform plans were the mean doses for the prostate and breast cases and the minimum tumor dose for the head and neck case. The TCP_LR model predictions agreed with expectations that TCP increases with increasing T_k in all cases. For standard fractionation, as T_k increased from 0 to 4 weeks, TCP increased for the patient distributions by 74.7% for the head and neck cancer, by 6.2% for the breast cancer, and by 2.4% for the prostate cancers. For the uniform dose distributions, the increases were 79.2%, 5.7%, and 2.3%, respectively. TCP increased as the number of weekend breaks decreased. The effect of weekend breaks decreased as the tumor proliferation rate decreased. For the head and neck tumor, notable decreases in TCP of 6.0% (uniform dose distribution) and 6.8% (actual plan dose distribution) were observed with Friday starts compared to Monday starts for the standard 5 fx/wk schedule (T_k = 4 wk). The 7 fx/wk schedule produced increases in TCP of 17.0% and 20.5% for the uniform and patient dose distributions, respectively, compared to the standard schedule. For the breast cancer, starting the 5 fx/wk schedule on Friday decreased the TCP by 0.2% (T_k = 4 wk) compared to a Monday start. The 7 fx/wk schedule produced increases of 0.3% and 0.4% in TCP compared to the standard schedule for the uniform and patient dose distributions, respectively (T_k = 4 wk). For the prostate cancer, the change in TCP for 5 fx/wk schedules starting on different days was 0.1%. The 7 fx/wk schedule increased TCP by 0.8% compared to the standard schedule (T_k = 4 wk). TCP values for the uniform dose distributions for the standard schedule (T_k = 4 wk) agreed with the TCP values for the actual dose distributions within 4.5% for the head and neck tumor and within 0.2% for the breast and prostate tumors. This good agreement suggests that the doses chosen for the uniform dose distributions were good approximations to the clinical doses. The results for head and neck tumors support, in part, the current practice of hyperfractionated/accelerated radiotherapy. They also suggest that shortening the overall treatment time for conventional fractions by eliminating weekend breaks might be beneficial. The predicted effect on TCP of the various schedules studied was insignificant for prostate and breast tumors, suggesting that a weekend treatment might not be necessary for patients starting radiotherapy on a Friday. There is significant uncertainty in the values of the model parameters chosen for these calculations, and no consideration was given to the potential effects of these various schedules on normal tissues.

Influence of inhomogeneous radiosensitivity distributions and intrafractional organ movement on the tumour control probability of focused IMRT in prostate cancer

PURPOSE

To evaluate the influence of radioresistance and intrafractional movement on the tumour control probability (TCP) in IMRT prostate treatments using simultaneous integrated boosts to PSMA-PET/CT-delineated GTVs.

MATERIALS AND METHODS

13 patients had PSMA-PET/CT prior to prostatectomy and histopathological examination. Two GTVs were available: GTV-PET and GTV-histo, which is the true cancer volume. Focused IMRT plans delivering 77 Gy in 35 fractions to the prostate and 95 Gy to PTV-PET were produced. For random portions of the true cancer volume, α and α/β were uniformly changed to represent different radiosensitivity reductions. TCP was calculated (linear quadratic model) for the true cancer volume with and without simulated intrafractional movement.

RESULTS

Intrafractional movement increased the TCP by up to 10.2% in individual cases and 1.2% averaged over all cases for medium radiosensitivity levels. At lower levels of radiosensitivity, movement decreased the TCP. Radiosensitivity reductions of 10-20% led to TCP reductions of 1-24% and 10-68% for 1% and 5% affected cancer volume, respectively. There is no linear correlation but a sudden breakdown of TCPs within a small range of radiosensitivity levels.

CONCLUSION

TCP drops significantly within a narrow range of radiosensitivity levels. Intrafractional movement can increase TCP when the boost volume is surrounded by a sufficiently high dose plateau.

Biological imaging for individualized therapy in radiation oncology: part I physical and technical aspects

Recently, there has been an increase in the imaging modalities available for radiotherapy planning and radiotherapy prognostic outcome: dual energy computed tomography (CT), dynamic contrast enhanced CT, dynamic contrast enhanced magnetic resonance imaging (MRI), diffusion-weighted MRI, positron emission tomography-CT, dynamic contrast enhanced ultrasound, MR spectroscopy and positron emission tomography-MR. These techniques enable more precise gross tumor volume definition than CT alone and moreover allow subvolumes within the gross tumor volume to be defined which may be given a boost dose or an individual voxelized dose prescription may be derived. With increased plan complexity care must be taken to immobilize the patient in an accurate and reproducible manner. Moreover the physical and technical limitations of the entire treatment planning chain need to be well characterized and understood, interdisciplinary collaboration ameliorated (physicians and physicists within nuclear medicine, radiology and radiotherapy) and image protocols standardized.

Uncertainty evaluation of image-based tumour control probability models in radiotherapy of prostate cancer using a visual analytic tool

Functional imaging techniques provide radiobiological information that can be included into tumour control probability (TCP) models to enable individualized outcome predictions in radiotherapy. However, functional imaging and the derived radiobiological information are influenced by uncertainties, translating into variations in individual TCP predictions. In this study we applied a previously developed analytical tool to quantify dose and TCP uncertainty bands when initial cell density is estimated from MRI-based apparent diffusion coefficient maps of eleven patients. TCP uncertainty bands of 16% were observed at patient level, while dose variations bands up to 8 Gy were found at voxel level for an iso-TCP approach.

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

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

Biology of high single doses of IORT: RBE, 5 R's, and other biological aspects

Intraoperative radiotherapy differs from conventional, fractionated radiotherapy in several aspects that may influence its biological effect. The radiation quality influences the relative biologic effectiveness (RBE), and the role of the five R’s of radiotherapy (reassortment, repair, reoxygenation, repopulation, radiosensitivity) is different. Furthermore, putative special biological effects and the small volume receiving a high single dose may be important. The present review focuses on RBE, repair, and repopulation, and gives an overview of the other factors that potentially contribute to the efficacy. The increased RBE should be taken into account for low-energy X-rays while evidence of RBE < 1 for high-energy electrons at higher doses is presented. Various evidence supports a hypothesis that saturation of the primary DNA double-strand break (DSB) repair mechanisms leads to increasing use of an error-prone backup repair system leading to genomic instability that may contribute to inactivate tumour cells at high single doses. Furthermore, the elimination of repopulation of residual tumour cells in the tumour bed implies that some patients are likely to have very few residual tumour cells which may be cured even by low doses to the tumour bed. The highly localised dose distribution of IORT has the potential to inactivate tumour cells while sparing normal tissue by minimising the volume exposed to high doses. Whether special effects of high single doses also contribute to the efficacy will require further experimental and clinical studies.

Optimization of the fractionated irradiation scheme considering physical doses to tumor and organ at risk based on dose-volume histograms

PURPOSE

Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose-volume histograms for tumor and normal tissues of organs around the tumor.

METHODS

Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose-volume histogram.

RESULTS

It was found that the optimization of fractionation scheme incorporating the dose-volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8-32 fractions with a daily dose of 2.2-6.3 Gy.

CONCLUSIONS

It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose-volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.

Tumor radio-sensitivity assessment by means of volume data and magnetic resonance indices measured on prostate tumor bearing rats

PURPOSE

Radiation therapy is one of the most common treatments in the fight against prostate cancer, since it is used to control the tumor (early stages), to slow its progression, and even to control pain (metastasis). Although many factors (e.g., tumor oxygenation) are known to influence treatment efficacy, radiotherapy doses and fractionation schedules are often prescribed according to the principle "one-fits-all," with little personalization. Therefore, the authors aim at predicting the outcome of radiation therapy a priori starting from morphologic and functional information to move a step forward in the treatment customization.

METHODS

The authors propose a two-step protocol to predict the effects of radiation therapy on individual basis. First, one macroscopic mathematical model of tumor evolution was trained on tumor volume progression, measured by caliper, of eighteen Dunning R3327-AT1 bearing rats. Nine rats inhaled 100% O2 during irradiation (oxy), while the others were allowed to breathe air. Second, a supervised learning of the weight and biases of two feedforward neural networks was performed to predict the radio-sensitivity (target) from the initial volume and oxygenation-related information (inputs) for each rat group (air and oxygen breathing). To this purpose, four MRI-based indices related to blood and tissue oxygenation were computed, namely, the variation of signal intensity ΔSI in interleaved blood oxygen level dependent and tissue oxygen level dependent (IBT) sequences as well as changes in longitudinal ΔR1 and transverse ΔR2(*) relaxation rates.

RESULTS

An inverse correlation of the radio-sensitivity parameter, assessed by the model, was found with respect the ΔR2(*) (-0.65) for the oxy group. A further subdivision according to positive and negative values of ΔR2(*) showed a larger average radio-sensitivity for the oxy rats with ΔR2(*)<0 and a significant difference in the two distributions (p < 0.05). Finally, a leave-one-out procedure yielded a radio-sensitivity error lower than 20% in both neural networks.

CONCLUSIONS

While preliminary, these specific results suggest that subjects affected by the same pathology can benefit differently from the same irradiation modalities and support the usefulness of IBT in discriminating between different responses.

The effect of elemene on lung adenocarcinoma A549 cell radiosensitivity and elucidation of its mechanism

OBJECTIVE

To investigate the effect of elemene on the radiosensitivity of A549 cells and its possible molecular mechanism.

METHODS

Apoptosis of A549 cells was detected by flow cytometry and fluorescence microscopy. The effect of double-strand break (DSB) damage repair in A549 cells was evaluated using the neutral comet assay. Protein expression levels were detected using western blotting, and the correlation between protein levels was analyzed.

RESULTS

Elemene exhibited a radiosensitizing effect on A549 cells. The level of apoptosis induced by elemene combined with radiation was significantly greater (p<0.01) than that elicited by either radiation or elemene alone. Following radiation and subsequent repair for 24 h, the tail intensity of A549 cells treated with a combination of elemene and radiation was greater than that of cells treated with either elemene or radiation alone (p<0.01). This result indicates that elemene inhibits cellular DSB repair. Both elemene combined with radiation and radiation alone decreased the protein expression of DNA-PKcs and Bcl-2 compared to elemene alone (p<0.01), while p53 protein expression was increased (p<0.01). A negative correlation was observed between DNA-PKcs and p53 expression (r=-0.569, p=0.040), while a positive correlation was found between DNA-PKcs and Bcl-2 expression (r=0.755, p=0.012).

CONCLUSIONS

Elemene exhibits a radiosensitizing effect on A549 cells, and its underlying molecular mechanism of action may be related to the downregulation of DNA-PKcs gene expression.

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.

To fractionate or not to fractionate? That is the question for the radiosurgery of hypoxic tumors

Object

This study aimed to investigate the impact of tumor hypoxia on treatment outcome for metastases commonly treated with radiosurgery using 1 fraction of radiation and the potential gain from reoxygenation if the treatment is delivered in a few radiation fractions.

Methods

In silico metastasis-like radiosurgery targets were modeled with respect to size, density of clonogenic cells, and oxygenation. Treatment plans were produced for the targets using Leksell GammaPlan, delivering clinically relevant doses and evaluating the tumor control probability (TCP) that could be expected in each case. Fractionated schedules with 3, 4, and 5 fractions resulting in similar biological effective doses were also considered for the larger target, and TCP was determined under the assumption that local reoxygenation takes place between fractions.

Results

The results showed that well-oxygenated small- and medium-size metastases are well controlled by radiosurgery treatments delivering 20 or 22 Gy at the periphery, with TCPs ranging from 90% to 100%. If they are moderately hypoxic, the TCP could decrease to 60%. For large metastases, the TCPs from single-fraction treatments ranged from 0% to 19%, depending on tumor oxygenation. However, for fractionated treatments, the TCP for hypoxic tumors could significantly increase up to 51%, if reoxygenation occurs between fractions.

Conclusions

This study shows that hypoxia worsens the response to single-fraction radiosurgery, especially for large tumors. However, fractionated therapy for large hypoxic tumors might considerably improve the TCP and might constitute a simple way to improve the outcome of radiosurgery for patients with hypoxic tumors.