An analysis of the relationship between radiosensitivity and volume effects in tumor control probability modeling

Treatment Planning Methods for Dose Painting by Numbers Treatment in Gamma Knife Radiosurgery

Purpose

Dose painting radiation therapy delivers a nonuniform dose to tumors to account for heterogeneous radiosensitivity. With recent and ongoing development of Gamma Knife machines making large-volume brain tumor treatments more practical, it is increasingly feasible to deliver dose painting treatments. The increased prescription complexity means automated treatment planning is greatly beneficial, and the impact of dose painting on stereotactic radiosurgery (SRS) plan quality has not yet been studied. This research investigates the plan quality achievable for Gamma Knife SRS dose painting treatments when using optimization techniques and automated isocenter placement in treatment planning.

Methods and Materials

Dose painting prescription functions with varying parameters were applied to convert voxel image intensities to prescriptions for 10 sample cases. To study achievable plan quality and optimization, clinically placed isocenters were used with each dose painting prescription and optimized using a semi-infinite linear programming formulation. To study automated isocenter placement, a grassfire sphere-packing algorithm and a clinically available Leksell gamma plan isocenter fill algorithm were used. Plan quality for each optimized treatment plan was measured with dose painting SRS metrics.

Results

Optimization can be used to find high quality dose painting plans, and plan quality is affected by the dose painting prescription method. Polynomial function prescriptions show more achievable plan quality than sigmoid function prescriptions even with high mean dose boost. Automated isocenter placement is shown as a feasible method for dose painting SRS treatment, and increasing the number of isocenters improves plan quality. The computational solve time for optimization is within 5 minutes in most cases, which is suitable for clinical planning.

Conclusions

The impact of dose painting prescription method on achievable plan quality is quantified in this study. Optimization and automated isocenter placement are shown as possible treatment planning methods to obtain high quality plans.

Modeling the Interplay Between Tumor Volume Regression and Oxygenation in Uterine Cervical Cancer During Radiotherapy Treatment

This paper describes a patient-specific mathematical model to predict the evolution of uterine cervical tumors at a macroscopic scale, during fractionated external radiotherapy. The model provides estimates of tumor regrowth and dead-cell reabsorption, incorporating the interplay between tumor regression rate and radiosensitivity, as a function of the tumor oxygenation level. Model parameters were estimated by minimizing the difference between predicted and measured tumor volumes, these latter being obtained from a set of 154 serial cone-beam computed tomography scans acquired on 16 patients along the course of the therapy. The model stratified patients according to two different estimated dynamics of dead-cell removal and to the predicted initial value of the tumor oxygenation. The comparison with a simpler model demonstrated an improvement in fitting properties of this approach (fitting error average value <5%, p < 0.01), especially in case of tumor late responses, which can hardly be handled by models entailing a constant radiosensitivity, failing to model changes from initial severe hypoxia to aerobic conditions during the treatment course. The model predictive capabilities suggest the need of clustering patients accounting for cancer cell line, tumor staging, as well as microenvironment conditions (e.g., oxygenation level).

First clinical implementation of the Capri applicator

This study was to assess the Capri applicator for patients with endometrial cancer undergoing high‐radiation dose treatments following external‐beam radiation therapy. The Capri applicator is an inflatable vaginal cylinder with multiple channels. It is used to tailor the dose distribution to an asymmetric vaginal disease, and better spare organs at risk. Five patients with high‐risk endometrial cancer were selected for this study. The patients were treated with a high dose of radiation using the Capri applicator: daily fraction of 7 Gy was prescribed for a total dose of 21 Gy. The treatment plans included radiobiological parameters such as equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and tumor control probability (TCP). Based on the dose‐volume histograms (DVH), we also calculated four quality factors: conformity index (CI), dose homogeneity index (DHI), dose nonuniformity index (DNR), and overdose index (OI). The TCP values range from 82.26% to 95.92%. Very low values of NTCP were observed for the bladder and rectum. The EUDs to organs at risk ranged from 4.65 Gy to 18.22 Gy for the bladder, and from 3.41 Gy from to 6.56 Gy for the rectum. The mean CI was 1.05(SD=0.0008). The mean DNR was 0.10(range0.0−0.295,SD=0.100). The mean OI was 0.019(SD=0.028). The DHIs were in the range of 1.0−0.754(mean0.886,SD=0.116). The use of a multichannel vaginal cylinder may not only help cover extensive vaginal disease, but also reduce the dose to the rectum. This dosimetric analysis shows that rectal doses could be reduced using a multichannel cylinder. However, the dose delivered to the bladder based on EUD calculation may be higher than that obtained with other methods. Each patient must be evaluated independently to determine if a multichannel treatment is appropriate. Clinical followup will show whether this rectal dose sparing translates into a real toxicity improvement.

PACS number: 3.6.96.0

Correlation of dose computed using different algorithms with local control following stereotactic ablative radiotherapy (SABR)-based treatment of non-small-cell lung cancer

PURPOSE

To retrospectively compute dose distributions for lung cancer patients treated with SABR, and to correlate dose distributions with outcome using a tumor control probability (TCP) model.

METHODS

Treatment plans for 133 NSCLC patients treated using 12 Gy/fxn × 4 (BED=106 Gy), and planned using a pencil-beam (1D-equivalent-path-length, EPL-1D) algorithm were retrospectively re-calculated using model-based algorithms (including convolution/superposition, Monte Carlo). 4D imaging was performed to manage motion. TCP was computed using the Marsden model and associations between dose and outcome were inferred.

RESULTS

Mean D95 reductions of 20% (max.=33%) were noted with model-based algorithms (relative to EPL-1D) for the smallest tumors (PTV<20 cm(3)), corresponding to actual delivered D95 BEDs of ≈ 60-85 Gy. For larger tumors (PTV>100 cm(3)), D95 reductions were ≈ 10% (BED>100 Gy). Mean lung doses (MLDs) were 15% lower for model-based algorithms for PTVs<20 cm(3). No correlation between tumor size and 2-year local control rate was observed clinically, consistent with TCP calculations, both of which were ≈ 90% across all PTV bins.

CONCLUSION

Results suggest that similar control rates might be achieved for smaller tumors using lower BEDs relative to larger tumors. However, more studies with larger patient cohorts are necessary to confirm this possible finding.

Lung dose for minimally moving thoracic lesions treated with respiration gating

PURPOSE

To evaluate incidental doses to benign lung tissue for patients with minimally moving lung lesions treated with respiratory gating.

METHODS AND MATERIALS

Seventeen lung patient plans were studied retrospectively. Tumor motion was less than 5 mm in all cases. For each patient, mid-ventilation (MidVen) and mid-inhalation (MidInh) breathing phases were reconstructed. The MidInh phase was centered on the end-of-inhale (EOI) phase within a 30% gating window. Planning target volumes, heart, and spinal cord were delineated on the MidVen phase and transferred to the MidInh phase. Lungs were contoured separately on each phase. Intensity-modulated radiotherapy plans were generated on the MidVen phases. The plans were transferred to the MidInh phase, and doses were recomputed. The evaluation metric was based on dose indices, volume indices, generalized equivalent uniform doses, and mass indices for targets and critical structures. Statistical tests were used to establish the significance of the differences between the reference (MidVen) and compared (MidInh) dose distributions.

RESULTS

Statistical tests demonstrated that the indices evaluated for targets, cord, and heart differed by within 2.3%. The index differences in the lungs, however, are in excess of 6%, indicating the potentially achievable lung sparing and/or dose escalation.

CONCLUSIONS

Respiratory gating is a clinical option for patients with minimally moving lung lesions treated at EOI. Gating will be more beneficial for larger tumors, since dose escalation in those cases will result in a larger increase in the tumor control probability.

Safety margin in irradiation of colorectal liver metastases: assessment of the control dose of micrometastases

Backround

Micrometastases of colorectal liver metastases are present in up to 50% of lesions. In this study we sought to determine the threshold dose for local control of occult micrometastases in patients undergoing CT (computed tomography)-guided brachytherapy of colorectal liver metastases.

Materials and methods

Nineteen patients demonstrated 34 local tumor recurrences originating from micrometastases after CT-guided brachytherapy of 27 colorectal liver metastases. We considered a local tumor recurrence as originating from a micrometastasis if tumor regrowth occurred adjacent to a formerly irradiated lesion and the distance of the 3D isocenter of the new lesion was ≤ 23.5 mm from the previous tumor margin. Follow-up MRI was fused with the planning-CT and dosimetry data. Two reviewers independently indicated the dose exposure at the isocenter of the micrometastases. Statistical analysis included an analysis of variance (ANOVA) using backward selection. 95% tolerance intervals with coverage of 87.5 and 75% of the data of the normal distribution were calculated.

Results

The median distance of the micrometastases to the margin of the originating colorectal metastases was 8.75 mm (1-21 mm). Dose exposure at the isocenter was 12.25 Gy (7-19.8) in median. We stratified according to the distance from the isocenter to the initial tumor margin: ≤ 9 mm, > 9-15 mm and > 15 mm. The median dose in the according isocenters was 13.18, 11.6 and 11.85 Gy. The threshold dose failing to prevent micrometastasis growth was sigificantly higher in a subgroup of lesions with ≤ 9 mm distance as compared to > 15 mm (13.18 vs 11.85 Gy). Adjuvant chemotherapy correlated with greater distance of micrometastasis growth to the tumor but not with the threshold dose.

Conclusion

To prevent loss of local tumor control by continuous growth of micrometastases a threshold dose of 15,4 Gy (single fraction) should be delivered at a distance of 21 mm to the gross tumor margin.

Is the α/β Value for Prostate Tumours Low Enough to be Safely Used in Clinical Trials?

There has been an intense debate over the past several years on the relevant alpha/beta value that could be used to describe the fractionation response of prostate tumours. Previously it has been assumed that prostate tumours have high alpha/beta values, similar to most other tumours and the early reacting normal tissues. However, the proliferation behaviour of the prostate tumours is more like that of the late reacting tissues, with slow doubling times and low alpha/beta values. The analyses of clinical results carried out in the past few years have indeed suggested that the alpha/beta value that characterises the fractionation response of the prostate is low, possibly even below the 3 Gy commonly assumed for most late complications, and hence that hypofractionation of the radiation treatment might improve the therapeutic ratio (better control at the same or lower complication rate). However, hypofractionation might also increase the complication rates in the surrounding late responding tissues and if their alpha/beta value is not larger that of prostate tumours it could even lead to a decrease in the therapeutic ratio. Therefore, the important question is whether the alpha/beta value for the prostate is lower than the alpha/beta values of the surrounding late responding tissues at risk. This paper reviews the clinical and experimental data regarding the radiobiological differential that might exist between prostate tumours and the late normal tissues around them. Several prospective hypofractionated trials that have been initiated recently in order to determine the alpha/beta value or the range of values that describe the fractionation response of prostate tumours are also reviewed. In spite of several confounding factors that interfere with the derivation of a precise value, it seems that most data support a trend towards lower alpha/beta values for prostate tumours than for rectum or bladder.

On the surviving fraction in irradiated multicellular tumour spheroids: calculation of overall radiosensitivity parameters, influence of hypoxia and volume effects

We model the heterogeneous response to radiation of multicellular tumour spheroids assuming position- and volume-dependent radiosensitivity. We propose a method to calculate the overall radiosensitivity parameters to obtain the surviving fraction of tumours. A mathematical model of a spherical tumour with a hypoxic core and a viable rim which is a caricature of a real tumour is constructed. The model is embedded in a two-compartment linear-quadratic (LQ) model, assuming a mixed bivariated Gaussian distribution to attain the radiosensitivity parameters. Ergodicity, i.e., the equivalence between ensemble and volumetric averages is used to obtain the overall radiosensitivities for the two compartments. We obtain expressions for the overall radiosensitivity parameters resulting from the use of both a linear and a nonlinear dependence of the local radiosensitivity with position. The model's results are compared with experimental data of surviving fraction (SF) for multicellular spheroids of different sizes. We make one fit using only the smallest spheroid data and we are able to predict the SF for the larger spheroids. These predictions are acceptable particularly using bounded sensitivities. We conclude with the importance of taking into account the contribution of clonogenic hypoxic cells to radiosensitivity and with the convenience of using bounded local sensitivities to predict overall radiosensitivity parameters.

Modeling the effect of tumor size in early breast cancer

SUMMARY BACKGROUND DATA

The purpose of this study was to determine the type of relationship between tumor size and mortality in early breast carcinoma.

METHODS

The data was abstracted from 83,686 cases registered in the Surveillance, Epidemiology, and End Results Program of women diagnosed with primary breast carcinoma between 1988 and 1997 presenting with a T1-T2 lesion and no metastasis in whom axillary node dissection was performed: 58,070 women were node-negative (N0) and 25,616 were node-positive (N+). End point was death from any cause. Tumor size was modeled as a continuous variable by proportional hazards using a generalized additive models procedure.

RESULTS

Functionally, a Gompertzian expression exp(-exp(-(size-15)/10)) provided a good fit to the effect of tumor size (in millimeters) on mortality, irrespective of nodal status. Quantitatively, for tumor size between 3 and 50 mm, the increase of crude cumulative death rate (number of observed deaths divided by the number of patients at risk) increased with size from 10% to 25% for N0 and from 20% to 40% for N+.

CONCLUSIONS

The functional relationship of tumor size with mortality is concordant with current knowledge of tumor growth. However, its qualitative and quantitative independence of nodal status is in contradiction with the prevailing concept of sequential disease progression from primary tumor to regional nodes. This argues against the perception that nodal metastases are caused by the primary tumor.

Statistical methods for clinical verification of dose–response parameters related to esophageal stricture and AVM obliteration from radiotherapy

The purpose of this work is to provide some statistical methods for evaluating the predictive strength of radiobiological models and the validity of dose-response parameters for tumour control and normal tissue complications. This is accomplished by associating the expected complication rates, which are calculated using different models, with the clinical follow-up records. These methods are applied to 77 patients who received radiation treatment for head and neck cancer and 85 patients who were treated for arteriovenous malformation (AVM). The three-dimensional dose distribution delivered to esophagus and AVM nidus and the clinical follow-up results were available for each patient. Dose-response parameters derived by a maximum likelihood fitting were used as a reference to evaluate their compatibility with the examined treatment methodologies. The impact of the parameter uncertainties on the dose-response curves is demonstrated. The clinical utilization of the radiobiological parameters is illustrated. The radiobiological models (relative seriality and linear Poisson) and the reference parameters are validated to prove their suitability in reproducing the treatment outcome pattern of the patient material studied (through the probability of finding a worse fit, area under the ROC curve and chi2 test). The analysis was carried out for the upper 5 cm of the esophagus (proximal esophagus) where all the strictures are formed, and the total volume of AVM. The estimated confidence intervals of the dose-response curves appear to have a significant supporting role on their clinical implementation and use.

Modeling killing and repopulation kinetics of subclinical cancer: direct calculations from clinical data

PURPOSE

Models for cell killing and repopulation can provide insight into the efficacy of therapies. Using clinical data on breast cancer recurrence after lumpectomy with or without radiotherapy (L+/-RT) and brain metastases after chemotherapy with or without prophylactic cranial irradiation (C+/-PCI) for small-cell lung cancer, estimates of cell killing and subclinical repopulation were tested against the results from simple radiobiologic models.

METHODS AND MATERIALS

The rates of local breast cancer recurrence after L+/-RT and of brain metastases after C+/-PCI were extracted from published randomized trials. In Method 1, assuming simple exponential growth, the cell number distributions after L+/-RT and C+/-PCI were calculated from the clinical data, and the impact of RT on these distributions was determined. In Method 2, "classic" radiobiology dictates that a typical course of breast RT and PCI results in approximately =7 and approximately =4.5 log of cell kill, respectively. Using an assumption of uniform log-kill, the clinical doubling times (CDTs) can be calculated directly from the clinical data.

RESULTS

Using Method 1, for breast cancer and assuming a CDT of 110 days and a clinically detectable cell number of 10(9), the calculated cell number distribution would be approximately uniformly distributed from 1 to 10(8) cells, with RT reducing the frequency at all points by approximately =75%. From the brain metastasis data, assuming a CDT of 55 days, a cell number distribution of 10(3) to 10(8) cells would be calculated. PCI reduces the frequency of metastases by roughly 40%. For both the breast and the brain data, the effects of RT on the cell number distribution are not consistent with uniform radiosensitivity. Using Method 2, assuming a cell number of 10 after L+/-RT, the calculated CDTs range from 14 to 124 days. For the brain metastasis case, assuming a starting cell number of 3.16 x 10(3), the CDTs would primarily be in the 10-30-day range.

CONCLUSION

The distribution of clinical responses to adjuvant RT suggests a broad range of radiosensitivity, rather than uniform log cell kill. The subpopulation of tumors with minimal cell kill appears to be significant. This heterogeneity may be due to radioresistant subpopulations, failure to irradiate tumor cells, and/or new tumor formation. Similarly, the computed CDTs consistent with the clinical data are shorter than those reported in the literature. Simple radiobiologic models that fail to incorporate heterogeneity of radiosensitivity and/or tumor cell repopulation do not adequately describe clinical outcomes.

Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: implications for the alpha/beta ratio

BACKGROUND AND PURPOSE

The recently obtained low value of approximately 1.5 for the alpha/beta of prostate cancer has led us to reexamine the optimal prostate tumor biology parameters, while taking into account everything known about the radiation response of prostate clonogens for use in a predictive dose-response model.

METHODS AND MATERIALS

Averages of the literature values of the alpha- and beta-inactivation coefficients for human prostate cancer cell lines were calculated. A robust tumor local control probability (TLCP) model was used that required average alpha and beta, as well as sigma(alpha), for the interpatient variation in single-hit killing (alpha). Median PO(2) values <or=1 mm Hg in the prostates of Fox Chase Cancer Center brachytherapy patients had been found in 21% of 115 cases. The oxygen enhancement ratios of 1.75 and 3.25 for alpha- and beta-inactivation, respectively, measured for tumor cells in vitro, were incorporated into the TLCP model, together with a clonogen density of approximately 10(5) cells/cm(3). Severe hypoxia and radioresistance were estimated for a proportion of tumors that was increased with PSA level.

RESULTS

For asynchronous human prostate cell lines irradiated in air, alpha(mean) was 0.26 +/- 0.07 (standard error) Gy(-1), sigma(alpha) = 0.06 Gy(-1), and beta(mean) was 0.0312 Gy(-2) +/- 0.0064 (standard error) Gy(-2). The TLCP data indicated that most tumors that contained aerobic cells would be cured, whereas most tumors that contained hypoxic cells would not be cured by total doses of 76 to 80 Gy. Clinical response data from the literature for external beam dose escalation, stratified by PSA value, and for low-dose-rate brachytherapy, were well predicted by the model, where the alpha/beta ratio was 8.5 and 15.5 for well-oxygenated and hypoxic clonogens, respectively.

CONCLUSIONS

Neither alpha/beta ratio nor clonogen number need be extremely low to explain the response of prostate cancer to brachytherapy and external beam therapy, contradicting other recent analyses. It is strongly suggested that severe hypoxia in the prostates of certain patients limits the overall cancer cure rate by conventional radiation therapy.

Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.

Should single or distributed parameters be used to explain the steepness of tumour control probability curves?

Linear quadratic (LQ) modelling allows easy comparison of different fractionation schedules in radiotherapy. However, estimating the radiation effect of a single fractionated treatment introduces many questions with respect to the parameters to be used in the modelling process. Several studies have used tumour control probability (TCP) curves in order to derive the values for the LQ parameters that may be used further for the analysis and ranking of treatment plans. Unfortunately, little attention has been paid to the biological relevance of these derived parameters, either for the initial number of cells or their intrinsic radiosensitivity, or both. This paper investigates the relationship between single values for the TCP parameters and the resulting dose-response curve. The results of this modelling study show how clinical observations for the position and steepness of the TCP curve can be explained only by the choice of extreme values for the parameters, if they are single values. These extreme values are in contradiction with experimental observations. This contradiction suggests that single values for the parameters are not likely to explain reasonably the clinical observations and that some distributions of input parameters should be taken into consideration.

Incorporating biologic measurements (SF(2), CFE) into a tumor control probability model increases their prognostic significance: a study in cervical carcinoma treated with radiation therapy

PURPOSE

To assess whether incorporation of measurements of surviving fraction at 2 Gy (SF(2)) and colony-forming efficiency (CFE) into a tumor control probability (tcp) model increases their prognostic significance.

METHODS AND MATERIALS

Measurements of SF(2) and CFE were available from a study on carcinoma of the cervix treated with radiation alone. These measurements, as well as tumor volume, dose, and treatment time, were incorporated into a Poisson tcp model (tcp(alpha,rho)). Regression analysis was performed to assess the prognostic power of tcp(alpha,rho) vs. the use of either tcp models with biologic parameters fixed to best-fit estimates (but incorporating individual dose, volume, and treatment time) or the use of SF(2) and CFE measurements alone.

RESULTS

In a univariate regression analysis of 44 patients, tcp(alpha,rho) was a better prognostic factor for both local control and survival (p < 0.001 and p = 0.049, respectively) than SF(2) alone (p = 0.009 for local control, p = 0.29 for survival) or CFE alone (p = 0.015 for local control, p = 0.38 for survival). In multivariate analysis, tcp(alpha,rho) emerged as the most important prognostic factor for local control (p < 0.001, relative risk of 2.81). After allowing for tcp(alpha,rho), CFE was still a significant independent prognostic factor for local control, whereas SF(2) was not. The sensitivities of tcp(alpha,rho) and SF(2) as predictive tests for local control were 87% and 65%, respectively. Specificities were 70% and 77%, respectively.

CONCLUSIONS

A Poisson tcp model incorporating individual SF(2), CFE, dose, tumor volume, and treatment time was found to be the best independent prognostic factor for local control and survival in cervical carcinoma patients.

Radiation response and cure rate of human colon adenocarcinoma spheroids of different size: the significance of hypoxia on tumor control modelling

PURPOSE

To evaluate the adequacy of a Poisson tumor control probability (tcp) model and the impact of hypoxia on tumor cure.

METHODS AND MATERIALS

A human colon adenocarcinoma cell line, WiDr, was grown as multicellular spheroids of different diameters. Measurements were made of cell survival and spheroid cure following 300-kV X-ray external beam irradiation in air and nitrogen. Cell survival data were fitted using a two-compartment and an oxygen diffusion model. Spheroid cure data were fitted using the tcp model.

RESULTS

Hypoxia was seen only for spheroids greater than 500 microm in diameter. For small spheroids tcp estimates of radiosensitivity and clonogenic number showed excellent agreement with experimentally derived values. For large spheroids, although tcp estimates of radiosensitivity were comparable with measurements, estimates of the clonogenic number were considerably lower than the experimental count. Reoxygenation of large spheroids before irradiation resulted in the tcp estimates of the number of clonogenic cells agreeing with measured values.

CONCLUSIONS

When hypoxia was absent, the tcp model accurately predicted cure from measured radiosensitivity and clonogen number. When hypoxia was present, the number of cells capable of regrowth in situ was considerably lower than the number of clonogenic cells that initially survived irradiation. As this counteracted the decreased radiosensitivity, hypoxia was less important for cure than predicted from cell survival assays. This finding suggests that chronic hypoxia may not limit directly the success of radiation therapy.