Estimation of parameters of dose-volume models and their confidence limits

Effects From Nonuniform Dose Distribution in the Spinal Nerves of Pigs: Analysis of Normal Tissue Complication Probability Models

PURPOSE

Our purpose was to evaluate normal tissue complication probability (NTCP) models for their ability to describe the increase in tolerance as the length of irradiated spinal nerve is reduced in a pig.

METHODS AND MATERIALS

Common phenomenological and semimechanistic NTCP models were fit using the maximum likelihood estimate method to dose-response data from spinal nerve irradiation studies in pigs. Statistical analysis was used to compare how well each model fit the data. Model parameters were then applied to a previously published dose distribution used for spinal cord irradiation in rats under the assumption of a similar dose-response.

RESULTS

The Lyman-Kutcher-Burman model, relative seriality, and critical volume model fit the spinal nerve data equally well, but the mean dose logistic and relative seriality models gave the best fit after penalizing for the number of model parameters. The minimum dose logistic regression model was the only model showing a lack of fit. When extrapolated to a 0.5-cm simulated square-wave-like dose distribution, the serial behaving models showed negligible increase in dose-response curve. The Lyman-Kutcher-Burman model and relative seriality models showed significant shifting of NTCP curves due to parallel behaving parameters. The critical volume model gave the closest match to the rat data.

CONCLUSIONS

Several phenomenological and semimechanistic models were observed to adequately describe the increase in the radiation tolerance of the spinal nerves when changing the irradiated length from 1.5 to 0.5 cm. Contrary to common perception, model parameters suggest parallel behaving tissue architecture. Under the assumption that the spinal nerve response to radiation is similar to that of the spinal cord, only the critical volume model was robust when extrapolating to outcome data from a 0.5-cm square-wave-like dose distribution, as was delivered in rodent spinal cord irradiation research.

Reliability of dose volume constraint inference from clinical data

Dose volume histogram points (DVHPs) frequently serve as dose constraints in radiotherapy treatment planning. An experiment was designed to investigate the reliability of DVHP inference from clinical data for multiple cohort sizes and complication incidence rates. The experimental background was radiation pneumonitis in non-small cell lung cancer and the DVHP inference method was based on logistic regression. From 102 NSCLC real-life dose distributions and a postulated DVHP model, an 'ideal' cohort was generated where the most predictive model was equal to the postulated model. A bootstrap and a Cohort Replication Monte Carlo (CoRepMC) approach were applied to create 1000 equally sized populations each. The cohorts were then analyzed to establish inference frequency distributions. This was applied to nine scenarios for cohort sizes of 102 (1), 500 (2) to 2000 (3) patients (by sampling with replacement) and three postulated DVHP models. The Bootstrap was repeated for a 'non-ideal' cohort, where the most predictive model did not coincide with the postulated model. The Bootstrap produced chaotic results for all models of cohort size 1 for both the ideal and non-ideal cohorts. For cohort size 2 and 3, the distributions for all populations were more concentrated around the postulated DVHP. For the CoRepMC, the inference frequency increased with cohort size and incidence rate. Correct inference rates  >[Formula: see text] were only achieved by cohorts with more than 500 patients. Both Bootstrap and CoRepMC indicate that inference of the correct or approximate DVHP for typical cohort sizes is highly uncertain. CoRepMC results were less spurious than Bootstrap results, demonstrating the large influence that randomness in dose-response has on the statistical analysis.

Influence of different dose calculation algorithms on the estimate of NTCP for lung complications

Due to limitations and uncertainties in dose calculation algorithms, different algorithms can predict different dose distributions and dose-volume histograms for the same treatment. This can be a problem when estimating the normal tissue complication probability (NTCP) for patient-specific dose distributions. Published NTCP model parameters are often derived for a different dose calculation algorithm than the one used to calculate the actual dose distribution. The use of algorithm-specific NTCP model parameters can prevent errors caused by differences in dose calculation algorithms. The objective of this work was to determine how to change the NTCP model parameters for lung complications derived for a simple correction-based pencil beam dose calculation algorithm, in order to make them valid for three other common dose calculation algorithms. NTCP was calculated with the relative seriality (RS) and Lyman-Kutcher-Burman (LKB) models. The four dose calculation algorithms used were the pencil beam (PB) and collapsed cone (CC) algorithms employed by Oncentra, and the pencil beam convolution (PBC) and anisotropic analytical algorithm (AAA) employed by Eclipse. Original model parameters for lung complications were taken from four published studies on different grades of pneumonitis, and new algorithm-specific NTCP model parameters were determined. The difference between original and new model parameters was presented in relation to the reported model parameter uncertainties. Three different types of treatments were considered in the study: tangential and locoregional breast cancer treatment and lung cancer treatment. Changing the algorithm without the derivation of new model parameters caused changes in the NTCP value of up to 10 percentage points for the cases studied. Furthermore, the error introduced could be of the same magnitude as the confidence intervals of the calculated NTCP values. The new NTCP model parameters were tabulated as the algorithm was varied from PB to PBC, AAA, or CC. Moving from the PB to the PBC algorithm did not require new model parameters; however, moving from PB to AAA or CC did require a change in the NTCP model parameters, with CC requiring the largest change. It was shown that the new model parameters for a given algorithm are different for the different treatment types.

Normal tissue complication probability (NTCP) parameters for breast fibrosis: pooled results from two randomised trials

INTRODUCTION

The dose-volume effect of radiation therapy on breast tissue is poorly understood. We estimate NTCP parameters for breast fibrosis after external beam radiotherapy.

MATERIALS AND METHODS

We pooled individual patient data of 5856 patients from 2 trials including whole breast irradiation followed with or without a boost. A two-compartment dose volume histogram model was used with boost volume as the first compartment and the remaining breast volume as second compartment. Results from START-pilot trial (n=1410) were used to test the predicted models.

RESULTS

26.8% patients in the Cambridge trial (5 years) and 20.7% patients in the EORTC trial (10 years) developed moderate-severe breast fibrosis. The best fit NTCP parameters were BEUD3(50)=136.4 Gy, γ50=0.9 and n=0.011 for the Niemierko model and BEUD3(50)=132 Gy, m=0.35 and n=0.012 for the Lyman Kutcher Burman model. The observed rates of fibrosis in the START-pilot trial agreed well with the predicted rates.

CONCLUSIONS

This large multi-centre pooled study suggests that the effect of volume parameter is small and the maximum RT dose is the most important parameter to influence breast fibrosis. A small value of volume parameter 'n' does not fit with the hypothesis that breast tissue is a parallel organ. However, this may reflect limitations in our current scoring system of fibrosis.

Toolkit for determination of dose-response relations, validation of radiobiological parameters and treatment plan optimization based on radiobiological measures

Accurately determined dose-response relations of the different tumors and normal tissues should be estimated and used in the clinic. The aim of this study is to demonstrate developed tools that are necessary for determining the dose-response parameters of tumors and normal tissues, for clinically verifying already published parameter sets using local patient materials and for making use of all this information in the optimization and comparison of different treatment plans and radiation techniques. One of the software modules (the Parameter Determination Module) is designed to determine the dose-response parameters of tumors and normal tissues. This is accomplished by performing a maximum likelihood fitting to calculate the best estimates and confidence intervals of the parameters used by different radiobiological models. Another module of this software (the Parameter Validation Module) concerns the validation and compatibility of external or reported dose-response parameters describing tumor control and normal tissue complications. This is accomplished by associating the expected response rates, which are calculated using different models and published parameter sets, with the clinical follow-up records of the local patient population. Finally, the last module of the software (the Radiobiological Plan Evaluation Module) is used for estimating and optimizing the effectiveness a treatment plan in terms of complication-free tumor control, P(+). The use of the Parameter Determination Module is demonstrated by deriving the dose-response relation of proximal esophagus from head and neck cancer radiotherapy. The application of the Parameter Validation Module is illustrated by verifying the clinical compatibility of those dose-response parameters with the examined treatment methodologies. The Radiobiological Plan Evaluation Module is demonstrated by evaluating and optimizing the effectiveness of head and neck cancer treatment plans. The results of the radiobiological evaluation are compared against dosimetric criteria. The presented toolkit appears to be very convenient and efficient for clinical implementation of radiobiological modeling. It can also be used for the development of a clinical data and health information database for assisting the performance of epidemiological studies and the collaboration between different institutions within research and clinical frameworks.

A comparison of dose-response models for the parotid gland in a large group of head-and-neck cancer patients

PURPOSE

The dose-response relationship of the parotid gland has been described most frequently using the Lyman-Kutcher-Burman model. However, various other normal tissue complication probability (NTCP) models exist. We evaluated in a large group of patients the value of six NTCP models that describe the parotid gland dose response 1 year after radiotherapy.

METHODS AND MATERIALS

A total of 347 patients with head-and-neck tumors were included in this prospective parotid gland dose-response study. The patients were treated with either conventional radiotherapy or intensity-modulated radiotherapy. Dose-volume histograms for the parotid glands were derived from three-dimensional dose calculations using computed tomography scans. Stimulated salivary flow rates were measured before and 1 year after radiotherapy. A threshold of 25% of the pretreatment flow rate was used to define a complication. The evaluated models included the Lyman-Kutcher-Burman model, the mean dose model, the relative seriality model, the critical volume model, the parallel functional subunit model, and the dose-threshold model. The goodness of fit (GOF) was determined by the deviance and a Monte Carlo hypothesis test. Ranking of the models was based on Akaike's information criterion (AIC).

RESULTS

None of the models was rejected based on the evaluation of the GOF. The mean dose model was ranked as the best model based on the AIC. The TD(50) in these models was approximately 39 Gy.

CONCLUSIONS

The mean dose model was preferred for describing the dose-response relationship of the parotid gland.

The Impact of Heart Irradiation on Dose–Volume Effects in the Rat Lung

PURPOSE

To test the hypothesis that heart irradiation increases the risk of a symptomatic radiation-induced loss of lung function (SRILF) and that this can be well-described as a modulation of the functional reserve of the lung.

METHODS AND MATERIALS

Rats were irradiated with 150-MeV protons. Dose-response curves were obtained for a significant increase in breathing frequency after irradiation of 100%, 75%, 50%, or 25% of the total lung volume, either including or excluding the heart from the irradiation field. A significant increase in the mean respiratory rate after 6-12 weeks compared with 0-4 weeks was defined as SRILF, based on biweekly measurements of the respiratory rate. The critical volume (CV) model was used to describe the risk of SRILF. Fits were done using a maximum likelihood method. Consistency between model and data was tested using a previously developed goodness-of-fit test.

RESULTS

The CV model could be fitted consistently to the data for lung irradiation only. However, this fitted model failed to predict the data that also included heart irradiation. Even refitting the model to all data resulted in a significant difference between model and data. These results imply that, although the CV model describes the risk of SRILF when the heart is spared, the model needs to be modified to account for the impact of dose to the heart on the risk of SRILF. Finally, a modified CV model is described that is consistent to all data.

CONCLUSIONS

The detrimental effect of dose to the heart on the incidence of SRILF can be described by a dose dependent decrease in functional reserve of the lung.

Acute esophageal toxicity in non-small cell lung cancer patients after high dose conformal radiotherapy

BACKGROUND AND PURPOSE

To correlate acute esophageal toxicity with dosimetric and clinical parameters for non-small cell lung cancer (NSCLC) patients treated with radiotherapy (RT) alone or with chemo-radiotherapy (CRT).

PATIENTS AND METHODS

We analyzed the data of 156 patients with medically inoperable or locally advanced NSCLC. Seventy-four patients were irradiated with high dose RT only, 45 patients with sequential CRT (Gemicitabine/Cisplatin) and 37 patients with concurrent CRT (Cisplatin daily 6 mg/m(2)). The radiation dose delivered ranged from 49.5 to 94.5 Gy (2.25-2.75 Gy per fraction) with an overall treatment time of 5-6 weeks. For all patients the maximal acute esophageal toxicity (RTOG/EORTC criteria) was scored and related to dose-volume parameters, as well as to clinical and treatment-related parameters. All parameters were tested univariable and multivariable in a binary logistic regression model. The toxicity data of a homogeneous subgroup was fitted to the Lyman-Kutcher-Burman model.

RESULTS

Grade 2 acute esophageal toxicity or higher occurred in 27% (n=42) of the patient population of which nine patients developed grade 3 toxicity and one patient grade 4. All 10 patients with grade>or=3 esophageal toxicity received concurrent CRT. At multivariable analysis, the most significant clinical parameter to predict acute esophageal toxicity was the concurrent use of CRT. The most significant dosimetric parameter was the esophagus volume that received at least 35 Gy. The data of the patients who did not receive concurrent CRT were well described by the Lyman-Kutcher-Burman normal tissue complication probability model. The optimal fit of the data of non-concurrent treated patients to this model was obtained using the following values for the parameters: TD(50)=47 Gy (41-60 Gy), n=0.69 (0.18-6.3) and m=0.36 (0.25-0.55) where the numbers between brackets denote the 95% confidence interval. Acute esophageal toxicity was not significantly increased for patients treated with sequential CRT.

CONCLUSION

Both concurrent CRT and the volume that receives at least 35 Gy were predictors of acute esophageal toxicity.

Radiation damage to the heart enhances early radiation-induced lung function loss

In many thoracic cancers, the radiation dose that can safely be delivered to the target volume is limited by the tolerance dose of the surrounding lung tissue. It has been hypothesized that irradiation of the heart may be an additional risk factor for the development of early radiation-induced lung morbidity. In the current study, the dependence of lung tolerance dose on heart irradiation is determined. Fifty percent of the rat lungs were irradiated either including or excluding the heart. Proton beams were used to allow very accurate and conformal dose delivery. Lung function toxicity was scored using a breathing rate assay. We confirmed that the tolerance dose for early lung function damage depends not only on the lung region that is irradiated but also that concomitant irradiation of the heart severely reduces the tolerance of the lung. This study for the first time shows that the response of an organ to irradiation does not necessarily depend on the dose distribution in that organ alone.

Data on dose–volume effects in the rat spinal cord do not support existing NTCP models

PURPOSE

To evaluate several existing dose-volume effect models for their ability to describe the occurrence of white matter necrosis in rat spinal cord after irradiation with small proton beams.

METHODS AND MATERIALS

A large number of dose-volume effect models has been fitted to data on the occurrence of white matter necrosis after irradiation with small proton beams. The fitting was done with the maximum likelihood method. For each model, the goodness of fit was calculated. An empirical tolerance dose-volume (eTDV) model was designed to describe data obtained after uniform irradiation.

RESULTS

The eTDV model, the critical element model, and critical volume model with inclusion of the repair-by-migration principle described by Shirato, were able to describe the data obtained after irradiation with uniform dose distributions of varying sizes. However, none of the models under investigation was able to describe all the data. Extension of the developed empirical model with a repair mechanism with a limited range resulted in a good description of the tolerance doses.

CONCLUSIONS

In the rat spinal cord, a nonlocal repair mechanism, acting from nonirradiated to irradiated tissue, plays an important role in the (prevention of the) occurrence of white matter necrosis after irradiation. Models that take into account this effect need to be developed.

Dose-volume effects in rat thoracolumbar spinal cord: an evaluation of NTCP models

PURPOSE

To evaluate models for normal-tissue-complication probability (NTCP) on describing the dose-volume effect in rat thoracolumbar spinal cord.

METHODS AND MATERIALS

Single-dose irradiation of four field lengths (4, 1.5, 1.0, and 0.5 cm) was evaluated by the endpoints paresis and white-matter necrosis. The resulting dose-response data were used to rank phenomenological and tissue architecture NTCP models.

RESULTS

The 0.5-cm field length showed a steep increase in radiation tolerance. Statistical analysis of the model fits, which included evaluation of goodness of fit (GOF) and confidence intervals, resulted in the rejection of all the models considered. Excluding the smallest field length, the Schultheiss (D(50) = 21.5 Gy, k = 26.5), the relative seriality (D(50) = 21.4 Gy, s = 1.6, gamma(50) = 6.3), and the critical element (D(50,FSU) = 26.6 Gy, gamma(50,FSU) = 2.3, n = 1.3) model gave the best fit.

CONCLUSION

A thorough statistical analysis resulted in a serial or critical-element behavior for the field lengths of 1.0 cm and greater. Including the 0.5-cm field length, the radiation response markedly diverged from serial properties, but none of the models applied acceptably described this dose-response relationship. This study suggests that the commonly assumed serial behavior of the spinal cord might be valid for daily use in external- beam irradiation.

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.

Treatment planning for conformal proton radiation therapy

Clinical results from various trials have demonstrated the viability of protons in radiation therapy and radiosurgery. This has motivated a few large medical centers to design and build expensive hospital based proton facilities based proton facilities (current cost estimates for a proton facility is around 100 million US dollars). Until this development proton therapy was done using retrofitted equipment originally designed for nuclear experiments. There are presently only three active proton therapy centers in the United States, 22 worldwide. However, more centers are under construction and being proposed in the US and abroad. The important difference between proton and x-ray therapy is in the dose distribution. X-rays deposit most of their dose at shallow depths of a few centimeters with a gradual decay with depth in the patient. Protons deliver most of their dose in the Bragg peak, which can be delivered at most clinically required depths followed by a sharp fall-off. This sharp falloff makes protons sensitive to variations in treatment depths within patients. Treatment planning incorporates all the knowledge of protons into a process, which allows patients to be treated accurately and reliably. This process includes patient immobilization, imaging, targeting, and modeling of planned dose distributions. Although the principles are similar to x-ray therapy some significant differences exist in the planning process, which described in this paper. Target dose conformality has recently taken on much momentum with the advent of intensity modulated radiation therapy (IMRT) with photon beams. Proton treatments provide a viable alternative to IMRT because they are inherently conformal avoiding normal tissue while irradiating the intended targets. Proton therapy will soon bring conformality to a new high with the development of intensity modulated proton therapy (IMPT). Future challenges include keeping the cost down, increasing access to conventional proton therapy as well as the clinical implementation of IMPT. Computing advances are making Monte Carlo techniques more accessible to treatment planning for all modalities including proton therapy. This technique will allow complex delivery configurations to be properly modeled in a clinical setting.