Risk of pneumonitis in breast cancer patients treated with radiation therapy and combination chemotherapy with paclitaxel.

BACKGROUND: Some chemotherapy (CT) drugs, including taxanes, may enhance the effectiveness of radiation therapy (RT). However, combining these therapies may increase the incidence of radiation pneumonitis, a lung inflammation. In a retrospective cohort study, we evaluated the incidence of radiation pneumonitis in breast cancer patients treated with RT and standard adjuvant CT by use of doxorubicin (Adriamycin) and cyclophosphamide, with and without paclitaxel. METHODS: Forty-one patients with breast cancer were treated with RT and adjuvant CT, including paclitaxel. Paclitaxel and RT (to breast-chest wall in all and lymph nodes in some) were delivered sequentially in 20 patients and concurrently in 21 patients. Paclitaxel was given weekly in some patients and every 3 weeks in other patients. The incidence of radiation pneumonitis was compared with that among patients in our database whose treatments did not include paclitaxel (n = 1286). The percentage of the lung volume irradiated was estimated. The Cox proportional hazards model was used to find covariates that may be associated with the observed outcomes. All P values were two-sided. RESULTS: Radiation pneumonitis developed in six of the 41 patients. Three patients received paclitaxel concurrently with RT, and three received it sequentially (P =.95). The mean percentage of lung volume irradiated was 20% in patients who developed radiation pneumonitis and 22% in those who did not (P =.6). For patients treated with CT including paclitaxel, the crude rate of developing radiation pneumonitis was 14.6% (95% confidence interval [CI] = 5.6% to 29.2%). For patients treated with CT without paclitaxel, the crude rate of pneumonitis was 1.1% (95% CI = 0.2% to 2.3%). The difference between the crude rates with or without paclitaxel is highly statistically significant (P<.0001). The mean time to develop radiation pneumonitis in patients treated concurrently with RT and paclitaxel was statistically significantly shorter in patients receiving paclitaxel weekly than in those receiving it every 3 weeks (P =.002). CONCLUSIONS: The use of paclitaxel and RT in the primary treatment of breast cancer should be undertaken with caution. Clinical trials with the use of combination CT, including paclitaxel plus RT, whether concurrent or sequential, must evaluate carefully the incidence of radiation pneumonitis.

Random search algorithm (RONSC) for optimization of radiation therapy with both physical and biological end points and constraints.

A new algorithm for the optimization of 3-dimensional radiotherapy plans is presented. The RONSC algorithm (Random Optimization with Non-linear Score functions and Constraints) is based on the idea of random search in the space of feasible solutions. RONSC takes advantage of some specific properties of the dose distribution and derivable information such as dose-volume histograms and calculated estimates of tumor control and normal tissue complication probabilities. The performance of the algorithm for clinical and test cases is discussed and compared with the performance of the simulated annealing algorithm, which is also based on the idea of random search.

Modeling of normal tissue response to radiation: the critical volume model.

PURPOSE: A model for calculating normal tissue complication probability in response to therapeutic doses of radiation is presented. METHODS AND MATERIALS: The model which we call the "critical volume model" is based on a concept of functional subunits defined either structurally (e.g., nephrons) or functionally, and an assumption that normal tissue complication probability is fully determined by the number or fraction of surviving functional subunits composing an organ or tissue. The essential features of the model are that it takes into account variations in tissue radiosensitivity and architecture of an organ for a single patient and for a patient population, and predicts the normal tissue complication probability under conditions of 3-dimensional inhomogeneity of the dose distribution. The model can be used for Integral Response, or "parallel," organs (where all functional subunits are performing the same function in parallel and the output of the organ is the sum of the outputs of the functional subunits and for Critical Element, or "serial," organs (where damage to one functional subunit results in an expression of damage for the whole organ). The model combines into one compact scheme new concepts and several ideas and models which have been previously developed by other investigators. RESULTS: The behavior of the model is presented and discussed for the example of the kidney, with clinical nephritis as the functional endpoint. CONCLUSIONS: The model has the potential to be a useful tool for evaluation and optimization of 3-dimensional treatment plans for a variety of types of normal tissues.

Optimization of 3D radiation therapy with both physical and biological end points and constraints.

A new optimization model is described and its clinical usefulness is demonstrated. The optimization technique was developed to allow computer optimization of 3-dimensional radiation therapy plans with biological models of tumor and normal tissue response to radiation as well as with scores based on physical dose. The emphasis was placed on the optimization model, which should describe, as closely as possible, the goal of the radiation treatment, which is eradication of the tumor while sparing normal tissues. Since the statement of the goals may vary from case to case, a technique that allows a variety of objective functions and types of constraints was developed. The optimization algorithm is capable of handling nonlinear and even discrete score (objective) functions and constraints and effectively explores the vast space of feasible solutions in a relatively short time (minutes of MicroVax 3200 CPU time). An example of computer optimization of radiation therapy of a chordoma of the sphenoid bone using x-ray and proton beams is shown and compared with the best plans achieved by an experienced planner. Directions for future development of the algorithm, allowing optimization of beam orientation, are presented.

Effect of incomplete repair on normal tissue complication probability in the spinal cord.

PURPOSE: To incorporate the effects of repair into a model for normal tissue complication probability (NTCP) in the spinal cord. METHODS AND MATERIALS: We used an existing model of NTCP for the spinal cord, based on a critical volume concept, into which we incorporated an incomplete repair (IR) scheme. Values for the repair half time were taken from existing experimental data. Repair corrections were expanded to account for the possibility of biphasic repair, namely the existence of long and short components of repair. RESULTS: We found that the model predicts complete repair to occur at approximately 15 hours, consistent with experimental data. The dependence of the model on the value of the dose per fraction was also studied. It was found that there is a sparing effect as the dose per fraction is decreased below 2 Gy. Surface plots of the NTCP as a function of both the interfraction interval (IFI) and the dose per fraction were generated. We investigated "iso-NTCP" curves, which may allow freedom in choice of treatment plans in terms of the optimal IFI and dose per fraction. As for biphasic repair, as the relative weights of the long and short components of repair were varied, the NTCP changed as well. The model showed little difference between mono- and bi-exponential repair in the time to complete repair, due to a dominance of the long component at long IFIs. CONCLUSIONS: Incorporating IR into NTCP modeling of the spinal cord is consistent with current experimental data. The concept of iso-NTCP curves is an approach which may be clinically useful.

Radiation dose-response of human tumors.

PURPOSE: The dose of radiation that locally controls human tumors treated electively or for gross disease is rarely well defined. These doses can be useful in understanding the dose requirements of novel therapies featuring inhomogeneous dosimetry and in an adjuvant setting. The goal of this study was to compute the dose of radiation that locally controls 50% (TCD50) of tumors in human subjects. METHODS AND MATERIALS: Logit regression was used with data collected from single institutions or from combinations of local control data accumulated from several institutions treating the same disease. RESULTS: 90 dose response curves were calculated; 62 of macroscopic tumor therapy, 28 of elective therapy with surgery for primary control. The mean and median TCD50 for gross disease were 50.0 and 51.9 Gy, respectively. The mean and median TCD50 for microscopic disease control were 39.3 and 37.9 Gy, respectively. At the TCD50, an additional dose of 1 Gy controlled an additional 2.5% (median) additional patients with macroscopic disease and 4.2% (median) additional patients with microscopic disease. For both macro- and microscopic disease, an increase of 1% of dose at the TCD50 increased control rates approximately 1% (median) or 2-3% (mean). A predominance of dose response curves had shallow slopes accounting for the discrepancy between mean and median values. CONCLUSION: Doses to control microscopic disease are approximately 12 Gy less than that required to control macroscopic disease, and are about 79% of the dose required to control macroscopic disease. The percentage increase in cures expected for a 1% increase in dose is similar for macroscopic microscopic disease, with a median value of approximately 1%/% and a mean of approximately 2.7%/%.

Conformal irradiation of the prostate: estimating long-term rectal bleeding risk using dose-volume histograms.

PURPOSE: Dose-volume histograms (DVHs) may be very useful tools for estimating probability of normal tissue complications (NTCP), but there is not yet an agreed upon method for their analysis. This study introduces a statistical method of aggregating and analyzing primary data from DVHs and associated outcomes. It explores the dose-volume relationship for NTCP of the rectum, using long-term data on rectal wall bleeding following prostatic irradiation. METHODS AND MATERIALS: Previously published data were reviewed and updated on 41 patients with Stages T3 and T4 prostatic carcinoma treated with photons followed by perineal proton boost, including dose-volume histograms (DVHs) of each patient's anterior rectal wall and data on the occurrence of postirradiation rectal bleeding (minimum FU > 4 years). Logistic regression was used to test whether some individual combination of dose and volume irradiated might best separate the DVHs into categories of high or low risk for rectal bleeding. Further analysis explored whether a group of such dose-volume combinations might be superior in predicting complication risk. These results were compared with results of the "critical volume model," a mathematical model based on assumptions of underlying radiobiological interactions. RESULTS: Ten of the 128 tested dose-volume combinations proved to be "statistically significant combinations" (SSCs) distinguishing between bleeders (14 out of 41) and nonbleeders (27 out of 41), ranging contiguously between 60 CGE (Cobalt Gray Equivalent) to 70% of the anterior rectal wall and 75 CGE to 30%. Calculated odds ratios for each SSC were not significantly different across the individual SSCs; however, analysis combining SSCs allowed segregation of DVHs into three risk groups: low, moderate, and high. Estimates of probabilities of normal tissue complications (NTCPs) based on these risk groups correlated strongly with observed data (p = 0.003) and with biomathematical model-generated NTCPs. CONCLUSIONS: There is a dose-volume relationship for rectal mucosal bleeding in the region between 60 and 75 CGE; therefore, efforts to spare rectal wall volume using improved treatment planning and delivery techniques are important. Stratifying dose-volume histograms (DVHs) into risk groups, as done in this study, represents a useful means of analyzing empirical data as a function of hetereogeneous dose distributions. Modeling efforts may extend these results to more heterogeneous treatment techniques. Such analysis of DVH data may allow practicing clinicians to better assess the risk of various treatments, fields, or doses, when caring for an individual patient.

Analysis of the relationship between tumor dose inhomogeneity and local control in patients with skull base chordoma.

PURPOSE: When irradiating a tumor that abuts or displaces any normal structures, the dose constraints to those structures (if lower than the prescribed dose) may cause dose inhomogeneity in the tumor volume at the tumor-critical structure interface. The low-dose region in the tumor volume may be one of the reasons for local failure. The aim of this study is to quantitate the effect of tumor dose inhomogeneity on local control and recurrence-free survival in patients with skull base chordoma. METHODS AND MATERIALS: 132 patients with skull base chordoma were treated with combined photon and proton irradiation between 1978 and 1993. This study reviews 115 patients whose dose-volume data and follow-up data are available. The prescribed doses ranged from 66.6 Cobalt-Gray-Equivalent (CGE) to 79.2 CGE (median of 68.9 CGE). The dose to the optic structures (optic nerves and chiasm), the brain stem surface, and the brain stem center was limited to 60, 64, and 53 CGE, respectively. We used the dose-volume histogram data derived with the three-dimensional treatment planning system to evaluate several dose-volume parameters including the Equivalent Uniform Dose (EUD). We also analyzed several other patient and treatment factors in relation to local control and recurrence-free survival. RESULTS: Local failure developed in 42 of 115 patients, with the actuarial local control rates at 5 and 10 years being 59% and 44%. Gender was a significant predictor for local control with the prognosis in males being significantly better than that in females (P = 0.004, hazard ratio = 2.3). In a Cox univariate analysis, with stratification by gender, the significant predictors for local control (at the probability level of 0.05) were EUD, the target volume, the minimum dose, and the D5cc dose. The prescribed dose, histology, age, the maximum dose, the mean dose, the median dose, the D90% dose, and the overall treatment time were not significant factors. In a Cox multivariate analysis, the models including gender and EUD, or gender and the target volume, or gender and the minimum target dose were significant. The more biologically meaningful of these models is that of gender and EUD. CONCLUSION: This study suggests that the probability of recurrence of skull base chordomas depends on gender, target volume, and the level of target dose inhomogeneity. EUD was shown to be a useful parameter to evaluate dose distribution for the target volume.

Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with a critical element architecture.

We investigate a model of normal tissue complication probability for tissues that may be represented by a critical element architecture. We derive formulas for complication probability that apply to both a partial volume irradiation and to an arbitrary inhomogeneous dose distribution. The dose-volume isoeffect relationship which is a consequence of a critical element architecture is discussed and compared to the empirical power law relationship. A dose-volume histogram reduction scheme for a "pure" critical element model is derived. In addition, a point-based algorithm which does not require precomputation of a dose-volume histogram is derived. The existing published dose-volume histogram reduction algorithms are analyzed. We show that the existing algorithms, developed empirically without an explicit biophysical model, have a close relationship to the critical element model at low levels of complication probability. However, we also show that they have aspects which are not compatible with a critical element model and we propose a modification to one of them to circumvent its restriction to low complication probabilities.

Implementation of a model for estimating tumor control probability for an inhomogeneously irradiated tumor.

This paper presents the details of a practical implementation of a model for the prediction of the tumor control probability (TCP) when a tumor is irradiated non-uniformly. The implementation is based on a previously published model and represents a simplified version of the model with a limited number (five) of parameters. We show how to derive the model parameters from clinically available data and offer pseudocode for computer implementation. The model should be a useful tool for evaluating and optimizing 3D dose distributions.

A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme.

The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

Reporting and analyzing dose distributions: a concept of equivalent uniform dose.

Modern treatment planning systems for three-dimensional treatment planning provide three-dimensionally accurate dose distributions for each individual patient. These data open up new possibilities for more precise reporting and analysis of doses actually delivered to irradiated organs and volumes of interest. A new method of summarizing and reporting inhomogeneous dose distributions is reported here. The concept of equivalent uniform dose (EUD) assumes that any two dose distributions are equivalent if they cause the same radiobiological effect. In this paper the EUD concept for tumors is presented, for which the probability of local control is assumed to be determined by the expected number of surviving clonogens, according to Poisson statistics. The EUD can be calculated directly from the dose calculation points or, from the corresponding dose-volume distributions (histograms). The fraction of clonogens surviving a dose of 2 Gy (SF2) is chosen to be the primary operational parameter characterizing radiosensitivity of clonogens. The application of the EUD concept is demonstrated on a clinical dataset. The causes of flattening of the observed dose-response curves become apparent since the EUD concept reveals the finer structure of the analyzed group of patients in respect to the irradiated volumes and doses actually received. Extensions of the basic EUD concept to include nonuniform density of clonogens, dose per fraction effects, repopulation of clonogens, and inhomogeneity of patient population are discussed and compared with the basic formula.

Comments on "Sampling techniques for the evaluation of treatment plans" [Med. Phys. 20, 151-161 (1993)].

We believe that, for the purpose of evaluation and optimization of treatment plans, quasirandom sampling is superior to grid sampling and should be the method of choice. We believe it to be on average more efficient than grid sampling (i.e., more accurate for any given number of dose estimates) and, even more importantly, more reliable in that it is subject to less variability due to shape and orientation of the particular VOI--as demonstrated in Fig. 2. As a rule of thumb we recommend using about 400 quasirandom samples per volume of interest. For many situations this number is a conservative estimate; for a few situations more samples might be necessary. Optimal sampling for the purpose of calculation and presentation of the dose distribution is a different story which we have addressed elsewhere.

The influence of the size of the grid used for dose calculation on the accuracy of dose estimation.

The standard presentation of a dose distribution as an isodose map is based on interpolation between dose values calculated on a matrix of equally spaced points. We explored the question of how the spacing of the grid used for the dose matrix affects the error due to interpolating the dose at any point. We defined two types of errors: the dose error, which is the difference between the interpolated and true dose at a given point; and the position error, which is the distance between the point of interest and the nearest point which has, in fact, the dose value estimated for the point of interest. We examine the problem using both an analytical beam profile (a Fermi function) and measured 60Co, x-ray and proton beam profiles. Our analysis showed that the interpolation errors are proportional to the curvature of the dose distribution and are relatively high in regions on either side of, but not including, the steepest part of the penumbra. Our results showed how big an interpolation error one should expect for a given size of the calculation grid. The specification of accuracy should be cast in the form of a pair of requirements, one for dose and the other for position. At a given point, only one of the two requirements needs to be satisfied. The position requirement is almost always the less demanding in clinical practice and permits the use of a larger grid spacing than if only a dose requirement is applied.(ABSTRACT TRUNCATED AT 250 WORDS)

The use of variable grid spacing to accelerate dose calculations.

Planning radiation therapy using three-dimensional patient data is a very time consuming process with current hardware and software. When calculating a three-dimensional dose distribution, the standard technique is to cover the volume of interest with a uniformly spaced matrix of points at which the dose is calculated. It is obvious that the dose is usually quite slowly varying in a large proportion of the region of interest; namely, in those regions which are either well inside or well outside the geometrical boundaries of the field. We have developed an algorithm which allows us to reduce the number of calculation points, and hence the time of calculation of the entire dose distribution, manyfold. We use a nonuniform grid of calculated points, based on the fact that the only regions which are troublesome for accurate dose interpolation are those in which large values of the second derivative of the dose as a function of position occur. We demonstrate that, at most grid points, the dose can be determined without decreasing accuracy below acceptable limits by simple linear interpolation between grid points much further apart than is usual in conventional techniques. We investigated our algorithm for one-, two-, and three-dimensional examples and for Co-60, 25-MV photon, and 160-MV proton beams. In situations for which an accuracy of about 1% in dose and 1.6 mm in position was desired, we found gain factors for the number of points needing direct calculation of approximately 3 (one-dimension), 6 to 10 (two-dimensions) and 16 (three-dimensions).

Random sampling for evaluating treatment plans.

We analyze the influence of sampling technique on the accuracy of estimating irradiated volumes, dose-volume histograms and tumor control and normal tissue complication probabilities. The sampling techniques we consider are uniform distribution of points on a regular Cartesian grid and random selection of points. For three-dimensional treatment planning, random sampling leads to a significant reduction in estimation error and/or in the number of calculation points necessary to achieve a required accuracy. We discuss advantages and drawbacks of random sampling, as compared to sampling on a regular grid. It is suggested that, in practical situations, at least 50 times fewer randomly sampled points per organ/volume of interest are needed for fast estimation of complication probability with the same accuracy, i.e., not exceeding 5% (within 95% confidence limits) in the worst case.

Dose-volume distributions: a new approach to dose-volume histograms in three-dimensional treatment planning.

A new approach to calculating and displaying dose-volume relationships in 3D radiation therapy is presented. We have developed a concept of a dose-volume distribution (DVD) and its corresponding differential dose-volume distribution (DDVD), based on organization of the data in the volume rather than in the dose domain. The new concepts make full use of the information that can be obtained from the dose calculation points and the sampling pattern and are designed to overcome shortcomings of the classical concepts of dose-volume histograms (DVH) and differential dose-volume histograms (DDVH). The new concepts can be applied to any number of dose calculation points, but they are especially advantageous when a small number of points is used. DVDs are particularly well suited to pseudo- and quasi-random sampling of dose distributions. We have developed an error analysis for DVDs and DDVDs in the case of pseudorandom sampling. We also describe an adaptive technique for minimizing the amount of data needed for purposes of display.

Comparison of proton and x-ray conformal dose distributions for radiosurgery applications.

Highly focused dose distributions for radiosurgery applications are successfully achieved using either multiple static high-energy particle beams or multiple-arc circular x-ray beams from a linac. It has been suggested that conformal x-ray techniques using dynamically shaped beams with a moving radiation source would offer advantages compared to the use of only circular beams. It is also thought that, generally, charged particle beams such as protons offer dose deposition advantages compared to x-ray beams. A comparison of dose distributions was made between a small number of discrete proton beams, multiple-arc circular x-ray beams, and conformal x-ray techniques. Treatment planning of a selection of radiosurgery cases was done for these three techniques. Target volumes ranged from 1.0-25.0 cm3. Dose distributions and dose volume histograms of the target and surrounding normal brain were calculated. The advantages and limitations of each technique were primarily dependent upon the shape and size of the target volume. In general, proton dose distributions were superior to x-ray distributions; both shaped proton and shaped x-ray beams delivered dose distributions which were more conformal than x-ray techniques using circular beams; and the differences between all proton and x-ray distributions were negligible for the smallest target volumes, and greatest for the larger target volumes.

Modelling the dose-volume response of the spinal cord, based on the idea of damage to contiguous functional subunits.

PURPOSE: To investigate the response of the spinal cord of experimental animals to homogeneous irradiation, the main purpose being to propose a new version of the Critical Volume Normal Tissue Complication Probability (NTCP) model, incorporating spatial correlation between damaged functional subunits (FSU). METHOD: The standard Critical Volume NTCP model and its modified version, the Contiguous Damage model promoted here, are described in mathematical terms. Also, a fiber-like structure of the spinal cord is considered, which is a more complex structure than the standard Critical Volume NTCP model assumes. It is demonstrated that the Contiguous Damage model predicts different responses to two-segment irradiation and to single-segment irradiation to the same combined length as observed in experiments on rats, a result that cannot be described by the standard Critical Volume NTCP model. RESULTS AND CONCLUSIONS: Both the Critical Volume model and the Contiguous Damage model, are fitted to two sets of canine spinal cord radiation data corresponding to two different fractionation regimes of irradiation. Whole-organ irradiation as well as partial irradiation to different lengths are considered, allowing the investigation of dose-volume effects. Formal goodness-of-fit investigation shows that both models fit the canine spinal cord data equally well.

Generalization of a model of tissue response to radiation based on the idea of functional subunits and binomial statistics.

This work investigates the existing biological models describing the response of tumours and normal tissues to radiation, with the purpose of developing a general biological model of the response of tissue to radiation. Two different types of normal tissue behaviour have been postulated with respect to its response to radiation, namely critical element and critical volume behaviour. Based on the idea that an organ is composed of functional subunits, models have been developed describing these behaviours. However, these models describe the response of an individual, a particular patient or experimental animal, while the clinically or experimentally observed quantity is the population response. There is a need to extend the models to address the population response, based on the ideas we have about the individual response. We have attempted here to summarize and unify the existing individual models. Finally, the population models are investigated by fitting to pseudoexperimental sets of data and comparing them with each other in terms of goodness-of-fit and in terms of their power to recover the values of the population parameters.