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

Comparison of conformal radiation therapy techniques within the dynamic radiotherapy project 'Dynarad'

The objective of the dynamic radiotherapy project 'Dynarad' within the European Community has been to compare and grade treatment techniques that are currently applied or being developed at the participating institutions. Cervical cancer was selected as the tumour site on the grounds that the involved organs at risk, mainly the rectum and the bladder, are very close to the tumour and partly located inside the internal target volume. In this work, a solid phantom simulating the pelvic anatomy was used by institutions in Belgium, France, Greece, Holland, Italy, Sweden and the United Kingdom. The results were evaluated using both biological and physical criteria. The main purpose of this parallel evaluation is to test the value of biological and physical evaluations in comparing treatment techniques. It is demonstrated that the biological objective functions allow a much higher conformality and a more clinically relevant scoring of the outcome. Often external beam treatment techniques have to be combined with intracavitary therapy to give clinically acceptable results. However, recent developments can reduce or even eliminate this need by delivering more conformal dose distributions using intensity modulated external dose delivery. In these cases the reliability of the patient set-up procedure becomes critical for the effectiveness of the treatment.

Analysis of biopsy outcome after three-dimensional conformal radiation therapy of prostate cancer using dose-distribution variables and tumor control probability models

PURPOSE

To investigate tumor control following three-dimensional conformal radiation therapy (3D-CRT) of prostate cancer and to identify dose-distribution variables that correlate with local control assessed through posttreatment prostate biopsies.

METHODS AND MATERIAL

Data from 132 patients, treated at Memorial Sloan-Kettering Cancer Center (MSKCC), who had a prostate biopsy 2.5 years or more after 3D-CRT for T1c-T3 prostate cancer with prescription doses of 64.8-81 Gy were analyzed. Variables derived from the dose distribution in the PTV included: minimum dose (Dmin), maximum dose (Dmax), mean dose (Dmean), dose to n% of the PTV (Dn), where n = 1%,...,99%. The concept of the equivalent uniform dose (EUD) was evaluated for different values of the surviving fraction at 2 Gy (SF(2)). Four tumor control probability (TCP) models (one phenomenologic model using a logistic function and three Poisson cell kill models) were investigated using two sets of input parameters, one for low and one for high T-stage tumors. Application of both sets to all patients was also investigated. In addition, several tumor-related prognostic variables were examined (including T-stage, Gleason score). Univariate and multivariate logistic regression analyses were performed. The ability of the logistic regression models (univariate and multivariate) to predict the biopsy result correctly was tested by performing cross-validation analyses and evaluating the results in terms of receiver operating characteristic (ROC) curves.

RESULTS

In univariate analysis, prescription dose (Dprescr), Dmax, Dmean, dose to n% of the PTV with n of 70% or less correlate with outcome (p < 0.01). The area under the ROC curve for Dmean is 0.64. In contrast, Dmin (p = 0.6), D98 (p = 0.2) or D95 (p = 0.1) are not significantly correlated with outcome. The results for EUD depend on the input parameter SF(2): EUD correlates significantly with outcome for SF(2) of 0.4 or more, but not for lower SF(2) values. Using either of the two input parameters sets, all TCP models correlate with outcome (p < 0.05; ROC areas 0.60-0.62). Using T-stage dependent input parameters, the correlation is improved (logistic function: p < 0.01, ROC area 0.67, Poisson models: p < 0.01, ROC areas 0.64-0.66). In comparison, the ROC area is 0.68 for the combination of Dmean and T-stage. After multivariate analysis, a model based on TCP, D20 and Gleason score is the best overall model (ROC area 0.73). However, an alternative model based on Dmean, Gleason score, and T-stage is competitive (ROC area 0.70).

CONCLUSION

Biopsy outcome after 3D-CRT of prostate cancer at MSKCC is not correlated with Dmin in the PTV and appears to be insensitive to cold spots in the dose distribution. This observation likely reflects the fact that much of the PTV, especially at the periphery, may not contain viable tumor cells and that the treatment margins were sufficiently large. Therefore, the predictive power of all variables which are sensitive to cold spots, like TCPs with Poisson models and EUD for low SF(2), is limited because the low dose region may not coincide with the tumor location. Instead, for MSKCC prostate cancer patients with their standardized CTV definition, substantial target motion and small dose inhomogeneities, Dmean (or any variable that downplays the effect of cold spots) is a very good predictor of biopsy outcome. While our findings may indicate a general problem in the application of current TCP models to clinical data, these conclusions should not be extrapolated to other disease sites without careful analysis.

Analysis of dose distribution in gamma knife radiosurgery for multiple targets

PURPOSE

The aim of this study is to evaluate the actual effect of irradiation for other targets in dose planning for the treatment of multiple metastases with Gamma Knife.

METHODS AND MATERIALS

We analyzed dose distributions for 51 targets in 10 patients with metastatic brain tumors who underwent radiosurgery with Gamma Knife for the treatment of more than one target in one session. We made dose plans with every attempt to include as many targets as possible and calculate dose distributions separately for each dose matrix. We also calculated the composite dose distribution by including the effect of all shots used. We compared these noncomposite and composite dose distributions.

RESULTS

The differences in the mean target dose between the noncomposite dose distribution and the composite one ranged from 0.0 to 4.5 Gy with a mean of 1.5 Gy and was more than 2 Gy in 12 (24%) targets. The difference tended to be larger when targets were small in volume and/or the number of targets was large.

CONCLUSIONS

The effect of irradiation from the shots for other targets was not negligible in some cases. This difference of dose distribution should be considered in the analysis of clinical outcomes of cases with multiple targets treated in one session.

The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy

PURPOSE

To provide an analytical description of the effect of random and systematic geometrical deviations on the target dose in radiotherapy and to derive margin rules.

METHODS AND MATERIALS

The cumulative dose distribution delivered to the clinical target volume (CTV) is expressed analytically. Geometrical deviations are separated into treatment execution (random) and treatment preparation (systematic) variations. The analysis relates each possible preparation (systematic) error to the dose distribution over the CTV and allows computation of the probability distribution of, for instance, the minimum dose delivered to the CTV.

RESULTS

The probability distributions of the cumulative dose over a population of patients are called dose-population histograms in short. Large execution (random) variations lead to CTV underdosage for a large number of patients, while the same level of preparation (systematic) errors leads to a much larger underdosage for some of the patients. A single point on the histogram gives a simple "margin recipe." For example, to ensure a minimum dose to the CTV of 95% for 90% of the patients, a margin between CTV and planning target volume (PTV) is required of 2.5 times the total standard deviation (SD) of preparation (systematic) errors (Sigma) plus 1.64 times the total SD of execution (random) errors (sigma') combined with the penumbra width, minus 1.64 times the SD describing the penumbra width (sigma(p)). For a sigma(p) of 3.2 mm, this recipe can be simplified to 2.5 Sigma + 0.7 sigma'. Because this margin excludes rotational errors and shape deviations, it must be considered as a lower limit for safe radiotherapy.

CONCLUSION

Dose-population histograms provide insight into the effects of geometrical deviations on a population of patients. Using a dose-probability based approach, simple algorithms for choosing margins were derived.

Optimization of inverse treatment planning using a fuzzy weight function

A fuzzy approach has been applied to inverse treatment planning optimization in radiation therapy. The proposed inverse-planning algorithm optimizes both the intensity-modulated beam (IMB) and the normal tissue prescription. In the IMB optimization, we developed a fast-monotonic-descent (FMD) method that has the property of fast and monotonic convergence to the minimum for a constrained quadratic objective function. In addition, a fuzzy weight function is employed to express the vague knowledge about the importance of matching the calculated dose to the prescribed dose in the normal tissue. Then, a validity function is established to optimize the normal tissue prescription. The performance of this new fuzzy prescription algorithm has been compared to that based on hard prescription methods for two treatment geometries. The FMD method presented here both provides a full-analytical solution to the optimization of intensity-modulated beams, and guarantees fast and monotonic convergence to the minimum. It has been shown that the fuzzy inverse planning technique is capable of achieving an optimal balance between the objective of matching the calculated dose to the prescribed dose for the target volume and the objective of minimizing the normal tissue dose.

Conformal irradiation of concave-shaped PTVs in the treatment of prostate cancer by simple 1D intensity-modulated beams

BACKGROUND

In the case of concave-shaped PTVs including prostate (P) and seminal vesicles (SV), intensity-modulated radiation therapy (IMRT) should improve the therapeutic ratio of the treatment of prostate cancer.

PURPOSE

Comparing IMRT by simple 1D modulations with conventional 3D conformal therapy (i.e. non-IMRT) in the treatment of concave-shaped PTVs including P+SV.

MATERIALS AND METHODS

For five patients having a concave-shaped PTV (P+SV) previously treated at our Institute with conformal radiotherapy, conventional 3- and 4-fields conformal plans were compared with IMRT plans in terms of biological indices. IMRT plans were generated by using five equi-spaced beams with a partial shielding of the rectum obtainable with our single-absorber modulation technique (Fiorino C, Lev A, Fusca M, Cattaneo GM, Rudello F, Calandrino R. Dynamic beam modulation by using a single dynamic absorber. Phys. Med. Biol. 1995;40:221-240). The modulation was one-dimensional and the shape of the beams was at single minimum in correspondence with the 'core' of the rectum; the beam intensity in the minimum was set equal to 20 or 40% of the open beam intensity. All plans were simulated on the CADPLAN TPS using a pencil-beam based algorithm (with 18 MV X-rays). Tumour control probability (TCP) and normal tissue complication probabilities (NTCPs) (for rectum, bladder and femoral head) were calculated for all situations when varying the isocentre dose from 60 to 90 Gy. Dose distributions were corrected taking dose fractionation into account through the linear-quadratic model; for the TCP/NTCP estimations the Webb-Nahum and the Lyman-Kutcher models were respectively applied. Three different scores were considered: (a) increase of TCP while keeping rectum NTCP equal to 5% (TCP(5%)); (b) increase of the uncomplicated tumour control probability (P+); (c) increase of the biological-based scoring function (S+), developed by Mohan et al. (Mohan R, Mageras GS, Baldwin B, Clinically relevant optimization of 3D conformal treatments. Med. Phys. 1992;19:933-944). The impact of the uncertainty in the knowledge of the parameters of the biological models was investigated for TCP(5%).

RESULTS

(a) The average gain in TCP(5%) when considering IMRT against non-IMRT conformal plans was 7.3% (range 5.0-13.5%); (b) the average increase of P+ was 3.4% (range: 1. 0-8.5%); and (c) the average increase of S+ was 5.4% (range 2.9-12. 4%). The largest gain was found for one patient (patient 5) showing a significantly larger overlapping between PTV and rectum.

CONCLUSIONS

Simple 1D-IMRT may clearly improve the therapeutic ratio in the treatment of concave-shaped PTVs including P and SV. In the range of clinically suitable values, the impact of the uncertainty of the parameters n and sigma(alpha) does not significantly alter the main results concerning the gain in TCP(5%). The reported gain in terms of P+ and S+ should be considered with great caution because of the intrinsic uncertainties of the model's parameters and, for bladder, because the 'true' DVH (considering variations of the shape and dimension due to variable filling) may be very different from the DVH calculated on a single CT scan. Further investigations should consider inversely-optimised 1D and 2D-IMRT plan in order to compare them in terms of cost-benefit.

Viability of the EUD and TCP concepts as reliable dose indicators

The concept of equivalent uniform dose (EUD) was introduced to provide a method of reporting radiotherapy dose distributions which takes account of the nonlinearity of tissue dose-response, whilst not attempting to make predictions of absolute outcome. The purpose of this investigation was to determine the level of sensitivity of EUD to model parameters for significant variations in dose distribution and consequently the reliability of the factor as a dose-indicator, and to compare EUD with the more familiar index, tumour control probability (TCP). EUD and TCP, derived from the linear-quadratic formalism, were investigated for a test tissue being irradiated non-uniformly. Variations in the parameters of the model (tissue cell characteristics, dose heterogeneity, fractionation parameters) indicated the sensitivity of EUD and TCP to them. For time independent factors--cell density, cell radiosensitivity, radiosensitivity heterogeneity (population averaged) and ratio alpha/beta--EUD was found to vary insignificantly in comparison with TCP, though this is a function of the actual form of the dose distribution under consideration. For fractionated treatments where the mean dose per fraction is varying (due to dosimetric/positioning errors for example), both EUD and TCP showed little variation with the degree of dose non-uniformity. For other time dependent factors, fractionation rate and cell repopulation times, TCP again showed significant variation relative to EUD. The relative insensitivity of EUD implies that this index will be useful for dose evaluation when parameters are not known with accuracy, for the intercomparison of dose control studies and as a radiobiologically based optimization objective. However, given confidence in model parameters, the sensitivity of TCP would make it a more reliable tool for indicating potentially successful and unsuccessful irradiation strategies. It is suggested that both parameters be used in conjunction, with EUD and TCP results viewed with an appreciation of the characteristics of each model.

Radiobiological considerations in the design of fractionation strategies for intensity-modulated radiation therapy of head and neck cancers

PURPOSE

The dose distributions of intensity-modulated radiotherapy (IMRT) treatment plans can be shown to be significantly superior in terms of higher conformality if designed to simultaneously deliver high dose to the primary disease and lower dose to the subclinical disease or electively treated regions. We use the term "simultaneous integrated boost" (SIB) to define such a treatment. The purpose of this paper is to develop suitable fractionation strategies based on radiobiological principles for clinical trials and routine use of IMRT of head and neck (HN) cancers. The fractionation strategies are intended to allow escalation of tumor dose while adequately sparing normal tissues outside the target volume and considering the tolerances of normal tissues embedded within the primary target volume.

METHODS AND MATERIALS

IMRT fractionation regimens are specified in terms of "normalized total dose" (NTD), i.e., the biologically equivalent dose given in 2 Gy/fx. A linear-quadratic isoeffect formula is applied to convert NTDs into "nominal" prescription doses. Nominal prescription doses for a high dose to the primary disease, an intermediate dose to regional microscopic disease, and lower dose to electively treated nodes are used for optimizing IMRT plans. The resulting nominal dose distributions are converted back into NTD distributions for the evaluation of treatment plans. Similar calculations for critical normal tissues are also performed. Methods developed were applied for the intercomparison of several HN treatment regimens, including conventional regimens used currently and in the past, as well as SIB strategies. This was accomplished by comparing the biologically equivalent NTD values for the gross tumor and regional disease, and bone, muscle, and mucosa embedded in the gross tumor volume.

RESULTS

(1) A schematic HN example was used to demonstrate that dose distributions for SIB IMRT are more conformal compared to dose distributions when IMRT is divided into a large-field phase and a boost phase. Both were shown to be significantly superior compared to dose distributions obtained using conventional beams for the large-field phase followed by IMRT for the boost phase. (2) The relationship between NTD and nominal dose for HN tumors was found to be quite sensitive to the choice of tumor clonogen doubling time but relatively insensitive to other parameters. (3) For late effect normal tissues embedded in the tumor volume and assumed to receive the same dose as the tumor, the biologically equivalent NTD for the SIB IMRT may be significantly higher. (4) Normal tissues outside the target volume receive lower dose due to the higher conformality of the IMRT plans. The biologically equivalent NTDs are even lower due to the lower dose per fraction in the SIB strategy.

CONCLUSIONS

IMRT dose distributions are most conformal when designed to be delivered as SIB. Using isoeffect radiobiological relationships and published HN data, fractionation strategies can be designed in which the nominal dose levels to the primary, regional disease and electively treated volumes are appropriately adjusted, each receiving different dose/fx. Normal tissues outside the treated volumes are at reduced risk in such strategies since they receive lower total dose as well as lower dose/fx. However, the late effect toxicities of tissues embedded within the primary target volume and assumed to receive the same dose as the primary may pose a problem. The efficacy and safety of the proposed fractionation strategies will need to be evaluated with careful clinical trials.

Treatment plan comparison using equivalent uniform biologically effective dose (EUBED)

With the continuing improvement in computer speed, dose distributions can be calculated quickly with confidence. However, the resulting biological effect is known with much less certainty, despite its critical importance when assessing treatment plans. To assess plans accurately, biologically based methods of ranking plans are necessary. Many authors have suggested the use of dose volume histograms with reduction schemes and Niemierko has recently introduced another method based on the cell kill occurring in the tumour. This study presents an investigation into this value and suggests a use in prescribing dose. Equivalent uniform dose (EUD) can obviously be used for assessing treatment plans, although in its current form it is not adequate for assessing normal tissues; however, it can also be used to adjust the prescription dose ensuring all plans deliver the same EUD to the tumour. Once this is performed, plans can more easily be assessed on the effects to the normal tissues. In calculating the EUD another concept is introduced--the equivalent uniform biologically effective dose (EUBED). This value considers the distribution of dose and dose per fraction when comparing plans. Reduced dose per fraction at the edge of the target volume will exacerbate the effect of reduced dose on cell kill. Two methods are suggested for calculating the necessary prescription dose: one using an iterative method and one using the gradient of the EUBED function. A comparison was made for a series of stereotactic cases using different collimator sizes. Interestingly, using this method, although the maximum doses were different, the dose volume histograms (DVHs) for the brainstem were similar in all cases.

Applying the equivalent uniform dose formulation based on the linear-quadratic model to inhomogeneous tumor dose distributions: Caution for analyzing and reporting

We apply the concept of equivalent uniform dose (EUD) to our data set of model distributions and intensity modulated radiotherapy (IMRT) treatment plans as a method for analyzing large dose inhomogeneities within the tumor volume. For large dose nonuniformities, we find that the linerar-quadratic based EUD model is sensitive to the linear-quadratic model parameters, alpha and beta, making it necessary to consider EUD as a function of these parameters. This complicates the analysis for inhomogeneous dose distributions. EUD provides a biological estimate that requires interpretation and cannot be used as a single parameter for judging an inhomogeneous plan. We present heuristic examples to demonstrate the dose volume effect associated with EUD and the correlation to statistical parameters used for describing dose distributions. From these examples and patient plans, we discuss the risk of incorrectly applying EUD to IMRT patient plans.

The potential for sparing of parotids and escalation of biologically effective dose with intensity-modulated radiation treatments of head and neck cancers: a treatment design study

PURPOSE

Conventional radiotherapy for cancers of the head and neck (HN) can yield acceptable locoregional tumor control rates, but toxicity of many normal tissues limits our ability to escalate dose. Xerostomia represents one of the most common complications. The purpose of this study is to investigate the potential of intensity-modulated radiotherapy (IMRT) to achieve adequate sparing of parotids and to escalate nominal and/or biologically-effective dose to achieve higher tumor control without exceeding normal tissue tolerances.

METHODS AND MATERIALS

An IMRT optimization system, developed at our institution for research and clinical purposes, and coupled to a commercial radiation treatment planning system, has been applied to a number of cases of HN carcinomas. IMRT plans were designed using dose- and dose-volume-based criteria for 4 and 6 MV coplanar but non-collinear beams ranging in number from 5 to 15 placed at equi-angular steps. Detailed analysis of one of the cases is presented, while the results of the other cases are summarized. For the first case, the IMRT plans are compared with the standard 3D conformal radiation treatment (3DCRT) plan actually used to treat the patient, and with each other. The aim of the 3DCRT plan for this particular case was to deliver 73 Gy to the tumor volume in 5 fractions of 2 Gy and 28 fractions of 2.25 Gy/fx; and 46 Gy to the nodes in 2 Gy/fx while maintaining critical normal tissues to below specified tolerances. The IMRT plans were designed to be delivered as a "simultaneous integrated boost" (SIB) using the "sweeping window" technique with a dynamic MLC. The simultaneous integrated boost strategy was chosen, partly for reasons of efficiency in planning and delivery of IMRT treatments, and partly with the assumption that dose distributions in such treatments are more conformal and spare normal tissues to a greater extent than those with sequential boost strategy. Biologically equivalent dose normalized to 2 Gy/fx, termed here as normalized total dose (NTD), for this strategy was calculated using published head and neck fractionation data.

RESULTS

IMRT plans were more conformal than the 3DCRT plans. For equivalent coverage of the tumor and the nodes, and for the dose to the spinal cord and the brainstem maintained within tolerance limits, the dose to parotids was greatly reduced. For the detailed example presented, it was shown that the tumor and the nodes in the 3DCRT plan receive NTDs of 78 and 46 Gy, respectively. For the IMRT plan, a nominal dose of 70 Gy could be delivered to the tumor in 28 fractions of 2.5 Gy each, simultaneously with 50.4 Gy to nodes with 1.8 Gy/fx. The two are biologically equivalent to 82 and 46 Gy, respectively, if delivered in 2 Gy/fx. Similar computations were carried out for other cases as well. The quality of IMRT plans was found to improve with increasing number of beams, up to 9 beams. Dose-volume-based criteria led to a modest improvement in IMRT plans and required less trial and error.

CONCLUSION

IMRT has the potential to significantly improve radiotherapy of HN cancers by reducing normal tissue dose and simultaneously allowing escalation of dose. SIB strategy is not only more efficient and yields better dose distributions, but may also be biologically more effective. Dose-volume-based criteria is better than purely dose-based criteria. The quality of plans improves with number of beams, reaching a saturation level for a certain number of beams, which for the plans studied was found to be 9.

Application of constrained optimization to radiotherapy planning

Essential for the calculation of photon fluence distributions for intensity modulated radiotherapy (IMRT) is the use of a suitable objective function. The objective function should reflect the clinical aims of tumor control and low side effect probability. Individual radiobiological parameters for patient organs are not yet available with sufficient accuracy. Some of the major drawbacks of some current optimization methods include an inability to converge to a solution for arbitrary input parameters, and/or a need for intensive user input in order to guide the optimization. In this work, a constrained optimization method was implemented and tested. It is closely related to the demanded clinical aims, avoiding the drawbacks mentioned above. In a prototype treatment planning system for IMRT, tumor control was guaranteed by setting a lower boundary for target dose. The aim of low complication is fulfilled by minimizing the dose to organs at risk. If only one type of tissue is involved, there is no absolute need for radiobiological parameters. For different organs, threshold dose, relative seriality of the organs or an upper dose limit could be set. All parameters, however, were optional, and could be omitted. Dose-volume constraints were not used, avoiding the possibility of local minima in the objective function. The approach was benchmarked through the simulation of both a head and neck and a lung case. A cylinder phantom with precalculated dose distributions of individual pencil beams was used. The dose to regions at risk could be significantly reduced using at least seven ports of beam incidence. Increasing the number of ports beyond seven produced only minor further gain. The relative seriality of organs was modeled through the use of an added exponent to the dose. This approach however increased calculation time significantly. The alternative of setting an upper limit is much faster and allows direct control of the maximum dose. Constrained optimization guarantees high tumor control probability, it is computationally more efficient than adding penalty terms to the objective function, and the input parameters are dose limits known in clinical practice.

Optimization of the dose level for a given treatment plan to maximize the complication-free tumor cure

During the past decade, tumor and normal tissue reactions after radiotherapy have been increasingly quantified in radiobiological terms. For this purpose, response models describing the dependence of tumor and normal tissue reactions on the irradiated volume, heterogeneity of the delivered dose distribution and cell sensitivity variations can be taken into account. The probability of achieving a good treatment outcome can be increased by using an objective function such as P+, the probability of complication-free tumor control. A new procedure is presented, which quantifies P+ from the dose delivery on 2D surfaces and 3D volumes and helps the user of any treatment planning system (TPS) to select the best beam orientations, the best beam modalities and the most suitable beam energies. The final step of selecting the prescribed dose level is made by a renormalization of the entire dose plan until the value of P+ is maximized. The index P+ makes use of clinically established dose-response parameters, for tumors and normal tissues of interest, in order to improve its clinical relevance. The results, using P+, are compared against the assessments of experienced medical physicists and radiation oncologists for two clinical cases. It is observed that when the absorbed dose level for a given treatment plan is increased, the treatment outcome first improves rapidly. As the dose approaches the tolerance of normal tissues the complication-free cure begins to drop. The optimal dose level is often just below this point and it depends on the geometry of each patient and target volume. Furthermore, a more conformal dose delivery to the target results in a higher control rate for the same complication level. This effect can be quantified by the increased value of the P+ parameter.

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.

A neural network to predict symptomatic lung injury

A nonlinear neural network that simultaneously uses pre-radiotherapy (RT) biological and physical data was developed to predict symptomatic lung injury. The input data were pre-RT pulmonary function, three-dimensional treatment plan doses and demographics. The output was a single value between 0 (asymptomatic) and 1 (symptomatic) to predict the likelihood that a particular patient would become symptomatic. The network was trained on data from 97 patients for 400 iterations with the goal to minimize the mean-squared error. Statistical analysis was performed on the resulting network to determine the model's accuracy. Results from the neural network were compared with those given by traditional linear discriminate analysis and the dose-volume histogram reduction (DVHR) scheme of Kutcher. Receiver-operator characteristic (ROC) analysis was performed on the resulting network which had Az = 0.833 +/- 0.04. (Az is the area under the ROC curve.) Linear discriminate multivariate analysis yielded an Az = 0.813 +/- 0.06. The DVHR method had Az = 0.521 +/- 0.08. The network was also used to rank the significance of the input variables. Future studies will be conducted to improve network accuracy and to include functional imaging data.

Optimization of planar high-dose-rate implants

PURPOSE

Brachytherapy has long been used to deliver localized radiation to the breast and other cancer sites. For interstitial implants, proper source positioning is critical in obtaining satisfactory dose distributions. The present work examines techniques for optimizing source guide placement in high-dose-rate (HDR) biplanar implants, and examines the effects of suboptimal catheter placement.

METHODS AND MATERIALS

Control of individual dwell times in HDR implants allows a high degree of dose uniformity in planes parallel to the implant planes. Biplanar HDR implants can be considered optimized when the dose at the implant center is equal to the dose at the symmetric target boundaries. It is shown that this optimal dose uniformity is achieved when the interplanar separation is related to the target thickness T through the direct proportionality, s = T/square root2. To quantify the significance of source positioning, the average dose and a related quantity, equivalent uniform dose (EUD), were calculated inside the treatment volume for two conditions of suboptimal catheter geometry. In one case, the interplanar spacing was varied from 1 cm up to the target thickness T, while a second study examined the effects of off-center placement of the implant planes.

RESULTS

Both the average dose and EUD were minimized when the interplanar spacing satisfied the relationship s = T/square root2. EUD, however, was significantly smaller than the average dose, indicating a reduced relative cell killing in the high dose regions near the dwell points. It was also noted that in contrast to the average dose, the EUD is a relatively weak function of catheter misplacement, suggesting that the biological consequences of suboptimal implant geometry may be less significant than is indicated by the increase in average dose.

CONCLUSION

A concise formula can be used to determine the interplanar separation needed for optimal dose uniformity in Manchester-type implants. Deviations from optimal source geometry result in an increase in the average dose inside the treatment volume, but the weaker dependence of the EUD suggests that the surviving fraction of cells may not be not strongly affected by suboptimal source geometry.

Calculated effects of displacement errors in external beam radiotherapy of prostatic adenocarcinoma

In order to evaluate the impact on the biological effective dose (BED) of irradiation delivered to a tumour with large displacement errors (LDE) and to estimate the effect on local control, simulated treatment of prostatic adenocarcinoma was performed. The calculation of BED in combination with the critical-voxel model and the LQ model was used to evaluate the effect of different combinations of LDEs. The model is called the Dose Volume Inhomogeneity Corrected BED (DVIC-BED) model. The dose-response curve was assumed to follow Poisson statistics. Different combinations of radiobiological parameters were used to test the model. A simulated clinical treatment with a dose of 66-80 Gy in 2 Gy fractions was carried out to evaluate displacement errors and non-optimal dose distributions. Five random LDEs excluding 33% of the target volume corresponded to an overall dose reduction of 3-5 Gy compared with a 10 Gy reduction if 100% of the target is missed five times. A 5 Gy decrease in dose corresponds to a reduction in clinical or chemical control up to 10-25% in the interval 65-85 Gy. LDEs in different directions are less deleterious than errors occurring in the same direction. Different alpha/beta-ratios (3-15) had little effect on the DIC-BED, but the effect of different alpha values (0.05, 0.2 and 0.5) was large. However, the results depend on radiobiological parameters for prostatic adenocarcinoma, which not are well known, and further studies in the field should be encouraged.

The delta-TCP concept: a clinically useful measure of tumor control probability

PURPOSE

The aim of this article is to provide a quantitative tool to evaluate the influence of the different dose regions in a non-uniformly irradiated tumour upon the probability of controlling that tumor.

METHODS AND MATERIALS

First, a method to generate a distribution of the probability of controlling the cells in a voxel (VCP) is explored and found not to be useful. Second, we introduce the concept of delta-TCP, which represents the gain or loss in the overall TCP as a result of each particular bin in a DVH not receiving the prescribed dose (the same concept is applicable to dose cubes or to a fraction of the bin). The delta-TCP method presented here is based on the Poisson TCP model, but any other model could also be used. Third, using this tool, with parameters appropriate to Stage C prostate tumors, the consequences of "cold" and "hot" dose regions have been explored.

RESULTS

We show that TCP is affected by the minimum dose, even if it is delivered to a very small volume (20% dose deficit to 5% of the volume makes the TCP decrease by 18%), and that a hot region may be "wasted" unless the boost is to the bulk of the volume. An example of the application of the delta-TCP concept to a prostate radiotherapy plan is also given.

CONCLUSION

The delta-TCP distribution adds more objective information to the original DVH by enabling the clinician or planner to directly evaluate the effects of a non-uniform dose distribution on local control.

Beam intensity modulation to reduce the field sizes for conformal irradiation of lung tumors: a dosimetric study

PURPOSE

In conformal radiotherapy of lung tumors, penumbra broadening in lung tissue necessitates the use of larger field sizes to achieve the same target coverage as in a homogeneous environment. In an idealized model configuration, some fundamental aspects of field size reduction were investigated, both for the static situation and for a moving tumor, while maintaining the dose homogeneity in the target volume by employing a simple beam-intensity modulation technique.

METHODS AND MATERIALS

An inhomogeneous phantom, consisting of polystyrene, cork, and polystyrene layers, with a 6 x 6 x 6 cm3 polystyrene cube inside the cork representing the tumor, was used to simulate a lung cancer treatment. Film dosimetry experiments were performed for an AP-PA irradiation technique with 8-MV or 18-MV beams. Dose distributions were compared for large square fields, small square fields, and intensity-modulated fields in which additional segments increase the dose at the edge of the field. The effect of target motion was studied by measuring the dose distribution for the solid cube, displaced with respect to the beams.

RESULTS

For the 18-MV beam, the field sizes required to establish a sufficient target coverage are larger than for the 8-MV beam. For each beam energy, the mean dose in cork can significantly be reduced (at least a factor of 1.6) by decreasing the field size with 2 cm, while keeping the mean target dose constant. Target dose inhomogeneity for these smaller fields is limited if the additional edge segments are applied for 8% of the number of monitor units given with the open fields. The target dose distribution averaged over a motion cycle is hardly affected if the target edge does not approach the field edge to within 3 mm.

CONCLUSIONS

For lung cancer treatment, a beam energy of 8 MV is more suitable than 18 MV. The mean lung dose can be significantly reduced by decreasing the field sizes of conformal fields. The smaller fields result in the same biological effect to the tumor if the mean target dose is kept constant. Intensity modulation can be employed to maintain the same target dose homogeneity for these smaller fields. As long as the target (with a 3 mm margin) stays within the field portal, application of a margin for target motion is not necessary.

Optimized radiation therapy based on radiobiological objectives

In the broad field of radiation therapy optimization, both simple and complex problems have their origins in the interaction of the radiation beams with the biological structures of normal and malignant tissues of the human body. Therefore, it is no great surprise that many treatment optimization problems are best handled by the use of well-designed radiobiological models. The classic way of quantifying dose-response relations for tumors and normal tissues as well as their cross-correlation with each other and their dependence on the underlying genetic and molecular biology of the cell are first briefly reviewed. Radiobiological objective functions, such as the probability of achieving complication-free cure and its expectation value under influence of stochastic processes during the course of treatment, are defined and shown to solve many of the problems of radiation therapy planning. Finally, it is shown through the use of these quantifiers that, simply by introducing biologically optimal intensity modulated dose delivery, the treatment outcome can be improved by about 20% or more in cases with a complex spread of the disease. Once radiobiological optimal plans have been developed, they can be approximated by ordinary physical planning, but the biological objective functions are still needed to have a figure of merit for the quality of the treatment.

Radiation pneumonitis as a function of mean lung dose: an analysis of pooled data of 540 patients

PURPOSE

To determine the relation between the incidence of radiation pneumonitis and the three-dimensional dose distribution in the lung.

METHODS AND MATERIALS

In five institutions, the incidence of radiation pneumonitis was evaluated in 540 patients. The patients were divided into two groups: a Lung group, consisting of 399 patients with lung cancer and 1 esophagus cancer patient and a Lymph./Breast group with 78 patients treated for malignant lymphoma, 59 for breast cancer, and 3 for other tumor types. The dose per fraction varied between 1.0 and 2.7 Gy and the prescribed total dose between 20 and 92 Gy. Three-dimensional dose calculations were performed with tissue density inhomogeneity correction. The physical dose distribution was converted into the biologically equivalent dose distribution given in fractions of 2 Gy, the normalized total dose (NTD) distribution, by using the linear quadratic model with an alpha/beta ratio of 2.5 and 3.0 Gy. Dose-volume histograms (DVHs) were calculated considering both lungs as one organ and from these DVHs the mean (biological) lung dose, NTDmean, was obtained. Radiation pneumonitis was scored as a complication when the pneumonitis grade was grade 2 (steroids needed for medical treatment) or higher. For statistical analysis the conventional normal tissue complication probability (NTCP) model of Lyman (with n=1) was applied along with an institutional-dependent offset parameter to account for systematic differences in scoring patients at different institutions.

RESULTS

The mean lung dose, NTDmean, ranged from 0 to 34 Gy and 73 of the 540 patients experienced pneumonitis, grade 2 or higher. In all centers, an increasing pneumonitis rate was observed with increasing NTDmean. The data were fitted to the Lyman model with NTD50=31.8 Gy and m=0.43, assuming that for all patients the same parameter values could be used. However, in the low dose range at an NTDmean between 4 and 16 Gy, the observed pneumonitis incidence in the Lung group (10%) was significantly (p=0.02) higher than in the Lymph./Breast group (1.4%). Moreover, between the Lung groups of different institutions, also significant (p=0.04) differences were present: for centers 2, 3, and 4, the pneumonitis incidence was about 13%, whereas for center 5 only 3%. Explicitly accounting for these differences by adding center-dependent offset values for the Lung group, improved the data fit significantly (p < 10(-5)) with NTD50=30.5+/-1.4 Gy and m=0.30+/-0.02 (+/-1 SE) for all patients, and an offset of 0-11% for the Lung group, depending on the center.

CONCLUSIONS

The mean lung dose, NTDmean, is relatively easy to calculate, and is a useful predictor of the risk of radiation pneumonitis. The observed dose-effect relation between the NTDmean and the incidence of radiation pneumonitis, based on a large clinical data set, might be of value in dose-escalating studies for lung cancer. The validity of the obtained dose-effect relation will have to be tested in future studies, regarding the influence of confounding factors and dose distributions different from the ones in this study.

Predicting the radiation control probability of heterogeneous tumour ensembles: data analysis and parameter estimation using a closed-form expression

A closed-form formula describing the tumour control probability (tcp) of a heterogeneous collection of tumours has been obtained by analytically averaging the homogeneous double-exponential tcp formula over inter-tumour distributions of clonogen radiosensitivity, density and repopulation rate, tumour volume and dose. The formula can be straightforwardly and relatively quickly fitted to clinical data, yielding radiobiological parameter values for use in tcp modelling. The formula was fitted to published tcp data which catalogued tumour control records grouped by dose and tumour volume, and treatment duration. Fitted parameter values, confidence intervals and goodness-of-fit statistics were determined. The sets of parameter values obtained are unique only to within a scaling factor. The formula provides non-rejectable fits to data which grouped tcp by dose and volume when radiosensitivity parameters take values close to laboratory estimates, the fitted volume dependence parameter, however, taking rather high values. Good fits are obtainable with the intuitively reasonable volume parameter value of one, but with radiosensitivity values around one-third of their laboratory estimates. Non-rejectable fits to data which grouped tcp by dose and treatment duration may be obtained with radiosensitivity and repopulation rate parameters lying close to laboratory estimates.

Evaluation of two dose-volume histogram reduction models for the prediction of radiation pneumonitis

PURPOSE

To evaluate the similarities between the mean lung dose and two dose-volume histogram (DVH) reduction techniques of 3D dose distributions of the lung.

PATIENTS AND METHODS

DVHs of the lungs were calculated from 3D dose distributions of patients treated for malignant lymphoma (44), breast cancer (42) and lung cancer (20). With a DVH reduction technique, a DVH is summarized by the equivalent uniform dose (EUD), a quantity which is directly related to the normal tissue complication probability (NTCP). Two DVH reduction techniques were used. The first was based on an empirical model proposed by Kutcher et al. (Kutcher, G.J., Burman, C., Brewster, M.S., Goitein, M. and Mohan, R. Histogram reduction method for calculating complication probabilities for three-dimensional treatment planning evaluations. Int. J. Radiat. Oncol. Biol. Phys. 21: 137-146, 1991), which needs a volume exponent n. Several values for n were tested. The second technique was based on a radiobiological model, the parallel functional subunit model developed by Niemierko et al. (Niemierko, A. and Goitein, M. Modeling of normal tissue response to radiation: the critical volume model. Int. J. Radiat. Oncol. Biol. Phys. 25: 135-145, 1993) and Jackson et al. (Jackson, A., Kutcher, G.J. and Yorke, E.D. Probability of radiation-induced complications for normal tissues with parallel architecture subject to non-uniform irradiation. Med. Phys. 20: 613-625, 1993), for which a local dose-effect relation needed to be specified. This relation was obtained from an analysis of perfusion and ventilation SPECT data.

RESULTS

It can be shown analytically that the two DVH reduction techniques are identical, if the local dose-effect relation obeys a power-law relationship in the clinical dose range. Local dose-effect relations based on perfusion and ventilation SPECT data can indeed be fitted with a power-law relationship in the range 0-80 Gy, from which values of n = 0.8-0.9 were deduced. These correspond to the commonly used value of n = 0.87 for lung tissue and yielded EUDn=0.87 values which were almost identical to the mean lung doses. For other n values, for which no experimental data are present, differences exist between EUD and mean dose values. Six patients with malignant lymphoma (6/44) and none of the breast cancer patients (0/42) developed radiation pneumonitis. These cases occurred only at high values for the mean lung dose.

CONCLUSION

The two DVH reduction techniques are identical for lung and are very similar to mean dose calculations. The two techniques are also relatively similar for other model parameter values.

A continuous penalty function method for inverse treatment planning

Conventional inverse treatment planning attempts to calculate dose distributions that may not be feasible given the specified dose levels to various anatomical structures. A technique for inverse treatment planning has been developed that uses only target dose levels which are easily selectable to be feasible. A nonlinear constrained minimization problem is formulated to reflect the goal of sparing critical organs as much as possible while delivering a certain target dose within specified uniformity. The objective function is the squared dose delivered to critical organs. The constraints require the delivery of certain target dose within specified uniformity and non-negative pencil beam weights. A continuous penalty function method is introduced as a method for solving the large-scale constrained minimization problem. The performance of the continuous penalty function method is optimized by numerical investigation of few numerical integration schemes and a pair of weighting functions which influence the utility of the method. Clinical examples are presented that illustrate several features of the technique. The properties of the continuous penalty function method suggest that it may be a viable alternative to conventional inverse treatment planning.