Comment on "Reporting and analyzing dose distributions: a concept of equivalent uniform dose" [Med. Phys. 24, 103-109 (1997)]

Revisiting the formalism of equivalent uniform dose based on the linear-quadratic and universal survival curve models in high-dose stereotactic body radiotherapy

PURPOSE

To examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT).

MATERIALS AND METHODS

For nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose-volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70-83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT.

RESULTS

For non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low [Formula: see text] ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT.

CONCLUSION

A uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose-response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.

Dose-response relationships of intestinal organs and excessive mucus discharge after gynaecological radiotherapy

BACKGROUND

The study aims to determine possible dose-volume response relationships between the rectum, sigmoid colon and small intestine and the 'excessive mucus discharge' syndrome after pelvic radiotherapy for gynaecological cancer.

METHODS AND MATERIALS

From a larger cohort, 98 gynaecological cancer survivors were included in this study. These survivors, who were followed for 2 to 14 years, received external beam radiation therapy but not brachytherapy and not did not have stoma. Thirteen of the 98 developed excessive mucus discharge syndrome. Three self-assessed symptoms were weighted together to produce a score interpreted as 'excessive mucus discharge' syndrome based on the factor loadings from factor analysis. The dose-volume histograms (DVHs) for rectum, sigmoid colon, small intestine for each survivor were exported from the treatment planning systems. The dose-volume response relationships for excessive mucus discharge and each organ at risk were estimated by fitting the data to the Probit, RS, LKB and gEUD models.

RESULTS

The small intestine was found to have steep dose-response curves, having estimated dose-response parameters: γ50: 1.28, 1.23, 1.32, D50: 61.6, 63.1, 60.2 for Probit, RS and LKB respectively. The sigmoid colon (AUC: 0.68) and the small intestine (AUC: 0.65) had the highest AUC values. For the small intestine, the DVHs for survivors with and without excessive mucus discharge were well separated for low to intermediate doses; this was not true for the sigmoid colon. Based on all results, we interpret the results for the small intestine to reflect a relevant link.

CONCLUSION

An association was found between the mean dose to the small intestine and the occurrence of 'excessive mucus discharge'. When trying to reduce and even eliminate the incidence of 'excessive mucus discharge', it would be useful and important to separately delineate the small intestine and implement the dose-response estimations reported in the study.

EQUIVALENT UNIFORM DOSE SENSITIVITY TO CHANGES IN ABSORBED DOSE DISTRIBUTION

Treatment planning in external beam radiation therapy (EBRT) utilizes dose volume histograms (DVHs) as optimization and evaluation tools. They present the fraction of planning target volume (PTV) receiving more than a given absorbed dose, against the absorbed dose values, and a number of radiobiological indices can be computed with their help. Equivalent uniform dose (EUD) is the absorbed dose that, uniformly imparted, would yield the same biological effect on a tumor as the dose distribution described by the DVH. Uncertainty and missing information can affect the dose distribution, therefore DVHs can be modeled as samples from a set of possible outcomes. This work studies the sensitivity of the EUD index when a small change in absorbed dose distribution takes place. EUD is treated as a functional on the set of DVHs. Defining a Lévy distance on this set and using a suitable expansion of the functional, a very simple expression for a bound on the variation of EUD when the dose distribution changes is found. This bound is easily interpreted in terms of standard treatment planning practice.

A quality index for equivalent uniform dose

Equivalent uniform dose (EUD) is the absorbed dose that, when homogeneously given to a tumor, yields the same mean surviving clonogen number as the given non-homogeneous irradiation. EUD is used as an evaluation tool under the assumption that two plans with the same value of EUD are equivalent, and their biological effect on the tumor (clonogen survival) would be the same as the one of a homogeneous irradiation of absorbed dose EUD. In this work, this assumption has been studied, and a figure of merit of its applicability has been obtained. Distributions of surviving clonogen number for homogeneous and non-homogeneous irradiations are found to be different even if their mean values are the same, the figure of merit being greater when there is a wider difference, and the equivalence assumption being less valid. Therefore, EUD can be closer to a uniform dose for some cases than for other ones (high α values, extreme heterogeneity), and the accuracy of the radiobiological indices obtained for evaluation, could be affected. Results show that the equivalence is very sensitive to the choice of radiobiological parameters, and this conclusion has been derived from mathematical properties of EUD.

Improved tumour response prediction with equivalent uniform dose in pre-clinical study using direct intratumoural infusion of liposome-encapsulated ¹⁸⁶Re radionuclides

Crucial to all cancer therapy modalities is a strong correlation between treatment and effect. Predictability of therapy success/failure allows for the optimization of treatment protocol and aids in the decision of whether additional treatment is necessary to prevent tumour progression. This work evaluated the relationship between cancer treatment and effect for intratumoural infusions of liposome-encapsulated ¹⁸⁶Re to head and neck squamous cell carcinoma xenografts of nude rats. Absorbed dose calculations using a dose-point kernel convolution technique showed significant intratumoural dose heterogeneity due to the short range of the beta-particle emissions. The use of three separate tumour infusion locations improved dose homogeneity compared to a single infusion location as a result of a more uniform radioactivity distribution. An improved dose-response correlation was obtained when using effective uniform dose (EUD) calculations based on a generic set of radiobiological parameters (R² = 0.84) than when using average tumour absorbed dose (R² = 0.22). Varying radiobiological parameter values over ranges commonly used for all types of tumours showed little effect on EUD calculations, which suggests that individualized parameter use is of little significance as long as the intratumoural dose heterogeneity is taken into consideration in the dose-response relationship. The improved predictability achieved when using EUD calculations for this cancer therapy modality may be useful for treatment planning and evaluation.

On cold spots in tumor subvolumes

Losses in tumor control are estimated for cold spots of various "sizes" and degrees of "cold dose." This question is important in the context of intensity modulated radiotherapy where differential dose-volume histograms (DVHs) for targets that abut a critical structure often exhibit a cold dose tail. This can be detrimental to tumor control probability (TCP) for fractions of cold volumes even as small as 1%, if the cold dose is lower than the prescribed dose by substantially more than 10%. The Niemierko-Goitein linear-quadratic algorithm with gamma50 slope 1-3 was used to study the effect of cold spots of various degrees (dose deficit below the prescription dose) and size (fractional volume of the cold dose). A two-bin model DVH has been constructed in which the cold dose bin is allowed to vary from a dose deficit of 1%-50% below prescription dose and to have volumes varying from 1% to 90%. In order to study and quantify the effect of a small volume of cold dose on TCP and effective uniform dose (EUD), a four-bin DVH model has been constructed in which the lowest dose bin, which has a fractional volume of 1%, is allowed to vary from 10% to 45% dose deficit below prescription dose. The highest dose bin represents a simultaneous boost. For fixed size of the cold spot the calculated values of TCP decreased rapidly with increasing degrees of cold dose for any size of the cold spot, even as small as 1% fractional volume. For the four-subvolume model, in which the highest dose bin has a fractional volume of 80% and is set at a boost dose of 10% above prescription dose, it is found that the loss in TCP and EUD is moderate as long as the cold 1% subvolume has a deficit less than approximately 20%. However, as the dose deficit in the 1% subvolume bin increases further it drives TCP and EUD rapidly down and can lead to a serious loss in TCP and EUD. Since a dose deficit to a 1% volume of the target that is larger than 20% of the prescription dose may lead to serious loss of TCP, even if 80% of the target receives a 10% boost, particular attention has to be paid to small-volume cold regions in the target. The effect of cold regions on TCP can be minimized if the EUD associated with the target DVH is constrained to be equal to or larger than the prescription dose.

Dose-volume specification: new challenges with intensity-modulated radiation therapy

It has long been recognized that the specification of volumes and doses is an important issue for radiation oncology. Although in any individual center, policies and procedures of treatment delivery may be well understood by staff, reporting of treatment techniques in the archival literature in an unambiguous manner has been found to be less than desirable in many instances. For clinical studies utilizing three-dimensional conformal radiation therapy (3D-CRT), and even more so, intensity-modulated radiation therapy (IMRT), the situation has become even more complex. 3D-CRT and IMRT are now recognized to be more sensitive to geometric uncertainties than conventional radiation therapy because of their ability to create sharper dose gradients around target volumes and organs at risk (OARs). This article reviews the current status of specifying target volumes and doses for 3D-CRT and IMRT, and discusses some of the pertinent issues regarding the use of recommendations in Reports 50 and 62 of the International Commission on Radiation Units and Measurements (ICRU) in this task. It is imperative that physician and physicist fully appreciate the need to account for clinical and spatial uncertainties in the planning and delivery of cancer patients' treatment, paying even more attention to these issues for those cases in which 3D-CRT and/or IMRT is used. A brief review of the reporting requirements for Radiation Therapy Oncology Group (RTOG) 3D-CRT and IMRT protocols is also presented.

Intensity-modulated radiotherapy: current status and issues of interest

PURPOSE

To develop and disseminate a report aimed primarily at practicing radiation oncology physicians and medical physicists that describes the current state-of-the-art of intensity-modulated radiotherapy (IMRT). Those areas needing further research and development are identified by category and recommendations are given, which should also be of interest to IMRT equipment manufacturers and research funding agencies.

METHODS AND MATERIALS

The National Cancer Institute formed a Collaborative Working Group of experts in IMRT to develop consensus guidelines and recommendations for implementation of IMRT and for further research through a critical analysis of the published data supplemented by clinical experience. A glossary of the words and phrases currently used in IMRT is given in the. Recommendations for new terminology are given where clarification is needed.

RESULTS

IMRT, an advanced form of external beam irradiation, is a type of three-dimensional conformal radiotherapy (3D-CRT). It represents one of the most important technical advances in RT since the advent of the medical linear accelerator. 3D-CRT/IMRT is not just an add-on to the current radiation oncology process; it represents a radical change in practice, particularly for the radiation oncologist. For example, 3D-CRT/IMRT requires the use of 3D treatment planning capabilities, such as defining target volumes and organs at risk in three dimensions by drawing contours on cross-sectional images (i.e., CT, MRI) on a slice-by-slice basis as opposed to drawing beam portals on a simulator radiograph. In addition, IMRT requires that the physician clearly and quantitatively define the treatment objectives. Currently, most IMRT approaches will increase the time and effort required by physicians, medical physicists, dosimetrists, and radiation therapists, because IMRT planning and delivery systems are not yet robust enough to provide totally automated solutions for all disease sites. Considerable research is needed to model the clinical outcomes to allow truly automated solutions. Current IMRT delivery systems are essentially first-generation systems, and no single method stands out as the ultimate technique. The instrumentation and methods used for IMRT quality assurance procedures and testing are not yet well established. In addition, many fundamental questions regarding IMRT are still unanswered. For example, the radiobiologic consequences of altered time-dose fractionation are not completely understood. Also, because there may be a much greater ability to trade off dose heterogeneity in the target vs. avoidance of normal critical structures with IMRT compared with traditional RT techniques, conventional radiation oncology planning principles are challenged. All in all, this new process of planning and treatment delivery has significant potential for improving the therapeutic ratio and reducing toxicity. Also, although inefficient currently, it is expected that IMRT, when fully developed, will improve the overall efficiency with which external beam RT can be planned and delivered, and thus will potentially lower costs.

CONCLUSION

Recommendations in the areas pertinent to IMRT, including dose-calculation algorithms, acceptance testing, commissioning and quality assurance, facility planning and radiation safety, and target volume and dose specification, are presented. Several of the areas in which future research and development are needed are also indicated. These broad recommendations are intended to be both technical and advisory in nature, but the ultimate responsibility for clinical decisions pertaining to the implementation and use of IMRT rests with the radiation oncologist and radiation oncology physicist. This is an evolving field, and modifications of these recommendations are expected as new technology and data become available.

Intensity modulated conformal therapy for intracranial lesions

The Peacock planning and delivery system was used to create treatment plans and deliver these plans to patients. The system involves an arc therapy delivery of small (2 cm long) slices of radiation combined with indexing of the couch to achieve target coverage. Two clinical examples are shown to demonstrate the system's capability and evaluate the resources required to produce and deliver the plans. One plan is an optic sheath meningioma and the other is a craniopharyngioma that surrounded the optic chiasm. The optic sheath meningioma was treated to 50 Gy in 25 fractions. The treatment involved delivery of two arcs. The total time to set up the patient and deliver the treatment was less than 15 min. Planning and plan validation after computed tomography required approximately 3 days. The patient had 100% restoration of her field of vision and is stable 3 years post therapy. The second patient is a 9-year-old who had a craniopharyngioma which surrounded the optic chiasm. The tumor was treated to 50.4 Gy in 28 fractions and the dose to the optic chiasm was limited to 45 Gy. The treatment required three arcs and total treatment time was less than 20 min. The patient is stable 15 months post therapy. The system is able to create and deliver radiation patterns that are unique. These plans can be created and delivered in times that rival conventional forward planning conformal radiotherapy systems that cannot produce or conveniently deliver such plans.

Biological integral dose: an alternate method for numerical scoring of rival plans

Numerical scoring of rival plans (NSRP) are usually based either on basis of dose-volume histograms (DVH) or the relative values of corresponding normal tissue complication probabilities (NTCP) and tumor control probabilities (TCP). An alternative method for NSRP based on biological integral dose (BID) is being proposed, which is illustrated using a case of pituitary tumor planned to receive a dose of 50 Gy in 25 fractions over 5 weeks. BID for the various alternate plans -2-field (2F), 3-field (3F), 220 degrees arc (ARC) and 3-field static multileaf collimator (MLC) were calculated using the integration of the product of extrapolated response dose and the corresponding mass of the tissue enclosed separately for tumor and the normal brain in the entire planned target volume or a selected range of dose (approximately 90% and above of the normalized dose). Ratios of the BID for the brain versus the tumor were obtained and the plans were ranked on the basis of the least value of this ratio. In all of these plans, although the DVHs for normal brain were different, the DVHs for tumor were almost identical. However, the BID values for brain for 2F, 3F, ARC, and MLC were 22.53 Joules (J), 21.176 J, 21.991 J, and 10.608 J, respectively, and for tumor 0.561 J, 0.552 J, 0.555 J, and 0.556 J, respectively. The corresponding brain/tumor values were 40.16 (2F), 38.36 (3F), 39.62 (ARC), and 19.08 (MLC), thus ranking the plans in order of merit as MLC, 3F, ARC, and 2F. The BID for volumes encompassed by 90% and more of the normalized dose magnified the differences between the plans, with 2F being 29.99, compared to 3.82 for MLC. Rankings of rival plans could be based on the concept of BID. It requires a lesser number of uncertain variables and therefore could be used as an alternative technique in evaluation of the different plans in routine clinical practice.

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.

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.

Intensity-Modulated Radiotherapy: First Results with this New Technology on Neoplasms of the Head and Neck

Intensity-modulated beam radiotherapy (IMRT) delivers a highly conformal, three-dimensional (3-D) distribution of radiation doses that is not possible with conventional methods. When administered to patients with head and neck tumors, IMRT allows for the treatment of multiple targets with different doses, while simultaneously minimizing radiation to uninvolved critical structures such as the parotid glands, optic chiasm, and mandible. With 3-D computerized dose optimization, IMRT is a vast improvement over the customary trial-and-error method of treatment planning.

We retrospectively reviewed the charts of the first 28 head and neck patients at our institution who were treated with IMRT. All had head and neck neoplasms, including squamous cell carcinoma, adenoid cystic carcinoma, paraganglioma, and angiofibroma. Total radiation doses ranged from 1,400 to 7,100 cGy, and daily doses ranged from 150 to 400 cGy/day. A quality assurance system ensured that computer-generated dosimetry matched film dosimetry in all cases. For midline tumors, this system allowed us to decrease the dose to the parotid glands to less than 3,000 cGy. The incidence of acute toxicity was drastically lower than that seen with conventional radiotherapy delivery to similar sites.

This is the first report of the application of IMRT strictly to head and neck neoplasms. We discuss the indications, technique, and initial results of this promising new technology. We also introduce the concept of the Simultaneous Modulated Accelerated Radiation Therapy boost technique, which has several advantages over other altered fractionation schemes.