The objective evaluation of alternative treatment plans: I. Images of regret

The mean absolute dose deviation-A common metric for the evaluation of dose-volume histograms in radiation therapy

Radiation therapy needs to balance between delivering a high dose to targets and the lowest possible dose to the organs at risk. Dose-volume histograms (DVHs) summarize the distribution of radiation doses in the irradiated structures. The interpretation can however be a challenge when the number of structures is high. We propose the use of a simple summary metric. We define the mean absolute dose deviation (MADD) as the average of absolute differences between a DVH and a reference dose. The properties are evaluated through numerical analysis. Calculus trivially shows the identity of the MADD and the area between curves, between DVH and reference dose. Computation of the MADD is the same regardless of structures' designation, whether organ at risk or target, on the same dose scale. Basic calculus properties open the perspective of applying the MADD to the evaluation of treatment plans.

Treatment plan evaluation using dose-volume histogram (DVH) and spatial dose-volume histogram (zDVH)

OBJECTIVE

The dose-volume histogram (DVH) has been accepted as a tool for treatment-plan evaluation. However, DVH lacks spatial information. A new concept, the z-dependent dose-volume histogram (zDVH), is presented as a supplement to the DVH in three-dimensional (3D) treatment planning to provide the spatial variation, as well as the size and magnitude of the different dose regions within a region of interest.

MATERIALS AND METHODS

Three-dimensional dose calculations were carried out with various plans for three disease sites: lung, breast, and prostate. DVHs were calculated for the entire volume. A zDVH is defined as a differential dose-volume histogram with respect to a computed tomographic (CT) slice position. In this study, zDVHs were calculated for each CT slice in the treatment field. DVHs and zDVHs were compared.

RESULTS

In the irradiation of lung, DVH calculation indicated that the treatment plan satisfied the dose-volume constraint placed on the lung and zDVH of the lung revealed that a sizable fraction of the lung centered about the central axis (CAX) received a significant dose, a situation that warranted a modification of the treatment plan due to the removal of one lung. In the irradiation of breast with tangential fields, the DVH showed that about 7% of the breast volume received at least 110% of the prescribed dose (PD) and about 11% of the breast received less than 98% PD. However, the zDVHs of the breast volume in each of seven planes showed the existence of high-dose regions of 34% and 15%, respectively, of the volume in the two caudal-most planes and cold spots of about 40% in the two cephalic planes. In the treatment planning of prostate, DVHs showed that about 15% of the bladder and 40% of the rectum received 102% PD, whereas about 30% of the bladder and 50% of the rectum received the full dose. Taking into account the hollow structure of both the bladder and the rectum, the dose-surface histograms (DSH) showed larger hot-spot volume, about 37% of the bladder wall and 43% of the rectal wall. The zDVHs of the bladder revealed that the hot-spot region was superior to the central axis. The zDVHs of the rectum showed that the high-dose region was an 8-cm segment mostly superior to the central axis. The serial array-like of the rectum warrants a closer attention with regard to the complication probability of the organ.

CONCLUSIONS

Although DVH provides an averaged dose-volume information, zDVH provides differential dose-volume information with respect to the CT slice position. zDVH is a 2D analog of a 3D DVH and, in some situations, more superior. It provides additional information on plan evaluation that otherwise could not be appreciated. The zDVH may be used along with DVH for plan evaluation and for the correlation of radiation outcome.

Tumor and target delineation: current research and future challenges

In the past decade, significant progress has been made in the imaging of tumors, three dimensional (3D) treatment planning, and radiation treatment delivery. At this time one of the greatest challenges for conformal radiation therapy is the accurate delineation of tumor and target volumes. The physician encounters many uncertainties in the process of defining both tumor and target. The sources of these uncertainties are discussed, as well as the issues requiring study to reduce these uncertainties.

Advances in 3-dimensional radiation treatment planning systems: room-view display with real time interactivity

PURPOSE

We describe our 3-dimensional (3-D) radiation treatment planning system for external photon and electron beam 3-D treatment planning which provides high performance computational speed and a real-time display which we have named "room-view" in which the simulated target volumes, critical structures, skin surfaces, radiation beams and/or dose surfaces can be viewed on the display monitor from any arbitrary viewing position.

METHODS AND MATERIALS

We have implemented the 3-D planning system on a graphics superworkstation with parallel processing. Patient's anatomical features are extracted from contiguous computed tomography scan images and are displayed as wireloops or solid surfaces. Radiation beams are displayed as a set of diverging rays plus the polygons formed by the intersection of these rays with planes perpendicular to the beam axis. Controls are provided for each treatment machine motion function. Photon dose calculations are performed using an effective pathlength algorithm modified to accommodate 3-D off-center ratios. Electron dose calculations are performed using a 3-D pencil beam model.

RESULTS

Dose distribution information can be displayed as 3-D dose surfaces, dose-volume histograms, or as isodoses superimposed on 2-D gray scale images of the patient's anatomy. Tumor-control-probabilities, normal-tissue-complication probabilities and a figure-of-merit score function are generated to aid in plan evaluation. A split-screen display provides a beam's-eye-view for beam positioning and design of patient shielding block apertures and a concurrent "room-view" display of the patient and beam icon for viewing multiple beam set-ups, beam positioning, and plan evaluation. Both views are simultaneously interactive.

CONCLUSION

The development of an interactive 3-D radiation treatment planning system with a real-time room-view display has been accomplished. The concurrent real-time beam's-eye-view and room-view display significantly improves the efficacy of the 3-D planning process.

The reliability of optimization under dose-volume limits

PURPOSE

An optimization algorithm improves the distribution of dose among discrete points in tissues, but tolerance depends on the distribution of dose across a continuous volume. This report asks whether an exact algorithm can be completed when enough points are taken to accurately model a dose-volume constraint.

METHODS AND MATERIALS

Trials were performed using a 3-dimensional model of conformal therapy of lung cancer. Trials were repeated with different limits placed on the fraction of lung which could receive > 20 Gy. Bounds were placed on cord dose and target dose inhomogeneity. A mixed integer algorithm was used to find a feasible set of beam weights which would maximize tumor dose. Tests of feasibility and optimality are introduced to check the solution accuracy.

RESULTS

Solutions were optimal for points used to model tissues. An accuracy of 3-4% in a volume condition could be obtained with models of 450-600 points. The error improved to 2% with 800 points to model the lung. Solution times increased six-fold at this level of accuracy.

CONCLUSION

The mixed integer method can find optimum weights which respect dose-volume conditions in usually acceptable times. If constraints are violated by an excessive amount, the optimization model should be rerun with more points.

A medical workstation for the evaluation of alternative 3D radiotherapy treatment plans

A medical workstation for the evaluation of alternative 3D radiotherapy plans is described. Our system can simultaneously apply qualitative as well as quantitative evaluation methods to as many as three 3D dose distributions. The user interface of the workstation has been designed with the demands of radiation oncologists in mind. The handling of the large amounts of 3D data (CT data, up to three 3D dose distributions, volumes of interest) is assisted by computer graphics.

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.

The objective evaluation of alternative treatment plans. III: The quantitative analysis of dose volume histograms

The computer program OSCAR evaluates dose-volume histograms in a consistent way for use in 3-dimensional treatment planning. Based on a dose prescription specified by a radiation oncologist, the technique provides a quantitative and easily understood visual analysis of a proposed dose distribution. Rapid, reliable, and consistent choices can be made between alternative treatment plans, and if necessary the results of OSCAR calculations can be used to guide the design of a plan that will be closer to the required prescription. The method is well suited to use in the definition of treatment protocols. The use of OSCAR is demonstrated by applying it to the evaluation of alternative volumetric treatment plans for ca lung. The results demonstrate the importance of using corrections for inhomogeneous tissue density in the calculation of 3-dimensional dose distributions.

The objective evaluation of alternative treatment plans: II. Score functions

A series of six patients with adenocarcinoma of the prostate, Stages A2, B1, or B2, were planned for treatment using a four-field box technique at 25 MV. Plans were prepared by three techniques: composite, mid-plane, and conformal. The dose distributions at the central plane and at two planes offset by +/- 2 cm were evaluated by means of score functions which quantify the magnitude of regret for target dose gradient, target over- and under-dose, non-target tissue overdose, and for overdose to the rectum, bladder, and femoral heads. The score functions are normalized to give values in the range from 10 (ideal) to zero (limit of acceptability), with negative values indicating unacceptable deviations from the prescribed dose limits. The scores for off-axis conformal plans were found to be essentially the same as for mid-plane plans on the central plane. However, mid-plane planning was shown to be totally inadequate for off-axis planes, where the average target gradient and underdose scores were reduced by 10 units. Composite planning resulted in adequate target coverage on all planes, but at the expense of unacceptable overdose to non-target tissue. The effect of reducing the posterior beam weight to half that of the other three beams was to reduce the target gradient score by 1.6 +/- 0.5 units and to increase the rectal score by 0.9 +/- 0.3 units.

Treatment planning for protocol-based radiation therapy

Many protocol studies are conducted in which patients are assigned to alternative treatment regimens. Typically the dosimetric specifications will define the maximal and minimal target doses and maximal doses to specified critical normal structures, and the success of the study will depend upon the consistency and reliability with which these dose specifications are applied. We have investigated the use of dose-area histograms to ensure complete adherence to protocol dose specifications. A dose prescription is prepared that defines upper and lower target doses as well as normal tissue dose tolerance levels for all organs of interest. In addition, dose-volume histograms are derived which provide quantitative measures of the extent to which each dose limit has been met. This technique can be used during treatment planning to prevent protocol violations of pre-defined severity, or for retroactive correlation of local tumor recurrence and treatment-related morbidity with dose levels in the target and normal tissues. An example is presented for a protocol study of ca prostate, stages A and B, in which seven treatments were evaluated at the mid-plane for protocol violations.