Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

Verification of tomotherapy dose delivery.

Seventy-one patient-specific delivery quality assurance (DQA) plans for the Tomotherapy HI-ART II helical tomotherapy system (TomoTherapy, Inc., Madison, WI, USA) were measured using film and ion chamber. The agreement in absolute point dose was 1.19 +/- 0.79%, 1.91 +/- 1.39%, 2.14 +/- 1.3%, 1.3 +/- 0.73% and 1.67 +/- 1.5% for head and neck, prostate, pelvis-abdomen sites, and for all other sites. The spatial agreement between the calculated and the measured film dose distributions was evaluated using the gamma metric distribution. The average frequency versus gamma interval was plotted as a bar graph to quantify the gamma index variation inside the region of interest for each body site.

Quality assurance of a helical tomotherapy machine.

Helical tomotherapy has been developed at the University of Wisconsin, and 'Hi-Art II' clinical machines are now commercially manufactured. At the core of each machine lies a ring-gantry-mounted short linear accelerator which generates x-rays that are collimated into a fan beam of intensity-modulated radiation by a binary multileaf, the modulation being variable with gantry angle. Patients are treated lying on a couch which is translated continuously through the bore of the machine as the gantry rotates. Highly conformal dose-distributions can be delivered using this technique, which is the therapy equivalent of spiral computed tomography. The approach requires synchrony of gantry rotation, couch translation, accelerator pulsing and the opening and closing of the leaves of the binary multileaf collimator used to modulate the radiation beam. In the course of clinically implementing helical tomotherapy, we have developed a quality assurance (QA) system for our machine. The system is analogous to that recommended for conventional clinical linear accelerator QA by AAPM Task Group 40 but contains some novel components, reflecting differences between the Hi-Art devices and conventional clinical accelerators. Here the design and dosimetric characteristics of Hi-Art machines are summarized and the QA system is set out along with experimental details of its implementation. Connections between this machine-based QA work, pre-treatment patient-specific delivery QA and fraction-by-fraction dose verification are discussed.

Assessment of patient-independent intrinsic error for a noninvasive frame for fractionated stereotactic radiotherapy.

The purpose of our study was to examine the extent of patient-independent intrinsic error associated with multiple, repeat remounting of the Laitinen Stereoadapter. The Laitinen frame was repeatedly mounted on a solid water phantom and imaged using computed tomography (CT). The phantom contained five targets located in the center, anterior, right, left, and posterior orientations. The images were processed, fused, and analyzed on the Pinnacle 3-D treatment planning system. The coordinate values (in the x, y, and z directions) for each target were determined for each mounting, and an absolute mean deviation was calculated for 11 repetitions. The mean deviation in the x, y, and z direction for the central and right target, and in the x and y direction for the posterior and anterior target was less than 2.0 mm. However, the mean error in the z direction of the anterior and posterior targets was 1.79 +/- 1.02 mm and 2.20 +/- 1.32 mm, respectively. Rotational misalignment during repeat frame fixation contributed to the observed deviations and in particular affected the antero-posterior plane. With the exception of two occasions where an obvious mounting error occurred, a significant portion of error from remounting the Laitinen Stereoadapter is associated with the operator and the imaging process. The observation of an angular displacement around the axis through the earplugs suggests that a certain degree of rotational misalignment in daily remounting is possible. Targets in the antero-posterior plane are most susceptible to localization error as a consequence of rotational misalignment. In summary, the overall error is within the limits of current imaging technology but not within submillimeter accuracy. Clinical application should take these errors into consideration when designing field margins.

Radiation injury from x-ray exposure during brachytherapy localization.

Two patients developed skin ulcers secondary to high doses of diagnostic-energy x rays received during localization procedures as part of brachytherapy treatments. Both were morbidly obese and diabetic. The obesity led to the delivery of estimated skin doses of 83 Gy in one case and 29 Gy in the other in attempts to produce readable images on localization radiographs. This report discusses the factors leading to the injuries, the progression of the injuries over time, and the variables involved in the localization procedures with the aim of preventing future mishaps. The greatest contribution to the large skin dose was the need, with the equipment available, to use multiple exposures to produce a single film, because of the effect of the resultant reciprocity failure.

A solid water pelvic and prostate phantom for imaging, volume rendering, treatment planning, and dosimetry for an RTOG multi-institutional, 3-D dose escalation study. Radiation Therapy Oncology Group.

PURPOSE: With increased interest in 3-D conformal radiation therapy and dose escalation, it is necessary to provide advanced techniques to assure quality in treatment delivery. Multi-institutional trials for these newer treatment techniques require methods of verifying the consistency of treatments between the participating institutions. For this reason, a phantom was designed to address the quality and consistency of Radiation Therapy Oncology Group (RTOG) 3-D prostate treatment protocol. METHODS AND MATERIALS: A solid water pelvic and prostate phantom for imaging, volume rendering, treatment planning, and dosimetry applications for performing comprehensive quality assurance has been designed and fabricated. Its configuration was based upon CT slices obtained from a patient study. Individual slices were machined with corresponding contours of the prostate, bladder, rectum, and the left and right femurs. Most of the phantom is made of solid water (Gammex/RMI, Middleton, WI), while the femurs are made of bone-equivalent material. The CT numbers from patient images were used to adjust the solid water composition within the organ volumes, providing image contrast from the remainder of the phantom. Cylindrical insertion grooves are machined in the phantom to allow placement of ionization chambers and thermal luminal dosimeters (TLDs) for dosimetry applications. During imaging, the cavities are filled with rods fabricated from solid water material. RESULTS: The phantom is being used to evaluate the consistency of a range of processes in radiation therapy simulation, planning, and delivery of 3-D-based treatments for prostate cancer. CONCLUSION: The ultimate study objective is to use the phantom to evaluate the accuracy and consistency of treatments delivered by institutions participating in national collaborative clinical trials involving 3-D conformal dose escalation.

Attenuation characteristics of a new compensator material: Thermo-Shield for high energy electron and photon beams.

A new thermoplastic material with extremely desirable physical and radiation shielding properties is presented. The material softens between 108 degrees F and 132 degrees F and can then be easily molded to any desired shape. As it cools down it hardens at about 102 degrees F, retaining its molded shape. It is very light (rho = 1.66 g/cc), compared to most other compensating and shielding materials used in the clinic. Its photon and electron attenuation characteristics have been measured and are compared with other materials relevant to radiotherapy. Possible applications as a bolus material, compensator and partial or total shielding material in clinical radiation therapy are discussed.

Improving dose homogeneity in routine head and neck radiotherapy with custom 3-D compensation.

BACKGROUND AND PURPOSE: Anatomic contour irregularity and tissue inhomogeneity can lead to significant radiation dose variation across the complex treatment volumes found in the head and neck (H&N) region. This dose inhomogeneity can routinely create focal hot or cold spots of 10-20% despite beam shaping with blocks or beam modification with wedges. Since 1992, we have implemented the routine use of 3-D custom tissue compensators fabricated directly from CT scan contour data obtained in the treatment position in order to improve dose uniformity in patients with tumors of the H&N. MATERIALS AND METHODS: Between July 1992 and January 1997, 160 patients receiving comprehensive H&N radiotherapy had 3-D custom compensators fabricated for their treatment course. Detailed dosimetric records have been analyzed for 30 cases. Dose uniformity across the treatment volume and clinically relevant maximum doses to selected anatomic sub-sites were examined with custom-compensated, uncompensated and optimally-wedged plans. RESULTS: The use of 3-D custom compensators resulted in an average reduction of dose variance across the treatment volume from 19+/-4% for the uncompensated plans to 5+/-2% with the use of 3-D compensators. Optimally-wedged plans were variable, but on average a 10+/-3% dose variance was noted. For comprehensive H&N treatment which encompassed the larynx within the primary field design, the peak doses delivered were reduced by 5-15% with 3-D custom compensation as compared to optimal wedging. CONCLUSIONS: The use of 3-D custom tissue compensation can improve dose homogeneity within the treatment volume for H&N cancer patients. Maximum doses to clinically important structures which often receive greater than 105-110% of the prescribed dose are routinely reduced with the use of 3-D custom compensators. Improved dose uniformity across the treatment volume can reduce normal tissue complication profiles and potentially allow for delivery of higher total doses in an attempt to enhance locoregional tumor control.

Analysis and convergence of the iterative convolution/superposition dose reconstruction technique for multiple treatment beams and tomotherapy.

An iterative convolution/superposition (C/S) algorithm has been created to reconstruct dose distributions in patients from exit dose measurements during a radiotherapy treatment. The method is based on an extended phantom which includes the patient CT representation and an electronic portal imaging device (EPID). The patient CT is assumed to be a true and rigid representation of the patient at the time of treatment. The C/S method computes the dose throughout the extended phantom which allows the exit dose to be predicted in the EPID. The process is then reversed to take the exit dose measurement and infer what the dose distribution must have been to produce the measured exit dose. The dose distribution is modeled without knowledge of the incident intensity distribution, and includes the effects of scatter in the computation. The iterative method begins by assuming that the exit primary energy fluence (PEF) is equal to the exit dose, the PEF is then backprojected through the extended phantom and superposed with the dose deposition kernel to determine a new prediction of the exit dose. The ratio of the computed PEF to exit dose is then multiplied by the measured exit dose image to produce a better representation of the exit PEF. Successive iterations then converge to the exit PEF image that would produce the measured exit dose image. Once convergence is established, the dose distribution is determined by backprojecting the exit PEF followed by superposition with the dose deposition kernel. The method is used to reconstruct the dose from a stimulated dynamic wedge and verified with film. Convergence and termination of the algorithm is then investigated with no noise and in the presence of noise. The method is then expanded to handle multiple treatment beams by separating the representation of the EPID from the patient or phantom representation in the computation process. Investigation of the effects of noise during the process of iterative dose reconstruction is necessary to understand the capabilities of the algorithm using exit dose images that may contain significant amounts of noise. The capability of the algorithm is evaluated for multiple field treatments to a cube phantom and a prostate patient CT representation in the presence of noise. The method is then used to simulate the dose reconstruction process for tomotherapy using 72 intensity-modulated fan beams. Dose reconstruction is shown to be capable of verifying the dose distributions in patients including multiple beams and dynamic collimation, provided the patient CT is known at the time of treatment.

A consistency monitor for radiation therapy treatments.

A thin, large area transparent transmission chamber mounted below the accessory tray is described and its suitability for daily treatment delivery consistency is investigated. The sensitivity of the detector to changes in monitor unit setting, field size, wedge size, missing blocks, and wedges is presented. Some of the other potential applications are also discussed.

Modeling dose distributions from portal dose images using the convolution/superposition method.

Post-treatment dose verification refers to the process of reconstructing delivered dose distributions internal to a patient from information obtained during the treatment. The exit dose is commonly used to describe the dose beyond the exit surface of the patient from a megavoltage photon beam. Portal imaging provides a method of determining the dose in a plane distal to a patient from a megavoltage therapeutic beam. This exit dose enables reconstruction of the dose distribution from external beam radiation throughout the patient utilizing the convolution/superposition method and an extended phantom. An iterative convolution/superposition algorithm has been created to reconstruct dose distributions in patients from exit dose measurements during a radiotherapy treatment. The method is based on an extended phantom that includes the patient CT representation and an electronic portal imaging device (EPID). The convolution/superposition method computes the dose throughout the extended phantom, which allows the portal dose image to be predicted in the EPID. The process is then reversed to take the portal dose measurement and infer what the dose distribution must have been to produce the measured portal dose. The dose distribution is modeled without knowledge of the incident intensity distribution, and includes the effects of scatter in the computation. The iterative method begins by assuming that the primary energy fluence (PEF) at the portal image plane is equal to the portal dose image, the PEF is then back-projected through the extended phantom and convolved with the dose deposition kernel to determine a new prediction of the portal dose image. The image of the ratio of the computed PEF to the computed portal dose is then multiplied by the measured portal dose image to produce a better representation of the PEF. Successive iterations of this process then converge to the exiting PEF image that would produce the measured portal dose image. Once convergence is established, the dose distribution is determined by back-projecting the PEF and convolving with the dose deposition kernel. The method is accurate, provided the patient representation during treatment is known. The method was used on three phantoms with a photon energy of 6 MV to verify convergence and accuracy of the algorithm. The reconstructed dose volumes agree to within 3% of the forward computation dose volumes. Furthermore, this technique assumes no prior knowledge of the incident fluence and therefore may better represent the dose actually delivered.

Calculation of portal dose using the convolution/superposition method.

The convolution/superposition method was used to predict the dose throughout an extended volume, which includes a phantom and a portal imaging device. From the calculated dose volume, the dose delivered in the portal image plane was extracted and compared to a portal dose image. This comparison aids in verifying the beam configuration or patient setup after delivery of the radiation. The phantoms used to test the accuracy of this method include a solid water cube, a Nuclear Associates CT phantom, and an Alderson Rando thorax phantom. The dose distribution in the image plane was measured with film and an electronic portal imaging device in each case. The calculated portal dose images were within 4% of the measured images for most voxels in the central portion of the field for all of the extended volumes. The convolution/superposition method also enables the determination of the scatter and primary dose contributions using the particular dose deposition kernels for each contribution. The ratio of primary dose to total dose was used to extract the primary dose from the detected portal image, which enhances the megavoltage portal images by removing scatter blurring. By also predicting the primary energy fluence, we can find the ratio of computed primary energy fluence to total dose. Multiplying this ratio by the measured dose image estimates the relative primary energy fluence at the portal imager. The image of primary energy fluence possesses higher contrast and may be used for further quantitative image processing and dose modeling.

Thermoradiotherapy of intraocular tumors in an animal model: concurrent vs. sequential brachytherapy and ferromagnetic hyperthermia.

PURPOSE: To compare concurrent vs. sequential ferromagnetic thermoradiotherapy in vivo. METHODS AND MATERIALS: Greene melanomas were implanted subretinally in rabbits and observed until they were 3-5 mm in diameter. Episcleral plaques were assembled with 125I seeds for radiation therapy, or with ferromagnetic (FM) thermoseeds and nonradioactive I seeds for hyperthermia. Rabbits were implanted by centering a plaque over the intraocular melanoma. After a given dose of radiation had been delivered, the plaque was removed and a nonradioactive plaque containing FM thermoseeds was inserted into the same extrascleral space. One hour later, hyperthermia (46-47 degrees C at the plaque-scleral interface) was initiated and continued for a period of 1 h by placing the rabbits in a magnetic induction coil powered to 1200 W. Tumor size was determined at 1- to 2-week intervals by indirect ophthalmoscopy and by ultrasound. RESULTS: Dose-response analysis of 27 treated eye melanomas showed 50% local tumor control at 43 Gy for 125I alone and 29.4 Gy for 125I followed by FM hyperthermia. The thermal enhancement ratio was 1.4. CONCLUSION: Comparison with a previously published thermal enhancement ratio of 4.4 (for concurrent 125I and FM hyperthermia) leads us to conclude that thermal enhancement of 125I brachytherapy is more efficient in this tumor model system when hyperthermia is delivered during, rather than after, the irradiation process.

Intercomparison of normalized head-scatter factor measurement techniques.

Normalized head-scatter factors were measured with cylindrical beam coaxial miniphantoms and high purity graphite buildup caps for 4-, 6-, 10-, and 24-MV photon beams at field sizes from 4 x 4 to 40 x 40 cm2. The normalized head-scatter factors determined by the two methods matched well for 4- and 6-MV photon beams. The miniphantom technique produced normalized head-scatter factors 1.5% and 4.8% lower than the buildup caps for the 10- and 24-MV beams for large field sizes, respectively. At small field sizes, the miniphantom technique produced larger normalized head-scatter factors than the buildup caps. Measurements made with an electromagnet indicate that a significant portion of the ionization measured in the buildup cap at 24 MV arises from contamination electrons. Measurements made with the miniphantom and magnet found no contamination electron contribution. The miniphantom technique may exclude such contamination electrons, potentially leading to inaccuracies in tissue-maximum ratios and phantom scatter factors, as well as inaccuracies in monitor unit calculations.

Accuracy of the point source approximation to high dose-rate Ir-192 sources.

The accuracy of the point source approximation used in dose calculations for an implant comprised of multiple high dose rate (HDR) Ir-192 source dwell positions is investigated. First, a single dwell position implant is modeled. The exposure rate about the source is calculated using both the point source approximation and the more rigorous line source formalism. A comparison of these calculated exposure rates is made. It is found that for each HDR Ir-192 source dwell position, the point source approximation results in a dose overestimation of 1% at a distance of 1 cm on the source transverse axis, while dose underestimations of more than 2% can be found at a distance of 1 cm on the source longitudinal axis. Even larger errors occur closer to the source. The results of this academic study are then extended to two clinical cases--an endobronchial treatment and a tandem and ovoids setup, both involving multiple source dwell positions. Since clinical HDR Ir-192 implants are comprised of many individual source dwell positions, there will be inaccuracy in the calculated overall dose distribution leading to dose delivery errors. For example, the dose delivered to a prescription point located 0.5 cm from an endobronchial applicator will be 3% lower than prescribed. Similar errors are produced in gynecologic implants. To decrease below 0.5% the dose delivery error resulting from the point source approximation, prescription points should be at a distance of at least 1 cm from any applicator. Since the dosimetry error is a direct result of the choice of model used to describe the source, the use of anisotropy factors accounting for the variation of photon fluence around the HDR Ir-192 source will not completely correct the calculation.

The use of generalized cell-survival data in a physiologically based objective function for hyperthermia treatment planning: a sensitivity study with a simple tissue model implanted with an array of ferromagnetic thermoseeds.

PURPOSE: A physiologically based objective function for identifying a combination of ferromagnetic seed temperatures and locations that maximizes the fraction of tumor cells killed in pretreatment planning of local hyperthermia. METHODS AND MATERIALS: An objective-function is developed and coupled to finite element software that solves the bioheat transfer equation. The sensitivity of the objective function is studied in the optimization of a ferromagnetic hyperthermia treatment. The objective function has several salient features including (a) a physiological basis that considers increasing the fraction of cells killed with increasing temperatures above a minimum therapeutic temperature (Tmin,thera), (b) a term to penalize for heating of normal tissues above Tmin,thera, and (c) a scalar weighting factor (gamma) that has treatment implications. Reasonable estimates for gamma are provided and their influence on the objective function is demonstrated. The cell-kill algorithm formulated in the objective function is based empirically upon the behavior of published hyperthermic cell-survival data. The objective function is shown to be independent of normal tissue size and shape when subjected to a known outer-surface, thermal boundary condition. Therefore, fractions of cells killed in tumors of different shapes and sizes can be compared to determine the relative performance of thermoseed arrays to heat different tumors. RESULTS: In simulations with an idealized tissue model perfused by blood at various rates, maxima of the objective function are unique and identify seed spacings and Curie-point temperatures that maximize the fraction of tumor cells killed. In ferromagnetic hyperthermia treatment planning, seed spacing can be based on maximizing the minimum tumor temperature and minimizing the maximum normal tissue temperature. It is shown that this treatment plan is less effective than a plan based on seed spacings that maximize the objective function. CONCLUSIONS: It is shown that under the assumptions of the model and based on a desired therapeutic goal, the objective function identifies a combination of thermoseed temperatures and locations that maximizes the fraction of tumor cells killed.

Effect of interseed spacing, tissue perfusion, thermoseed temperatures and catheters in ferromagnetic hyperthermia: results from simulations using finite element models of thermoseeds and catheters.

Finite element heat-transfer models of ferromagnetic thermoseeds and catheters are developed for simulating ferromagnetic hyperthermia. These models are implemented into a general purpose, finite element computer program to solve the bioheat transfer equation. The seed and catheter models are unique in that they have fewer modeling constraints than other previously developed thermal models. Simulations are conducted with a 4 x 4 array of seeds in a multicompartment tissue model. The heat transfer model predicts that fractions of tumor greater than 43 degrees C are between 8 and 40% lower when seed temperatures depend on power versus models which assume a constant seed temperature. Fractions of tumor greater than 42 degrees C, in simulations using seed and catheter models, are between 3.3 and 25% lower than in simulations with bare seeds. It is demonstrated that an array of seeds with Curie points of 62.6 degrees C heats the tumor very well over nearly all blood perfusion cases studied. In summary, results herein suggest that thermal models simulating ferromagnetic hyperthermia should consider the power-temperature dependence of seeds and include explicit models of catheters.

Temperature-dependent versus constant-rate blood perfusion modelling in ferromagnetic thermoseed hyperthermia: results with a model of the human prostate.

Finite-element solutions to the Pennes bioheat equation are obtained with a model of a tumour-containing, human prostate and surrounding normal tissues. Simulations of ferromagnetic hyperthermia treatments are conducted on the tissue model in which the prostate is implanted with an irregularly spaced array of thermoseeds. Several combinations of thermoseed temperatures with different Curie points are investigated. Non-uniform, constant-rate blood perfusion models are studied and compared with temperature-dependent descriptions of blood perfusion. Blood perfusions in the temperature-dependent models initially increase with tissue temperature and then decrease at higher temperatures. Simulations with temperature-dependent versus constant-rate blood perfusion models reveal significant differences in temperature distributions in and surrounding the tumour-containing prostate. Results from the simulations include differences (between temperature-dependent and constant-rate models) in (1) the percentage of normal tissue volume and tumour volume at temperatures > 42 degrees C, and (2) temperature descriptors in the tumour (subscript t) and normal (subscript n) tissues including Tmax.t, Tmin.t and Tmax.n. Isotherms and grey-scale contours in the tumour and surrounding normal tissues are presented for four simulations that model a combination of high-temperature thermoseeds. Several simulations show that Tmin.t is between 1.7 and 2.6 degrees C higher and Tmax.n is between 2.1 and 3.3 degrees C higher with a temperature-dependent versus a comparable constant-rate blood perfusion model. The same simulations reveal that the percentages of tumour volume at temperatures > 42 degrees C are between 0 and 68% higher with the temperature-dependent versus the constant-rate perfusion model over all seed combinations studied. In summary, a numerical method is presented which makes it possible to investigate temperature-dependent, continuous functions of blood perfusion in simulations of hyperthermia treatments. Simulations with this numerical method reveal that the use of constant-rate instead of temperature-dependent blood perfusion models can be a conservative approach in treatment planning of ferromagnetic hyperthermia.

Implementation of a three-dimensional compensation system based on computed tomography generated surface contours and tissue inhomogeneities.

A computed tomography (CT) based system that compensates for patient surface contour and internal tissue inhomogeneity was implemented in our clinic. The compensators are fabricated with a mixture of tin granules and bee's wax. The tin/wax mixture was optimized for tin granule size and tin granule to wax ratio. The narrow beam attenuation coefficients were measured for 4-, 6-, 10-, and 24-MV photon beams. The compensator design and fabrication methodology were verified by measuring the dose distribution for a known surface contour irradiated with a compensated beam and for a known inhomogeneity that was submerged in a water phantom and irradiated with a compensated beam. For the surface contour, the uncompensated isodose levels varied by as much as 10% in the compensation plane and the compensator restored the isodose level to a variation of less than 1.3%. Measured and calculated doses for this surface contour were found to differ by less than 3.4%. For the inhomogeneity, the uncompensated isodose levels varied by 27% in the compensation plane and the compensator restored the isodose level to a variation of less than 1.5%. Measured and calculated doses for the known inhomogeneity were found to differ by less than 2%. Measurements of depth-dose curves indicate that the presence of the compensator in the beam does not significantly increase the surface dose. Twenty-six compensators have now been fabricated for clinical cases. In these patients, dose variations as great as 19% occurred in the plane of compensation prior to placing the compensator in the beam.(ABSTRACT TRUNCATED AT 250 WORDS)