Medical Physics, Vol. 29, No. 7, pp. 1430–1437, July 2002
©2002 American Association of Physicists in Medicine. All rights reserved.
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Dose^{ }broadening due to target position variability during fractionated breathheld radiation^{ }therapy
W. G. O'Dell,^{a)}^{,}^{b)}M. C. Schell,^{b)}D. Reynolds, and P. Okunieff
Department of Radiation Oncology, University of^{ }Rochester School of Medicine and Dentistry, Rochester, New York 146428647
Received: 30 November^{ }2001; accepted: 22 April 2002; published: 20 June 2002Recent advances in Stereotactic Radiosurgery/Conformal Radiotherapy^{ }have made it possible to deliver surgically precise radiation therapy^{ }to small lesions while preserving the surrounding tissue. However, because^{ }of physiologic motion, the application of conformal radiotherapy to extracranial^{ }tumors is, at present, geared toward slowing the progression of^{ }disease rather than obtaining a cure. At the University of^{ }Rochester, we are investigating the use of patient breathholding to^{ }reduce respiratoryderived motion in fractional radiotherapy. The primary targeting problem^{ }then becomes the small variation in tumor location over repeated^{ }breathholds. This paper describes the effects of residual target position^{ }uncertainty on the dose distribution observed by small extracranial tumors^{ }and their neighboring tissues during fractional radiation treatment using breath^{ }holding. We employ two computational methods to study these effects:^{ }numerical analysis via Monte Carlo simulation and analytical computation using^{ }threedimensional convolution. These methods are demonstrated on a 2arc, 10fraction^{ }treatment plan used to treat a representative lung tumor in^{ }a human subject. In the same human subject, the variability^{ }in position of a representative lung tumor was measured over^{ }repeated endexpiration breathholds using volumetric imaging. For the 7×7×10 mm^{ }margin used to treat this 12 mm diameter tumor and^{ }the measured target position variability, we demonstrated that the entire^{ }tumor volume was irradiated to at least 48 Gy—well above^{ }the tumoricidal threshold. The advantages, in terms of minimizing the^{ }volume of surrounding lung tissue that is radiated to high^{ }dose during treatment, of using endexpiration breath holding compared with^{ }endinspiration breathholding are demonstrated using representative tumor size and position^{ }variability parameters. It is hoped that these results will ultimately^{ }lead to improved, if not curative, treatment for small (5–20^{ }mm diameter) lung, liver, and other extracranial lesions. © 2002^{ }American Association of Physicists in Medicine.^{ }
Contents
I. BACKGROUND^{ }AND SIGNIFICANCE
Recent advances in Stereotactic Radiosurgery/Conformal Radiotherapy have made it^{ }possible to deliver surgically precise radiation therapy to small lesions^{ }while preserving function to surrounding structures. This radiosurgical approach is^{ }used routinely by physicians to eradicate small, stationary lesions in^{ }the cranium. Unfortunately, the application of 3D conformal radiotherapy to^{ }isolated tumors in the chest and abdomen is, at present,^{ }geared toward slowing the progression of disease rather than obtaining^{ }a cure. This is because these organs can experience significant^{ }physiologic motion, thwarting the benefits of current approaches to conformal^{ }therapy. The primary source of this motion is respiration. In^{ }the treatment of lung and liver tumors, the traditional therapeutic^{ }approach is to measure the range over which the tumor^{ }moves during the respiratory cycle and to then irradiate a^{ }volume that encloses the entire tumor over its entire motion^{ }range. The oncologist's dilemma is that in prescribing a lethal^{ }radiation dose to the tumor, a sufficiently large volume of^{ }healthy tissue would be damaged to cause significant clinical repercussions,^{ }including organ failure. In our radiation treatment center we are^{ }investigating the use of patient breath holding to reduce respiratoryderived^{ }motion during fractionated radiotherapy. The primary targeting problem then becomes^{ }the small variation in tumor location from one breathhold to^{ }the next. Previous research had focused on the dose effects^{ }from relatively large target position uncertainties resulting from respiration and^{ }bladder/bowel motions. These studies involved comparatively large lesions (typically ~10^{ }cm diameter) such as primary cancer of the prostate,^{1}^{,}^{2}^{,}^{3}^{,}^{4}^{,}^{5}^{,}^{6} liver,^{7}^{,}^{8}^{ }lung,^{5} nasopharynx,^{9} and esophagus.^{2} The sizes of the lesions involved^{ }precluded the use of lethal doses of radiation, thereby the^{ }aims in these earlier studies were to achieve the optimum^{ }tradeoff between therapeutic response and complication risk. In contrast, our^{ }investigations involve smaller, 5–20 mm diameter lesions wherein the intent^{ }of treatment is the ablation of the target, with minimization^{ }of radiation damage to the surrounding tissue as an important,^{ }but secondary concern. In the present study, our aim is^{ }to model the effects of target repositioning variability due to^{ }breathhold reproducibility error on the dose field observed by small^{ }metastatic lung lesions and surrounding tissue in hopes that this^{ }will ultimately lead to an improved understanding of this phenomenon^{ }and improved approaches to clinical radiotherapy planning of similarly sized^{ }lesions. ^{ }
A. Cancer statistics
According to American Cancer Society statistics,^{10} lung^{ }cancer will account for the second greatest number of new^{ }cancer cases for both men and women this year (followed^{ }only by prostate cancer in men and breast cancer in^{ }women). Lung cancer has surpassed breast cancer as the leading^{ }cause of cancer death in women and is expected to^{ }account for 25% of all female cancer deaths in 2002.^{ }It is estimated that 85% of all new lung cancer^{ }patients will die from their cancer.^{11} The lungs are also^{ }the second most frequent site of metastatic disease and, in^{ }20% of these cases, the lungs are the only site^{ }of metastases.^{12} The liver is the most prevalent site of^{ }metastasis, with autopsy series reporting a range of 30% to^{ }70% for all patients who die of cancer.^{13} For example,^{ }colorectal cancer is among the top four cancers in both^{ }incidence and death rates. However, death is usually the result^{ }of metastases, and in 80% of these patients (19 200 people^{ }per year) the liver is the only site of metastases.^{14}^{ }Similar data is available for breast cancer wherein 40% of^{ }patients with metastases eventually develop liver disease and 80% eventually^{ }develop lung disease.^{15} ^{ }
B. Impact of aggressive therapy
Aggressive management of^{ }lung and liver metastases is likely to significantly improve the^{ }survival and quality of life for these patient groups.^{16} It^{ }has been shown that in colorectal cancer patients with isolated^{ }metastases to the liver, curative resection of the liver lesions^{ }leads to 30–40% 5year survival^{17} and a complete freedom from^{ }disease in 30% of these patients.^{14} Unfortunately, 75–80% of all^{ }liver lesions are deemed unresectable due to their anatomic location^{ }and size and/or because of diseaseassociated hepatic cirrhosis, hyperbilirubinemia, and^{ }physical weakness that prevents surgical intervention. Faced with a significant^{ }risk of morbidity and mortality, patients often choose to forego^{ }surgery. Since there is currently no longterm effective chemotherapy for^{ }primary or metastatic liver cancer, there is very little that^{ }can be done for patients with unresectable liver tumors. If^{ }one takes into account the successes and failures of treatment^{ }for metastatic disease over the past 20 years, the technically^{ }sophisticated but intellectually simple concept of locally sterilizing metastatic disease^{ }using externalbeam radiotherapy has the potential of outperforming many, if^{ }not all, of the advances in the field of the^{ }past two decades. ^{ }
II.^{ }METHODS
The target position probability density was modeled as a threedimensional^{ }(3D) ellipsoidal Gaussian distribution. The effect of randomized target repositioning^{ }was assessed through numerical simulation using Monte Carlo analysis and^{ }through analytical computation using 3D convolution. These methods were demonstrated^{ }on a representative 2arc, 10fraction treatment plan that was used^{ }to treat individual tumors in a human subject presenting with^{ }multiple metastatic lung lesions. The effect of the magnitude of^{ }the position variability on the changes in the observed dose^{ }was studied using standard deviations in tumor position that ranged^{ }from 1 to 4 mm. For the same human subject,^{ }tumor position variability data was gathered from pretreatment magnetic resonance^{ }image (MRI) datasets. The measured variability values were also applied^{ }in the analysis. Using representative tumor position variability values and^{ }corresponding margin definitions, a comparison was made between the volumes^{ }of lung tissue that would be expected to receive harmful^{ }doses of radiation using endexpiration breath holding versus endinspiration breathholding^{ }during treatment planning and radiation delivery. Dose volume histograms (DVHs)^{ }were employed to assess exposure to both the target and^{ }the surrounding healthy tissue, as well as to compare the^{ }results across the various methods. ^{ }
A. Target position variability model
For^{ }fractionated radiotherapy with breathholding, the variability in position of the^{ }target over all the repeated breathholds was modeled as a^{ }Gaussian distribution. The standard deviation in position about the mean^{ }position was allowed to vary independently with coordinate direction, where^{ }the coordinates were defined with respect to the patient: Superior–inferior^{ }(SI); anterior–posterior (AP); and right–left (RL). The resulting 3D Gaussian^{ }ellipsoid was sampled at 1 mm intervals in each direction^{ }to create a digitized position probability matrix. It is important^{ }to sample the Gaussian probability matrix out a sufficient distance^{ }to ensure that the target position probability at the edge^{ }voxels is very small. This was achieved by sampling out^{ }to a distance equal to 3 times the Gaussian standard^{ }deviation. For the 4 mm position variability model, the Gaussian^{ }probability matrix was generated over 25×25×25 grid where each voxel^{ }corresponds to 1 cubic millimeter. ^{ }
B. Dose perturbation via convolution
As^{ }the number of treatment fractions approaches infinity, the cumulate dose^{ }seen by the target can be modeled as the convolution^{ }of the 3D dose distribution with the 3D Gaussian probability^{ }distribution for target position, as described previously by several authors.^{1}^{,}^{2}^{,}^{5}^{,}^{8}^{ }The convolution operator is described by the equation^{18}
where g^{ }is the original (planned) dose field represented as a 3D^{ }matrix (of size L×M×N) of dose values, h is the^{ }3D Gaussian distribution model represented by a 3D matrix of^{ }size I×J×K, and f is the resulting, altered dose distribution.^{ }The values of I, J, and K increase (decrease) with^{ }increasing (decreasing) position variability in the SI, AP, and RL^{ }directions, respectively. The analyses using convolution and the generation of^{ }dose field plots and their derivatives were performed using dedicated^{ }Java code written by the authors and based on the^{ }NIH ImageJ software package (developed at the U.S. National Institutes^{ }of Health and available on the Internet at http://rsb.info.nih.gov/ij/). ^{ }
C.^{ }Target position variability via Monte Carlo simulation
The dose field perturbation^{ }for a finite number of treatment fractions can be assessed^{ }using Monte Carlo simulation, as demonstrated by Leong,^{19} and others^{4}^{,}^{8}^{,}^{9}^{ }and validated against the convolution method by Bel,^{3} Lujan,^{7} and^{ }McCarter et al.^{6} A randomnumber generator was modified to produce both^{ }negative and positive output displacements that fall within a prescribed^{ }Gaussian distribution.^{20} The generator's output was used to shift the^{ }prescribed dose field in each of the SI, AP, and^{ }RL directions randomly for 10, 20, 100, or 1000 treatment^{ }fractions. The method of Monte Carlo simulation applied to a^{ }digitized dose field requires displacements of the target to be^{ }integer valued. The numbers returned from the random number generator^{ }were first scaled to fit the desired Gaussian distribution and^{ }then rounded to the nearest whole number. This analysis was^{ }performed using Microsoft Visual Basic running within Excel. ^{ }
D. Lung^{ }lesion treatment plan
A realistic treatment 3D dose field was obtained^{ }from a conventional conformal beam treatment plan for a representative^{ }lung lesion in a human subject. The selected lesion was^{ }approximately 12 mm in diameter and located posteriorly inferiorly in^{ }the patient's left lung. The treatment plan for this lesion^{ }consisted of 6MV X rays applied in two, 110degree arc^{ }pathways separated by 20 degrees. The clinical target volume (CTV)^{ }was defined by the observable tumor as manually segmented using^{ }the commercial planning system software. The planning target volume was^{ }defined as the CTV with a margin specification of 7×7×10^{ }mm in the AP, RL, and SI directions, respectively. The^{ }plan was created using the BrainLAB Novalis system and BrainScan^{ }5.0 software and implemented at the University of Rochester's R.^{ }J. Flavin Novalis Shaped Beam Surgery Center. Each arc was^{ }administered daily, during independent 15 second breathholds. The external beam^{ }radiation was administered daily over 10 days of treatment to^{ }give a total dose to the lesion of 50 Gy.^{ }A diagram of the treatment plan dose distribution is shown^{ }in Fig. 1. Patient repositioning between treatment days was performed^{ }using BrainLAB's ExacTrac Patient Positioning System (EPPS). The EPPS tracks^{ }skinaffixed retroreflective markers with a pair of infrared cameras. The^{ }Novalis unit was designed for stereotactic radiosurgery with an alignment^{ }tolerance of 0.75 mm. The EPPS positioning uncertainty is typically^{ }0.5 to 1.5 mm. ^{ }
Figure 1. E. Lung lesion position variability measurements
Prior^{ }to radiation therapy, repeated volumetric MRI datasets of the lungs^{ }were acquired in the patient volunteer. All procedures were performed^{ }in accordance with federal and university guidelines and the patient^{ }had given informed consent. The three sets of chest MRI^{ }volume data were acquired during ~30 second periods of patient^{ }breathhold at relaxed endexpiration. The patient volunteer was instructed to^{ }perform two deep breaths followed by a relaxed expiration and^{ }breathhold. Each MRI 3D dataset consisted of 168 overlapping sagittal^{ }slices with slice thickness 4 mm and slice centertocenter separation^{ }of 1 mm. For each of the five lesions, the^{ }centroid was manually demarked and the mean position and standard^{ }deviations about the mean position were then computed. ^{ }
F. Endexpiration^{ }breathholding versus deep endinspiration breathholding
A secondary hypothesis is that the^{ }improved target localization with endexpiration breathholding (EEBH) and accompanying reduction^{ }in treatment margin will more than compensate for the decreased^{ }lung density but larger margins associated with deep endinspiration breathholding^{ }(DIBH). The current literature provides no quantification of the motion^{ }of isolated tumors in the lung and/or liver during respiration,^{ }nor of tumor position reproducibility over multiple breathholds. However, studies^{ }have been performed looking at diaphragm position during free breathing^{ }and over repeated breathholds, suggesting that target position variability is^{ }improved with EEBH compared to DIBH. Using these values, treatment^{ }plans were constructed using conventional margin specifications to ablate the^{ }representative lung lesion. Lung density changes from endexpiration to deep^{ }inspiration were included in the estimate of the volume of^{ }surrounding lung tissue exposed to high dose in each treatment^{ }approach. ^{ }
III. RESULTS
A. Target^{ }position variability and dose broadening
The result of the convolution of^{ }the dose matrix by the position variability matrix is an^{ }eroded version of the original dose distribution, as depicted in^{ }Fig. 2(A) and as described by previous authors.^{1}^{,}^{19} The target^{ }position variability alters the original dose distribution by increasing the^{ }dose field width at the lower doses, reducing the width^{ }at the higher doses, and decreasing the slope of the^{ }dose profile edges. Figure 2(A) shows a comparison of the^{ }original and eroded profiles for standard deviation in position (ranging^{ }from 0–4 mm) computed using the convolution equation. The effect^{ }of target position variability on the cumulative dose seen by^{ }the target is depicted by the corresponding DVHs for the^{ }target. The relationship between the leftward shift of the tumor^{ }DVH curve and the magnitude of the position variability is^{ }monotonic but nonlinear, as seen quantitatively in Fig. 2(B). The^{ }decrease in the dose at the 50% tumor volume at^{ }1 mm target position standard deviation is less than 0.2%,^{ }but the decrease in dose becomes 1.7% for a standard^{ }deviation of 4 mm. The volume of surrounding tissue receiving^{ }50% dose and that receiving 80% dose dropped as the^{ }position standard deviation increased, as plotted in Fig. 2(C). ^{ }
Figure 2. B.^{ }Finite versus infinite number of treatment fractions
Figure 3(A) shows a^{ }comparison of the original and shifted tumor DVHs for a^{ }4 mm standard deviation in position computed using both the^{ }convolution equation and Monte Carlo method using single trials at^{ }10, 20, 100, and 1000 fractions. The results for the^{ }100fraction and the 1000fraction Monte Carlo runs were nearly identical,^{ }suggesting that 100 fractions are sufficient to achieve convergence for^{ }this approach. The DVH values and dose profiles for the^{ }convolution method were indistinguishable from those of the 1000fraction Monte^{ }Carlo method, determining the equivalence of the approaches. There is^{ }a statistical relationship between the expected results from any given^{ }10fraction simulation and the finitefraction results (the convolution method), as^{ }described by sampling theory. Namely, the expected standard deviation of^{ }the mean, _{M}, for N number of fractions is given^{ }by = /N, where _{P} is variance of the total population.^{ }To better illustrate this phenomenon, 50 trials using 10 fractions^{ }were conducted using the Monte Carlo approach. From the 50^{ }trials, the mean, 25th quartile, and 75th quartile DVH curves,^{ }computed as percent tumor volume varying as a function of^{ }percent dose, were compiled and plotted in Fig. 3(B) along^{ }side the DVH curve computed using the convolution method. This^{ }analysis was repeated for 50 runs of 20 fractions and^{ }the results for these are plotted in Fig. 3(C). These^{ }graphs give the expected spread in the DVH outcomes associated^{ }with using a finite number (10 or 20) of treatment^{ }fractions. The randomly chosen 20fraction trial shown in Fig. 3(A)^{ }happens to lie outside the 20fraction quartile range shown in^{ }Fig. 3(C), but this is not unexpected in light of^{ }the sampling theory. ^{ }
Figure 3. C. Lung lesion position variability measurement and^{ }dose broadening
Breathholding for the duration of the MRI acquisition (~30^{ }seconds) was well tolerated by the patient volunteer. As shown^{ }in Table I, the average variability in position for all^{ }five lesions and over three repeated breathholds was found to^{ }be less than 3 mm in any direction, with the^{ }greatest variability in the superior–inferior direction compared to the anterior–posterior^{ }and lateral directions. Our findings are comparable to those found^{ }by Holland et al.^{21} and Balter et al.^{22} for position reproducibility of^{ }the diaphragm. Lesion 1, shown in Fig. 1, was a^{ }12 mm diameter tumor with position standard deviations of 2.5,^{ }1.3, and 0.8 mm in the SI, AP, and RL^{ }directions, respectively. At physiologic variability values, the percent of tumor^{ }volume seeing 100% of the dose (50 Gy) was 44%,^{ }compared to 56% for a fixed target. However, in both^{ }cases all of the tumor volume observed 96% dose (or^{ }48 Gy)—above the tumoricidal threshold. ^{ }
D. Endexpiration breathholding versus endinspiration^{ }breathholding
With breathholding protocols, the reproducibility of the endexpiration location of^{ }the diaphragm from breathhold to breathhold is less than 0.4^{ }mm, while that for endinspiration is approximately 1.3 mm.^{22} The^{ }diaphragm also moves during a breathhold. During a relaxed breathhold^{ }at endexpiration (EEBH) the diaphragm displaces superiorly at a rate^{ }of 0.15 mm/s ±0.7 mm/s.^{21} This leads to an overall^{ }shift in the superior–inferior direction of 1.9 mm ±1.4 mm^{ }for a 20second breathhold. For breathholds at relaxed endinspiration, the^{ }total displacement is 2.3 mm ±1.2 mm with a very^{ }nonlinear velocity profile. Korin et al. also performed a preliminary study^{ }looking at the global motion of the liver. They found^{ }that the motion of the liver follows closely that of^{ }the diaphragm during relaxed breathing, with SI motion dominant, and^{ }AP and RL motions <2 mm.^{23} In comparison, Hanley et al.^{24}^{ }reported that diaphragm repositioning error for repeated deep inspiration breathholding^{ }(DIBH) was 2.5 mm and that motion during each breathhold^{ }was 1.0 mm (standard deviation about the mean position). These^{ }DIBH studies were performed using a spirometer to improve the^{ }reproduction of inspiration levels. A conservative treatment plan would entail^{ }specifying a planning target volume (PTV) with treatment margins around^{ }the tumor equal to two times the expected standard deviation^{ }in position plus two times the expected motion range. First,^{ }using a backoftheenvelope comparison of planning target volumes, we consider^{ }a 12 mm diameter clinical target volume. Using the inspiration^{ }data from Balter's and Holland's papers (1.3 mm and 2.3^{ }mm, respectively), 7.2 mm of margin would be needed. This^{ }leads to a planning target volume of 9.6 cm^{3}. The^{ }corresponding margin for an endexpiration breathhold, based on Balter's and^{ }Holland's results (0.4 mm and 1.9 mm, respectively), would be^{ }4.6 mm, giving a planning target volume of 5.0 cm^{3}.^{ }This represents a reduction in healthy tissue volume within the^{ }PTV of 4.6 cm^{3}, or 53%, using the EEBH plan^{ }compared to the DIBH plan. For an expected decrease in^{ }DIBH lung density of 26% (Ref. 24) compared with the^{ }EEBH technique, the DIBH technique would result in a less^{ }favorable lung mass exposure compared with the endexpiration breathholding approach.^{ }For a 20 mm diameter CTV (perhaps more reasonable for^{ }this 12 mm lesion considering the inherent inaccuracies in the^{ }diagnostic imaging system and the potential for microscopic extent of^{ }the disease) the same analysis gives a reduction in healthy^{ }tissue volume being irradiated of 8.3 cm^{3}, or 48%, when^{ }using EEBH compared to DIBH. With the inclusion of dose^{ }spread effects, the results were similar. Two treatment plans were^{ }created for the representative lung lesion in the manner described^{ }earlier but with axisymmetric treatment margins of 4.6 and 7.2^{ }mm, to represent the EEBH and DIBH plans, respectively. The^{ }treatment plan with the 4.6 mm margin was then convolved^{ }with a Gaussian target position variability model with an axisymmetric^{ }target position standard deviation of 2.3 mm. This was repeated^{ }for the 7.2 mm margins plan and a 3.6 mm^{ }standard deviation of target position. For the EEBH case the^{ }absolute volume of surrounding lung tissue receiving 50% dose was^{ }9.4 cm^{3}. That for the DIBH values, after adjustment for^{ }the 26% decrease in lung tissue density due to increase^{ }air volume, was 12.4 cm^{3} (a difference of 24%). For^{ }the volume of lung tissue receiving 80% dose, the EEBH^{ }and DIBH methods gave 2.39 and 3.15 cm^{3}, respectively: a^{ }difference again of 24% and very similar to the backoftheenvelope^{ }calculation result above. ^{ }
IV.^{ }DISCUSSION
A. Preliminary clinical results
The clinical radiotherapy plan and shortterm outcome^{ }for the initial patient subject have been presented in detail^{ }previously.^{25} In regards to the measurement, modeling, and verification of^{ }the dose broadening effect, the results were as follows. A^{ }treatment margin specification of 7×7×10 mm, in the AP, RI,^{ }and SI directions, respectively, was chosen by the attending physicians.^{ }The target repositioning variability results from the repeat endexpiration MRI^{ }datasets indicate that these margins represent a size equal to^{ }or greater than three times the expected standard deviation in^{ }position. For a typical 12 mm diameter tumor, this size^{ }margin would ensure that the entire tumor remains within the^{ }highdose region for each fraction with 99.87% certainty, assuming that^{ }sources of target position variability other than that due to^{ }breathholding error are negligible. The results presented in this paper^{ }demonstrated that the entire tumor volume was irradiated to a^{ }minimum of 48 Gy—well above the tumoricidal threshold. This finding^{ }was substantiated by the clinical results: there was evidence of^{ }tumor shrinkage during treatment and all but one of the^{ }lesions had disappeared completely by the end of the 10day^{ }therapy. At the 6month and 12month followups, all five lesions^{ }had been eradicated with no indication of disease recurrence at^{ }the treatment sites. ^{ }
B. Edge effects
As described in detail by^{ }Lujan et al.,^{7} artifacts will occur at the boundaries of the^{ }dose field when the dose does not fall to zero^{ }smoothly, such as occurs at the surface–air interface and at^{ }the edges of the sampled dose field. The size of^{ }the boundary zone where artifacts may appear is determined by^{ }the standard deviation () of the target position probability distribution^{ }and for most practical purposes is limited to 3. In^{ }the current study, the dose field was sampled over a^{ }10×10×10 cm region centered about the lung lesion. For simplicity^{ }of the calculation using the convolution and Monte Carlo methods,^{ }the dose values for locations outside the sampled dose field^{ }were assumed to be zero. However, the measured dose on^{ }the perimeter of the sampled dose field was found to^{ }be significant at some locations, with a maximum dose at^{ }the border of the sampled region of 41%. The error^{ }is reflected in Fig. 2(A) where there is an abrupt^{ }dose profile dropoff at the outermost 2–7 mm of the^{ }measured dose profiles. This solution to the edge artifact is^{ }to sample the dose field out into the zerovalued regions,^{ }or at least sufficiently far from the target and the^{ }lung volumes so that the edge effects do not corrupt^{ }the DVH results. The limited spatial extent of the dose^{ }field sampling also prevents an accurate determination of the lung^{ }tissue DVH values for doses less than ~41%, although the^{ }spatial extent of the sampling was sufficient for an accurate^{ }determination of all tumor DVH values and lung tissue DVH^{ }values 50%. In addition, because of the relatively small size^{ }of the planning target volume compared with the entire left^{ }lung volume, 12 cm^{3} versus 1700 cm^{3}, less than 2%^{ }of the left lung volume sees 50% dose. ^{ }
C. Patient^{ }surface to radiation source distance changes and effects
Neither the Monte^{ }Carlo nor the convolution methods as used herein take into^{ }account the changes in dose as the target moves randomly^{ }toward or away from the radiation source during each fraction.^{ }However, the effects of changes in both the distance from^{ }the patient surface to the radiation source (SSD), and the^{ }changes in the depth of the target relative to the^{ }surface were studied by McCarter and Beckham,^{6} wherein they concluded^{ }that the variations in position both above and below the^{ }mean depth added to give an insignificant net effect, even^{ }for very large standard deviations (up to 100 mm). In^{ }addition, Bel et al.^{3} quantified the SSD effect to be less^{ }than 1% for a relatively large, onetime 7.5 mm shift^{ }along the beam trajectory of one beam in a 3beam^{ }plan. ^{ }
D. EEBH versus DIBH
Using endinspiration breathholds to compensate for^{ }respiratoryderived lung tumor motion results in a less favorable lung^{ }mass exposure in the high dose region compared to using^{ }an endexpiration breathholding approach, even after considering the decrease in^{ }lung tissue density due to the increased volume of air^{ }in the lungs for DIBHs. This is primarily a result^{ }of the larger variability in diaphragm position over repeated breath^{ }holds at endinspiration compared to endexpiration, even when lung volume^{ }feedback via a spirometer is used in the endinspiration method^{ }and not in the EEBH method. Endexpiration breathholding is therefore^{ }recommended over DIBH for fractional radiation therapy of small lung^{ }and liver lesions because of improved target position reproducibility, decreased^{ }radiation exposure to the surrounding tissue, and because it can^{ }be used successfully without the aid of a spirometer or^{ }similar device that may diminish patient comfort and compliance. ^{ }
E.^{ }Mathematical description of target position probability
A goal of subsequent research^{ }in this field is to establish the efficacy of using^{ }common statistical models, such as a Gaussian distribution, to represent^{ }tumor position variability for these lesions. A much larger pool^{ }of organ and target repositioning data must be first acquired^{ }before any statistical representation can be accepted with confidence. However,^{ }the adherence of tumor repositioning to a common statistical model^{ }is not strictly required for the application of either the^{ }convolution or the Monte Carlo approaches. These methods required only^{ }the determination of the 3D target location probability distribution. ^{ }
F.^{ }Margin size versus target position variability
The current study used the^{ }dose field sampled from a treatment plane using clinical margins^{ }of 7×7×10 mm (AP×R×SI). These margins are large in comparison^{ }to the expected and tested target position variability values, thus^{ }the effect of target position variability on the tumor DVH^{ }response was correspondingly small. Dose broadening studies on dose fields^{ }created using smaller treatment margins produce larger changes in the^{ }tumor DVH response (data not presented), but the nature of^{ }the response remains the same. ^{ }
G. Future work
Breathholding enables us^{ }to reduce margin size such that a lethal dose can^{ }be administered to the tumor while the volume of healthy^{ }tissue receiving toxic dose is kept within clinically acceptable limits.^{ }However, radiation toxicity to the surrounding tissue remains a major^{ }concern. In our initial patient treatment protocol, a margin size^{ }of 7×7×10 mm was used for each of five lesions.^{ }For a representative 12 mm diameter lesion, 11.3cc of total^{ }tissue volume is thereby irradiated with lethal dose, of which^{ }only 8% is the tumor. For five such lesions in^{ }a patient, a total of 52cc of healthy tissue is^{ }destroyed, along with an equally large volume of lung tissue^{ }exposed to harmful but nonlethal levels of radiation. In otherwise^{ }healthy patients, this loss of lung tissue volume does not^{ }pose a serious health risk; however it is conceivable that^{ }additional lung lesions may present in these patients over their^{ }lifetimes. The cumulative loss of lung volume for a larger^{ }number of sites may prove clinically significant. An application of^{ }our ability to model the dose erosion effects due to^{ }target repositioning error is to improve the methods used for^{ }selecting treatment margins. We hope to determine, for each patient,^{ }optimal margins that will minimize the volume of surrounding healthy^{ }tissue that is irradiated with harmful dose while delivering a^{ }lethal dose to each tumor. ^{ }
V.^{ }CONCLUSION
During fractionated radiotherapy, target position variability over repeated breathholds will^{ }broaden and diminish the amplitude of the dose distribution seen^{ }by the target and surrounding tissue, compared with that seen^{ }by a fixed target. If the distribution of target positions^{ }can be described by a probabilistic model, then this doseerosion^{ }effect can be quantified using image convolution theory and Monte^{ }Carlo simulation. Using dose distributions acquired from radiotherapy treatment plans,^{ }we have shown that the changes in the dose distribution^{ }for target position variability of less than 1 mm are^{ }negligible. Using pretreatment MRI acquisitions over repeated breathholds, we were^{ }able to estimate the expected target repositioning error for an^{ }individual subject and use this to predict the changes in^{ }the dose field that occurred during the subsequent treatment. We^{ }were then able to show that the entire tumor was^{ }subjected to a cumulative dose in excess of 47 Gy—well^{ }above the tumoricidal threshold. This result was supported by the^{ }6 and 12month clinical followup findings wherein all five lesions^{ }treated in this patient were eradicated with no evidence of^{ }disease recurrence at the treatment sites. This information suggests that^{ }curative treatment of lung and liver lesions is possible when^{ }simple endexpiration breath holding is used to compensate for respiratoryderived^{ }motion. In the future, it is conceivable that all treatment^{ }planning of extracranial targets will take into consideration the effects^{ }of target repositioning error assessed prior to treatment, further improving^{ }the expected clinical outcome for these patients. ^{ }
ACKNOWLEDGMENTS
The authors wish to^{ }acknowledge the contributions from Emma Gerzhog and Dr. Calvin Maurer,^{ }Jr. Financial support of this project was provided through a^{ }research agreement with BrainLAB AG (Ammerthalstrasse 8, 85551 Heimstette, Bundesrepublik^{ }Deutschland). ^{ }
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FIGURES
Full figure (49 kB)Fig. 1. Isodose contours overlaid onto^{ }a CT image of lung of cancer patient. 100% dose=5^{ }Gy. The yellow arrow and central pink contour were manually^{ }defined to mark the location of one ~1 cm diameter^{ }tumor. The central purple and orange contours mark the location^{ }of the tumor in subsequent CT image acquisitions. The surrounding^{ }contours (red, green, purple, yellow, and orange) are the isodose^{ }contours as described in the legend. First citation in article
Full figure (14 kB)Fig. 2. (A) Dose profiles across the^{ }central slice for the planned dose distribution of lung lesion^{ }1 and target position variability of 1–4 mm in each^{ }direction ("1, 2, 3, 4 mm") and for the measured^{ }position variability ("Physiologic"). (B) Dosevolume histogram of the tumor for^{ }the corresponding studies. (C) Plots of the absolute volume of^{ }surrounding lung tissue exposed to 50% and 80% doses, as^{ }a function of the amount of tumor position variability. First citation in article
Full figure (17 kB)Fig. 3. (A) DVH^{ }of the tumor for target position standard deviation of 0^{ }mm ("Original") and 4 mm as computed using the Monte^{ }Carlo method with randomly chosen trials of 10, 20, 100,^{ }and 1000 fractions, and using convolution. DVH plots including the^{ }mean and quartile curves for 50 repeated trials of (B)^{ }10fraction and (C) 20fraction Monte Carlo runs. Mean and quartiles^{ }were computed with respect to varying percent tumor volume for^{ }a fixed dose percentage. First citation in article
TABLES
Table I. MRIbased measurement of reproducibility of^{ }lesion position over multiple endexpiration breathholds. Values are given as^{ }standard deviation (in mm) of position about the average position,^{ }over 3 trials. 
 Lesion 1  Lesion 2  Lesion 3  Lesion 4  Lesion 5 
Superior–inferior  2.5  2.9  2.0  2.0  2.2^{ } 
Anterior–posterior  1.3  2.1  2.8  1.4  1.3 
Lateral  0.8  1.5  1.5  0.8  0.8 
First citation in articleFOOTNOTES
^{a}Author to whom correspondence should be addressed.^{ }Electronic mail: wodell@rochester.edu
^{b}Also at Department of Biomedical Engineering.
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