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Lawrence B Marks

Publications and source records attributed to Lawrence B Marks.

17 recordsLinked to original sources

Risk of long-term complications after TFG-beta1-guided very-high-dose thoracic radiotherapy.

PURPOSE: To report the incidence of late complications in long-term survivors of very-high-dose thoracic radiotherapy (RT) treated on a prospective clinical trial. METHODS AND MATERIALS: Patients with locally advanced or medically inoperable non-small-cell lung cancer received three-dimensional conformal RT to the primary tumor and radiographically involved lymph nodes to a dose of 73.6 Gy at 1.6 Gy twice daily. If the plasma transforming growth factor-beta1 (TGF-beta1) level was normal after 73.6 Gy, additional twice-daily RT was delivered to successively higher total doses until the maximal tolerated dose was reached. Patients within a given dose level were followed for 6 months before escalation to the next dose level was permitted. Late complications were defined according to Radiation Therapy Oncology Group/European Organization for Research and Treatment of Cancer criteria. RESULTS: Thirty-eight patients were enrolled between 1996 and 1999. Twenty-four patients were not eligible for radiation dose escalation beyond 73.6 Gy because of persistently abnormal TGF-beta1 levels. Fourteen patients received dose escalation (80 Gy in 8; 86.4 Gy in 6). Grade 3 or greater late complications occurred in 4 of 24, 1 of 8, and 2 of 6 patients treated to 73.6, 80, and 86.4 Gy, respectively. The corresponding patient numbers with late Grade 4-5 toxicity were 3 of 24, 0 of 6, and 0 of 8. Overall, 7 (18%) of the 38 patients developed Grade 3-5 late toxicity. Nonpulmonary complications predominated (4 of 7). Five (71%) of seven serious complications developed within 11 months after RT; however, the remaining two complications (29%) occurred very late (at 43 and 62 months). The 5-year actuarial risk of late Grade 3-5 complications was 33%. CONCLUSION: Long-term survivors of very-high-dose RT for non-small-cell lung cancer have a significant risk of severe treatment-related complications. At these high dose levels, the predominant toxicity may no longer be pulmonary. All Grade 4-5 complications occurred in patients whose dose was limited to 73.6 Gy because of a persistently elevated TGF-beta1. Thus, persistently elevated plasma TGF-beta1 levels toward the end of RT may identify patients at greatest risk of severe complications.

Adult↗

Long-term changes in pulmonary function tests after definitive radiotherapy for lung cancer.

PURPOSE: To evaluate the long-term changes in pulmonary function tests (PFTs) in patients surviving at least 2 years after definitive radiotherapy (RT) for unresectable lung cancer. METHODS AND MATERIALS: Between 1992 and 2000, 277 patients were enrolled in a prospective clinical study to relate RT-induced changes in lung function with dosimetric and functional metrics. Of these, 128 received definitive RT for lung cancer, and 13 of these had follow-up PFTs for approximately >/=2 years without evidence of recurrent or progressive cancer. PFTs were obtained before RT and approximately every 6 months after RT. The results were evaluated on the basis of each study's "percentage of predicted" of normal values (i.e., adjusted for age, gender, height), and a patient's sequential examinations were compared with their initial study and a percentage of the baseline value was calculated. Follow-up PFTs were available for a median of 38 months (range 23-95). The median patient age was 65 years (range 40-74), 6 patients were men, and 10 were white. Most had Stage T2-T4 and N2-N3. The median RT dose was 71.4 Gy (range 60-73), 6 had twice-daily RT. Four patients received chemotherapy, one concurrent and three neoadjuvant. None of the patients continued to smoke after their treatment. The median pre-RT PFT results were (percentage of predicted) forced expiratory volume in 1 s, 67% (range 24-121); forced vital capacity, 72% (range 45-116); and diffusing capacity of lung for carbon monoxide, 70% (range 41-129). RESULTS: At 6 months, all PFT values had declined, with some stabilization by 1 year. However, after 1 year, a gradual reduction occurred in all three parameters. Ten patients (77%) developed RT-induced respiratory symptoms (2 cough only, 8 dyspnea) at 2-21 months (median 5) after treatment. Two patients required inhalers, another required long-term steroids and oxygen. Of the 8 patients with dyspnea, 7 had an increase in symptoms beyond 2 years. No patient died of RT-induced pulmonary insufficiency. CONCLUSION: RT caused a decline in PFTs that was apparent at 6 months and continued well beyond 1 year. The continued decline in PFTs is suggestive of progressive/evolving RT-induced lung injury. "Late" pulmonary symptoms have also occurred in these patients. Because of the high mortality rate of unresectable lung cancer, few patients can be evaluated for long-term analysis. Additional studies and pooling of data from multiple institutions may help to clarify better the long-term impact of RT on pulmonary function in this subset of patients.

Adult↗

Routine use of approximately 60 Gy once-daily thoracic irradiation for patients with limited-stage small-cell lung cancer.

PURPOSE: To review the outcome of patients with limited-stage small-cell lung cancer receiving daily thoracic irradiation (RT) to approximately 60 Gy. METHODS AND MATERIALS: The records of patients treated with RT for limited-stage small-cell lung cancer between 1991 and 1999 at Duke University were retrospectively reviewed. Sixty-five patients were identified who had received continuous course once-daily 1.8-2 Gy fractions to approximately 60 Gy (range 58-66). All patients received chemotherapy (CHT); 32 received concurrent RT/CHT and 33 sequential CHT and then RT. Prophylactic cranial RT was administered to 17 patients. The time from diagnosis to local failure, tumor progression, and death was assessed using actuarial methods. The median follow-up for all patients was 16.7 months and for surviving patients was 29.6 months. The median age was 64 years (range 36-83), and the median Karnofsky performance status was 80 (range 50-100). RESULTS: The 3-year actuarial rate of local failure, progression-free survival, and overall survival was 40%, 25%, and 23%, respectively. One case of acute Grade 3 esophagitis developed. Ten late complications occurred: four pulmonary, two esophageal, two infectious, one leukemia, and one retinal toxicity with prophylactic cranial RT. Six were mild and resolved with treatment. CONCLUSION: CHT plus approximately 60 Gy of once-daily RT for limited-stage small-cell lung cancer was generally well tolerated. The survival rates were less than have been reported using 45 Gy in 1.5-Gy twice-daily fractions (2-year overall survival rate 47% compared with 30% in this study), but may be comparable because fewer than one-half our patients received concurrent CHT/RT and only 26% received prophylactic cranial RT. The relatively low rate of normal tissue morbidity in our patients supports the use of conventional once-daily fractionation to > or = 60 Gy. A randomized trial would be required to compare the outcomes after maximally tolerated dose twice-daily RT vs. maximally tolerated dose daily RT.

Adult↗

Breast conservation rates-barriers between tertiary care and community practice.

PURPOSE: Low rates of breast conservation therapy (BCT) are reported in the southern United States. We evaluated the influence on BCT rates of opening a radiotherapy (RT) clinic at a community hospital in North Carolina. Before opening, RT was available 5 miles away at a tertiary care center. METHODS AND MATERIALS: A review of the pathology database of the community hospital identified patients who underwent definitive surgery for invasive breast malignancy or ductal carcinoma in situ between 1994 and 1995, and 1997 and 1998, before and after the opening of the RT clinic in 1996. From these data, the mode of therapy, mastectomy or BCT, was determined. The results were compared using logistic regression analysis. Surgical and RT physician staffing were unchanged throughout the study period. RESULTS: A total of 586 patients was evaluated. The BCT rate at the community hospital for 1994-1995 and 1997-1998 was 29% and 44%, respectively. On both univariate and multivariate logistic regression analysis, the era of treatment was statistically significant in its impact on the procedure performed (p <0.001). CONCLUSION: The use of BCT increased at a community hospital after the opening of an on-site RT facility, even though RT was available 5 miles away previously.

Breast Neoplasms↗

Myocardial perfusion changes in patients irradiated for left-sided breast cancer and correlation with coronary artery distribution.

PURPOSE: To evaluate postradiation regional heart perfusion changes with single photon emission tomography (SPECT) myocardial perfusion imaging in 69 patients treated with tangential photon beams radiation therapy (RT) for left-sided breast cancer. To correlate SPECT changes with percent irradiated left ventricle (LV) volume and risk factors for coronary artery disease (CAD). METHODS AND MATERIALS: Rest SPECT of the LV was acquired pre-RT and at 6-month intervals post-RT. The extent of defects (%) with a severity > 1.5 standard deviations below the mean was quantitatively analyzed for the distributions of the left anterior descending (LAD) artery, left circumflex (LCX) artery, and right coronary artery (RCA) based on computer assisted polar map reconstruction (i.e., bull's-eye-view). Changes in perfusion were correlated with percent irradiated LV receiving > 25 Gy (range 0-32%). Data on patient- and treatment-related factors were collected prospectively (e.g., cardiac premorbidity, risk factors for CAD, chemotherapy, and hormonal treatment). RESULTS: In the LAD distribution, there were increased perfusion defects at 6 months (median 11%; interquartile range 2-23) compared with baseline (median 5%; interquartile range 1-14) (p < 0.001). There were no increases in perfusion defects in the LCX or RCA distributions. In multivariate analysis, the SPECT perfusion changes in the LAD distribution at 6 months were independently associated with percent irradiated LV (p < 0.001), hormonal therapy (p = 0.005), and pre-RT hypercholesterolemia (p = 0.006). The SPECT defects in the LAD distribution at 12 and 18 months were not statistically different from those at 6 months. The perfusion defects in the LAD distribution were limited essentially to the regions of irradiated myocardium. CONCLUSION: Tangential photon beam RT in patients with left-sided breast cancer was associated with short-term SPECT defects in the vascular distribution corresponding to the radiation portals. Factors related to the extent of perfusion defects included the percent irradiated LV, hormonal treatment, and pre-RT hypercholesterolemia.

Adult↗

Radiation-induced lung injury.

Radiation therapy (RT) for thoracic-region tumors often causes lung injury. The incidence of lung toxicity depends on the method of assessment (eg, radiographs, patient's symptoms, or functional endpoints such as pulmonary function tests). Three-dimensional (3D) treatment planning tools provide dosimetric predictors for the risk of symptomatic RT-induced lung injury and allow for beams to be selected to minimize these risks. A variety of cytokines have been implicated as indicators/mediators of lung injury. Recent work suggests that injury-associated tissue hypoxia perpetuates further injury. Sophisticated planning/delivery methods, such as intensity modulation, plus radioprotectors such as amifostine, hold promise to reduce the incidence of RT-induced lung injury.

Animals↗

Normal tissue effects: reporting and analysis.

Any effective cancer therapy developed to date is associated with a spectrum of normal tissue effects of varying incidence and severity. With an increasing number of novel therapeutic approaches undergoing clinical testing and an increased effort to optimize the established treatment modalities, methods for reliable quantification of normal tissue effects have become a key element in advancing cancer care. Here, we present a review of many of the issues involved in reporting and analyzing clinical normal tissue effect data. A distinction is introduced between explorative (science-driven) and pragmatic (patient-centered) studies. The desirable properties of criteria for reporting and grading toxicity are discussed from a biological and clinical perspective. Validation of toxicity criteria and the statistical issues involved in analyzing this type of data are presented with special emphasis on descriptors of the time evolution of toxicity. Finally, we discuss surrogate markers for late effects, mechanistic studies, and the design of clinical studies with normal tissue endpoints as a primary outcome. It is concluded that a consensus is required on guidelines for the reporting of normal tissue effects to improve the comparability of published reports on treatment outcome.

Antineoplastic Agents↗

Receiver operating characteristic curves to assess predictors of radiation-induced symptomatic lung injury.

PURPOSE: To assess the utility of dosimetric/functional metrics as predictors of symptomatic radiation pneumonitis using receiver operating characteristic curves. METHODS: Between 1991 and 1999, 277 patients were enrolled on a prospective clinical study to relate radiation therapy (RT) induced changes in lung function with dosimetric and functional metrics. Pre-RT whole and regional functional assessments included pulmonary function tests and single photon emission computed tomography lung perfusion scans. Patients had three-dimensional planning scans and dose calculations (reflecting tissue density heterogeneity) to provide a dose-volume histogram of the lung and associated dosimetric parameters (MLD = mean lung dose, V30 = % of lung receiving >or=30 Gy). Fusion of single photon emission computed tomography and computed tomography scans provides perfusion-weighted dose-function histograms and associated dosimetric parameters (mean perfusion-weighted lung dose). The incidence of clinically relevant radiation pneumonitis requiring steroids was related to the dosimetric and functional metrics. The predictive abilities of models (sensitivity and specificity) were calculated and compared based on the area beneath receiver operating characteristic (ROC) curves (Wilcoxon rank-sum and chi-square). RESULTS: Twenty-seven of 162 evaluable patients with >or=6 months' follow-up developed pneumonitis requiring steroids. Single metrics were typically not good predictors for pneumonitis ( area under ROC curve = 0.5-0.68). The two-dimensional models (e.g., MLD and pre-RT diffusion capacity for carbon monoxide) generally provided greater ROC areas (0.61-0.72). Overall, the models that considered a measure of pre-RT lung function (i.e., pulmonary function tests), the MLD, and mean perfusion-weighted lung dose were best correlated with outcome (ROC area: 0.7) (p < 0.05 compared to unidimensional models). However, because the area under the ROC curve for these models was <<1, they too seemed not to be ideal. CONCLUSION: Predicting symptomatic radiation pneumonitis remains difficult. Multiparameter models that consider pre-RT pulmonary function and the three-dimensional dose distribution seem to be best able to predict outcome. Additional studies are needed to better understand the dosimetric/functional determinants of radiation pneumonitis.

Adolescent↗

Influence of tumor volume on survival in patients irradiated for non-small-cell lung cancer.

PURPOSE: To investigate the importance of CT-defined total tumor volume (TTV) on overall survival (OS) in patients with unresectable or medically inoperable non-small-cell lung carcinoma (NSCLC). METHODS AND MATERIALS: Between 1991 and 1998, 150 evaluable patients with Stage I-IIIB NSCLC were treated with three-dimensionally planned conformal radiotherapy and curative intent at Duke University Medical Center. On the treatment-planning CT, the primary tumor and nodal volumes were identified and subsequently combined to form the TTV. The TTV was compared with the stage and outcome with respect to OS, local progression-free survival, and distant failure-free survival using the Kruskall-Wallis analysis of variance and Kaplan-Meier actuarial method. To account for the potentially confounding effects of therapeutic and patient-specific covariates on survival, the Cox proportional hazard regression model was used. RESULTS: The TTVs in patients with Stage I disease (median 19 cm3) were smaller than in patients with Stage II (median 80 cm3) or Stage III (median 97 cm3; p <0.001) disease. The Stage II TTVs were not significantly different from those of Stage III (post-hoc test according to Bonferroni). Prolonged OS was independently associated with a small TTV (<80 vs. >80 cm3 [median]; p = 0.01), young age (<60 vs. > or =60 years; p = 0.03), high Karnofsky performance status (< o r =70 vs. >70; p = 0.04), and female gender (p = 0.04). Both stage (p = 0.7) and T stage (p = 0.06) were of less importance for OS than was the TTV, according to multivariate modeling. Increased local progression-free survival (p = 0.001) and distant failure-free survival (p = 0.03) were independently associated with a small TTV (i.e., <80 cm3). The results were unchanged if the TTV was analyzed as a continuous variable. CONCLUSION: A strong independent association between a small CT-defined TTV and prolonged survival in patients with NSCLC selected for curative/definitive RT was found. Future therapeutic studies in NSCLC should consider stratifying/adjusting for differences in TTV to avoid confounding effects on survival from variations in the TTV at baseline.

Adult↗

Predictors for pneumonitis during locoregional radiotherapy in high-risk patients with breast carcinoma treated with high-dose chemotherapy and stem-cell rescue.

BACKGROUND: To study the predictive value of serial pulmonary function testing (PFT) for toxicity in patients who have received high-dose chemotherapy (HDCT) and stem-cell rescue for breast carcinoma. These patients are at risk of developing therapy-related pneumonitis (TRP) during or after radiotherapy (RT). METHODS: Sixty-eight patients who received induction chemotherapy (CT) and consolidation HDCT (cyclophosphamide, cisplatin, carmustine) underwent serial PFTs before induction CT, after HDCT, and before locoregional RT. The rate of TRP, i.e., pulmonary complications of Grade 2 or higher (World Health Organization classification), was studied during and 2 months after RT. We analyzed the time-course of changes in the diffusing capacity of carbon monoxide (DLCO) and forced expiratory volume at one second (FEV(1)) and studied the differences between patients who developed TRP and those who did not. RESULTS: The incidence of TRP was 46%. There were marked reductions in DLCO and FEV(1) at the time of RT compared with baseline (Wilcoxon signed rank test: P < 0.001). However, pre-RT PFT values did not predict subsequent development of TRP. Instead, the ratio of pre-RT DLCO to the minimum post- HDCT DLCO, i.e., trend of improvement, predicted the development of TRP in patients (logistic regression analysis: P = 0.048). At a cutoff level of 1, the positive and negative predictive values for this ratio were 61% and 87%, respectively. There was an association between this ratio and a longer interval between HDCT and RT (Spearman rank correlation: P = 0.002). CONCLUSIONS: The results suggest that the directional trend of DLCO after HDCT, i.e., no recovery from nadir values, is a predictor for TRP. TRP patients have a shorter median interval between HDCT and RT than asymptomatic patients. To minimize the occurrence of TRP, one should consider either delaying RT beyond 2 months following carmustine-based HDCT to allow the PFTs to partly recover, or confirm apositive directional trend for improvement of DLCO at the start of RT compared to the post-HDCT nadir value.

Adult↗

Technical factors associated with radiation pneumonitis after local +/- regional radiation therapy for breast cancer.

PURPOSE: To assess the incidence of, and clinical factors associated with, symptomatic radiation pneumonitis (RP) after tangential breast/chest wall irradiation with or without regional lymph node treatment. METHODS AND MATERIALS: The records of 613 patients irradiated with tangential photon fields for breast cancer with >6 months follow-up were reviewed. Clinically significant RP was defined as the presence of new pulmonary symptoms requiring steroids. Data on clinical factors previously reported to be associated with RP were collected, e.g., tamoxifen or chemotherapy exposure and age. The central lung distance (CLD) and the average of the superior and inferior mid lung distance (ALD) in the lateral tangential field were measured on simulator films as a surrogate for irradiated lung volume. Many patients were treated with partly wide tangential fields that included a heart block shielding a part of the lower lung. RESULTS: RP developed in 15/613 (2.4%) patients. In the univariate analysis, there was an increased incidence of RP among patients treated with local-regional radiotherapy (RT) (4.1%) vs. those receiving local RT only (0.9%) (p = 0.02), and among patients receiving chemotherapy (3.9%) vs. those not treated with chemotherapy (1.4%) (p = 0.06). According to multivariate analysis, only the use of nodal RT remained independently associated with RP (p = 0.03). There was no statistically significant association between ranked CLD or ALD measurements and RP among patients treated with nodal irradiation with tangential beams. However, there was a statistically nonsignificant trend for increasing rates of RP with grouped ALD values: below 2 cm (4% RP rate), between 2 and 3 cm (6%), and above 3 cm (14%). CONCLUSIONS: RP was an uncommon complication, both with local and local-regional RT. The addition of regional lymph node irradiation slightly increased the incidence of RP among patients treated with the partly wide tangential field technique. Concern for RP should, however, not deter patients with node-positive breast cancer from receiving local-regional RT.

Analysis of Variance↗

The time course of radiation therapy-induced reductions in regional perfusion: a prospective study with >5 years of follow-up.

PURPOSE: To assess the time-dependence of radiation therapy (RT)-induced reductions in regional lung perfusion, as measured by single photon emission computed tomography (SPECT) lung perfusion scans. METHODS AND MATERIALS: Between 1991 and 1999, 79 patients had SPECT lung perfusion scans before and serially after RT. Changes in regional perfusion were correlated with regional dose using 3D planning tools and image fusion (PLUNC-Plan UNC). Multiple post-RT follow-up scans were evaluated to determine the temporal nature of RT-induced regional perfusion changes. To facilitate the comparison of dose-response curves (DRCs) at different post-RT intervals, each DRC was fit to a linear model and thus described by its slope. RESULTS: There was a dose-dependent reduction in regional perfusion at nearly all time points post-RT (p = 0.0001). The slope of the DRCs for RT-induced reductions in regional perfusion became steeper at essentially each successive follow-up interval (p = 0.0001). However, the increases in slope became progressively smaller at later follow-up intervals. Overall, about 80% of the long-term RT-induced regional perfusion injury was manifest within 12 months post-RT. CONCLUSION: There is a progression of RT-induced reductions in regional perfusion, with most of this injury manifest within 12 months post-RT. Additional regional injury appears to evolve for years.

Adult↗

Influence of dose calculation model on treatment plan evaluation in conformal radiotherapy: a three-case study.

In modern conformal radiotherapy (CRT), we attempt to increase its therapeutic ratio, thus improving the survival chances and/or quality of life for patients. It is common to acknowledge that poor local tumor control or increased normal tissue complications may arise from inaccurate targeting of the tumor, failure to conform the high-dose distribution to the target volume, and inaccurately delivered radiation doses. A further cause for concern is the influence that errors or inaccuracies in the dose calculation may have on the management of radiation therapy. Such errors arise from inherent limitations in the calculation algorithm used, which are more significant in some anatomical sites than others. Furthermore, an estimate of the therapeutic ratio is given by the ratio of tumor control probability (TCP) and normal tissue complication probability (NTCP). The effectiveness of these predictive indicators also depends on the accuracy of the calculated dose distributions in the target and surrounding normal structures. In this work, we compared CRT dose distributions of plans for the treatment of prostate, head-and-neck, and lung tumors using the measurement-based Clarkson and model-based Superposition dose calculation algorithms. Dose-volume histograms (DVHs) for the planning target volume (PTV) and sensitive structures, as well as NTCP and TCP, were compared. Dose distributions, observed in the lung and head-and-neck plans, vary significantly with respect to dose conformity as a function of algorithm used. Differences in the calculated maximum dose of up to 14% were observed in the PTV and sensitive structures for the lung and head-and-neck Clarkson-based plans, respectively, compared to the Superposition-based plans. Furthermore, a difference in the biological outcomes of up to 14% in the NTCP and 4% in the TCP was noticed. The CRT plans show the importance of accurate modeling of the effect of tissue inhomogeneities on dose distributions in the target and critical structures for lung and head-and-neck treatments.

Algorithms↗

High-dose chemotherapy and hematopoietic support for patients with high-risk primary breast cancer and involvement of 4 to 9 lymph nodes.

Despite modern chemotherapy, advanced breast cancer remains a significant cause of cancer morbidity and mortality in women. Patients with disease involvement of multiple lymph nodes represent a subgroup with a high risk of relapse. In particular, 50% of patients with 4 to 9 axillary lymph nodes involved will relapse after standard chemotherapy. In an effort to improve the survival of patients with 4 to 9 involved nodes, we performed a phase II study in which 61 patients with surgically diagnosed stage II or III breast cancer and 4 to 9 positive lymph nodes received 3 cycles of doxorubicin and 5-fluorouracil followed by high-dose chemotherapy consisting of cisplatin, cyclophosphamide, and carmustine and infusion of autologous hematopoietic progenitor cells. All patients received posttransplantation localized radiotherapy unless contraindicated, and all patients with hormone receptor-positive disease received tamoxifen. After a median patient follow-up of 6.7 years (range, 4.6-8.6 years), the 5-year overall survival rate was 79% (95% CI, 69%-90%), with relapse-free survival of 73% (95% CI, 62%-85%). Treatment-related mortality was 3%. Interstitial pneumonitis occurred in 69% of patients but did not contribute to mortality. Our study presents long-term favorable results regarding the use of consolidative HDC with autologous hematopoietic support in previously untreated patients with high-risk primary breast cancer.

Adult↗

Optimization of a 90Sr/90Y radiation source train stepping for intravascular brachytherapy.

A steepest-descent gradient algorithm is developed to optimize the stepping of a 90Sr/90Y radiation source train (RST) for intravascular brachytherapy (IVB). The objective function is to deliver a uniform dose in a coronary target vessel and minimize the dose in adjacent normal vessel tissue at the proximal and distal edges of the coronary target vessel. Based on the target length and number of dwell points (number of steps), the algorithm modulates the dwell times and corresponding dwell positions that optimize the weighted addition of staggered EGS4 Monte Carlo (MC) calculated dose distribution from a single RST. Stepping treatment plans are generated for target vessel lengths of 3.0, 3.3, and 3.8 cm. For both the unoptimized and optimized plans, the dose heterogeneity in the target vessel wall, and length of nontarget vessel receiving 3 Gy, is assessed to compare plans. Optimization results show a 14% dose uniformity within the target is achievable for all vessel lengths. Further, the dose in the adjacent normal tissue is lower in the optimized plans than the unoptimized plans. The work presented in this paper provides a model to address the finite length of RST in IVB treatments. While the results presented are specific to the 90Sr/90Y RST, the methods should apply to other finite length RSTs.

Algorithms↗