Shorter Delivery Time Research Articles

Stereotactic radiotherapy for peripheral lung tumors: A comparison of volumetric modulated arc therapy with 3 other delivery techniques

Purpose Volumetric modulated arc therapy (RapidArc) allows for fast delivery of stereotactic body radiotherapy (SBRT) delivery in stage I lung tumors. We compared dose distributions and delivery times between RapidArc and common delivery techniques in small tumors. Methods In 18 patients who completed RapidArc SBRT for tumors measuring <70 cm 3, new treatment plans were generated using non-coplanar 3D conformal fields (conf-SBRT) and dynamic conformal arc radiotherapy (DCA). For 9 patients with tumors adjacent to the chest wall, co-planar intensity-modulated radiotherapy (IMRT) plans were also generated. PTV dose coverage, organs at risk (OAR) doses and treatment delivery times were assessed. Results RapidArc plans achieved a superior conformity index (CI) and lower V 45Gy to chest wall ( p < 0.05) compared to all other techniques. RapidArc led to a small increase in V 5Gy to contralateral lung compared to conf-SBRT (4.4 ± 4% versus 1.2 ± 1.8%, p = 0.011). For other OAR, RapidArc and conf-SBRT plans were comparable, and both were superior to DCA plans. Delivery of a 7.5 Gy-fraction required 3.9 min (RapidArc), 11.6 min (conf-SBRT), and 12 min (IMRT). Conclusions In stage I lung tumors measuring <70 cm 3, RapidArc plans achieved both the highest dose conformity and shortest delivery times.

Target tracking using DMLC for volumetric modulated arc therapy: A simulation study

Target tracking using dynamic multileaf collimator (DMLC) is a promising approach for intrafraction motion management in radiation therapy. The purpose of this work is to develop a DMLC tracking algorithm capable of delivering volumetric-modulated arc therapy (VMAT) to the targets that experience two-dimensional (2D) rigid motion in the beam's eye view. The problem of VMAT delivery to moving targets is formulated as a control problem with constraints. The relationships between gantry speed, gantry acceleration, MLC leaf-velocity, dose rate, and target motion are derived. An iterative search algorithm is developed to find numerical solutions for efficient delivery of a specific VMAT plan to the moving target using 2D DMLC tracking. The delivery of five VMAT lung plans is simulated. The planned and delivered fluence maps in the target-reference frame are calculated and compared. The simulation demonstrates that the 2D tracking algorithm is capable of delivering the VMAT plan to a moving target fast and accurately without violating the machine constraints and the integrity of the treatment plan. The average delivery time is only 29 s longer than that of no-tracking delivery, 101 versus 72 s, respectively. The fluence maps are normalized to 200 MU and the average root-mean-square error between the desired and the delivered fluence is 2.1 MU, compared to 14.8 MU for no-tracking and 3.6 MU for one-dimensional tracking. A locally optimal MLC tracking algorithm for VMAT delivery is proposed, aiming at shortest delivery time while maintaining treatment plan invariant. The inconsequential increase of treatment time due to DMLC tracking is clinically desirable, which makes VMAT with DMLC tracking attractive in treating moving tumors.

SmartArc-Based Volumetric Modulated Arc Therapy for Oropharyngeal Cancer: A Dosimetric Comparison With Both Intensity-Modulated Radiation Therapy and Helical Tomotherapy

To investigate the roles of volumetric modulated arc therapy with SmartArc (VMAT-S), intensity-modulated radiation therapy (IMRT), and helical tomotherapy (HT) for oropharyngeal cancer using a simultaneous integrated boost (SIB) approach. Eight patients treated with IMRT were selected at random. Plans were computed for both IMRT and VMAT-S (using Pinnacle TPS for an Elekta Infinity linac) along with HT. A three-dose level prescription was used to deliver 70 Gy, 63 Gy, and 58.1 Gy to regions of macroscopic, microscopic high-risk, and microscopic low-risk disease, respectively. All doses were given in 35 fractions. Comparisons were performed on dose-volume histogram data, monitor units per fraction (MU/fx), and delivery time. VMAT-S target coverage was close to that achieved by IMRT, but inferior to HT. The conformity and homogeneity within the PTV were improved for HT over all strategies. Sparing of the organs at risk (OAR) was achieved with all modalities. VMAT-S (along with HT) shortened delivery time (mean, -38%) and reduced MU/fx (mean, -28%) compared with IMRT. VMAT-S represents an attractive solution because of the shorter delivery time and the lower number of MU/fx compared with IMRT. However, in this complex clinical setting, current VMAT-S does not appear to provide any distinct advantage compared with helical tomotherapy.

A Study on Design Methodology and Concurrent Engineering on Scroll Vacuum Pump

The concept of concurrent engineering is that designers, manufacturing engineers and all other members of the new product development team can work simultaneously or co-operate closely to avoid redesign and other problems at a later stage. The finite element method/FEM is the kernel of the approach. It enables the designed outputs to be optimal, robust and efficient so that high quality products could be achieved at a low cost in the shortest delivery time. The scroll components work in a high pressure and high temperature environment, which results in the deformation of the scroll wall. If the deformation was too great the vacuum pump would fail and would have to be redesigned and remanufactured. The designer can seek optimization under the limitations imposed by the displacement or stress of the scroll wall. The FEM and optimization can evaluate the deformation due to the cutting force and compensate accordingly.

Volumetric Modulated Arc Therapy for Prostate Radiotherapy

Intensity modulated radiotherapy (IMRT) is an effective treatment modality for prostate carcinoma. A new technology, Volumetric Modulated Arc Therapy (VMAT), allows the radiation dose to be delivered continuously in a single gantry rotation. This technology promises to shorten delivery time as well as reduce the total MUs. This retrospective treatment planning study compares dosimetric quality and delivery efficiency of VMAT plans to clinically delivered IMRT plans.

Poster — Thur Eve — 08: Dosimetric Comparison Study of Rotational and Static IMRT Treatment Plans for the Prostate

It has been reported that for certain clinical applications, Rotational Intensity Modulated Radiation Therapy (R‐IMRT) techniques such as Volumetric Modulated Arc Therapy are capable of improved target dose coverage and shorter delivery time when compared to static, step‐and‐shoot IMRT. Five similar early stage prostate cases were used to generate R‐IMRT and static IMRT plans. The R‐IMRT plans consisted of 72 single‐segmented 6MV beams, equally spaced with beam angle separations of 5 degrees. The static IMRT plans employed 7 multi‐segmented 6 MV beams. Both types of plans were optimized with the direct machine parameter optimization algorithm using the same set of optimization objectives. Dose volume histograms were obtained for both types of plans and were comparatively evaluated based on target coverage and dose to organs at risk. For 3 out of 5 cases, target coverage was found to be better with R‐IMRT: standard deviations were consistently lower, and V95 values were equal or better. Critical structure sparing was better for static IMRT with mean dose, V50 and V75 values for the rectum and bladder consistently lower for the majority of the 5 cases. In cases where target coverage was better for static IMRT, the critical structure sparing was better for R‐IMRT. Treatment time was approximately 3 times as long for R‐IMRT due to the lack of dynamic MLC's on the Primus linac. It was found that R‐IMRT can provide improved target coverage in certain applications when compared to static IMRT, however critical structures may receive a slightly higher dose with this technique.

SU‐GG‐I‐177: The Dosimetric Comparision of RapidArc with Fixed Gantry Static IMRT for Liver Metastatic Carcinoma

Objective To compare the dosimetric difference of RapidArc and fixed gantry static IMRT for liver carcinoma.Methods Ten CT datas of liver cancer patients were studied retrospectively. The IMRT and RapidArc plans were generated using either one or two arcs.The PTV Dosimetric distrubition, the OAR dose, the normal tissue dose, mornitor units and treatment time were compared. Results The maximum dose of PTV of RapidArc was lower than IMRT and there was statistically significant. RapidArc had an improved 90% prescription dose conformity index than IMRT(CI90=1.35±0.20 for RA1, 1.33±0.18 for RA2 and 1.62±0.41for IMRT) and there was statistically significant. For organs at risk all techniques respected planning objectives. RapidArc plan had a lower dose in V40 of stomach and Small bowel than IMRT plan, but higher in mean dose of left kidney. Concerning the V5 V10 and V15 of healthy tissue RapidArc plan was lower than IMRT plan. The V20 V25 and V30 of healthy tissue of RapidArc plan was lower than IMRT plan. The number of computed MU/fraction of Rapid Arc plan was 40% or 46%of IMRT Plan and the treatment time reduced at least60%. Conclusion All techniques respected planning objectives. RapidArc showed improvements in conformity index and healthy tissue sparing with uncompromised target coverage. This, In combination with the less MU and short delivery time, can lead to clinically significant advances in the liver cancer. Key words: RapidArc IMRT Liver metastatic carcinoma Dosimetric

SU-GG-T-121: An Initial Study of Dose Distribution in the Junction of SmartArc and 3D Superclavical Fields for Head and Neck Tumors

Purpose: It has been common practice in head and neck radiotherapy to combine IMRT and 3d fields for larynx protection. Half beam block technique ensures a smooth dose distribution in the junction volume. The newly emerged VMAT technique, such as SmartArc, has proved in a variety of cases to achieve similar, or even better, dosimetrictumor coverage and critical organ protection compared with IMRT with the advantage of less needed MU and shorter delivery time. However, dose distribution of junction of VMAT fields with other fields is still an underexplored area. This abstract will present the result of our study on this topic and discuss issues exiting if VAMT is to replace IMRT for head and neck cases in combination with 3D fields. Method and Materials:Treatment planning was performed using Pinnacle version 9.0 planning system on Varian's 21EX Linac treatment machine with constant jaw. Coplanar double arc of 360° was selected in combination with 2 superclavical 3D fields. Control point spacing of the arc beams was set at the default 4°. Results: Dose distribution in the conjunction volume is very sensitive to the collimator angle. With the commonly preferred collimator angle of 45°, dose in the junction volume can be as high as double the prescription dose. Decreasing the collimator angle improved dose uniformity in the junction, but the tumor coverage in proximity to the junction could be compromised. 0° degree angle proved to produce the best tumor coverage and junction dose uniformity. Best jaw match requires a collimator angle of 90°, but it proved to product the coldest tumor coverage from the VMAT fields. Conclusion: More study and efforts are needed to resolve the issue of dose uniformity in the junction volume if VMAT fields are to be combined with 3D fields for head and neck tumors.

SU‐GG‐T‐551: Spinal Radiosugery: Comparison between Volumetric Modulated Arc Therapy and Static Gantry IMRT

Purpose: Image Guided Radiosurgery (IGRS) has been used successfully to treat lesions involving the spine. Treatment plans usually involve multiple static Intensity Modulated Radiotherapy (IMRT) fields. Conformality is paramount in spinal RS treatments to maximize the dose to the target while sparing the intimately associated spinal cord. To improve conformality, it is necessary to increase the number of fields, increasing the complexity of the treatment as well as time of delivery. Delivery time is crucial with this group of patients as it is difficult for them to remain on the couch without moving for long periods of time. Volumetric Modulated Arc Therapy (VMAT) can deliver treatment in a shorter time. In this study, we compared the conformality of plans created with VMAT and IMRT. Materials and Methods: Four patients were planned using both RapidArc VMAT and IMRT. The same structure sets were used for both planning methods. Plans were normalized such that prescription dose covered 95% of the planning target volume. Optimization was accomplished with comparable constraints and maximum cord dose was desired. Once acceptable plans had been achieved, the conformality index was calculated. Results: In comparing the plans for the two methods, the Paddick Conformality Index for VMAT ranged from 0.7553 to 0.8938 while for IMRT it went from 0.7315 to 0.8186. Conformality was consistently better for VMAT than for IMRT. Maximum cord dose differed by no more than 5%. Conclusion: Although planning time for VMAT was longer than for IMRT, conformality was consistently better. This study has shown that faster delivery time does not compromise quality of the dose distribution. Shorter delivery time also increases accuracy due to less patient movement during treatment. VMAT is a viable and effective tool for treating patients where spine SRS is indicated. Research supported by Varian Medical Systems

SU-GG-T-143: MLC-Based CyberKnife Radiotherapy for Prostate Cancer

Purpose: The Cyberknife system allows for real‐time organ motion correction and it enables delivery of a large number of non‐isocentric, non‐coplanar beams. A CyberKnife using multi‐leaf collimators(MLC) may achieve an improved dose advantage while maintaining a short delivery time. The purpose of this study is to evaluate the plan quality of MLC‐based prostate roboticradiotherapy.Method and Materials:Treatment plans were compared between regular IMRT, CyberKnife using the IRIS collimator (CK IRIS) and CyberKnife using a MLC (CK MLC). The IMRT plan and the CK MLC plan were generated using the Eclipse inverse planning system. Various numbers of non‐coplanar fields have been tried for CK MLC plans. With the CK IRIS plan, all 12 possible collimator sizes were included in the optimization process to achieve the best performance. Results: Isodoses for the IMRT plan, the CK MLC plan and the CK IRIS plan are compared in the same mid‐axial plane. All plans provide very conformai and complete converge of the target. However, the 50% isodose clearly demonstrates that the CK MLC plan provides much sharper dose fall off than the IMRT and the CK IRIS plans. The CK IRIS plan shows the worst rectal sparing with the 50% isodose line covering more than half of the rectum. A further comparison of DVHs shows significantly improved sparing of rectum and bladder with the CK MLC plan, when compared to the IMRT plan and the CK IRIS plan. Conclusions: The CyberKnife with MLC can produce superior dose distributions for sparing rectum and bladder and excellent DVHs for the target compared with IMRT and CyberKnife IRIS plans, and produces similar dose heterogeneities as IMRT plans. With significantly less beams, it can deliver a 2Gy/fx treatment in 10 minutes.

Development and Application of the Optimization Design of Progressive Die Based on Transfer Unit

The objective of this study was to research a newly progressive die , which unifies the merit of high efficiency of the progressive dies and the high material-using ratio of the project dies. This paper analyzes the forming process methods of IHS(Intel Heat Spreader), and develop a set of progressive die with transfer unit , which turns project die to progressive die. The cooperation between the transfer unit and the die was studied, and the key technology of the newly progressive dies were investigated. Compared with the traditional die, the mechanization and electrization are realized to increase the production efficiency and get highly precise IHS. The newly designed transfer unit is expected to be a helpful reference for designers facing demands for higher quality, lower cost and shorter delivery time for some special products.

Does Low Molecular Weight Heparin Shorten Term Labor?

Clinical experience has fostered the belief among some clinicians that women who receive low molecular weight heparins (LMWHs) are less likely to have protracted labor and therefore, less likely to require operative delivery. Previous studies have identified changes in the uterine and cervical extracellular matrix of heparan sulfate proteoglycans in normal and protracted labor. These changes and clinical observations suggest that LMWHs may influence the parturition process and shorten delivery time. This retrospective study investigated the effects of LMWHs on parturition time in pregnant women with a history of thrombotic disorders. The study subjects were 99 nulliparous pregnant women who had been treated with an LMWH (dalteparin) because of a history of previous venous thromboembolism, thrombophilia, or an acute venous thromboembolism during the current pregnancy. The women had been treated for 1 to 6 months before delivery. The control group was comprised of 198 untreated healthy nulliparous women with spontaneous onset of labor matched according to age and parity. The study and control groups were compared with respect to labor time, proportion of operative deliveries, and neonatal outcomes. Among women who had a spontaneous vaginal delivery, labor time was significantly shorter in those treated with dalteparin than in the untreated controls (6 vs. 9 hours, P < 0.0001). The number of operative deliveries was the same in the dalteparin and control groups, but the dalteparin-treated women required fewer operative interventions due to protracted labor (P = 0.0014). There was no difference in neonatal outcome between the groups. These findings suggest that LMWH therapy is associated with shorter labor time and a decreased number of operative interventions for protracted labor.

The Concept of Time-Based Competition in the Context of Management Theory

Speed as a competitive factor is gaining more and more importance for companies involved in global market competition. The company tends to compete for rapid response to consumer demand and new products and technologies introduced to the market. This type of competition in terms of reaction time is described as timebased competition (TBC). Regardless of a number of practicians and scholars admitting in their works that time management will enable the company to achieve competitive advantage, there is still a lack of empirical research for proving this statement. In addition, today the concept of TBC requires a holistic attitude to time-based management that would integrate a great deal of different concepts, methods and tools of management theory, and would adjust production control systems, cost accounting systems and, at the same time, performance measurement systems with regard to time perspective. The problem is that there is no sufficient research on determining the importance of the time factor in the context of management theory or on systematizing various management concepts for establishing what influence they have on the contemporary perception of TBC. Hence, the main objective of this article is to systematize and analyze data provided by scientific literature sources in relation to the concept of TBC and its development in the context of management theory. In the present article the theoretical research involved the systematic and comparative analysis of scientific literature. The first segment of the article includes the definition of TBC, the analysis of advantages and implementation challenges provided by this concept. The second segment of the article involves the theoretical research on the significance of the time factor in the development of management theory and emphasizes the effect and/or contribution of the basic management concepts on/to the formation of the TBC concept and the emerging need for it in the immediate future. Companies engaged in TBC seek to reduce the amount of time devoted during each stage of the general cycle by eliminating non-value adding activities, shortening time and/or efficiently coordinating value adding activities. When response time to consumer needs is shorter than the one demonstrated by rivals, the company can achieve competitive supremacy that is greater and, on a frequent basis, tends to be dominant and is expressed in speed, which contributes to short delivery time, lower costs, higher quality, flexibility and credible delivery. The research demonstrated that although the term TBC is relatively new, the very concept of time-based management has been applied numerous times. The significance of time management dates back to the early 20th century, while dealing with works of classical management theory from a tactical perspective, and later on other concepts of management theory were applied to its development and expansion, for example, the contribution of the Management School to creating quantitative methods for time management; the systematic attitude that was used to prove the significance of time-based information in production and operations management and to stress the importance of process management within the organization both externally and internally, including quick response to changes, the elimination of “bottleneck”, resource use and management, and the synchronization of all existing links within the whole organization, and that served as foundation for the emergence of the TBC concept; and the dynamic attitude that expanded the concept of TBC by placing emphasis on the importance of time management as a constant process in the changing organization.

Local strategic networks in the software industry: an empirical analysis of the value continuum

This paper explores long-term partnership benefits of local strategic alliances in knowledge-intensive industries. A structural model of the value continuum is formulated and tested on small and mid-size enterprises in the software industry. Partial least squares path analysis is used to investigate the cause?effect relationships between the foundation values – efficiency and effectiveness – and the innovation value. The results show that the innovation value of localised inter-firm networks originates from costs savings and quality improvements. Conversely, alliance-induced 'speed' benefits (measured by the R&D process's acceleration), which improve flexibility and/or shorten delivery time, have no significant impact on market-based performance. An alliance's time-related benefits may be important to maintain competitive parity, but they do not significantly support competitive advantage, market development and market penetration. Instead, value is created via, for example, an exchange of tacit knowledge and a reduction in transaction costs, and particularly by a reduction in customer service costs.

Does low molecular weight heparin shorten term labor?

Dalteparin, a low molecular weight heparin (LMWH), is given to pregnant women with thrombotic disorders. Clinical observations together with the documented changes of heparan sulfate proteoglycans in normal and protracted labor fostered the idea that LMWH shortens delivery time. Labor time was retrospectively determined among nulliparous pregnant women treated with dalteparin because of previous venous thromboembolism (VTE), thrombophilia or acute VTE during current pregnancy. Their labor time was compared to matched untreated controls. The proportion of instrumental deliveries and neonatal outcome was also compared. The dalteparin-treated group showed a significantly (30%) shorter labor time compared to matched controls. Total instrumental deliveries were the same in the two groups but operative intervention due to protracted labor was significantly less common in dalteparin-treated women. There was no difference in neonatal outcome. Dalteparin most likely shortens parturition time and may decrease the number of operative interventions due to protracted labor.

China as Hegemon of the Global Electronics Industry: How It Got That Way and Why It Won't Change

By the end of 2008, companies based on the business model of offshore production were observed to be rethinking their business models, tending to consider the repatriation of production bases in order to lower costs and shorten delivery times. In this article, the authors of China's Electronics Industry (2009 Edition), M. Pecht and L. Zuga, (City University of Hong Kong Press, Hong Kong, China, 2009) argue that repatriation is not likely to occur in the electronics industry, where expensive and complex production facilities have been moved offshore over a period of several decades. In particular, China has taken advantage of the West's offshore production model and its associated technology transfer to develop a manufacturing capability that has resulted in the ldquoChina Pricerdquo in electronics. As a result, China now has the infrastructure and electronics supply chain necessary to produce a wide range of products, from simple components to embedded systems and systems integration. This gives China the capability to produce complex electronics applications domestically, including computers, automotive controls, medical instrumentation, avionics, and even sophisticated military command and control systems. The resultant gain in Chinese capabilities, commensurate with the loss in Western capabilities through use of the offshore production model, makes the repatriation of the electronics industry to its former bastions in the United States and Western Europe doubtful. This will have a strong impact on resource allocation, research planning, and innovation. The authors present their argument through a series of brief case studies.

Development of The New High Specific Speed Fixed Blade Turbine Runner

The paper concerns the description of the step by step development process of the new fixed blade runner called "Mixer" suitable for the uprating of the Francis turbines units installed at the older low head hydropower plants. In the paper the details of hydraulic and mechanical design are presented. Since the rotational speed of the new runner is significantly higher then the rotational speed of the original Francis one, the direct coupling of the turbine to the generator can be applied. The maximum efficiency at prescribed operational point was reached by the geometry optimization of two most important components. In the first step the optimization of the draft tube geometry was carried out. The condition for the draft tube geometry optimization was to design the new geometry of the draft tube within the original bad draft tube shape without any extensive civil works. The runner blade geometry optimization was carried out on the runner coupled with the draft tube domain. The blade geometry of the runner was optimized using automatic direct search optimization procedure. The method used for the objective function minimum search is a kind of the Nelder-Mead simplex method. The objective function concerns efficiency, required net head and cavitation features. After successful hydraulic design the modal and stress analysis was carried out on the prototype scale runner. The static pressure distribution from flow simulation was used as a load condition. The modal analysis in air and in water was carried out and the results were compared. The final runner was manufactured in model scale and it is going to be tested in hydraulic laboratory. Since the turbine with the fixed blade runner does not allow double regulation like in case of full Kaplan turbine, it can be profitably used mainly at power plants with smaller changes of operational conditions or in case with more units installed. The advantages are simple manufacturing, installation and therefore lower expenses and short delivery time for turbine uprating.

A fast radiotherapy paradigm for anal cancer with volumetric modulated arc therapy (VMAT).

Background/PurposeRadiotherapy (RT) volumes for anal cancer are large and of moderate complexity when organs at risk (OAR) such as testis, small bowel and bladder are at least partially to be shielded. Volumetric intensity modulated arc therapy (VMAT) might provide OAR-shielding comparable to step-and-shoot intensity modulated radiotherapy (IMRT) for this tumor entity with better treatment efficiency.Materials and methodsBased on treatment planning CTs of 8 patients, we compared dose distributions, comformality index (CI), homogeneity index (HI), number of monitor units (MU) and treatment time (TTT) for plans generated for VMAT, 3D-CRT and step-and-shoot-IMRT (optimized based on Pencil Beam (PB) or Monte Carlo (MC) dose calculation) for typical anal cancer planning target volumes (PTV) including inguinal lymph nodes as usually treated during the first phase (0-36 Gy) of a shrinking field regimen.ResultsWith values of 1.33 ± 0.21/1.26 ± 0.05/1.3 ± 0.02 and 1.39 ± 0.09, the CI's for IMRT (PB-Corvus/PB-Hyperion/MC-Hyperion) and VMAT are better than for 3D-CRT with 2.00 ± 0.16. The HI's for the prescribed dose (HI36) for 3D-CRT were 1.06 ± 0.01 and 1.11 ± 0.02 for VMAT, respectively and 1.15 ± 0.02/1.10 ± 0.02/1.11 ± 0.08 for IMRT (PB-Corvus/PB-Hyperion/MC-Hyperion). Mean TTT and MU's for 3D-CRT is 220s/225 ± 11MU and for IMRT (PB-Corvus/PB-Hyperion/MC-Hyperion) is 575s/1260 ± 172MU, 570s/477 ± 84MU and 610s748 ± 193MU while TTT and MU for two-arc-VMAT is 290s/268 ± 19MU.ConclusionVMAT provides treatment plans with high conformity and homogeneity equivalent to step-and-shoot-IMRT for this mono-concave treatment volume. Short treatment delivery time and low primary MU are the most important advantages.

Volumetric Modulated Arc Therapy Improves Dosimetry and Reduces Treatment Time Compared to Conventional Intensity-Modulated Radiotherapy for Locoregional Radiotherapy of Left-Sided Breast Cancer and Internal Mammary Nodes

Volumetric modulated arc therapy (VMAT) is a novel extension of conventional intensity-modulated radiotherapy (cIMRT), in which an optimized three-dimensional dose distribution may be delivered in a single gantry rotation. VMAT is the predecessor to RapidArc (Varian Medical System). This study compared VMAT with cIMRT and with conventional modified wide-tangent (MWT) techniques for locoregional radiotherapy for left-sided breast cancer, including internal mammary nodes. Therapy for 5 patients previously treated with 50 Gy/25 fractions using nine-field cIMRT was replanned with VMAT and MWT. Comparative endpoints were planning target volume (PTV) dose homogeneity, doses to surrounding structures, number of monitor units, and treatment delivery time. For VMAT, two 190 degrees arcs with 2-cm overlapping jaws were required to optimize over the large treatment volumes. Treatment plans generated using VMAT optimization resulted in PTV homogeneity similar to that of cIMRT and MWT. The average heart volumes receiving >30 Gy for VMAT, cIMRT, and MWT were 2.6% +/- 0.7%, 3.5% +/- 0.8%, and 16.4% +/- 4.3%, respectively, and the average ipsilateral lung volumes receiving >20 Gy were 16.9% +/- 1.1%, 17.3% +/- 0.9%, and 37.3% +/- 7.2%, respectively. The average mean dose to the contralateral medial breast was 3.2 +/- 0.6 Gy for VMAT, 4.3 +/- 0.4 Gy for cIMRT, and 4.4 +/- 4.7 Gy for MWT. The healthy tissue volume percentages receiving 5 Gy were significantly larger with VMAT (33.1% +/- 2.1%) and IMRT (45.3% +/- 3.1%) than with MWT (19.4% +/- 3.7%). VMAT reduced the number of monitor units by 30% and the treatment time by 55% compared with cIMRT. VMAT achieved similar PTV coverage and sparing of organs at risk, with fewer monitor units and shorter delivery time than cIMRT.

Asymptotic Behavior of the Kleinberg Model

We study Kleinberg navigation (the search of a target in a d-dimensional lattice, where each site is connected to one other random site at distance r, with probability approximately r(-alpha) by means of an exact master equation for the process. We show that the asymptotic scaling behavior for the delivery time T to a target at distance L scales as T approximately ln(2)L when alpha=d, and otherwise as T approximately L(x), with x=(d-alpha)/(d+1-alpha) for alpha<d, x=alpha-d for d<alpha<d+1, and x=1 for alpha>d+1. These values of x exceed the rigorous lower bounds established by Kleinberg. We also address the situation where there is a finite probability for the message to get lost along its way and find short delivery times (conditioned upon arrival) for a wide range of alpha's.