Stomata coordinate with plant hydraulics to regulate transpiration response to vapour pressure deficit in wheat.

Genotypic variation in transpiration (Tr) response to vapour pressure deficit (VPD) has been studied in many crop species. There is debate over whether shoots or roots drive these responses. We investigated how stomata coordinate with plant hydraulics to mediate Tr response to VPD and influence leaf water status in wheat (Triticum aestivum L.). We measured Tr and stomatal conductance (gs) responses to VPD in well-watered, water-stressed and de-rooted shoots of eight wheat genotypes. Tr response to VPD was related to stomatal sensitivity to VPD and proportional to gs at low VPD, except in the water-stressed treatment, which induced strong stomatal closure at all VPD levels. Moreover, gs response to VPD was driven by adaxial stomata. A simple linear Tr response to VPD was associated with unresponsive gs to VPD. In contrast, segmented linear Tr to VPD response was mostly a function of gs with the breakpoint depending on the capacity to meet transpirational demand and set by the shoots. However, the magnitude of Tr response to VPD was influenced by roots, soil water content and stomatal sensitivity to VPD. These findings, along with a theoretical model suggest that stomata coordinate with plant hydraulics to regulate Tr response to VPD in wheat.

Difference in Freezing Tolerance Between Young Potato Plants Derived From Tissue Culture Plantlets and Seed Tubers.

BACKGROUND: Although potato as a crop is commercially grown from seed tubers, plants grown from tissue culture plantlets are often used in physiological studies including freezing tolerance determination. OBJECTIVE: This study aimed to examine the effects of the source of plants on freezing tolerance of potato plants at young developmental stages. MATERIALS AND METHODS: We compared freezing tolerance and contents of soluble proteins and sugars of Solanum tuberosum plants derived from tissue culture with those derived from tubers before and after cold acclimation. RESULTS: Tuber-derived plants showed significantly higher freezing tolerance than tissue-culture-derived plants after cold acclimation, although non-acclimated plants did not show any marked differences. Soluble protein contents were higher in tuber-derived plants regardless of cold acclimation. Sucrose content increased to a higher level in tuber-derived plants after cold acclimation. CONCLUSION: These results suggest that source of plant tissue can have a significant effect on the response of young potato plants to freezing stress and that the use of tissue culture plants in freezing tolerance studies may not accurately reflect the frost tolerance of commercially grown plants.

Treatment data and technical process challenges for practical big data efforts in radiation oncology.

The term Big Data has come to encompass a number of concepts and uses within medicine. This paper lays out the relevance and application of large collections of data in the radiation oncology community. We describe the potential importance and uses in clinical practice. The important concepts are then described and how they have been or could be implemented are discussed. Impediments to progress in the collection and use of sufficient quantities of data are also described. Finally, recommendations for how the community can move forward to achieve the potential of big data in radiation oncology are provided.

Innovations in Radiotherapy Technology.

Many low- and middle-income countries, together with remote and low socioeconomic populations within high-income countries, lack the resources and services to deal with cancer. The challenges in upgrading or introducing the necessary services are enormous, from screening and diagnosis to radiotherapy planning/treatment and quality assurance. There are severe shortages not only in equipment, but also in the capacity to train, recruit and retain staff as well as in their ongoing professional development via effective international peer-review and collaboration. Here we describe some examples of emerging technology innovations based on real-time software and cloud-based capabilities that have the potential to redress some of these areas. These include: (i) automatic treatment planning to reduce physics staffing shortages, (ii) real-time image-guided adaptive radiotherapy technologies, (iii) fixed-beam radiotherapy treatment units that use patient (rather than gantry) rotation to reduce infrastructure costs and staff-to-patient ratios, (iv) cloud-based infrastructure programmes to facilitate international collaboration and quality assurance and (v) high dose rate mobile cobalt brachytherapy techniques for intraoperative radiotherapy.

Development of a golden beam data set for the commissioning of a proton double-scattering system in a pencil-beam dose calculation algorithm.

PURPOSE: The purpose of this investigation is to determine if a single set of beam data, described by a minimal set of equations and fitting variables, can be used to commission different installations of a proton double-scattering system in a commercial pencil-beam dose calculation algorithm. METHODS: The beam model parameters required to commission the pencil-beam dose calculation algorithm (virtual and effective SAD, effective source size, and pristine-peak energy spread) are determined for a commercial double-scattering system. These parameters are measured in a first room and parameterized as function of proton energy and nozzle settings by fitting four analytical equations to the measured data. The combination of these equations and fitting values constitutes the golden beam data (GBD). To determine the variation in dose delivery between installations, the same dosimetric properties are measured in two additional rooms at the same facility, as well as in a single room at another facility. The difference between the room-specific measurements and the GBD is evaluated against tolerances that guarantee the 3D dose distribution in each of the rooms matches the GBD-based dose distribution within clinically reasonable limits. The pencil-beam treatment-planning algorithm is commissioned with the GBD. The three-dimensional dose distribution in water is evaluated in the four treatment rooms and compared to the treatment-planning calculated dose distribution. RESULTS: The virtual and effective SAD measurements fall between 226 and 257 cm. The effective source size varies between 2.4 and 6.2 cm for the large-field options, and 1.0 and 2.0 cm for the small-field options. The pristine-peak energy spread decreases from 1.05% at the lowest range to 0.6% at the highest. The virtual SAD as well as the effective source size can be accurately described by a linear relationship as function of the inverse of the residual energy. An additional linear correction term as function of RM-step thickness is required for accurate parameterization of the effective SAD. The GBD energy spread is given by a linear function of the exponential of the beam energy. Except for a few outliers, the measured parameters match the GBD within the specified tolerances in all of the four rooms investigated. For a SOBP field with a range of 15 g/cm2 and an air gap of 25 cm, the maximum difference in the 80%-20% lateral penumbra between the GBD-commissioned treatment-planning system and measurements in any of the four rooms is 0.5 mm. CONCLUSIONS: The beam model parameters of the double-scattering system can be parameterized with a limited set of equations and parameters. This GBD closely matches the measured dosimetric properties in four different rooms.

SU-E-T-211: Peer Review System for Ensuring Quality of Radiation Therapy Treatments.

PURPOSE: To demonstrate a Web-based electronic peer review system that has the potential to improve quality of care for radiation therapy patients. The system provides tools that allow radiation oncologists to seek peer review of target and critical structure delineation, treatment plans, and share clinical data with peers to optimize radiation therapy treatments. MATERIAL AND METHODS: Peer review of radiation therapy treatment planning data prior to its initiation improves the quality of radiation therapy and clinical outcomes. Web-based access to radiation therapy treatment planning data and medical records mitigate existing geographical and temporal constraints. With internet access, the healthcare provider can access the data from any location and review it in an interactive and collaborative manner. Interoperability standard like DICOM-RT and IHE-RO compliant RT Systems have facilitated the design and implementation of PRS with Silverlight Web technology, .net Framework and SQL Server. Local DICOM-RT archive and cloud based services are deployed to facilitate remote peer reviews. RESULTS: To validate the PRS system, we tested the system for 100 patients with Philips Pinnacle v 9.0 and Varian Eclipse v 8.9 treatment planning system (TPS). We transmitted the DICOM RT data from the TPS to the cloud based services via the PRS local DICOM RT Archive. Various CT simulation based parameters such as orientation of CT, properties of RT structures etc. were compared between the TPS and PRS system. Data integrity of other parameters such as patient demographics (patient name, ID, attending physician etc.) and dose volume related parameters were also evaluated. Such rigorous testing allowed us to optimize the functionalities and clinical implementation of the PRS. CONCLUSIONS: We believe that the PRS will improve the quality and safety of a broad spectrum of radiation therapy patients treated in underserved areas while discouraging the overutilization of expensive radiation treatment modalities. This research and development project is supported by the James and Ester King Biomedical Research Program grant # RC1-09KW-09-26829.

Dosimetric evaluation of a novel polymer gel dosimeter for proton therapy.

PURPOSE: The aim of this study is to evaluate the dosimetric performance of a newly developed proton-sensitive polymer gel formulation for proton therapy dosimetry. METHODS: Using passive scattered modulated and nonmodulated proton beams, the dose response of the gel was assessed. A next-generation optical CT scanner is used as the readout mechanism of the radiation-induced absorbance in the gel medium. Comparison of relative dose profiles in the gel to ion chamber profiles in water is performed. A simple and easily reproducible calibration protocol is established for routine gel batch calibrations. Relative stopping power ratio measurement of the gel medium was performed to ensure accurate water-equivalent depth dose scaling. Measured dose distributions in the gel were compared to treatment planning system for benchmark irradiations and quality of agreement is assessed using clinically relevant gamma index criteria. RESULTS: The dosimetric response of the gel was mapped up to 600 cGy using an electron-based calibration technique. Excellent dosimetric agreement is observed between ion chamber data and gel. The most notable result of this work is the fact that this gel has no observed dose quenching in the Bragg peak region. Quantitative dose distribution comparisons to treatment planning system calculations show that most (> 97%) of the gel dose maps pass the 3%/3 mm gamma criterion. CONCLUSIONS: This study shows that the new proton-sensitive gel dosimeter is capable of reproducing ion chamber dose data for modulated and nonmodulated Bragg peak beams with different clinical beam energies. The findings suggest that the gel dosimeter can be used as QA tool for millimeter range verification of proton beam deliveries in the dosimeter medium.

Independent dosimetric calculation with inclusion of head scatter and MLC transmission for IMRT.

Independent verification of the MU settings and dose calculation of IMRT treatment plans is an important step in the IMRT quality assurance (QA) procedure. At present, the verification is mainly based on experimental measurements, which are time consuming and labor intensive. Although a few simplified algorithms have recently been proposed for the independent dose (or MU) calculation, head scatter has not been precisely taken into account in all these investigations and the dose validation has mainly been limited to the central axis. In this work we developed an effective computer algorithm for IMRT MU and dose validation. The technique is superior to the currently available computer-based MU check systems in that (1) it takes full consideration of the head scatter and leaf transmission effects; and (2) it allows a precise dose calculation at an arbitrary spatial point instead of merely a point on the central axis. In the algorithm the dose at an arbitrary spatial point is expressed as a summation of the contributions of primary and scatter radiation from all beamlets. Each beamlet is modulated by a dynamic modulation factor (DMF), which is determined by the MLC leaf trajectories, the head scatter, the jaw positions, and the MLC leaf transmission. A three-source model was used to calculate the head scatter distribution for irregular segments shaped by MLC and the scatter dose contributions were computed using a modified Clarkson method. The system reads in MLC leaf sequence files (or RTP files) generated by the Corvus (NOMOS Corporation, Sewickley, PA) inverse planning system and then computes the doses at the desired points. The algorithm was applied to study the dose distributions of several testing intensity modulated fields and two multifield Corvus plans and the results were compared with Corvus plans and experimental measurements. The final dose calculations at most spatial points agreed with the experimental measurements to within 3% for both the specially designed testing fields and the clinical intensity modulated field. Furthermore, excellent agreement (mostly within +/- 3.0%) was also found between our independent calculation and the ion chamber measurements at both central axis and off-axis positions for the multifield Corvus IMRT plans. These results indicate that the approach is robust and valuable for routine clinical IMRT plan validation.

Dosimetric effect of source centering and residual plaque for beta-emitting catheter based intravascular brachytherapy sources.

Catheter-based radiation delivery systems employing both beta-particle and gamma-ray emitters are currently being investigated for their efficacy in addressing restenosis following percutaneous coronary intervention (PCI). The dosimetric consequences of source centering within the arterial lumen and presence of residual plaque are potentially important issues for the uniform delivery of dose to the arterial tissue. In this study, we have examined the effect of source centering on the resulting dose to the arterial wall from clinical intravascular brachytherapy sources containing 32P and 90Sr/Y90. Monte Carlo simulations using the MCNP code were performed for these catheter-based sources with offsets of 0.5 mm and 1 mm from the center of the arterial lumen in homogenous water medium as well as in the presence of residual plaque. Three different positions were modeled and the resulting dose values were analyzed to assess their impact on the resulting dose distribution. The results indicate a variation ranging from -40% to +70% for 32P source and -30% to +50% for 90Sr/90Y at a radial distance of 2 mm from the center of the coronary artery, relative to the dose from a centered source, for a 0.5 mm offset. The variation for a 1 mm offset ranges from -65% to +182% for 32P source and to -50% to +140% for 90Sr/90Y. A concentric residual plaque layer was also modeled so as to assess the combined influence of offset and residual plaque on the dosimetry. Finally the effect of cardiac motion and its potential impact on catheter position and hence the dose distribution is also examined by considering two separate cases of catheter displacement. The results indicate that dose variations range between -28% to +91% when it is assumed that cardiac motion causes catheter movement during coronary lesion irradiation.

An algorithm for automatic, computed-tomography-based source localization after prostate implant.

Permanent implant of the prostate using I-125 and Pd-103 seeds is a popular choice of treatment for early-stage prostate cancer in the United States. Evaluation of the quality of the implant is best based on the calculated dose distribution from postimplant computed tomography (CT) images. This task, however, has been time-consuming and inaccurate. We have developed an algorithm for automatic source localization from postimplant CT images. The only requirement of this algorithm is knowledge of the number of seeds present in the prostate, thus minimizing the need for human intervention. The algorithm processes volumetric CT data from the patient, and pixels of higher CT numbers are categorized into classes of definite and potential source pixels. A multithresholding technique is used to further determine the number of seeds and their precise locations in the CT volume data. A graphic user interface was developed to facilitate operator review of and intervention in the calculation and the results of the algorithm. This algorithm was tested on two phantoms containing nonradioactive seeds, one with 20 seeds in discrete locations and another with 100 seeds with small distances between seeds. The tests showed that the algorithm was able to identify the seed locations to within 1 mm of their physical locations for discrete seed locations. It was further able to separate seeds at close proximity to each other while maintaining an average seed localization error of less than 2 mm, with no operator intervention required.

External-beam radiation therapy for improved dialysis access patency: feasibility and early safety.

Rectenwald, J. E., Pretus, H. A., Seeger, J. M., Huber, T. S., Mendenhall, N. P., Zlotecki, R. A., Palta, J. R., Li, Z. F., Hook, S. Y., Sarac, T. P., Welborn, M. B., Klingman, N. V., Abouhamze, Z. S. and Ozaki, C. K. External-Beam Radiation Therapy for Improved Dialysis Access Patency: Feasibility and Early Safety. Radiat. Res. 156, 53-60 (2001).Prosthetic dialysis access grafts fail secondary to neointimal hyperplasia at the venous anastomosis. We hypothesized that postoperative single-fraction external-beam radiation therapy to the venous anastomosis of hemodialysis grafts can be used safely in an effort to improve access patency. Dogs (n = 8) underwent placement of expanded polytetrafluoroethylene grafts from the right carotid artery to the left jugular vein. Five dogs received single-fraction external-beam photon irradiation (8 Gy) to the venous anastomosis after surgery. Controls were not irradiated. Shunt angiograms were completed 3 and 6 months postoperatively. Anastomoses, mid-graft, and the surrounding tissues were analyzed. Immunohistochemistry for smooth muscle cell alpha-actin, proliferating cellular nuclear antigen (PCNA), and apoptosis was performed. Incisions healed well, though all animals developed wound seromas. One control suffered graft thrombosis 4 months postoperatively. Angiography/histology confirmed severe neointimal hyperplasia at the venous anastomosis. The remaining seven dogs developed similar amounts of neointimal hyperplasia. PCNA studies showed no accelerated fibroproliferative response at irradiated anastomoses compared to controls. Skin incisions and soft tissues over irradiated anastomoses revealed no radiation-induced changes or increase in apoptosis. Thus we conclude that postoperative single-fraction external-beam irradiation of the venous anastomosis of a prosthetic arteriovenous graft that mimics the situation in humans is feasible and safe with regard to early wound healing.

Gas exchange by pods and subtending leaves and internal recycling of CO(2) by pods of chickpea (Cicer arietinum L.) subjected to water deficits.

Terminal drought markedly reduces leaf photosynthesis of chickpea (Cicer arietinum L.) during seed filling. A study was initiated to determine whether photosynthesis and internal recycling of CO(2) by the pods can compensate for the low rate of photosynthesis in leaves under water deficits. The influence of water deficits on the rates of photosynthesis and transpiration of pods and subtending leaves in chickpea (cv. Sona) was investigated in two naturally-lit, temperature-controlled glasshouses. At values of photosynthetically active radiation (PAR) of 900 micromol m(-2) s(-1) and higher, the rate of net photosynthesis of subtending leaves of 10-d-old pods was 24 and 6 micromol m(-2) s(-1) in the well-watered (WW) and water-stressed (WS) plants when the covered-leaf water potential (Psi) was -0.6 and -1.4 MPa, respectively. Leaf photosynthesis further decreased to 4.5 and 0.5 micromol m(-2) s(-1) as Psi decreased to -2.3 and -3.3 MPa, respectively. At 900--1500 micromol m(-2) s(-1) PAR, the net photosynthetic rate of 10-d-old pods was 0.9-1.0 micromol m(-2) s(-1) in the WW plants and was -0.1 to -0.8 micromol m(-2) s(-1) in the WS plants. The photosynthetic rates of both pods and subtending leaves decreased with age, but the rate of transpiration of the pods increased with age. The rates of respiration and net photosynthesis inside the pods were estimated by measuring the changes in the internal concentration of CO(2) of covered and uncovered pods during the day. Both the WW and WS pods had similar values of internal net photosynthesis, but the WS pods showed significantly higher rates of respiration suggesting that the WS pods had higher gross photosynthetic rates than the WW pods, particularly in the late afternoon. When (13)CO(2) was injected into the gas space inside the pod, nearly 80% of the labelled carbon 24 h after injection was observed in the pod wall in both the WW and WS plants. After 144 h the proportion of (13)C in the seed had increased from 19% to 32% in both treatments. The results suggest that internal recycling of CO(2) inside the pod may assist in maintaining seed filling in water-stressed chickpea.

Experimental measurements of dosimetric parameters on the transverse axis of a new 125I source.

Permanent prostate implant using 125I or 103Pd sources is a common treatment choice in the management of early prostate cancer. As sources of new designs are developed and marketed for application in permanent prostate implants, it is of paramount importance that their dosimetric characteristics are carefully determined, in order to maintain a high accuracy of patient treatment. This report presents the results of experimental measurements of the dosimetric parameters performed for a newly available 125I seed source, the model MED3631-A/M source (IoGold), manufactured by North American Scientific, Inc. The measurements were performed in a large scanning water phantom, using a diode detector. The positioning of the source and the diode detector was achieved by a computer-controlled positioning mechanism in the scanning water phantom. The dose rate constant in water for the new 125I source was measured in comparison with an existing 125I source of similar design and verified using thermoluminescent dosimetry (TLD) measurement. The radial dose function values for the source were measured using the diode detector. The measurement technique and the results are compared with the dose distribution parameters for the 125I sources discussed in the AAPM TG43 report and elsewhere [Med. Phys. 26, 570-573 (1999)]. For the dose rate constant in water of the new source, it is recommended that a value of 0.950 cGy/U-hr be used based on the NIST 1985 air-kerma strength calibration standard, or 1.060 cGy/U-hr based on the 1999 NIST air-kerma strength standard. The measured radial dose function values for the MED3631-A/M source agree closely with those of the model 6702 source. It is therefore recommended that the radial dose function values for the model 6702 125I source, as recommended by the AAPM TG43 report, be adopted for the new source as well.

Monte Carlo calculations and experimental measurements of dosimetry parameters of a new 103Pd source.

Permanent prostate implantation using 125I (iodine) or 103Pd (palladium) sources is a popular treatment option in the management of early prostate cancer. As sources of new designs are developed and marketed for application in permanent prostate implantations, their dosimetric characteristics must be carefully determined in order to maintain the accuracy of patient treatment. This report presents the results of experimental measurements and Monte Carlo calculations of the dosimetric parameters performed for a newly available 103Pd seed source. The measurements were performed in a large scanning water phantom using a diode detector. The positioning of the source and detector was achieved by a computer-controlled positioning mechanism in the scanning water phantom. The dose rate constant in water for the new 103Pd source was determined from measurements with the diode detector calibrated with 125I sources of known air-kerma strength. The radial dose function values for the source were measured using the diode detector. Monte Carlo photon transport calculations were then used to calculate the dosimetric parameters of dose rate constant, radial dose function, and anisotropy function using an accurate geometric model of the source. The measured dose rate constant of 0.693 cGy/U-hr compares well with the Monte Carlo calculated value of 0.677 cGy/U-hr. These results are further compared with data on existing 103Pd sources.

Specific inhibition of rat brain phospholipase D by lysophospholipids.

Although the importance of phospholipase D (PLD) in signal transduction in mammalian cells is well documented, the negative regulation of PLD is poorly understood. This is primarily due to a lack of known specific inhibitors of PLD. We herein report that the activity of partially purified rat brain PLD is inhibited by certain lysophospholipids, such as lysophosphatidylinositol, lysophosphatidylglycerol, and lysophosphatidylserine in a highly specific manner. Inhibition of PLD by lysophospholipids was dose-dependent: the concentration of lysophosphatidylinositol required for half-maximal inhibition was about 3 micrometer. An analysis of the enzyme-kinetics suggested that lysophospholipids act as non-competitive inhibitors of PLD activity. As expected, PLD activity was stimulated by ADP-ribosylation factor (Arf) and phosphatidylinositol 4,5-bisphosphate (PIP(2)). The inhibition of PLD by lysophospholipids, however, was not affected by the presence or absence of Arf or by an increase in PIP(2) concentration. A protein-binding assay suggested that lysophospholipids bind directly to PLD. These results indicate that the observed inhibition of PLD by lysophospholipids is due to their direct interaction rather than to an interaction between lysophospholipids and either Arf or PIP(2). The present study suggests that certain lysophospholipids are specific inhibitors of rat brain PLD in a cell-free system and may provide the new opportunities to investigate mechanisms by which PLD is regulated by lysophospholipids, presumably liberated by phospholipase A(2) activation, in mammalian cells.

Two-effective-source method for the calculation of in-air output at various source-to-detector distances in wedged fields.

A simple algorithm was developed for calculation of the in-air output at various source-to-detector distances (SDDs) on the central axis for wedged fields. In the algorithm we dealt independently with two effective sources, one for head scatter and the other for wedge scatter. Varian 2100C with 18 and 8 MV photon beams was used to examine this algorithm. The effective source position for head scatter for wedged fields was assumed to be the same as that for open fields, and the effective source position for wedge scatter was assumed to be a certain distance upstream from the physical location of the wedge. The shift of the effective source for wedge scatter, w, was found to be independent of field size. Moreover, we observed no systematic dependency of w on wedge angle or beam energy. One value, w = 5.5 cm, provided less than 1% difference in in-air outputs through the whole experimental range, i.e., 6 x 6 to 20 x 20 cm2 field size (15 x 20 cm2 for 60 degrees wedge), 15 degrees-60 degrees wedge angle, 80-130 cm SDD, and both 18 and 8 MV photon beams. This algorithm can handle the case in which use of a tertiary collimator with an external wedge makes the field size for the determination of wedge scatter different from that for head scatter. In this case, without the two-effective-source method, the maximum of 4.7% and 2.6% difference can be given by the inverse square method and one-effective-source method in a 45 degrees wedged field with 18 MV. Differences can be larger for thicker wedges. Enhanced dynamic wedge (EDW) fields were also examined. It was found that no second effective source is required for EDW fields.

A generalized solution for the calculation of in-air output factors in irregular fields.

Three major contributors of scatter radiation to the in-air output of a medical linear accelerator are the flattening filter, wedge, and tertiary collimator. These were considered separately in the development of an algorithm to be used to set up an in-air output factor calculation formalism for open and wedge fields of irregular shape. A detector's eye view (DEV) field defined at the source plane was used to account for the effects of collimator exchange and the partial blockage of the flattening filter by the tertiary collimator in the determination of head scatter. An irregular field determined at the source plane by a DEV was segmented and mapped back into the detector plane by a field-mapping method. Field mapping was performed by using a geometric conversion factor and equivalent field relationships for head scatter. The scatter contribution of each segmented equivalent field at the detector plane was summed by Clarkson integration. The same methodology was applied for determining both tertiary collimator and wedge scatter contribution. However, the field size that determined the amount of scatter contribution was not the same for each component. For tertiary collimator scatter and external wedge scatter, a field projected to the detector plane was used directly. Comparisons of calculated and measured values for in-air output factors showed good agreement for both open and external wedge fields. This algorithm can also be used for multileaf collimator (MLC) fields irrespective of the position of the MLC (i.e., whether the MLC replaces one secondary collimator or is used as a tertiary collimator). The measurement and parameterization of tertiary collimator scatter is necessary to account for its contribution to the in-air output. Because a source-plane field is mapped into the detector plane, no additional dosimetric data acquisition is necessary for the calculation of head scatter.

The equivalent square concept for the head scatter factor based on scatter from flattening filter.

The equivalent field relationship between square and circular fields for the head scatter factor was evaluated at the source plane. The method was based on integrating the head scatter parameter for projected shaped fields in the source plane and finding a field that produced the same ratio of head scatter to primary dose on the central axis. A value of sigma/R approximately equal to 0.9 was obtained, where sigma was one-half of the side length of the equivalent square and R was the radius of the circular field. The assumptions were that the equivalent field relationship for head scatter depends primarily on the characteristics of scatter from the flattening filter, and that the differential scatter-to-primary ratio of scatter from the flattening filter decreases linearly with the radius, within the physical radius of the flattening filter. Lam and co-workers showed empirically that the area-to-perimeter ratio formula, when applied to an equivalent square formula at the flattening filter plane, gave an accurate prediction of the head scatter factor. We have analytically investigated the validity of the area-to-perimeter ratio formula. Our results support the fact that the area-to-perimeter ratio formula can also be used as the equivalent field formula for head scatter at the source plane. The equivalent field relationships for wedge and tertiary collimator scatter were also evaluated.