Biomedical subjects

X R Zhu

Publications and source records attributed to X R Zhu.

At least 19 recordsLinked to original sources

PubMed2006

Measurements of in-air output ratios for a linear accelerator with and without the flattening filter.

The in-air output ratio (Sc) for photon beams from linear accelerators describes the change of in-air output as a function of the collimator settings. The physical origin of the Sc is mainly due to the change in scattered radiation that can reach the point of measurement as the geometry of the head changes. The flattening filter (FF) and primary collimator are the major sources of scattered radiation. The change in amount of backscattered radiation from the collimator into the beam-monitoring chamber also contributes to the variation of output. In this work, we measured the Sc and backscatter factors (Sb) into the beam-monitoring chamber for a linear accelerator with and without the FF. We measured the Sc with a Farmer-type chamber in a miniphantom at the depth of 10 g/cm2 for 6- and 18-MV x-ray beams from a Varian Clinac 2100EX linear accelerator. The Sb were measured with a universal pulse counter and a diode array with build-in counting hardware and software. The head scatter component (Sh) was then derived from the relationship Sc= Sh x Sb, where Sb was the linear fit of measured results. Significant differences were observed for Sc with and without the FF. Within the range of experimental uncertainty, the Sb was similar with and without the FF. The variations in Sh differed significantly over the range of field sizes of 3 X 3 to 40 X 40 cm2 with and without the FF; for the 6-MV beam, it was 8% vs 3%, and for the 18-MV beam, 7% vs 1%. By analyzing the contributions of backscatter factor and total in-air output ratios with and without the FF, we directly gained insight into the contributions of different components to the total variations in Sc of a linear accelerator. Sc, Sb, and Sh are basic and useful dosimetric quantities for delivery of intensity-modulated radiation therapy using a linear accelerator operating in a mode without the FF.

Air↗

PubMed2005

Derivation of the distribution of extrafocal radiation for head scatter factor calculation.

Head scatter factors for high energy photon beams from linear accelerators can be modeled using a two-source model consisting of focal and extrafocal radiation. The focal radiation can be approximated as a point source, and the distribution of the extrafocal radiation is a two-dimensional (2D) radial symmetric function. Various methods, including analytical, Monte Carlo, and empirical trial functions, have been used to determine the radial symmetric function of extrafocal radiation distribution. This article describes a method for directly determining the extrafocal radiation distribution without assuming any empirical trial function. The extrafocal radiation distribution is determined with measured head scatter factors for rectangular fields defined by the lower jaw (X) fixed at 40 cm and the upper jaw (Y) varying from 3 to 40 cm. The derivatives of the measured head scatter factors, with respect to the Y jaw position projected in the plane of extrafocal radiation, are proportional to the one-dimensional (1D) projection (also called the line spread function) of the extrafocal radiation distribution. Two methods are used to solve the radial function of extrafocal radiation from the 1D projection. The first method uses a 2D filtered backprojection algorithm, originally developed for parallel beam computed tomography reconstruction, to directly derive the radial dependence of the extrafocal radiation distribution. The method has been applied to 6 and 18 MV photon beams from a Siemens linear accelerator and has been tested by comparing measured and calculated head scatter factors for square and rectangular fields. The second method uses a Fourier transform followed by a Fourier-Bessel transform to solve the problem. The distributions of extrafocal radiation derived from these two methods are virtually identical.

Algorithms↗

PubMed2003

Characteristics of sensitometric curves of radiographic films.

A new type of radiographic film, EDR (extended dose range) film, has been recently become available for film dosimetry. It is particularly attractive for composite isodose verification of intensity modulated radiation therapy because of its low sensitivity relative to the more common Kodak XV film. For XV film, the relationship between optical density and dose, commonly known as the sensitometric curve, depends linearly on the dose at low densities. Unlike XV film, the sensitometric curve of EDR film irradiated by megavoltage x rays is not linearly dependent on the dose at low densities. In this work, to understand the mechanisms governing the shape of the sensitometric curves, EDR film was studied with kilovoltage x rays, 60Co gamma rays, megavoltage x rays, and electron beams. As a comparison, XV film was also studied with the same beams mentioned above. The model originally developed by Silberstein [J. Opt. Soc. Am. 35, 93-107, 1945)] is used to fit experimental data. It is found that the single hit model can be used to predict the sensitometric curve for XV films irradiated by all beams used in this work and for EDR films exposed to kilovoltage x rays. For EDR film irradiated by 60Co gamma rays, megavoltage x rays, and electron beams, the double hit model is used to fit the sensitometric curves. For doses less than 100 cGy, a systematic difference between measured densities and that predicted by the double hit model is observed. Possible causes of the observed differences are discussed. The results of this work provide a theoretical explanation of the sensitometric behavior of EDR film.

Dose-Response Relationship, Radiation↗

PubMed2002

Evaluation of Kodak EDR2 film for dose verification of intensity modulated radiation therapy delivered by a static multileaf collimator.

A new type of radiographic film, Kodak EDR2 film, was evaluated for dose verification of intensity modulated radiation therapy (IMRT) delivered by a static multileaf collimator (SMLC). A sensitometric curve of EDR2 film irradiated by a 6 MV x-ray beam was compared with that of Kodak X-OMAT V (XV) film. The effects of field size, depth and dose rate on the sensitometric curve were also studied. It is found that EDR2 film is much less sensitive than XV film. In high-energy x-ray beams, the double hit process is the dominant mechanism that renders the grains on EDR2 films developable. As a result, in the dose range that is commonly used for film dosimetry for IMRT and conventional external beam therapy, the sensitometric curves of EDR2 films cannot be approximated as a linear function, OD = c * D. Within experimental uncertainty, the film sensitivity does not depend on the dose rate (50 vs 300 MU/min) or dose per pulse (from 1.0 x 10(-4) to 4.21 x 10(-4) Gy/pulse). Field sizes and depths (up to field size of 10 x 10 cm2 and depth = 10 cm) have little effect on the sensitometric curves. Percent depth doses (PDDs) for both 6 and 23 MV x rays were measured with both EDR2 and XV films and compared with ion chamber data. Film data are within 2.5% of the ion chamber results. Dose profiles measured with EDR2 film are consistent with those measured with an ion chamber. Examples of measured IMRT isodose distributions versus calculated isodoses are presented. We have used EDR2 films for verification of all IMRT patients treated by SMLC in our clinic. In most cases, with EDR2 film, actual clinical daily fraction doses can be used for verification of composite isodose distributions of SMLC-based IMRT.

Adult↗

PubMed2001

Dependence of virtual wedge factor on dose calibration and monitor units.

One of the important features of the Siemens Virtual Wedge (VW) is that the VW factor (VWF) is approximately equal to unity for all beams with a total deviation for a given wedge no greater than 0.05, as specified by Siemens. In this note we report the observed dependence of VWF on dose calibration (cGy/MU), monitor units (MU), and beam tuning for a Primus, a linear accelerator with two dose-rate ranges available for VW operation. The VWF is defined as the ratio of doses measured on the beam central axis for the wedge field to the open field; the open field dose is always measured with the nominal high dose-rate beam. When VW operates in the high dose-rate range, the VWF is independent of calibration (cGy/MU). When VW works in the low dose-rate range, the VWF varies linearly with the calibration of the low dose-rate mode. For a linear accelerator that has only one dose-rate range for VW, there is no observable dependence of VWF on the calibration. We also studied the monitor unit dependence of VWF. A discontinuity in VWF was observed at the switching point between the high and low dose-rate ranges. Working with Siemens, we have investigated causes of this discontinuity. As a result of this investigation, the discontinuity in VWF as a function monitor unit is practically removed.

Biophysical Phenomena↗

PubMed2000

Comparison of dosimetric characteristics of Siemens virtual and physical wedges.

Dosimetric properties of Virtual Wedge (VW) and physical wedge (PW) in 6 and 23 MV photon beams from a Siemens Primus linear accelerator, including wedge factors, depth doses, dose profiles, peripheral doses and surface doses, are compared. While there is a great difference in absolute values of wedge factors, VW factors (VWFs) and PW factors (PWFs) have a similar trend as a function of field size. PWFs have a stronger depth dependence than VWF due to beam hardening in PW fields. VW dose profiles in the wedge direction, in general, match very well with PW, except in the toe area of large wedge angles with large field sizes. Dose profiles in the nonwedge direction show a significant reduction in PW fields due to off-axis beam softening and oblique filtration. PW fields have significantly higher peripheral doses than open and VW fields. VW fields have similar surface doses as the open fields while PW fields have lower surface doses. Surface doses for both VW and PW increase with field size and slightly with wedge angle. For VW fields with wedge angles 45 degrees and less, the initial gap up to 3 cm is dosimetrically acceptable when compared to dose profiles of PW. VW fields in general use less monitor units than PW fields.

Humans↗

PubMed2000

Total scatter factors and tissue maximum ratios for small radiosurgery fields: comparison of diode detectors, a parallel-plate ion chamber, and radiographic film.

Two p-type diode detectors, a parallel-plate ion chamber, and radiographic film were used to measure total scatter factors and tissue maximum ratios (TMRs) for a stereotactic radiosurgery system with circular fields ranging from 5 to 50 mm in diameter. One diode has a square detection diagonal of 2.3 mm and the other diode has a circular detection diameter of 1 mm. It is found that the two diodes measured essentially the same total scatter factors for all field sizes. Total scatter factors measured by film are within 3% of diode values. Our results also suggest that the parallel-plate ion chamber could underestimate total scatter factors for fields as large as 15 mm in diameter, although it is recommended for field diameters > or = 12.5 mm. The total scatter factors used in our clinic are combined from data measured with the ion chamber and the 2-mm-diam diode. The combined total scatter factors generally agree with published data. While film overestimates TMRs for the smallest fields at large depths because of energy dependence of the film, the measurements with the 1-mm-diam diode agree with published data measured with thermoluminescent dosimeters. It is demonstrated that the accurate measurements of total scatter factors and TMRs for small fields can be obtained by combining results of the commercially available detectors used in this study.

Biophysical Phenomena↗

PubMed2000

Implementation and verification of virtual wedge in a three-dimensional radiotherapy planning system.

Virtual Wedge (VW) is a Siemens treatment modality which generates wedge-shaped dose distributions by moving a collimator jaw from closed to open at a constant speed while varying the dose rate in every 2 mm jaw position. In this work, the implementation and verification of VW in a radiotherapy treatment planning (RTP) system is presented. The VW implementation models the dose delivered by VW using the Siemens monitor units (MU) analytic formalism which determines the number of MU required to generate a wedge-fluence profile at points across the VW beam. For any set of treatment parameters, the VW algorithm generates an "intensity map" that is used to model the modification of fluence emanating from the collimator. The intensity map is calculated as the ratio of MU delivered on an axis point, divided by the monitor units delivered on the central-axis MU(0). The dose calculation is then performed using either the Clarkson or Convolution/ Superposition algorithms. The VW implementation also models the operational constraints for the delivery of VW due to dose rate and jaw speed limits. Dose verifications with measured profiles were performed using both the Clarkson and Convolution/Superposition algorithms for three photon beams; Siemens Primus 6 and 23 MV, and Mevatron MD 15 MV. Agreement within 2% or 2 mm was found between calculated and measured doses, over a large set of test cases, for 15, 30, 45, and 60 degree symmetric and asymmetric VW fields, using the manufacturer's supplied mu and c values for each beam.

Algorithms↗

PubMed2000

Entrance dose measurements for in-vivo diode dosimetry: Comparison of correction factors for two types of commercial silicon diode detectors.

Silicon diode dosimeters have been used routinely for in-vivo dosimetry. Despite their popularity, an appropriate implementation of an in-vivo dosimetry program using diode detectors remains a challenge for clinical physicists. One common approach is to relate the diode readout to the entrance dose, that is, dose to the reference depth of maximum dose such as d(max) for the 10x10 cm(2) field. Various correction factors are needed in order to properly infer the entrance dose from the diode readout, depending on field sizes, target-to-surface distances (TSD), and accessories (such as wedges and compensate filters). In some clinical practices, however, no correction factor is used. In this case, a diode-dosimeter-based in-vivo dosimetry program may not serve the purpose effectively; that is, to provide an overall check of the dosimetry procedure. In this paper, we provide a formula to relate the diode readout to the entrance dose. Correction factors for TSD, field size, and wedges used in this formula are also clearly defined. Two types of commercial diode detectors, ISORAD (n-type) and the newly available QED (p-type) (Sun Nuclear Corporation), are studied. We compared correction factors for TSDs, field sizes, and wedges. Our results are consistent with the theory of radiation damage of silicon diodes. Radiation damage has been shown to be more serious for n-type than for p-type detectors. In general, both types of diode dosimeters require correction factors depending on beam energy, TSD, field size, and wedge. The magnitudes of corrections for QED (p-type) diodes are smaller than ISORAD detectors.

Humans↗

PubMed2000

Parkin expression in the adult mouse brain.

Mutations in a protein designated Parkin were shown to be involved in the pathogenesis of autosomal recessive juvenile parkinsonism. Nothing is known about its regional and subcellular distribution in the mouse. In order to elucidate the Parkin mRNA and protein distribution in the adult mouse, the mouse cDNA was cloned and polyclonal antisera were generated against the N-terminal part of mouse Parkin. The antibodies were shown to be specific using Western blot analysis, immunostaining of cells transfected with mouse Parkin and pre-absorption tests. The Parkin protein expression profile was studied using immunohistochemistry and Western blot analysis and was compared with that of the mRNA yielded by in situ hybridization and RT-PCR analysis. Parkin protein was widely distributed in all subdivisions of the mouse brain. Low levels were found in the telencephalon and diencephalon, while the brainstem contained a large number of cells heavily expressing Parkin. Ultrastructural analysis and double immunohistochemistry revealed that the majority of Parkin-expressing cells were neurons, while only single glial cells exhibited immunostaining. The protein was distributed nonhomogeneously throughout the entire cytoplasm. A subpopulation of Parkin-immunopositive cells displayed speckled immunodeposits in the nucleus. Dopaminergic cells of the substantia nigra pars compacta exhibited high levels of Parkin mRNA but no Parkin protein, while the striatum contained immunopositive profiles but no mRNA signals. Our data indicate that Parkin is neither restricted to a single functional system nor associated with a particular transmitter system. The speckled nuclear distribution of Parkin immunoreactivity strongly suggests a role for Parkin in gene expression.

Amino Acid Sequence↗

PubMed1999

Structural and functional characterization of Kv6.2 a new gamma-subunit of voltage-gated potassium channel.

We have cloned and functionally expressed Kv6.2, a new member of the Kv6 subfamily of voltage-gated potassium channel subunits. The human Kv6.2 (KCNF2) gene was mapped at 18q22-18q23. Kv6.2 mRNA is preferentially expressed in rat and human myocard. Rat and human Kv6.2 subunits appear to be unable to form functional Kv channels in a heterologous expression system, but, when coexpressed with Kv2.1 alpha subunits, heteromultimeric Kv channels were formed mediating voltage-activated delayed-rectifier type outward currents. Their kinetics and conductance-voltage relationship were different from those mediated by homomultimeric Kv2.1 channels. Yeast two-hybrid reporter assays indicated that Kv6.2 amino-termini are able to interact specifically with the Kv2.1 amino-terminus. It is proposed that this protein protein interaction underlies Kv2.1/Kv6.2 subunit assembly and the expression of functional heteromultimeric Kv2.1/Kv6.2 channels. The most resiliant feature of the Kv2.1/Kv6.2 channels was their submicromolar sensitivity to the antiarrhythmic drug propafenone. The data suggest that delayed-rectifier type channels containing Kv6.2 subunits may contribute to cardiac action potential repolarization.

Amino Acid Sequence↗

PubMed1999

Characterization of human Kv4.2 mediating a rapidly-inactivating transient voltage-sensitive K+ current.

A human cDNA for the voltage-sensitive potassium channel subunit Kv4.2 has been cloned and functionally characterized. The human Kv4.2 (KCND2) gene was mapped at 7q31-32. Kv4.2 mRNA is prominently expressed in human brain. Relatively high concentrations of Kv4.2 mRNA occurred in mRNA preparations of amygdala, caudate nucleus, cerebellum, hippocampus, substantia nigra, and thalamus. Kv4.2 mRNA was not detected in human heart, kidney, liver, lung, pancreas, and skeletal muscle. The derived Kv4.2 open reading frame consists of 630 amino acids. In comparison to rat Kv4.2, the human Kv4.2 sequence is highly conserved showing amino acid sequence differences at five positions only. The Kv4.2 subunits were expressed heterologously in human embryonic kidney (293) cells and mediated a rapidly inactivating, A-type outward K+ current. The gating kinetics of the Kv4.2-mediated currents were very similar to those of rat Kv4.2-mediated currents. Both the Kv4.2 and Kv4.3 subunits have been implicated in mediating the transient outward K+ current Ito in rodent cardiac myocytes. In contrast we did not detect Kv4.2. but solely Kv4.3 mRNA in human heart RNA preparations. This may suggest that Kv4.2 subunits do not contribute to the rapid transient outward K+ current of atrial and ventricular myocytes in humans.

Amino Acid Sequence↗

PubMed1998

Multiple machine implementation of enhanced dynamic wedge.

PURPOSE: After acquiring 4 years of experience with Dynamic Wedge, a software-driven one-dimensional (1D) compensation system, we implemented a new software version called Enhanced Dynamic Wedge (EDW). The EDW allows larger (30 cm) and asymmetric field sizes and additional angles for wedged fields. We implemented this software on four similar dual-energy accelerators that also possess upper and lower physical wedge sets. Our goal was to implement EDW with one common wedge factor (WF) table and one set of treatment-planning files. METHODS AND MATERIALS: We measured WFs with an ionization chamber and isodose profiles with both film and a diode array. We used a calculation scheme that requires only entry of the wedge angle and fixed jaw value. Filters for computerized treatment planning were configured for each wedge angle. We also examined to what degree the multileaf collimation (MLC) orientation, which is orthogonal to the EDW direction, was compromised for specific treatment sites. As a comparative test, we examined the dosimetric consistency for the 8 sets of physical wedges on the four machines. Finally, we updated our DW quality assurance program for EDW. RESULTS: The measured EDW WF was common for all four machines to within +/- 1.5% and the calculation scheme held to within 1.5%. The EDW isodoses were consistent among the machines as measured by film and diode array. The treatment-planning filters provided computed isodose profiles that were nearly identical to measured profiles. Regarding MLC orientation, we found that the collimator angle needed for EDW did not compromise isodose distributions, as apparent in measured isodoses and calculated dose-volume histograms. The consistency of the physical wedges did not fare as well. Two of the lower wedge sets had Wfs and profiles different (> 3%) from the other wedge sets. CONCLUSIONS: We have successfully implemented EDW on four machines using only one WF table and one set of treatment-planning filters. The EDW provides for improved treatment techniques for particular sites due to the large field sizes and additional angles available. Daily treatment efficiency has increased because of the remote capability provided by EDW.

Humans↗

PubMed1998

Integrin-mediated short-term memory in Drosophila.

Volado is a new memory mutant of Drosophila. The locus encodes two isoforms of a new alpha-integrin, a molecule that dynamically mediates cell adhesion and signal transduction. The Volado gene is expressed preferentially in mushroom body cells, which are neurons known to mediate olfactory learning in insects. Volado proteins are concentrated in the mushroom body neuropil, brain areas that contain mushroom body processes in synaptic contact with other neurons. Volado mutants display impaired olfactory memories within 3 min of training, indicating that the integrin is required for short-term memory processes. Conditional expression of a Volado transgene during adulthood rescues the memory impairment. This rescue of memory is reversible, fading over time along with expression of the transgene. Thus the Volado integrin is essential for the physiological processes underlying memory. We propose a model in which integrins act as dynamic regulators of synapse structure or the signalling events underlying short-term memory formation.

Amino Acid Sequence↗

PubMed1998

Geometric and dosimetric analysis of multileaf collimation conformity.

BACKGROUND AND PURPOSE: There is concern over the stepped edges of multileaf collimator (MLC) fields for target coverage compared with those of cerrobend. Despite recent reports dispelling this concern, users are still cautious when using MLCs for small fields. Leaf orientation can be a problem if one is required to orient the leaves along an axis not ideal for conformity (such as dynamic or universal wedge cases). In this study we examined the dependence of MLC field conformity on field size and elongation. MATERIALS AND METHODS: We examined circles of varying diameter and ellipses of varying eccentricity with leaves oriented along the major and minor axes of ellipses. The tests were both geometric, comparing areas of overblocking or underblocking (leaves inside and outside the field), and dosimetric, using radiographic films at depth in the beam's eye view plane. RESULTS: For the geometric comparison there is a rapid increase in non-conformity, defined as the percentage of overblocking or underblocking area, as the circle diameter decreases. For ellipses, when the leaves move along one axis direction, the conformity does not depend on the diameter of the same axis, but instead improves as the dimension of the axis in the non-leaf motion direction increases. The best conformity is achieved when the maximum number of leaves is used to shape the field. When the dosimetry is analyzed, the predictability of these trends decreases due to the impact of undulations (scatter), leaf inaccuracies and dosimetric uncertainties. CONCLUSIONS: We recommend that for small round fields MLC should be used with caution and that for ellipses the direction of leaf movement should be aligned with the minor axis whenever possible. Though these experiments are for idealized geometries, the observations can be applied to clinical fields. An MLC with a thinner leaf width could be beneficial for small round fields.

Humans↗

PubMed1997

The influence of angular misalignment on fixed-portal intensity modulated radiation therapy.

A method has been developed to estimate potential dose errors due to linear accelerator angular setting misalignments of Intensity Modulated Radiation Therapy (IMRT) treatments. A first-order approximation to the dose error at a point is modeled as the dot product of the dose gradient and the shift vector of the point due to the rotational error. The analysis method is applied to a previously published set of optimized fluences for a 50 MV IMRT pelvis irradiation. Three of the published cases exhibiting a wide range of modulation are presented; a rectangular open field, a field optimized for a static multileaf collimator defining the portal outline coupled with a single broad bremsstrahlung profile modulation, and a fully modulated field using a physical modulator. To examine the energy dependence of angle setting errors, the study is repeated using the same fluence distributions, but with a dose-spread kernel appropriate for a 6 MV photon beam. The collimator angle error is set to 2 degree, and the dose error determined with both a centrally located isocenter and an isocenter chosen to model a split-field geometry. The dose error due to a 2 degree gantry setting error is assessed at a plane 10 cm distal to the isocenter. The mathematical form of the dose error due to couch motion is similar to the other two errors, so the dose error resulting from a couch angle missetting is not presented. The magnitude of the errors is largest for the 6 MV beam, while the volume encompassed by the errors is greater for the 50 MV beam. The gantry error yields the largest dose error values, with the 6 MV modulated case presenting dose errors of greater than 40%.

Humans↗

PubMed1995

minibrain: a new protein kinase family involved in postembryonic neurogenesis in Drosophila.

The development of the adult central nervous system of Drosophila requires a precise and reproducible pattern of neuroblast proliferation during postembryonic neurogenesis. We show here that mutations in the minibrain (mnb) gene cause an abnormal spacing of neuroblasts in the outer proliferation center (opc) of larval brain, with the implication that mnb opc neuroblasts produce less neuronal progeny than do wild type. As a consequence, the adult mnb brain exhibits a specific and marked size reduction of the optic lobes and central brain hemispheres. The insufficient number of distinct neurons in mnb brains is correlated with specific abnormalities in visual and olfactory behavior. The mnb gene encodes a novel, cell type-specific serine-threonine protein kinase family that is expressed and required in distinct neuroblast proliferation centers during postembryonic neurogenesis. The mnb kinases share extensive sequence similarities with kinases involved in the regulation of cell division.

Amino Acid Sequence↗

PubMed1995

A convolution-adapted ratio-TAR algorithm for 3D photon beam treatment planning.

A convolution-adapted ratio of tissue-air ratios (CARTAR) method of dose calculation has been developed at the Mallinckrodt Institute of Radiology. This photon pencil-beam algorithm has been developed and implemented specifically for three-dimensional treatment planning. In a standard ratio of tissue-air ratios (RTAR) algorithm, doses to points in irregular field geometries are not adequately modeled. This is inconsistent with the advent of conformal therapy, the goal of which is to conform the dose distribution to the target volume while sparing neighboring sensitive normal critical structures. This motivated us to develop an algorithm that can model the beam penumbra near irregular field edges, while retaining much of the speed for the original RTAR algorithm. The dose calculation algorithm uses two-dimensional (2D) convolutions, computed by 2D fast Fourier transform, of pencil-beam kernels with a beam transmission array to calculate 2D off-axis profiles at a series of depths. These profiles are used to replace the product of the transmission function and measured square-field boundary factors used in the standard RTAR calculation. The 2D pencil-beam kernels were derived from measured data for each modality using commonly available dosimetry equipment. The CARTAR algorithm is capable of modeling the penumbra near block edges as well as the loss of primary and scattered beam in partially blocked regions. This paper describes the dose calculation algorithm, implementation, and verification.

Algorithms↗