Volume 31, Issue 7, July 2004
 POINT/COUNTERPOINT


Very high energy electromagneticallyscanned electron beams are an attractive alternative to photon IMRT
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 RADIATION THERAPY PHYSICS


Monte Carlo parametric study of stent impact on dose for catheterbased intravascular brachytherapy with
View Description Hide DescriptionThe radiation treatment of catheterbased βemitter sources is being used to prevent restenosis following interventional coronary procedures. We present the results of a Monte Carlo calculation study to assess the dosimetric impact in the vessel tissue due to the presence of the stent. A catheterbased βemitter system is modeled using the MonteCarlo code MCNP4B. Dose distributions are calculated in annular voxels section) along the axis of a 40 mm. source with and without the stent (at a distance of 1.5–3.0 mm from the longitudinal axis of the source). The main results include: (a) a clear difference between the local perturbation just behind the strut and a more general perturbation seen deeper into the vessel tissue; (b) the local perturbations disappears at a depth of 300–400 μm while the more general perturbation affects the tissue in its full thickness including the prescription point; (c) in the local perturbation the maximum impact is determined mainly by the material and the thickness of the strut while the spatial attenuation of this impact is defined mainly by the strut width; (d) in the general perturbation, the most important magnitude is the freearea ratio for the path of the electrons, being the materialcharacteristics and strut thickness of secondary importance; (e) analytical expressions are presented to estimate the magnitude of this perturbation according to the complete characteristics of the expanded strut, i.e., thickness, freearea ratio, and material; and (f) a simple algorithm is presented for estimating the freearea ratio when this information is not available.

Contrast effects on dosimetry of a partial breast irradiation system
View Description Hide DescriptionMammoSite^{®} is a highdose rate brachytherapy procedure for partial breast irradiation, which uses a balloon filled with radiopaque iodinebased contrast solution and catheter for insertion of highdoserate source. The radiopaque material helps visualizing the balloon contour, catheter, and source position within the balloon, which is essential for computerized tomographybased treatment planning and for daily QA using xray radiographs. Because of the high content of iodine in contrast media, increased absorption and attenuation of photons may take place within the balloon, which would affect the resultant dose rates outside the balloon. The impact of the concentration of the radiopaque solution on the physical dosimetry of this brachytherapy procedure is investigated in this study using MCNPX (version 2.4) Monte Carlo simulation. Calculations were based on a 30 cm diameter water sphere phantom. The source geometry was that of the Nucletron microSelectron HDR v2 source. Concentration of the iodinebased radiopaque solution was varied from 5% to 25% by volume, a range recommended by the balloon’s manufacturer. Balloon diameters of 4, 5, and 6 cm were simulated. Dose rate per unit airkerma strength was calculated in 1 mm scoring bin steps. The dose rate reduction at the typical prescription line of 1 cm away from the balloon surface ranged from for the smallest balloon diameter and contrast concentration to a maximum of for the largest balloon diameter and contrast concentration, relative to a waterfilled balloon. Limiting the contrast concentration to 10% would insure less than 3% reduction in the prescription dose, regardless of balloon diameter.

Elimination of ghost markers during dual sensorbased infrared tracking of multiple individual reflective markers
View Description Hide DescriptionThe accuracy of dose delivery in radiotherapy is affected by the uncertainty in tumor localization. Motion of internal anatomy due to physiological processes such as respiration may lead to significant displacements which compromise tumor coverage and generate irradiation of healthy tissue. Realtime tracking with infraredbased systems is often used for tracking thoracic motion in radiation therapy. We studied the origin of ghost markers (“crosstalk”) which may appear during dual sensorbased infrared tracking of independent reflective markers. Ghost markers occur when two or more reflective markers are coplanar with each other and with the sensors of the two camerabased infrared tracking system. Analysis shows that sensors are not points but they have a finite extent and this extent determines for each marker a “ghost volume.” If one reflective marker enters the ghost volume of another marker, ghost markers will be reported by the tracking system; if the reflective markers belong to a surface their “ghost volume” is reduced to a “ghost surface” (ghost zone). Appearance of ghost markers is predicted for markers taped on the torso of an anthropomorphic phantom. This study illustrates the dependence of the shape, extent, and location of the ghost zones on the shape of the anthropomorphic phantom, the angle of view of the tracking system, and the distance between the tracking system and the anthropomorphic phantom. It is concluded that the appearance of ghost markers can be avoided by positioning the markers outside the ghost zones of the other markers. However, if this is not possible and the initial marker configuration is ghost markerfree, ghost markers can be eliminated during realtime tracking by virtue of the fact that they appear in the coordinate data sequence only temporarily.

A new approach in dose measurement and error analysis for narrow photon beams (beamlets) shaped by different multileaf collimators using a small detector
View Description Hide DescriptionDose measurement for narrow stereotactic beams and intensity modulation radiotherapy beamlets is difficult and errorprone due to the lack of lateral electron equilibrium. A small detector position error and finite sensitive volume as well as the nonfocus collimation could result in considerable (>10%) measurement errors. A new method is introduced here to measure the dose and error components so that the accuracy and precision of the dose measurement can be improved. Based on superposition principle, we can create exactly the small field of interest by subtraction of a reference open field (Ofield) and two strip fields (Sfields) from the sum of four quadrant fields (Qfields). The position effect on the dose measurement is determined by the standard deviation of the four Qfield readings. The collimator leafedge effect (LEE) is quantified by the difference between the readings of the two Sfields using a detector that has very small sensitive volume. The detectorvolume effect can be analytically estimated from the integrals of the dose distributions of the two Sfields over the detector volume. Using a pinpoint ion chamber (PTW N31006) and a stereotactic silicon diode detector (Scanditronix, DEB050), we have measured scatter factors (SF) and tissuemaximum ratios for 6MV xray fields with sizes of 3×3 and 6×6 mm^{2} shaped by a BrainLAB micromultileaf collimator (microMLC) (M3), 4.4×4.4 and 8.8×8.8 mm^{2} shaped by a 3DLine doublefocus MLC, and 5×5 and 10×10 mm^{2} by a Varian Millennium MLC. Our experimental results demonstrate that the large errors are often caused by a small setup error or measuring point displacement from the central ray of the beam. The LEE is almost independent of the depth but closely related to the field size and the type of MLC. The volume effect becomes significant when the detector diameter is comparable to the half size of the small fields. Application of the new method using different detectors had achieved less than 8.3% total experiment error for all of the small fields of interest except for the SF of the 3×3 mm^{2} field from the pinpoint ion chamber that has 15% volume effect. Importantly, the new method using a solid water phantom is clinically convenient and highly reproducible.

Laser electron accelerators for radiation medicine: A feasibility study
View Description Hide DescriptionTabletop laser wakefield accelerators (LWFAs), proposed theoretically in 1979, have now generated individual electron bunches in the laboratory with a significant number of electrons having energies up to 10 MeV and beyond with the maximum energy reaching tens of MeV and charge per laser pulse of The attained electron beam properties have stimulated a discussion about the possible applications of LWFAs to medical radiation treatment, either directly or via conversion to xrays. Our purpose in this paper is to analyze whether or not such applications are feasible, or can be made feasible with existing laser technology. Clinical electron beam applications require the selection of specific electron energies in the range of 6–25 MeV with a narrow energy bin for depth control, and a beam expansion to as much as for various tumorradiation treatments. As a result, we show that present LWFA sources provide a dose rate that falls short of the requirements for clinical application by at least an order of magnitude. We then use particle simulations to evaluate the feasibility of developing an improved LWFAbased medical accelerator. Current LWFA sources require such high peak intensity that laser repetition rate is restricted to A scheme to lower the threshold and increase the repetition rate of efficient LWFA thus appears essential. We analyze one such scheme. We show that by “seeding” the primary laser pulse with a second, hundredfold less intense pulse that is shifted downward in frequency by approximately the plasma frequency LWFA produces a yield of clinically useful electrons per pulse comparable to that provided by an unseeded source, except that the primary pulse energy is now more than one order of magnitude lower than that in current LWFAs. This enables a repetition rate of or more using existing laser technology, and thus dose rates (several Gy/min) in the range required for medical radiation applications.

Dose properties of a laser accelerated electron beam and prospects for clinical application
View Description Hide DescriptionLaser wakefield acceleration (LWFA) technology has evolved to where it should be evaluated for its potential as a future competitor to existing technology that produces electron and xraybeams. The purpose of the present work is to investigate the dosimetric properties of an electron beam that should be achievable using existing LWFA technology, and to document the necessary improvements to make radiotherapy application for LWFA viable. This paper first qualitatively reviews the fundamental principles of LWFA and describes a potential design for a 30 cm accelerator chamber containing a gas target. Electron beam energy spectra, upon which our dose calculations are based, were obtained from a uniform energy distribution and from twodimensional particleincell (2D PIC) simulations. The 2D PIC simulation parameters are consistent with those reported by a previous LWFA experiment. According to the 2D PIC simulations, only approximately 0.3% of the LWFA electrons are emitted with an energy greater than 1 MeV. We studied only the highenergy electrons to determine their potential for clinical electron beams of central energy from 9 to 21 MeV. Each electron beam was broadened and flattened by designing a dual scattering foil system to produce a uniform beam (103%>offaxis ratio>95%) over a 25×25 cm^{2} field. An energy window ranging from 0.5 to 6.5 MeV was selected to study centralaxis depth dose,beam flatness, and dose rate. Dose was calculated in water at a 100 cm sourcetosurface distance using the EGS/BEAMMonte Carlo algorithm. Calculations showed that the beam flatness was fairly insensitive to However, since the falloff of the depth–dose curve and the dose rate both increase with a tradeoff between minimizing and maximizing dose rate is implied. If is constrained so that is within 0.5 cm of its value for a monoenergetic beam, the maximum practical dose rate based on 2D PIC is approximately 0.1 Gy min^{−1} for a 9 MeV beam and 0.03 Gy min^{−1} for a 15 MeV beam. It was concluded that current LWFA technology should allow a tabletop terawatt laser to produce therapeutic electron beams that have acceptable flatness, penetration, and falloff of depth dose; however, the dose rate is still 1%–3% of that which would be acceptable, especially for higherenergy electron beams. Further progress in laser technology, e.g., increasing the pulse repetition rate or number of high energy electrons generated per pulse, is necessary to give dose rates acceptable for electron beams. Future measurements confirming dosimetric calculations are required to substantiate our results. In addition to achieving adequate dose rate, significant engineering developments are needed for this technology to compete with current electron acceleration technology. Also, the functional benefits of LWFA electron beams require further study and evaluation.

Determination of the depth of 50% of maximum ionization, for electron beams by the divided difference method
View Description Hide DescriptionA new characterization of depthionization parameters for electron beams is empirically deduced from our data analysis based on the divided difference method (the DD method), which employs the numerical differential of an ionization curve. The important feature of the present method is that it does not necessarily require normalized percent depthionization (NPDI) data. The depth of 50% of maximum ionization, which is an important parameter for electron beamdosimetry, can be deduced from the analysis of an unnormalized (or partial) depthionization (UDI) curve obtained over a short interval of depth. The values of determined by the DD method are in agreement to within 0.1 mm for energies of 4, 6, and 9 MeV, compared with the ones determined by the TG51 protocol method (or the conventional method), and the difference was 0.9 mm for 12 and 15 MeV. The dose at the reference depth, calculated from by the DD method, is found to be in agreement with TG51 to within 0.1%. The field size dependence of the DD method using UDI data was studied for three field sizes: 6×6, 10×10, and 20×20 cm^{2}. For all energies, the discrepancies of as determined by both methods were 0.9 mm on average for the 6×6 cm^{2} fields and 0.6 mm for the other two field sizes. This dependence was remarkable for 6×6 cm^{2} fields for 12 and 15 MeV, and the discrepancies shown by the DD method were 1.2 mm for 12 MeV and 1.8 mm for 15 MeV, respectively. Since the reference field size in clinical dosimetry is usually 10×10 cm^{2}, this dependence will not affect clinical dosimetry. The DD method could be an alternative option for checking beam quality in dose calibration.

Phantom size in brachytherapy source dosimetric studies
View Description Hide DescriptionAn important point to consider in a brachytherapydosimetry study is the phantom size involved in calculations or experimental measurements. As pointed out by Williamson [Med. Phys. 18, 776–786 (1991)] this topic has a relevant influence on final dosimetric results. Presently, onedimensional (1D) algorithms and newlydeveloped 3D correction algorithms are based on physics data that are obtained under full scatter conditions, i.e., assumed infinite phantom size. One can then assume that reference dose distributions in sourcedosimetry for photonbrachytherapy should use an unbounded phantom size rather than phantomlike dimensions. Our aim in this paper is to study the effect of phantom size on brachytherapy for radionuclide and mainly used for clinical purposes. Using the GEANT4 Monte Carlo code, we can ascertain effects on derived dosimetry parameters and functions to establish a distance dependent difference due to the absence of full scatter conditions. We have found that for and a spherical phantom with a 40 cm radius is the equivalent of an unbounded phantom up to a distance of 20 cm from the source, as this size ensures full scatter conditions at this distance. For and the required radius for the spherical phantom in order to ensure full scatter conditions at 10 cm from the source is A simple expression based on fits of the dose distributions for various phantom sizes has been developed for and in order to compare the dose rate distributions published for different phantom sizes. Using these relations it is possible to obtain radial dose functions for unbounded medium from bounded phantom ones.

Use of EPID for leaf position accuracy QA of dynamic multileaf collimator (DMLC) treatment
View Description Hide DescriptionWe describe in this paper an alternative method for routine dynamic multileaf collimator (DMLC) quality assurance (QA) using an electronic portal imaging device(EPID). Currently, this QA is done at our institution by filming an intensitymodulated radiotherapy(IMRT) test field producing a pattern of five 1mm bands 2 cm apart and performing a visual spotcheck for leaf alignment, motion lags, sticking and any other mechanical problems. In this study, we used an amorphous silicon aS500 EPID and films contemporaneously for the DMLC QA to test the practicality and efficacy of EPIDvisàvis film. The EPIDimage was transformed to an integrated dose map by first converting the reading to dose using a calibration curve, and then multiplying by the number of averaged frames. The EPIDdose map was then backprojected to the central axis plane and was compared to the film measurements which were scanned and converted to dose using a film dosimetry system. We determined the fullwidth halfmaximum (FWHM) of each band for both images, and evaluated the dose to the valley between two peaks. We also simulated mechanical problems by increasing the band gap to 1.5 mm for some leaf pairs. Our results show that EPID is as good as the film in resolving the band pattern of the IMRT test field. Although the resolution of the EPID is lower than that of the film (0.78 mm/pixel vs 0.36 mm/pixel for the film), it is high enough to faithfully reproduce the band pattern without significant distortion. The FWHM of the EPID is 2.84 mm, slightly higher than the 2.01 mm for the film. The lowest dose to the valley is significantly lower for the EPID (15.5% of the peak value) than for the film (28.6%), indicating that EPID is less energy independent. The simulated leaf problem can be spotted by visual inspection of both images; however, it is more difficult for the film without being scanned and contrastenhanced. EPIDimages have the advantage of being already digital and their analysis can easily be automated to flag leaf pairs outside tolerance limits of set parameters such as FWHM, peak dose values, peak location, and distance between peaks. This automation is a new feature that will help preempt MLC motion interlocks and decrease machine downtime during actual IMRT treatment. We conclude that since EPIDimages can be acquired, analyzed and stored much more conveniently than film, EPID is a good alternative to film for routine DMLC QA.

Attenuation of intracavitary applicators in HDR brachytherapy
View Description Hide DescriptionUnlike the penetrating monoenergetic 662 keV gamma rays emitted by LDR sources, the spectrum of used in HDR brachytherapy contains lowenergy components. Since these are selectively absorbed by the highatomic number materials of which intracavitary applicators are made, the traditional neglect of applicator attenuation can lead to appreciable dose errors. We investigated the attenuation effects of a uterine applicator, and of a set of commonly used vaginal cylinders. The uterine applicator consists of a stainless steel source guide tube with a wall thickness of 0.5 mm and a density of whereas the vaginal cylinders consist of the same stainless steel tube plus concentric polysulfone cylinders with a radius of 1 or 2 cm and a density of Monte Carlo simulations were performed to compute dose distributions for a bare HDR source, and for the same source located within the applicators. Relative measurements of applicator attenuation using ionchambers confirmed the Monte Carlo results within 0.5%. We found that the neglect of the applicator attenuation overestimates the dose along the transverse plane by up to 3.5%. At oblique angles, the longer photon path within applicators worsens the error. We defined attenuationcorrected radial dose and anisotropy functions, and applied them to a treatment having multiple dwell positions inside a vaginal cylinder.

Accurate Monte Carlo simulations for nozzle design, commissioning and quality assurance for a proton radiation therapy facility
View Description Hide DescriptionMonte Carlodosimetry calculations are essential methods in radiation therapy. To take full advantage of this tool, the beam delivery system has to be simulated in detail and the initial beam parameters have to be known accurately. The modeling of the beam delivery system itself opens various areas where Monte Carlo calculations prove extremely helpful, such as for design and commissioning of a therapy facility as well as for quality assurance verification. The gantry treatment nozzles at the Northeast Proton Therapy Center (NPTC) at Massachusetts General Hospital (MGH) were modeled in detail using the GEANT4.5.2 Monte Carlo code. For this purpose, various novel solutions for simulating irregular shaped objects in the beam path, like contoured scatterers, patient apertures or patient compensators, were found. The fourdimensional, in time and space, simulation of moving parts, such as the modulator wheel, was implemented. Further, the appropriate physics models and cross sections for proton therapy applications were defined. We present comparisons between measured data and simulations. These show that by modeling the treatment nozzle with millimeter accuracy, it is possible to reproduce measured dose distributions with an accuracy in range and modulation width, in the case of a spreadout Bragg peak (SOBP), of better than 1 mm. The excellent agreement demonstrates that the simulations can even be used to generate beam data for commissioning treatment planning systems. The Monte Carlo nozzle model was used to study mechanical optimization in terms of scattered radiation and secondary radiation in the design of the nozzles. We present simulations on the neutron background. Further, the Monte Carlo calculations supported commissioning efforts in understanding the sensitivity of beam characteristics and how these influence the dosedelivered. We present the sensitivity of dose distributions in water with respect to various beam parameters and geometrical misalignments. This allows the definition of tolerances for quality assurance and the design of quality assurance procedures.

Technical Note: Output and energy fluctuations of the tomotherapy HiArt helical tomotherapy system
View Description Hide DescriptionThe output and energy calibrations for the first clinical HiArt 2.0 helical tomotherapy system have been reviewed. Fixedgantry/fixedcouch and rotationalgantry/fixedcouch measurements were made on a daily basis over a period of 20 weeks to investigate system stability. Static gantry measurements were taken at 10 cm depth in a rectangular stack of Virtual Water at an SSD distance of 90 cm and a field size of Rotational gantry measurements were taken in a cylindrical phantom Virtual Water phantom for a field size of The HiArt 2.0 system has maintained its calibration to within and energy to within over the initial 20 week period.

A dosimetric approach to patientspecific radioiodine treatment of Graves’ disease with incorporation of treatmentinduced changes in thyroid mass
View Description Hide DescriptionThe traditional algorithms (Marinelli–Quimby and MIRD) used for the absorbed dose calculation in radionuclide therapy generally assume that the mass of the target organs does not change with time. In radioiodine therapy for Graves’ disease this approximation may not be valid. In this paper a mathematical model of thyroid mass reduction during the clearance phase (30–35 days) after administration to patients with Graves’ disease is presented. A new algorithm for the absorbed dose calculation is derived, taking into account the reduction of the mass of the gland resulting from the therapy. It is demonstrated that thyroid mass reduction has a considerable effect on the calculated radiationdose. Either the model of the thyroid mass reduction or the new equation for the absorbed dose calculation depend on a parameter k for each patient. This parameter can be calculated after the administration of a diagnostic amount of radioiodine activity (0.37–1.85 MBq). Thus, thyroid absorbed dose and thyroid mass reduction during the first month after therapy can be predicted before therapy administration. The absorbed dose values calculated by the new algorithm are compared to those calculated by the traditional Marinelli–Quimby and MIRD algorithms.

A practical approach to prevent gantry–couch collision for linacbased radiosurgery
View Description Hide DescriptionGantry–couch collision is a serious concern for treatment planning of the linear accelerator(linac) based stereotactic radiosurgery(SRS). The ability to detect collision at the time of planning eliminates the need for backup plans and preserves the useful beam angles that would be deemed unsafe and discarded otherwise. Most collisiondetection schemes embedded in commercial planning software guard only against the most apparent collisions. On the other hand, a foolproof collisionmap or lookup table often requires detailed measurement of machine geometry and complex graphic operations. In this study, we have developed a simple analytical method for collision detection with the use of quick machinespecific measurements. The collision detection is mathematically solved by determining whether two facets in threedimensional space, representing gantry and couch surfaces, intersect with each other. A computer code was implemented and tested on a Varian Clinac 600C linac equipped with a BrainLab micromultileaf collimator(MLC) device. To measure machinespecific parameters, the lesion isocenter was set to the origin of the stereotactic coordinate system. The reference coordinates of couch bracket corners and microMLC to the linac isocenter were measured only once in the treatment room before they were incorporated into the computer program. Couch, gantry, and collimator were subsequently translated and rotated to study the clearance of various beam arrangements and lesion locations. Predicted results were verified at the machine. Our method correctly confirmed clearance for a retrospective study of 54 previously treated SRS plans (76 isocenters). It also accurately predicted the collisions for all ten artificially created cases. In conclusion, we have developed an analytical method for SRS collision detection that is accurate, easy to implement, and computationally inexpensive.

Monte Carlo computation of dosimetric amorphous silicon electronic portal images
View Description Hide DescriptionThis study develops and tests a method to compute dosimetricimages for an amorphous silicon flatpanel detector so that an accurate quantitative comparison between measured and computed portal images may be made. An EGS4based Monte Carlo(MC) algorithm is developed to efficiently tally the energy deposition through the use of a virtual detectordosescoring methodology. The complete geometry of the imager is utilized in the MC calculation up to the imager rear housing, which is replaced with a uniform thickness material slab. The detectormounting hardware is modeled as a uniform backscattering material. The amount of backscatter material required to reproduce the measured backscatter is 0.98 g/cm^{2} of water. A floodfield irradiation, performed in the measurement imaging session, is used to crosscalibrate the computed images with the measured images. Calibrated MCcomputed images reproduce measured fieldsize dependencies of the electronic portal imaging device(EPID) response to within <1%, without the need for optical glare or other empirical corrections. A 10% dose difference between measured and computed images was observed outside the field edge for a field that was entirely blocked by the multileaf collimator(MLC). However, this error corresponded with less than 0.15% of the openfield dose. For fields produced by 5 and 20 mm dynamically sweeping MLC gaps, more than 98% of the points were found to have a gamma less than one with a 2%, 2 mm criteria. For an intensity modulated radiation therapy(IMRT) patient test field, over 99% of the points were found to have a gamma less than one with a 2%, 2 mm criteria. This study demonstrates that MC can be an effective tool for predicting measured portal images and may be useful for IMRT EPIDbased dosimetry.
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 RADIATION IMAGING PHYSICS


The conebeam algorithm of Feldkamp, Davis, and Kress preserves oblique line integrals
View Description Hide DescriptionThe algorithm of Feldkamp, Davis, and Kress [J. Opt. Soc. Am. A 1, 612–619 (1984)] is a widely used filteredbackprojection algorithm for threedimensional image reconstruction from conebeam (CB) projections measured with a circular orbit of the xray source. A wellknown property of this approximate algorithm is that the integral of the reconstructed image along any axial line orthogonal to the plane of the orbit is exact when the conebeam projections are not truncated. We generalize this result to oblique line integrals, thus providing an efficient method to compute synthetic radiographs from conebeam projections. Our generalized result is obtained by showing that the FDK algorithm is invariant under transformations that map oblique lines onto axial lines.

On the noise variance of a digital mammography system
View Description Hide DescriptionA recent paper by Cooper et al. [Med. Phys. 30, 2614–2621 (2003)] contains some apparently anomalous results concerning the relationship between pixel variance and xray exposure for a digital mammography system. They found an unexpected peak in a display domain pixel variance plot as a function of 1/mAs (their Fig. 5) with a decrease in the range corresponding to high display data values, corresponding to low xray exposures. As they pointed out, if the detector response is linear in exposure and the transformation from raw to display data scales is logarithmic, then pixel variance should be a monotonically increasing function in the figure. They concluded that the total system transfer curve, between input exposure and display image data values, is not logarithmic over the full exposure range. They separated data analysis into two regions and plotted the logarithm of display image pixel variance as a function of the logarithm of the mAs used to produce the phantom images. They found a slope of minus one for high mAs values and concluded that the transfer function is logarithmic in this region. They found a slope of 0.6 for the low mAs region and concluded that the transfer curve was neither linear nor logarithmic for low exposure values. It is known that the digital mammography system investigated by Cooper et al. has a linear relationship between exposure and raw data values [Vedantham et al., Med. Phys. 27, 558–567 (2000)]. The purpose of this paper is to show that the variance effect found by Cooper et al. (their Fig. 5) arises because the transformation from the raw data scale (14 bits) to the display scale (12 bits), for the digital mammography system they investigated, is not logarithmic for raw data values less than about 300 (display data values greater than about 3300). At low raw data values the transformation is linear and prevents overranging of the display data scale. Parametric models for the two transformations will be presented. Results of pixel variance measurements made on raw data images will be presented. The experimental data are in good agreement with those of Cooper et al. It will be shown that the slope of 0.6 found by Cooper et al. for the loglog plot at low exposure is not due to transfer function nonlinearity, it occurs because of an additive variance term—possibly due to electronic noise. It will also be shown, using population statistics from clinical images, that raw data values below 300 are rare in tissue areas. Those tissue areas with very low raw data values are within about a millimeter of the chest wall or in very dense muscle at corners of images.

Assessment of analysisofvariancebased methods to quantify the random variations of observers in medical imaging measurements: Guidelines to the investigator
View Description Hide DescriptionThe random variations of observers in medical imaging measurements negatively affect the outcome of cancer treatment, and should be taken into account during treatment by the application of safety margins that are derived from estimates of the random variations. Analysisofvariance (ANOVA) based methods are the most preferable techniques to assess the true individual random variations of observers, but the number of observers and the number of cases must be taken into account to achieve meaningful results. Our aim in this study is twofold. First, to evaluate three representative ANOVAbased methods for typical numbers of observers and typical numbers of cases. Second, to establish guidelines to the investigator to determine which method, how many observers, and which number of cases are required to obtain the a priori chosen performance. The ANOVAbased methods evaluated in this study are an established technique (pairwise differences method: PWD), a new approach providing additional statistics (residuals method: RES), and a generic technique that uses restricted maximum likelihood (REML) estimation. Monte Carlo simulations were performed to assess the performance of the ANOVAbased methods, which is expressed by their accuracy (closeness of the estimates to the truth), their precision (standard error of the estimates), and the reliability of their statistical test for the significance of a difference in the random variation of an observer between two groups of cases. The highest accuracy is achieved using REML estimation, but for datasets of at least 50 cases or arrangements with 6 or more observers, the differences between the methods are negligible, with deviations from the truth well below ±3%. For datasets up to 100 cases, it is most beneficial to increase the number of cases to improve the precision of the estimated random variations, whereas for datasets over 100 cases, an improvement in precision is most efficiently achieved by increasing the number of observers. For datasets of at least 50 cases, the standard error ranges between 30% or less with 3 observers down to 10% or less with 8 observers, and the differences in precision between the methods are negligible. The F test (PWD) is very anticonservative and should not be used, while the t test (RES) is reliable for datasets of at least 2×50 cases evaluated by 4 or more observers. The likelihoodratiotest (REML estimation) consistently indicates the significance of a difference in the random variation of an observer between two groups of cases, regardless of the number of cases, and regardless of the number of observers. If a statistical package to perform REML estimation is available, and the investigator feels confident using it, this is the preferred method for studies that involve less than 50 cases evaluated by less than 6 observers. Otherwise, the RES method is an excellent alternative, because of its straightforward implementation, its completeness with respect to the provided statistics, and its overall sufficient accuracy, precision, and reliability of the provided statistical test. If neither the RES method nor REML estimation can provide sufficient performance, either more observers or more cases must be included.

The cause of the artifact in 4slice helical computed tomography
View Description Hide DescriptionThe causes of the image artifacts in a 4slice helical computed tomography have been discussed as follows: (1) changeover in pairs of data used in zinterpolation, (2) sampling interval in z, and (3) the cone angle. This study analyzes the first two causes of the artifact and describes how the current algorithm [K. Taguchi and H. Aradate, Radiology 205P, 390 (1997); 205P, 618 (1997); Med. Phys. 25, 550–561 (1998); H. Hu, ibid. 26, 5–18 (1999); S. Schaller et al., IEEE Trans. Med. Imaging19, 822–834 (2000); K. Taguchi, Ph.D. thesis, University of Tsukuba, 2002] solves the problem. An interpolatedsinogram for a slice at the edge of a ball phantom shows discontinuity caused by the changeover. If we extend the streak artifact in the reconstructed image, it crosses the focus orbit at the corresponding projection angle. Applying z filtering can reduce such causes by its feathering effect and mixing data obtained by different cone angles; the best results are provided when z filtering is applied to densely sampled helical data.
