Volume 16, Issue 5, September 1989
Index of content:

On the use of effective dose in the treatment planning of high linear‐energy‐transfer radiation
View Description Hide DescriptionTreatment planning for conventional radiations is based on the assumption that the effect of a combination of doses at any location in the treatment field in a multibeam plan will be equivalent to that of a single dose made up of the total sum of the doses delivered to that location. This is obviously valid for conventional low linear‐energy‐transfer (LET) radiations when the dose contributions from various beam components are associated with the same relative biological effectiveness (RBE) value of unity. However, this is not the case for the new generation of charged particle beams whose RBEs have been shown to vary significantly with depth. A concept of effective dose, defined as the mathematical product of physical dose and RBE value evaluated for an effect level, is developed for the treatment planning of these high‐LET particle radiations. Based on radiobiological results in mixed radiation experiments, it is shown that these effective doses are linearly additive like physical doses and hence, can be used directly for general treatment planning using linear algorithms already developed for the use of physical doses. This is illustrated using examples of simplified one‐dimensional plans for the TRIUMF pionbeam.

Electron dose rate and photon contamination in electron arc therapy
View Description Hide DescriptionThe electron dose rate at the depth of dose maximum d _{max} and the photon contamination are discussed as a function of several parameters of the rotational electron beam. A pseudoarc technique with an angular increment of 10° and a constant number of monitor units per each stationary electron field was used in our experiments. The electron dose rate is defined as the electron dose at a given point in phantom divided by the number of monitor units given for any one stationary electron beam. For a given depth of isocenter d _{ i } the electron dose rates at d _{max} are linearly dependent on the nominal field width w, while for a given w the dose rates are inversely proportional to d _{ i }. The dose rates for rotational electron beams with different d _{ i } are related through the inverse square law provided that the two beams have (d _{ i },w) combinations which give the same characteristic angle β. The photon dose at the isocenter depends on the arc angle α, field width w, and isocenter depth d _{ i }. For constant w and d _{ i } the photon dose at isocenter is proportional to α, for constant α and w it is proportional to d _{ i }, and for constant α and d _{ i } it is inversely proportional to w. The w and d _{ i } dependence implies that for the same α the photon dose at the isocenter is inversely proportional to the electron dose rate at d _{max}.

Electron dose calculation using multiple‐scattering theory: Second‐order multiple‐scattering theory
View Description Hide DescriptionThis article is part of a series on the calculation of electron dose using multiple‐scattering theory. It presents systematically the second‐order multiple‐scattering theory which is a generalization of the (first‐order) Fermi–Eyges theory, outlining its derivation and giving explicit formulas for its defining functions. The predictions of the Fermi–Eyges theory and of the second‐order theory are compared with modified Monte Carlo calculations, demonstrating the increased accuracy of the latter multiple‐scattering theory. We derive and compare broad‐beam angular distributions for the two theories, and note the effect of large‐angle scattering upon dose profiles. Finally, we present the second‐order theory in Fourier‐transformed space, which is appropriate to a high‐speed dose‐calculation algorithm using the fast Fourier transform (FFT) technique.

Electron dose calculation using multiple‐scattering theory: Thin planar inhomogeneities
View Description Hide DescriptionIn this article in our series on electron dose calculation using multiple‐scattering theory, we apply the Fermi–Eyges theory to the problem of a thin planar inhomogeneity present in an otherwise‐layered medium. We derive expressions for the distribution function P and the location distribution L (which multiplied by the restricted mass collision stopping power is the dose directly deposited by the primary electrons) for various types of incident beams: a completely arbitrary distribution, a Gaussian point source, a pencil beam, an isotropic point source, and a broad parallel beam. We show how divergent‐beam dose distributions can be determined from parallel‐beam calculations, through use of equivalent configurations dependent upon the depth of dose calculation. Also, we indicate how this work can be applied to the design of wedges (or ‘‘compensators’’) for beam shaping to provide desired dose distributions or to match juxtaposed radiation fields. Explicit formulas for thin plates are then worked out, and we examine the appearance of hot and cold spots distal to the edge of a localized inhomogeneity, for thin half‐slabs and for narrow strips. Finally, considering the case of a thin straight wedge‐shaped inhomogeneity, we theoretically discover the phenomenon of a ‘‘focused hot spot’’ without an accompanying cold spot, and suggest the design of a ‘‘multiple‐scattering lens’’.

Tissue doses from radiotherapy of cancer of the uterine cervix
View Description Hide DescriptionFor use in an epidemiologic study of subsequent tumors, absorbed doses from brachytherapy and external beam radiotherapy were measured and calculated for various tissues of patients treated for cancer of the uterine cervix. External beams included orthovoltage x rays (1.9 and 3.0 mm Cu half‐value layer), cobalt‐60 gamma rays, 2 MV x rays, and 25 MV x rays. The brachytherapysources were encapsulated radium. Measurements were made in an Alderson anthropomorphic phantom and a water phantom; calculations were made using a Monte Carlo technique or standard radiotherapy methods. Depending upon stage of disease and radiation energy, the absorbed doses (cGy) from typical treatment regimes to tissues of interest were: ovaries, 1400–5200; stomach, 130–320; kidneys, 120–310; pancreas, 100–260; lungs, 22–48; breasts, 19–52; thyroid, 6–17; salivary glands, 4–11; brain, 2–7, and total active bone marrow, 320–1100. The lower values of each range were for stage I of the disease.

Low‐energy imaging with high‐energy bremsstrahlung beams
View Description Hide DescriptionA method is described for portal imaging with low‐energy (≲150 keV) photons from a radiotherapy accelerator operating in a diagnostic mode. The low‐energy photons are produced in the bremsstrahlung process, but are normally filtered out by thick high atomic number (Z) target materials. This absorption can be reduced by choosing a low Z target with the minimum thickness required to stop the electrons in the target. If, in addition, the operating energy is kept low (∼5 MeV) and the flattening filter is removed, low‐energy photonimages can be produced from the broad spectrum of photonenergies by using standard diagnostic radiology high‐Z fluorescent screen/film systems that strongly absorb at low but not high photonenergies. Motion artifacts can then be avoided since only a small dose is required for such a procedure.

Two interpolating filters for scatter estimation
View Description Hide DescriptionWe have previously reported on a dual‐measurement sample‐and‐estimate technique for scatter correction. In this paper, we present a scatter‐correction technique that uses the previous sampling scheme but a different method of estimation. To provide samples of the scatter directly, an array of small, uniformly spaced lead disks is placed immediately before the object during only the first measurement. Interpolating from these samples we form an estimate of the scatter. We subtract this estimate from the second measurement to form a scatter‐corrected image. Previously, we used least‐squares interpolation to estimate the scatter. Because the samples are uniformly spaced, classical sampling theory motivated the investigation of interpolating filters for scatter estimation. To form the scatter image, we convolved the sample set with two different interpolating filters—a sinc function from classical sampling theory and a jinc function because the scatter function is radially symmetric. Using phantoms as objects, we applied both filters for scatter correction in vessel imaging and energy‐subtraction imaging. Initial corrected images contained an artifact attributed to aliasing. We modified the filter widths to reduce the aliasing. Although improvements in image quality were measured and the artifact was less pronounced, the artifact was still present. We present the phantom results obtained with this class of filters and discuss methods for its improved performance.

A review of mammography test objects for the calibration of resolution, contrast, and exposure
View Description Hide DescriptionMandated and voluntary accreditation and quality control programs for mammography require the use of standardized mammography test objects. We evaluated eleven commercially available test objects and three prototype test objects, comparing them with respect to their resolution targets, contrast targets, and the dose they required when imaged by the same automatic exposure meter. Ion chamber and/or thermoluminescent dosimeter measurements of exposure were made with each test object, while attenuation was measured for seven. Measurements of dosage using acrylic (5 test objects) and tissue equivalent epoxy (9 test objects) showed as much as a 400% variation in the radiation supplied by the same automatic exposure device when differences in thicknesses of test objects were normalized. Speck visibility was as dependent on the composition of the specks and of the surrounding material as on the size of the specks. Contrast targets were adequate in only three test objects. Optical density differences between images of a 4‐cm‐thick breast and of different test object materials, also 4 cm in thickness, exposed to the same radiation, imply that untested acrylic or epoxy resin materials should not used in the calibration of automatic exposure controls.

A technique for measuring regional bone mineral density in human lumbar vertebral bodies
View Description Hide DescriptionA method for measuring the regional bone mineral density (rBMD) in human lumbar vertebral bodies using a series of contiguous computed tomographyimages, each 1 mm thick, is fully described. The technique has a sample volume of 0.004 cm^{3}, a sample spacing of 0.8 × 0.8 × 1.0 mm, and results in a bone marrow radiation dose of 1.59 to 2.75 rads (0.016–0.028 Gy). The use of physical density (mg/cm^{3}) is introduced and the measurement noise (0.7–1.3%), accuracy (2.7%), and serial precision (0.2%) have been evaluated i n v i t r ousing appropriate phantoms. The corresponding percentage errors for accuracy and precision relative to K_{2}HPO_{4} concentration were 6.9% and 2.0%, respectively. A multiple region density measurement is described and evaluated.

Effect of finite phosphor thickness on detective quantum efficiency
View Description Hide DescriptionIn this paper we describe theoretically the relationship between the finite thickness of a phosphor screen and its spatial‐frequency‐dependent detective quantum efficiency DQE( f ). The finite thickness of the screen causes a variation in both the total number of light quanta emitted from the screen in a burst from a given x‐ray interaction and in the spatial distribution of the quanta within the light burst [i.e., shape or point spread function (PSF) of the light burst]. The variation in magnitude of the burst gives rise to a spatial‐frequency‐independent reduction in DQE, characterized by the scintillation efficiency A _{ S }. The variation in PSF causes a roll off in DQE with increasing spatial frequency which we have characterized by the function R _{ C } ( f ). Both A _{ S } and R _{ C } ( f ) can be determined from the moments of the distribution of the spatial Fourier spectrum of light bursts emitted from the phosphor and thus they are related: A _{ S } is a scaling factor for R _{ C } ( f ). Our theory predicts that it is necessary for all light bursts which appear at the output to have the same magnitude to maximize A _{ S } and the same shape to maximize R _{ C } ( f ). These requirements can lead to the result that the fluorescent screen with the highest modulation transfer function will not necessarily have the highest DQE( f ) even at high spatial frequencies.

Eddy current disruption: Effect on nuclear magnetic resonance coil impedance and power loss
View Description Hide DescriptionWe present a theoretical development and experimental verification of a description of power loss and sample resistance for a lossy sample in a nuclear magnetic resonanceradio frequency coil for a sample geometry where the eddy current streamlines are disrupted from their usually assumed circular paths. Specifically treated is the case of a lossy hemisphere. The problem is solved for two orientations; with the induction parallel and perpendicular to the flat surface of the hemisphere. Results of this analysis as well as those for the full sphere as presented by Hoult and Lauterbur are compared with observation for a variety of sample conductivities and orientation.

Effects of axial spatial resolution and sampling on object detectability and contrast for multiplanar positron emission tomography
View Description Hide DescriptionA multiplanar positron emission tomography(PET)system is simulated using Gaussian curves to model the axial point spread functions (PSFs) of the planes to study the effects of resolution and sampling. Poor spatial resolution or insufficient sampling may cause deleterious data losses or artifacts in the reconstructed image. For a multiplanar PETsystem with an axial full width at half‐maximum (FWHM) of 6 mm and a 12 to 13 mm ring separation, a ripple in sensitivity of 9% is observed. A 1 mm object placed at the central direct plane results in detection of 59% of the signal in that plane. The theoretical observed contrast of a 3 mm object positioned at the center plane is 25% of the true contrast and decreases to 24% when the object is positioned between the central direct and cross planes. A PETsystem with an axial FWHM of 12 mm and a ring separation of 5–6 mm has a uniform sensitivity. A 1 mm object placed at the central direct plane detects 14% of the object signal in that plane. The theoretical observed contrast for a 3 mm object is 13% of true contrast when the object is positioned between the central direct and cross planes. It should be noted that all dimensions refer to the z direction through the center of the gantry in the simulated multiplanar system. The uniform sensitivity due to wider axial FWHMs decreases the amount of data loss for inter‐ring gaps; however, the blurring associated with wider FWHMs decreases observed contrast. This tradeoff between narrow or wide FWHMs and small or large inter‐ring gaps must be considered carefully in the design of a multiplanar PETsystem.

Measurement of replacement factors for a parallel‐plate chamber
View Description Hide DescriptionWe have measured the replacement correction factors (P _{repl}) for a PTW/Markus parallel plate chamber at mean incident electron energies of 3.1, 4.4, 8.9, 13.0, 16.3, and 18.8 MeV. The factors are significantly different from unity at low energies.

The dosimetric properties of an intraoperative radiation therapy applicator system for a Mevatron‐80
View Description Hide DescriptionAn applicator system for intraoperative radiation therapy has been fabricated which does not require physical docking with the accelerator. A dosimetric study has been completed which documents the properties of this system for a variety of electron beam energies, applicator sizes, collimator settings, both primary and secondary, and source–surface distance (SSD) settings. Sensitivity of the system to common misalignment errors was also determined. Results indicate (a) applicator leakage of less than 5%, (b) beam flatness to within plus or minus 5% at the d _{MAX} with a single primary collimator setting, (c) smooth changes in output with cone size, beam energy and SSD, and (d) negligible changes in dose distributions within alignment errors permitted by the system.

Scatter factor corrections for elongated fields
View Description Hide DescriptionMeasurements have been made to determine scatter factor corrections for elongated fields of Cobalt‐60 and for nominal linear accelerator energies of 6 MV (Siemens Mevatron 67) and 18 MV (AECL Therac 20). It was found that for every energy the collimatorscatter factor varies by 2% or more as the field length‐to‐width ratio increases beyond 3:1. The phantom scatter factor is independent of which collimator pair is elongated at these energies. For 18 MV photons it was found that the collimatorscatter factor is complicated by field‐size‐dependent backscatter into the beam monitor.

Equations for N _{gas} and N _{air} in terms of N _{ X } and N _{ K }
View Description Hide DescriptionTask Group 21 of the American Association of Physicists in Medicine defined the cavity‐gas calibration factor N _{gas} for ionization chambers in a protocol for radiotherapydosimetry published in this journal [Med. Phys. 1 0, 741 (1983)]. Later, Schulz e t a l., [Med. Phys. 1 3, 755 (1986)] published a letter of clarification that proposed a revised equation for N _{gas} in which the effect of atmospheric humidity was specifically dealt with. The present report points out errors in both of those presentations of the N _{gas}equation, and derives formulations for cases where the standardization laboratory does or does not correct for ambient humidity during chamber calibration. In the case where humidity is corrected for, the resulting quantity is more properly called ‘‘N _{air}.’’ The N _{gas}equation is stated in terms of the air kerma calibration factor N _{ K } as well as the more familiar exposure calibration factor N _{ X }.

Lead shielding thickness for dose reduction of 5 MeV electrons
View Description Hide DescriptionThe relative percent intensity reduction by lead (Pb) of 5 MeV electrons produced by Siemens Mevatron 77/74 for 5 cm diameter, 10×10, 15×15, and 20×20 cm^{2}cones both with and without buildup is measured. The thickness of lead (Pb) required to attenuate the intensity of the primary electron beam to 95% and 98% depends upon the cone size and upon the depth in phantom at which transmission measurements are made.

Multiphoton, time‐of‐flight three‐dimensional radionuclide imaging
View Description Hide DescriptionA method for applying time‐of‐flight (TOF) information to the three‐dimensional (3‐D) localization of multiple‐photon‐emitting radionuclides is presented. The same principle used for TOF imaging of positron annihilation photons is suggested for use with nuclides that emit two photons (gamma or x rays) in near coincidence. Two photons originating from the same decay event are detected. The locations at which they are detected become the foci of a hyperbola described by the difference in their path length. If one detector is collimated a line is established by the photon it detects, which intersects the hyperbola at the origin of the event. Should TOF imaging become a reality, this technique would extend its usefulness to nuclides that do not emit positrons.

Improved detectability in low signal‐to‐noise ratio magnetic resonance images by means of a phase‐corrected real reconstruction
View Description Hide DescriptionWe show that for magnetic resonance(MR)images with signal‐to‐noise ratio (SNR)<2 it is advantageous to use a phase‐corrected real reconstruction, rather than the more usual magnitude reconstruction. We discuss the results of the phase correction algorithm used to experimentally verify the result. We supplement the existing literature by presenting closed form expressions (in an MR context) for the probability distribution and first moments of the signal resulting from a magnitude reconstruction.

Image formats: Five years after the AAPM standard for digital image interchange
View Description Hide DescriptionThe publication of AAPM Report No. 10 was the first attempt to standardize image formats in the medical imaging community. Since then, three other groups have formed (CART—the Scandinavian collaboration for Computer Assisted Radiation Therapytreatment planning; ACR–NEMA, a collaboration whose purpose is to formulate a standard digital interface to medical imaging equipment; and COST B2 Nuclear Medicine Project a European collaboration whose purpose is to define a format for digital image exchange in Nuclear Medicine). The AAPM format uses key‐value pairs in plain text to keep track of all information associated with a particular image. The radiation oncology community in the U.S. has been defining key‐value pairs for use with CT, nuclear medicine and magnetic resonance (MR)images. The COST B2 Nuclear Medicine Project has also adopted this format and together with the Australian/New Zealand Society of Nuclear Medicine Technical Standards Sub‐Committee which has also adopted this format, has defined an initial set of key‐value pairs for Nuclear Medicineimages. Additionally, both ACR–NEMA and CART have been defining fields for use with the same types of images. The CART collaboration has introduced a database which is available electronically, but is maintained by a group of individuals. ACR–NEMA operates through committee meetings. The COST B2 Nuclear Medicine Project operates through electronic (and postal where necessary) mail. To insure a consistent set of field names in such a rapidly developing arena requires the use of a server rather than a committee. Via a server a person would inquire if a particular field had been defined. If so, the defined name would be returned. If not, the person would be given the opportunity to define the field. The next inquiry would return the previously defined field. As new modalities are added to the imaging repetoire, it would be easier and faster to ensure the consistency and adequacy of the database; e.g., in the present version of its standard, the ACR–NEMA fields are adequate for CT but there are very few fields suitable for describing the parameters associated with nuclear medicine and MRimages.