Index of content:
Volume 21, Issue 3, March 1994
21(1994); http://dx.doi.org/10.1118/1.597302View Description Hide Description
An iterative pencil beam algorithm for optimization of multidimensional radiation therapydose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time–dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavity and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.
Implementation of a three‐dimensional compensation system based on computed tomography generated surface contours and tissue inhomogeneities21(1994); http://dx.doi.org/10.1118/1.597303View Description Hide Description
A computed tomography (CT) based system that compensates for patient surface contour and internal tissue inhomogeneity was implemented in our clinic. The compensators are fabricated with a mixture of tin granules and bee’s wax. The tin/wax mixture was optimized for tin granule size and tin granule to wax ratio. The narrow beam attenuation coefficients were measured for 4‐, 6‐, 10‐, and 24‐MV photon beams. The compensator design and fabrication methodology were verified by measuring the dose distribution for a known surface contour irradiated with a compensated beam and for a known inhomogeneity that was submerged in a water phantom and irradiated with a compensated beam. For the surface contour, the uncompensated isodose levels varied by as much as 10% in the compensation plane and the compensator restored the isodose level to a variation of less than 1.3%. Measured and calculated doses for this surface contour were found to differ by less than 3.4%. For the inhomogeneity, the uncompensated isodose levels varied by 27% in the compensation plane and the compensator restored the isodose level to a variation of less than 1.5%. Measured and calculated doses for the known inhomogeneity were found to differ by less than 2%. Measurements of depth‐dose curves indicate that the presence of the compensator in the beam does not significantly increase the surface dose. Twenty‐six compensators have now been fabricated for clinical cases. In these patients, dose variations as great as 19% occurred in the plane of compensation prior to placing the compensator in the beam. Measured and calculated dose profiles with the compensators in place have been found to agree within 2.3%.
21(1994); http://dx.doi.org/10.1118/1.597383View Description Hide Description
To calculate electron beam dose distributions accurately, numerical methods of electron transport calculations must account for the statistical variation (or ‘‘straggling’’) in electron energy loss. This paper shows that the various energy straggling theories that are applicable to short path lengths all derive from a single statistical model, known as the compound Poisson process. This model in turn relies on three assumptions: (1) the number of energy‐loss events in a given path length is Poisson distributed; (2) events are mutually independent; and (3) each event has the same probability distribution for energy loss (i.e., the same energy‐loss cross section). Applying the principles of the compound Poisson process and using fast Fourier transforms, a new method for calculating energy‐loss spectra is developed. The spectra calculated using this method for 10, 20, and 30 MeV electrons incident on graphite and aluminum absorbers agreed with Monte Carlo simulations (E G S4) within 1% in the spectral peak. Also, stopping powers derived from the calculated spectra agreed within 1.2%, with stopping powers tabulated by the International Commission on Radiation Units and Measurements. Several numerical transport methods ‘‘propagate’’ the electron distribution (in position, direction, and energy) over small discrete increments of path length. Thus the propagation of our calculated spectra over multiple path length increments is investigated. For a low atomic number absorber (graphite in this case), calculated spectra agreed with E G S4 Monte Carlo simulations over the full electron range, provided the path length increments were sufficiently small (less than 0.5 g/cm2). It is concluded from these results that numerical methods of electron transport should restrict the size of path length increments to less than 0.5 g/cm2 if energy straggling is to be modeled accurately.
The use of a radiochromic detector for the determination of stereotactic radiosurgery dose characteristicsa)21(1994); http://dx.doi.org/10.1118/1.597384View Description Hide Description
The measurement of absorbed dose as well as dose distributions (profiles and isodose curves) for small radiation fields (as encountered in stereotactic surgery) has been difficult due to the usual large detector size or densitometer aperture (≳1 mm) relative to the radiation field (as small as 4 mm). The radiochromic direct‐imaging film, when read with a scanning laser microdensitometer (laser beam diameter 0.1 mm), overcomes this difficulty and has advantages over conventional film in providing improved precision, better tissue equivalence, greater dynamic range, higher spatial resolution, and room light handling. As a demonstration of suitability, the calibrated radiochromic film has been used to measure the dose characteristics for the 18‐, 14‐, 8‐, and 4‐mm fields from the gamma‐ray stereotactic surgery units at Mayo Clinic and the University of Pittsburgh. Intercomparisons of radiochromic film with conventional methods of dosimetry and vendor‐supplied computational dose planning system values indicate agreement to within ±2%. The dose, dose profiles, and isodose curves obtained with radiochromic film can provide high‐spatial‐resolution information of value for acceptance testing and quality control of dose measurement and/or calculation.
21(1994); http://dx.doi.org/10.1118/1.597385View Description Hide Description
Standard silver‐based films are usually too sensitive to be used as direct indicators of dose in dynamic radiosurgery because of optical saturation. This paper describes the use of a new radiochromic film to measure 6‐MV radiosurgery doses and dose distributions in a head phantom. Dose calibration of the radiochromic film was performed in the range of 2.3–50.2 Gy using light of 632‐ and 530‐nm wavelengths. Radiosurgery dose distributions were measured using the radiochromic film in a head phantom undergoing the same treatment as a patient, and were compared with the planned distributions. For an example case (nominal 2.0‐cm‐diam cone), film measurement verified the calculated dose distribution in one plane. The simple measurement technique described led to experimental uncertainties of ±0.1 cm for the 90% and 50% isodose lines, ±0.3 cm for the 20% line, and ±0.5 cm for the 10% line. Isocenter dose was measured with an uncertainty of ±3%. Refinements to the technique should allow more precise measurements. It is concluded that the radiochromic film, with some limitations, is a convenient and useful tool for dynamic radiosurgeryquality assurance.
21(1994); http://dx.doi.org/10.1118/1.597304View Description Hide Description
A computer‐assisted method for selecting beam orientation in a one‐step procedure is presented. Inverse and adjoint techniques are developed to obtain the best beam directions. Both methods rely on determining the ‘‘path of least resistance’’ to radiation from the tumor location to the surface of the section. The effectiveness of beam directions is then determined by monitoring the dose distribution along the section boundary. The inverse and adjoint calculations are performed for three tumor cases using a two‐dimensional discrete ordinates transport code. The proposed treatment plans from these calculations are verified against typical treatment plans. The new techniques improved the dose distribution in the treated section. The inverse calculations are useful in sections involving low‐density tissues. The adjoint technique can effectively deal with multiple target volumes and/or sections with complex geometry. The proposed method is potentially useful in selecting beam orientations for three‐dimensional planning systems and in determining beam intensities in rotational and conformal therapy.
21(1994); http://dx.doi.org/10.1118/1.597386View Description Hide Description
X‐ray fields that are shifted away from the conventional central axis exhibit alterations in output, beam profile, and beam energy. An extension of a conventional dose calculation algorithm to correct for these perturbations is presented. This algorithm employs the product of three functions describing the dose at the center of the field at d max, the relative off‐center dose at d max, and the relative dose at depth along a fanline passing through the point of interest. The nature of the problem is characterized, a basic data set necessary to support the algorithm is described and an abridged set of data that may assist in the development of an independent collimator dose calculation capability is presented. The appropriateness of this technique for both conventional and dynamically collimated fields is illustrated.
21(1994); http://dx.doi.org/10.1118/1.597305View Description Hide Description
The depth of dose maximum, d max, of megavoltage x‐ray beams was studied as a function of beam energy and field size for 6‐, 10‐, and 18‐MV x‐ray beams and field sizes ranging from 1×1 to 30×30 cm2. For a given beam energy, d max increases rapidly with increasing field size at small fields, reaches a maximum around 5×5 cm2 and then gradually decreases with increasing field size for large fields. Monte Carlo simulations combined with measurements verified that the effect observed at small field sizes is caused by in‐phantom scatter, while at large fields the effect is due to scatter contamination of the primary beam from the linac head. A comparison between the d max behavior of flattened beams to that of unflattened beams indicates that the d max decrease at large fields for flattened beams is caused mainly by contamination electrons which are produced in the flattening filter and further scattered by collimator jaws and air.
A spatial‐frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems21(1994); http://dx.doi.org/10.1118/1.597401View Description Hide Description
The detective quantum efficiency (DQE) is a system parameter that can be used to accurately describe imagenoise transfer characteristics through many imagingsystems. A simpler approach used by some investigators, particularly when evaluating new ideas and system designs, is to describe the system as a series of cascaded stages. Each stage may correspond to either an increase in the number of quanta (e.g., conversion from x‐ray to optical quanta in a radiographic screen), or a loss (a detection or coupling probability). The number of secondary quanta at each stage per incident primary quantum is given by the product of all preceding gains, and can be displayed graphically for convenient interpretation. The stage with the fewest quanta is called the ‘‘quantum sink,’’ limiting the pixel signal‐to‐noise ratio to less than the square root of the number of quanta per pixel. This conventional zero‐spatial‐frequency ‘‘quantum accounting diagram’’ (QAD), however, neglects the spatial spreading of secondary quanta and can seriously underestimate imagenoise. It is shown that this problem is avoided with the introduction of a spatial‐frequency dependent QAD, expressed as the product of the gains and squared modulation‐transfer functions (MTF) of each stage. A generalized expression is developed for the DQE of a cascaded imagingsystem that is dependent only on the gain, gain Poisson excess (related to the variance), and MTF, of each stage. A direct relationship is then shown to exist between the DQE and values in the QAD. The QAD of a hypothetical system consisting of a charge‐coupled device camera and a scintillating screen is evaluated as an illustrative example. The conventional zero‐frequency analysis suggests two quantum sinks occur with approximately equal importance: one in the number of x rays, and one in the number of optical quanta. The spatial‐frequency dependent analysis, however, shows the optical quantum sink becomes severe and dominates at nonzero frequencies. The necessary increase in gain or optical numerical aperture required to prevent the optical quantum sink for spatial frequencies of interest is determined from the QAD analysis. The visual impact of this nonzero spatial‐frequency quantum sink is shown in images generated using a Monte Carlo simulation of the cascading process.
Longitudinal resolution in volumetric x‐ray computerized tomography—Analytical comparison between conventional and helical computerized tomography21(1994); http://dx.doi.org/10.1118/1.597306View Description Hide Description
The primary advantage of helical computerized tomography(CT) is the capability of scanning a complete anatomical volume in a single breath hold. Due to the table motion and subsequent interpolation process, the slice sensitivity profile (SSP) in helical CT is worse than the response function of the detector array. In this paper, image longitudinal resolution in volumetric x‐ray CT is analytically characterized, and a comparison made between conventional and helical CT. First, the SSPs are derived for both conventional and helical CT with the half‐scan interpolation method under the condition that the table increment and detectorcollimation are the same. Then, the corresponding transfer functions are obtained for bandwidth determination, which directly describe the spatial resolution. Both one‐tenth‐cutoff and mean‐square‐root measures are used to quantify the bandwidth. Although it appears that broadening the SSP in helical CT could adversely affect longitudinal resolution, it is proved that for a given x‐ray dose, helical CT allows substantially better longitudinal resolution than conventional CT due to its inherent retrospective reconstruction capability. To make full use of the potential of helical CT scan data, it is recommended that about five slices be reconstructed per table increment. Helical CT is superior in applications requiring a high longitudinal resolution.
21(1994); http://dx.doi.org/10.1118/1.597388View Description Hide Description
A new scatter compensation technique for computed radiography based on posterior beam stop (PBS) sampled scatter measurements and the bicubic spline interpolation technique was proposed. Using only a single exposure, both the clinical image and an array of scatter measurements, which were interpolated into a smooth scatter‐only image, were simultaneously acquired. The scatter was subtracted from the clinical image to generate the primary‐only image. To gauge the accuracy of scatter estimation, both quantitative and interpolation errors were evaluated. The PBS measurements were compared against the standard beam stop method at 16 locations in an anatomical phantom, resulting in quantitative errors of 2.7% relative to the scatter or 6.8% relative to the primary. Also measured were the interpolation error over 64 interpolation sample locations and 64 midpoint sample locations in the anatomical phantom. The combined interpolation error was 1.9% relative to the scatter or 8.0% relative to the primary. At the interpolation sample locations, the errors were identical between the phantom radiograph and digital portable chest radiographs from five patients. By summing the quantitative and interpolation errors in quadrature, the overall error of the PBS SISTER (scatter interpolation‐subtraction technique for radiography) method was 3.3% relative to the scatter or 10% relative to the primary, which was adequate for dual‐energy imaging purposes (less than 10% error relative to the scatter or 20% relative to the primary). The change of image contrast, noise, and signal‐to‐noise ratio (SNR) at six locations in the anatomical phantom were quantitatively analyzed. Contrast and noise were equally enhanced in all anatomical regions, resulting in approximately the same SNR before and after compensation. The average contrast over all six locations increased 2.8 times, average noise increased 4.9 times, and average SNR barely decreased to 99%. This technique therefore provided accurate scatter compensation by custom measurements of each patient, preserved the SNR, required only one exposure with no dose increase, and performed at low computational cost.
Computerized detection of masses in digital mammograms: Automated alignment of breast images and its effect on bilateral‐subtraction technique21(1994); http://dx.doi.org/10.1118/1.597307View Description Hide Description
An automated technique for the alignment of right and left breast images has been developed for use in the computerized analysis of bilateral breast images. In this technique, the breast region is first identified in each digital mammogram by use of histogram analysis and morphological filtering operations. The anterior portions of the tracked breast border and computer‐identified nipple positions are selected as landmarks for use in image registration. The paired right and left breast images, either from mediolateral oblique or craniocaudal views, are then registered relative to each other by use of a least‐squares matching method. This automated alignment technique has been applied to our computerized detection scheme that employs a nonlinear bilateral‐subtraction method for the initial identification of possible masses. The effectiveness of using bilateral subtraction in identifying asymmetries between corresponding right and left breast images is examined by comparing detection performances obtained with various computer‐simulated misalignments of 40 pairs of clinical mammograms. Based on free‐response receiver operating characteristic and regression analyses, the detection performance obtained with the automated alignment technique was found to be higher than that obtained with simulated misalignments. Detection performance decreased gradually as the amount of simulated misalignment increased. These results indicate that automatic alignment of breast images is possible and that mass‐detection performance appears to improve with the inclusion of asymmetric anatomic information but is not sensitive to slight misalignment.
21(1994); http://dx.doi.org/10.1118/1.597308View Description Hide Description
An automated digital image subtraction technique for temporally sequential chest images has been developed in order to aid radiologists in the detection of interval changes. A number of small regions of interest (ROIs) are selected automatically in the lung areas of two temporally sequential chest images. A local matching, based on a cross‐correlation method, is performed on each pair of corresponding ROIs in order to determine shift values for the coordinates of two images. A proper warping of x,y coordinates is obtained by fitting two‐dimensional polynomials to the distributions of shift values. One of the images is warped and then subtracted from the other. Forty six pairs of chest images (42 with interval changes and 4 without interval change) were processed using this method. The subtraction images were able to enhance various important interval changes, such as differences in the size of tumor masses, changes in heart size, and changes in pulmonary infiltrates or pleural effusions. Approximately 70% of the pairs showed reasonably good registration.
21(1994); http://dx.doi.org/10.1118/1.597387View Description Hide Description
Spatial resolutionproperties of a 2048×2048 matrix image intensifier (II) TV based real‐time digital radiography (DR) system were investigated. The presampling modulation transfer function(MTF), which includes the unsharpness of the detector and the blurring effect of the sampling aperture, was measured by a slit method. Also determined was the limiting resolution using a bar pattern. It was found that, the spatial resolution in this system is substantially improved relative to previous II‐TV based DR systems, and is comparable or even superior to that in a computed radiography system depending on the imaging plate employed. However, the presampling MTF for 2048×2048 matrix is comparable to that for 1024×1024 matrix in this DR system, because the same sampling aperture is assumed to be used for both matrices. Even under these conditions obtained the improved clinical image since the Nyquist frequency is doubled for 2048×2048 matrix. It should be noted that the resolution property in the II‐TV based DR system depends on the signal current from the TV image pickup tube (level of image pixel value) and also on the size of the iris in the TV lens. We must pay attention to these parameters when acquiring clinical images and evaluating the resolution properties. Finally, it was demonstrated that smaller focus than that used in a screen–film system can be employed in the DR system due to its high sensitivity, so the geometric unsharpness can be reduced. Therefore, the image resolution of our system was found to be superior to a screen–film system at some geometric magnification factors.
21(1994); http://dx.doi.org/10.1118/1.597309View Description Hide Description
The x‐ray fovea (U.S. patents pending) is a device for reducing x‐ray dose to patients and operators during x‐ray fluoroscopy. It consists of a semitransparent collimator with an open, circular, central hole. The fovea collimator is placed at the exit of the x‐ray tube, and the attenuation of the peripheral x‐ray beam reduces x‐ray exposure to patients and operators. The shadow caused by the x‐ray fovea can be compensated using real‐time image processing hardware. Accurate compensation is demonstrated for both linearly and logarithmically acquired images using a model that accounts for beam hardening in the fovea collimator. The central fovea region has improved image quality due to reduced scatter and veiling glare from the periphery. From beam‐stop measurements, a 40% reduction in scatter plus veiling glare is measured using the fovea. A contrast improvement ratio of 1.5 is measured throughout the central region. In the compensated periphery, noise is increased by a factor of 1.66 because fewer photons are detected, but a small amount of temporal filtering compensates this degradation. The Roentgen area product (RAP) exposure to patients is reduced by ≊70%, while scattered exposure to operators is reduced by ≊60%.
21(1994); http://dx.doi.org/10.1118/1.597310View Description Hide Description
A new method for computing the modulation transfer function(MTF) of magnetic resonance(MR)imagers is presented. Previous attempts to compute the MTF of MRimagers used nonlinear magnitude reconstructed images, resulting in erroneous MTFs. By using complex domain images, the new method produces predisplay MTFs which describe the spatial frequency transfer characteristics of the entire image formation process, except the magnitude operator, eliminating the artifacts previously found in MRimagerMTFs. The use of complex domain images results in two‐sided MTFs which differentiate the positive and negative frequencies associated with positive and negative phase encoding or positive and negative time relative to the echo formation. Experimental results are presented which confirm the theoretically predicted form of MRimagerMTFs and the need for two‐sided MTFs.