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Volume 22, Issue 8, August 1995

Influence of blood vessels on the measurement of hemoglobin oxygenation as determined by time‐resolved reflectance spectroscopy
View Description Hide DescriptionWe report the development of a heterogeneous resin‐tube model to study the influence of blood vessels on the apparent absorption of the system, μ_{ a }(sys), using a time‐resolved technique. The experimental results show that μ_{ a }(sys) depends on the absorption inside the tubes, μ_{ a }(tube), tube diameters, and tube‐to‐sample volume ratios. A mathematical expression relating μ_{ a }(sys) and μ_{ a }(tube) is derived based on the experimental results and is verified by time‐resolved Monte Carlo simulations for heterogeneous models. This analytical formula predicts that the apparent absorption coefficient measured on a biological organ is a volume‐weighted sum of the absorption coefficients of different absorbing components. We present some apparent absorption coefficients measured in vivo in animals and humans and discuss improved algorithms that calculate the hemoglobin saturation by including background‐tissue absorption and blood vessel distribution.

Determination of 3D imaging geometry and object configurations from two biplane views: An enhancement of the Metz–Fencil technique
View Description Hide DescriptionWe present a new technique based on the method developed by Metz and Fencil for estimation of the 3D imaging geometry and 3D object configurations from biplane angiographic acquisitions. The new method employs the 3D configuration of points calculated by the Metz–Fencil technique as an initial estimate. A 3D Procrustes algorithm is employed to translate, rotate, and scale the configuration until it aligns optimally with the set of lines that connects a focal spot with the corresponding set of image points. This alignment procedure is applied independently for each view. The rotation and translation that relate the two aligned data sets are then determined by an additional 3D Procrustes calculation. These steps are applied iteratively. Evaluations were based on Monte Carlo simulation and phantom studies. With this new technique, the mean absolute errors in magnification, in the relative position of the points, and in the angles defining the rotation and translation matrices were approximately 3.0%, 1.5 mm, and 5° and 3°, respectively, for rms input errors in the image data up to 2.0 pixels (0.7 mm). Errors in the results can be as small as 0.5%, 0.16 mm, 0.6°, and 0.3°, respectively, if input image‐data error is 0.035 mm. The improvement of the Metz–Fencil technique described here may provide a basis for precise estimation of the biplane imaging geometry and the 3D positions of vessel bifurcation points.

The effect of fat on the coherent‐to‐Compton scattering ratio in the calcaneus: A computational analysis
View Description Hide DescriptionThe coherent‐to‐Compton scattering ratio (CCSR) is a technique that has been proposed for measuring trabecular bone mineral density (TBMD). This paper investigates the effect of fat on the CCSR and its correlation to the error in TBMD measurements. It is a computational study to determine the relationship between the magnitude of fat error and the momentum‐transfer variable x, which represents the incident photon energy and the scattering angle. Variation in fat content contributes significantly to the error in CCSR measurements. When employing a typical ^{241}Am source (E _{γ}=59.45 keV), the resulting error decreases with increasing momentum‐transfer variable or angle. For example, the error ranges from +14 mg/cc at an angle of 45° (x=18.3) to +3 mg/cc at an angle of 135° (x=44.3) for an osteoporotic trabecular region (100 mg/cc mineral) of a calcaneus that contains 6% less fat than a calibration standard. The error is about 0.3–1.2 mg/cc less for regions containing 2–3× more bone mineral and is reduced and opposite in sign for regions containing about 7% more fat than the calibration standards (e.g., −9 mg/cc at 45° and −1.5 mg/cc at 135°). Others have shown that the intrinsic sensitivity of the CCSR method for measuring TBMD at a given photon energy generally increases with increasing detector angle. Thus large angles are advantageous both for reduced sensitivity to fat variation and increased sensitivity to bone mineral variation. The primary disadvantage is reduced count rates that degrade precision unless long counting times are employed. For experimental studies, a compromise angle must be chosen to insure adequate counting statistics for reasonable precision and examination times while providing moderate mineral sensitivity and moderate fat error.

The spectrum and angular distribution of x rays scattered from a water phantom
View Description Hide DescriptionTo calculate the response of an image receptor to the x rays emerging from a scattering medium, it is necessary to know the x‐ray spectrum and intensity as a function of the angle of incidence on the receptor. To permit this calculation for any x‐ray spectrum incident on a medium, these functions must be known for monoenergetic x rays. For monoenergetic x rays in the range 20–70 keV we have measured with a high‐purity germanium detector the spectrum and intensity of x rays emitted from a water phantom at angles of 0°–50° to the direction of the primary beam. The spectrum and intensity of emitted x rays have also been calculated by the Monte Carlo method. At small exit angles, most of the x rays have energies close to the incident energy. As the exit angle increases, the fraction of multiply scattered x rays increases. At very large exit angles, the dominant feature of the spectrum is the peak due to these multiply scattered x rays. For small scattering angles the Monte Carlo calculations are in good agreement with the measurements over the range of energies. For large scattering angles the scattered photon fluence predicted by Monte Carlo modeling is consistently lower than the measurement in the region just below the full energy peak. The cause of the discrepancies is not fully understood, but cannot be accounted for by Compton broadening alone. An alternate approach to model incoherent scattering is proposed.

Tree structured wavelet transform segmentation of microcalcifications in digital mammography
View Description Hide DescriptionA novel multistage algorithm is proposed for the automatic segmentation of microcalcification clusters (MCCs) in digital mammography. First, a previously reported tree structured nonlinear filter is proposed for suppressing image noise, while preserving image details, to potentially reduce the false positive (FP) detection rate for MCCs. Second, a tree structured wavelet transform (TSWT) is applied to the images for microcalcification segmentation. The TSWT employs quadrature mirror filters as basic subunits for both multiresolution decomposition and reconstruction processes, where selective reconstruction of subimages is used to segment MCCs. Third, automatic linear scaling is then used to display the image of the segmented MCCs on a computer monitor for interpretation. The proposed algorithms were applied to an image database of 100 single view mammograms at a resolution of 105 μm and 12 bits deep (4096 gray levels). The database contained 50 cases of biopsy proven malignant MCCs, 8 benign cases, and 42 normal cases. The measured sensitivity (true positive detection rate) was 94% with a low FP detection rate of 1.6 MCCs/image. The image details of the segmented MCCs were reasonably well preserved, for microcalcification of less than 500 μm, with good delineation of the extent of the microcalcification clusters for each case based on visual criteria.

Bayesian image estimation of digital chest radiography: Interdependence of noise, resolution, and scatter fraction
View Description Hide DescriptionPreviously, it has been shown that Bayesian image estimation (BIE) can reduce the effects of scattered radiation and improve contrast‐to‐noise ratios (CNR) in digital radiographs of anthropomorphic chest phantoms by improving contrast while constraining noise. Here, the use of BIE as a noise reduction technique is reported. An anthropomorphic phantom was imaged with a previously calibrated photostimulable phosphor system using standard bedside chest radiography protocols. The Bayesian technique was then used to process this image. BIE incorporates a radial exponential convolution scatter model with two adjustable parameters. In previous reports, these parameters were optimized to reduce the residual fraction of scattered radiation in the processed image. Here, the parameters were adjusted to evaluate the potential of BIE to reduce image noise. While the full width at half maximum of the scatter model was held constant, the magnitude was varied. Evaluation was based on residual scatter fractions and CNR. The magnitude of the kernel in the scatter model was varied from 0.0 to 2.5 in steps of 0.5. Previously, it was found that an ‘‘ideal’’ scatter kernel magnitude of 2.33 provided a minimum residual scatter fraction. This magnitude corresponds to the average scatter‐to‐primary ratio in the chest radiograph. As the magnitude was increased, the residual scatter fraction decreased and the CNR increased in both the lungs and the mediastinum. However, as the magnitude was decreased, the percent noise also decreased; therefore, a lower magnitude kernel reduces noise. By varying the magnitude of the kernel used, differing amounts of noise reduction and contrast enhancement can be obtained. These results demonstrate that Bayesian image estimation can be used to both increase contrast and decrease noise in digital chest radiography.

Energy imparted in computed tomography
View Description Hide DescriptionMonte Carlo techniques were used to study a generalized CT dose index D(r) as a function of the radius r of a cylindrical dosimetry phantom. The relationship between D(r) and the energy deposited in the phantom was investigated. For a specified x‐ray spectrum, the energy imparted to head or body dosimetry phantoms can be obtained from measured D(r) values. This approach to CTdosimetry permits the energy imparted to phantoms (or patients) to be determined as CT technique parameters, or type of scanner, are changed.

A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm
View Description Hide DescriptionWe have derived a maximum a posteriori (MAP) approach for iterative reconstruction based on a weighted least‐squares conjugate gradient (WLS‐CG) algorithm. The WLS‐CG algorithm has been shown to have initial convergence rates up to 10× faster than the maximum‐likelihood expectation maximization (ML‐EM) algorithm, but WLS‐CG suffers from rapidly increasing image noise at higher iteration numbers. In our MAP‐CG algorithm, the increasing noise is controlled by a Gibbs smoothing prior, resulting in stable, convergent solutions. Our formulation assumes a Gaussian noise model for the likelihood function. When a linear transformation of the pixel space is performed (the ‘‘relaxation’’ acceleration method), the MAP‐CG algorithm obtains a low‐noise, stable solution (one that does not change with further iterations) in 10–30 iterations, compared to 100–200 iterations for MAP‐EM. Each iteration of MAP‐CG requires approximately the same amount of processing time as one iteration of ML‐EM or MAP‐EM. We show that the use of an initial image estimate obtained from a single iteration of the Chang method helps the algorithm to converge faster when acceleration is not used, but does not help when acceleration is applied. While both the WLS‐CG and MAP‐CG methods suffer from the potential for obtaining negative pixel values in the iterated image estimates, the use of the Gibbs prior substantially reduces the number of pixels with negative values and restricts them to regions of little or no activity. We use SPECT data from simulated hot‐sphere phantoms and from patient studies to demonstrate the advantages of the MAP‐CG algorithm. We conclude that the MAP‐CG algorithm requires 10%–25% of the processing time of EM techniques, and provides images of comparable or superior quality.

Magnetically enhanced protection of bone marrow from beta particles emitted by bone‐seeking radionuclides: Theory of application
View Description Hide DescriptionUtilization of radiopharmaceuticals that directly target radioactivity to tumors for treatment has a great deal of promise. Ideally, lethal doses of radiation could be delivered precisely to areas of disease, while, for the most part, sparing normal tissues. This potential, however, has not yet been fully realized. Current limitations of this approach are low tumor uptake of radiopharmaceuticals and dose‐limiting radiotoxicity. In an effort to offset low uptake, radionuclides that emit high average‐energy electrons have been proposed. Unfortunately, use of these radionuclides increases myelosuppression on a per decay basis. In order to allow for the utilization of high doses of this class of high‐energy beta emitters, we propose the application of a strong static homogeneous magnetic field to constrain the beta particles.Monte Carlo computer simulations indicate that application of a 10 T magnetic field can decrease the total radiationdose from bone‐avid tracers to marrow located in shafts of human long bones by 14%. More significantly, however, the penetration depth of high‐energy electrons from the bone surface into the marrow can be reduced by up to 74.6%. Preservation of marrow in areas distal to the bone has previously been shown to facilitate relatively rapid recovery from pancytopenia produced by radiation damage to trabecular marrow (without marrow transplantation). Magnetically enhanced protection of bone marrow, therefore, may allow administered doses of high‐energy beta‐emitting radionuclides to be increased. By raising the limits on injected quantities of such highly ionizing radionuclides, amounts of the radiationdose absorbed by both soft and calcified tissuetumors will be increased, compared to conventional treatments. Hence, it is possible that this technique will, in part, aid in the realization of the promise of radionuclide therapy by permitting the delivery of therapeutic levels of radiation exposure to tumors.

Proton activation analysis of stable isotopes for a molybdenum biokinetics study in humans
View Description Hide DescriptionMolybdenum is a trace element essential to life. Nevertheless, little information is available on its metabolism in humans. A methodology based on stable isotope administration that combines compartmental analysis, simultaneous use of two tracers, and proton nuclear activation (PNA) is presented. A four‐compartment metabolic model was adopted. The compartments are stomach, small intestine, transfer compartment, and unquantified tissue pool. The employment of two different stable isotopes of the element under investigation as tracers was made possible by PNA. Optimization of the technique for molybdenum determination in plasma led to the choice of ^{95}Mo and ^{96}Mo as tracers. Their concentrations in plasma can be determined measuring the disintegration γ lines of the corresponding technetiumradioisotopes produced via (p,n) reaction. In the adopted experimental conditions, a minimum detectable concentration of 2 ng isotope/ml plasma was attained. A kinetics study was performed on two healthy volunteers. To both subjects one tracer was orally administered, and the other intravenously injected. Venous blood samples were withdrawn at different postinjection times and the concentrations for both isotopes determined. The model parameters describing molybdenum kinetics were obtained for the two individuals. Total absorbed fraction was found to be 0.84±0.03 and 0.86±0.07, respectively.

A method to evaluate tracer kinetics in small laboratory animals using a series of thermoluminescent dosimeters
View Description Hide DescriptionMiniature detector probes have previously been used in large animal models to investigate myocardial ^{201}Tl clearance kinetics. The results of these studies helped develop clinical imaging protocols that greatly improved the accuracy of thallium scintigraphy. However, miniature detector probes are too large to be used in small animals. Thus, if a method could be developed to measure regional time activity curves in small animals, it would provide a cost‐effective alternative to both experiments in large animals and/or multiple experiments at varying time points that can produce results only by postmortem analysis of several animals. Accordingly, we developed a method to measure a regional time activity curve of a tracer in rabbits by using a series of thin thermoluminescent dosimeters [CaF_{2}(dopant)TLDs, 1 mm thick] placed on the surface of the myocardium. Background contributions associated with high blood pool activity are modeled and then subtracted from the initial TLD response. To validate and illustrate this method, thallium kinetics were determined for nonischemic rabbit myocardium (n=6). Myocardial thallium concentration decreased monoexponentially with a mean half‐time equal to 396±141 min. Arterial blood activity decreased triexponentially with a final half‐time of 243±73 min. No significant difference was found when the myocardial half‐time was compared to the final arterial half‐time. These findings are consistent with previous work using a cadmium telluride probe in a canine model. Therefore, TLD analysis can provide a cost‐effective, reliable, and reproducible method to measure regional myocardial clearance kinetics.

The calibration and use of plane‐parallel ionization chambers for dosimetry of electron beams
View Description Hide DescriptionThe AAPM TG 39 protocol has proposed three different methods of calibrating plane‐parallel ionization chambers, i.e., in‐phantom irradiation with a high‐energy electron beam and in‐phantom and in‐air ^{60}Co irradiation. To verify the consistency of the three methods, we have measured values using each of these techniques for the five most commonly used plane‐parallel chambers considered by the protocol. Our results demonstrate that the measured values for the three different methods for any of the chambers agree to within ±0.6%. Once was measured, the determination of absorbed dose for electron beams with different energies for an AECL Therac 20 and Philips SL25 was carried out according to the AAPM TG 39 protocol. The results show that the determinations of the absorbed dose outputs for any of the five chambers agree to within ±0.7% for electron‐beam energies of 4–20 MeV if all five chambers had values determined by the electron‐beam method. The uncertainties are well within the expected error for these approaches.

A convolution‐adapted ratio–TAR algorithm for 3D photon beam treatment planning
View Description Hide DescriptionA 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 of 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.

Parametrization of head‐scatter factors for rectangular photon fields using an equivalent square formalism
View Description Hide DescriptionHead‐scatter factors of symmetric square and rectangular fields (field center on the central beam axis) defined by the upper (Y) and lower (X) jaws for 6 and 15 MV photon beams from 2300CD and 600C accelerators (Varian Associates Inc., Palo Alto, CA) were measured, as well as those for fields shaped by the Y jaws and the multileaf collimator(MLC) of the 2300CD. For rectangular fields, the head‐scatter factor for the field (x=a and y=b) was different from that for the field (y=a and x=b). This difference was 2%–3% for fields defined by conventional collimators when x−y was large, and became 4%–5% when the MLC and Y jaws were used to shape the fields with the X jaws retracted. In order to calculate values for head‐scatter factors of rectangular fields accurately using an equivalent square formalism, the side of the equivalent square should be obtained with different weights for lower and upper jaws, as proposed by Vadash and Bjärngard [Med. Phys. 20, 733‐734 (1993)]. Our measurements demonstrate that the relative weight (G) of upper and lower jaws is strongly dependent on their distances from the x‐ray source, while the beam energy has little effect on the value of G. We further show that G can be calculated simply from these distances. An analytical representation for head‐scatter factors of square and rectangular fields is also developed in this paper. The quality of this representation was judged by the root‐mean‐square (rms) deviation from measured head‐scatter factors, which ranged from 0.11%–0.27%.

An evaluation of the recommendations of the TG‐25 protocol for determination of depth dose curves for electron beams using ionization chambers
View Description Hide DescriptionAAPM Radiation Therapy Committee Task Group 25 has recently outlined a protocol for the determination of relative dose curves for electron beams [Med. Phys. 18, 73–109 (1991)]. We have performed an evaluation of this protocol by comparing the central axis depth dose curves determined from measurements using two different ionization chambers and three different phantom materials. Measurements were made with a Farmer‐type PTW and Capintec ionization chamber in solid water, PMMA, and clear polystyrene phantoms irradiated by 6‐ and 15‐MeV electron beams. Central axis depth dose curves were generated from the measured depth‐ionization data using the new protocol. For both the chambers and energies investigated in this study, excellent agreement was observed among all the depth doses in water obtained from measurements in all of the three phantoms studied.

Scattered photons from wedges in high‐energy x‐ray beams
View Description Hide DescriptionThe presence of a wedge increases the fraction of ‘‘head‐scattered’’ photons in a high‐energy x‐ray beam. We have compared internal and external wedges for x‐ray beam energies between 6 and 25 MV by determining their SPR_{ w }, i.e., the ratio of the dose contribution from photonsscattered by the wedge and photons either coming directly from the target or scattered by other structures, including the flattening filter. Marked differences were observed. First, SPR_{ w } for the thickest external wedge (60°) was 1.8% at a field size of 10×10 cm^{2} and mildly dependent on the photon energy, while SPR_{ w } for internal wedges for this field size varied between 4.4% and 5.4% depending mostly on the location and size of the wedge and marginally on the photon energy. Second, the variation of SPR_{ w } with the collimator setting c×c was different for the internal and external wedges. SPR_{ w } for the internal wedge approached a limiting value at large c and could be fitted with an error function, while SPR_{ w } for the external wedge increased quadratically with c. As a result, the difference in SPR_{ w }(c) for internal and external wedges is reduced for large fields.

A QA phantom for dynamic stereotactic radiosurgery: Quantitative measurements
View Description Hide DescriptionA spherical acrylic phantom was designed for quality assurance measurements of dynamic radiosurgery. The phantom consists of two mating hemispheres mounted on a base plate. The interhemispheric plane may be oriented at any angle to the base, the angle being identified by visible marks on the base plate of the phantom. The phantom has a set of replaceable, radiologically identifiable markers, suitable for Computed Tomography(CT),Magnetic Resonance(MR), and Digital Subtraction Angiography(DSA)imaging. The frame coordinates of each marker are calculated from its known positions with respect to the center of the sphere. The measured errors of these positions using CT and MRimages, were within the voxel size of the displayed image, while for DSAimages the error was greater than 2.5 mm at the periphery of the image. The calculated depths from the planning software, for various beam intersection points to the isocenter, agreed within 0.6 mm with the known depths. A variation of 3.6±2.6 mm in the calculated depths was observed between using MR and CTimage data. This difference results in a 1% variation in Tissue Maximum Ratio (TMR) calculations. Comparisons of measured and known volumes resulted in differences of 8%–10%.

Source localization for brachytherapy implants loaded with an afterloader
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