[en] A printed error has been discovered in table 1, p 793 of the above paper. The printed k parameter values were exactly a factor of 100 too small. The C values remain unchanged. The table caption, modified for clarity, and the corrected table are shown. It is emphasized that these corrections have no effect on other results presented in that paper

[en] A printed error has been discovered on pages 1771 and 1772 of the above paper. Figures 4 and 5 should have been the other way around (the captions were correct as printed). For the correct version see the electronic journal. (author)

[en] It has been pointed out by Dr Biao Chen of the University of Rochester that there is an error in the original version of the above article. The error occurs in table 3, in which the parameters for a least-square curve fit are given for the linear attenuation coefficients of the phantom materials tested. Two of the coefficients (a₂ and a₃) were expressed with too few significant digits. Unfortunately, these coefficients are for the highest degree terms, and round-off errors can produce rather dramatic changes in the values calculated from the equation in table 3, especially at high energy. For example, using the original values for CIRS: Gland, {a₀, a₁, a₂, a₃}={23.84, -16.2, 3.48, -0.25}, the linear attenuation appears to be 0.697 which is 271% greater than the value determined from the basis material technique given in table 2 (0.188). Using the parameters in the correct table which are expressed with greater precision, the linear attenuation is calculated to be 0.1886, yielding much better agreement (∼0.3%). In all cases, the linear attenuation coefficients calculated with the non-linear least-squares parameters from table 3 are within 4% of the coefficients determined in table 2. The correct table 3 is presented in full

[en] X-ray diagnostics gives the largest contribution to the population dose from man-made radiation sources. Strategies for reduction of patient doses without loss of diagnostic accuracy are therefore of great interest to society and have been focussed in general terms by the ICRP (ICRP 1996) through the introduction of the concept of diagnostic reference levels. The European Union has stimulated research in the field, and, based on patient dose measurements and radiologists' appreciation of acceptable image quality, good radiographic techniques have been identified and recommended (EUR 1996a, b) for conventional screen-film imaging. These efforts have resulted in notable dose reductions in clinical practices (Hart et al 1996). In spite of 100 years of use of x-rays for diagnostics, the choice of technique parameters still relies to a great extent on experience. Scientific efforts to optimize the choice in terms of finding the parameter settings which yield sufficient image quality at the lowest possible cost in dose are still rare. True optimization requires (1) estimation of the image quality needed to make a correct diagnosis and (2) methods to investigate all possible means of achieving this image quality in order to be able to decide which of them gives the lowest dose. The paper by Tapiovaara, Sandborg and Dance published in this issue of Physics in Medicine and Biology (pages 537-559) addresses the optimization of paediatric fluoroscopy, a timely and important topic. Fluoroscopy procedures, used to guide x-ray examinations or interventional procedures, are little standardized and may result in high dose levels; radiation exposure in childhood is likely to result in a higher lifetime risk than the same exposure later in life. The authors represent an interesting mix of expertise within various scientific fields: the theory of medical imaging and assessment of image quality, the physics of diagnostic radiology and radiation dosimetry. They provide good insights into the technical performance and limitations of clinical x-ray equipment and the functioning of x-ray image intensifiers (XRIIs), and discuss the problem in an educational manner. The authors have succeeded in producing a paper that combines high scientific merit and valuable practical guidelines towards the optimization of paediatric fluoroscopy and radiography. This information, if properly utilized by practitioners, will contribute to significant (50%) reduction in radiation doses without sacrificing image quality and diagnostic accuracy. Fluoroscopy using XRIIs is one of the x-ray procedures that allows the possibility of bringing patient doses to an absolute minimum: quantum-noise due to the inevitable stochastic nature of the interactions of x-rays with the image receptor will ultimately limit the possibility for further dose reduction. In a well designed (quantum-noise limited) system, patient dose ( D) increases proportionally with the square of signal-to-noise ratio (SNR). The SNR of the ideal observer (ICRU 1996) may be used as image quality descriptor. To ascertain minimum patient dose, the just detectable SNR level of critical image details in a given diagnostic procedure should be determined. The dose-to-information conversion factor SNR²/D is independent of patient dose, thus providing a useful figure-of-merit for optimization of the technique parameters of an imaging task. In the cited study, the strategy for optimization is to maximize the SNR²/D ratio, leaving the absolute requirement on SNR (and patient dose) to be determined by the user. Technique factors which strongly influence the SNR²/D ratio are the energy spectrum (tube potential and total filtration) and the choice of anti-scatter technique. These can be adjusted by the user of clinical x-ray equipment and are focussed in the paper. A powerful tool used in executing the study is a carefully developed and validated computational model of the imaging chain (Tapiovaara and Sandborg 1995) allowing simultaneous calculation of SNR and D, and flexible variation of the parameters. The results indicate that optimal parameter settings may differ significantly from those recommended on the basis of previous experience: low tube potential techniques are suggested to improve dose efficiency as well as use of appropriately designed anti-scatter (fibre) grids. The detection task, or the type of important detail, also influences the choice of preferred technique. The current study has important implications for other x-ray imaging procedures which, like XRII fluoroscopy, are not restricted by the requirement of optical density as in conventional screen-film imaging. It suggests the importance of optimizing the imaging techniques for digital radiographic systems so that their advantages over conventional systems can be fully utilized. Another natural extension of the current work is high dose fluoroscopy in interventional procedures which has been a major concern of radiation risks to patients (Shope 1996). A search for improved techniques to minimize exposure in general fluoroscopy is a continued challenge to imaging physicists. An even greater challenge is posed to the fluoroscopic x-ray equipment manufacturers. Some systems will need to be redesigned to allow users greater flexibility of selecting a desired strategy for the automatic brightness compensation control. It will also be essential to provide higher output for fluoroscopic systems to accommodate low kV and heavy filtration operations. In summary, the paper by Tapiovaara et al (1999) is an important contribution to development of dose efficient techniques which will influence future practices and manufacturers of x-ray equipment. Scientific investigations such as this one will serve as a driving force for practical implementation of these dose efficient techniques. (author)

[en] Further to the recent work on slat gamma camera collimators by Britten and Klie (see above), the authors would like to add some references on the early work in gamma camera slat collimators, which should have been included for completeness. These papers are the original publication by Keyes (1975), and the work carried out by Webb et al (1992, 1993) deriving equations for geometric sensitivity and showing Monte Carlo modelling of performance. (author)

[en] We here present LINCON_FAST which is an exact method for 3D reconstruction from cone-beam projection data. The new method is compared to the LINCON method which is known to be fast and to give good image quality. Both methods have O(N³ log N) complexity and are based on Grangeat's result which states that the derivative of the Radon transform of the object function can be obtained from cone-beam projections. One disadvantage with LINCON is that the rather computationally intensive chirp z-transform is frequently used. In LINCON_FAST, FFT and interpolation in the Fourier domain are used instead, which are less computationally demanding. The computation tools involved in LINCON_FAST are solely FFT, 1D eight-point interpolation, multiplicative weighting and tri-linear interpolation. We estimate that LINCON_FAST will be 2-2.5 times faster than LINCON. The interpolation filter belongs to a special class of filters developed by us. It turns out that the filter must be very carefully designed to keep a good image quality. Visual inspection of experimental results shows that the image quality is almost the same for LINCON and the new method LINCON_FAST. However, it should be remembered that LINCON_FAST can never give better image quality than LINCON, since LINCON_FAST is designed to approximate LINCON as well as possible. (author)

[en] For 3D PET normalization methods, a balance must be struck between statistical accuracy and individual detector or line-of-response (LOR) fidelity. Methods with potentially the best LOR accuracy tend to be statistically poor, while techniques to improve the statistical quality tend to reduce the individual detector fidelity. We have developed and implemented a 3D PET normalization method for our ECAT 953B scanner (Siemens/CTI) that determines the detector normalization factors (NFs) as a product of a four-dimensional matrix of measured geometric factors (GFs) and single detector efficiency factors (ε). The effects of various alterations to the algorithm on the accuracy of the normalization have been examined through the impact on reconstructed images. An accurate set of GFs is crucial, as inaccurate NFs can result if LORs with similar but not identical geometric symmetries are grouped together. The general method can be extended to other tomographs, although the dimensionality of a GF matrix may be scanner-specific; the key is to determine the optimal number of dimensions in the GF matrix. The GFs for our scanner are specified by: (i) the two detector rings for each LOR; (ii) the radial distance of the LOR from the tomograph centre; and (iii) the positions within the detector block of the two crystals defining the LOR. Some residual radial non-uniformities are present in all the NF variations we examined. For the NF method presented here, the radial non-uniformities are attributed to the interaction between object-dependent scatter and normalization. Results indicate that this non-uniformity is detectable for scans with as few as 13 million total counts. (author)

[en] We address the issue of reconstructing the shape of an object with uniform interior activity from a set of projections. We estimate directly from projection data the position of a triangulated surface describing the boundary of the object while incorporating prior knowledge about the unknown shape. This inverse problem is addressed in a Bayesian framework using the maximum a posteriori (MAP) estimate for the reconstruction. The derivatives needed for the gradient-based optimization of the model parameters are obtained using the adjoint differentiation technique. We present results from a numerical simulation of a dynamic cardiac imaging study. A first-pass exam is simulated with a numerical phantom of the right ventricle using the measured system response of the University of Arizona FASTSPECT imager, which consists of 24 detectors. We demonstrate the usefulness of our approach by reconstructing the shape of the ventricle from 10 000 counts. The comparison with an ML-EM result shows the usefulness of the deformable model approach. (author)

[en] A method for the fully computerized determination and optimization of positions of target points and collimator sizes in convergent beam irradiation is presented. In conventional interactive trial and error methods, which are very time consuming, the treatment parameters are chosen according to the operator's experience and improved successively. This time is reduced significantly by the use of a computerized procedure. After the definition of target volume and organs at risk in the CT or MR scans, an initial configuration is created automatically. In the next step the target point positions and collimator diameters are optimized by the program. The aim of the optimization is to find a configuration for which a prescribed dose at the target surface is approximated as close as possible. At the same time dose peaks inside the target volume are minimized and organs at risk and tissue surrounding the target are spared. To enhance the speed of the optimization a fast method for approximate dose calculation in convergent beam irradiation is used. A possible application of the method for calculating the leaf positions when irradiating with a micromultileaf collimator is briefly discussed. The success of the procedure has been demonstrated for several clinical cases with up to six target points. (author)

[en] We have proposed a new dose optimization method for proton and heavy ion therapy using generalized sampled pattern matching, where an optimal beam weight distribution for scanning is obtained as a solution. Using water phantom models, one-dimensional lateral and depth dose distributions were separately optimized, each resulting in a uniform dose distribution within a target region and minimum dose fall-off to minimize undesired irradiation onto neighbouring tissues. Subsequently, we have applied the technique to broad beam three-dimensional proton therapy, leading to a homogeneous dose distribution inside a target and minimized distal and lateral dose fall-off for most convex tumour shapes. (author)