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A simplified intensity modulated radiation therapy technique for the breast.

A simplified intensity modulated radiation therapy (sIMRT) technique for the breast is presented. The technique aims to produce a uniform dose distribution in the entire breast volume. Using the standard tangential beam arrangement, we first determine for each pencil beam the midpoint of the segment that intersects the treatment volume. The dose to the midpoint from the open field is then calculated. The intensity of the pencil beam is determined as proportional to the inverse of the open field dose. With this intensity modulated beam, the dose delivered to the midpoint of each pencil beam segment that intersects the treatment volume is now equalized. The dose distribution in the entire treatment volume is nearly as uniform as can be achieved under the given beam arrangement. Fifteen left breast patients were planned with the sIMRT technique. For comparison, the same group of patients was also planned with the standard wedged pair technique and the full-fledged volume-based IMRT (vIMRT) technique. Both the sIMRT and the vIMRT techniques achieved more homogeneous dose in the treatment volume than the standard plan. Doses to the heart, the ipsilateral lung, and the contralateral breast were also reduced. The planning time and the treatment time for the sIMRT technique were comparable to that of the standard technique, and significantly less than that required by the vIMRT technique. The sIMRT technique is practical for large-scale implementation in a busy clinic without requiring significant increase of resources.

Adult↗

A quasiexact reconstruction algorithm for helical CT using a 3-Pi acquisition.

Recently, an exact reconstruction method for helical CT was published by A. Katsevich. The algorithm is of the filtered backprojection type and is, therefore, computationally efficient. Moreover, during backprojection, only data are used which correspond to an illumination interval of 180 degrees as seen from the object-point. We propose a new reconstruction method, which is applicable to data obtained with a 3-Pi acquisition [IEEE Trans. Med. Imaging 19, 848-863 (2000)]. The method uses the same filter types as the Katsevich algorithm, but the directions and the number of the filter lines are chosen differently. For the derivation of the new algorithm, we analyze the relationship of the Katsevich method and radon inversion. A certain radon plane can intersect with the backprojection interval related to a 3-Pi acquisition either once, three, or five times. In analogy to the definition of quasiexactness introduced by Kudo et al. for a 1-Pi acquisition, we use the term quasiexactness for algorithms on a 3-Pi acquisition, if radon planes with one or three intersections within the backprojection interval are treated correctly. Using the results on the relationship with radon inversion, we can prove that our algorithm is quasiexact in this sense. We use simulation results in order to demonstrate that the algorithm yields excellent image quality.

Algorithms↗

A procedure to determine the radiation isocenter size in a linear accelerator.

Measurement of radiation isocenter is a fundamental part of commissioning and quality assurance (QA) for a linear accelerator (linac). In this work we present an automated procedure for the analysis of the stars-shots employed in the radiation isocenter determination. Once the star-shot film has been developed and digitized, the resulting image is analyzed by scanning concentric circles centered around the intersection of the lasers that had been previously marked on the film. The center and the radius of the minimum circle intersecting the central rays are determined with an accuracy and precision better than 1% of the pixel size. The procedure is applied to the position and size determination of the radiation isocenter by means of the analysis of star-shots, placed in different planes with respect to the gantry, couch and collimator rotation axes.

Biophysical Phenomena↗

Strategies for inner volume 3D fast spin echo magnetic resonance imaging using nonselective refocusing radio frequency pulses.

Fast spin echo (FSE) trains elicited by nonselective "hard" refocusing radio frequency (RF) pulses have been proposed as a means to enable application of FSE methods for high-resolution 3D magnetic resonance imaging (MRI). Hard-pulse FSE (HPFSE) trains offer short (3-4 ms) echo spacings, but are unfortunately limited to imaging the entire sample within the coil sensitivity thus requiring lengthy imaging times, consequently limiting clinical application. In this work we formulate and analyze two general-purpose combinations of 3D HPFSE with inner volume (IV) MR imaging to circumvent this limitation. The first method employs a 2D selective RF excitation followed by the HPFSE train and focuses on required properties of the spatial excitation profile with respect to limiting RF pulse duration in the 5-6 ms range. The second method employs two orthogonally selective 1D RF excitations (a 90x degrees - 180y degrees pair) to generate an echo from magnetization within the volume defined by their intersection. Subsequent echoes are formed via the HPFSE train, placing the focus of the method on (a) avoiding spurious echoes that may arise from transverse magnetization located outside the slab intersection when it is unavoidably affected by the nonselective refocusing pulses and (b) avoiding signal losses due to the necessarily different spacing (in time) of the RF pulse applications. The performance of each method is experimentally measured using Carr-Purcell-Meiboom-Gill (CPMG) multi-echo imaging, enabling examination of the magnetization evolution throughout the echo train. The methods as implemented achieve 95% to 97% outer volume signal suppression, and higher suppression appears to be well within reach, by further refinement of the selective RF excitations. Example images of the human brain and spine are presented with each technique. We conclude that the SNR efficiency of volume imaging in conjunction with the short echo spacing afforded by hard pulse trains enables high-resolution 3D HPFSE MRI of a small field-of-view (FOV) with minimal aliasing artifact.

Algorithms↗

Analytic evaluation of depths of dose calculation points for external beam radiation therapy treatment planning.

A method has been developed to calculate the depth of a point in a patient contour analytically. In this method, the patient contour is approximated by a Fourier series comprising 5-10 terms. The depth of a calculation point is the distance between the calculation point and the intersection of the ray line with the contour line. Depth calculations using this method are compared with calculations using a more conventional method in which the intersection is found by representing the contour as a set of straight-line segments between pairs of contour points. This method gives depth values comparable in accuracy to the more conventional method and computed approximately twice as fast.

Biophysical Phenomena↗

Extension of Fourier methods to the calculation of effective depths in heterogeneous media of arbitrary contour.

The description of patient contours and internal structures by means of truncated Fourier series can be extended to continuous contours of arbitrary shape and location by expressing the x and z Cartesian coordinates of the contour as independent Fourier series in a parameter t. An analytic equation for the intersection of the contour and a ray line is then written as an equation in the parameter t. The equation can be solved using numerical methods yielding the Cartesian coordinates of the intersection point directly.

Fourier Analysis↗

Analytic evaluation of heterogeneity locations for external beam treatment planning.

A method has been developed to calculate depths of calculation points analytically in patient contours containing internal heterogeneities. In this method, each contour is approximated by a Fourier series comprising five to ten terms. Using this approximation, the intersections of a ray line with each contour are found as the solution of a transcendental equation. Once these intersections have been located, effective depths used in heterogeneity calculations can readily be calculated.

Algorithms↗

Volume-based geometric modeling for radiation transport calculations.

Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon's approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed.

Algorithms↗

An automated image-registration technique based on multiple structure matching.

A new image-registration technique that matches multiple structures on complementary imaging data sets (e.g., CT and MRI) has been developed and tested with both phantom and patient data. The algorithm assumes a rigid-body transformation and is suitable for correlating structures within the cranium or at the skull base. The basic premise of the new technique is that an optimum transformation is achieved when the relative volume lying outside of the intersection between a structure and its transformed counterpart is a minimum. This relative volume is calculated numerically using a random sampling approach, and a binary searching algorithm was used to step through the nine-dimensional parameter space consisting of three rotation angles, three scaling factors and three components of a translation vector. For the nine tests using phantom data, the automated structure-matching technique was able to predict the correct rotation angles to within +/- 1 degree. The expected clinical performance of the new technique was assessed by comparing results obtained with the new method to those obtained using other techniques for 12 patients who were treated with charged particles at Lawrence Berkeley Laboratory (LBL) and who had image-registration studies performed as part of their treatment plan. For 9 of the 12 patients considered, the new structure-matching technique produced a significantly better registration than the older methods, as measured by the resultant average relative volume lying outside of the intersection between any structure and its transformed counterpart. For the other three patients, results were not significantly different for the new structure-matching method and the older techniques.

Algorithms↗

Semiautomated matching and seed position location for implanted ribbons.

A difficult, error-prone, and time consuming problem in brachytherapy is the determination of the three-dimensional (3-D) positions of implanted seeds. To triangulate 3-D seed positions, the corresponding seed images in radiographs taken at different parallax (gantry) angles must be identified (matched). With only two radiographs, there is an inherent problem of ambiguity in matching individual seed images. The use of the assignment algorithm cannot bypass this ambiguity. However, when seeds are implanted within ribbons, their positions in 3-D space can be determined accurately and (almost always) without ambiguity. This follows because the matching of ribbon images is much less ambiguous than the matching of individual seed images. We describe a semi-automated procedure to match the ribbon images on two radiographs, determine the 3-D loci of the ribbons, and locate the 3-D position of each seed on each ribbon. The ribbon matching problem involves a double application of the assignment algorithm. After image matching, the 3-D locus of each ribbon is found from the intersection of the ray sets from its radiographic images and the analysis of a 3-D spanning tree through the derived ray set intersection points. The seed positions on a ribbon locus are determined by interpolation of equally spaced seed intervals along the 3-D ribbon locus. Experiments with a phantom show that for two radiographs separated by any parallax between 20 degrees and 90 degrees, our technique provides a systematic error in 3-D seed location of 3.0 mm, and a random error of less than 2 mm.

Algorithms↗

Dose-surface histograms as treatment planning tool for prostate conformal therapy.

Dose-surface histograms are studied and compared with dose-volume histograms, as an evaluation tool for prostate treatment planning. For thin walled hollow organs, such as the rectum and bladder, the surface area irradiated is a more appropriate measure of the biological effect than the full volume. It is also more accurate and efficient to define the surface for a hollow structure and compute the surface area histograms. Application of the dose-surface histograms provide new insights into prostate treatment planning. A simple idealized geometry model demonstrates that the percentage surface area intersected by the geometric beam edge differs from the percentage volume intersected. For a group of prostate patients, it is shown that the dose-surface histograms yield substantially different results from the dose-volume histograms in ranking four-, six-, and, eight-field treatment plans and in calculating the fraction of the rectum irradiated to high dose. The difference in terms of surface area between these plans in the high-dose region is usually less than that in terms of the volume, and a reverse of plan ranking order can consequently occur. The percentage of organ surface irradiated to high dose is typically greater than the percentage volume by 5% to 10%. The use of the dose-surface histograms in analysis of organ motion and/or patient setup uncertainty, and analysis of rectal complications, is also discussed.

Biophysical Phenomena↗

The effects of bandwidth on the detectability of narrow- and wideband signals.

The effects of masker bandwidth on the detection of narrow- and wideband signals have been investigated. For both kinds of signals, plots of threshold as a function of masker bandwidth yielded by both narrow- and wideband signals are reasonably described with two intersecting lines. Threshold initially increase with masker bandwidth and then become independent of further increases. The rate of increase depends on the signal spectrum. The bandwidth at which the lines intersect varies with signal bandwidth and also mode of masker presentation (i.e., whether the masker is gated with the signal or is present continuously). Internal filtering is most accurate when the masker is present continuously. A model is proposed in which a listener's decisions about the presence of narrow-band signals are based upon estimates of stimulus energy within a critical band. These estimates are degraded by bandwidth-dependent processing errors. When the signal to be detected spans several critical bands (i.e., is wideband), the model forms a test statistic by summing the outputs of the relevant critical bands. The model permits the contribution of each band to the sum to vary with masker bandwidth because it incorporates a form of lateral suppression. Thresholds of narrow-band signals in gated maskers and wideband signals in gated and continuous maskers are predicted by the model. However, the model fails to account for the detectability of narrow-band signals in continuous maskers.

Attention↗

Locating animals from their sounds and tomography of the atmosphere: experimental demonstration.

Calling animals are located using widely distributed receivers, and the sounds from the animals are used to map the sound speed and wind fields by means of tomography. In particular, two Red-Winged Blackbirds Agelaius phoeniceus are correctly located within a meter using recordings from five receivers spread over a 20 by 30 m region. The demonstration hinges on two new developments. First, a new algorithm for blindly estimating the impulse response of the channel is shown capable of estimating the differences in the time of first arrivals at two receivers. Since it is known that the first arrivals travel along nearly straight paths, the difference in time constrains the animal's location to a hyperboloid, and the animal is located by intersecting hyperboloids from many pairs of receivers. Second, in order to accurately find the intersection point and map the sound speed and wind fields using tomography, a nonlinear equation is solved. The new algorithm for blindly estimating the impulse response of a channel offers a new way for locating sounds and making tomographic maps of the environment without any requirement for a model for the propagation of sound such as is needed for focalization and matched field processing.

Algorithms↗

Sound propagation and speech transmission in a branching underground tunnel.

The characteristics of sound propagation and speech transmission along a tunnel with a "T" intersection were investigated. At receivers within sight of the sound source, low frequencies were mainly attenuated around the intersection than high frequencies. At receivers out of sight of the source, high frequencies were extensively attenuated. The overall pattern of sound attenuation along the different sections of tunnel, which was calculated by the conical beam method, agreed well with the measurements in this study. Numerical calculations of reflected and diffracted waves with minimum transmission paths in a two-dimensional plane showed that reflected waves were the primary contributors to sound fields out of sight of the source. The articulation scores measured at receivers within sight of the source were high, and most of the confusion concerned syllables that could easily be misheard, even if there were a high signal-to-noise ratio. The types of syllable confusions observed at the receivers out of sight of the source appeared to have been caused by the greater deterioration in speech signals along this part of the tunnel, especially at high frequencies. The evaluation by rapid speech transmission indices (RASTI) appeared to be overestimated at the receivers out of sight of the source. Taking into account the early decay times of impulsive sound and the calculation procedures used in RASTI, it is concluded that speech intelligibility may not have been evaluated correctly by RASTI.

Adult↗

The role of collinear interaction in dislocation-induced hardening.

We connected dislocation-based atomic-scale and continuum models of plasticity in crystalline solids through numerical simulations of dislocation intersections in face-centered cubic crystals. The results contradict the traditional assumption that strain hardening is governed by the formation of sessile junctions between dislocations. The interaction between two dislocations with collinear Burgers vectors gliding in intersecting slip planes was found to be by far the strongest of all reactions. Its properties were investigated and discussed using a multiscale approach.

Journal Article↗

Theoretical study of geometric phase effects in the hydrogen-exchange reaction.

The crossing of two electronic potential surfaces (a conical intersection) should result in geometric phase effects even for molecular processes confined to the lower surface. However, recent quantum simulations of the hydrogen exchange reaction (H + H2 --> H2 + H) have predicted a cancellation in such effects when product distributions are integrated over all scattering angles. We used a simple topological argument to extract reaction paths with different senses from a nuclear wave function that encircles a conical intersection. In the hydrogen-exchange reaction, these senses correspond to paths that cross one or two transition states. These two sets of paths scatter their products into different regions of space, which causes the cancellation in geometric phase effects. The analysis should generalize to other direct reactions.

Journal Article↗

Ethylene oxide gaseous sterilization. I. Concentration and temperature effects.

The relationships of reaction temperature and concentration of gaseous ethylene oxide to the time required for inactivation of air-dried Bacillus subtilis var. niger spores are more complex than previously reported. A plot of temperature vs. the logarithm of "thermochemical death time" (TCDT) resulted in a straight line between 18 and 57 C for systems of "high" ethylene oxide concentration. The TCDT values were independent of ethylene oxide concentrations above certain temperature-dependent limits. A given ethylene oxide concentration produced a TCDT curve identical in the upper temperature regions with that for higher concentrations. As the temperature was lowered beyond a critical point, this curve diverged from that for higher concentrations, as a straight line of lesser slope. Thus, a series of curves exists for a range of ethylene oxide concentrations. They are characterized by two segments, both logarithmic, intersecting at a critical temperature for each concentration. The intersecting point is at a temperature inversely related to the ethylene oxide gas concentration. The temperature quotient for the high temperature segments of all systems was 1.8. This value was characteristic for ethylene oxide concentrations of 440 and 880 mg/liter at temperatures above 40.6 and 33.4 C, respectively. Below these critical temperatures, the Q(10) values for the respective systems were 3.2 and 2.3.

Bacillus subtilis↗

Bioenergetic constraints on tactical decision making in middle distance running.

BACKGROUND: The highest velocity that a runner can sustain during middle distance races is defined by the intersection of the runner's individual velocity-time curve and the distance-time curve. The velocity-time curve is presumably fixed at the onset of a race; however, whereas the race distance is ostensibly fixed, the actual distance-time curve is not. That is, it is possible for a runner to run further than the race distance if he or she runs wide on bends in track races. In this instance, the point of intersection of the individual velocity-time curve and the distance-time curve will move downwards and to the right, reducing the best average velocity that can be sustained for the distance. METHODS: To illustrate this point, the race tactics used by the gold and silver medallists at 800 m and 5000 m in the Sydney Olympics were analysed. The paths taken by the runners were carefully tracked and the total distance they covered during the races and the average velocity they sustained over the distances they actually covered were calculated. RESULTS: In both the Olympic 800 m and 5000 m finals, for example, the winner was not the runner who ran at the highest average velocity in the race. Rather, the winners of these races were able to husband their metabolic resources to better effect by running closer to the actual race distance. CONCLUSIONS: Race results in middle distance running events are dependent not just on the energetic potential of the runners at the start of the race and their strategy for pace allocation, but also on the effect of their tactical approach to positioning on the total distance covered in the race. Middle distance runners should be conscious of minimising the distance covered in races if they wish to optimise their performance.

Decision Making↗