Off-axis Plane Research Articles

Three-dimensional dose distribution of tangential breast irradiation: results of a multicentre phantom dosimetry study.

One aspect of good radiotherapeutic practice is to achieve dose homogeneity. Dose inhomogeneities occur with breast tangent irradiation, particularly in women with large breasts. Ten Australian radiation oncology centres agreed to participate in this multicentre phantom dosimetry study. An Alderson radiation therapy anthropomorphic phantom with attachable breasts of two different cup sizes (B and DD) was used. The entire phantom was capable of having thermoluminescent dosimeters (TLD) material inserted at various locations. Nine TLD positions were distributed throughout the left breast phantom including the superior and inferior planes. The ten centres were asked to simulate, plan and treat (with a prescription of 100 cGy) the breast phantoms according to their standard practice. Point doses from resultant computer plans were calculated for each TLD position. Measured and calculated (planning computer) doses were compared. The dose planning predictability between departments did not appear to be significantly different for both the small and large breast phantoms. The median dose deviation (calculated dose minus measured dose) for all centres ranged from 2. 3 to 5.3 cGy on the central axis and from 2.1 to 7.5 cGy for the off-axis planes. The highest absolute dose was measured in the inferior plane of the large breast (128.7 cGy). The greatest dose inhomogeneity occurred in the small breast phantom volume (median range 93.2-105 cGy) compared with the large breast phantom volume (median range, 100.1-107.7 cGy). There was considerable variation in the use (or not) of wedges to obtain optimized dosimetry. No department used 3D compensators. The results highlight areas of potential improvement in the delivery of breast tangent radiotherapy. Despite reasonable dose predictability, the greatest dose deviation and highest measured doses occurred in the inferior aspects of both the small and large breast phantoms.

Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors

Metallic surface-relief diffractive cylindrical mirrors are designed for on-axis and off-axis focusing and incidence configurations. These diffractive structures are analyzed by both rigorous and scalar integral methods. Two design methods, based on initial assumptions of zero-thickness and finite-thickness structures, are presented for determining the zone-boundary locations and the surface-relief mirror profiles for the general case of an off-axis incident plane wave and off-axis focusing. With the use of these methods, continuous diffractive, multilevel diffractive, and continuous nondiffractive mirrors were designed. Rigorous analysis is performed for both TE and TM polarizations by using an open-region formulation of the boundary element method (BEM) suitable for regions of complex refractive index such as finite-conductivity metals. Three scalar integral methods corresponding to Dirichlet, Neumann, and Kirchhoff boundary conditions are also used to analyze the diffractive mirrors. The diffracted fields from both the rigorous BEM and the scalar methods of analysis are used to calculate a number of performance metrics including diffraction efficiency, sidelobe power, total reflected power, and focal spot size. The performance of the mirrors is evaluated, and the accuracy of the various scalar methods is determined.

Endoluminal MR imaging of the rectum and anus: technique, applications, and pitfalls.

Anorectal diseases (e.g., fecal incontinence, perianal and anovaginal fistulas, anorectal tumors) require imaging for proper case management. Endoluminal magnetic resonance (MR) imaging has become an important part of diagnostic work-up in such cases. Optimal endoluminal MR imaging requires careful attention to patient preparation, imaging protocols, and potential pitfalls in interpretation. Comfortable positioning and the use of an antiperistaltic drug are vital for adequate patient preparation. Selected sequences and imaging planes are used in imaging protocols tailored for specific diseases. In fecal incontinence, three-dimensional sequences allow detailed demonstration of the anal anatomy and related defects. In perianal and anovaginal fistulas, longitudinal imaging planes help determine the superior extent of the abnormality. In anorectal tumors, T1-weighted turbo spin-echo MR imaging can help detect extension into the perirectal fat and T2-weighted turbo spin-echo MR imaging is used to optimize contrast between tumor and the rectal wall. Off-axis and radial imaging planes are used in all anorectal diseases to minimize partial volume effects. Potential pitfalls include various parts of the normal anal anatomy mimicking sphincter defects, veins and hemorrhoids mimicking fistulas and abscesses, and overhanging tumor mimicking more extensive tumor. Adequate patient preparation combined with proper technique and a knowledge of potential pitfalls will allow optimal endoluminal MR imaging of the rectum and anus.

Modeling surface kinetics and morphology during 3C, 2H, 4H, and 6H–SiC (111) step-flow growth

A Monte Carlo surface kinetics model has been developed to predict growth rate, morphology, and the atomic content of thin films of various SiC polytypes (3C, 2H, 4H, 6H). The model represents the crystal lattice on a structured mesh which retains fixed atom positions and bond partners indicative of a perfect crystal lattice. Specified events occurring at different rates and probabilities change the configuration and the atomic content of the lattice. Events in the model include precursor transport to surface, adatom adsorption, diffusion, and desorption from surface, growth and etching reactions between adatoms and lattice atoms, and evaporation. The initial validation of the model for SiC consists of replicating trends seen when experimentally growing polytypes of SiC (111) on circular mesas and on off-axis vicinal planes. The model can predict the (111) plane faceting seen in β-SiC and the hexagonal structures seen when growing on α-SiC. Also, step flow growth rates which change with flow direction are predicted by the model. Step flow growth on a (111) plane in 〈112̄0〉 directions is faster than growth in 〈11̄00〉 directions. The model is used to investigate step bunching. Step bunching is shown to be due in part to the growth rate variability of 〈11̄00〉 directions and the hexagonal stacking content in the α-SiC polytype. The chemical variation of the step risers in the step bunch could lead to reaction rate limited growth of some steps over others leading to further bunching. The model is used to predict growth rate differences between the Si and C face of SiC. The face growth rate differences are a function of the SiH4 and CH4 surface reaction probabilities.

On the reliability of quantitative phase measurements by low magnification off-axis image plane electron holography

We experimentally found that the object wave function of an electron wave in a transmission electron microscope can depend on the diameter of the condenser aperture and on the excitation of the objective lens. This can be seen by low magnification holograms utilizing as sample electrically charged latex spheres of different diameters, the electric field at a pn-junction and the magnetic leakage field of a magnetic memory cell.

Dosimetric analysis of intact breast irradiation in off-axis planes

Purpose/Objective : The purpose of this investigation is to quantify dose inhomogeneity of intact breast irradiation in off-axis planes, and determine how dose inhomogeneity varies according to patient breast size and anatomical region of the breast. Methods and Materials : Eleven patients treated with intact breast radiation underwent a treatment-ptanning computer tomography (CT) scan with 1-cm slices through the entire breast. The area of breast tissue was defined on each CT slice. Treatment planning with lung correction factors was performed using a two-dimensional treatment-planning system that calculates off-axis dose distributions on a slice-by-slice basis. Each plan utilized tangential beams with matched nondivergent posterior borders and with collimator rotation to match the chest wall slope. Dose inhomogeneity within the central plane was minimized during treatment planning by the use of a wedge on the lateral tangent field and by the differential weighting of fields. Dose was normalized at the breast and pectoratis major interface at midseparation in the central plane. Off-axis dose inhomogeneity was not considered in the optimization of the treatment plan. Dose distributions were plotted for each 1-cm slice, and the area of each isodose curve within the breast on each CT slice was calculated. The results of each slice were summed to give an approximation of dose-volume relationships. Results : For the entire population, an average of 10% of the breast volume (range 1–40%) received 110% or greater of the prescribed dose. Increasing dose inhomogeneity was positively correlated with increasing breast sizes ( r = 0.72, p = 0.01—Spearmen rank test). Analysis of dose as a function of location within the breast, revealed that the greatest dose inhomogeneity occurred in the lower anatomical quadrants of the breast ( p = 0.003—Kruskal-Wallis test). For the group, the mean breast volume that received a 110% or greater dose was: 30% at 6 cm 3 below central axis, 14% at 4 cm 3 below central axis, 6% at central axis, 5% at 4 cm 3 above central axis, and 7% at 6 em above central axis. Conclusion : Our study demonstrates that a significant volume of breast tissue receives 110% or greater of the prescribed dose. This inhomogeneity is greatest in women with larger breast sizes, providing a possible explanation for the poorer cosmetic result seen in this subset of patients compared to women with small breast sizes. In addition, our results show the greatest dose inhomogeneity in the lower quadrants of the breast. Off-axis dose inhomogeneity should be considered in the planning of tumor bed boosts in women with lower quadrant tumors.

Dosimetric comparison of treatment planning systems in irradiation of breast with tangential fields

The objectives of this study are: (1) to investigate the dosimetric differences of the different treatment planning systems (TPS) in breast irradiation with tangential fields, and (2) to study the effect of beam characteristics on dose distributions in tangential breast irradiation with 6 MV linear accelerators from different manufacturers. Nine commercial and two university-based TPS are evaluated in this study. The computed tomographic scan of three representative patients, labeled as "small", "medium" and "large" based on their respective chest wall separations in the central axis plane (CAX) were used. For each patient, the tangential fields were set up in each TPS. The CAX distribution was optimized separately with lung correction, for each TPS based on the same set of optimization conditions. The isodose distributions in two other off-axis planes, one 6 cm cephalic and the other 6 cm caudal to the CAX plane were also computed. To investigate the effect of beam characteristics on dose distributions, a three-dimensional TPS was used to calculate the isodose distributions for three different linear accelerators, the Varian Clinac 6/100, the Siemens MD2 and the Philips SL/7 for the three patients. In addition, dose distributions obtained with 6 MV X-rays from two different accelerators, the Varian Clinac 6/100 and the Varian 2100C, were compared. For all TPS, the dose distributions in all three planes agreed qualitatively to within +/- 5% for the "small" and the "medium" patients. For the "large" patient, all TPS agreed to within +/- 4% on the CAX plane. The isodose distributions in the caudal plane differed by +/- 5% among all TPS. In the cephalic plane in which the patient separation is much larger than that in the CAX plane, six TPS correctly calculated the dose distribution showing a cold spot in the center of the breast contour. The other five TPS showed that the center of the breast received adequate dose. Isodose distributions for 6 MV X-rays from three different accelerators differed by about +/- 3% for the "small" patient and more than +/- 5% for the "large" patient. For two different 6 MV machines of the same manufacturer, the isodose distribution agreed to within +/- 2% for all three planes for the "large" patient. The differences observed among the various TPS in this study were within +/- 5% for both the "small" and the "medium" patients while doses at the hot spot exhibit a larger variation. The large discrepancy observed in the off-axis plane for the "large" patient is largely due to the inability of most TPS to incorporate the collimator angles in the dose calculation. Only six systems involved agreed to within +/- 5% for all three patients in all calculation planes. The difference in dose distributions obtained with three accelerators from different manufacturers is probably due to the difference in beam profiles. On the other hand, the 6 MV X-rays from two different models of linear accelerators from the same manufacturer have similar beam characteristics and the dose distributions are within +/- 2% of each other throughout the breast volume. In general, multi-institutional breast treatment data can be compared within a +/- 5% accuracy.

Off-axis illumination and its relation to partial coherence

We calculate the partially coherent images of an edge in one dimension by the method of adding intensities, that is, by modeling the illumination as an array of mutually incoherent plane waves incident over a range of angles. In order to visualize the transition between coherent and incoherent imaging, we display images that result from such off-axis plane waves; these images change considerably as the angle of illumination changes. The calculations are easily carried out on a microcomputer with a high-level mathematics program. The results shed light on off-axis and dark-field illumination as well. Finally, we elucidate a distinction between imaging with the aperture stop in the transform plane and imaging with the aperture stop distant from the transform plane.

Calculation models for determining the absorbed dose in water phantoms in off-axis planes of rectangular fields of open and wedged photon beams

Beam models are proposed for the calculation of the dose in off-axis planes of rectangular photon fields, when the data set used in the treatment planning system is based on the simple storage model of Milan and Bentley (1974). For open beams the model separates the off-axis ratio into an envelope profile and two boundary profiles. The envelope profile gives the field intensity of the maximal position of the jaws and has rotational symmetry. The boundary profiles describe the boundaries of the field actually formed by the jaws. In the case of a wedged beam, the model also separates the off-axis ratio into envelope profiles and boundary profiles. To determine these profiles for the non-wedge direction from open beam profiles, the wedge thickness is converted to an equivalent water thickness. In the case of an asymmetric field, the boundary profiles are shifted to the field centre. Results of calculation with these models have been compared with measurements and the simple multiplication of profiles, which has often been used with the Milan-Bentley model. The new models agree within a few per cent with the measurements and are a great improvement compared to the simple multiplication of profiles.

Computer-generated holograms of tilted planes by a spatial frequency approach

Computer-generated holograms of plane surfaces tilted and shifted with respect to the hologram plane are considered. The analysis is made in the spatial frequency domain by using the translation and rotation transformations of angular spectra. The frequency approach permits the use of the fast-Fourier-transform algorithm, which decreases the computation time and makes it possible to consider any position of the planes in space. Various configurations of tilted and shifted planes have been investigated, and computer-generated holograms of off-axis planes have been obtained. Computer and optical reconstructions, both of which show the feasibility of the proposed approach, have been carried out.

Three-dimensional focal curves generated by one-dimensional gradient-index tapers

Three-dimensional focal curves generated by one-dimensional gradient-index taper have been obtained when the taper is illuminated by an off-axis plane wave. The intensity distribution along the focal curve was evaluated by taking into account the particular form of the exit pupil produced by this gradient-index medium.

Three-dimensional focal curves generated by one-dimensional gradient-index tapers

Three-dimensional focal curves generated by one-dimensional gradient-index taper have been obtained when the taper is illuminated by an off-axis plane wave. The intensity distribution along the focal curve was evaluated by taking into account the particular form of the exit pupil produced by this gradient-index medium.

Three-dimensional photon treatment planning of the intact breast

Three-dimensional treatment planning for the intact breast was performed on two patients who had undergone CT scanning. A total of 38 treatment plans were evaluated. Multiple plans were evaluated for each patient including plans with and without inhomogeneity corrections, plans using varying photon energies of 60Co, 4 MV, 6 MV, 10 MV, and 15 MV, and three-dimensionally unconstrained plans. Increased hot spots were appreciated in the central axis plane when lung inhomogeneity corrections were used. Additional hot spots were appreciated in off-axis planes towards the cephalad and caudad aspects of the target volume because of lung inhomogeneity corrections and changes in the breast contour. The use of 60Co was associated with an increase in the magnitude and volume of hot spots, whereas the use of higher energy photons such as 10 MV and 15 MV was associated with an unacceptable target coverage at shallow depths. Therefore, for the two patients studied, the use of a medium energy photon beam (such as from a 6 MV linear accelerator) appeared to be the energy of choice for treatment of the intact breast. The three-dimensionally unconstrained plans were able to improve slightly upon the standard plans, particularly with relationship of dose to normal tissue structures. Areas for future research were identified, including the use of tissue compensators.

The objective evaluation of alternative treatment plans: II. Score functions

A series of six patients with adenocarcinoma of the prostate, Stages A 2, B 1, or B 2, were planned for treatment using a four-field box technique at 25 MV. Plans were prepared by three techniques: composite, mid-plane, and conformal. The dose distributions at the central plane and at two planes offset by ±2 cm were evaluated by means of score functions which quantify the magnitude of regret for target dose gradient, target over- and under-dose, non-target tissue overdose, and for overdose to the rectum, bladder, and femoral heads. The score functions are normalized to give values in the range from 10 (ideal) to zero (limit of acceptability), with negative values indicating unacceptable deviations from the prescribed dose limits. The scores for off axis conformal plans were found to be essentially the same as for mid-plane plans on the central plane. However, mid-plane planning was shown to be totally inadequate for off-axis planes, where the average target gradient and underdose scores were reduced by 10 units. Composite planning resulted in adequate target coverage on all planes, but at the expense of unacceptable overdose to non-target tissue. The effect of reducing the posterior beam weight to half that of the other three beams was to reduce the target gradient score by 1.6 ± 0.5 units and to increase the rectal score by 0.9 ± 0.3 units.

Effect of measurement errors on sonographic evaluation of ventriculomegaly.

Ventriculomegaly is a sensitive indicator of maldevelopment of the fetal brain and spinal cord. The fetal ventricular atrium is an optimal portion of the lateral ventricular system to measure in order to judge ventriculomegaly. We tested the susceptibility of this measurement to inaccuracies created by errors in cursor placement or improper selection of the plane of section for measurement in 52 normal fetuses. This measurement was shown to be reasonably insensitive to errors in cursor placement along the axis of the ventricular system. However, choice of an off-axis image plane of section, an angled measurement, or improper choice of ventricular boundary leads to a relatively large number of false-positive test results (approximately 10%). None of the simulated errors in atrial measurements underestimates the size of the ventricle, and thus, they are unlikely to result in a diminution of test sensitivity.

Analysis of a four parallel wire antenna system by the spatial Fourier transform method

The electromagnetic fields and currents associated with an infinite four parallel wire transmission line are analyzed through the use of the spatial Fourier transform method. The near and far electromagnetic fields and currents that are associated with frill and gap voltage excitations are analyzed by the Fourier transform method. Possible VHF compact range applications of a four parallel wire antenna system are discussed, including the possibility of simulating an off-axis EM plane wave by the appropriate adjustment of the exciting voltage phase on each of the four parallel wires. Comparisons of Fourier transform method solutions with method-of-moments solutions and finite-difference-time-domain solutions are made for an infinite four parallel wire antenna system. >

Treatment of tumours of the parotid gland and middle ear using obliquely reconstructed computed tomographic images.

Conventional planning of radiotherapy of tumours of the parotid, middle ear and other tumours in the head and neck often requires the treatment plane to be non-transverse. This produces major problems in delineating the tumour as well as verifying that vital structures such as the spinal cord are not included in the target volume. The use of computed tomography (CT) generally overcomes some of these problems and we have developed an algorithm to reconstruct transverse CT images into the appropriate oblique plane. Software has been written on the Picker Independent Treatment Planning System (ITPS) to allow planning on central axis and off-axis oblique planes. In addition we have used a beam's eye view facility to aid in the verification process.

Dose intercomparison at the radiotherapy centers in The Netherlands. 2. Accuracy of locally applied computer planning systems for external photon beams

As part of a quality assurance program in The Netherlands, the performance of computer planning systems was tested. Relative dose values, determined with an ionization chamber, were compared with dose values obtained from locally applied computer planning systems. Several clinically relevant situations were investigated: perpendicular incident beams, wedged beams, oblique incident beams, variable source-surface distances (SSD) and off-axis planes. The mean value of the ratios of calculated to measured dose values is 0.994, with an uncertainty of 2.4% (1 S.D.) and a maximum deviation of 9%, for all combinations of energies, planning systems and geometries investigated. The uncertainty for each situation separately was less than 2% (1 S.D.), except for the wedged beams and off-axis plane, which showed uncertainties of 2.6% (1 S.D.). Part of the additional uncertainty for the wedged beams originates from the value chosen for the wedge factor. Systematic deviations between calculated and measured dose values were investigated for three commercially available planning systems, separately. The mean deviation was smaller than 1% (1 S.D.), for most situations. Only for the wedged beams, larger deviations, up to a mean deviation of 2.6%, were observed.

Electron arc therapy: Beam data requirements and treatment planning

In electron arc therapy a long narrow beam defined by a secondary collimator is used to sweep across the treatment area of the patient. Central axis percentage depth doses and off-axis ratios measured with such a collimator show variations with the source-to-surface distance (SSD). Errors may be introduced into isodose distributions calculated with the effective SSD method when beam data measured at a fixed SSD are used. A treatment planning algorithm using beam data measured at two SSDs to allow an interpolation and extrapolation procedure to account for SSD variations has been implemented. For calculations in off-axis planes, off-axis ratios normal to the plane of rotation are also required. Results of the calculations were checked with film dosimetry measurements and found to be in good agreement.

Orbital tumor irradiation using non-coplanar beams.

Irradiation of the orbit is often associated with substantial dose inhomogeneity resulting from the insertion of lens blocks. We postulated that such dose inhomogeneity, which often exceeds 40%, could be halved by the use of two pairs of wedged beams, one angled in the sagittal plane and the other in the commonly employed transverse plane. The sagittal plane is obtained by turning the treatment couch 90 degrees. All beams carried a central-axis lens block and were angled 30 degrees relative to the vertical. Verification of dose distribution was obtained by film dosimetry in a head phantom for central- and off-axis planes. These measurements indicate that significant improvement in dose homogeneity over alternate methods can be achieved with this technique.