a bi-monthly peer-reviewed research journal
TCRT April 2005
Volume 4No. 2 (p 121-226) April 2005 ISSN 1533-0338
Open Access Poster Abstracts from Workshop on Alternatives to Mammography (p. 183-192)Posters from Workshop on Alternatives to Mammography, Winnipeg, Manitoba, Canada, September 19-20, 2004.
Open Access Article The Use of Control Angles with MART (Multiplicative Algebraic Reconstruction Technique) MART (Multiplicative Algebraic Reconstruction Technique) is an iterative CT (computed tomography) algorithm [1]. A cycle is completed when all projections have been processed at least once. Iterations of each projection are performed within cycles. In this work, we explore the concept that one or more projections can be iterated multiple times within one cycle. The basic equation is:  [1]
where ρqi j is the qth estimate of the grey value ρ for pixel (i,j), Pkθ is the raysum of the kth ray of the projection at angle θ, which intersects (i,j), and P qk∂ is the raysum of the same ray prior to the correction made by Equation [1]. Note that, immediately after application of Equation [1] to a ray, P q+1k∂ = Pkθ. In other words, MART forces a match of each ray to its raysum. MART and other ART algorithms converge at different rates, depending on the order in which the rays are considered. The worst case seems to be considering the angles consecutively, as in our original work (1) and we and others have devised projection orderings that are better than random (2, 3, 4, 5, 6, 7), though not yet optimal (8). All projection orderings proposed so far have only used each projection once per cycle. Here we repeat orthogonal pairs of certain projections (cf. (9)) using three ray tracing methods to define the relationship between the pixels and the projection data (10, 11, 12), i.e., the weights wi jkθ in:  [2]
Most of our testing with our C++ test bed software is with fan beams, -120° to 120°, with a projection every 6°, and equal pixel and detector widths. We define a ?control pair? to be two mutually perpendicular projections. We considered three ?Control Angle? options:
In between the control pairs, we process the remaining projections in one of three different ways:
In dealing with reconstruction, we have to be concerned with two sets of values: the range of values of the image, and the range of displayable values. In our case, they both happen to be the same, but this is not always the case. To display values > 255, we can clip them, i.e., set any value over 255 to 255, or we can apply a factor to all values to bring them into displayable range 0 to 255. We can also constrain the image values when reconstructing, either just the control angles, or the other projection values, or both. Reconstructions of the Shepp-Logan phantom with the three alternate ray tracing methods, with MART and the three control angle scenarios, for parallel and fan beams, with various numbers of non-control projections processed between control projections, will be shown and compared. The Siddon method works poorly. The use of control angles speeds up convergence. Acknowledgements Supported in part by grants from Manitoba Institute for Child Health, Friends You Can Count On, and CancerCare Manitoba. References
Glen D. Colquhoun1 Richard Gordon1,2,* 1Silver Bog Research Inc. 350 Inkster Blvd. Winnipeg R2W 0K3, Canada 2Dept. of Radiology University of Manitoba 820 Sherbrook Avenue Winnipeg R3A1R9, Canada *GordonR@ms.Umanitoba.ca Key words: MART, Computed tomography algorithms, Projection orderings. Abbreviations: ART, Algebraic Reconstruction Technique; CT, Computed tomography; MART, Multiplicative ART. BCD Using Ground Penetrating Radar Techniques In Canada today, one woman in nine can expect to develop breast cancer during her lifetime and one in 25 will die from the disease (Health Canada data). Currently, X-ray mammography is the most effective technique for early stage breast cancer detection. However, due to structure noise and the low contrast between cancer and normal tissue observed in X-ray imagery, mammography yields to a high false negative rate (4%-34%) and a high false positive rate (70%). As a result of these constraints, several alternative approaches for breast imaging have been proposed. Some of them, like MRI or ultrasound, have been shown to be effective for breast cancer detection. However, MRI is too expensive and ultrasound does not have sufficient spatial resolution to be considered for mass screening. In recent years, researchers from the University of Calgary, Dartmouth College, University of Wisconsin-Madison -- to name a few -- have been investigating the use of microwave imaging technology for Breast Cancer Detection (BCD) purposes. As shown by Surowiec et al., the dielectric properties of cancer and normal tissue exhibit excellent contrast at the microwave frequency range. However, this technique lacks the high spatial resolution provided by X-ray mammography due to its small frequency operation range. As shown by Hagness et al., radar techniques such as confocal imaging, reference substraction, and surface removal can be successfully used to form Breast Microwave Images (BMI) with a high contrast between cancer and normal tissue. The motivation of this work is to present an alternative focusing method for breast imaging, coupled with the use of digital signal processing techniques for increasing the spatial resolution in microwave breast imagery. The department of Electrical and Computer Engineering at the University of Manitoba has developed a Stepped Frequency Continuous Wave Ground Penetrating Radar (GPR) test system with a bandwidth of 11 GHz based on a vector network analyzer and a horn antenna that are connected to a PC laptop that uses a GPIB communications protocol. This type of system allows the synthetization of different pulse shapes that can be more appropriate for the application mentioned above. Another advantage of such a type of system is the possibility of working at different operational frequencies that can be more suitable for the different target compositions. We have investigated the use of the Frequency-wavenumber (F-K) migration technique -- a popular method for focusing targets in GPR used by the Geological Sciences community -- using a phantom that consists of saline water and a corn syrup mixture to model cancer and breast tissue respectively as suggested by P. M. Meaney of Dartmouth College. This algorithm analyzes the frequency behavior of the scans both in the range and the scan direction in order to converge the scatter responses to its original position on the image. In GPR, the hyperbolic signatures usually seen in GPR images can be collapsed to represent the spatial geometry of for example, a landmine. Essentially, F-K migration is designed to back propagate the wave equation so that the position of a point source or an ensemble of point sources, i.e., the target, can be visualized. The algorithm involves a simple mapping from the frequency domain to the vertical wavenumber by means of an interpolation procedure for the data samples known as the Stolt interpolation. The F-K algorithm only requires the propagation speed on the medium, and unlike GPR, in BMI this value can be known a priori. In order to increase the spatial resolution of our system, a digital signal processing algorithm based on Auto-Regressive (AR) modeling was used. The coefficients of the AR model were calculated using the Burg method, and the order was obtained using the minimum square error, variance and mean differences between the model output and the original signal. Our initial results have generated focused images with higher resolution when scanning in a configuration similar to stripmap Synthetic Aperture Radar. With the development of innovative signal and image processing techniques, the ultra wideband microwave system already available in our department has the potential to detect very small cancer tumors before metastatis occurs. Acknowledgments The authors would like to thank Stephanie Moorhouse, Department of Microbiology, and Maryam Heshmatzadeh, Department of Electrical and Computer Engineering, both at the University of Manitoba, for their time and help. Daniel Flores-Tapia1 Gabriel Thomas1,* Sima Noghanian1 Manivannan Poyvasi1 S. Pistorius2 1Dept. of Electrical and Computer Engineering University of Manitoba Winnipeg, Canada, R3T 6A8 2CancerCare Manitoba Depts. of Physics and Astronomy & Radiology University of Manitoba Winnipeg, Canada R3T 6A8 *thomas@ee.umanitoba.ca Key words: Breast cancer detection, Microwave, Ground penetrating radar. Abbreviations: BCD, Breast Cancer Detection; GPR, Ground Penetrating Radar); BMI, Breast Microwave Images. A Pseudo-tangential IMRT Technique for the Whole Large Left Breast Radiation Therapy Using Helios/Eclipse System Purpose: To improve the dose uniformity of standard tangential IMRT plan for the whole large left breast radiation therapy. Materials and Methods: Using the Helios/Eclipse treatment planning system, 6 patients with left breast cancer were planned to receive radiation therapy as a part of their breast conservation therapy following lumpectomy. The separations of these breasts were between 22-26 cm. This is a volume-based inverse planning approach. CT simulation was performed for each patient, and images of 3-mm slices were obtained. The PTV includes the whole breast with 2 cm-sup/inf margins, the posterior margin was along the lung/chest wall border and the medial/lateral wires, and anterior was 3 mm below the skin surface. The PTV contour basically follows the parenchyma. The heart and lung were defined as the organs at risk (OAR). The dose prescribed to the whole breast was 50.4 Gy delivered with 1.8 Gy per fraction. The pseudo tangential IMRT technique (PT-IMRT) basically combines the 4 tangential beams of dual energies (6+18X) with two additional beams angled less than 15 degree from each side. The two additional beams are primarily used to reduce the high dose volume. If the maximum dose is larger than 110%, an additional OAR was drawn at the lateral side. After the inverse optimization, 2 cm skin flash was added to each beam. Multiple static segments were used for the IMRT delivery. The comparisons were made for (i) V95 (volume receiving ≥ 95% relative dose) and V90 for PTV; (ii) V10, V20, V30 and V60 (cc) for heart; (iii) V10, V20, V30, and V40 (cc) for left lung; (iv) the maximum dose; (v) the V105 (cc) (volume receiving doses ≥ 105% in cc) for external; (vii) a reference point dose for the right breast (5 cm right and 1 cm posterior to the P point). The calculation was made for each patient. Besides the PT-IMRT plan, a 3D plan and a tangential IMRT (T-IMRT) plan, both using 4 beams of dual energies, were also generated. Results: For each patient, the parameters stated above were calculated. The V95 and V90 (especially V95) for PTV were better using the PT-IMRT technique compared to the other two. Most importantly, the V105 (cc) for external was substantially reduced with the technique. The maximum dose of T-IMRT is the largest. The maximum dose of the 3D plan was comparable to PT-IMRT, but its V105 (cc) was usually the largest. Also, for each patient, the V30 for heart and lung was comparable for all three techniques but the V10 and V20 was higher for PT-IMRT compared to T-IMRT and 3D. The V60 (cc) for heart and V40 (cc) for left lung were comparable for all three techniques. The point reference dose to the right breast was about 1.8% higher for the PT-IMRT technique compared to 3D. Conclusion: The PT-IMRT technique resulted in the most homogenous dose distribution for PTV, the lowest maximum dose for each of the 6 patients. The higher V10 and V20 for the heart and lung are at fairly low doses (at about 5 Gy and 10 Gy, respectively) and as such would be clinically insignificant because the excessive risks for heart and lung were aroused from V60(cc) and V40(cc), respectively. Improved dose distribution thus achieved with PT-IMRT showed less acute effects and is expected to cause less late side effects as well. Huaiqun (Harrison) Guan Department of Radiation Oncology Henry Ford Hospital Detroit, MI 48202 hquan1@hfhs.org Key words: Breast cancer treatment, IMRT. Abbreviations: OAR, Organs at Risk; IMRT, Intensity Modulated Radiation Therapy; CT, Computer Tomography; PTV, Planning Target Volume. |
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