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- Ariel, Gil, et al.
(författare)
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Gaussian Beam Decomposition of High Frequency Wave Fields Using Expectation-Maximization
- 2011
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 230:6, s. 2303-2321
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Tidskriftsartikel (refereegranskat)abstract
- A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation–maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.
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- Engquist, M., et al.
(författare)
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Surgery versus nonsurgical treatment of cervical radiculopathy : A prospective, randomized study comparing surgery plus physiotherapy with physiotherapy alone with a 2-year follow-up
- 2013
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Ingår i: Spine. - : Lippincott Williams & Wilkins. - 0362-2436 .- 1528-1159. ; 38:20, s. 1715-1722
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Tidskriftsartikel (refereegranskat)abstract
- STUDY DESIGN.: Prospective randomized controlled trial. OBJECTIVE.: To study the outcome of anterior cervical decompression and fusion combined with a structured physiotherapy program compared with the same physiotherapy program alone for patients with cervical radiculopathy. SUMMARY OF BACKGROUND DATA.: Knowledge concerning the effects of interventions for patients with cervical radiculopathy is scarce due to a lack of randomized studies. METHODS.: Sixty-three patients were randomized to surgery with postoperative physiotherapy (n = 31) or physiotherapy alone (n = 32). The surgical group was treated with anterior cervical decompression and fusion. The physiotherapy program included general/specific exercises and pain-coping strategies. The outcome measures were disability (Neck Disability Index), neck and arm pain intensity (visual analogue scale), and the patient's global assessment. Patients were followed for 24 months. RESULTS.: The result from the repeated-measures analysis of variance showed no significant between-group difference for Neck Disability Index (P = 0.23). For neck pain intensity, the repeated-measures analysis of variance showed a significant between-group difference during the study period in favor of the surgical group (P = 0.039). For arm pain intensity, no significant between-group differences were found according to the repeated-measures analysis of variance (P = 0.580). Eighty-seven percent of the patients in the surgical group rated their symptoms as "better/much better" at the 12-month follow-up compared with 62% in the nonsurgical group (P < 0.05). At 24 months, the corresponding figures were 81% and 69% (P = 0.28). The difference was significant only at the 12-month follow-up in favor of the surgical group. Significant reduction in Neck Disability Index, neck pain, and arm pain compared with baseline was seen in both groups (P < 0.001). CONCLUSION.: In this prospective, randomized study of patients with cervical radiculopathy, it was shown that surgery with physiotherapy resulted in a more rapid improvement during the first postoperative year, with significantly greater improvement in neck pain and the patient's global assessment than physiotherapy alone, but the differences between the groups decreased after 2 years. Structured physiotherapy should be tried before surgery is chosen. Copyright © 2013 Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
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- Tanushev, Nicolay M., et al.
(författare)
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Gaussian beam decomposition of high frequency wave fields
- 2010
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 228:23, s. 8856-8871
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a method of decomposing a highly oscillatory wave field into a sparse superposition of Gaussian beams. The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. The methodology is described for Rd with numerical examples for d=2. In the first example, a field generated by an interface reflection of Gaussian beams is decomposed into a superposition of Gaussian beams. The beam parameters are reconstructed to a very high accuracy. The data in the second example is not a superposition of a finite number of Gaussian beams. The wave field to be approximated is generated by a finite difference method for a geometry with two slits. The accuracy in the decomposition increases monotonically with the number of beams.
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