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  • 1.
    Eriksson, Henrik
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Eriksson, Kimmo
    Karlander, Johan
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Svensson, Lars Erik
    KTH, Superseded Departments, Mathematics.
    Wästlund, Johan
    KTH, Superseded Departments, Mathematics.
    Sorting a bridge hand2001In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 241, no 1-3, p. 289-300Article in journal (Refereed)
    Abstract [en]

    Sorting a permutation by block moves is a task that every bridge player has to solve every time she picks up a new hand of cards. It is also a problem for the computational biologist, for block moves are a fundamental type of mutation that can explain why genes common to two species do not occur in the same order in the chromosome, It is not known whether there exists an optimal sorting procedure running in polynomial time. Bafna and Pevzner gave a polynomial time algorithm that sorts any permutation of length n in at most 3n/4 moves. Our new algorithm improves this to [(2n - 2)/3] for n greater than or equal to 9. For the reverse permutation, we give an exact expression for the number of moves needed, namely [(n + 1)/2]. Computations of Bafha and Pevzner up to n = 10 seemed to suggest that this is the worst case; but as it turns out, a first counterexample occurs for n = 13, i.e. the bridge player's case. Professional card players never sort by rank, only by suit. For this case, we give a complete answer to the optimal sorting problem.

  • 2.
    Laksov, Dan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Svensson, Lars
    Thorup, Anders
    Copenhagen University, Dept. of Mathematics.
    The spectral mapping theorem, norms on rings, and resultants2000In: L'Enseignement Mathématique. Revue Internationale. 2e Série, ISSN 0013-8584, Vol. 46, no 3-4, p. 349-358Article in journal (Refereed)
  • 3.
    Olivecrona, Henrik
    et al.
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Olivecrona, Lotta
    Karolinska Institutet, Department of Clinical Science, Intervention and Technology, Division of Radiology.
    Weidenhielm, Lars
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Noz, Marilyn E.
    New York University, Department of Radiology.
    Maguire Jr., Gerald Q.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Zeleznik, Michael P.
    RAHD Oncology Products, St. Lous, MO, USA.
    Svensson, Lars E.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Jonson, T.
    Stability of acetabular axis after total hip arthroplasty, repeatability using CT and a semiautomated program for volume fusion2003In: Acta Radiologica, ISSN 0284-1851, E-ISSN 1600-0455, Vol. 44, no 6, p. 653-661Article in journal (Refereed)
    Abstract [en]

    Purpose: To validate a CT method for detecting changes in acetabular cup orientation after THA. Material and Methods: 26 CT examinations were obtained from a pelvic model with an uncemented acetabular cup. The model position was altered between acquisitions, but the cup axis angle vis-a-vis the pelvis was maintained. Data sets were combined into 37 pairs, each containing a unique positioning error. The pelvi in different examinations were fused, creating transformed volumes. Landmarks corresponding to the cup before and after fusion were placed interactively by two independent examiners. The orientation of the acetabular axis was calculated for each volume and compared across volumes. Results: Before fusion the mean angle error between the acetabular axes was 4.17degrees (SD +/- 1.95degrees). After fusion the mean angle error was 0.36degrees (SD +/- 0.17). The 95% repeatability limits were below 0.7degrees. There was no significant interobserver difference. Analysis of the cup landmarking pattern by condition numbers and individual landmark errors showed stability. Conclusion: Non-invasive fusion of CT volumes and a stable landmarking pattern for the acetabular cup outperforms routine plain radiography in detecting changes in the orientation of the acetabular axis over time. The method delivers both visual and numerical output and could be used in clinical practice.

  • 4.
    Olivecrona, Henrik
    et al.
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Weidenhielm, Lars
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Olivecrona, Lotta
    Karolinska Institutet, Department of Clinical Science, Intervention and Technology, Division of Radiology.
    Beckman, M. O.
    Stark, Andreas
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Noz, Marilyn E.
    New York University, Department of Radiology.
    Maguire Jr., Gerald Q.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Zeleznik, Michael P.
    RAHD Oncology Products, St. Loius MO, USA.
    Svensson, Lars E.
    KTH, Superseded Departments, Mathematics.
    Jonson, T.
    A new CT method for measuring cup orientation after total hip arthroplasty: A study of 10 patients2004In: Acta Orthopaedica Scandinavica, ISSN 0001-6470, Vol. 75, no 3, p. 252-260Article in journal (Refereed)
    Abstract [en]

    Background It is difficult to assess the orientation of the acetabular component on routine radiographs. We present a method for determining the spatial orientation of the acetabular component after total hip arthroplasty (THA) using computed tomography. Patients and methods Two CT-scans, 10 min apart, were obtained from each of 10 patients after THA. Using locally developed software, two independent examiners measured the orientation of the acetabular component in relation to the pelvis. The measurements were repeated after one week. To be independent of the patient position during scanning, the method involved two steps. Firstly, a 3D volumetric image of the pelvis was brought into a standard pelvic orientation, then the orientation of the acetabular component was measured. The orientation of the acetabular component was expressed as operative anteversion and inclination relative to an internal pelvic reference coordinate system. To evaluate precision, we compared measurements across pairs of CT volumes between observers and trials. Results Mean absolute interobserver angle error was 2.3degrees for anteversion (range 0-6.6degrees), and 1.1degrees for inclination (range 0-4.6degrees). For interobserver measurements, the precision, defined as one standard deviation, was 2.9degrees for anteversion, and 1.5degrees for inclination. A Student's West showed that the overall differences between the examiners, trials, and cases were not significant. Data were normally distributed and were not dependent on examiner or trial. Interpretation We conclude that the implant angles of the acetabular component in relation to the pelvis could be detected repeatedly using CT, independently of patient positioning.

  • 5.
    Olivecrona, Henrik
    et al.
    Soder Sjukhuset, Dept Hand Surgery.
    Weidenhielm, Lars
    Karolinska Hosp, Dept Orthoped.
    Olivecrona, Lotta
    Karolinska Hosp, Dept Radiologyy.
    Noz, Marilyn E.
    New York University, Department of Radiology.
    Maguire Jr., Gerald Q.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Zeleznik, Michael P.
    RAHD Oncology Products, St. Louis, MO, USA.
    Svensson, Lars E.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Jonson, T.
    Spatial component position in total hip arthroplasty - Accuracy and repeatability with a new CT method2003In: Acta Radiologica, ISSN 0284-1851, E-ISSN 1600-0455, Vol. 44, no 1, p. 84-91Article in journal (Refereed)
    Abstract [en]

    Purpose: 3D detection of centerpoints of prosthetic cup and head after total hip arthroplasty (THA) using CT. Material and Methods: Two CT examinations, 10 min apart, were obtained from each of 10 patients after THA. Two independent examiners placed landmarks in images of the prosthetic cup and head. All landmarking was repeated after 1 week. Centerpoints were calculated and compared. Results: Within volumes, all measurements of centerpoints of cup and head fell, with a 95% confidence, within one CT-voxel of any other measurement of the same object. Across two volumes, the mean error of distance between center of cup and prosthetic head was 1.4 mm (SD 0.73). Intra- and interobserver 95% accuracy limit was below 2 mm within and below 3 mm across volumes. No difference between intra- and interobserver measurements occurred. A formula for converting finite sets of point landmarks in the radiolucent tread of the cup to a centerpoint was stable. The percent difference of the landmark distances from a calculated spherical surface was within one CT-voxel. This data was normally distributed and not dependent on observer or trial. Conclusion: The true 3D position of the centers of cup and prosthetic head can be detected using CT. Spatial relationship between the components can be analyzed visually and numerically.

  • 6.
    Olivecrona, Lotta
    et al.
    Karolinska Institutet, Department of Clinical Science, Intervention and Technology, Division of Radiology.
    Aspelin, Peter
    Karolinska Institutet, Department of Clinical Science, Intervention and Technology, Division of Radiology.
    Weidenhielm, Lars
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Stark, Andreas
    Karolinska Institute, Department of Molecular Medicine and Surgery.
    Noz, Marilyn E.
    New York University, Department of Radiology.
    Maguire Jr., Gerald Q.
    KTH, School of Information and Communication Technology (ICT), Communication Systems, CoS.
    Zeleznik, Michael P.
    RAHD Oncol Prod, St Louis, MO USA .
    Svensson, Lars E.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Olivecrona, Henrik
    Soder Sjukhuset, Dept Hand Surgery.
    Standard orientation of the pelvis: Validation on a model and ten patients2005In: Acta Radiologica, ISSN 0284-1851, E-ISSN 1600-0455, Vol. 46, no 1, p. 74-82Article in journal (Refereed)
    Abstract [en]

    Purpose: To validate an image post-processing method for re-orienting the pelvis in CT volumes to a standardized orientation in a model and in 10 patients. Material and Methods: Twenty-four CT volumes of a pelvic model and 10 pairs of postoperative total hip arthroplasty (THA) patient CT scans were rotated to a defined pelvic standard orientation and the rotation was recorded. For precision, a test-retest procedure was used. For accuracy, three exactly represented coordinate points were used. For clinical application, the standard orientation was used for calculating the direction of acetabular cup migration from a previous model study. Results: Precision of pelvic standard orientation, calculated as maximal directional error, was better than 1degrees in the model study and better than 1.5degrees in the patient study. Accuracy, expressed as angle between ideal and measured coordinate axes, was 0.1degrees for x, y, z axes. No measurable systematic errors were found. When applied to acetabular cup migration in the model, standardization of pelvic orientation had no significant effect on the measurements. Conclusion: Reorienting the pelvis during image post-processing was shown to be accurate. It enables measurements relative to the pelvis and minimizes the dependency of patient positioning.

  • 7.
    Olivecrona, Lotta
    et al.
    Karolinska Hospital, Department of Radiology.
    Crafoord, Joakim
    Karolinska Hospital, Department of Radiology.
    Olivecrona, Henrik
    Karolinska Hosp, Dept Orthopaed.
    Noz, Marilyn E.
    New York University, Department of Radiology.
    Maguire Jr., Gerald Q.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Zeleznik, Michael P.
    RAHD Oncology Products, St. Louism MO, USA.
    Svensson, Lars E.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Weidenhielm, Lars
    Karolinska Hosp, Dept Orthopaed.
    Acetabular component migration in total hip arthroplasty using CT and a semiautomated program for volume merging2002In: Acta Radiologica, ISSN 0284-1851, E-ISSN 1600-0455, Vol. 43, no 5, p. 517-527Article in journal (Refereed)
    Abstract [en]

    Purpose: To develop a non-invasive method for detection of acetabular cup migration after total hip arthroplasty (THA) with a higher degree of accuracy than routine plain radiography. Material and Methods: Two CT examinations, 10 min apart, were obtained from each of 10 patients that had undergone THA. Using an in-house developed semiautomated program for volume merging, the pelves in the two examinations were fused and the acetabular cup was visually and numerically evaluated to test the method's accuracy in detecting migration. Results: In the visual evaluation of the best match a 1-mm translation of the cup was detectable. The numerical evaluation, comparing landmarks placed in the images of the acetabular cup and the head of the femur component in the two examinations, showed the mean difference in orientation of acetabular axes to be 2.5degrees, the mean distance between centre of cup face to be 2.5 mm and the mean distance between centre of the head of the prosthetic femoral component to be 1 mm. Conclusion: This method has a significantly higher accuracy than routine plain radiography in detecting acetabular cup migration and could be used in clinical practice. It gives both a visual and a numerical correlate to migration.

1 - 7 of 7
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