GNSS multi-interference source centroid location based on clustering centroid convergence

In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

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Weighted centroid location algorithm in wireless sensor network

IET International Communication Conference on Wireless Mobile and Computing (CCWMC 2011) ◽

10.1049/cp.2011.0921 ◽

2011 ◽

Cited By ~ 1

Author(s):

Lixiong Tan ◽

Fei Luo ◽

Kai Liu

Keyword(s):

Wireless Sensor Network ◽

Sensor Network ◽

Wireless Sensor ◽

Location Algorithm ◽

Centroid Location

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Effect of signal truncation on centroid location error estimation

Optical Engineering ◽

10.1117/1.600609 ◽

1996 ◽

Vol 35 (4) ◽

pp. 1221 ◽

Cited By ~ 3

Author(s):

Ikram E. Abdou

Keyword(s):

Error Estimation ◽

Location Error ◽

Centroid Location

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Reliability of Tibiofemoral Contact Area and Centroid Location in an Upright, Open MRI (UO-MRI)

10.21203/rs.2.22418/v2 ◽

2020 ◽

Author(s):

Andrew Schmidt ◽

David J. Stockton ◽

Michael A. Hunt ◽

Andrew Yung ◽

Bassam A. Masri ◽

...

Keyword(s):

Measurement Error ◽

Contact Area ◽

Joint Mechanics ◽

Detectable Change ◽

Intra Class Correlation ◽

Open Mri ◽

Smallest Detectable Change ◽

Knee Joint Mechanics ◽

Standard Error Of Measurement ◽

Centroid Location

Abstract Background: Biomechanical studies are often performed using conventional closed-bore MR, which has necessitated simulating weightbearing load on the joint. The clinical applicability of these biomechanical findings is unclear because of the limitations of simulating weightbearing. Upright, open MRI (UO-MRI) can be used to assess knee joint mechanics, in particular contact area and centroid location. However, it is not clear how reliably measurements of contact area and centroid location can be made in upright weightbearing postures. Methods: Manual segmentation of cartilage regions in contact was performed and centroids of those contact areas were automatically determined for the medial (MC) and lateral (LC) tibiofemoral compartments. To assess reliability, inter-rater, test-retest, and intra-rater reliability were determined by intra-class correlation (ICC 3,1 ), standard error of measurement (SEM), smallest detectable change with 95% confidence (SDC 95 ). Accuracy was assessed by using a high-resolution, 7T MRI as a reference and determined by measurement error (%). Results: Contact area and centroid location reliability (inter-rater, test-retest, and intra-rater) for sagittal scans in the MC demonstrated ICC 3,1 values from 0.95-0.99 and 0.98-0.99 respectively, and in the LC from 0.83-0.91 and 0.95-1.00 respectively. The smallest detectable change in contact area was 1.28% in the MC and 0.95% in the LC. Contact area and centroid location reliability for coronal scans in the MC demonstrated ICC 3,1 values from 0.90-0.98 and 0.98-1.00 respectively, and in the LC from 0.76-0.94 and 0.93-1.00 respectively. The smallest detectable change in contact area was 0.65% in the MC and 1.41% in the LC. Contact area segmentation was accurate to within 4.81% measurement error. Conclusions: Knee contact area and contact centroid location can be assessed in upright weightbearing MRI with good to excellent reliability and accuracy within 5%. The lower field strength used in upright, weightbearing MRI does not compromise the reliability of tibiofemoral contact area and centroid location measures.

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Reliability of tibiofemoral contact area and centroid location in upright, open MRI

BMC Musculoskeletal Disorders ◽

10.1186/s12891-020-03786-1 ◽

2020 ◽

Vol 21 (1) ◽

Author(s):

Andrew M. Schmidt ◽

David J. Stockton ◽

Michael A. Hunt ◽

Andrew Yung ◽

Bassam A. Masri ◽

...

Keyword(s):

Contact Area ◽

Soft Tissues ◽

Cruciate Ligament ◽

Lateral Compartment ◽

Medial Compartment ◽

Detectable Change ◽

Lower Field ◽

Open Mri ◽

Smallest Detectable Change ◽

Centroid Location

Abstract Background Imaging cannot be performed during natural weightbearing in biomechanical studies using conventional closed-bore MRI, which has necessitated simulating weightbearing load on the joint. Upright, open MRI (UO-MRI) allows for joint imaging during natural weightbearing and may have the potential to better characterize the biomechanical effect of tibiofemoral pathology involving soft tissues. However open MRI scanners have lower field strengths than closed-bore scanners, which limits the image quality that can be obtained. Thus, there is a need to establish the reliability of measurements in upright weightbearing postures obtained using UO-MRI. Methods Knees of five participants with prior anterior cruciate ligament (ACL) rupture were scanned standing in a 0.5 T upright open MRI scanner using a 3D DESS sequence. Manual segmentation of cartilage regions in contact was performed and centroids of these contact areas were automatically determined for the medial and lateral tibiofemoral compartments. Inter-rater, test-retest, and intra-rater reliability were determined and quantified using intra-class correlation (ICC3,1), standard error of measurement (SEM), and smallest detectable change with 95% confidence (SDC95). Accuracy was assessed by using a high-resolution 7 T MRI as a reference. Results Contact area and centroid location reliability (inter-rater, test-retest, and intra-rater) for sagittal scans in the medial compartment had ICC3,1 values from 0.95–0.99 and 0.98–0.99 respectively. In the lateral compartment, contact area and centroid location reliability ICC3,1 values ranged from 0.83–0.91 and 0.95–1.00 respectively. The smallest detectable change in contact area was 1.28% in the medial compartment and 0.95% in the lateral compartment. Contact area and centroid location reliability for coronal scans in the medial compartment had ICC3,1 values from 0.90–0.98 and 0.98–1.00 respectively, and in the lateral compartment ICC3,1 ranged from 0.76–0.94 and 0.93–1.00 respectively. The smallest detectable change in contact area was 0.65% in the medial compartment and 1.41% in the lateral compartment. Contact area was accurate to within a mean absolute error of 11.0 mm2. Conclusions Knee contact area and contact centroid location can be assessed in upright weightbearing MRI with good to excellent reliability. The lower field strength used in upright, weightbearing MRI does not compromise the reliability of tibiofemoral contact area and centroid location measures.

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Relative Nucleus Pulposus Area and Position Alter Disk Joint Mechanics

Journal of Biomechanical Engineering ◽

10.1115/1.4043029 ◽

2019 ◽

Vol 141 (5) ◽

Cited By ~ 1

Author(s):

Bo Yang ◽

Yintong Lu ◽

Colin Um ◽

Grace D. O'Connell

Keyword(s):

Nucleus Pulposus ◽

Computational Models ◽

Complex Loading ◽

Element Model ◽

Axial Rotation ◽

Intervertebral Disk ◽

Joint Mechanics ◽

Peak Pressures ◽

Flexion And Extension ◽

Centroid Location

Aging and degeneration of the intervertebral disk are noted by changes in tissue composition and geometry, including a decrease in nucleus pulposus (NP) area. The NP centroid is positioned slightly posterior of the disk's centroid, but the effect of NP size and location on disk joint mechanics is not well understood. We evaluated the effect of NP size and centroid location on disk joint mechanics under dual-loading modalities (i.e., compression in combination with axial rotation or bending). A finite element model (FEM) was developed to vary the relative NP area (NP:Disk area ratio range = 0.21–0.60). We also evaluated the effect of NP position by shifting the NP centroid anteriorly and posteriorly. Our results showed that compressive stiffness and average first principal strains increased with NP size. Under axial compression, stresses are distributed from the NP to the annulus, and stresses were redistributed toward the NP with axial rotation. Moreover, peak stresses were greater for disks with a smaller NP area. NP centroid location had a greater impact on intradiscal pressure during flexion and extension, where peak pressures in the posterior annulus under extension was greater for disks with a more posteriorly situated NP. In conclusion, the findings from this study highlight the importance of closely mimicking NP size and location in computational models that aim to understand stress/strain distribution during complex loading and for developing repair strategies that aim to recapitulate the mechanical behavior of healthy disks.

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Tibiofemoral contact and alignment in patients with anterior cruciate ligament rupture treated nonoperatively versus reconstruction

The Bone & Joint Journal ◽

10.1302/0301-620x.103b9.bjj-2020-1955.r1 ◽

2021 ◽

Vol 103-B (9) ◽

pp. 1505-1513

Author(s):

David J. Stockton ◽

Andrew M. Schmidt ◽

Andrew Yung ◽

Jane Desrochers ◽

Honglin Zhang ◽

...

Keyword(s):

Acl Reconstruction ◽

Contact Area ◽

Cruciate Ligament ◽

Acl Injury ◽

Acl Rupture ◽

Healthy Controls ◽

The Mean ◽

Anterior Cruciate ◽

Time Since Injury ◽

Centroid Location

Aims Anterior cruciate ligament (ACL) rupture commonly leads to post-traumatic osteoarthritis, regardless of surgical reconstruction. This study uses standing MRI to investigate changes in contact area, contact centroid location, and tibiofemoral alignment between ACL-injured knees and healthy controls, to examine the effect of ACL reconstruction on these parameters. Methods An upright, open MRI was used to directly measure tibiofemoral contact area, centroid location, and alignment in 18 individuals with unilateral ACL rupture within the last five years. Eight participants had been treated nonoperatively and ten had ACL reconstruction performed within one year of injury. All participants were high-functioning and had returned to sport or recreational activities. Healthy contralateral knees served as controls. Participants were imaged in a standing posture with knees fully extended. Results Participants’ mean age was 28.4 years (SD 7.3), the mean time since injury was 2.7 years (SD 1.6), and the mean International Knee Documentation Subjective Knee Form score was 84.4 (SD 13.5). ACL injury was associated with a 10% increase (p = 0.001) in contact area, controlling for compartment, sex, posture, age, body mass, and time since injury. ACL injury was associated with a 5.2% more posteriorly translated medial centroid (p = 0.001), equivalent to a 2.6 mm posterior translation on a representative tibia with mean posteroanterior width of 49.4 mm. Relative to the femur, the tibiae of ACL ruptured knees were 2.3 mm more anteriorly translated (p = 0.003) and 2.6° less externally rotated (p = 0.010) than healthy controls. ACL reconstruction was not associated with an improvement in any measure. Conclusion ACL rupture was associated with an increased contact area, posteriorly translated medial centroid, anterior tibial translation, and reduced tibial external rotation in full extension. These changes were present 2.7 years post-injury regardless of ACL reconstruction status. Cite this article: Bone Joint J 2021;103-B(9):1505–1513.

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