Using a numerical method to precisely evaluate the alpha angle in a hip image

  • Chung-Liang Lai
  • Wei-Min Chi
  • Ying-Jui Ho
  • Chien-Chung Lin
  • Hsiao-Che Lin
  • Chin-Liang Kuo
  • Jian-Horng ChenEmail author
Original Article


The alpha angle is a parameter extensively used to assess for cam-type femoroacetabular impingement (FAI) in a 2D image of the hip. As this angle requires estimation of the axis of the femoral neck, the drawing of this axis often results in measurement errors due to subjective judgment, influencing inter-rater and intra-rater agreements. In the present study, sampling points were captured from the edges of a femoral neck and head in the 2D image, and the best curves of the two were fitted respectively by using the curve fitting method. The morphology of the femoral neck was outlined by two polynomials, and the femoral head was represented by an equation of a circle. By means of the proposed method, the results reveal that the inter-rater ICCs in X-ray and MRI were respectively 0.905 and 0.969, and the intra-rater ICCs in X-ray and MRI were respectively 0.892 and 0.840. The Bland-Altman plot shows that the values obtained by the proposed method and the conventional method were not consistent; nevertheless, the linear regression analysis indicated the two measurement results had a significant association (p < 0.001). This study provides a repeatable and agreed α angle measuring method, which contributes to identifying normal and abnormal femoral head-neck morphologies. The proposed numerical method would contribute to diagnose early FAI.


Femoroacetabular impingement Alpha angle Femoral neck axis Numerical method 



We would like to show our gratitude to all the people who greatly assisted the research, and we also thank three anonymous reviewers for their comments.

Funding information

This research project was supported by the Ministry of Science and Technology of the Republic of China, Taiwan, under Contract No. MOST104-2221-E-040-002-MY2.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflicts of interest.


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Copyright information

© International Federation for Medical and Biological Engineering 2019

Authors and Affiliations

  • Chung-Liang Lai
    • 1
    • 2
  • Wei-Min Chi
    • 3
  • Ying-Jui Ho
    • 4
  • Chien-Chung Lin
    • 5
    • 6
  • Hsiao-Che Lin
    • 7
  • Chin-Liang Kuo
    • 8
  • Jian-Horng Chen
    • 8
    • 9
    Email author
  1. 1.Department of Occupational TherapyAsia UniversityTaichungTaiwan, Republic of China
  2. 2.Department of Physical Medicine and Rehabilitation, Taichung HospitalMinistry of Health and WelfareTaichungTaiwan, Republic of China
  3. 3.College of Mechanical and Automotive EngineeringZhaoqing UniversityZhaoqingChina
  4. 4.Department of PsychologyChung Shan Medical UniversityTaichungTaiwan, Republic of China
  5. 5.Orthopedic DepartmentTaichung Armed Forces General HospitalTaichungTaiwan, Republic of China
  6. 6.Department of Orthopedic Surgery, Tri-Service General HospitalNational Defense Medical CenterTaipeiTaiwan, Republic of China
  7. 7.Central Region CampusIndustrial Technology Research InstituteNantouTaiwan, Republic of China
  8. 8.School of Physical TherapyChung Shan Medical UniversityTaichungTaiwan, Republic of China
  9. 9.Department of OrthopedicsChung Shan Medical University HospitalTaiwanRepublic of China

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