ISSN 0972-978X 

  About COAA








Trıangle Theorem For Developmental Dysplasıa Of Hıp

Cem Copuroglu, Mert Ozcan
Department of Orthopaedıcs and Traumatology, Trakya unıversıty, edırne-turkey.

Address for Correspondence:
Department of Orthopaedıcs and Traumatology,
Trakya Unıversıty, Edırne-Turkey.

Phone: +90 284 2357641-4707, +90 532 3361923
Fax: +90 284 2353941


Introduction Ultrasonography and roentgenography are basic imaging modalities to detect developmental dysplasia of the hip (DDH). Accepted normal value for ultrasonographically measured alpha angle according to Grafs’ technique is 60 degrees or more and accepted normal value for an acetabular index measured on a plane roentgenogram is 30 degrees or less, in a mature hip. The aim of this study is to point out the negative correlation between the ultrasonographically measured alpha angle and the radiologically measured acetabular index. 
As these images are put over each other in a vertical manner; a right angled triangle is formed when the deepest point of the acetabulum is the intersection point. We name this triangle; ‘DDH triangle’. 
When the alpha angle increases, the opposite leg of the triangle which corresponds to the acetabular depth increases and the other angle of the triangle; acetabular index decreases. 
The sum of alpha and acetabular index degree is usually 90 degrees and the right angle formed by the Hilgenreiners line and the straight line tangent to the ilium is 90 degrees. These three angles form a triangle, which the sum of inner angles of a triangle is 180 degrees.

J.Orthopaedics 2009;6(2)e2


Triangle; Alpha angle;  Acetabular index;  Developmental Dysplasia of the Hip


Various techniques have been proposed for the imaging of the infant hip. Ultrasonography is a well accepted imaging modality in the detection of developmental dysplasia of the hip (DDH) in the neonatal period. When assessment of the bony acetabulum is concerned, radiography of the pelvis is beneficial (1).

 The ultrasonographic assessment of acetabular development may be done using either the alpha angle method of Graf (2) or d/D ratio of Harcke (3). Ultrasonography is an effective method, if applied properly; the position of the patient, the position of the probe and signing the landmarks for measuring the angles are important factors for a reliable result (4). The high level of agreement between different observers is encouraging (5).

In the early times of life, when the femoral heads are composed entirely of cartilage, radiography is of limited value unless a dislocation is present. By 4 to 6 months of age, radiographs become more reliable. Radiography of the pelvis should be obtained with hips in neutral position. Dislocation or subluxation of the femoral head can be recognized by evaluating the relationship of the ossific nucleus of the femoral head and metaphysis to the acetabulum. The radiographic evaluation consists predominantly of a visual assessment; however, measurement of the acetabular index is an objective parameter that may be used in the diagnosis and follow-up of patients with DDH (6).

There is a negative correlation between the alpha angle and the acetabular index degree. It looks like the relation between the inner angles of a right angled triangle. We aimed to examine the relation between the alpha angle and the acetabular index by making a class with a triangle. This is an expert opinion study based on a retrospective study.

Materials and Methods:

Between January 2008 and July 2008, 30 hips of 15 patients, who had pelvis roentgenography when they appealed to our clinic were evaluated ultrasonographically. These roentgenographies were taken in some other clinics which don’t have ultrasonography device. Mean age of the patients was 2.53 (range 1 to 6) months. We use ultrasonography as an imaging tool up to 4 months age in our daily practice. Two, 6 months aged patients having pelvis roentgenogram, who upgrade the mean age, were also included to the study. Ultrasonography was applied to the patients using the Graf technique with the help of a 7.5 MHz, 80 mm linear transducer (Hitachi EUB-405, Hitachi Medical Co., Sendai, Japan).

According to Graf’s technique, the ultrasound picture is taken laterally in a coronal plane and the coronal plane should pass through the center of the hip joint. The center of the hip joint is marked by the lower limb of the os ilium in the acetabulum. If the picture is taken in the correct plane, not directed dorsally or ventrally, some reference points must be identified. Deepest point of the acetabulum, inferior osseous edge of the ilium, and the labrum are seen. To classify certain hip types, Graf has introduced an angle of the bony acetabular roof ‘α’ (alpha) and another for the cartilaginous acetabular roof ‘β’ (beta) (7).

For measuring the alpha and the beta angle, a coronal image of the hip is obtained, and three lines are constructed: base line (drawn parallel to the ossified lateral wall of the ilium), cartilage roof line (drawn from the labrum to the osseous edge of the ilium where concavity of the acetabulum turns to convexity) and the bony roof line (drawn from the deepest point of the acetabulum to the osseous edge of the ilium) (2). Two angles are formed. The alpha angle is formed by the intersection of the base line and the bony roof line (Figure 1). Alpha angle reflects osseous coverage of the femoral head by the acetabulum, the greater the obliquity of the acetabulum roof the smaller the degree of dislocation. Normal value for the alpha angle is 60 degrees. The beta angle is formed by the intersection of the base line and the cartilage roof line. A beta angle of more than 77 degrees indicates eversion of the labrum and subluxation of the hip (8).

Figure 1) Alpha angle. 

Some of our patients who are younger than 6 months, had plane roentgenograms when they appealed to our clinic. Thirty hips of these 15 roentgenograms, thought to be in good quality having a standard measurement plane to carry out a reproducible measurement, were regarded as acceptable and were included to the study.

On a pelvic radiograph various lines may be drawn to help evaluate acetabular maturity and femoral head position. Hilgenreiners line is a horizontal line connecting the superior margins of the triradiate cartilages. Perkins line is a line vertical to Hilgenreiners line drawn through the most superolateral margin of the ossified acetabulum. Acetabular index is the angle between Hilgenreiners line and a line drawn from the most superolateral margin of the ossified acetabulum to the superolateral margin of the triradiate cartilage. DDH is associated with an increased acetabular index angle (9). Normal value for the acetabular index is 30 degrees.

In order to examine whether there is correlation between the alpha angles and the acetabular index degrees, the ultrasonographic images were put over the pelvis AP roentgenograms as they are in vertical planes to each other and the intersection point is the deepest point of the acetabulum (Figure 2a). The intersection of the radiological Hilgenreiners line and the ultrasonographical base line is 90 degrees. A right angled triangle is formed (Figure 2b). Schematic demonstration of this triangle is in Figure 2c. The sum of normal value of alpha angle, normal value of acetabular index and the right angle makes totally 180 degrees, as the total of inner angles of a triangle is always 180 degrees.

Figure 2a: USG image put over the roentgenogram vertically, 2b: DDH triangle, 2c: Schematic presentation of DDH triangle.  

The measurements were done by two assistant professors of Orthopaedics and Traumatology who are interested in pediatric orthopaedics. Measurements were analyzed statistically using a PC program (SPSS for Windows, version 13.0, SPSS Inc., Chicago, Illinois, USA). Correlation between acetabular index and alpha angle was analyzed via calculation of the Pearson correlation coefficient.

Results :

Mean acetabular index was 23.67° for the right hips and 24.67° for the left hips. Right alpha angle and right acetabular index Pearson Correlation Coefficient was -0.343, left alpha angle and left acetabular index Pearson Correlation Coefficient was -0.753. The negative Pearson correlation shows that; when one of the parameter increases, the other parameter decreases.

We realized that at 22 of the 30 hips; the sum of the alpha angle and the acetabular index for the same hips makes 90 degrees. In 5 hips the sum was between 90-94 degrees. In 3 hips the sum was between 86-90 degrees. The total is usually around 90 degrees.

If the alpha angle increases, acetabular index degree decreases. This shows the maturity of the hip. Geometrically, if the opposite leg of an angle is long, the angle is big in a triangle (Figure 3). If the alpha angle is big, it is positively correlated with the opposite leg which shows the depth of the acetabulum(d).That means that if the alpha angle increases, it causes an increase in the depth of the acetabulum. The acetabular index degree decreases as the alpha angle increases at the same time.

Figure 3: DDH triangle  

By using the ultrasonographically measured alpha angle and acetabular index on plane radiographs which both show the bony acetabular depth, we realized that the sum of these angles usually make 90 degrees. When the ultrasonographic image is put over the pelvis roentgenography in a vertical manner; there occurs a triangle which we name ‘DDH triangle’. It is a right angled triangle formed by the intersection of the lines showing the acetabular index, alpha angle and a right angle made by the intersection of the Hilgenreiners line and ultrasonographic straight lateral margin of the ilium(like Perkins line).

Discussion :

Ultrasonography helps to confirm the diagnosis and to identify more subtle forms of DDH (10). Roentgenography is another imaging modality in the diagnosis and follow-up of DDH. As the maturity goes on, the depth of the acetabulum is bigger when the alpha angle increases and the acetabular index decreases.

In a study by Morin et al. (1), one hundred and fifty infant hips were studied using simultaneous ultrasonography and radiography. The reliability of measurement was found to be similar for alpha angle and d/D ratio. For measuring the d/D ratio, two straight lines parallel to the iliac line are drawn, one tangent to the lateral aspect of the femoral head and the other tangent to the deepest point of the acetabulum. The ratio of d (depth of the acetabulum) to D (diameter of the femoral head) multiplied by one hundred gave the index of acetabular depth (1).

However, the acetabular index correlated much better with the d/D ratio than with the alpha angle. The study showed that d/D ratio decreased as the acetabular index increased and d/D ratio decreased as the alpha angle decreased. We realized the negative correlation between the alpha angle and the acetabular index in our study.

Gunay et al. (11) examined 1037 infants’ 2034 hips for detecting DDH. They measured the femoral head coverage, as the ratio of the acetabular width to the maximal femoral head diameter. They found that femoral head coverage is positively correlated with alpha angle.

In another study by Morin et al. (3), they examined 171 infants. The authors used ultrasonography to calculate a parameter which they called femoral head coverage, and this was compared to the acetabular indices obtained via anteroposterior radiographs of the pelvis in the same patients. All hips having femoral head coverage greater than 58% had normal acetabular indices, while all hips with coverage less than 33% had abnormal acetabular indices for their age group. The authors point out that although these threshold values eliminate the possibility of false negatives and thus provide criteria having 100% specificity; the sensitivity is low due to the large region between the two threshold values where normal and abnormal hips both occur. For example, of the 236 hips that had normal acetabular indices, only 107 were above the threshold value of 58% femoral head coverage, which gives a specificity of 45%.

In another study by Melzer (12), sonomorphologic and radiomorphologic examinations were performed on 14 hip joints of children between 36 weeks and 12.5 months of age. A discrepancy between the X-ray and ultrasound image is always found when the contour line of the acetabulum does not correspond to the mid-portion but rather to the ventral or dorsal section of the acetabulum in correct projection of the X-ray image. If the radiologic contour line of the acetabulum is determined by the mid-portion of the acetabulum, the angle of the acetabulum in the X-ray image and the alpha angle in the ultrasound image always add up to 90 degrees (12).  We also realized that the total of alpha angle, the acetabular index and a right angle (formed by the Hilgenreiners line and the straight line tangent to the ilium) makes 180 degrees as the sum of the inner angles of a triangle.

As we described in our triangle theorem; when the depth of the acetabulum is deep (d), alpha angle is big, acetabular index degree is small, femoral head coverage and d/D ratio is big. In a triangle, length of a leg of a triangle is positively correlated with the opposite angle. If the alpha angle is big, acetabulum is deep, the other angle (acetabular index) is small and the hip is more mature.

The relationship between the ultrasonographic alpha angle and the acetabular index in this study  represents a mathematical computation. It initially seems complex but in reality represents the normal changes between normal and abnormal acetabular development. In clinical practice, when a clinician sees an ultrasonographic alpha angle of a patient, he may have knowledge about the acetabular index and femoral head coverage.

Reference :

  1. Morin C, Zouaoui S, Delvalle-Fayada A, Delforge PM, Leclet H. Ultrasound assessment of the acetabulum in the infant hip. Acta Orthopaedica Belgica. 1999; 65(3):261-265.

  2. Graf R. Diagnosis and Management of Infant Hip Dysplasia. Second Edition, Springer. 2007

  3. Morin C, Harcke T, MacEwen GD. The infant hip: Real time US assessment of acetabular development. Radiology. 1986; 157:673-677.

  4. Graf R. New possibilities for diagnosis of congenital hip joint dislocation by ultrasonography. J.Pediatr. Orthop. 1983; 3:354-359.

  5. Graf R. Gelişimsel kalça displazisinde ultrasonografi. (Article in Turkish) Acta Orthop Traumatolo Turc. 2007; 41 Suppl 1:6-13.

  6. Kay RM, Watts HG, Dorey FJ. Variability in the assessment of acetabular index. J. Pediatr Orthop. 1997; 17(2):170-173.

  7. Tönnis D, Storch K, Ulbrich H. Results of newborn screening for cdh with and without sonography and correlation of risk factors. J Pediatr Orthop. 1990; 10:145-152.

  8. Wientroub S, Grill F. Current concepts review. Ultrasonography in developmental dysplasia of the hip. J Bone Joint Surg Am. 2000; 82-A;1004-1018.

  9. Spatz DK, Reiger M, Klaumann M, et al. Measurement of acetabular index intraobserver and interobserver variation. J. Pediatr Orthop. 1997; 17(2):174-175.

  10. Weinstein SL, Mubarak SJ, Wenger DR. Developmental hip dysplasia and dislocation: part 1. J Bone Joint Surg Am. 2003; 85:1824-1832.

  11. Gunay C, Atalar H, Dogruel H, Yavuz OY. Correlation of femoral head coverage and Graf α angle in infants being screened for developmental dysplasia of the hip. International Orthopaedics. 2008; DOI 10. 1007/s00264-008-0570-7

  12. Melzer C. Correlation between ultrasound and  X-ray imaging. Orthopade. 1997; 26:43-48.

This is a peer reviewed paper 

Please cite as: Cem Copuroglu: Trıangle Theorem For Developmental Dysplasıa Of Hıp

J.Orthopaedics 2009;6(2)e2





Arthrocon 2011

Refresher Course in Hip Arthroplasty

13th March,  2011

At Malabar Palace,
Calicut, Kerala, India

Download Registration Form

For Details
Dr Anwar Marthya,
Ph:+91 9961303044



Powered by



© Copyright of articles belongs to the respective authors unless otherwise specified.Verbatim copying, redistribution and storage of this article permitted provided no restrictions are imposed on the access and a hyperlink to the original article in Journal of Orthopaedics maintained. All opinion stated are exclusively that of the author(s).
Journal of Orthopaedics upholds the policy of Open Access to Scientific literature.