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Roof arc width: The novel calculation method for calculation of patient specific roof arc width in acetabular fractures
∗Corresponding author: Lokesh Gudda Naik. drortholokesh@gmail.com
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Received: ,
Accepted: ,
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.
Abstract
Abstract
Roof arc angle (RAA) is determined by measuring angle between a vertical line drawn from center of the acetabulum towards the acetabular dome and a second line drawn from center of acetabulum to the fracture through the acetabulum. Joel and Matta demonstrated that when roof arc angle was less than 45° on Pelvic AP and Judet's views, the fracture line is considered to be passing through the weight-bearing dome and require surgical fixation. The main purpose of the study is to calculate patient-specific angle and width for the better evaluation and management of acetabular fractures.
Radiographs of normal hips were retrieved from electronic data and parameters were calculated. Two observers calculated the parameters at two different intervals. Pearson correlation formula was used to find a correlation between groups.
Fifty radiographs of 28 patients were reviewed. The mean age of patients was 75.58 years ±13.28. The radius of the acetabulum, the radiographic measurement of sector width for 45° angulation at the roof, and the mathematical calculation for roof arc for 45° angle had significant positive correlation for both observers at two different occasions.
The measured roof arc width ranges from a minimum of 16.20 mm–31.50 mm and the calculated arc width for a 45-degree angle varies from a minimum of 15 mm–25.56 mm. These values are higher than the described values of 10 mm equals to 45 degrees. Hence, the values measured in this study should be considered for decision making in the management of acetabular fractures.
Keywords
Acetabulum
Acetabular fracture
Roof arc angle
Subchondral arc
Weight bearing dome
1 Introduction
The roof arc angle (RAA) is determined on a pelvic radiograph by a vertical line drawn from the center of acetabulum through the acetabular dome and a second line drawn from the center of the acetabulum to the fracture line through the acetabulum. The angle that is formed between these two lines is called the roof arc angle. Matta et al.1 developed a system for roughly quantifying the acetabular dome after fracture, which they called the roof arc measurements. These measurements involved determining how much of the roof remains intact on each of the three standard radiographic views: anteroposterior, obturator oblique, and iliac oblique. The angles formed on all the three above radiographs are the medial, posterior, and anterior roof arc angles respectively. If the roof arc angle is less than 45° on any of these three views, the fracture is considered to pass through the weight-bearing acetabular dome and may require surgical fixation. If the angle is more than 45° on all views, the weight-bearing dome is spared, and the patient may be a candidate for nonsurgical management.1–5 Olson et al.6 demonstrated that if a fracture does not intersect the articular surface of the acetabulure within 10 mm of the most cephalad portion of the dome, the corresponding roof arc measurement is > 45 °.
On the CT scan, it was determined that the cranial-most 10 mm of the acetabulum, referred to as the CT subchondral arc, is equivalent to the weight-bearing dome, which is determined by using a 45° roof arc angle.7 Three-dimensional surface-rendered CT image of the acetabulum, obtained in anatomic position with digital transection in the coronal plane, shows a 45° roof arc angle and a 10-mm subchondral arc, the superior most 10 mm of the acetabulum and the arc subtended by the 45° roof arc angle.7 A fracture crossing the acetabular dome within 45° of the center is considered to involve the weight-bearing dome.8
In this study, we are trying to define the exact measurement of the acetabular roof arc angle specifically for each individual. In general RAA cannot be a fixed number. As per the current literature, the value of 10 mm corresponding to the 45-degree arc is inaccurate, the arc size depends on the size of the acetabulum. Smaller acetabulum will have smaller RAA and larger will have larger RAA.
2 Materials and methods
This is a radiological assessment of the Roof arc angle in an anteroposterior pelvic radiograph, by using hospital electronic data from the NetWeaver Business Client 5.0 with inbuilt measuring tools to calculate radiological parameters like length, angle, diameter and radius of the acetabulum. Patient X-rays were selected where there is clear joint space and a normal hip joint without signs of degeneration of the joint. The following parameters were calculated: 1) Radius and diameter of the acetabulum; 2) Arc width for 45-degree angle was measured depicted in Figs. 1–4; 3) Mathematically calculated roof arc width using radius for 45 degree angle. Both observers measured and calculated these parameters twice at a ten-day interval for the same radiographs for intra-observer and inter-observer variability. Statistical methods in the form of Pearson correlation formula was used to find correlation between groups. As this is a radiographic based analysis, for which patient identity was not revealed, the informed consent and IRB approval was not requested.
3 Results
Fifty radiographs of twenty-eight patients were reviewed, 22 (78.57%) radiographs of patients were bilateral and 6 (21.43%) were unilateral. The mean age of the patients was 75.58 years ±13.28.
The mean diameter of the acetabulum was 54.90 ± 5.61 mm, 55.34 ± 5.83 mm, 55.12 ± 5.20 mm and 55.38 ± 5.39 mm and the minimum and the maximum diameters were, 38.20 mm & 63.90 mm, 40 mm & 64 mm, 37.80 mm & 61.34 mm and 38.46 mm & 62.68 mm for both observers at two different occasions.
The mean radius of the acetabulum in millimeter was 27.44 mm ± 2.80, 27.37 mm ± 2.69, 27.55 mm ± 2.59 & 27.29 mm ± 2.53 for both observers at different occasions.
The radiographic measurement of sector width for 45-degree angulation at roof arc with a vertical line from the center of acetabulum and second-line subtending 45 medially in AP view of the hip was 23.93 mm ± 2.44, 26.66 mm ± 2.79, 27.25 mm ± 2.81 and 25.96 ± 2.34 mm respectively for both observers at two different occasions had positive correlation.
The mathematical calculation for roof arc of 45 degree by using formula “perimeter of a circle equals to 2πr" where ‘r' is the radius of the circle drawn for the acetabulum on radiograph was 21.55 mm ± 2.20, 22.03 mm ± 2.57, 21.64 mm ± 2.04 and 22.45 mm ± 2.16 respectively for 45 degrees between both observers at two different occasions had positive correlation.
The value of R and R2, for comparison between both observers and on different occasions, indicated a strong positive correlation. This suggests that the high values of one group go with high values of all other compared groups.
3.1 Parameters measured and calculated (Table 1)
The important parameters were, 1) The radius of the acetabulum, 2) Arc width measured for 45 degree angle, 3) Calculated width of arc for measured radius.
3.2 Minimum and maximum
Observer one (O1): Minimum acetabular radius was 19.10 mm and the maximum was 31.95 mm, arc with for 45-degree angle, minimum width was 16.2 mm and maximum of 28 mm and calculated width of the sector was, minimum of 15.00 mm and maximum of 25.09 mm.
Observer two (O2): Minimum acetabular radius was 20 mm and the maximum was 32 mm, arc with for 45-degree angle, minimum width was 19.8 mm and maximum of 31.5 mm and calculated width of the sector was, minimum of 15.70 mm and maximum of 25.13 mm.
Observer one after ten days (O1-ten): Minimum acetabular radius was 18.90 mm and the maximum was 30.67, arc with for 45-degree angle, minimum width was 15.98 mm and maximum of 27.8 mm and calculated width of the sector was, minimum of 16.23 mm and maximum of 25.56 mm.
Observer two after ten days (O2-ten): Minimum acetabular radius was 19.23 mm and maximum was 31.34 mm, arc with for 45-degree angle, minimum width was 16.12 mm and maximum of 26.93 mm and calculated width of the sector was, minimum of 15.83 mm and maximum of 24.74 mm.
3.3 Mean and standard deviations
The mean radius of the acetabulum in millimeters was 27.44 mm ± 2.80, 27.37 mm ± 2.69, 27.55 mm ± 2.59 & 27.29 mm ± 2.53 for both observers at different occasions.
The radiographic measurement of sector width for 45° of angulation at roof arc with a vertical line from the center of acetabulum and second-line subtending 45 degrees at more sclerosed part of the weight-bearing portion of acetabulum medially in AP view of the hip was, 23.93 mm ± 2.44, 26.66 mm ± 2.79, 27.25 mm ± 2.81 and 25.96 ± 2.34 for both observers at different occasions.
The mathematical calculation for roof arc by using formula “perimeter of a circle equals to 2πr", where ‘r' is the radius of the circle drawn for the acetabulum on radiograph was 21.55 mm ± 2.20, 22.03 mm ± 2.57, 21.64 mm ± 2.04 and 22.45 mm ± 2.16 for both observers at different occasions.
3.4 Pearson's correlation formula (Table 2)
3.4.1 Intra-observer
The value of R was 0.9123 and R2 = 0.9076, for correlation of radius of acetabulum between O1 and O1-ten. The value of R for arc measured for 45-degree angle was 0.8765 and R2 = 0.7645 between O1 and O1-ten and the value of R for calculating the width of sector arc was 0.9428 and 0.9131 between O1 and O1-ten. Indicating a strong positive correlation, wherein high values of O1 go with high values of O1-ten.
The value of R was 0.9236 and R2 = 0.8854, for correlation of radius of acetabulum between O2 and O2-ten. The value of R for arc measured for 45-degree angle was 0.8760 and R2 = 0.8234 between O2 and O2-ten and the value of R for calculating the width of sector arc was 0.9765 and R2 = 0.9548 between O2 and O2-ten. Indicating a strong positive correlation, wherein high values of O2 go with high values of O2-ten.
3.4.2 Inter-observer
The value of R was 0.9915 and R2 = 0.9831, for correlation of radius of acetabulum between O1 and O2. The value of R for arc measured for 45-degree angle was 0.8695 and R2 = 0.7560 between O1 and O2 and the value of R for calculating the width of sector arc was 0.9915 and 0.9831 between O1 and O2. Indicating a strong positive correlation, wherein high values of O1 go with high values of O2.
The value of R was 0.9897 and R2 = 0.8976, for correlation of radius of acetabulum between O1-ten and O2-ten. The value of R for arc measured for 45-degree angle was 0.8865 and R2 = 0.8145 between O1-ten and O2-ten and the value of R for calculating the width of sector arc was 0.9863 and R2 = 0.9512 between O1-ten and O2-ten. Indicating a strong positive correlation, wherein high values of O1-ten go with high values of O2-ten.
4 Discussion
An acetabular fracture involving the superior weight-bearing area shows poor results. Moreover, the stability of the hip depends on adequate acetabular coverage of the femoral head. Roof arc angle is a method to evaluate adequate acetabular coverage and stability of the femoral head. Matta1 and Matta & Merritt9 study based on clinical findings and suggested that the fracture crosses acetabular weight-bearing dome when <45° medial, anterior and posterior roof arc angles necessitates surgical intervention as fracture crossing the acetabular dome within 45° of the center is considered to involve the weight-bearing dome.9–12
The present calculation, however, is arbitrary and not patient-specific. Allocating a fixed number of 45 degrees arc equals 10 mm of weight bearing zone is likely to cause an error of judgment while deciding on the most appropriate line of management and depending upon angle the arc width changes with the size of the acetabulum.
The Acetabulum- Morphological and Morphometrical Studies show that the average diameter as per literature is as follows: As per Funda T A et al.13 acetabular diameter was 54.29 ± 3.8 mm, Gaurang P et al.14 was 42.54 ± 3.6 mm and Thoudan B D et al.15 was 50.99 ± 1.99 mm. In our study, the average diameter of the acetabulum was 54.90 ± 5.61, 55.34 ± 5.83, 55.12 ± 5.20 and 55.38 ± 5.39 for O1, O1-ten, O2, and O2-ten. These values from our study were comparable to the existing studies in the literature (Table 3).
| Parameters and observation details | Sample (n) | Mean age (Years) and standard deviation | Mean diameter of acetabulum (mm) and standard deviation | Mean radius of acetabulum (mm) and standard deviation | Arc width in mm measured for 45 degree angle and standard deviation | Mathematical calculation for roof arc width in mm for 45 degree angle and standard deviation |
| Observer 1 | 50 | 75.58 ± 13.28 | 54.9 ± 5.61 | 27.44 ± 2.80 | 23.93 ± 2.44 | 21.55 ± 2.20 |
| Observer 1-10th day | 50 | 75.58 ± 13.28 | 55.34 ± 5.83 | 27.37 ± 2.69 | 26.66 ± 2.79 | 22.03 ± 2.57 |
| Observer 2 | 50 | 75.58 ± 13.28 | 55.12 ± 5.20 | 27.55 ± 2.59 | 27.25 ± 2.81 | 21.64 ± 2.04 |
| Observer 2-10th day | 50 | 75.58 ± 13.28 | 55.38 ± 5.39 | 27.29 ± 2.53 | 25.96 ± 2.34 | 22.45 ± 2.16 |
| Pearson's correlation (n = 50) | Observation details | Mean radius of acetabulum (mm) and standard deviation | Arc width in mm measured for 45 degree angle and standard deviation | Mathematical calculation for roof arc width in mm for 45 degree angle and standard deviation | |||
| R | R2 | R | R2 | R | R2 | ||
| Intra -Observer | Observer 1 and Observer 1-10th day | 0.9123 | 0.9076 | 0.8765 | 0.7645 | 0.9428 | 0.9131 |
| Observer 2 and Observer 2-10th day | 0.9236 | 0.8854 | 0.8760 | 0.8234 | 0.9765 | 0.9548 | |
| Inter -Observer | Observer 1 and Observer 2 | 0.9915 | 0.9831 | 0.8695 | 0.7560 | 0.9915 | 0.9831 |
| Observer 1 10th day and Observer 2 10th day | 0.9897 | 0.8976 | 0.8865 | 0.8145 | 0.9863 | 0.9512 | |
| Average Acetabular diameter with standard deviation. | Funda TA et al.12 (a) (N = 154) | Gaurang P et al.13 (b) (N = 100) | Thoudam B et al.14 (c) (N = 100) | Present Study (N = 50) |
| Observer 1 | 54.29 ± 3.8 mm | 42.54 ± 3.6 mm | 50.99 ± 1.99 mm | 54.90 mm ± 5.61 |
| Observer 1–10th day | 55.34 mm ± 5.83 | |||
| Observer 2 | 55.12 mm ± 5.20 | |||
| Observer 2-10th day | 55.38 mm ± 5.39 |
The minimum and maximum diameters were, 38.20 mm & 63.90 mm, 40 mm & 64 mm, 37.80 mm & 61.34 mm and 38.46 mm & 62.68 mm for O1, O1-ten, O2, and O2-ten respectively, which were comparable to the existing literature except the minimum values from our study were on the lower side but within 2 standard deviations (Table 4).
| Minimum and Maximum Acetabular diameter in millimeters | Funda TA et al.12 (a) | Gaurang P et al.13 (b) | Thoudam B et al.14 (c) | Present Study | ||||
| Min | Max | Min | Max | Min | Max | Min | Max | |
| Observer 1 | 44.8 mm | 65.5 mm | 42.54 mm | 56.60 mm | 42.8 mm | 61.5 mm | 38.20 mm | 63.90 mm |
| Observer 1–10th day | 40 mm | 64 mm | ||||||
| Observer 2 | 37.80 mm | 61.34 mm | ||||||
| Observer 2-10th day | 38.46 mm | 62.68 mm | ||||||
4.1 Limitations of the study
1.We have used AP view of normal pelvis for the calculations, the dimensions on the Judet view will be same as we are not considering fractured acetabulum.2.Even though Intra and Inter-observer variability have been calculated and a strong positive correlation is noted, a possibility of radiological calculation error is still possible.3.This needs validation by applying it to the decision making algorithm of Acetabular fracture considering both 45 degree angle and its arc measurement as per size of the acetabulum.
5 Conclusions
The existing method of assessing a 45-degree arc equivalent to 10 mm of roof arc angle is not patient-specific and when applied universally will lead to potential errors. We believe that this has a widespread application in clinical decision making for acetabular fractures specifically on follow-up where usually X rays are done than CT scan. According to our study, the measured roof arc width ranges from minimum of 16.20 mm–31.50 mm and the calculated arc width for 45 degree angle varies from minimum of 15 mm–25.56 mm. The mean measured roof arc width for 45 degree angle was 25.95 mm and the calculated mean roof arc width was 21.92 mm. These values are much higher than the textbook described values of 10 mm equals to 45 degrees. Hence, the values measured in this study should be considered in future for decision making in management of acetabular fractures.
Our Recommendation for calculating patient specific roof arc width:
Patient specific Roof arc width (in mm) for 45 degrees = 0.7854 x r (radius of the acetabulum).
Derivation:
As mentioned earlier,360° = 2πrSo, 1° = 2πr/360Therefore, 45° = 45 x 2πr/360= πr/4 (taking π = 3.1416)= 0.7854 x r (radius of the acetabulum)
References
- Fractures of the acetabulum: accuracy of reduction and clinical result in patients managed operatively within three weeks after the injury. J Bone Joint Surg Am. 1996;78:1632-1645.
- [Google Scholar]
- Posterior acetabular arc angle of the femoral head assesses instability of posterior fracture-dislocation of the hip. Int Orthop. 2013;37:1141-1145.
- [Google Scholar]
- Posterior acetabular arc angle of unstable posterior hip fracture-dislocation. Int Orthop. 2013;37:2443-2449.
- [Google Scholar]
- The computerized tomography subchondral arc: a new method of assessing acetabular articular continuity after fracture (a preliminary report) J Orthop Trauma. 1993;7:402-413.
- [Google Scholar]
- Acetabular fractures: what radiologists should know and how 3D CT can aid classification. Radiographics. 2015;35(2):555-557.
- [Google Scholar]
- 2013:2870.
- [Google Scholar]
- Fractures of the acetabulum: a retrospective analysis. Clin Orthop. 1986;205:230-240.
- [Google Scholar]
- Fractures of the acetabulum: early results of a prospective study. Clin Orthop. 1986;205:241-250.
- [Google Scholar]
- Decision making in acetabulum fractures – when to operate and when not to? Trauma International. 2017;3(1):6-9.
- [Google Scholar]
- Int J Biol Med Res. 2013;4(1):2924-2926.
- [Google Scholar]
- The rule of 57: orthopaedic trigonometry made easy. J Am Acad Orthop Surg. 2019;27(24):e1110-e1114.
- [Google Scholar]