

ORIGINAL ARTICLE 

Year : 2022  Volume
: 8
 Issue : 1  Page : 7883 

A linear regression model using computed tomography of forearm osteology to predict radius and ulna characteristics for surgical planning
Henry Sean Pretorius, Nando Ferreira, Marilize Cornelle Burger
Department of Surgical Sciences, Division of Orthopaedic Surgery, Faculty of Medicine and Health Sciences, Stellenbosch University, Cape Town, South Africa
Date of Submission  20Mar2022 
Date of Decision  20May2022 
Date of Acceptance  21May2022 
Date of Web Publication  30Jun2022 
Correspondence Address: Henry Sean Pretorius Department of Surgical Sciences, Division of Orthopaedic Surgery, Faculty of Medicine and Health Sciences, Stellenbosch University, Cape Town 7505 South Africa
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jllr.jllr_5_22
Introduction: The radius and ulna are commonly fractured bones. The restoration of the native anatomy is the primary surgical objective but can be difficult due to a mismatch between the bones' shape and available implants. A thorough understanding of the underlying anatomical relationships between the radius and ulna could allow for a more accurate prediction of variables, thus enabling the surgeon to treat patients more effectively. Methods: A crosssectional investigation of forearm computed tomography scans and measurements were conducted on 97 forearms. Pearson's correlations were used to evaluate relationships between variables, and those with a coefficient of r > 0.4 and P < 0.001, as well as those considered clinically relevant, were carried forward into a multiple linear regression for each outcome variable, namely: (i) radius length, (ii) radius of curvature, (iii) the minimum diameter of the radial canal, (iv) ulna length, and (v) the minimum diameter of the ulna canal. A stepwise approach was used for the multiple linear regression analysis, with a significance level of 0.05 for predictor variables. Results: Radius length: in the multiple linear regression model, only ulna length remained in the model (adjusted R^{2} = 0.85). The radius of curvature: the final model only included ulna length (adjusted R^{2} = 0.30). Radius canal minimum width: three measurements were included in the final model (adjusted R^{2} = 0.82). Ulna Length: six independent correlations between individual measurements and the ulna length were observed, with radius length and the radial neck length being included in the final model (adjusted R^{2} = 0.86). Ulna canal minimum width: the final regression model included four variables: the maximum diameter of the distal third of the radial canal, the minimum diameter of the radial canal, and the minimum diameter of the proximal and middle third aspects of the ulna canal (adjusted R^{2} = 0.80). Conclusion: The results of this investigation illustrate that anatomical predictions for bone size can be made using other anatomical landmarks except for the radius of curvature. The clinical application and implementation of this statistical model need further research.
Keywords: Anatomy, osteology, radius, radius of curvature, regression model, ulna
How to cite this article: Pretorius HS, Ferreira N, Burger MC. A linear regression model using computed tomography of forearm osteology to predict radius and ulna characteristics for surgical planning. J Limb Lengthen Reconstr 2022;8:7883 
How to cite this URL: Pretorius HS, Ferreira N, Burger MC. A linear regression model using computed tomography of forearm osteology to predict radius and ulna characteristics for surgical planning. J Limb Lengthen Reconstr [serial online] 2022 [cited 2022 Dec 2];8:7883. Available from: https://www.jlimblengthrecon.org/text.asp?2022/8/1/78/349421 
Introduction   
The radius and ulna are commonly fractured bones.^{[1]} The restoration of the native anatomy is the primary surgical objective but can be difficult due to a mismatch between the bones' shape and available implants.^{[2],[3]} A fracture of one, or both, bones in the forearm may result in difficulty reestablishing the normal anatomy, especially in the presence of comminution or segmental fractures. The radius poses a surgical challenge to restore the radius of curvature, and failure to do so may lead to higher nonunion rates as well as affect rotation if the loss of curvature is excessive.^{[4],[5]}
A thorough understanding of the underlying anatomical relationships between the radius and ulna could allow for a more accurate prediction of variables that may assist in reconstructing the forearm anatomy, thus enabling the surgeon to treat patients more effectively. When the different implants used for the fixation of the radius and ulna are considered, surface anatomy is essential for plate design. However, when it comes to intramedullary design, the size of the medullary canal is of utmost importance and the ability to predict this would be valuable. The contralateral arm can be used but may also be unreliable for accurate predictions, especially in the setting of bilateral injuries.^{[6]} Mathematical formulae for calculating, for example., the length of the radius and its radius of curvature by using the ulna as a reference, could potentially assist in managing injuries with segmental comminution or bone loss. Alao et al. showed that a measurement from the olecranon's tip to the distal interphalangeal joint of the 5^{th} finger correlates to the intramedullary nail length for femur fractures.^{[7]} Karakas and Harma showed the same correlation using the fibula length, adding the femoral head diameter as a clinically useful measurement predictor of femoral length.^{[8]} It could potentially be possible to predict certain aspects of forearm bony anatomy by measuring available anatomy to reconstruct the original anatomy accurately.
With this in mind, the clinical relevance of this study is to determine whether intramedullary implant size and bone length in anthropological specimens can be predicted if bone fragments are missing. The specific objectives included determining whether (i) radius length and radius of curvature, (ii) minimum diameter of the radial canal, (iii) ulna length, and (iv) minimal diameter of the ulna canal can be predicted using relationships between ulna and radius anatomical measurements.
Methods   
A crosssectional investigation of forearm computed tomography (CT) scans was conducted. Scans of adult patients, who received a CT scan of their forearm between January 2014 and October 2015, were included. All patients with fractures of the radius or ulna or other anatomical deformities were excluded. Ethics committee approval and institutional clearance were obtained before the commencement of data collection. A waiver of informed consent was obtained, and all patient data were anonymized.
All CT scans were performed with a Siemens SOMATOM Emotion 6 with minimum slice thicknesses of 0.23 mm. Image files were stored as Digital Imaging and Communications in Medicine format (DICOM) files. All measurements were made using RadiAnt 4.2.1 (Medixant, Poland) DICOM viewing software. The collected images were processed using image processing software, and measurements were taken by a single investigator. Images were visualized in a multiplanar reconstruction mode to standardize the measurements. Specific methods and calculations of measurements of specific anatomical areas, previously described by Pretorius et al., were taken to highlight the pertinent anatomy. Including measurement of the radius head size and neck length, radius length, and the radius of curvature.^{[9]} The ulna was also measured for size and length, including the ulna head.^{[9]}
Data were analyzed using Stata v15 (StataCorp LLC). All data were normally distributed and are described as means ± standard deviations with 95% confidence intervals (CI) indicated in parentheses. Categorical data are represented as frequencies with the count shown in parentheses. Pearson's correlations were used to evaluate relationships between variables and those with a coefficient of r > 0.4 and P < 0.001, as well as those considered clinically relevant and able to be measured on a standard Xray, were carried forward into a multiple linear regression for each outcome variable, namely: (i) radius length, (ii) radius of curvature, (iii) the minimum diameter of the radial canal, (iv) ulna length, and (v) the minimum diameter of the ulna canal. A stepwise approach was used for the multiple linear regression analysis, with a significance level of 0.05 for predictor variables. The final equation is presented in a y = mx + c format, where y is the outcome of interest, m is the regression coefficient, x is the specific variable measurement, and c is the regression constant.
Results   
A total of 97 scans were included with an equal distribution between left (49%, n = 47) and right (51%, n = 49) forearms. The cohort consisted of predominantly male patients (84%, n = 82) with a mean age of all the patients of 34.91 ± 13.33 years (95% CI 32.22–37.59).^{[9]}
Radius length
Various correlations of the periarticular measurements with radius length were observed [Table 1]. The most significant correlation was with the ulna length (r = 0.92, P < 0.001). Only ulna length remained in the multiple linear regression model (adjusted R^{2} = 0.85) [Table 2].  Table 1: Bivariate correlations between predictor variables and radial length
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Radial length can therefore be predicted with the following formula:
Radial length = 0.86 (ulna length measurement) +16.30.
Radius of curvature
Ulna length (r = 0.56, P < 0.001) was independently correlated with the radius of curvature [Table 3]. Although the diameter of the ulna head in the plane of the styloid did not meet the statistical criteria for inclusion in the multivariable linear model, the clinical value of being measurable on a plain radiograph was considered significant enough to include in the model. However, the final model only included ulna length (adjusted R^{2} = 0.30) [Table 4].  Table 3: Bivariate correlations between predictor variables and the radius of curvature
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The minimum diameter of the radial canal
Various correlations between individual measurements and the minimum diameter of the radial canal were observed [Table 5]. Three measurements, including the maximum diameter of the radial canal in the middle third, the maximum diameter of the distal radius, and the ulna canal's minimum diameter, were included in the final model (adjusted R^{2} = 0.82) [Table 6].  Table 5: Bivariate correlations between predictor variables and the minimum diameter of the radial canal
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 Table 6: Multiple linear regression for minimum diameter of radial canal
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Radial canal minimum diameter can therefore be predicted using the following formula:
Min diameter of radial canal = 0.70 (max diameter of radial canal – middle third) + 0.07 (distal radius max diameter) + 0.18 (ulna canal min diameter) –1.09.
Ulna length
Six bivariate correlations between individual measurements and the ulna length were observed [Table 7], with radius length and the radial neck length being included in the final model (adjusted R^{2} = 0.86) [Table 8].  Table 7: Bivariate correlations between predictor variables and ulna length
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Ulna length can therefore be predicted using the following formula:
Ulna length = 0.94 (radius length) +0.23 (radial neck length) +27.00.
The minimum diameter of the ulna canal
Several correlations between individual measurements and the minimum diameter of the ulna canal were observed [Table 9]. The final regression model included four variables, including the maximum diameter of the distal third of the radial canal, the minimum diameter of the radial canal and the minimum diameter of the proximal and middle third aspects of the ulna canal (adjusted R^{2} = 0.80) [Table 10].  Table 9: Bivariate correlations between predictor variables and the minimum diameter of the ulna canal
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 Table 10: Multiple linear regression for the minimum diameter of the ulna canal
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Ulna canal minimum diameter can therefore be predicted with the following formula:
Min diameter of the ulna canal =0.06 (max diam of radial canal– distal third) +0.12 (min diameter of radial canal) +0.41 (max diameter of ulna canal– middle third) +0.45 (max diameter of the ulna canal– distal third) +0.04.
Discussion   
This study aimed to investigate clinically meaningful relationships between ulna and radius anatomical measurements; although this may seem obvious, it has not been quantified. The data's clinical relevance could help predict the bones' relative lengths and the size of the canal of both the radius and ulna when planning a surgical reconstruction of these bones. This is specifically relevant to intramedullary fixation, where the predicted length does not need to be accurate, and an 85%–90% value may be adequate for the 1 cm increments of implant choice. The same argument can be made for anthropological measurements if there are missing fragments or bones or if only one forearm bone is found, the other bones' length could be extrapolated.
In predicting radial length, the ulna length is the strongest predictor, with variation in the ulna length accounting for approximately 85% of the variability in the radius length. In a clinical scenario where a radius fracture with loss of length, such as a Galeazzi fracture or severely comminuted fractures like gunshot wounds, was present, the ulna length could be used to calculate an approximate radius length. This may be relevant to the choice of intramedullary implants such as nails or flexible rods, which ultimately influences the management of the patient.^{[10],[11]}
In clinical practice, the radius of curvature of the radius should be restored as a general clinical principle of anatomical reduction. With the excessive loss of curvature, forearm pronation or supination may be impeded. Failure to restore the curvature of the radius may also contribute to problems with fracture healing.^{[4],[5],[12],[13],[14],[15],[16]} The measurements taken in the present study did not contribute to a model that can reliably predict the radius of curvature. The mean radius of curvature value, 561.93 ± 93.49 mm, may still be of value in the clinical reduction of the radial curve in patients with forearm fractures. In addition, since most intramedullary implants can be bent, the surgeon can manipulate the curve manually to enable an optimal environment for union. However, more research in predicting the radius of curvature is required to ensure a more accurate prediction of this value.
The minimum canal diameter of the radius is clinically relevant in cases where intramedullary fixation is required.^{[15],[17]} The final model used to predict the minimum radial canal diameter was the maximum diameter of both the radial canal and the distal radius and the minimum diameter of the ulna canal. All three variables are easy to measure on a standard Xray, and the final model in the present study accounted for 82% of the variability in the minimum canal diameter of the radius. This finding is clinically useful where a portion of the radial canal is obscured, and the surgeon cannot accurately measure the minimum diameter.^{[18]}
Similar to radial length, the length of the ulna becomes important to predict in cases where substantial shortening of the ulna is present, such as Monteggia fractures with extensive comminution. The length of the radius and the radial neck contributed to the final model, which together accounted for 86% of the variability of the ulna length.^{[10],[19],[20]}
Finally, the minimum diameter of the ulna canal is an important measurement in cases where intramedullary fixation of the ulna is considered. This minimum diameter of the ulna can be extrapolated by combining the minimum diameter of the radius, the maximum canal diameter of the distal third of the radius and the maximum diameter in the middle and distal thirds of the ulna in a model, which accounts for 80% of the variability in the minimum ulna canal diameter. Similarly to the radius, the formula obtained from the final model can predict the required implant size in the ulna.^{[21],[22]}
Limitations
The statistical nature of the article may have practical implications for the clinical scenario but will need further clinical investigation to ascertain the practical use of the data. In addition, the scans that were used were only for a single hospital and may therefore not be able to be extrapolated to other geographical regions. The measurements were done by a single investigator on one occasion even though the measurements showed a normal distribution the authors acknowledge this may be a limiting factor.
Conclusion   
The results of this investigation illustrate that anatomical predictions for bone size can be made using other anatomical landmarks except for the radius of curvature. The clinical application and implementation of this statistical model needs further research.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8], [Table 9], [Table 10]
