Developing of a Mathematical Model to Perform Measurements of Axial Vertebral Rotation on Computer-Aided and Automated Diagnosis Systems, Using Raimondi’s Method

Abstract

Introduction. Axial vertebral rotation (AVR) is a basic parameter in the study of idiopathic scoliosis and on physical two-dimensional images. Raimondi’s tables are the most used method in the quantification of AVR. The development of computing technologies has enabled the creation of computer-aided or automated diagnosis systems (CADx) with which measurement on medical images can be carried out more quickly, simply, and with less intra and interobserver variabilities than manual methods. Although there are several publications dealing with the measurement of AVR in CADx systems, none of them provides information on the equation or algorithm used for the measurement applying Raimondi’s method. Goal. The aim of this work is to perform a mathematical modelling of the data contained in Raimondi’s tables that enable the Raimondi method to be used in digital medical images more precisely and in a more exact manner. Methods. Data from Raimondi’s tables were tabulated on a first step. After this, each column of Raimondi’s tables containing values corresponding to vertebral body width (D) were adjusted to a curve determined by AVR = f (d). Third, representative values of each rotation divided by D were obtained through the equation of each column D. In a fourth step, a regression line was fitted to the data in each row, and from its equation, the mean value of the D/d distribution is calculated (value corresponding to the central column, D = 45). Finally, a curve was adjusted to the obtained data using the least squares method. Summary and Conclusion. Our mathematical equation allows the Raimondi method to be used in digital images of any format in a more accurate and simplified approach. This equation can be easily and freely implemented in any CADx system to quantify AVR, providing a more precise use of Raimondi’s method, as well as being used in traditional manual measurement as it is performed with Raimondi tables.

Predicting curve progression for adolescent idiopathic scoliosis using random forest model

“…Thoracic Kyphosis (T2-T12) and lumbar lordosis (L1-L5) angles were measured manually from lateral radiographs. Axial rotation of the apical level was measured in the frontal radiograph based on Raimondi’s method [ 49 , 50 ].…”

Validity and Absolute Reliability of Axial Vertebral Rotation Measurements in Thoracic and Lumbar Vertebrae

“…Based on the position of the two closest lateral faces, the vertebral body points, and the two opposite sides of the shadow of the pedicle which is turned towards the centre of the vertebra in the anteroposterior projection, the software calculated the width of the vertebral body (D) and the distance from the centre of the pedicle to the side of the vertebral body (d) (Figure 1). From the position of these points, the software obtained the vertebral rotation, using the equation [Equation (1)] published by our group [37]. To calculate the AVR in digital X-ray images, we used software based on equations [37], which applies an improved version of Raimondi's method [28].…”

“…From the position of these points, the software obtained the vertebral rotation, using the equation [Equation (1)] published by our group [37]. To calculate the AVR in digital X-ray images, we used software based on equations [37], which applies an improved version of Raimondi's method [28]. The software (registered under the name TraumaMeter v.873) was developed in C++ language under the Microsoft Visual Studio 2019 development environment, using the OpenCV 3.4.10 artificial vision libraries and the DCMTK libraries, from the OFFIS-Institute for Information Technology, to operate with DICOM (Digital Imaging and Communication On Medicine) files.…”