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.