Mathematical model of three-dimensional determination of the degree of spine deformation in adolescent idiopathic scoliosis

Abstract

It is known that in Ukraine every fourth child has postural disorders. According to the Public Health Center of the Ministry of Health of Ukraine, in 2019, 99.467 children were diagnosed with adolescent idiopathic scoliosis of varying severity, and according to the Medical Statistics Center of the Ministry of Health of Ukraine, only during preventive examinations in 2020, 92.322 children aged 0‑17 were found to have adolescent idiopathic scoliosis, of whom 45.553 were boys. Objective – to comprehensively assess the severity of spinal deformity in the sagittal, frontal, and axial planes, taking into account the primary scoliotic curvature in patients with adolescent idiopathic scoliosis. Since scoliosis is a deformity in three planes, its grading requires quantitative assessment of the scoliotic (frontal plane), kyphotic (sagittal plane), and rotational (axial plane) components. It has been proven that visual analysis of vertebral spatial orientation in adolescents with scoliotic deformity based on two-dimensional radiographs is usually misleading and does not provide reliable data, as flat images cannot accurately depict the true frontal (coronal) and lateral (sagittal) linear parameters of anatomical structures (the corresponding vertebra). To calculate the degree of scoliotic spinal deformity considering vertebral rotational displacement, a coordinate system of their specific reference points was constructed in two planes: sagittal and frontal. Unlike some researchers who measured vertebral rotation around the vertical axis using the width of the vertebral body at half its height, we selected the plane of the surfaces of the vertebral end plates as the basic reference for determining the tilt angle of each individual vertebra. This choice is intuitively clear and objectively justified, since the end plates are active growth zones in adolescents, are clearly visualized on radiographs in this age group, and allow accurate identification of the midpoint of the vertebral body, significantly aiding in constructing computational schemes for assessing the parameters of this anatomical structure. Conclusions. A mathematical model has been developed and proposed to determine the true magnitude of spinal curvature in adolescent idiopathic scoliosis by means of 3D reconstructive modeling of two-dimensional radiographic images in frontal and sagittal projections. This enables consideration of all components of vertebral deformity across spatial vectors: scoliotic, kyphotic, and axial (rotational). The proposed computational mathematical model for determining the degree of spinal curvature in idiopathic scoliosis in children can be applied for both right-sided and left-sided pathology regardless of its severity. The developed three-dimensional model for assessing the degree of spinal deformity in adolescent idiopathic scoliosis makes it possible to predict the course of the pathology depending on the side of curvature formation. For example, in right-sided scoliosis, grade III is determined when Th2 tilt reaches maximal values. Solving the corresponding linear equations indicates more destructive (pronounced) manifestations in left-sided pathology, including a higher frequency and greater severity of the rib hump.