Variational model of scoliosis

Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, Stepan Bober

Scoliosis, being one of the most widespread spine diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of three-dimensional deformation of human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. The numerical properties of the first stage of scoliosis are investigated, which is shown to have the highest influence on the development of the disease.