Shape Analysis of Vestibular Systems in Adolescent Idiopathic Scoliosis Using Geodesic Spectra

Abstract

Abstract. Adolescent Idiopathic Scoliosis (AIS) characterized by the 3D spine deformity affects about 4% schoolchildren worldwide. One of the prominent theories of the etiopathogenesis of AIS was proposed to be the poor postural balance control due to the impaired vestibular function. Thus, the morphometry of the vestibular system (VS) is of great importance for studying AIS. The VS is a genus-3 structure situated in the inner ear and consists of three semicircular canals lying perpendicular to each other. The high-genus topology of the surface poses great challenge for shape analysis. In this work, we propose an effective method to analyze shapes of high-genus surfaces by considering their geodesic spectra. The key is to compute the canonical hyperbolic geodesic loops of the surface, using the Ricci flow method. The Fuchsian group generators are then computed which can be used to determine the geodesic spectra. The geodesic spectra effectively measure shape differences between highgenus surfaces up to the hyperbolic isometry. We applied the proposed algorithm to the VS of 12 normal and 15 AIS subjects. Experimental results show the effectiveness of our algorithm and reveal statistical shape difference in the VS between right-thoracic AIS and normal subjects.

Euclidean Geodesic Loops on High-Genus Surfaces Applied to the Morphometry of Vestibular Systems

“…The resultant geodesic loops are in Euclidean metric, thus characterizing the intrinsic geometric properties of the VS based on the real background geometry. This leads to more accurate results than the existing methods, such as the hyperbolic Ricci flow method [13]. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than [13].…”

“…The drawback was that the complete geometry of the surface has not been fully analyzed. In [13], Zeng et al proposed to extract the geodesic spectra of the VS to compare geometric difference between the normal and unhealthy groups. This algorithm requires the computation of uniformization metric, which is computed by discrete Ricci flow or Yamabe flow [5].…”

“…One popular hypothesis was suggested to be the structural changes in the VS that induce the disturbed balance perception, and further cause the spinal deformity [1,4,9]. Some recent works have also revealed the statistical difference in global morphology of the VS between right-thoracic AIS and normal controls [8,13]. Hence, analyzing the shape of VS is crucial for understanding AIS.…”

“…This leads to more accurate results than the existing methods, such as the hyperbolic Ricci flow method [13]. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than [13]. To test the effectiveness of our proposed method, we applied the algorithm to the VS of normal and AIS subjects.…”

EM-ICP strategies for joint mean shape and correspondences estimation: Applications to statistical analysis of shape and of asymmetry

“…The shape analysis of the inner ear, and especially of the vestibular system (composed of the three semicircular canals) could be relevant to understand diseases such as adolescent idiopathic scoliosis, which affects about 3% of children between 10 and 16 worldwide [10]. More generally, the morphometric analysis of the bony/osseous labyrinth (that houses the membranous semicircular canals, the vestibule and the cochlea) has been shown to be key to the establishment of phylogenetic affinities between fossil hominids [11].…”