Quantification of the spatial strain distribution of scoliosis using a thin-plate spline method

Yoshimori Kiriyama, Kota Watanabe, Morio Matsumoto, Yoshiaki Toyama, Takeo Nagura

Research output: Contribution to journalArticle

1 Citation (Scopus)


The objective of this study was to quantify the three-dimensional spatial strain distribution of a scoliotic spine by nonhomogeneous transformation without using a statistically averaged reference spine. The shape of the scoliotic spine was determined from computed tomography images from a female patient with adolescent idiopathic scoliosis. The shape of the scoliotic spine was enclosed in a rectangular grid, and symmetrized using a thin-plate spline method according to the node positions of the grid. The node positions of the grid were determined by numerical optimization to satisfy symmetry. The obtained symmetric spinal shape was enclosed within a new rectangular grid and distorted back to the original scoliotic shape using a thin-plate spline method. The distorted grid was compared to the rectangular grid that surrounded the symmetrical spine. Cobb's angle was reduced from 35° in the scoliotic spine to 7° in the symmetrized spine, and the scoliotic shape was almost fully symmetrized. The scoliotic spine showed a complex Green-Lagrange strain distribution in three dimensions. The vertical and transverse compressive/tensile strains in the frontal plane were consistent with the major scoliotic deformation. The compressive, tensile and shear strains on the convex side of the apical vertebra were opposite to those on the concave side. These results indicate that the proposed method can be used to quantify the three-dimensional spatial strain distribution of a scoliotic spine, and may be useful in quantifying the deformity of scoliosis.

Original languageEnglish
Pages (from-to)302-307
Number of pages6
JournalJournal of Biomechanics
Issue number1
Publication statusPublished - 2014 Jan 3



  • Adolescent idiopathic scoliosis
  • Spatial strain distribution
  • Thin-plate spline (TPS)

ASJC Scopus subject areas

  • Biophysics
  • Orthopedics and Sports Medicine
  • Biomedical Engineering
  • Rehabilitation

Cite this