Annals of Biomedical Engineering

, Volume 35, Issue 7, pp 1175–1187 | Cite as

Noninvasive Determination of Ligament Strain with Deformable Image Registration

  • Nikhil S. Phatak
  • Qunli Sun
  • Seong-Eun Kim
  • Dennis L. Parker
  • R. Kent Sanders
  • Alexander I. Veress
  • Benjamin J. Ellis
  • Jeffrey A. WeissEmail author


Ligament function and propensity for injury are directly related to regional stresses and strains. However, noninvasive techniques for measurement of strain are currently limited. This study validated the use of Hyperelastic Warping, a deformable image registration technique, for noninvasive strain measurement in the human medial collateral ligament using direct comparisons with optical measurements. Hyperelastic Warping determines the deformation map that aligns consecutive images of a deforming material, allowing calculation of strain. Diffeomorphic deformations are ensured by representing the deformable image as a hyperelastic material. Ten cadaveric knees were subjected to six loading scenarios each. Tissue deformation was documented with magnetic resonance imaging (MRI) and video-based experimental measurements. MRI datasets were analyzed using Hyperelastic Warping, representing the medial collateral ligament (MCL) with a hexahedral finite element (FE) model projected to a manually segmented ligament surface. The material behavior was transversely isotropic hyperelastic. Warping predictions of fiber stretch were strongly correlated with experimentally measured strains (R 2 = 0.81). Both sets of measurements were in agreement with previous ex vivo studies. Warping predictions of fiber stretch were insensitive to bulk:shear modulus ratio, fiber stiffness, and shear modulus in the range of +2.5SD to −1.0SD. Correlations degraded when the shear modulus was decreased to 2.5SD below the mean (R 2 = 0.56), and when an isotropic constitutive model was substituted for the transversely isotropic model (R 2 = 0.65). MCL strains in the transitional region near the joint line, where the material behavior and material symmetry are more complex, showed the most sensitivity to changes in shear modulus. These results demonstrate that Hyperelastic Warping requires the use of a constitutive model that reflects the material symmetry, but not subject-specific material properties for accurate strain predictions for this application. Hyperelastic Warping represents a powerful technique for noninvasive strain measurement of musculoskeletal tissues and has many advantages over other image-based strain measurement techniques.


Strain measurement Ligament Deformable image registration Hyperelastic Warping 



Financial support from NSF #BES-0134503 is gratefully acknowledged. The authors thank Garry Gold of Stanford University for suggesting the use of a nonuniform acquisition matrix, and Marianne Bergquist, Jeff McCann and Anita Apte for assistance with experiments and image acquisition.


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Copyright information

© Biomedical Engineering Society 2007

Authors and Affiliations

  • Nikhil S. Phatak
    • 1
  • Qunli Sun
    • 1
  • Seong-Eun Kim
    • 2
  • Dennis L. Parker
    • 2
  • R. Kent Sanders
    • 2
  • Alexander I. Veress
    • 1
  • Benjamin J. Ellis
    • 1
  • Jeffrey A. Weiss
    • 1
    Email author
  1. 1.Department of BioengineeringUniversity of UtahSalt Lake CityUSA
  2. 2.Department of RadiologyUniversity of UtahSalt Lake CityUSA

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