Noninvasive Determination of Ligament Strain with Deformable Image Registration

Abstract

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 in the Left Ventricle During Systole with Deformable Image Registration

“…The relative insensitivity of the strain predictions from Hyperelastic Warping to changes in material coefficients is consistent with the results of our previous studies of myocardial strain (Veress et al, 2005a), ligament strain (Phatak et al, 2007), coronary artery strain and PET imaging (Veress et al, 2008). While the warping solution is ultimately driven by the image data as a "hard constraint" as enforced with the augmented Lagrangian method, active fiber contraction combined with the constitutive model act as a "soft constraint", which guides the solution with realistic estimates for deformation in regions of sparse image data.…”

“…Since the technique requires the application of tags prior to imaging, the resolution is necessarily limited by tag spacing and fading of tags (Axel et al, 2005;Moore et al, 1992). In contrast, the resolution of strain predictions from Hyperelastic Warping is limited by thickness of the pixel, the resolution of the finite element mesh and the image content itself (Veress et al, 2005a,b;Phatak et al, 2007). Relative to MRI tagging analysis, a disadvantage of the Hyperelastic Warping technique is that it is more computationally expensive.…”

Effect of six degrees of freedom knee kinematics on ligament length and moment arm in an intact knee model

“…For instance, computer modeling of the knee joint and surrounding tissues has been useful [15]. Finite element analysis may help describe the stress-strain characteristics of the knee joint and surrounding tissues, but is unsuitable for assessing high DOF motion associated with ligament length changes and moment arms due to the high computational and time costs [16][17][18][19]. Multibody dynamics software studies may be used to simulate the effect of ligament deficiencies on the knee and provide faster joint analyses over wide ranges of motion [20].…”

Simple and accurate methods for quantifying deformation, disruption, and development in biological tissues

“…Analysis of images to detect and quantify spatial variations in deformation is critical for understanding morphogenesis [1], wound healing [2], tissue mechanics [3][4][5] and structural mechanics [6]. A standard approach for such analysis involves estimating displacement fields inferred by comparing images of the same system taken at different times or under different conditions [7,8].…”