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      Integrating MR imaging with full-surface indentation mapping of femoral cartilage in an ex vivo porcine stifle

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      Journal of the Mechanical Behavior of Biomedical Materials
      Elsevier BV

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          Abstract

          <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" class="first" id="d8575504e83">The potential of MRI to predict cartilage mechanical properties across an entire cartilage surface in an ex vivo model would enable novel perspectives in modeling cartilage tolerance and predicting disease progression. The purpose of this study was to integrate MR imaging with full-surface indentation mapping to determine the relationship between femoral cartilage thickness and T2 relaxation change following loading, and cartilage mechanical properties in an ex vivo porcine stifle model. Matched-pairs of stifle joints from the same pig were randomized into either 1) an imaging protocol where stifles were imaged at baseline and after 35 min of static axial loading; and 2) full surface mapping of the instantaneous modulus (IM) and an electromechanical property named quantitative parameter (QP). The femur and femoral cartilage were segmented from baseline and post-intervention scans, then meshes were generated. Coordinate locations of the indentation mapping points were rigidly registered to the femur. Multiple linear regressions were performed at each voxel testing the relationship between cartilage outcomes (thickness change, T2 change) and mechanical properties (IM, QP) after accounting for covariates. Statistical Parametric Mapping was used to determine significance of clusters. No significant clusters were identified; however, this integrative method shows promise for future work in ex vivo modeling by identifying spatial relationships among variables. </p>

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              Point set registration: coherent point drift.

              Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.
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                Author and article information

                Contributors
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                Journal
                Journal of the Mechanical Behavior of Biomedical Materials
                Journal of the Mechanical Behavior of Biomedical Materials
                Elsevier BV
                17516161
                March 2023
                March 2023
                : 139
                : 105651
                Article
                10.1016/j.jmbbm.2023.105651
                36640543
                358260ed-5ce3-458c-a5e2-0c1f454a14a9
                © 2023

                https://www.elsevier.com/tdm/userlicense/1.0/

                https://doi.org/10.15223/policy-017

                https://doi.org/10.15223/policy-037

                https://doi.org/10.15223/policy-012

                https://doi.org/10.15223/policy-029

                https://doi.org/10.15223/policy-004

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