(G-278) Validation of Elastography Pipeline to Determine Mechanical Properties from Dynamic MRI Deformation Analysis

Introduction:: Elastography is a non-invasive imaging approach that is commonly used to quantify the material properties of soft tissues of the body. Quantification of material stiffness can provide a powerful approach to understanding structure-function relationships in load-bearing tissues, specifically in cartilage. In osteoarthritis (OA) pathogenesis, cartilage softening is a functional hallmark due to structural changes to the collagen network and depletion of proteoglycans. Therefore, quantifying changes to cartilage material properties non-invasively in vivo is of substantial interest as a potential diagnostic tool.



While elastography seems like an ideal approach to accomplish this, current conventional elastography methods, most commonly using ultrasound, lack the ability to penetrate deep within the musculoskeletal tissues of the joint space, due to the dissipation of high frequency shear waves. MRI is unique among imaging tools as it can characterize tissues with high spatial detail, has a deep penetration depth, and can assess tissues non-invasively. Recently, spiral displacement encoded stimulated echo (spiral DENSE) MRI has been used to calculate pixel-level full-field displacement maps of soft tissues under repetitive motion [1]. In this work, we first developed synthetic displacement maps of MRI phantoms and heterogenous cartilage under load using finite element modeling. We then use these synthetic displacement maps as input to validate a biomechanical model-based elasticity imaging pipeline [2], that has the capability to quantify cartilage stiffness maps non-invasively.

Materials and Methods:: In brief, DENSE MRI is used to calculate in vivo cartilage displacement data, which are then used as input to the biomechanical elasticity imaging pipeline. Here, we focus on in silico estimation of error, in preparation for in vivo work. An initial elastic input is calculated from input displacements using the virtual fields method [3]. An objective-function defined by the sum of squared error mismatch between the observed and model-estimated displacement fields is then minimized via the adjoint method [2]. An L-BFGS quasi-Newton algorithm is used to iteratively update the modulus estimates for each element until the overall error is minimized [2].



To validate the pipeline, we constructed forward simulations representative of tissue heterogeneity. Simulations of a phantoms of increasing stiffness (500 to 1000 Pa) with and without a soft inclusion (200 mPA) under 10 percent unconfined compression (Figure 1A-C) were run in FEBio. Displacements for each node were used as input to the elasticity pipeline. To analyze error, we applied Monte Carlo simulations. Within each iteration of the 100 Monte Carlo simulations, random Gaussian noise was added to the ideal displacements of all nodes (Figure 1B). To analyze the effect of smoothing on stiffness reconstruction error, LOWESS smoothing was separately applied to the noisy displacements during Monte Carlo simulations, and percent error from the known stiffness was calculated. In preparation for in vivo work, spiral DENSE MRI was used to quantify in vivo cartilage displacements under a varus-valgus load, as previously described [1].


Results, Conclusions, and Discussions:: The elasticity pipeline successfully reconstructed the gradient pattern of stiffness defined in the forward simulation (Figure 1A). Percent error of stiffness for each element remained under 2 percent. With the addition of LOWESS smoothing to the displacements prior to the calculation of stiffness, the stiffness calculation was robust to increasing noise levels present due to MRI acquisition (Figure 1B). When six rounds of LOWESS smoothing were applied to the displacements, the average percent error was minimized to less than 5 percent for all noise cases. The elasticity pipeline also successfully reconstructed the stiffness of a phantom with a soft inclusion, although error was higher in the inclusion area that included discontinuous material properties, and that reached up to 15 percent (Figure 1C).



This work provides a proof-of-concept and validation of an elasticity imaging framework. When combined with dualMRI to noninvasively extract full field displacements (Figure 1D), this method will be able to quantify the cartilage stiffness map in vivo. We hypothesize based upon ex vivo cartilage mechanical studies, changes in stiffness to the medial cartilage middle and deep zones are potential biomarkers for osteoarthritis pathogenesis. Ultimately, we hope this framework can provide a step forward to measure cartilage material properties in a clinical MRI setting and could potentially be extended to other load-bearing musculoskeletal tissues, including ligament and intervertebral disc.


Acknowledgements (Optional): : This work was supported by NIH grant 2 R01 AR063712.


References (Optional): : [1] Lee W et al., Magn Reson Med. 2023

[2] Miller CE et al., J Med Imaging. 2021

[3] Mei Y et. Al., Comput Mech. 2021