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Title: Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization

Tissues and engineered biomaterials exhibit exquisite local variation in stiffness that defines their function. Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development offinite deformation elastographythat utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint spacein situfor the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independentT2measurements. We additionally describe technical challenges needed to achievein vivoelastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration.

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Publication Date:
Journal Name:
Scientific Reports
Nature Publishing Group
Sponsoring Org:
National Science Foundation
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    Graft placement is a modifiable and often discussed surgical factor in anterior cruciate ligament (ACL) reconstruction (ACLR). However, the sensitivity of functional knee mechanics to variability in graft placement is not well understood.


    To (1) investigate the relationship of ACL graft tunnel location and graft angle with tibiofemoral kinematics in patients with ACLR, (2) compare experimentally measured relationships with those observed with a computational model to assess the predictive capabilities of the model, and (3) use the computational model to determine the effect of varying ACL graft tunnel placement on tibiofemoral joint mechanics during walking.

    Study Design:

    Controlled laboratory study.


    Eighteenmore »participants who had undergone ACLR were tested. Bilateral ACL footprint location and graft angle were assessed using magnetic resonance imaging (MRI). Bilateral knee laxity was assessed at the completion of rehabilitation. Dynamic MRI was used to measure tibiofemoral kinematics and cartilage contact during active knee flexion-extension. Additionally, a total of 500 virtual ACLR models were created from a nominal computational knee model by varying ACL footprint locations, graft stiffness, and initial tension. Laxity tests, active knee extension, and walking were simulated with each virtual ACLR model. Linear regressions were performed between internal knee mechanics and ACL graft tunnel locations and angles for the patients with ACLR and the virtual ACLR models.


    Static and dynamic MRI revealed that a more vertical graft in the sagittal plane was significantly related ( P < .05) to a greater laxity compliance index ( R2= 0.40) and greater anterior tibial translation and internal tibial rotation during active knee extension ( R2= 0.22 and 0.23, respectively). Similarly, knee extension simulations with the virtual ACLR models revealed that a more vertical graft led to greater laxity compliance index, anterior translation, and internal rotation ( R2= 0.56, 0.26, and 0.13). These effects extended to simulations of walking, with a more vertical ACL graft inducing greater anterior tibial translation, ACL loading, and posterior migration of contact on the tibial plateaus.


    This study provides clinical evidence from patients who underwent ACLR and from complementary modeling that functional postoperative knee mechanics are sensitive to graft tunnel locations and graft angle. Of the factors studied, the sagittal angle of the ACL was particularly influential on knee mechanics.

    Clinical Relevance:

    Early-onset osteoarthritis from altered cartilage loading after ACLR is common. This study shows that postoperative cartilage loading is sensitive to graft angle. Therefore, variability in graft tunnel placement resulting in small deviations from the anatomic ACL angle might contribute to the elevated risk of osteoarthritis after ACLR.

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