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Affolter, C., Kedzierska, J., Vielma, T., Weisse, B., & Aiyangar, A. (2020). Estimating lumbar passive stiffness behaviour from subject-specific finite element models and in vivo 6DOF kinematics. J. Biomech., 102, 11 pp.
Abstract: Passive rotational stiffness of the osseo-ligamentous spine is an important input parameter for estimating in-vivo spinal loading using musculoskeletal models. These data are typically acquired from cadaveric testing. Increasingly, they are also estimated from subject-specific imaging-based finite element (FE) models, which are typically built from CT/MR data obtained in supine position and employ pure rotation kinematics. We explored the sensitivity of FE-based lumbar passive rotational stiffness to two aspects of functional in-vivo kinematics: (a) passive strain changes from supine to upright standing position, and (b) in-vivo coupled translation-rotation kinematics. We developed subject-specific FE models of four subjects' L4L5 segments from supine CT images. Sagittally symmetric flexion was simulated in two ways: (i) pure flexion up to 12 degrees under a 500 N follower load directly from the supine pose. (ii) First, a displacement-based approach was implemented to attain the upright pose, as measured using Dynamic Stereo X-ray (DSX) imaging. We then simulated in-vivo flexion using DSX imaging-derived kinematics. Datasets from weight-bearing motion with three different external weights [(4.5 kg), (9.1 kg), (13.6 kg)] were used. Accounting for supine-upright motion generated compressive pre-loads approximate to 468 N (+/- 188 N) and a “pre-torque” approximate to 2.5 Nm (+/- 2.2 Nm), corresponding to 25% of the reaction moment at 10 degrees flexion (case (i)). Rotational stiffness estimates from DSX-based coupled translation-rotation kinematics were substantially higher compared to pure flexion. Reaction Moments were almost 90% and 60% higher at 5 degrees and 10 degrees of L4L5 flexion, respectively. Within-subject differences in rotational stiffness based on external weight were small, although between-subject variations were large. (C) 2020 Elsevier Ltd. All rights reserved.
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Aiyangar, A. K., Vivanco, J., Au, A. G., Anderson, P. A., Smith, E. L., & Ploeg, H. L. (2014). Dependence of Anisotropy of Human Lumbar Vertebral Trabecular Bone on Quantitative Computed Tomography-Based Apparent Density. J. Biomech. Eng.-Trans. ASME, 136(9), 10 pp.
Abstract: Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property-density relationships have presented results for the superior-inferior (SI), or “ on-axis” direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCT-based apparent density of HVTB and its apparent compressive mechanical propertieselastic modulus (E-app), yield strength (sigma(y)), and yield strain (epsilon(y))-in the SI and TR directions for future clinical QCT-based continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, rho(CT). Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, rho(app), showed significant correlation with rho(CT) [rho(CT) = 1.0568 x rho(app), r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (E-app) and yield strength (sigma(y)) were linearly related to the rho(CT) in the axial direction [E-SI = 1493.8 x (rho(CT)), r = 0.77, p < 0.01; sigma(Y,SI) = 6.9 x (rho(CT)) = 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [E-TR 3349.1 x (rho(CT))(1.94), r = 0.89, p < 0.01; sigma(Y,TR) 18.81 x (rho(CT)) 1.83, r = 0.83, p < 0.01]. No significant correlation was found between epsilon(y) and rho(CT) in either direction. E-app and sigma(y) in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, epsilon(y) exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CT-based densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.
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Collins, C. J., Vivanco, J. F., Sokn, S. A., Williams, B. O., Burgers, T. A., & Ploeg, H. L. (2015). Fracture healing in mice lacking Pten in osteoblasts: a micro-computed tomography image-based analysis of the mechanical properties of the femur. J. Biomech., 48(2), 310–317.
Abstract: In the United States, approximately eight million osseous fractures are reported annually, of which 5-10% fail to create a bony union. Osteoblast-specific deletion of the gene Pten in mice has been found to stimulate bone growth and accelerate fracture healing. Healing rates at four weeks increased in femurs from Pten osteoblast conditional knock-out mice (Pten-CKO) compared to wild-type mice (WT) of the same genetic strain as measured by an increase in mechanical stiffness and failure load in four-point bending tests. Preceding mechanical testing, each femur was imaged using a Skyscan 1172 micro-computed tomography (mu CT) scanner (Skyscan, Kontich, Belgium). The present study used μCT image-based analysis to test the hypothesis that the increased femoral fracture force and stiffness in Pten-CKO were due to greater section properties with the same effective material properties as that of the WT. The second moment of area and section modulus were computed in ImageJ 1.46 (National Institutes of Health) and used to predict the effective flexural modulus and the stress at failure for fourteen pairs of intact and callus WT and twelve pairs of intact and callus Pten-CKO femurs. For callus and intact femurs, the failure stress and tissue mineral density of the Pten-CKO and WT were not different; however, the section properties of the Pten-CKO were more than twice as large 28 days post-fracture. It was therefore concluded, when the gene Pten was conditionally knocked-out in osteoblasts, the resulting increased bending stiffness and force to fracture were due to increased section properties. (C) 2014 Elsevier Ltd. All rights reserved.
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