Oliver M. O’Reilly

A musculoskeletal model for the lumbar spine.

A new musculoskeletal model for the lumbar spine is described in this paper. This model features a rigid pelvis and sacrum, the five lumbar vertebrae, and a rigid torso consisting of a lumped thoracic spine and ribcage. The motion of the individual lumbar vertebrae was defined as a fraction of the net lumbar movement about the three rotational degrees of freedom: flexion–extension lateral bending, and axial rotation. Additionally, the eight main muscle groups of the lumbar spine were incorporated using 238 muscle fascicles with prescriptions for the parameters in the Hill-type muscle models obtained with the help of an extensive literature survey. The features of the model include the abilities to predict joint reactions, muscle forces, and muscle activation patterns. To illustrate the capabilities of the model and validate its physiological similarity, the model’s predictions for the moment arms of the muscles are shown for a range of flexion–extension motions of the lower back. The model uses the OpenSim platform and is freely available on https://www.simtk.org/home/lumbarspine to other spinal researchers interested in analyzing the kinematics of the spine. The model can also be integrated with existing OpenSim models to build more comprehensive models of the human body.

Minimizing errors associated with calculating the location of the helical axis for spinal motions

One of the more common comparative tools used to quantify the motion of the vertebral joint is the orientation and position of the (finite) helical axis of motion as well as the amount of translation along, and rotation about, this axis. A survey of recent studies that utilize the helical axis of motion to compare motion before and after total disc replacement reveals a lack of concern for the relative errors associated with this metric. Indeed, intrinsic algorithmic and experimental errors that arise when interpreting motion tracking data can easily lead to a misinterpretation of the changes caused by replacement disc devices. While previous studies examining these errors exist, most have overlooked the errors associated with the determination of the location of the helical axis and its intersection with a chosen plane. The purpose of the study presented in this paper was to evaluate the sensitivity and reliability of the helical axis of motion as a comparative tool for kinematically evaluating spinal prostheses devices. To this end, we simulated a typical spine biomechanics testing experiment to investigate the accuracy of calculating the helical axis and its associated parameters using several popular algorithms. The resultant data motivated the development of a new algorithm that is a hybrid of two existing algorithms. The improved accuracy of this hybrid method made it possible to quantify some of the changes to the kinematics of a spinal unit that are induced by distinct placements of a total disc replacement.

On the Stiffness Matrix of the Intervertebral Joint: Application to Total Disk Replacement

The traditional method of establishing the stiffness matrix associated with an intervertebral joint is valid only for infinitesimal rotations, whereas the rotations featured in spinal motion are often finite. In the present paper, a new formulation of this stiffness matrix is presented, which is valid for finite rotations. This formulation uses Euler angles to parametrize the rotation, an associated basis, which is known as the dual Euler basis, to describe the moments, and it enables a characterization of the nonconservative nature of the joint caused by energy loss in the poroviscoelastic disk and ligamentous support structure. As an application of the formulation, the stiffness matrix of a motion segment is experimentally determined for the case of an intact intervertebral disk and compared with the matrices associated with the same segment after the insertion of a total disk replacement system. In this manner, the matrix is used to quantify the changes in the intervertebral kinetics associated with total disk replacements. As a result, this paper presents the first such characterization of the kinetics of a total disk replacement.

The Dual Euler Basis: Constraints, Potentials, and Lagrange’s Equations in Rigid-Body Dynamics

Given a specific set of Euler angles, it is common to ask what representations conservative moments and constraint moments possess. In this paper, we discuss the role that a non-orthogonal basis, which we call the dual Euler basis, plays in the representations. The use of the basis is illustrated with applications to potential energies, constraints, and Lagrange’s equations of motion.

On the Nonlinear Dynamics of Tether Suspensions for MEMS

Many MEM devices feature tether suspensions and it is known that the tethers induce a stiffening behavior In this paper, we develop a model for a tether and, from it, establish several useful expressions for the nonlinear restoring forces and torques it provides. For a specific gyroscope, the expressions we find are compared to experimental results.

Influence of Sensor Substrate Geometry on the Sensitivity of MEMS Micro-Extensometers

In order to determine the influence of the silicon chip substrate on measurement fidelity in a silicon MEMS micro-extensometer, finite element modeling of strain transfer efficiency from a steel beam through a bond layer and silicon chip is investigated over a range of chip and steel beam geometries under both axial and pure bending load conditions. The finite element model results are verified against experimental data. An analytical model that incorporates both influence of the bonded substrate on the effective load and shear-lag phenomenon in the bond is developed and is shown to compare favorably to the finite element model over a wide range of chip and beam geometries. Based on these results, a partially-trenched silicon chip is also investigated as an alternate means of locally enhancing the strain transfer to the micro-extensometer without compromising the ability of the substrate to act as part of the encapsulation of moving elements of the micro-extensometer from the environment. The partially-trenched substrate in bending is experimentally shown to generate strains that are 118% of the strain applied to the substrate—a 23% percent improvement over the equivalent unpatterned substrate geometry.Copyright

On geodesics of the rotation group SO(3)

Geodesics on SO(3) are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in optometry and the latter features in the interpolation of rotations in computer graphics. The simplicity of these two disparate interpretations belies the complexity of the corresponding rotations. Using a quaternion representation for a rotation, we present a simple proof of the equivalence of the aforementioned characterizations and a straightforward method to establish features of the corresponding rotations.

On Adhesive and Buckling Instabilities in the Mechanics of Carbon Nanotubes Bundles

© 2015 by ASME. Many recently synthesized materials feature aligned arrays or bundles of carbon nanotubes (CNTs) whose mechanical properties are partially determined by the van der Waals interactions between adjacent tubes. Of particular interest in this paper are instances where the resulting interaction between a pair of CNTs often produces a forklike structure. The mechanical properties of this structure are noticeably different from those for isolated individual CNTs. In particular, while one anticipates buckling phenomena in the forked structure, an adhesion instability may also be present. New criteria for buckling and adhesion instabilities in forklike structures are presented in this paper. The criteria are illuminated with a bifurcation analyses of the response of the forklike structure to applied compressive and shear loadings.

Verifying the equivalence of representations of the knee joint moment vector from a drop vertical jump task

Biomechanics software programs, such as Visual3D, Nexus, Cortex, and OpenSim, have the capability of generating several distinct component representations for joint moments and forces from motion capture data. These representations include those for orthonormal proximal and distal coordinate systems and a non-orthogonal joint coordinate system. In this article, a method is presented to address the challenging problem of evaluating and verifying the equivalence of these representations. The method accommodates the difficulty that there are two possible sets of non-orthogonal basis vectors that can be used to express a vector in the joint coordinate system and is illuminated using motion capture data from a drop vertical jump task.

A Kinect-based movement assessment system: marker position comparison to Vicon

Abstract Accurate movement analysis systems are prohibitive in cost and size to be accessible to the general population, while commercially available, affordable systems lack the accuracy needed for clinical relevance. To address these limitations, we developed a Depth Camera Movement Assessment System (DCMAS) featuring an affordable, widely available depth camera (e.g. Microsoft Kinect). After examining 3D position data for markers adhered to participants and a flat surface, captured with both DCMAS and the industry standard Vicon system, we demonstrated DCMAS obtained measurements comparable, within soft tissue artifact, to the Vicon system, paving the way for a breakthrough technology in preventative medicine.