On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective

Metzger, Melodie F.; Senan, Nur Adila Faruk; O’Reilly, Oliver M.

doi:10.1007/s11044-010-9205-z

Cited by 12 publications

(21 citation statements)

References 17 publications

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“…This was because the ensuing change in the results was not significant enough to justify the increase in computational cost as a result of the increase in the model's complexity. The incorporation of a stiffness matrix to model the intervertebral joint kinematics (Metzger et al 2010;Panjabi et al 1976;Stokes et al 2002;O'Reilly et al 2009) would overcome this in an analytically and numerically tractable manner. Aside from allowing for coupled motion, the stiffness matrix representation of the joint would also permit a more transparent relationship between the joint displacements and rotations and the accompanying forces and moments.…”

Section: Discussionmentioning

confidence: 99%

A Musculoskeletal model for the lumbar spine

Christophy

Senan

Lotz

et al. 2011

Biomech Model Mechanobiol

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228

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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.

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Section: Discussionmentioning

confidence: 99%

A Musculoskeletal model for the lumbar spine

Christophy

Senan

Lotz

et al. 2011

Biomech Model Mechanobiol

Self Cite

259

228

View full text Add to dashboard Cite

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“…Rather our intention is to provide a solid and well-documented basis for future, more detailed models. Particularly useful additions include the ability for the stiffness matrix elements to be written as functions of the preload as in [22], incorporation of a damping matrix, as well as the addition of contact forces upon articulation of the vertebral facet faces.…”

Section: Anterior-posterior Translationmentioning

confidence: 99%

“…We emphasize that using ∆y S as opposed to y S in (22) ensures that no forces and moments are exerted in the neutral posture. Implicit in (22) and (23) is the assumption that the elements of K E are determined using the components of the forces and displacements measured in the frame of reference of the lower body, the relative rotations and increments in moments measured in the Euler and dual Euler basis respectively, and that the SpineBushing frames S 1 and S 2 have the same orientation as the body-fixed frames, and are situated at the landmark points used to determine the elements of K E .…”

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confidence: 99%

“…Implicit in (22) and (23) is the assumption that the elements of K E are determined using the components of the forces and displacements measured in the frame of reference of the lower body, the relative rotations and increments in moments measured in the Euler and dual Euler basis respectively, and that the SpineBushing frames S 1 and S 2 have the same orientation as the body-fixed frames, and are situated at the landmark points used to determine the elements of K E . If a different set of basis vectors are used, then appropriate modifications need to be made to the expressions for F S K , and ∆y S to ensure compatibility with K E .…”

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confidence: 99%

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On the modeling of the intervertebral joint in multibody models for the spine

et al. 2012

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The need to develop feasible computational musculoskeletal models of the spine has led to the development of several multibody models. Central features in these works are models for the ligaments, muscles, and intervertebral joint. The purpose of the present paper is to show how experimental measurements of joint stiffnesses can be properly incorporated using a bushing element. The required refinements to existing bushing force functions in musculoskeletal software platforms are discussed and further implemented using a SpineBushing element specific to the intervertebral joint. Four simple lumbar spine models are then used to illustrate the accompanying improvements. Electronic supplemental material for this article includes a complementary review of formulations of stiffness matrices for the intervertebral joint.

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“…However, the corresponding developments for the kinetics were not immediately forthcoming. A primary difficulty in finding clinically relevant descriptions for the forces and moments at the knee joint can be traced to the geometry of the joint and the fact that the axes of rotation for the two of the Euler angles are not orthogonal: g 1 ⊥ g 3 . Progress towards a useful representation of the forces and moments was made in 1996 by Fujie et al [2].…”

Section: Introductionmentioning

confidence: 99%