Muscle-driven and torque-driven centrodes during modeled flexion of individual lumbar spines are disparate
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ORIGINAL PAPER
Muscle‑driven and torque‑driven centrodes during modeled flexion of individual lumbar spines are disparate Robert Rockenfeller1 · Andreas Müller2,3 · Nicolas Damm2 · Michael Kosterhon4 · Sven R. Kantelhardt4 · Rolfdieter Frank1 · Karin Gruber2 Received: 6 March 2020 / Accepted: 24 August 2020 © The Author(s) 2020
Abstract Lumbar spine biomechanics during the forward-bending of the upper body (flexion) are well investigated by both in vivo and in vitro experiments. In both cases, the experimentally observed relative motion of vertebral bodies can be used to calculate the instantaneous center of rotation (ICR). The timely evolution of the ICR, the centrode, is widely utilized for validating computer models and is thought to serve as a criterion for distinguishing healthy and degenerative motion patterns. While in vivo motion can be induced by physiological active structures (muscles), in vitro spinal segments have to be driven by external torque-applying equipment such as spine testers. It is implicitly assumed that muscle-driven and torque-driven centrodes are similar. Here, however, we show that centrodes qualitatively depend on the impetus. Distinction is achieved by introducing confidence regions (ellipses) that comprise centrodes of seven individual multi-body simulation models, performing flexion with and without preload. Muscle-driven centrodes were generally directed superior–anterior and tail-shaped, while torque-driven centrodes were located in a comparably narrow region close to the center of mass of the caudal vertebrae. We thus argue that centrodes resulting from different experimental conditions ought to be compared with caution. Finally, the applicability of our method regarding the analysis of clinical syndromes and the assessment of surgical methods is discussed. Keywords Axis of rotation · Finite helical axis · Confidence ellipse · Biomechanics · Spine model · Hill-type muscle model
1 Introduction
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10237-020-01382-9) contains supplementary material, which is available to authorized users. * Robert Rockenfeller rrockenfeller@uni‑koblenz.de 1
Mathematical Institute, University Koblenz-Landau, Universitätsstr. 1, 56070 Koblenz, Germany
2
Institute for Medical Engineering and Information Processing (MTI Mittelrhein), University Koblenz-Landau, Universitätsstr. 1, 56070 Koblenz, Germany
3
Mechanical Systems Engineering Laboratory, EMPA-Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstr. 129, 8600 Dübendorf, Switzerland
4
Department of Neurosurgery, University Medical Centre, Johannes Gutenberg-University, Langenbeckstr. 1, 55131 Mainz, Germany
Relative movement between (lumbar) vertebrae occurs during most daily motions. In three dimensions, such a relative movement between two time instances can be represented by a finite helical (or screw) axis (FHA), i.e., an (instantaneous) axis of rotation that points toward the direction of possible t
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