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Mathematical modeling and simulation of seated stability.

Authors
Tanaka-ML; Ross-SD; Nussbaum-MA
Source
J Biomech 2010 Mar; 43(5):906-912
NIOSHTIC No.
20037008
Abstract
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the "wobble chair"). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.
Keywords
Back-injuries; Biodynamics; Biomechanical-modeling; Biomechanics; Environmental-control; Environmental-physiology; Muscle-physiology; Muscles; Muscle-contraction; Muscle-tension; Musculoskeletal-system; Physical-reactions; Posture; Spinal-cord; Spinal-cord-disorders; Kinesiology; Kinetics; Author Keywords: Basin of stability; Spinal stability; Lyapunov; Lagrangian coherent structures; LCS; Forward dynamic simulation
Contact
Martin L. Tanaka, Department of Orthopaedic Surgery, Wake Forest University, Winston-Salem, NC 27157, USA
CODEN
JBMCB5
Publication Date
20100322
Document Type
Journal Article
Email Address
mtanaka@wfubmc.edu
Funding Type
Grant
Fiscal Year
2010
NTIS Accession No.
NTIS Price
Identifying No.
Grant-Number-R01-OH-008504
Issue of Publication
5
ISSN
0021-9290
Source Name
Journal of Biomechanics
State
NC; VA
Performing Organization
Virginia Polytechnic Institute and State University
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