Musculoskeletal support of lumbar spine stability H. Wagner, Ch. Anders, Ch. Puta, A. Petrovitch, F. Mörl, N. Schilling, H. Witte, R. Blickhan  Pathophysiology  Volume 12, Issue 4, Pages 257-265 (December 2005) DOI: 10.1016/j.pathophys.2005.09.007 Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 1 (A) Schematic representation of the model. The upper body is represented by a point mass. The angle α describes lateral bending of the upper body. Two antagonistic muscles are included in the model. According to their geometric arrangement (origins and insertions at the bones, cf. Table 1), these muscles can generate a moment; (B) schematic illustration of stability analysis. For a given trajectory (solid line), the initial condition is perturbed (filled circles), e.g. due to an external moment. The system can react to this in different ways. Shortly after the perturbation the new trajectory is completely different, like the trajectory envisioned by the dash-dotted line. In this case at least one eigenvalue of the system is positive. If each eigenvalue is negative the system is stable (dotted lines) and the perturbed trajectory converges into the prescribed trajectory. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 2 Schematic representation of the perturbation device. M: marker; A: motor; F: ground plate; H: rope; B: thud guard; G: handle; K: load cell; k: load cell connector cable. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 3 Typical record of force data obtained from the load cell. The trigger signal enabled a simultaneous analysis of kinematics and force data. The arrows indicate the instants of perturbation, which were determined using a semi-automatic algorithm in Matlab®. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 4 Maximum eigenvalues (numbers on contour lines) for a given cyclic lateral flexion-extension movement of the upper body. The geometric arrangement (horizontal axis) and the position of the instantaneous centre of rotation (vertical axis) vary gradually. Two stable areas do exist, one for negative attachment angles of the muscles and the instantaneous centre of rotation at lower positions, e.g. obliquus internus muscle, and one for positive attaching angles more cranially, e.g. obliquus externus or multifidus muscles. Positive values of maximum eigenvalues indicate unstable situations. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 5 Influence of the physiological cross-sectional area (vertical axis) and the insertion angle (horizontal axis) of the trunk muscles on the maximum eigenvalue (contour lines) of the applied lateral flexion-extension movement. For PCSA less about 70cm2 no self-stabilising movements can be generated. For PCSA larger than 70cm2 a self-stabilized area with angles of attack from 25 to 40° can be found. This area is only slightly influenced by variations of PCSA. Positive values of maximum eigenvalues indicate unstable situations. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 6 Influence of fibre-type distribution on the stability of the simulated movement. Muscles with a high percentage of FT-fibres can stabilize the simulated movement with a less steep insertion angle. Positive values of maximum eigenvalues (contour lines) indicate unstable situations. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 7 Typical reaction patterns of two subjects. Similar loading (Ramp I) and quick-release (Ramp IV) experiments are compared between subject #2 (first row) and subject #8 (second row). Subjects show individual reaction patterns. These typical kinematic patterns are due to individual trunk muscle activation patterns. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 8 Loading and quick-release experiments with different amplitudes of the perturbation result in different amplitudes of the maximum relative angles along the spine, which correspond to perturbation amplitude. Compared to quick-release experiments (Ramp I+II, left) the differences of the amplitudes in loading experiments (Ramp III+IV, right) are about two times as high with increased amplitude of the external perturbation. Filled circles: higher amplitude, open circles: lower amplitude. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions

Fig. 9 Differences of mean maximum/minimum relative angle along the spine between slight and intense perturbations for each subject, hand and perturbation type, respectively. In all cases significant differences were found (Wilcoxon test of paired samples, (*) p<0.05, (**) p<0.001). The lines represent the individual results of subjects. In the first two columns the differences between slight and intense perturbations are given, where the sign differs between left and right hand side. In the third column these differences are compared between loading and quick-release perturbations. Pathophysiology 2005 12, 257-265DOI: (10.1016/j.pathophys.2005.09.007) Copyright © 2005 Elsevier Ireland Ltd Terms and Conditions