Ergoniza Intelligent

12.1 Calculating compression and shear in the L4/L5 intervertebral disc

The compression force acting on the lumbar intervertebral discs does not depend solely on the weight of an external load. The weight of body segments and sustained loads generates moments in the lumbar region that must be balanced by the trunk muscles. These include the posterior erector spinae and several abdominal-wall muscles. The muscle forces required to maintain equilibrium can add a substantial compression component to the disc, so the calculation must jointly consider external loads, body weight, and estimated muscle activity.

Intra-abdominal pressure70F1 also contributes to the mechanical equilibrium of the lumbar region. Coordinated contraction of the abdominal wall, diaphragm, and pelvic floor increases pressure within the abdominal cavity and generates a force whose moment can help balance the flexion moment. In the model, this contribution reduces part of the moment that the trunk muscles must counteract. However, intra-abdominal pressure and muscle activation are related, so its effect on disc compression must not be interpreted as direct unloading independent of the other forces.

Decomposing forces into axial-compression and shear components requires an estimate of the spatial orientation of the L4/L5 disc in the analyzed posture. Ergoniza Intelligent calculates this orientation from the configuration of the trunk and lower extremities and projects the muscle forces, intra-abdominal pressure, and resultant external loads onto the disc's local coordinate system.

The calculation therefore requires the resultant force and moment of the body segments above L4/L5 and the external loads, an estimate of the contribution of intra-abdominal pressure and the trunk muscles, and the local orientation of the disc. These quantities yield the axial-compression force and the anteroposterior and lateral shear components.

Ergoniza Intelligent performs these calculations using a three-dimensional model with ten trunk muscles grouped into five bilateral pairs. The calculation is performed at the L4/L5 intervertebral level, for which anatomical information is available on muscle areas, lines of action, and moment arms used by this type of model.

Figure 62 illustrates the procedure. First, Ergoniza Intelligent estimates the orientation of the transverse plane of the L4/L5 intervertebral disc from the posture of the trunk and lower extremities71F2. This plane and its local reference system are shown in blue in the figure.

The objective is to calculate the disc compression force (C in Figure 62) and the anteroposterior (Cor y) and lateral (Cor x) shear forces. These three components form the reaction required to balance the resultant of the other forces in the disc's local coordinate system. The vector sum of moments about L4/L5 must also equal zero.

The forces considered are the force associated with intra-abdominal pressure (Fa), the weight of the segments above L4/L5 and sustained loads (P), the contraction forces of the ten trunk muscles (Xd, Xi, Id, Ii, Ed, Ei, Ld, Li, Rd, and Ri), and the three components of the disc reaction.

The resultant P and the moment it generates about L4/L5 are obtained through the joint-load analysis described in Section 8. Force Fa and its moment are calculated using the procedure described in Section 12.1.1.

The model includes five pairs of trunk muscles: Latissimus dorsi, Erector spinae, Rectus abdominis, Obliquus externus, and Obliquus internus. A cross-sectional area, line of action, and moment arm about L4/L5 are defined for each muscle. Ergoniza Intelligent uses separate parameter sets for men and women derived from the wide range of studies addressing abdominal-muscle geometry72F3.

Three-dimensional model for calculating L4/L5 intervertebral-disc compression.

Figure 62: Three-dimensional model for calculating L4/L5 intervertebral-disc compression.

When the model is seated on a chair and Backrest is enabled, Ergoniza Intelligent applies the simplification described in Section 7.7.6. If the local flexion-extension component of the moment at L4/L5 corresponds to flexion, that component is set to zero before muscle activity is calculated. The lateral-flexion and rotation components are retained and the external reaction forces are not modified because neither the geometry nor the application point of the backrest reaction is modeled. The program recalculates muscle activity, compression, and shear forces from the corrected moment. Compression therefore does not necessarily become zero or decrease in every case.

Determining muscle forces is a statically indeterminate problem because there are more unknown forces than independent equilibrium equations. Ergoniza Intelligent solves it using two successive linear-programming problems, described in Section 12.1.2. The force associated with intra-abdominal pressure and its moment arm are described first.

  1. Jacek Cholewicki, Krishna Juluru, and Stuart M. McGill, “Intra-Abdominal Pressure Mechanism for Stabilizing the Lumbar Spine,” Journal of Biomechanics 32, no. 1 (1999): 13–17, doi:10.1016/S0021-9290(98)00129-8.↩︎

  2. Anderson, Chaffin, and Herrin, “A Study of Lumbosacral Orientation under Varied Static Loads.”↩︎

  3. Michael E. Gerling and Stephen H.M. Brown, “Architectural Analysis and Predicted Functional Capability of the Human Latissimus Dorsi Muscle,” Journal of Anatomy 223, no. 2 (2013): 112–22, doi:10.1111/joa.12074; J. G. Reid and P. A. Costigan, “Geometry of Adult Rectus Abdominis and Erector Spinae Muscles,” Journal of Orthopaedic and Sports Physical Therapy, 1985, doi:10.2519/jospt.1985.6.5.278; Hyung Woo Koh, Sung Hyoun Cho, and Cheol Yong Kim, “Comparison of the Effects of Hollowing and Bracing Exercises on Cross-Sectional Areas of Abdominal Muscles in Middle-Aged Women,” Journal of Physical Therapy Science 26, no. 2 (2014): 295–99, doi:10.1589/jpts.26.295; S. M. McGill, N. Patt, and R. W. Norman, “Measurement of the Trunk Musculature of Active Males Using CT Scan Radiography: Implications for Force and Moment Generating Capacity about the L4 L5 Joint,” Journal of Biomechanics 21, no. 4 (1988): 329–41, doi:10.1016/0021-9290(88)90262-X; J. Gavin Reid, P. A. Costigan, and W. Comrie, “Prediction of Trunk Muscle Areas and Moment Arms by Use of Anthropometric Measures,” Spine 12, no. 3 (1987): 273–75, doi:10.1097/00007632-198704000-00015; Gunnar Németh and Hans Ohlsén, “Moment Arm Lengths of Trunk Muscles to the Lumbosacral Joint Obtained in Vivo with Computed Tomography,” Spine 11, no. 2 (1986): 158–60, doi:10.1097/00007632-198603000-00011; Shrawan Kumar, “Moment Arms of Spinal Musculature Determined from CT Scans,” Clinical Biomechanics 3, no. 3 (1988): 137–44, doi:10.1016/0268-0033(88)90059-9; S. Kumar, Don B. Chaffin, and Mark Redfern, “Isometric and Isokinetic Back and Arm Lifting Strengths: Device and Measurement,” Journal of Biomechanics 21, no. 1 (1988): 35–44, doi:10.1016/0021-9290(88)90189-3; Chaffin et al., “Lumbar Muscle Size and Locations from CT Scans of 96 Women of Age 40 to 63 Years.”↩︎

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