1 The role of and facet in force distribution on lumbosacral

Y.H. Lin*, C.K. Cheng0

* Department of Physical Therapy, Chang Gung University, Taoyuan, Taiwan,

0 Institute of Biomedical Engineering, National Yang Ming University, Taipei, Taiwan. Introduction Low-back pain may be caused by a mechanical disruption of spinal tissues: facets and ligaments, and the disc (King, et al. 1975). During daily activities the disc is loaded subjected to a combination of compression, bending and torsion (Lindh, 1989). Since force on the spinal elements is difficult to measure in vivo, it is often calculated biomechanically, and only the spinal disc and musculature are considered as the internal tissues in the models(Chaffin, 1969, Schulz, et al., 1981; 1982). Whereas, the roles of ligaments and facets have not been addressed in the models to estimate the force distribution on the lumbar spine. The aim of this study is to investigate the role of ligaments and facet joints in the force distribution on the L5/S1 joint. Methods A mathematical model was used in this study (Cheng, 1998)(Figure1). The intersegmental resultant forces and moments were estimated and were partitioned into the tissues at L5/S1 joint. Four pairs of trunk muscles, two spinal ligaments, two facet joints, and L5/S1 disc were recruited to calculation. The optimization toolbox 1.5 of Matlab was used for calculation. Cost function was to minimize the summation of squared muscle stress with equilibrium of forces and moments. A global coordinate system with X-axis on medio-lateral plane, Y-axis on anterio-posterior plane and Z-axis in the vertical direction was set. A man of 176cm and 72 kg lifting a 100N object was simulated. The posture was 20 degrees of forward bending, side bending, and trunk rotation to the right. Four models were manipulated with muscles, disc (MD), or added with, (MDF), or ligaments (MDL), and all tissues combined (MDFL).

Disc Force

1500

1000

500

0 Dx Dy Dz Newtons(N) -500 MD MDF MDL MDFL

-1000

-1500

-2000 Figure 1. The simulated lifting posture of a virtual man for calculation of force distribution on the lumbosacral joint 2 Results & Discussion The comparisons of force distribution were made under different combinations of the ligaments and facets. The addition of facets shifted the trunk muscle force to left erector spinae and decreases the force of the abdominalis obliqus and increased disc horizontal force and decreased the disc compression force. The facet anteriolateral force was much higher than that at the x direction. As the ligaments were added, the disc force increased at the all directions and decreased the trunk muscles force. The disc compressive force in MDLF model was decreased but higher than that in the model of MDF. Table 1. Force distributions on the internal tissues around lumbosacral joints

MD MDF MDL MDFL

Muscle Erector spinae R 689 0 506 0 Erector spinae L 739 1253 636 1013 Abdominalis Obliqus L 473 30 440 115 Disc Dx -3 -56 -6 -33 Dy 3 971 11 970 Dz -1392 -782 -1481 -1032 Facets Fxr 1387 1423 Fyr 347 372 Fxl 1617 1581 Fyl 663 618 Ligaments IL - - 118 118 LF - - 287 287

Dx: Force on the lumbosacral disc along the x-axis in the mediolateral direction

Dy: Force on the lumbosacral disc along the y-axis in the anterio-posterior direction

Dz: Force on the lumbosacral disc along the z-axis (-: compression force)

Fxr: Force on the right side of facet joint along the x-axis in the mediolateral direction

Fyr: Force on the right side of facet joint along the y-axis in the anterio-posterior direction 3 Fxl: Force on the left side of facet joint along the x-axis in the mediolateral direction

Fyl: Force on the left side of facet joint along the y-axis in the anterio-posterior direction

IL: Interspinous

LF: Ligamentum Flavum Ligaments and facet joints were considered to study the force distribution on the tissues at L5/S1 joint in addition to the and muscles of the conventional biomechanical models. Force distribution of intervertebral disc was affected significantly by the imposed components of ligaments and facet joints in the spinal biomechanical model(Figure 2). The spinous ligaments play a interactive role to share the load imposed with the trunk muscles during spinal movement. The facet could partitioned the external loads from disc force to protect the disc structure from excessive forces and moments. It suggests to consider the role of ligaments and facet joints in the mathematical model to calculate the force distribution on the intervertebral disk.

Disc Force

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0 Dx Dy Dz Newtons(N) -500 MD MDF MDL MDFL

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Figure 2. The disc force estimation under different considerations with ligaments and facets. References

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Acknowledgements

We acknowledge the grant support of the National Science Council, the Executive Yuan of R.O.C. (NSC 89-2320-B-182 -020 -)