Loads distributed in vivo among vertebrae, muscles, spinal ligaments, and intervertebral discs in a passively flexed lumbar spine

Abstract

The load distribution among lumbar spinal structures—still an unanswered question—has been in the focus of this hybrid experimental and simulation study. First, the overall passive resistive torque-angle characteristics of healthy subjects’ lumbar spines during flexion–extension cycles in the sagittal plane were determined experimentally by use of a custom-made trunk-bending machine. Second, a forward dynamic computer model of the human body that incorporates a detailed lumbar spine was used to (1) simulate the human–machine interaction in accordance with the experiments and (2) validate the modeled properties of the load-bearing structures. Third, the computer model was used to predict the load distribution in the experimental situation among the implemented lumbar spine structures: muscle–tendon units, ligaments, intervertebral discs, and facet joints. Nine female and 10 male volunteers were investigated. Lumbar kinematics were measured with a marker-based infrared device. The lumbar flexion resistance was measured by the trunk-bending machine through strain gauges on the axes of the machine’s torque motors. Any lumbar muscle activity was excluded by simultaneous sEMG monitoring. A mathematical model was used to describe the nonlinear flexion characteristics. The subsequent extension branch of a flexion–extension torque–angle characteristic could be significantly distinguished from its flexion branch by the zero-torque lordosis angle shifted to lower values. A side finding was that the model values of ligament and passive muscle stiffnesses, extracted from well-established literature sources, had to be distinctly reduced in order to approach our measured overall lumbar stiffness values. Even after such parameter adjustment, the computer model still predicts too stiff lumbar spines in most cases in comparison with experimental data. A review of literature data reveals a deficient documentation of anatomical and mechanical parameters of spinal ligaments. For instance, rest lengths of ligaments—a very sensitive parameter for simulations—and cross-sectional areas turned out to be documented at best incompletely. Yet by now, our model well reproduces the literature data of measured pressure values within the lumbar disc at level L4/5. Stretch of the lumbar dorsal (passive) muscle and ligament structures as an inescapable response to flexion can fully explain the pressure values in the lumbar disc. Any further external forces like gravity, or any muscle activities, further increase the compressive load on a vertebral disc. The impact of daily or sportive movements on the loads of the spinal structures other than the disc cannot be predicted ad hoc, because, for example, the load distribution itself crucially determines the structures’ current lever arms. In summary, compressive loads on the vertebral discs are not the major determinants, and very likely also not the key indicators, of the load scenario in the lumbar spine. All other structures should be considered at least equally relevant in the future. Likewise, load indicators other than disc compression are advisable to turn attention to. Further, lumbar flexion is a self-contained factor of lumbar load. It may be worthwhile, to take more consciously care of trunk flexion during daily activities, for instance, regarding long-term effects like lasting repetitive flexions or sedentary postures.

Appendix

1.1 The implemented point-to-plane contact elements (PPCEs)

There are six PPCEs at the HAUT body. Two are located at the HAUT’s right side and model the trunk of the subjects, which lie on their right sides in the experiment, being supported by the mobile table part of the machine. In these two PPCEs, their plane is fixed to the table, with their normal vector pointing upwards (to HAUT), while the contact points are fixed on HAUT: at shoulder height and width, each one 4 cm dorsally and ventrally, respectively.

Four further PPCEs are introduced to model the fastening of the subject’s trunk to the shoulder cushion roll by the fixation belt, both on their part fixed to the mobile table (Fig. 1b). The belt is for pulling the trunk back to the roll in case the trunk would tilt away from the roll down to the surface of the mobile table. The roll–shoulder interaction is implemented by two of these PPCEs which are fixed to the HAUT’s backside: their plane in common is located 5 cm dorsally from the HAUT’s centre of mass (COM) and its normal vector points dorsally. The belt fastening is simply implemented by the another PPCEs with a second plane in common. This plane is likewise fixed on the HAUT’s backside, however, located 6 cm dorsally from HAUT’s COM, and its normal vector points ventrally.

Each the dorsal and ventral PPCE plane on HAUT can interact with both a lower (1.5 cm above table surface) and an upper (33.5 cm above table surface) contact point locating the shoulder cushion roll. The modeled roll is fixed on the machine’s mobile table part (Fig. 1a) a distance of 18 cm away (at $\mathcal {K}$) from the axis $\mathcal {S}$ of the frictionless hinge joint by which the mobile table is linked to the lever construction A-B-$\mathcal {S}$ which is again linked by hinge A to the machine’s base table part. The latter is eventually fixed to the ground. The two possible contact points on the roll are chosen so as to enable its contacting with HAUT in the regions nearby the heights of both shoulder joints.

To sum shoulder fixation up, two PPCEs support the right shoulder region of HAUT against gravity and another four PPCEs make a ‘rail’ gap for HAUT of 1 cm width, roughly representing a subject’s trunk backside supported by the cushion roll and its front side being pulled back to the cushion roll by the fixation belt. During flexion movements (forward rotations), two PPCEs guide the HAUT body mainly by normal pressure to the trunk’s backside—partly superposed by reversible tangential stick-slip interaction. Enforced pronounced HAUT backward rotations (trunk overextension) can be enforced by the A-B-$\mathcal {S}$ lever arm system around the machine’s motor axis $\mathcal {A}$ pulling the HAUT shoulder region backwards by means of the fifth and sixth PPCEs.

Like the shoulder region is ‘railed’ by PPCEs, the pelvis is ‘clamped’ to the base table by another four PPCEs in accordance to the experiments (Fig. 1b). Their contact points are fixed to the base table, all located 5 cm footward of the axis $\mathcal {A}$ and either 6 cm or 30 cm, respectively, above the base table plane. The corresponding planes fixed to the pelvis are located such that all four PPCEs are usually strained by few millimeters: in the model, the pelvis is thus viscoelastically ‘clamped’. Similar to HAUT at the shoulder cushion roll, both model’s shanks are also ‘railed’ by four further PPCEs. In the shanks, however, the ‘railing’ planes are fixed to the base table instead of the bodies, in parallel to the posterior edge of the base table where the model is lying on its left side on. The contact points are fixed to the shanks at the positions of their respective COM positions in caudal–cranial direction.

Eventually, the pelvis on its right, lying side, the right thigh, the right shank, and the right foot are supported against gravity by altogether six PPCEs of which their planes, like at the right shoulder height of HAUT, all represent the surface of the base table. From proximal to distal (numbers given as distances from the body’s respective COM), the contact points fixed to the bodies are located on the pelvis at 17.5 cm laterally below its COM and 5.8 cm cranially, on the thigh at 6 cm laterally and 13.5 cm proximally as well as 4.5 cm laterally and 25.5 cm distally, on the shank at 4.5 cm laterally and 13.5 cm proximally as well as 4.5 cm laterally and 25.5 cm distally, and on the foot 4.5 cm laterally at about the heel position.

All main parameters of the PPCEs were chosen the same: normal stiffness as $1.5\times 10^{4}$ N m$^{-1}$, the nonlinear normal damping factor according to Eq. (3) as $d_{PPCE,damp}$ = 1 s m$^{-1}$, tangential (stick) stiffness as $2.0\times 10^{3}$ N m$^{-1}$, the coefficients of static and kinetic (sliding, slipping) friction as $\mu _{s}$ = 0.8 and $\mu _{k}$ = 0.7, respectively, and the critical velocity for the slip–stick transition as $v_{crit}$ = 1 cm s$^{-1}$.