Effects of Muscle Dysfunction on Lumbar Spine Mechanics

Effects of Muscle Dysfunction on Lumbar Spine Mechanics. A Finite Element Study Based on a Two Motion Segments Model
Kong, W. Z., Goel, V. K., Gilbertson, L. G., and Weinstein, J. N.

Abstract: Study Design. A combined element and optimization approach was developed to investigate the clinically relevant biomechanical parameters of the muscular lumbar spine under five quasistatic back-lifting conditions.

Objectives. To quantify the effects of muscle "dysfunction" on the mechanical behavior of the lumbar spine.

Summary of Background Data. Trunk muscles have been proven to play an important role in the normal functioning of the spine. Although passive structures of the spine are believed to be subjected increasingly to mechanical stresses when muscular support is inadequate, supportive quantitative data have been lacking.

Methods. External loads at L3-L4 for various lifting tasks were estimated experimentally and partitioned to the disc and muscles across the L3-L4 segment using an optimization scheme. These forces were incorporated into a finite element model of the ligamentous L3-L5 lumbar spine. Muscle "dysfunction" was simulated by decreasing the computed muscle forces.

Results. The range of motion, intradiscal pressure, forces in ligaments, and load across facets increased nonlinearly with the increases in trunk flexion and the load held in hands. At higher loads or at larger flexed postures, muscles were found to play a more crucial role in stabilizing the spine compared with the passive structures. Muscle "dysfunction" destabilized the spine, reduced the role of facet joints in transmitting load, and shifted loads to the discs and ligaments.

Conclusions. Muscle dysfunction disturbs the normal functioning of other spinal components and may cause spinal disorders.

Trunk muscles play an important role in the normal functioning of the spine: providing stability, kinematic control, and protecting other structures from overloading. The paravertebral muscles also are considered to be of etiologic significance in spinal disorders. Poorly functioning muscles may shift loads to the passive structures of the spinal system, which may induce injury or remodeling over time in these structures and result in abnormal spinal function. {34} In an in vitro study, El-Bohy et al {10} simulated the superficial extensors of the spine and found that the facet pressure increased with an increase in the muscle force applied to balance the external flexion moment. Panjabi et al {35} applied simulated intersegmental muscle forces to cadaveric lumbar spine and investigated the effects of muscle force on the range of motion and neutral zone of intact and injured specimens. Wilke et al {42} found that muscles forces decreased motion but increased the intradiscal pressure in a test of cadaveric lumbar specimens. Bergmark {4} studied the mechanical stability of the thoracolumbar spine for the upright posture and found that minimal muscle stiffness was needed for the system to maintain its stability under a given load. The multisegmental muscles were found more effective than intersegmental muscles in stabilization, especially for lateral bending. {6} The total force in intersegmental muscles, however, must be larger than a minimum value to maintain spinal stability.

External loads applied to the lumbar spine in a work setting or in daily life are partitioned to different spinal structures. Extensive studies concerning force and moment sharing among spinal structures have been conducted using optimization-based and electromyography (EMG)-based biomechanical (force) models. {23, 30, 32} Besides delineation of the forces in the disc and various muscles, another finding is that the contributions of soft tissues to resist the external moments are minimal. Finite element models have been widely used to study the mechanical behavior of the ligamentous lumbar spine under varous loading conditions. {12, 24, 40} Dietrich et al {7} calculated tension distribution along muscle fibers using a finite element model of the entire thoracolumbar spine including the rib cage. Goel et al {11} recently combined an optimization-based force model and a finite element model to investigate the effects of muscular forces on a lumbar motion segment under two extreme conditions: with normal muscles and totally devoid of muscles. The segment became more stable in the presence of muscular forces, and the intradiscal pressure and stresses in all of the the spinal components with the exception of the facet joints decreased.

In a healthy person or in a patient, muscle strength may be reduced because of injury, fatigue, aging, and degeneration, but it may not actually reach zero. {29, 36} If changes are not to occur, they will likely take place gradually rather than suddenly. {20} Thus, the results and conclusions obtained from the authors' previous study {11} may not indicate what happens "in reality," where some muscle activity is usually present. It is believed that the passive structural components of the spine are subject increasingly to mechanical stresses when active muscular support is inadequate. {31, 37} Panjabi {34} proposed that the passive subsystem consisting of disc, ligaments, and facets compensates for the decreased stabilizing ability of the active muscular subsystem. There are no data, however, to show how this is accomplished by individual components of the passive subsystem. The objective of the current study is to investigate quantitatively the effects of muscle dysfunction on the mechanical behavior of the spine using an optimization-based biomechanical model combined with a finite element model of the two motion segments lumbar spine (L3-L5).

Methods
A combined optimization and finite element approach was used in the current study as in our previous study. {11} Forces in the muscles and disc across the L3-L4 segment were obtained from an experimental-cum-theoretic force model. Five healthy men free of low back pain performed lifting tasks under controlled conditions. {18} The external loads applied at L3-L4 were determined from kinetic analysis and were partitioned to the disc and muscles using a nonlinear optimization algorithm. These forces in the disc and muscles were incorporated appropriately into a finite element model of the lumbar motion segment to determine and quantify the role of muscles in stabilizing the ligamentous spine. A similar approach was used for the present study. For completeness, these procedures are described briefly in the following paragraphs.

Biomechanical Model. Because it is not practical to determine experimentally the forces in all spinal structures, a number of optimization-based and EMG-based models have been formulated to determine forces in these structures during lifting tasks. {3, 28, 38} In our previous study, {18} a comprehensive model involving optimization and EMG activity measurements was formulated to estimate forces in the L3-L4 segment during dynamic and static lifting with the knees straight. Relevant findings are presented briefly as follows; the details are described elsewhere. {18}

Eight computed tomography (CT) scans from T11 to the sacrum (one at each level) in the neutral posture were obtained for each of the five subjects. The three-dimensional (3D) spatial orientation of the body segments, ground reaction forces and moments, and muscle activities were recorded during lifting as a function of time. The subjects stood on a force platform while performing a specified lifting task. The positions of light-emitting diodes (LED) attached to the legs, thighs, and back were tracked during lifting using an automated 3D motion measurement system (Selspot II System, Innovision, Southfield, MI). With the knees straight, the subjects extended their trunk from a fully flexed posture to an upright posture while holding in their hands either no load, 90 N, or 180 N. The data were recorded under dynamic conditions during lifting and in selected static postures. The kinematic data were used to compute angular positions of the body segments and inertia forces and moments in the 3D space. The corresponding ground reactions at discrete points during the lifting cycle were used to calculate the reaction forces and moments at L3-L4 from the equilibrium of the body segments inferior to the midplane of the L3-L4 disc. These reactions were partitioned to the disc and muscles across the L3-L4 segment. Significant muscles spanning L3-L4 level were included in the formulation. No sagittal plane symmetry of the muscles was assumed during the model formulation. The contributions of the ligamentous motion segment including disc, ligaments, and facet joints werwe represented by three forces, and its net contributions to resist external moments were assumed negligible. The partitioning problem was statically indeterminate, and a solution for forces in the muscles and disc was sought using a nonlinear optimization algorithm. The rectified raw EMG signal was used to estimate the activities of various muscles during lifting to "validate" the predicted muscle forces.

Finite Element Model. The finite element model of the ligamentous two motion segments lumbar spine with muscular forces simulated in the current study is shown in Figure 1. The model was modified from our previously developed ligamentous L3-L5 model to accommodate the muscle attachments. {22} The facet joints also were refined. The anulus fibrosis was modeled as a laminated composite with each lamina modeled as fiber-reinforced composite elements rather than superimposing "criss-crossing" fibers in a solid matrix as was done in the previous studies. {11, 22} The angle of the fibers and the number of fiber layers in a composite element may be controlled easily. The fibers were treated as unidirectional layers embedded in the ground substance for each element. The shear stress on the interfaces of the neighboring layers of the anulus fibrosis was defined as the interlaminar shear stress (ILSS). ILSS has two components: axial and circumferential. Local coordinate systems were defined for the anulus elements to obtain these two ILSS components directly from finite element analyses.

To improve the accuracy of the gross response and ILSS distribution in the ground substance, a finer mesh than that of the previous models was used for the anulus as shown in Figure 1. {11, 22} Convergence analysis of the model under pure axial compression was undertaken to determine the least number of elements needed to predict various parameters accurately. The nondimensionalized changes (in the anteroposterior translation of the L3 centroid - L3 anteroposterior, intradiscal pressure [IDP], disc bulge in the anterior region, and the maximum axial ILSS) as a function of the number of elements used to model the anulus are shown in Figure 2. The parameters were normalized with respect to the predictions corresponding to the 8 X 8 annulus mesh. Six element layers in the radial direction (or laminae) and eight layers in the axial direction (6 X 8 mesh) were chosen because the differences in the parameters between this case and a finer mesh (8 X 8 mesh) were negligible (Figure 2). Each layer of the ground substance has two layers of fibers embedded, with a total of 12 layers of fibers, close to the reported values in the literature. {41} The fibers of successive layers were inclined alternatively +/- 30 degrees to the transverse plane, and the volume of fibers was 16% of the anulus fibrosis volume. {16} The L5 vertebra was rotated by 9 degrees in the sagittal plane to simulate lordosis based on the lateral CT scan of the specimen. The inferior surface of the inferior-most vertebral body (L5) and its spinous process were fixed in all directions. The material properties of all components of the finite element model are similar to those used in our previous studies. {11, 13, 22}

The muscles were simulated in the finite element model by force vectors. Nine muscles attached to the L3-L5 segment were considered as shown in Figure 1. The musculature parameters including attachments, lines of action (Table 1), and areas were based on detailed dissections of the lumbar spine, {5, 8, 9, 25-27} which delineated all fascicles of large muscles such as the multifidus and erector spinae. The computed force in a multisegmental muscle from the force model was redistributed among its fascicles attached to various vertebral bodies (L3, L4, and L5) in proportion to their cross-sectional areas as percentages of the total area of the muscle at L3-L4. Thus, the same force intensity was assumed for all fascicles of a muscle. The forces in intersegmental muscle across the L2-L3 or L4-L5 segment and the forces applied to the superior surface of the L3 vertebra were calculated from equilibrium of the L3 and L4 vertebra. The forces and moments on the superior surface of L3 vertebra and fascicle and muscle forces were applied to the finite element model of the ligamentous two motion segments.

Five quasistatic back-lifting cases were analyzed in the current study: a subject bending forward 30 degrees, 60 degrees, or 90 degrees with no load held in hands (30 degrees/0 N, 60 degrees/0 N, and 90 degrees/0 N; lifts 1, 2, and 3) and bending forward 30 degrees with a 90- or 180-N weight held in hands (30 degrees/90 N and 30 degrees/180 N; lifts 4 and 5). The geometric changes in musculature (including the physiologic cross-sectional areas, directions, and moment arms relative to the spinal column) resulting from posture change were neglected. Forces in the muscles and disc across the L3-L4 segment derived from the optimization-based force model were represented in a local coordinate system located at the center of the L3-L4 disc and are listed in Tables 2 and 3. To simulate muscle dysfunction, muscle forces predicted from the force model were uniformly scales to 90%, 80%, or 70% of the normal values. Because the external loads at any disc level for a given lifting task remained the same regardless of muscle strength, the unbalanced forces and moment were transferred to the L3 superior surface and incorporated into the finite element model.

The finite element model, under application of the forces and moments on the L3 superior surface and forces in muscles and fascicles attached to the L3-L5 segments, was executed using the nonlinear finite element program ABAQUS (Hibbitt, Karlsson & Sorrensen, Inc., Pawtucket, RI) to obtain the displacements and stresses. The data were processed further to yield a number of other clinically relevant biomechanical parameters, e.g., the disc bulge, IDP, and forces in various spinal structures including disc and their moment contributions. The moments were calculated with respect to the axes located at the corresponding geometric center of a disc.

Results
The predicted biomechanical parameters were found to be influenced by the posture and handled load. In response to applied loads, the relative vertebral body displacements were mainly in the sagittal plane; out-of-the-plane motions were very small (Tables 4, 5). The translation of the L3 centroid in the anteroposterior direction, moment contributions of the ligaments, facets and the disc, and other parameters increased in a nonlinear manner, with an increase in angle of forward bending (lifts 1, 2, and 3; Figure 3) and with an increase in load held in hands (lifts 1, 4, and 5; Figure 4). The increase in the magnitude of these parameters was nonlinear; the relative increase was less at larger flexion postures and at larger loads held in hands. As an example, the moment contribution by the ligaments in the sagittal plane increased 1.07 Nm when the load held in hands increased from 0 N to 90 N, whereas forward bending was kept at 30 degrees. The corresponding increase was only 0.21 Nm when the load changed from 90 N to 180 N for the same posture.

A decrease in muscles effectiveness led to an increase in all of the parameters shown in Figures 3 and 4 (dotted lines for 90% effectiveness vs. solid lines for 100% effectiveness), except the load borne by the facets. The load across the facets decreased. There was no tension in the anterior longitudinal ligament for all analyzed lifting cases including those subjects with muscle dysfunction. The strains in all other ligaments increased with muscle dysfunction. Furthermore, the effects of muscle dysfunction on the IDP, ILSS, and the axial force in the disc were marginal. The stress distribution patterns were similar for all lifting cases. Stress concentrations existed in the anterior and posterior regions of the endplates and at the junction of the upper posterior cortical wall and the pedicles. The highest axial ILSS was in the anterior and posterior parts of superior and inferior surfaces of a disc. The maximum circumferential ILSS was a the midheight inner posterolateral part of a disc. The maximum von-Mises stress in cancellous bone increased with muscle dysfunction, whereas the corresponding value in the cortical bone decreased (Tables 4, 5).

Discussion
As stated previously, the present two motion segments "muscular" model is an extension of our previous one motion segment model. {11} (The predictions of the previous model agreed reasonably with the in vivo and in vitro experimentally determined data reported in the literature.) The present two motion segments model, however, is more realistic and refined compared with the previous model. The muscle forces predicted from the force model were partitioned into fascicles in the present finite element model. Thus, the simulation of muscles was more realistic. The anulus fibrosis was modeled as a laminated composite with its normal pattern along the radial direction as opposed to the "criss-crossing" pattern used in the previous model. The former is a more realistic representation of the anatomic structure of the anulus. With this approach, there also is no geometric restriction on the element meshing because the angle of collagenous fibers to the transverse plane and number of fiber layers can be changed easily without modifying the matrix mesh. The composite approach also is superior to a transversely isotropic model. {39} In a transversely isotropic model, fibers and matrix experience not only the same strains but also the same stresses, which is clearly not the actual situation. Additional calculation is required to distinguish stress states of one from the other. The predicted results of models with anulus fibrosis modeled as the "criss-crossing" pattern or as a laminated composite, however, were similar. As an example, for lift 1 (30 degrees/0 N), the flexion-rotation (degrees), IDP (MPa), and axial facet force (N) across the L3-L4 segment were 2.72, 1.10, 124.5, and 2.65, 1.10, 130.5, respectively, for the criss-crossing and laminated composite anulus models.

Predictions across the L3-L4 segment of the current two motion segments model (L3-L5) agree closely with those of the muscular one motion segment model (L3-L4) from our previous study under the same loading conditions. {11} The only exception is that the maximum von-Mises stress in cortical bone of the current model was larger than that of the previous model. For example, these stresses were 16.58 and 10.92 MPa in the L3-L5 and L3-L4 models, respectively, for lift 1 (30 degrees/0 N). This difference probably results from different boundary conditions of the L4 vertebral body. The spinous process of L4 was fixed in the one motion segment model but was free to move in the two motion segments model. The forces exerted on the superior facets of L4 in the L3-L5 model created large tensile stresses in the lateral direction in the upper posterior cortical wall of the L4 vertebra. The decrease of the maximum von-Mises stress in cortical bone with muscle dysfunction also attributed to this because less force is borne by the facets with muscle deficit. That one motion segment model and two motion segments model predicted similar results suggests, to a certain extent, that the predictions are representative of the whole lumbar spine. Numerous studies have shown that disc rupture or separation often happens in the posterolateral portion of a disc, although the mechanisms are not clear. {17, 41} With the anular structure similar to a laminated composite, we hypothesize that the anular separation may result from the relative slippage of the layers under repeated loading that the human spine experiences during lifting and daily living. The relative slippage will initiate when the induced maximum ILSS exceeds bonding shear strength of the anular interfaces or reaches a threshold value that can deteriorate the bonding strength under repeated loads. Our results show that the anulus layers in the posterior region experienced the maximum axial and circumferential ILSS values. Thus, the laminar separation and rupture is likely to initiate in this region. However, there are no data indicating the ILSS value at which the anulus layers might separate. Additional experimental and theoretic studies are necessary to clarify this issue.

The changes in the contributions of the passive structures in stabilizing the spine as a function of the posture, the magnitude of the load held, and muscle effectiveness have helped us quantify the role of passive structures for the first time. All of the predicted biomechanical parameters (e.g., range of motion, IDP, forces in ligaments, load across facets) increased with an increase in angle of forward bending or in the lifted load (Figures 3, 4). The increase in the load borne by facets, despite an increase in the relative flexion-rotation across the motion segments, primarily results from the increased muscle forces required to balance the increase in external loads imposed on the spine. These results agree with the trends identified in other studies. {10, 42} The increase in the magnitude of these parameters was identified as nonlinear in the current study; the relative increase was less at larger loads held in hands or at larger flexion posture of the spine, which suggests that at higher loads or at larger flexed postures, the muscles play a more crucial role in stabilizing the spine compared with the passive structures. Thus, a decrease in muscle strength (e.g., resulting from fatigue) will increase forces more significantly in the ligaments and other passive structures, which in turn imposes an increased risk on these structures.

The strength of back muscles may decrease with injury, disease, degeneration, and fatigue. {1, 2, 21} Muscle dysfunction was simulated by decreasing all of the muscle forces predicted from the force model. Muscle dysfunction was not expressed as a scaling factor of maximum capacity of muscles because no upper stress limit was imposed to muscles in the optimization scheme. Because the lifting cases analyzed require only moderate efforts and because the predicted stresses in muscles were well below the reported upper stress limit in the literature, the muscle stresses would not be expected to change significantly with a small change (e.g., 10%) of the upper stress limit. Whatever the cause, decrease in muscle strength can be represented mechanically by reducing its capability in generating forces. No exact correlates were made regarding the simulated muscle dysfunction and relevant clinical phenomena because there are few data available in the literature to quantify the mechanical changes associated with specific clinical conditions. The range of simulated muscle effectiveness we studied (70-90%) was somewhat arbitrary, but it was systematic.

It is believed that the passive tissues (disc, ligaments, and facets) compensate for the decreased stabilizing ability of the muscles; there are, however, no quantitative data to show how this is accomplished by individual passive components. The results clearly show that the contribution of the intervertebral disc and ligaments in resisting external moments increased significantly with muscle dysfunction for all of the lifting tasks studied (Figures 3, 4; solid vs. dotted lines). However, the role of the facet joints in transmitting the load and stabilizing the spinal system decreased with muscle dysfunction, which place the disc and ligaments at higher risk. The disc and ligaments compensate for the destabilizing effects of muscle dysfunction, but the facets do not. Muscle dysfunction also makes the spine more unstable. (i.e., hypermobile). With muscle dysfunction, the axial force from the passive tissues needed to balance the external loads decreased. Because of the increase in total ligament forces and the decrease in facet forces, the compressive force in a disc decreased only by small values. Therefore, the increases in the IDP and ILSS also were marginal.

The compensating effects of the passive components, however, may be at the cost of potential injury and structural changes. The lifting cases analyzed in the present study would require only a moderate effort from a subject, and the predicted strains and stresses were well below the ultimate values reported in the literature. {19, 33} The maximum strain in every ligament for all lifting cases analyzed was less than half of the corresponding ultimate strain. However, strains and stresses in the posterior ligaments increased significantly with muscle dysfunction. As an example, with a 10% decrease in muscle strength, the strains in the posterior ligaments increased approximately 65%. The maximum strains and stresses in ligaments could approach their yield values for heavier lifting or with severer muscle dysfunction. In this situation, a threshold of "biomechanically acceptable" muscle dysfunction, which depends on posture and the lifted load, may be identified. A biologic tissue also adaptively changes its structure when its mechanical stress is beyond a certain value over time. Muscle dysfunction may trigger adaptive remodeling of these structures, such as stiffening of disc, calcification of ligaments, and osteophytic growth. {14, 15} In reality, both of these phenomena (bone adaptive remodeling and microfractures of various elements) occur simultaneously. Hence, spinal disorders may ensue, and in some patients, these may precipitate in the form of sudden ruptures, (e.g., disc prolapse) at some stage.

The present two motion segment model is more realistic than our earlier one motion segment model, however, there is room for improvement. Muscle dysfunction was simulated by scaling down all of the muscle forces predicted from the force model, although dysfunction may not occur in all muscles simultaneously. There are also possibly other methods to model muscle dysfunction. The effects of postural changes on muscle geometry (including cross-sectional areas, direction, and moment arms) have not been lack of data. The net contribution of the soft tissues including the disc, ligaments, and facet joints in resisting external moments was assumed negligible. These assumptions may not be true for lifting cases involving large loads and flexed postures, in which substantial motion across a segment would alter muscle geometry and the partitioning of loads among the muscles and passive tissues. The load partitioning derived from the force model at the beginning differs from the one in the final equilibrium configuration of the finite element model. One way to address this issue is to calculate initially the contributions of the disc and ligaments based on their deformations and constitutive relations. {30} A radiographic film in the lateral view can be used to determine the relative motion across a segment for each lift. The rotation of an individual segment also can be approximated from the total rotation of the trunk using empiric relations. {30}

Although representative biomechanical parameters can be predicted from short segmental models as discussed previously, complexity of the spinal musculature with its major muscles spanning the thoracolumbar region makes it more legitimate to model the entire region rather than a small part of it. An extension of the present model to include the entire thoracolumbar segment also would enable us to study the effects of lordosis, injury, or a surgical procedure on the adjacent segments-- issues that currently are not feasible for investigation using short segmental models. Efforts are underway to accomplish these tasks.

In summary, the current study has predicted alternations in the mechanical behavior of the spine resulting from decrease of muscle strength. Muscle dysfunction reduced the stability of the spinal system, shifted loads to the intervertebral discs and ligaments, and decreased the role of the facet joint in transmitting load and stabilizing the spine. All of these may have clinical significance.

All references and tables excluded in this transcript are available in the original published journal or upon request.