# 15 Mechanical Aspects of the Lumbar Spine

10.1055/b-0036-140430

## 15 Mechanical Aspects of the Lumbar Spine

### 15.1 Load on the Lumbar Spine

#### 15.1.1 Plane Model Calculation

The load on the lumbar spine when a mass is held in the hands can be estimated in a plane model calculation if some simplifying assumptions are made. In Fig. 15.1 the gravitational force of the mass acts perpendicularly downwards. Its moment arm is the distance between the center of mass of the load and the center of rotation, assumed to be in the center of the intervertebral disk. The force of the extensor muscles is represented by a single muscle force F; its direction is approximately equal to the direction of the gravitational force. The moment arm of the muscle force F is to be estimated. Its minimum value is equal to the distance from the center of the disk to the nearest muscle; its maximum value is equal to the distance from the center of the disk to the surface of the skin. As a compromise we accept as moment arm the distance between the center of the disk and the geometrical center of the cross-sectional area of the extensor muscles. This corresponds roughly to a distance of 5 cm. With a mass of 20 kg held in the hands (corresponding to a weight of approximately 200 N) and a moment arm of the gravitational force of 25 cm, we obtain from the equilibrium of moments (signs according to the sign convention for moments):

If we count the downward directed force components (muscle and gravitational force) as negative, we obtain from the equilibrium condition of forces the component G of the joint load G.

The positive sign of G indicates that the direction of G is opposite to the direction of the muscle and gravitational forces. The joint is loaded in compression.

If the total load on the lumbar spine is to be estimated in the posture shown in Fig. 15.2 , the moment of the body weight cranial to the segment in question has to be taken into consideration in addition to the moment of the weight held in the hands. To simplify the model calculation and to allow easy adaptation to different postures, the body is subdivided into the segments head, arms, and trunk ( Fig. 15.2 ). The masses and the locations of the centers of mass of the segments are approximately known (see Chapter 11 ). With m1 and L1 as the mass and moment arm of the hand-held mass, m2 to m4 and L2 to L4 as the masses and moment arms of the head, arms, and trunk segments, g as gravitational acceleration, and F and L5 as the force and moment arm of the extensors of the back, we obtain in equilibrium of moments:

In equilibrium of forces G is calculated as

It is concluded from this equation that, even without any external load (m1 = zero), the lumbar spine is loaded by the body weight and in addition by the muscle force required to balance the moment of the weight of the head, arms, and trunk in the forward bent posture. This load increases with increased forward bending.

If an object is not only held or lifted very slowly but is noticeably accelerated in the lifting process, inertial forces have to be taken into account. When a mass is being lifted ( Fig. 15.3 ) the accelerations of the mass and the body segments are directed upwards. Thus the inertial force F in = −m · a is directed downwards and points in the same direction as the gravitational force. It follows that, when the object and the body segments are being accelerated (dynamic case), the extensor muscles of the back have to develop a higher force than during pure holding of the object (static case). Employing realistic data for the acceleration of objects being lifted, obtained by observation in industrial workplaces, Leskinen et al 1 calculated that the load on the L5/S1 segment during lifting of a mass of 15 kg using four different lifting techniques amounted to between 5800 and 6600 N. A static calculation (excluding inertial forces) showed loads between 3900 and 4600 N. This comparison demonstrates that inertial forces can contribute substantially to spinal loading.

As an extreme example of spinal loading, Granhed et al 2 calculated the load on the L3 vertebra of weight lifters. With masses of over 300 kg being lifted, a load of over 30 kN is predicted. A load of this magnitude amounts to several times the normal compressive strength of L3 (see Section 15.2.1). To explain how it is possible to perform such exercises at all, the authors point to the unusually high bone density in the spine of these athletes. One has to assume that their vertebrae are composed almost entirely of compact bone.

#### 15.1.2 Three-Dimensional Model Calculations

In the plane model described in the section above, muscle forces were represented by a single muscle force. Employing this model, loading configurations in the sagittal plane can be analyzed with adequate accuracy. An advantage of this procedure is that no additional assumptions have to be made to solve the equations. If, however, the load on the lumbar spine is to be estimated in any given posture or with any given directions of external forces, a model with only a single muscle is no longer applicable. To the contrary, all the muscles of the trunk need to be taken into account. For example, in a posture with the trunk bent forwards and rotated sideways, the calculation must take into account not only the muscle forces of the extensors, but also those of the obliques.

For the foundation of a three-dimensional model calculation, a detailed model of bones, muscles, and joints has to be compiled. The points (or areas) of insertion of muscles and tendons, the directions of their tensile forces, and their moment arms in relation to the joints have to be determined from anatomical observations. If more than a single muscle is taken into account, the equilibrium equations form an indeterminate system. However, the multitude of solutions can be reduced to a single solution by making additional assumptions. Various assumptions (objective functions) have been proposed. It can, for example, be postulated that the joint load, or the sum, or the sum of the squares of the muscle stresses has a minimum value. The choice of postulate is based on assumptions about the neuromuscular control strategy. Is it intended to limit joint loading? Are the muscles intended to be protected from overload or fatigue? The results of such model calculations do, of course, depend on the choice of assumptions, but the resulting uncertainty seems small compared with the uncertainties inherent in the anatomic models.

Schultz and Andersson 3 proposed a model incorporating ten muscle groups ( Fig. 15.4 ). Minimization of the joint load was used as the objective function; in addition a maximum value of the muscle stress (muscle force divided by muscle cross section) was prescribed. This limiting value, known from muscle physiology (approx. 40 N/cm2), ensures that individual muscles are not assigned unphysiologically high muscle forces in the calculation. 4 The model of Schultz and Andersson3 has been applied for calculating the load on the lumbar spine in asymmetric body postures. Jäger 5 developed a model which represented the musculature of the back and the abdomen by eight muscles. The objective function employed by Jäger was the sum of the muscle forces. This model has been applied for determining loads on the lumbar spine in the workplace—for example, in one-handed brick laying, or when transporting waste containers. 6, 7

In certain postures, antagonistic muscle activation is inevitable. If, for example, the trunk is bent forwards and simultaneously rotated to the right, the force of the oblique muscles must be compensated (due to their location anterior to the spine) by additional generation of force from the extensor muscles. A model calculation using objective functions allows correctly for this effect. However, any additional anticipated or involuntary, mechanically “unnecessary” activation of muscles cannot be taken into account without additional information or assumptions. As a simple example, the reader is referred to the calculation of the load on the elbow joint with activation of the biceps and triceps (see Chapter 12 and Fig. 12.7). If, in addition to the force of the biceps required for equilibrium, the triceps is activated voluntarily, there is no way to calculate the joint load. To find a solution for this, the magnitude of the additional muscle force has to be known.

To deal with the antagonistic muscle activation that occurs in certain postures and during certain activities, so-called electromyography (EMG)-based model calculations have been developed (see, for example, Granata and Marras 8). These model calculations are likewise based on a model of the architecture of muscles and joints, but the muscle forces in the postures or during the activities under investigation are not calculated but are determined from EMG measurements. Insertion of these forces in the anatomical model then allows the joint loads to be calculated in a second step. To do this, the EMG signal must have been calibrated against the muscle force before the measurements are carried out. This is done in pilot experiments that determine the conversion factors between the maximum muscle force and the EMG signal amplitude. EMG signals are then recorded during the activity under investigation by means of electrodes placed on the skin, and correction factors are applied to account for the effect of length change and shortening velocity of the muscles. The study by Knapik and Marras 9 presents an example of an EMG-driven model calculation. A discussion of the foundations of the various model calculations is presented in the paper by Reeves et al. 10

#### 15.1.3 Intra-abdominal Pressure and the Load on the Lumbar Spine

Experience shows that many subjects spontaneously generate a pressure in the abdomen when they lift a heavy object. Why the intra-abdominal pressure is generated and what its effect is on the load of the lumbar spine is still a subject of debate. Some investigators hypothesize that the intra-abdominal pressure relieves the load on the lumbar spine. The reasoning is that a pressure in the abdominal cavity acts in all directions, resulting in a force F 1 on the diaphragm and a force F 2 on the floor of the pelvis ( Fig. 15.5 ). These forces generate an extension moment in the opposite direction to and partially compensating the flexion moment generated by the load in the hands. In consequence, it is argued, the force of the extensor muscles and the load on the spine will decrease.

A closer look at the muscles generating the intra-abdominal pressure prompts some doubts about this argument. The pressure in the abdominal cavity is generated essentially by activation of the oblique and the transversus abdominis muscles. The forces of these muscles have components whose direction is parallel to the spine ( Fig. 15.5 ), and these force components load the lumbar spine. In addition, the extensor muscles must develop higher forces to prevent forward bending of the trunk when the oblique muscles are activated. (This additional tensing of the extensors can easily be verified by palpating them while voluntarily generating intra-abdominal pressure.) In effect, the generation of muscle forces posterior and anterior to the spine results in an increase in spinal load. At best this increase can be partially compensated by the extension moment generated by the intra-abdominal pressure. The conclusion that the generation of intra-abdominal pressure increases the load on the spine is in agreement with the observations of Nachemson et al. 11 These authors documented an increase in intradiskal pressure during voluntary generation of intra-abdominal pressure. This also agrees with observations in patients with spinal complaints: when they generate intra-abdominal pressure—for example, when they cough—their load-dependent symptoms increase.

Various conjectures have been put forward in answer to the question of why intra-abdominal pressure is generated (since it obviously does not unload the spine). It is possible that generation of intra-abdominal pressure is not intentional but merely a by-product of the contraction of the muscles of the trunk. Activation of these muscles serves to stabilize the upper with respect to the lower trunk. Marras et al 12 showed that, in rapid lifting exercises, peak values of the pressure are reached before peak values of the external moment are observed. This agrees with the observation that healthy subjects activate the transversus abdominis muscle before an anticipated activation of the deltoid muscle and subsequent movement of the arm is made. 13 In addition, the above hypothesis is supported by the observation that a high intra-abdominal pressure is usually generated during sit-up exercises. In these exercises the extension moment due to the pressure is directed in the opposite direction to the intended movement (that is, flexion) of the trunk. 14

On the other hand, the pressure generated in the abdominal cavity is usually not very high; peak values of 100 mmHg (corresponding to 13.3 kPa) are exceeded only when lifting very heavy objects. 15, 16 However, the pressure acts on a relatively large area and generates a posteriorly directed force on the lumbar spine (F 3 in Fig. 15.5 ). This posteriorly directed force may serve to prevent an excessive increase in the lordotic curvature if the spine is under high axial (longitudinally directed) load. 17 In any event, the intra-abdominal pressure permits the muscles of the trunk to contract while preventing a collapse of the abdominal cavity.

Despite the many unanswered questions, broad belts are available commercially that promise to reduce the load on the spine in physically demanding workplaces. Measurements have demonstrated, however, that wearing such belts neither increases the isometric force of the extensor muscles of the back, nor decreases the rate of injuries to the lumbar spine. 1820 At most, belts limit the range of motion of the trunk with respect to flexion. 21, 22

#### 15.1.4 Recommendations for Lifting and Carrying

Guidelines and recommendations for lifting and carrying at the workplace, in the household, and in leisure activities serve several goals 23:

• They are intended to protect people against muscular exhaustion and cardiovascular overload. For this purpose, maximum values for the frequency of lifts performed are recommended, related to the mass lifted and the posture attained. The recommended limits are based on measurements of heart rate and energy turnover derived from respiratory gas analysis.

• They are intended to prevent accidents. For this purpose, risk factors such as slippery floors, missing handles, or obstruction of the view due to excessive size of the objects being handled have to be eliminated.

• They are intended to protect the lumbar spine against overload. Injuries due to a single episode of overloading or to repeated high loads are to be avoided by limiting the maximum mass of the objects handled and by avoiding certain postures when lifting and carrying. The recommended limits of the masses are based both on epidemiological studies and on a comparison of the results of biomechanical model calculations with the experimentally determined compressive strength of vertebral bodies and disks. Strictly speaking, it would be more correct to state limits for the moments exerted on the spine rather than limits for the masses handled, because spinal loading depends on the moments and not on the magnitude of the masses. However, specifying just the masses and the postures makes it easier to apply the recommendations.

The moment of a mass handled is proportional to its moment arm. For practical applications it follows that, for a given mass, the load on the lumbar spine will be smallest when the moment arm chosen is the smallest possible. For this reason it is recommended that objects being lifted or carried should be positioned as close as possible to the spine. If the object is carried anteriorly, the minimum magnitude of the moment arm is limited by the presence of the abdomen to approximately 20 cm ( Fig. 15.6 ). Backward bending of the upper trunk, shifting the common center of mass of the body and the object closer to the spine, will bring about a reduction of spinal load in this posture.

If the arms hang down and a weight is held in the hands (for example when carrying a suitcase or a stretcher, or when lifting a wheelbarrow), the moment arm in relation to the spine is small. If an object is carried posteriorly (for example when lifting a piece of furniture behind the back), the moment arm may well be less than 10 cm. At the same time, the moment arm of the abdominal muscles balancing the moment of the weight is substantially larger than that of the extensors of the back. It follows that lifting posteriorly may unload the spine in comparison with an anterior lift.

The components of the force loading the spine that are directed perpendicular to the vertebral endplates and those that are directed parallel to them follow a characteristic pattern that depends on posture ( Fig. 15.7 ). Ignoring for the time being the natural curvature of the spine, the moment arm L of a mass being carried in the erect posture is virtually constant. The moment of the gravitational force, the required muscle force, and the resulting force directed longitudinally along the spine are thus virtually identical in all segments of the lumbar spine. In this posture, the magnitude of shear forces acting in the plane of the disks is small. This is true even for the L5/S1 segment, which is tilted some 45° out of the horizontal. This is because by far the largest part of the spinal load stems from the force of the extensor muscles, and the direction of the muscles closely follows the direction of the spine.

By contrast, in the forward bent posture the moment arm of the weight increases in the craniocaudal direction and, consequently, so does the additional axial load (directed perpendicular to the endplates) on the lumbar spine. To some extent the lumbar spine is adapted to increased loading in the craniocaudal direction, as the compressive strength of the vertebral bodies increases from T12 to L5. In the forward bent posture, the magnitude of the shear force acting in the plane of the disks (again ignoring the curvature of the spine) equals the weight of the mass handled in addition to the weight of the body mass located cranial to the segment under consideration. The shear force is largely resisted by the facet joints, and to a much lesser extent by the disks.

It is generally correct that, in any given posture, the load on the lumbar spine will be smallest when the moment arm of the object being lifted or carried is selected to be as small as possible. Further recommendations on specific postures to be assumed when lifting or carrying can, however, be problematic, for a number of reasons.

• Fig. 15.8 compares lifting an object with the trunk bent forwards and lifting with the knees bent. It is assumed that the dimensions of the object are such that it cannot be lifted between the knees. In forward bending ( Fig. 15.8a ) the moment arm of the object related to the L5/S1 segment is smaller than it is in posture (b) where the knees are bent. The moment arm of the body weight, by contrast, is greater in the forward bending posture ( Fig. 15.8a ) than in the knees-bent posture ( Fig. 15.8b ). In the borderline case of a very heavy object and very lightweight lifter, therefore, posture a would result in minimal spinal loading and would thus be advantageous, whereas in the case of a heavy lifter and a lightweight object, posture b would be preferable. If the mass of the subject and the mass of the object are known, it is, of course, possible to decide which of the two postures results in the smaller axial load on the lumbar spine. If the masses are not known, no generally valid advice can be given. In other words: if only one posture were recommended for lifting and carrying, it might well be the wrong posture in a particular situation. 24

• Even if a calculation in the individual case yielded the result that posture b loads the lumbar spine less than posture a, lifting with the knees bent cannot be recommended to all persons without reservation. This is because the load on the femorotibial and femoropatellar joints increases considerably as the bending angle of the knee increases. In elderly persons with incipient or advanced osteoporosis, a deep knee bend has the potential to damage the trabecular bone below the tibial plateau.

• In addition, it must be borne in mind that frequent lifting with the knees bent is energy-consuming and thus very tiring, because every straightening up from a knee bend requires lifting of the bodyʹs center of mass.

### 15.2 Strength of Lumbar Vertebrae

#### 15.2.1 Compressive Strength

Strength is defined as the load that causes irreparable damage to a structure. In principle, bones can be loaded by compression, tension, shear, bending, torsion, or a combination of these. For vertebral bodies, the loading mode of interest is compression by a force directed perpendicular to the endplates. In both erect stance and forward bending, this force is transmitted to the vertebral bodies via the disks. Only at the limit of extension may a fraction of the load be transmitted by the facet joints and the vertebral arch, but the major part of the load is still exerted by axial compression. So far as fractures are concerned, tensile forces acting on the vertebral body via the ligaments or the disk are of importance only in situations of extreme load or in accidents. Forces acting in the plane of the disk and moments about the long axis of the spine are resisted by the facet joints. So long as the facet joints do not fracture (which almost never occurs except in accidents), shear forces and moments can be ignored when discussing the strength of vertebral bodies.

Fig. 15.9 shows the force–deformation curve of a lumbar vertebral body, determined in vitro. After an initial region under small load, deformation increases in line with force. Once a particular force value is reached, the curve deviates from a straight line: the deformation (compression) increases rapidly whereas the force hardly increases at all. This force value is called the compressive strength of the vertebra. If the force is now reduced to zero, the vertebra remains deformed. In almost all cases, the trabecular bone beneath the endplates fractures under overload, resulting in clefts and stepped or rounded impressions in the endplates, sometimes associated with intrusion of disk tissue into the trabecular bone. Wedge-type fractures or a decrease in the height of the entire vertebral body are less frequently seen. After a fracture, the vertebral body has a reduced load bearing capacity; in the example illustrated in Fig. 15.9 this amounts to approximately 7 kN.

In addition to the compressive strength under one single loading cycle, the fatigue strength of lumbar vertebrae has been investigated. 26 The results show that the probability of a fatigue fracture undergoes a sharp increase if the amplitude of the cyclic load exceeds 50% of the load that results in vertebral fracture in one single loading cycle. The results of this experiment in vitro should, however, be regarded only as approximate values. In living persons the development of microdamage, eventually leading to fatigue fracture, competes with physiologic repair processes. In vitro experiments demonstrate that, unlike traumatic, multiple fractures, fatigue fractures rarely destroy a vertebral body completely. This suggests that the characteristic morphological alterations in vertebral shape seen in patients with advanced osteoporosis are in most cases due to fatigue fractures.

The results of in vitro strength tests of lumbar vertebrae allow elucidation of the parameters that determine compressive strength. As an example, Fig. 15.10 shows the compressive strength of lumbar vertebrae measured in vitro in relation to the product of the bone density of the trabecular bone [mg/mL K2HPO4] and the area of one of the endplates [cm2].25 The bone density in the central volume of the vertebrae and the endplate area were both determined by computed tomography (CT). To allow comparison of bone density measurements made on different scanners, the density is quoted not in milligrams per cubic centimeter [mg/cm3], but in units of the density of a potassium salt used as a reference substance for calibration [mg/mL K2HPO4]. The data from this experiment show that the compressive strength of vertebrae increases as the bone density and the dimensions of the vertebral body increase. The scatter of the data about the regression line shown in Fig. 15.10 indicates that compressive strength is influenced (though to a minor extent) by additional factors besides endplate area and bone density. The architecture and the material properties of the trabecular bone within the vertebral body may play a role here. If bone density and endplate area are measured in vivo by CT, the in vivo strength of vertebrae can be predicted from the data shown in Fig. 15.10 within error limits of ± 1 kN. The study by Brinckmann et al25 showed that in a given spine the bone densities of vertebrae T12 to L5 are virtually equal. The compressive strength of the vertebrae increases craniocaudally by approximately 300 N per segment; the increase is due to the increase in endplate area of the vertebrae.

Other investigators (see, for example, Eriksson et al 27) correlated the in vitro strength of lumbar vertebrae with their bone mineral density as measured by dual photon or dual X-ray absorptiometry (DPA, DXA). For a discussion of the experiments and the results, see Ebbesen et al. 28 It turns out that the compressive strength of a vertebra can be predicted from the bone mineral density [g/cm] or from the product of the trabecular bone density [g/cm3] and the endplate area [cm2] with almost equal accuracy. This is because the dimensions of the bone are implicitly contained in the bone mineral density data: the product of volumetric density and area [g/cm3 · cm2 = g/cm] has the identical dimension to that of bone mineral density [g/cm]. The difference between the two measuring methods is due to the fact that volumetric bone density is determined only from the trabecular bone, whereas the measurement of bone mineral density also includes the cortical bone of the vertebral body. That both procedures still lead to approximately the same result is probably because there is a correlation between the densities of trabecular bone and cortical bone. It may be possible to achieve greater precision in the prediction of compressive strength if the model calculations into which the bone density measurements are fed take account of the individual architecture of the vertebra. 29