Value of biomechanical macromodels as suitable tools forthe prevention of work-related low back problemsCitation for published version (APA):Delleman, N. J., Drost, M. R., & Huson, A. (1992). Value of biomechanical macromodels as suitable tools for theprevention of work-related low back problems. Clinical Biomechanics, 7(3), 138-148.

Document status and date:Published: 01/01/1992

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:

www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

providing details and we will investigate your claim.

Download date: 29. Dec. 2019

Clin. Biomech. 1992; 7: 138- 148

Lecture

Value of biomechanica1 macromodels as suitable tools for the prevention of work-related low back problems

N J Delleman MSC’,~, M R Drost PhD1,2,4, A Huson MD phD1,2,4

‘Department of Anatomy and Embryology, Faculty of Medicine, University of Leiden, Leiden; *Faculty of Mechanica1 Engineering, Eindhoven University of Technology, Eindhoven; 3Currently at TNO Institute of Preventive Health Care, Department of Posture and Movement Research, Leiden; 4Currently at Department of Movement Sciences, University of Limburg, Maastricht, The Netherlands

Summary

Biomechanica1 macromodels are evaluated with respect to their possible usefulness for health professionals and ergonomists, as wel1 as for applied research on the prevention of low back problems. It is concluded that in the context stated geometrically simple models, in particular the model by Schultz and co-workers, are to be favoured over more complex models. However, load predictions in extreme trunk postures should be dealt with carefully. It is recommended that the model load predictions should be used only in the comparison of work situations and not for an assessment of the absolute acceptability of a work situation.

Relevante Low back problems are related to mechanica1 (over)load at work. This study shows the pros and cons of various biomechanica1 macromodels as tools for health professionals and ergonomists, as well as for applied research on the prevention of work-related low back problems.

Key words: Low-back pain, work-related, prevention, lumbar, spine, biomechanics, models, evaluation

Introduction

Low back problems and related work absente and disability are a common and expensive problem in western countries. Epidemiological data show a rela- tionship between exposure to mechanica1 (over)load at work and the incidence rate of low back pain’,2. The exact nature of this relationship, however, stil1 remains obscure.

Occupational health professionals, ergonomists, and applied researchers often have to cape with various issues of the prevention of low back problems, e.g. effects of ergonomie adaptations at the workplace or changes in the work method, acceptability of a work

Received: 11 January 1991 Accepted: 8 August 1991 Correspondence and reprint requests to: Nico J Delleman MSc, TNO Institute of Preventive Health Care, Department of Posture and Movement Research, PO Box 124, 2300 AC Leiden, The Netherlands

0 1992 Butterworth-Heinemann Ltd 0268-0033/92/030138-11

situation (comparison with norms), selection of workers, and return to work of employees after a period of absente. To handle in a proper way the issues of prevention mentioned before, while assuming that low back problems are related to mechanica1 load on low back structures, the professionals involved should ideally provide answers to one or more of the following questions:

Which structures in the low back are supposed to be overloaded (intervertebral disc, vertebra, muscle, or ligament) and under which types of load, e.g. compression force, shear force, or axial torque (i.e. the load criteria)? What is the actual load value for each load criterion in a working situation? What is the maximum acceptable load value for each load criterion (i.e. the norm)?

Generally, compression force on an intervertebral disc (Ls-L4, L4-Ls, or L5-SI) is chosen as the only load criterion. The lower parts of the lumbar region are chosen because most damage is found to occur in this region. The maximum acceptable value for this load

Delleman et ai.: Macromodels and low back problems 139

criterion can nowadays be obtained experimentally by loading postmortem specimens (following an assump- tion on the transformation of the results to the in-vivo situation), and in the future possibly by so-called micromodels. Micromodels represent a smal1 part of the spine in detail, usually a functional spinal unit, i.e. two adjacent vertebrae and the intervertebral disc in between.

The actual load value in the work situation can be estimated by a macromodel. Most macromodels consist of two parts, i.e. a so-called free-body diagram and a distribution model. A free-body diagram (see Figure 3, upper part) is used to calculate the forces and moments on the location of interest (here a lower intervertebral disc). This can be done by defining several segments together as a free body (here the upper trunk, the arms, the head, the neck, and a load if present). On the basis of fundamental physical laws the forces and moments, respectively along and around the main axis or axes of the coordinate system, acting on the free body have to be balanced. Here, the forces and moments generated by internal body structures have to counterbalance the forces and moments caused by the so-called external moment (i.e. the weight and position of the various segments included in the free body and various other forces acting on the free body). A distribution model (see Figures 2 and 5) splits these counterbalancing forces and moments into separate contributions of muscle(s), ligament( and bony structures.

In this paper pubiished macromodels used within the framework of prevention of work-related low back problems wil1 be evaluated. The evaluation wil1 be focused on the value of the currently available models for applied research, occupational health professionals, and ergonomists. Their needs and interests form the basis of the authors’ viewpoints in the evaluation. Therefore the indisputable (potential) value of certain models for increase of insight into low back mechanics wil1 not be so prominent. For a description of future directions of model development and fundamental research the reader is referred to a paper by Chaffin3.

To describe and evaluate the various models of interest we have selected seven characteristics. First, these characteristics and the criteria for evaluation wil1 be elucidated; next a description of the models is presented, followed by their evaluation.

Macromodel characteristics and evaluation criteria (see Table 1) The first four characteristics have to do with model intrinsics. In Table 1, the characteristics 5-7 deal with the models’ practica1 usefulness. Evaluation criteria are presented at the end of each subsection and in Table 1. The text in this section wil1 be extensive in order to present existing alternative approaches and viewpoints, to give the authors’ viewpoints, and to prevent ambiguity of certain definitions as it was observed in the literature.

Table 1. Comparison and evaluation of macromodels on the basis of seven model characteristics

Model

Characteristic Ml MZa M2b M3 M4 M5 M6

1. Geometrical complexity Muscles Ligaments

2.

3.

Model techniques

Validation

4. Muscle force calculation

5. Static or dynamic input

6. Symmetrie or asymmetrie input (No. axes in the model)

7. Acquisition of input data

Low Low NO ligaments NO ligaments

Correct Correct

Good resultsz6 See Ml

Force and Force and Force and moment moment moment equations equations equations

Static/ dynamic

Static

Symmetrie/ Symmetrie/ asymmetrie asymmetrie** (1 V(2) (1 I/(3)

Easy Easy

Moderate Moderate Moderate High High High NO ligaments NO ligaments High High

Correct Correct Correct Correct

NO adequate Moderatel results good results

Force and moment equations t optimization technique

Static

Symmetrie

(1)

Easy

Static/ dynamicz7

Asymmetrie

NO validation NO validation experiments experiments

Force and Force and moment moment equations equations t optimization + EMG data technique

NO adequate results

Force and moment equations t optimization technique

Dynamic Dynamic Static

Asymmetrie Symmetrie

13) (1)

Easy Difficult

Symmetrie for lifting (1)

Ml = cantilever modelsZ5~26~2s-42. M2 = models by Chaffin et al.:

(a) whole-body mode12**44-47 (bl distribution model by Anderson, Chaffin, Herrin, and Matthews4s,50.

M3 = model by Schultz et al.6*51-56. M4 = model by Jager and Luttmann57-5s. M5 = model by McGill and Norman4,43,60,6’. M6 = model by Gracovetsky et al.8-‘o~62-65.

140 Clin. Biomech. 1992; 7: NO 3

1. Geometrical complexity

In genera1 models are used to study a complex relationship in the physical world, i.e. transmission of forces through the back, after a reduction of this complexity to the essential factors (components) and features involved. The centra1 problem is the danger of a reduction leading to neglect of essential parts. On the other hand, increasing the complexity with respect to one group of characteristics, e.g. the geometrical data, should be accompanied generally by a series of related data, e.g. material properties, recruitment patterns of active parts, etc. If such related data are only partially available, the gain of adding more (geometrical) characteristics may be negative in the end. Models of a low leve1 of complexity (‘simple models’) and of a high leve1 of complexity (‘complex models’) have both advantages and disadvantages. Simple models do not simulate the exact geometry, e.g. al1 muscle bundles with their different lines of action. These models use many simplifying approximations. The effects of these approximations are unknown apriori; they can only be estimated. In genera1 the required input parameters to the model can be obtained easily. Complex models allow simulation of more subtle effects. However, it is difficult to obtain al1 required input parameters. A complex model does not necessarily produce better numerical results than a simple model. Here ‘bette? means showing more resemblance to the in-vivo situation. In many cases the more global results of simple models are easier to validate and can be interpreted easier than complex models’ results.

The geometrical complexity of a macromodel depends largely on its representation of the morphology of muscles and ligaments. A strict requirement for a model is that the structures generating large forces are modelled explicitly. Muscles can deliver force actively, but also passively when stretched. Active muscle forces are more important in ‘flat back’ situations4, passive forces (ligaments and muscles) are important in al1 extreme trunk postures, e.g. at full flexion of the trunk5. So a model without muscles is useless, and a model without passive forces is of limited use. The actual number of muscles and ligaments required remains questionable.

The relative positions of the pelvis, lumbar vertebrae, and thorax (denoted by the concept ‘truncal kinematics’) determine the lengths of ligaments and muscles in the lower parts of the trunk, and hence their force and force capacity respectively. Neglecting truncal kinematics in a model may introduce con- siderable error in extreme trunk postures. Taking truncal kinematics into account makes a model very complex. It wil1 be difficult to obtain accurate input data, as wel1 as data to validate its predictions.

A special phenomenon to be considered in relation to the mechanics of the low back is the so-called intra-abdominal pressure (IAP). The most commonly assumed role of IAP in counterbalancing flexion moments on the low back is a combination of direct loadbearing and the generation of an extending

moment. In both ways the compression force on the spine is reduced. IAP may be incorporated in macromodels. However, this does not seem to be of great influence. The compression force on the spine was estimated to vary between a reduction of about 15% on average and a slight increase’ due to IAP. IAP is also supposed to have other roles, such as straining the Iumbodorsal fascia8,9 or supporting the spine hydraulicallyr’. IAP wil1 not be discussed in the macromodel evaluation here, because there are up-to-date reviews on this topic11,‘2.

Concerning the evaluation of the models’ geo- metrical complexity the authors take a view that a complex model should justify its use instead of a simple model. In case of model predictions on the same load criterion, the predictions of the complex model should deviate from the simple model’s predictions. It should be recognized that this standpoint holds only within the framework of model use by occupational health professionals, ergonomists, and applied researchers as a practica1 tool to prevent work-related low back problems. This implies that a complex model can stil1 increase insight into the mechanics of the low back without producing outcomes deviating from a simple model. Predictions from complex models on load criteria not given by simple models due to their character are a justification in itself for the use of the complex model. Apart from this the validity of al1 model predictions, either from a simple or from a complex model, has to be shown (cf. characteristic 3).

2. Model techniques

With respect to model techniques a methodological part can be discerned from a numerical part, i.e. the way in which the equations of a model are solved. Although the numerical part often has a considerable influence on the outcome and value of the model, it cannot be evaluated properly on the basis of its description in a paper. Therefore only the methodo- logica1 part of the models wil1 be discussed.

First of al1 the model descriptions should be clear, correct, and unambiguous. In general, descriptions have to be present on the assumptions at the root of the calculation procedures and the calculation procedures themselves (e.g. free-body diagrams, force and moment equations), as wel1 as on the values of input parameters. The modelling of, for example, muscles and ligaments with respect to cross-sectional areas, lengths, lines of action, attachment points, and maximum tension should be described in detail.

3. Validation

Validation is a crucial issue in the use of mathematica1 models. After all, a mathematica1 model is only a set of equations. Its link to reality is through the physical properties of the system it is meant to simulate13. Validation is defined as the comparison of a model prediction and a measurement result on the same

Delleman et al.: Macromodels and low back problems 141

parameter or related parameters. In the latter case a strong relationship between both parameters should be demonstrable. Also the criteria for comparison should be given. If a model is to be used for the comparison of conditions (inputs, e.g. work situations, working postures) a linear relationship with or without an intercept differente between predicted and measured values (showing the same trend at certain conditions) is sufficient. For purposes of determination of absolute acceptability of a certain condition an exact one-to-one relationship is necessary. Ideally, validation experi- ments should be done for a wide variety of conditions within the scope of applicability of the model. Within the framework of prevention of work-related low back problems, validation on a parameter related to this issue is essential.

Validation is particularly important in complex models containing many phenomenological relation- ships. Macromodels calculate forces in ligaments, muscles, and joints, the degree of detail depending on the model. Except for some cases of invasive research14, in genera1 these forces either are not or cannot be measured directly in vivo, due to ethica1 or technical reasons. Active muscle forces can be estimated in a semidirect way from electromyography (EMG). However, the conversion factor (gain factor) between electrical and mechanica1 activity varies among different positions of electrodes on a muscle and among muscles l5 If force predictions are validated . using EMG, it is implicitly assumed that passive forces are negligible, or at least constant. This can be assumed to be true in non-extreme and in static postures only. Passive forces (from muscles and ligaments) might at best be approximated by estimating the strain of the structures (length minus resting length x 100) and calculating the stress (force per unit area) with the aid of a (known) stress-strain relationship. From the calculated stress and the cross-sectional area the force can be calculated.

The statements made in this subsection so far reflect a pure scientific viewpoint. It is imaginable that for policy-making less strict requirements are accepted. In that case at least sufficient confidence should stil1 be presented on the correctness and the scope of applicability of model predictions. Confidence on the correctness of model predictions can be presented by carrying out sensitivity analyses. For example, ligament strain depends heavily on truncal kinematics. Therefore, the effects of estimated measurement error and true variation with respect to this factor should be calculated in order to get insight into the confidence interval for the ligament strain predicted.

4. Muscle force calculation

The human body usually has more than one way of distributing the total amount of required counter- balancing forces (and moments) over the available active muscle components and the passive structures (ligaments and passive muscle components). The forces

delivered by passive structures depend directly on their strain, stress-strain relationship, and cross-sectional area. The remaining force to be counterbalanced has to be delivered by muscles.

In the low back for the counterbalance of each force (or moment) more than one muscle is available. The maximum force of a muscle is determined by its physiological cross-sectional area, its maximum force per unit area, its strain, and its strain rate (strain per unit time). The actual force delivered by a muscle depends on the activity of its nerves.

The strategy the body follows in force (and moment) distribution is not known. This means that in a model of the low back the system is not determined. An assumption must be followed in order to be able to calculate the forces of the individual muscles. Three approaches are commonly used:

Muscles are grouped in functional units til1 the system is determined. Actually this is equivalent to a simulation with fewer muscles. The activity of muscles in a model is prescribed using a measured EMG signal. The major flaw of this method is that in genera1 it is impossible to convert a measured EMG signal to a muscle force, except for special static conditionsr5. The use of EMG therefore requires assumptions on gain factors, i.e. the relation between measured EMG and the muscle force (mV/N). The muscle forces are calculated by optimization techniques. Often the technique of linear programming is used. A linear programme is an optimization model that can be stated in following farm’?

n minimize 2 CjXj (the objective function

j=l )

n

the

subject to: 2 aij Xj 2 bi, i=1,2,...,m (the constraints) j=l

Xj 2 0, j=1,2 ,..., n

where Cj, bi and aij are the known parameters and x1 are the unknown variables. The known parameters include moment arm lengths, line-of-action orienta- tions, muscle cross-sectional areas, and external moments. The unknown variables are the joint reaction and muscle forces.

The problem of the distribution of forces over individual muscles around a joint is discussed vividly”-**. Of special interest within the frame- work of this study is a study on the influence of the physiological cross-sectional area of muscles around the hip23. It emerged that the calculated forces for the individual muscles vary much more (a factor 2 to 8) than the calculated joint compression force (11%). This suggests that forces of individual muscles are much more sensitive to the optimization approach chosen than joint compression forces.

142 Clin. Biomech. 1992; 7: NO 3

It is the authors’ view that grouping of muscles (approach 1) should not be preferred in solving the indeterminate problem. In al1 conceivable load- ing conditions, except for pure flexion moments, the geometrically complex arrangement of trunk muscles causes undeniably counterbalancing forces and moments around two or three main axes of the coordinate system. This reality is violated by choosing approach 1. Furthermore, measured EMG signals (approach 2) are also not preferred, leaving their use for validation. The remarks above lead to a preferente for an optimization technique to take away the indeterminate problem.

5. Statie or dynamic input

Neglecting inertial effects, as occurs in static modelling, may cause considerable error in calculated loads24,25. Moreover, the ability to deal with dynamic loading enlarges the scope of applicability of the model. Any model can be made quasidynamic by including inertial forces of the load and the upper body.

6. Symmetrie or asymmetrie input (number of axes in the model)

During labour there is hardly any situation which loads the body in a symmetrical way. As in the previous model characteristic, the ability to deal with asym- metric loads and trunk postures enlarges the scope of applicability of the model considerably.

A one-axial model has the ability to handle loads around one major axis of a local coordinate system at the low back, e.g. the frontal, the sagittal, or the longitudinal axis. Two- or three-axial models can handle (combined) loads around two or three of the axes mentioned before.

Taking a closer look at the model characteristics static/dynamic (cf. characteristic 5) and symmetrie/ asymmetrie, it is felt that the ability of a model to handle asymmetrie loads should be given a higher value than the ability to deal with (quasi)dynamic loads. The reason for this distinction is the fact that making a model able to handle asymmetrie loads requires a

P X-I-Y-d

Figure 1. Simple, one-axial cantilever model”. A load, L, carried at a distance x from a fulcrum is balanced by a muscle force, F, acting at a distance y. The moments have to be equal so that Lx = -Fy. The distance y is about 7.5 cm43.

Figure 2. More complex, one-axial cantilever mode138. x-x =

0

(Y

Wt

Wl

Fp

FX

Ftll

FC

FS

the transverse plane midway through the intervertebral disc. the instantaneous centre of rotation within the disc. the angle between the X-X plane and the horizontal. the weight of the head, neck, and that part of the trunk above the X-X plane acting through its centre of gravity gt at a distance drfrom 0. the weight of the arms plus any weight being held acting through the shoulder joint at g7 at a distance d, from 0. the force exerted by the intra-abdominal pressure acting at its centre of pressure,p, at a distance dP from 0. the force exerted by the extensor muscles of the back acting at a distance d, from 0. the longitudinal component of force in the abdominal muscles acting through its centre of force m at a distance d,,, from 0. the reaction force acting at 0 to produce compression in the intervertebral disc. the reaction force acting in the X-X plane to produce shear in the intervertebral disc and a force on the inferior facets.

(Reprinted with permission from Reference 38.)

major change of the distribution model of the low back. The process of accurate data acquisition gets more difficult while making a model able to handle quasidynamic loads as wel1 as while making a model able to handle asymmetrie loads.

7. Acquisition of input data

The process of acquiring input data gets more difficult by the number and the type of input variables required. This is important for the user of the model, especially in field situations.

Description of the macromodels

Six macromodels have been distinguished. The first macromodel, i.e. a cantilever model, has been des- cribed by many authors. The other five macromodels

Deleman er al.: Macromodels and low back problems 143

come from research groups around one or two centra1 authors. Table 1 compares the macromodels according to the characteristics mentioned in the previous section. The models are presented in sequence of increasing geometrical complexity. As the free-body diagrams of most macromodels are rather similar, the description wil1 be focused mainly on the distribution models.

Cantilever models (M1)25,26,29-42 describe the spine as a cantilever in which the external moment is counterbalanced by increased tension in an activator at the back, representing al1 force-producing structures (or its analogue at the ventral or lateral side of the trunk). One-axial cantilever models contain only one activator (Figures 1 and 2), two-axial models (Figure 3), two activators. There is no distribution problem, because the number of unknown activator forces equals the number of moment equations. Some cantilever

Mid-sagittal plane

R’ L Erector spinae muscles

Figure 3. Two-axial cantilever modelz6.

Ir = the moment arm in the frontal plane between

1s the intervertebral disc and the lifted weight.

= the moment arm in the sagittal plane between the intervertebral disc and the lifted weight.

W = the lifted weight. dr = the muscle moment arm in the frontal plane.

L = the muscle moment arm in the sagittal plane. = the lelt erector spinae muscle force.

R = the right erector spinae muscle force.

(Reprinted with permission from Reference 26.)

Figure 4. Segment-representation used in the whole- body model by Chaffin and co-workersz8. The feet are not considered as segments. The hands are part of the elbow-to-hand grip segments. A = ankle joint centres. B = ball of foot.

LG = elbow joint centres. = centre of grip of the hand.

K = knee joint centres. L5-SI = L5-S, intervertebral disc centre. S = shoulder joint centres.

(Reprinted with permission from Reference 28.)

models have been validated by comparing, for instance, calculated forces and measured EMGz6.

The model by Chaffin and co-workers (M2a)28,“-47 was used originally to determine the load capacity of the whole body. For the low back the model incorporates a simple cantilever model. The body consists of ten rigid segments (Figure 4). The positions of the feet and the load at the hands are prescribed. The relative positions of the segments can be varied by the model in such a way that the loading moment on any major body joint does not exceed its muscular strength, and that the compression force on the functional spinal unit L5-Sr does not go beyond a maximum accepted value. The model was used to

144 Clin. Biomech. 1992; 7: NO 3

formulate guidelines for maximum forces to be exerted by hand for any hand position relative to the position of the feet. The maximum hand force exerted in a seated position as predicted by the model shows a strong correlation with the maximum hand force measured2’. This kind of validation is only acceptable for this type of model, but not for a distribution model. The model can be considered to have had a major influence on the NIOSH guidelines for manual lifting of loads48.

Later versions of the model are user-friendly, 2D and 3D computer programmes to calculate muscle load to load capacity at the major body joints as wel1 as the compression force on the low back for a given body posture and force on the hands.

The sagittal plane distribution model by Anderson, Chaffin, Herrin, and Matthews (M2b)49,50 includes two extensor muscles (erector spinae muscle and multifidus muscle) and various ligaments around the Ls-Si functional spinal unit. Ls-Si kinematics are used to predict ligament strains. The model was validated by comparing model predictions on intradiscal pressure and on intra-abdominal pressure with measurement results from literature. In a minority of cases the same trend was observed for measurement results and model predictions. This concerned a rise in intradiscal

Figure 5. Schematic diagram of the distribution model by Schultz and co-workers51. The five pairs of bilaterally arranged single muscle equivalents represent the rectus abdominis, the internal and external oblique abdominal, the erector spinae, and those parts of the latissimus dorsi muscles which cut the trunk-sectioning plane. Contraction forces are denoted R, 1, X, E, and L respectively, with the subscripts denoting left and right sides. Inclination angles p, 6, and y were all set to 45”. Motion segment compression force is denoted C, anterior shear force S,, right lateral shear force Sr, and abdominal pressure cavity resultant P.

(Reprinted with permission from Reference 51.)

pressure for increased trunk flexion as wel1 as for increased load in the hands. Within the framework of model use as a practica1 tool for prevention of low back problems, this is considered not convincing for a moderately complex model. The benefits from using the model instead of a simple model are not visible. Furthermore, within the framework mentioned the use of intra-abdominal pressure for validation purposes is questionable. The relationship between intra- abdominal pressure and the load on the lower lumbar spine may be rather weak6.

The three-dimensional distribution model by Schultz and co-workers (M3)6P51-56 mainly contains five pairs of bilaterally arranged muscles (Figure 5). The force in each muscle is calculated using linear programming. Several objective functions have been used, e.g. minimum spine compression, and minimum muscle contraction intensity. The model is validated for the group of test subjects by comparing quantitatively calculated muscle force and measured EMG (for the erector spinae muscle(s) the average EMG from four skin electrodes was taken)6,51,54,56. The correlation coefficients for the erector spinae muscles were high for sagittal plane trunk postures and various types of asymmetrie loading (r > 0.91)6,54,56, but lower for more complex asymmetrie trunk postures and loading (0.60 < r < 0.88) 51 Next the model is validated by . comparing quantitatively calculated spine compression force and measured intradiscal pressure (r = 0.94)6.

This model was followed by models with seven and eleven pairs of bilaterally arranged muscles52, both having a more refined erector spinae representation, the latter including the psoas and quadratus lumborum muscles. These more complex models turned out to be as valid as the model with five pairs of bilaterally arranged muscles.

The three-dimensional distribution model by Jager and Luttmann (M4)57-59 contains one rectus abdominal muscle and a pair of bilaterally arranged erector spinae muscles. Next to this, two oblique abdominal muscles, representing the left internal and right external oblique muscles and vice versa, are incorporated. Individual muscle forces are calculated by an optimization procedure, minimizing the sum of al1 muscle forces required.

The distribution model by McGill and Norman (M5) 4,43,60,61 incorporates extensive anatomical detail of the three-dimensional musculoligamentous skeletal system. Muscular activity is prescribed by a measured EMG signal. Truncal kinematics is included in the model. The data (force per unit area of muscles, stress-strain relationships of ligaments, etc.) used in the simulations are described in the thesis by McGilla. The model is very complex.

The distribution model by Gracovetsky and co-workers (M6)8-‘o*62-65 also incorporates extensive anatomical detail. The description of the model is, however, very scanty. NO free-body diagrams are presented. Many details of the model are omitted, e.g. stress-strain relationships, moment arms and

Delleman et al.: Macromodels and low back problems 145

lengths of ligaments, as wel1 as force per unit area of muscles. The model seems to be extremely complex. Predicted back muscle forces were compared with EMG measurements from literature for lifting up to 27 kg with a 40” bent back. Although a resemblance, i.e. the same trend, was found, this cannot be con- sidered a validation for this model as a whole with its enormous pretensions. The model postulates a subtle relationship between the role of the ligamentous system and the roles of the muscles. This relationship depends on the amount of trunk flexion and related truncal kinematics, and the amount of load lifted up to about 200 kilogram. Furthermore, two roles of IAP, i.e. by functioning as a hydraulic amplifier and by straining the lumbodorsal fascia, are described to get the ligamen- tous system under active muscle control. None of the predictions related to these essentials of the model has been validated.

Evduation of the models

A comparison and evaluation of the models based upon the model characteristics and criteria described before is given in Table 1. In this section first the model characteristic number 1, geometrical complexity, wil1 be evaluated by comparing the models. Secondly, more information wil1 be presented on the evaluation with respect to the model characteristics 2-4, model techniques, validation, and muscle force calculation respectively. Thirdly, the evaluation on model characteristics 5-7, static versus dynamic input, symmetrie versus asymmetrie input, and acquisition of input data respectively, wil1 be elucidated. The last three characteristics can be grouped under the heading ‘practica1 usefulness’.

Geometrical complexity

With regard to the geometrical complexity of the macromodels, it can be seen that the cantilever models, the whole-body model by Chaffin and co-workers, the model by Schultz and co-workers, and the model by Jager and Luttmann do not describe the complexity of the back in enough detail to provide more insight into its mechanics. Contrary to the more complex models, the simple models are insensitive for truncal kine- matics, which determines the lengths of muscles and ligaments and hence their force capacity and force respectively.

In the opinion of the authors the use of complex models has to be justified by experimental results, or at least sufficient confidence, showing that predictions not given by simple models or predictions deviating from simple models’ predictions on the same load criterion are valid.

None of the moderately or highly complex models studied fulfils the requirement of presenting experi- mental results or by providing sufficient confidence on the validity of model predictions that are additional to the predictions from simple models. This concerns

mainly the predictions on ligament strain. NO con- fidence intervals are presented based on a sensitivity analysis on the effects of estimated (measurement) error and true variation with respect to the factors in the models that determine ligament strain.

The sole load criterion available for comparison of models is the predicted compression force on lower lumbar discs under sagittal plane loading conditions, as only for this criterion could enough data be found in the literature. In a cantilever model and in the model by Jager and Luttmann the erector spinae muscle(s) generates 100% of the counterbalancing moment; in the model by Schultz and co-workers this is roughly estimated at 90% (remainder by the latissimus dorsi muscle) 16; in the model by Anderson, Chaffin, Herrin, and Matthews49 around 80% (including the multifidus muscle); and in the model by McGill and Norman 75-80% (sacrospinalis muscle), leaving aside the possible role of intra-abdominal pressure in al1 these models. The compression force on the lower lumbar discs is determined largely by these muscular forces. Compression force is also dependent on the muscle moment arm(s) used in a model. According to McGill and Norman almost no differences in calculated compression forces existed between their complex model and a cantilever model using an extensor muscle moment arm of 7.5 cm43 (instead of the previously often used 5 cm moment arm). It can be assumed that an (average) moment arm of 7.5 cm is more realistic, due to its basis in extensive anatomical study. This notion leads to two conclusions. First, an anatomically complex model served a basic scientific purpose by providing relevant modelling data, but for model application purposes within the framework discussed in this study a simple model with a 7.5 cm extensor muscle moment arm can be used instead. Second, modelling uncertainty with respect to muscle moment arm is considerably reduced, i.e. to a smal1 range around 7.5 cm.

The importante of the magnitude of the numerical differences among the models shown above (muscle force and moment arm contributions, and their effect on compression force) can be seen by comparison with measured compression forces in vivo during sagittal plane loading conditions. Nachemson has determined that the compression force on a lower lumbar disc (L3-L4) equals about 700 N during upright standing66, approximately 2500 N while holding 40 kg with a 20” bent back66s67, and 3400 N when lifting 20 kg with a bent back and straight knees66. The magnitude of compression force measured during various activities can thus be reckoned to vary by a factor of 3-5. This means that the differences in calculated compression forces among the models are relatively smal1 as compared to the differences occurring among different loading conditions. So there is no ground to express a strong preferente for one particular model.

On the basis of the reasoning before in this subsection it is concluded that for loading conditions in the sagittal plane the use of a simple cantilever model

146 Clin. Biomech. 1992; 7: NO 3

(including the whole-body model by Chaffin et al.) is sufficient to assist a health professional in comparing, for example, the effects on low back load of ergonomie adaptations at a workplace or the differences between work methods (e.g. lifting techniques). This holds also for the Schultz et al. model that acts like a cantilever model under these loading conditions.

Model techniques, validation, and muscle force calculation

The major flaw of the model by Gracovetsky and co-workers is its incomplete description, which makes the model rather useless for a thorough and fair evaluation. Many of Gracovetsky’s ideas might prove to be interesting, if presented adequately.

The McGill and Norman model has to be credited for the inclusion of an increased number of anatomical details on muscle lines of action and moment arms43. As a consequente in simple cantilever models an extensor muscle moment arm of 7.5 cm can be used instead of the previously often used 5 cm moment arm. Also the model raises two points of criticism. Firstly, EMG signals from only six electrodes are used to drive as many as 36 muscles in the model. Secondly, the model uses a common gain factor (error term) to correct al1 individual (EMG-based) predicted muscle forces in such a way that their moment sum balances the external moment. From the descriptions and data presented it can be deduced that in the dynamic situations studied this common gain factor varies by a factor of 2 during the period of high loading, meaning that a large discrepancy exists between the muscle forces required to balance the external moment and the predicted muscle forces. This discrepancy most certainly reflects a complex of problems accompanying the determination of dynamic muscle forces on the basis of a dynamic EMG and a static EMG-muscle force relationship.

A major advantage of the model by Schultz et al. as opposed to al1 other models described is its moderate to good score on validation experiments for a wide variety of (a)symmetric loading conditions and upper body postures seen most during physical labour.

Static OY dynamic input, symmetrie or asymmetrie input, and acquisition of input data

At last we come to the three model characteristics related to the practica1 usefulness of the various models. Two-axial cantilever models (Figure 3) can to a certain extent deal with some asymmetrie postures of arms and trunk flexion/extension, and lateral flexion. The Schultz et al. model and the Jager and Luttmann model can be used for the same purposes, but in addition are able to deal with axial rotation loads, with or without axially rotated trunk postures. The advantage of the more recent versions of the whole-body model by Chaffin et al. is that its low back cantilever model is included in a whole-body

biomechanica1 model. This whole-body model determines the muscle load to strength ratio on most of the major body joints in addition to the calculation of the low back load. Furthermore, it is included in a user-friendly computer program.

Al1 models need input on the posture of the major body segments (arms, neck, trunk, etc.). Some of them can handle dynamic movements. Model predictions in extreme trunk postures should be dealt with carefully because of the likely increased contribution of passive forces5 and their as yet limited validation.

The model by McGill and Norman has limited potential for practica1 use. Because it is rather cumbersome to get the EMG input needed, the model can be used under laboratory conditions, and possibly in some real work environments. Large-scale applica- tion by health professionals is certainly not realistic.

Discussion

In the introduction several issues were raised which are to be dealt with by health professionals, ergonomists, and applied researchers. In terms of quantifying the relative effects on the back load of ergonomie adaptations at the workplace and changes of the work method, the use of any simple macromodel wil1 do, as stated in the evaluation of the models’ geometrical complexity.

To deal with issues related to the absolute accepta- bility of a work situation, however, i.e. a comparison with certain norms, apart from a macromodel norms are also needed. In these cases the exactitude of the absolute load value calculated by a macromodel is very important. The authors of this article doubt whether the absolute load values predicted by the current macromodels are valid. For example compression forces on functional spinal units strongly depend on the muscle moment arm(s) chosen. Let US assume that during trunk flexion the major part of the counter- balancing moment is delivered by the erector spinae muscle (or sacrospinalis muscle4). A moment arm of 7.5 cm43 instead of the more commonly used 5 cm yields a 33% decrease for the component of the compression force generated by the muscle, which is by and large the most important component.

Of no less importante to the issues related to the absolute acceptability of a work situation is the validity of the norms used. These norms are derived from loading experiments on postmortem specimens. The maximum acceptable load values found show a large variation among the various studies and specimens used57’60@. This means that to provide a safety norm for a large percentile of the (worker) population (e.g. 95th or 99th percentile) the norm has to be set so low that hardly any loading situation during work is allowed, even with very conservative macromodel load predictions. Future research with respect to norms should at least focus on explanatory parameters for the current large variation in load capacity (e.g. compressive strength) between specimens. Brinckmann

Delleman et al.: Macromodels and low back problems 147

et al.@ have related the compressive strength of a functional spinal unit to the product of bone mineral content and the surface area of its vertebral endplate. The two independent variables may be determined in vivo, directly or by some intermediate relationship. This opens an interesting perspective for the com- parison and the possible translation of the postmortem results in the in-vivo situation.

It is concluded that at this juncture a determination of the absolute acceptability of a working situation with respect to its effects on the low back by comparing a macromodel load prediction to a norm derived from experimental data on postmortem specimens cannot be recommended. The authors fee1 that a promising alternative way is offered by large-scale epidemiologi- cal research. In this approach model load predictions on the same denominator(s), i.e. any load criterion, in various work situations are related to the prevalente and severity of low back problems1,2. On the basis of results a norm can be set or adapted.

Conclusions

1.

2.

3.

The use of simple macromodels is sufficient for comparing low back load predictions for sagittal plane loading conditions. The macromodel by Schultz and co-workers is to be favoured above others due to its simplicity, its three-dimensional character, and its moderate to good results on validation experiments for various (a)symmetric loading conditions and trunk postures. Macromodel load predictions in extreme trunk postures have to be dealt with carefully.

Acknowledgements

This research was financed by the Directorate-Genera1 of Labour of the Dutch Ministry of Social Affairs and Employment (grant DGA 530-01). The stimulating comments of Dr Jan Dul during the process of this work are gratefully acknowledged.

References 24

Chaffin DB, Park KS. A longitudinal study of low-back pain as associated with occupational weight lifting factors. Am Znd Hyg Assoc J 1973; 34: 513-25 Herrin GD, Jaraiedi M, Anderson CK. Prediction of overexertion injuries using biomechanica1 and psychophysical models. Am Znd Hyg Assoc J 1986; 47: 322-30 Chaffin DB. Biomechanica1 modelling of the low back during load lifting. In: Adams AS, Hall RR, McPhee BJ, Oxenburgh MS, eds. Ergonomics International 88. Proceedings of the Tenth Congress of the International Ergonomics Association. London, New York, Philadelphia: Taylor and Francis, 1988: 21-32 McGill SM, Norman RW. Partitioning of the L4-L5 dynamic moment into disc, ligamentous and muscular components during lifting. Spine 1986; 11: 666-78 Floyd WF, Silver PHS. Function of the erectores spinae in flexion of the trunk. Lancet 1951; 1: 133-4

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

An KN, Kwak BM, Chao EY, Morrey BF. Determination of muscle and joint forces: A new technique to solve the indeterminateproblem. J Biomech Eng i984; 106: 364-7 Crowninshield RD. Use of optimization techniques to predict muscle forces. J Biomech Eng 1978; 100: 88-92 Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech 1981; 14: 793-801

23 Brand RA, Pedersen DR, Friedrich JA. The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J Biomech 1986; 19: 589-96 McGill SM, Norman RW. Dynamically and statically determined low back moments during lifting. J Biomech 1985; 18: 877-85

25

26

27

Leskinen TPJ. Comparison of static and dynamic biomechanica1 models. Ergonomics 1985; 28: 285-91 Seroussi RE, Pope MH. The relationship between trunk muscle electromyography and lifting moments in the sagittal and frontal planes. J Biomech 1987; 20: 135-46 Kromodihardjo S, Mital A. Kinetic analysis of manual lifting activities: Part 1 - development of a three-dimensional computer model. Znt J Znd Ergon 1986; 1: 77-90

28 Garg A, Chaffin DB. A biomechanica1 computerized simulation of human strength. AZZE Trans 1975; 7: 1-15

29 Morris JM, Lucas DB, Bresler B. The role of the trunk in stability of the spine. J Bom Joint Surg [Am] 1961; 43: 327-51

Schultz A, Anderson G, Örtengren R, et al. Loads on the lumbar spine: Validation of a biomechanica1 analysis by measurements of intradiscal pressure and myoelectric signals. J Bone Joint Surg [Am] 1982; 64: 713-20 Beam JG. The significante of the activity of the abdominal muscles in weight lifting. Acts Anat 1961; 45: 83-9 Gracovetsky S. Function of the spine. J Biomech Eng 1986; 8: 217-23 Gracovetsky S, Farfan H, Helleur C. The abdominal mechanism. Spine 1985; 10: 317-24 Gracovetsky S, Farfan HF, Lamy C. A mathematica1 model of the lumbar spine using an optimized system to control muscles and ligaments. Orthop Clin North Am 1977; 8: 135-53 Aspden RM. Intraabdominal pressure and its role in spinal mechanics. Clin Biomech 1987; 2: 168-74 McGill SM, Norman RW. Reassessment of the role of intra-abdominal pressure in spinal compression. Ergonomics 1987; 30: 1565-88 Panjabi MM. Validation of mathematica1 models. J Biomech 1979; 12: 238 Gregor RJ, Komi PV, Järvinen M. Achilles tendon forces during cycling. Znt J Sports Med [Suppl] 1987; 8: 9- 14 Hof AL, Berg Jw van den. EMG to force processing 1: an electrical analogue of the Hill muscle model. J Biomech 1981; 14: 747-58 Bean JC, Chaffin DB, Schultz AB. Biomechanica1 model calculation of muscle contraction forces: a double linear programming method. J Biomech 1988; 21: 59-66 Barbenel JC. The application of optimization methods for the calculation of joint and muscle forces. Eng Med 1983; 12: 29-33 Dul J, Townsend MA, Shiavi R, Johnson GE. Muscular Synergism - 1. On criteria for load sharing between synergistic muscles. J Biomech 1984; 17: 663-73 Dul J, Johnson GE, Shiavi R, Townsend MA. Muscular synergism - 11. A minimum-fatigue criterion for load sharing between synergistic muscles. J Biomech 1984; 17: 675-84

30 Eie N, Wehn P. Measurements of the intra-abdominal pressure in relation to weight bearing of the lumbo-sacral spine. J Oslo City Hosp 1962; 12: 205-17

148 Clin. Biomech. 1992; 7: NO 3

31

32

33

34

3.5

36

37

38

39

40

41

42

43

44

45

46

47

48

49

Cappozzo A, Felici F, Figura F, Gazzani F. Lumbar spine 50 Anderson CK, Chaffin, DB, Herrin GD. A study of loading during half-squat exercises. Med Sci Spurts Exerc lumbosacral orientation under varied static loads. Spine 1985; 17: 613-20 1986; 11: 456-62 Bejjani FJ, Gross CM, Pugh IW. Model for static lifting: relationship of loads on the spine and the knee. J Biomech 1984; 17: 281-6 Ekholm J, Arborelius UP, Nemeth G. The load on the lumbo-sacral joint and trunk muscle activity during lifting Ergonomics 1982; 25: 14.5-61 Eklund JAE, Corlett EN, Johnson F. A method for measuring the load imposed on the back of a sitting person. Ergonomics 1983; 26: 1063-76 Lee KW. Biomechanica1 Modelling of Cart Pushing and Pulling. Thesis. University of Michigan: Center for Ergonomics ,1982 Gagnon M, Chehade A, Kemp F, Lortie M. Lumbo-sacral loads and selected muscle activity while tuming patients in bed. Ergonomics 1987; 30: 1013-32 Groh H, Thös FR, Baumann W. Die Belastung der 5 Lendenbandscheibe beim Halten einer Last. Znt 2 angew Physioll967; 24: 150-63 Hutton WC, Stott JRR, Cyron BM. Is spondylolysis a fatigue fracture? Spine 1977; 2: 202-9 Park KS, Chaffin DB. A biomechanica1 evaluation of two methods of manual load lifting. AZZE Trans 1974; 6: 105-13

51 Schultz AB, Anderson GBJ, Haderspeck K et al. Analysis and measurements of lumbar trunk loads in tasks involving bends and twists. J Biomech 1982; 15: 669-75

52 Schultz A, Haderspeck K, Warwick D , Porti110 D . Use of lumbar trunk muscles in isometrie performance of mechanically complex standing tasks. J Orthop Res 1983; 1: 77-91

53 Schultz AB, Haderspeck-Grib K, Sinkora G, Warwick DN. Quantitative studies of the flexion-relaxation phenomenon in the back muscles. J Orthop Res 1985; 3: 189-97

54 Schultz A, Andersson GBJ, Örtengren R et al. Analysis and quantitative myoelectric measurements of loads on the lumbar spine when holding weights in standing postures. Spine 1982; 7: 390-7

55 Andersson GBJ, Ortengren R, Schultz A. Analysis and measurement of the load on the lumbar spine during work at a table. J Biomech 1980; 13: 513-20

56 Schultz AB. Andersson GBJ. Analvsis of loads on the

51

Leskinen TPJ, Stalhammer HR, Kuorinka IAA, Troup JDG. A dynamic analysis of spinal compression with different lifting techniques. Ergonomics 1983; 26: 595-604

lumbar spine. Spine 1981; 6: 76-82- Jager M, Luttmann A. Biomechanica1 analysis and assessment of lumbar stress during load lifting using a dynamic 19-segment human model. Ergonomics 1989; 32: 93-112

58

Freivalds A, Chaffin DB, Garg A, Lee KS. A dynamic biomechanica1 evaluation of lifting maximum acceptable loads. .l Biomech 1984; 17: 251-62 Garg A, Herrin GD. Stoop or squat: a biomechanica1 and metabolic evaluation. AZZE Trans 1979; 11: 293-302 McGill SM, Norman RW. Effects of an anatomically detailed erector spinae model on L4/L5 disc compression and shear. J Biomech 1987; 20: 591-600 Chaffin DB. A computerized biomechanica1 model - development of and use in studying gross body actions. J Biomech 1969; 2: 429-41

Jager M. Biomechanisches Model1 des Menschen zur Analyse und Beurteilung der Belastung der Wirbelsäule bei der Handhabung von Lasten. VDZ-Reihe 17 No. 33. Düsseldorf: VDI-Verlag, 1987: 1-128

59 Jager M, Luttmann A, Laurig W. The load on the spine during the transport of dustbins. Appl Ergon 1984; 15(2): 91-8

Chaffin DB, Baker WH. A biomechanica1 model for analysis of symmetrie sagittal plane lifting. AZZE Trans 1970; 2: 16-27

60 McGill SM. Partitioning of the LdL, Dynamic Moment into Muscular, Ligamentous, and Disc Components for Calculation of Tissue Loads during Lifting. Thesis. University of Waterloo, 1986

61 McGill SM. A biomechanica1 perspective of sacro-iliac pain. Clin Biomech 1987; 2: 145-51

62 Farfan HF. Muscular mechanism of the lumbar spine and the position of power and efficiency. Orthop Clin North Am 1975; 6: 135-44

Martin JB, Chaffin DB. Biomechanica1 computerized simulation of human strength in sagittal-plane activities. AZZE Trans 1972; 4: 19-28 Garg A, Sharma D, Chaffin DB, Schmidler JM. Biomechanica1 stresses as related to motion trajectory of lifting. Hum Factors 1983; 25: 527-39 NIOSH. Work Practices Guide for Manual Lifting. DHHS (NIOSH) Publication No. 81-122. Cincinnatti, Ohio: US Dept of Health and Human Services, 1981 Anderson CK, Chaffin DB, Herrin GD, Matthews LS. A biomechanica1 model of the lumbosacral joint during lifting activities. J Biomech 1985; 18: 571-84

63 Gracovetsky S. The Spinal Engine. Wien: Springer Verlag, 1988

64 Gracovetsky S, Farfan HF, Lamy C. The mechanism of the lumbar spine. Spine 1981; 6: 249-62

65 Gracovetsky S, Farfan H. The optimum spine. Spine 1986; 11: 543-73

66 Nachemson A. Lumbar intradiscal pressure. In: Jayson MIV, ed. The Lumbar Spine and Back Pain. London: Pitman, 1980: 341-58

67 Nachemson A. The load on lumbar discs in different positions of the body. Clin Orthop 1966; 45: 107-22

68 Brinckmann P, Biggemann M, Hilweg D. Fatigue fracture of human lumbar vertebrae. Clin Biomech [Suppl] 1988; 1: 1-23