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1986; 66:351-359.PHYS THER.

AndrewsWilliam F Dostal, Gary L Soderberg and James GActions of Hip Muscles

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A c t i o n s o f Hip M u s c l e s

W I L L I A M F . D O S T A L ,

G A R Y L . S O D E R B E R G ,

a n d J A M E S G . A N D R EW S

This article describes and explains the moment arm vector (MAV) concept, uses

the concept for the quantitative classification of hip muscles according to action,and applies the findings to selected clinical problems. A three-dimensional,straight-line model of hip musculature was used. Measurements made on amatched, dry bone specimen provided muscle attachment point location data forthe model. Straight lines of muscle action between attachment sites were simulated for a variety of hip configurations during simple hip motions in three principalanatomical planes. W e used the M A V concept to identify the three contributionsof a muscle (flexion-extension, abduction-adduction, and internal-external rotation) tending to rotate the thigh segment relative to the pelvis. Muscles wereclassified according to their action or turning effect at 0, 40, and 90 degrees ofhip flexion. Certain muscles exhibited significant changes in their action duringthese simple motions. Model results were verified using an articulated, dry bonespecimen with elastic strings stretched between muscle attachment sites. Basedon this geometrical model, a "pathological posture" of hip flexion, adduction, andinternal rotation was identified, which is a posture prevalent in spastic, brain

damaged patients.

Key Words: Anatomic models, Hip, Muscles.

A thorough understanding of the kinesiology of hip function, both in normal and pathological circumstances, is vitalto the physical therapist. An important part of this understanding concerns the specific action or turning effect ofindividual muscles and groups of muscles that cross the hip.Degutis described how the location of the line of action of amuscle force with respect to the axes of rotation of a joint

contributes to m ovement com binations at the joint.

1

Biome-chanical studies by Morrison2 and Paul3 have contributedsignificantly to the u nderstand ing of hip muscle action duringvarious activities. In recent years, the moment arm vector(MAV) concept has been developed and used in bioengineer-ing studies of the musculoskeletal system.3,4 The MAV concept quantitatively identifies the action of a muscle in tendingto rotate one body segment relative to the other about threeintersecting and mutually perpendicular axes at a joint centercommon to both segments. This concept, together with thestraight-line model of muscle action, has proven useful inunderstanding the functional role played by hip musclesduring gait and other activities of daily living.5-7

Although a mathematical description of the MAV conceptis available in the literature, no detailed discussion of the

physical or geometrical aspects of this concept has been

published.6 The purposes of this paper are 1) to describe and

explain the MAV concept, 2) to utilize the MAV concept for

the quantitative classification of hip muscles according to

their action in a variety of standard hip configurations, and3) to apply the findings to selected clinical problems encoun tered by the physical therapist.

REVIEW OF TH E L ITERA TURE

Various approaches have been used to determine th e action

of muscles. These have included cadaver experim ents, electro

myography, and geometrical modeling based on cadaver observations in conjunction with analytical procedure s.3,4,8-17

Inm an used radiographs ofcadavers to determ ine the spatial

relationship between hip abductor muscle lines of action and

the joint center.9 Olson et al, in a study of hip abduction

strength, applied Inman's findings in conjunction with radi

ographic data of their own to determine hip abductor mom ent

arm values for healthy subjects.13 Both the Inman and the

Olson et al studies were restricted to th e frontal plan e. Pohtilla

strung wires through cadaver muscles and used radiographs

to determine moment arms for various hip muscles in a

sagittal plane study of various hip configurations.14 He also

determined the lengthened state of the muscles for variousdegrees of hip flexion. Paul used two of the three MAV

components to specify the actions of hip "muscle equivalen ts"

for a number of typical joint configurations exhibited during

gait.3 He did not, however, attach a special name to this

vector.

Jensen and associates, in a series of publications, described

the curved paths taken by selected hip muscles with the joint

in the anatomical position.4,10,11 These investigators froze an d

transversely sectioned cadaver specimens and traced muscle

perimeters in serial sections. They then determined the cen-

troid of each muscle cross section and constructed a sm oothed

line through these centroids, called the centroid line, whichrepresented the muscle's line-of-action. They also defined a

"unit mom ent vector" for each muscle to compare the action

Dr. Dos ta l is Supervisor, Neuromuscular Division, Department o f Physical

Therapy, Un iversity of Iowa Hospitals and Clinics, Iowa City, IA 5 2242 (U SA).

Dr. Soderberg is Associate Professor and Associate Director, Physical Therapy

Education Programs, College o f Medicine, University o f Iowa, Iowa City, IA52242 .

Mr. Andrews is Professor, Mechanical Engineering, College o f Engineering,

University of Iowa.This article was submitted M arch 19,1984 ; was with the authors for rev ision

37 weeks; a n d was accepted July 11,1985.

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of selected muscles for straight- and centroid-line musclemodels. The unit moment vector is identical to the MAV.We prefer the latter terminology because the magnitude ofthis vector is equal to the moment arm of the muscle forceabout the joint, and because the MAV is not a unit vector.All of these methods for establishing the actions of a muscle

Fig . 1. A) The femur in a convenient, laboratory-based referenceframe, B) standardized reference frames embedded in the pelvis andfemur, and C) the zero hip joint configuration.

require that a significant amount of detailed anatomical information be known and available in precise mathematicalform.

M E T H O D

The MAV was used in this study to specify the action ofhip muscles. A gain, the MAV concept quantitatively identifiesthe action of a muscle in tending to rotate one body segmentrelative to another about three intersecting and mutuallyperpendicular axes through a joint center common to both

segments. If the joint axes, as in this study, are of flexion-extension, abduction-adduction, and internal-external rotation, then the corresponding components o f the MAV specifythe muscles' relative contributions to the production of aflexion or extension, abduction or adduction, and internal orexternal rotation mom ent.

The most general expression relating the moment (M) tothe MAV d is

M = fd

where f is the magnitude of the muscle force producing the

moment. In our study, we used a three-dimensional hip

muscle model. Therefore, the MAV d always had three com

ponents, one for each principal orthogonal anatomical plane(sagittal, frontal, and transverse). If the moment were ex

pressed in newton-meters, then the force would be expressed

in newtons and the MAV in meters. Centimeters were the

units used in this work because, given the magnitude of the

TABLE 1

Components of Mom ent Arm Vectors for the Zero Joint Conf igurat ion (cm)

Muscles

SartoriusRectus femoris

Gracilis

Pectineus

Adductor longus

Adductor brevis

Adductor minimus

Adductor magnus (middle)

Adductor magnus (posterior)

Gluteus maximus

Gluteus medius (anterior)

Gluteus m edius (middle)

Gluteus m edius (posterior)

Gluteus minimus (anterior)Gluteus minimus (middle)

Gluteus m inimus (posterior)

Tensor fasciae latae

Piriformis

Obturator internus

Gemellus superior

Gemellus inferior

Quadratus femoris

Obturator externus

Biceps femoris

Semitendinosus

Semimembranosus

Iliopsoas

Abbreviation

SARRF

GRA

PEC

ADL

ADB

AD Ml

AD MID

AD POST

G MAX

G MED ANT

G MED MID

G MED POST

G MIN ANTG MIN MID

G MIN POST

TFL

PIR

OB IN

GEM SUP

GEM INF

QUAD FEM

OB EX

BI FEM

SEM TEN

SEM MEM

PM/I

Frontal

- 3 . 7- 2 . 3

7.1

3.27.1

7.6

7.6

6.2

3.4

0.7- 6 . 7

- 6 . 0

- 4 . 3

- 5 . 8- 5 . 3

- 3 . 9

- 5 . 2

- 2 . 1

0.7

- 0 . 1

0.9

4.4

2.41.9

0.90.4

- 0 . 7

Planes of Motiona

Sagittal

- 4 . 0- 4 . 3

- 1 . 3

- 3 . 6

- 4 . 1

- 2 . 1

- 0 . 9

3.9

5.8

4.6

0.8

1.4

1.9

- 1 . 0- 0 . 2

0.3

- 3 . 9

0.1

0.3

0.3

0.4

0.2

- 0 . 7

5.4

5.64.6

- 1 . 8

Transverse

- 0 . 3- 0 . 2

- 0 . 3

1.0

0.7

0.5

0.0

- 0 . 3

0.4

- 2 . 1

2.3

0.1

- 2 . 4

1.7- 0 . 3

- 1 . 4

0.0

- 3 . 1

- 3 . 2

- 3 . 1

- 3 . 3

- 3 . 4

- 0 . 4

- 0 . 6

0.50.3

0.5

" Frontal plane: + = adduction, - = abduction. Sagittal plane: + = extension, - = flexion. Transverse plane: + = internal rotation, - =

external rotation.

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PRACTICE

results obtained, centimeters provided convenient units. Amore detailed description and an explanation of the MAVare found in the Appendix. The m athematical derivation ofthe MAV is based on the vector cross-product expression.6

Our application of the MAV concept to the study of hipmuscle action required exact anatomical data. Approximatehip muscle attachment points were marked on the bony pelvisand femur of an adult m ale dry bone specimen. The coordi

nates of the attachments and those of key bony landmarkswere measured in a convenient, laboratory-based referenceframe (Fig. 1A). The coordinate data then were reexpressedin terms of standardized reference frames embedded in thepelvis and femur (Fig. 1B). We adopted a standard hip position or configuration called the zero joint configuration (Fig.1C). In the zero joint configuration, the orientation of thefemur relative to the pelvis was similar to the anatomicalposition. All hip configurations were expressed relative to th iszero joint configuration. All steps in the methodology havebeen d etailed elsewhere.6,18

The straight-line model of muscle behavior represented theforce transmitted by a muscle as directed along the straight

line connecting the approximate origin point of the muscleon the pelvis and the approximate insertion point on thefemur. Muscles with broad regions of attachment were assigned multiple line representations. These muscles included

the gluteus medius and gluteus minimus, each of which wasdivided into anterior, middle, and posterior segments; theadductor magnus was divided into minimus, middle, andposterior segments. Hip muscles that wrapped around boneor soft tissue during part or all of a hip movement wereassigned fictitious attachments near the first point of contactwith the obstruction. These muscles included the iliopsoasand o bturator externus. The gluteus maximus muscle represented a special case that we will discuss later. Two-jointmuscles that crossed both the hip and the knee also wereassigned fictitious a ttachm ents tha t closely approxima ted theirtrue locations at the distal end of the femur. As with themathematical derivation of the MAV, details relating to themuscle model, coordinate data for bony landmarks and muscle attachment points, and reliability information pertainingto the procedures for identifying, marking, and measuringcoordinates have been presented elsewhere.6,18

Coordinate data for 27 hip muscles were used to calculateMAVs for a number of hip configurations. These includedthe zero joint and other hip configurations occurring duringsimple movements of the thigh relative to the pelvis in thethree principal anatomical planes. Muscles were classified

according to action for the zero joint configuration and for40 and 90 degrees of hip flexion. The ac tions or turning effectsof these 27 muscles were based on the three MAV com ponentsfor each muscle in each of these three hip configurations.

TABLE 2

C lass i f i ca t i o n o f Musc l e sa

Ac co rd i ng t o A c t i o n a t 0 , 40 , and 90 Degrees o f H ip F l ex io n

Degrees

A ll

0 and 40 on ly

0 and 90 on ly

40 and 90 only

0 on ly

40 only

90 only

Extens ion F lex ion Adduc t ion

BI FEMSEM TEN

SEM M EM

AD POST

AD M IDb

QUAD FEMC

G M A Xe

GR Ad

AD M IDd

A DBd

A DLd

RFSA R

PM/I

TFLb

PECC

A DLb

A DBA DL

A D M l

A D M I D c ,d

GRA

PECb

OB EX

AD POSTb, d

QUAD FEM

Ac t i o n

Abduc t ion

TF Lc ,d

PIRb

G M ED ANTC

G M ED MID

G M ED POST

G M IN ANTC

G M IN MID

G M IN POST

SA Rb, d

RFb, d

GEM SUPC

OB IN

Internal External

Rotat ion Rotat ion

G MED ANTG MIN ANT

G M ED MIDC

G M IN MIDC

G M ED POST

G M IN POST

PIRd

QUAD FEMb ,d

GEM SUP

OB IN

GEM INF

OB EXc

PIR

G MED POSTb

aSee Table 1 for a guide to muscle abbreviations.

b Secondary action at 0 degrees.c

Secondary action at 40 degrees.d Secondary action at 90 degrees.e Model not valid for flexed configurations.

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Fig . 2. A su per io r v iew o f the l ines o f ac t ion o f r ight hip muscu latu rein a t ransverse p lane pro jec t ion re la t ive to the h ip jo in t cen te r (©) .L ines are d i rec ted tow ard o r ig in po in t s .

Fig. 3. A la te ral v iew o f l i nes o f ac t ion o f r ight hip musc u la tu re in asagi t ta l p lane pro jec t ion re lat ive to the h ip jo in t c en te r (). Lines are

d i rec ted toward o r igin po in t s .

RESULTS A ND DISCUSSION

Table 1 presents com ponents of MAVs for all hip musclesfor the zero joint configuration. Note that for the adductormagnus muscle, components are given for each of the threesegments (minimus, middle, posterior). Components aregiven also for each of the segments of the gluteus medius andgluteus minimus muscles. Table 1 illustrates that, for thesartorius m uscle, for example, the dom inant a ction (turningeffect) was flexion (-4.0), followed closely by abduction(-3. 7). Th is muscle had o nly a relatively small external rotation com ponent in the zero joint configuration (-0.3 ).

We considered numerous possible criteria for classifyingmuscles according to action using the MAV component values. The first criterion proved to be both useful and convenient. For each m uscle, the action corresponding to the largestMAV component was called the primary action. If, of theremaining tw o MA V com ponents , either one was equal to orgreater than 50% of the largest com ponen t value, the corresponding action was designated the secondary action. Themu scle then was assigned to two different functional groupsfor that joint configuration. The 50% cutoff level, althoughsomewhat arbitrary, was high enough that muscles often

exhibited secondary actions. No muscle was found to havetwo secondary actions for the zero joint configuration.

The rectus femoris muscle may be used to illustrate the

functional classification schem e (Ta b. 1). In the zero joint

configuration, the largest MAV component for the rectus

femoris was that for flexion (-4 .3). The next largest comp o

nent, having a value greater than 53% of the largest co m po

nent, corresponded to abduction (-2.3) . The com ponent for

external rotation (-0.2) was very small in comparison with

both other actions. The rectus femoris, in the zero joint

configuration, therefore, was primarily a flexor and second

arily an abductor according to this classification scheme.

Thus , we included it in two functional groups in the zero

joint configuration. Table 2 lists the functional groups of hip

m uscles for various hip configurations and various collections

of hip configurations.

Based on the straight-line m uscle mod el and M AV concept,

the functional groups of h ip m uscles generally were consistent

with traditional anatomical and clinical d escriptions of muscle

action for the zero joint configuration. No te that those mu s

cles having a secondary action in addition to their primary

action are identified in T able 2. The rectus femoris m uscle,

for exam ple, appeared in the  flexor group and in the abductor

group. Note also that, to use Table 2 to classify hip muscles

according to action for any single joint configuration (0, 40,

90 degrees) or for any pair o f hip configurations (0 and 40, 0

and 90 ,4 0 and 90 degrees), all the corresponding entries listed

abov e that configuration or pair of configurations in the table

mu st be added together. Th us, to determine all those m uscles

that function either primarily or secondarily as hip extensors

in the 40-degree configuration, add together all those muscles

in the extensor column that fall into this category ("all," "0

and 4 0 o nly," "40 and 90 only").

Table 2 also indicates that no hip muscles functioned

primarily or secondarily as internal rotators in the zero joint

configuration. The 50% criterion for the secondary muscle

action would have to have been lowered below 35% of the

largest component value before any hip muscle could havebeen classified as an internal rotator in the zero con figura tion.

354 PHYSICAL THERAPY

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PRACTICE

If the cutoff level were changed to 35%, however, numerouship muscles would have appeared in additional functionalgroups, and some muscles would have had two secondaryactions and would have appeared in three functional groups.Table 1 data may be used to make such determinations forthe zero joint configuration.

The lines of action were studied extensively on graphsprojected on principal anatomical planes for the zero joint

configuration. Figures 2 to 4 allow easy visualization of themoment arm projection on which a muscle acted in therespective plane. Comparison of one line of action to anotheralso was possible. We emphasize, however, that the component of a moment arm projected onto a given plane is not ofthe same magnitude as the component of the MAV for themoment in that plane.

We also studied the lines of action for each hip muscleusing an elastic string skeletal model (Fig. 5). Elastic stringsand rubber bands were strung between screw eyes placed atthe appropriate muscle attachment points on a dry bonespecimen. T he elastic string model results verified the resultsobtained using the MAV concept. Consequently, we have no

reservations about using the MAV concept in conjunctionwith the straight-line muscle m odel to characterize hip m uscleaction for the zero joint configuration.

As the hip moved through a simulated range of motion,the straight lines of the muscle model shifted locations andorientations relative to the join t center of rotation and relativeto each other. Consequently, changes occurred both in themom ent arm and in the direction of the line of action of themuscle force, resulting in MAV changes.

Figure 6 shows the variations in the three MAV components with joint configuration changes for the anterior segment of the gluteus medius muscle for hip movement from a20-degree extended to a 90-degree flexed position. The abduction component became progressively smaller while theinternal rotation component increased. The flexion-extensioncomponent initially had a small extension value in the extended position but, as flexion progressed, reversed action tothat of flexion. Thus, the functional group or groups intowhich a muscle was placed on the basis of the relative magnitudes and algebraic signs of the three MAV componentsdepended on the joint configuration in which the classificationwas made. We studied graphs similar to Figure 6 for allmuscles for simple rotations in the three principal a natomicalplanes.

As previously noted, no hip muscle satisfied the criterion

for inclusion in the internal rotation group for the zero jointconfiguration. The findings were much different, however,

when hip muscles were classified for the 40- or 90-degree

positions of hip flexion. In the 40-degree position (Tab. 2),

the m ore anterior portions of the gluteus medius and gluteus

minimus muscles became primary internal rotators. When

the functional classification was carried out for the 90-degree

flexed position (Tab. 2), all portions of both the gluteus

medius and gluteus minimus became either primary or sec

ondary internal rotators. This finding may relate to the inter

nal rotation posture seen with spastic patients having marked

hip flexion in standing. Most of the external rotators in the

zero joint configuration became strong abductors in the 90-degree flexed position. One may question whether an abduc

tion force generated by this group could support the body

Fig. 4. A posterior view of lines of action of right hip musculature ina frontal plane projection relative to the hip joint center (©).

Fig. 5. Elastic string model.

Fig. 6. Changes in the components of the moment arm vector ofthe anterior portion of the gluteus medius muscle for actions in thefrontal (O), sagittal (v), and transverse (□) planes during hip flexion.

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during the stance phase of gait for a person with marked hipflexion.

In addition, Table 2 shows that the primary or secondaryactions of muscles causing flexion, extension, and adductionare fairly stable throughout the range of hip  flexion from 0 to90 degrees, a range common to many functional activities.This is not the case for the actions of muscles causing abduction and rotation. The gluteus medius muscle is in the bestposition for abduction in the 0- to 40-degree range. As hipflex ion progresses, its anterior, middle, and posterior portions

Fig. 7. Changes in sagittal plane components of selected adductorsduring hip flexion.

lose their efficacy for abduction, leaving the small externalrotators to abduct. Only the tensor fasciae latae and thepiriformis muscles maintain a fairly stable abduction actionthroughout the range of flexion considered in this study. Thehip must flex to about 40 degrees or beyond before musclesare configured in an advantageous position for internal rotation. These muscles include the portions of the gluteus mediusthat have, by then, lost their efficacy for abduction. Externalrotators, like abductors, also are in their most advantageousposition for performing their action in the 0- to 40-degree

range of hip flexion, before becoming abductors.The actions of the hip muscles in the 40- and 90-degreeflex ed positions were consistent with our results using theelastic string skeletal model. The only exception was thegluteus maximus muscle, where the straight-line representation was not valid when flexion exceeded approximately 5degrees because of impingement on underlying bone andmuscle. In a previous study of gait that included the gluteusmaximus, the extension value of the MAV for this musclewas never allowed to fall below that for the 5-degree flexedconfiguration.

5

The three perpendicular components (actions) of the MAVfor each hip muscle changed in magnitude and occasionally

in algebraic sign (reversed action) for each of the three simplehip movem ents studied. Therefore, we studied a total o f ninechanges (three actions multiplied by three movements) forany given muscle or group of muscles. Figure 7 shows changes

TABLE 3Number of Action Changes for Three Simple Hip Movements

Action Changes

Frontal plane

Adduction

↓a

↑c

c

Abduction

↓↑c

Sagittal plane

Extension

↓↑c

Flexion

↓↑c

Transverse plane

Internal rotation

↓↑c

External rotation

↓↑c

20° Abduction →

15° Adduction

14

13

15

12

10

17

6 (2b)

8

0

12 (2b)

10

2 (0 b )

3

10

2 (0 b )

5

5

3 (1b)

07

6 (0 b )

29

Movements

20° Extension →

40° Flexion

168 (4 b )

6

2

11

5 (0b)

51

156 (4 b )

8

1

12

7 (3 b )

5

0

115(3 b )

33

16

9(7 b )

4

3

15° External Rotation →

15° Internal Rotation

11

16

18

9

12

15

5(0 b )

2

4

8(4b)

62

11(4b)

2

5

5 (0 b )

3

1

6 (3 b )

33

11(3 b )

13

a ↑↓Component of MAV increased or decreased during movement.b Action reversed.c C Component of MAV varied by less than 0.2 cm.

35 6 PHYSICAL THERAPY

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PRACTICE

in the flexion-extension actions of a selected group of hipadductors that occurred with sagittal plane movement (oneaction, one group, one movem ent). Portions of the adductormagnus muscle exhibited maximal extension values. Fouradductors having flexion components in the 20-degree extended position showed changes in sagittal plane action (fromflexion to extension) as flexion progressed. The hip extensioncontribution of the posterior and middle fibers of the adductormagnus may play an important role in hip deceleration and

forward thrust of the body during locomotion. The extensionrole of hip add uctors also m ay assist with leaping and liftingwhen the hip is in a flexed configuration.

Table 3 summarizes all nine action changes studied for thethree simple hip movements. (We disregarded the 50% criterion here to provide a m ore global accoun t of action changes.)Based on the MAV componen t value at the starting point ofeach movement, each muscle was assigned an initial actionfor each of the frontal, sagittal, and transverse planes. Eachcomponent then was observed as the hip progressed throughthe simple movement to determine if the action increased,decreased, remained fairly constant, or reversed (changedalgebraic sign). For exam ple, in the 20-degree abduc ted position, 14 muscles had an adduction action, 13 an abductionaction, and 15 an extension action. Of the 13 with an abduction action, 12 decreased in this capability (2 reversed a ction),1 increased, and no muscles remained essentially constant asadduction progressed. As internal rotation progressed, 11muscles decreased extension capability (4 reversed action),and 11 also decreased external rotation capability (3 reversedaction). As flexion progressed, 9 muscles showed a decreasein external rotation capability (7 reversed action).

Many patients with spastic neurological disorders showexaggerated flexion, adduction, and internal rotation at thehip in standing posture. From an analysis of the information

presented in Table 3, this clearly seems to be a pathologicalposture in the sense that geometrical changes governing muscle action contribute to further exaggeration rather than correction or control of the posture. This occurs because, inadduction, the abductor muscles reduce their action. Similarly, in internal rotation, both the extensors and the externalrotators reduce their action. Finally, in flexion, the externalrotators reverse their action.

A reasonable therapeutic approach in dealing with this

postural problem, therefore, would appear to be an emphasis

on hip extension, abduction, and external rotation, while

inhibiting spasticity and facilitating normal equilibrium re

sponses in neurodevelopmental postures such as knee-stand

ing, half-kneeling (stance limb), and standing. Such an approach has been advocated by the Bobaths.19

Likewise, for musculoskeletal disorders of the hip, our study

supports the use of extension and abduction as the positions

of maximu m stability. Working backward, Table 3 shows that

12 of 13 abducto r muscles increased their abduction capability

as abduction progressed. The fact that 6 of 15 muscles in

creased extension capability during hip extension, when

related to concurrent stretch of the anterior capsule and

iliofemoral ligament of the hip, should further reinforce the

clinician's use of hip abduction and extension as the position

of stability.

Caution should be taken when applying the results dis

played in Table 3 to general posture or gait. The MAV

com ponents th at led to these results were generated for simplerotational movements in principal anatomical planes aboutmutually pe rpendicular joint axes. Posture and gait, however,are not restricted to such simple joint configurations, andmust be analyzed, therefore, with considerable care if theresults truly are to represent in vivo events.

We also should point out tha t the straight-line mo del of hipmuscu lature is a gross simplification of this complex system.The three-dimensional curvilinear contractile element connecting adjacent segments, packed between bones and subcutaneous tissue and constrained by a facial labyrinth ofbindings, is reduced to a straight line, unfettered in m ost casesby adjacent structures. The advantage of the model is simplification of the system t o a degree that allows easy analysis ofmechanical action in an efficient and reasonably accurateman ner. T his model has been used successfully to analyze theforces and moments acting on the hip during normal andpathological gait.5 Coordinate data used in this study were farmore complete than any anatomical data previously gatheredfor the analysis of hip muscle mechanics.3'4'9"11131416 Onlythree previous studies provided data for various joint config

urations. Inman9 and Olson et al13 presented moment armmeasurements, but only for hip abductors and only forchanges with frontal plane mo veme nt. Pohtilla provided similar information about certain flexors and extensors forchanges with sagittal plane move ments.14

Work with the MAV and the straight-line muscle model isbut one of many early steps taken by us to gain a betterunderstanding of hip mecha nics. An application of the mo del

to the study of gait in conjunction with kinema tic and kineticanalyses answered pragmatic questions asked by engineersdesigning hip replacements and surgeons inserting them .5 An

application to functional activities in conjunction with an

electromyographic analysis helped us to understand the complexity of the neurocon trol of the gluteus medius m uscle.7 To

date, the model has not been applied systematically in conjunction with kinematic, kinetic, or EMG analyses to thestudy of therapeutic exercises of the h ip (including m at activ

ities) or to specific h ip configurations comm only seen duringthe neurodevelopmental sequence. Such applications wouldhave to include configurations encountered with diagonal

movement patterns. The anatomical model also should beexpanded beyond the hip and tailored to fit ndividual patientsor subjects. The first effort to tailor or individualize bony

landmark and muscle attachment point data of the hip wasof limited success.18 Use of the MAV concept, in conjunctionwith the straight-line muscle model, should improve our

understanding of muscle action at any joint. The computersimulations presented here to study a variety of hip configurations illustrate problems associated with the classification

of hip muscles according to their action. We hope this investigation has raised significant questions about the role of hipmuscles in various hip configurations and will lead to furtherconstructive research.

S U M M A R Y

The MAV concept provides a convenient quantitativemethod for characterizing the action of a muscle with the

joint in any general configuration. The MAV concept was

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presented in both descriptive and geometrical terms. W e useda straight-line model of muscle behavior in conjunction withthe M AV concept to specify the action of 27 hip muscles forboth the zero joint configuration (a neutral joint configurationcorresponding to the anatomical position) and for configurations associated with simple thigh movements in the sagittal,frontal, and trans verse plane s. Muscles were classified according to their action for hip configurations at 0, 40, and 90degrees of hip flexion. Changes in the functional capabilitiesof muscles also were described and discussed for selectedgroups of hip muscles, and these changes were related toclinical problems. Based on geometrical findings, a "pathological posture" of hip flexion, adduction, and internal rotation was identified. The MAV concept and the straight-linemuscle model have proven to be useful and convenient instudying the kinesiology and pathok inesiology of hip function.

REFERENCES

1. Degutis EW: A problem solving approach to muscle action. KinesiologyReview 2:20-31,1971

2. Morrison J B: The mechanics of muscle function in locomotion. J Biomech3:431-451,1970

3. Paul J P : Biomechanics and related bio-engineering topics. In: P roceedings:A Symposium on Bio-Engineering Studies of the Forces Transmitted by

J oints. Glasgow, Scotland, September 1964, Part II: Engineering Analysis.Oxford, England, Pergamon Press Ltd, 1965, pp 369-380

4. J ensen R H, Davy DT: An investigation of muscle lines of action about thehip: A centroid line approach vs. the straight line approach. J Biomech8:103-110,1975

5. Crowinshield RD, J ohnston RC , Andrews J G, et al: A biomechanicalinvestigation of the human hip. J Biomech 1 1:75- 85,19 78

6. Dostal WF , Andrews J G: A three-dimensional biomechanical model of hipmusculature. J Biomech 14:803-812,1981

7. Soderberg GL , Dostal WF : Electromyographic study of three parts of thegluteus medius muscle during functional activities. Phys Ther 58:691-696,1978

8. Basmajian J V: M uscles Alive: Their Functions Revealed by Electromyography, ed 3. Baltimore, MD, Williams & Wilkins, 1974

9. Inman VT : Functional aspects of the abductor muscles of the hip. J BoneJ oint Surg [Am] 29:607-619,19 47

10. J ensen RH: Muscles as C entroid Lines. Doctoral Dissertation. Iowa City,

IA, University of Iowa, 197311. J ensen R H, Metcalf WK: A systematic approach to the quantitative de

scription of musculoskeletal geometry. J Anat 119:209- 221,197512. Lieb FJ , Perry J : Quadriceps function: An anatomical and mechanical study

using amputated limbs. J Bone J oint Surg [Am] 5 :1535-1548,1968

13. Olson VL, S midt GL , J ohnston RC : The maximum torque generated bythe eccentric, isometric, and concentric contractions of the hip abductormuscles. Phys Ther 52:149-158,1972

14. Pohtilla VF : Kinesiology of hip extensors at se lected angles of pelvifemoralextension. Am J Phys Med 50:241- 250,1969

15. Seireg A, Arvikar R J : The prediction of muscular load sharing and jointforces in the lower extremities during walking. J Biomech 8:89-1 02,1975

16. Sorbi C, Zalter R: Biomechanics and related bio-engineering topics. In:P roceedings: A Symposium on Bio-Engineering S tudies of the F orcesTransmitted by J oints. Glasgow, S cotland, September 1964, Part I: Engineering Analysis. Oxford, England, Pergamon Press Ltd, 1965, pp 359-367

17. Steindler A: Kines iology: Of the Human Body Under Normal and Pathological Conditions. Springfield, IL, C harles C Thomas, Publisher, 1955

18. Dostal WF: The P rediction of Coordinates of Bony Landmark and HipMuscle Attachment Po ints. Doctoral Dissertation. Iowa City, IA, Universityof Iowa, 1979

19. Bobath K, Bobath B: The facilitation of normal postural reactions in thetreatment of cerebral palsy. Physiotherapy 50:246-262,1964

F i g . A 1 . S agittal plane view through joint J in segme nt B sho wingmuscle force f applied at point P with moment arm d abou t J .

The turning effect of f is about the z-axis in the x, y plane.

F i g . A 2. General MA V d, with x, y, z components dX, d y , d z , and x,

y, z unit vectors i, j , k.

358 PHYSICAL THERAPY

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PRACTICE

A P P E ND IXM o m e n t A r m Ve c t o r C o n c e p t

T o u n d e r s t a n d t h e M A V c o n c e p t , c o n s i d e r f ir s t t h e s i m p l e c a s e

w h e n a m u s c l e f o r c e ( f) a c t s o n s e g m e n t B a t p o i n t P in t h e

n e i g h b o r h o o d o f j o i n t c e n t e r J a n d l i e s in a p r in c i p a l a n a t o m i ca l p l a n e

(eg , t h e s a g i t t al x , y p l a n e c o n t a i n i n g J ; F i g . A 1 ) . T h e m a g n i t u d e ( M )

o f t h e m o m e n t o r t u r n i n g e f fe c t o f f ab o u t J i s de f i n e d a s t h e p r o d u c t

o f t h e m a g n i t u d e (f ) o f t h e f o r c e v e c t o r f a n d t h e l e n g t h o f t h e m o m e n t

a r m ( d ) , o r sh o r t e s t ( p e r p e n d i c u l a r ) d i s t a n c e f r o m J t o t h e l i n e o f

a c t i o n o f f . T h u s , M = f d

T h e t u r n i n g e f f e c t o f f a b o u t J a l s o h a s a d i r e c t i o n o r r o t a t i o n a l

s e n s e ( c l o c k w i s e o r c o u n t e r c l o c k w i s e ) t h a t m a y b e d e s c r i b e d c o n

v e n i e n t l y u s i n g t h e r i g h t -h a n d r u l e . T h i s r u l e s t a t e s t h a t w h e n t h e

r i g h t -h a n d f i n g e r s a re c u r l e d in t h e d i r e c t i o n o f t h e t u r n i n g e f f e c t

a b o u t J (c l o c k w i s e o r c o u n t e r c l o c k w i s e ) , t h e d i re c t i o n o f t h e e x t e n d e d

r i gh t -h an d t h u m b i s u s e d , fo r c o n v e n i e n c e , t o i n d i c a te t h e d i r e c t i o n

o r s e n s e o f t h e r o t a t i o n . T h u s , in t h is i n s t a n c e , t h e d i re c t e d t u r n i n g

e f f e c t (M ) o f f a b o u t J c a n b e e x p r e s s e d s i m p l y a s M = f d k , w h e r e k

i s a u n i t v e c t o r i n t h e p o s i t i ve z -d i r e c t i o n .

T h i s m e t h o d o f d e s c r i b i n g t h e d i r e c t e d t u r n i n g e ff e c t o f a m u s c l e

f o r c e ( f ) a b o u t a j o i n t ( J ) ca n b e g e n e r a l i z e d e a s i l y , and_ t h e m o s t

g e n e r a l d i r e c t e d t u r n i n g e f f e c t c a n b e e x p r e s s e d a s M = f d , w h e r e d

i s t h e M A V . In t h e p r e v i o u s e x a m p l e , d = d k . I n t h e g e n e r a l c a s e , d

= d u , w h e r e d i s t h e m o m e n t a r m , o r s h o r t e s t d i s t a n c e f r o m J t o t h e

l i n e o f a c t i o n o f f, an d u i s a u n i t v e c t o r i n d i ca t i n g t h e d i re c t i o n o r

s e n s e o f t h e r o t a t i o n a l e f f e c t i n a c c o r d a n c e w i t h t h e r i g ht - h an d r u l e .

W e sh o u l d e m p h a s i z e t h a t , a l t h o u g h d h a s a s i t s m a g n i t u d e t h e

l e n g t h o f t h e m o m e n t a r m ( d) , t h e d i r ec t i o n o f d d o e s n o t c o i n c i d e

w i t h t h e o r i e n t a t i o n o f t h e m o m e n t a r m ( d ). R a t h e r , t h e d i r e c t i o n o f d

i s al o n g t h e a x i s o f r o t at i o n a b o u t w h i c h t h e t u r n i n g e f f e c t o c c u r s .

N o t e t h a t t h i s a x i s i s p e r p e n d i c u l a r t o t h e p l a n e c o n t a i n i n g J a n d f ,

a n d i t s d i re c t i o n i s e s t a b l i s h e d i n a c c o r d a n ce w i t h t h e r i g h t -h a n d r u l e .

T h e g o v e r n i n g e q u a t io n M = f d i n d ic a t e s t h a t t h e d i re c t i o n o f t h e

d i r e c t e d t u r n i n g e f f e c t ( M ) o f a p a rt i c u l ar m u s c l e a n d t h e d i r ec t i o n o f

d a r e t h e s a m e . T h e v e c t o r M i s m e r e ly a s c a l ar m u l t i p l e o f t h e v e c t o r

d, w h e r e t h e s ca l ar m u l t i p l i e r i s t h e m a g n i t u d e ( f) o f t h e f o r c e v e c t o r

(f). T h e d i s , i n fa c t , e q u al t o M w h e n t h e m u s c l e f o r c e m a g n i t u d e ( f)

i s e q u a l t o u n i t y . Th i s o b s e r v at i o n a p p a re n t l y l e d Je n s e n a n d D a v y

t o d e s c r i b e d a s t h e u n i t m o m e n t v e c t o r , o r t h e m o m e n t v e c t o r p e r

u n i t o f f o r c e .4

In t h e g en e r a l c a s e , t h e d i re c t i o n o f d , o r t h e di r e c t io n o f t h e

d i r e c t e d t u r n i n g e f f e c t ( M ) , w il l n o t b e p a r al l e l t o a p r i n c i p a l a n a t o m i c a l

a xi s ( i e, t h e ax e s o f f l e xi o n o r e x t e n s i o n , a bd u c t i o n o r a d d u c t i o n , an d

i n t e r n a l o r e x t e r n a l r o t a t i o n ) . I n s t e a d , d w i l l b e i n c l i n e d t o t h e t h r e e

p r i n c i p a l a n a t o m i ca l a x e s ( x , y , z ) a t t h e j o i n t , a n d m a y b e d e co m

p o se d r e a d i l y i n t o x , y , a n d z c o m p o n e n t s . T h u s , r e f e r r i n g t o F i g u r e

A 2, d c a n b e e x p r e s s e d a s d = d x i + d yj + d zk , whe re i , j , and k a re

u n i t v e c t o r s i n t h e p o s i t i v e x , y , an d z d i r e c t i o n s , r e s p e c t i v e l y , an d

d x , d y , an d d z a re t h e c o r r es p o n d i n g M A V c o m p o n e n t s .

T h e d i r e c t e d t u r n i n g e f fe c t o f f a b o u t J , at an y in s t a n t , t h e r e f o r e ,

ca n b e d e s c r i b e d b y t h e v e c t o r M , w h e r e M = f d , a n d d ca n b e

d e c o m p o s e d a n d e x p r e s s e d i n t e r m s o f t h r e e c o m p o n e n t s p a r al l e l t o

t h e t h re e p r i n c i p al an a t o m i c a l jo i n t a x e s . T h e s e t h r e e M A V c o m p o

n e n t s , d x , d y , and d z , d e s c r i b e t h e t u r n i n g e f fe c t s o f f ab o u t e a c h o f

t h e t h r e e j o i n t a x e s p a s s i n g t h r o u g h J o r i n d i ca t e t h e t h r e e s i m u l t a

n e o u s t u r n i n g a c t i o n s o f t h e m u s c l e a t t h a t i n s t a n t . T h u s , t h e c o m

p o n e n t w i t h t h e l a rg e s t m a g n i t u d e (d o m i n a n t t u r n i n g e f f e c t ) re p r e

s e n t s t h e p r i m ar y ac t i o n o f t h e m u s c l e , t h e c o m p o n e n t o f i n t e r m e d i a t e

m a gn i t u d e c o r r e s p o n d s t o t h e i n t e r m e d i a t e m u s c l e a c t i o n , a n d t h e

c o m p o n e n t w i t h t h e s m a l l es t m a gn i t u d e i s a s s o c i a t e d w i t h t h e l e as t

s i g n i f i c a n t a c t i o n o f t h e m u s c l e . T h e a l g e b r a i c s i g n ( p o s i t i v e o r n e g

a ti v e ) o f t h e c o m p o n e n t i n d i c at e s i f t h e t u r n i n g e f f e c t i s d i r e c t e d a l o n gt h e p o s i t i v e o r n e g a t i v e c o o r d i n a t e a x i s (i n ac c o r d a n c e w i t h t h e r i g h t -

hand r u l e ) .

T o i l l u s t ra te t h e M A V c o n c e p t , c o n s i d e r t h e c a s e w h e n , f o r a

s p e c i f ic j o i n t c o n f i gu r a t io n , t h e M A V f o r a p a rt i c u l ar m u s c l e A i n t h e

n e i g h bo r h o o d o f j o i n t J h a s t h e fo l l o w i n g x , y , a n d z c o m p o n e n t s : d x

= 1.5 cm , d y = - 2 . 5 c m , d z = - 1 . 0 c m . L e t t h e p o s i t i v e x , y , a n d z

a x e s a t J c o r r e s p o n d t o a d du c t i o n , e x t e n s i o n , an d i n t e r n al r o t a t io n ,

r e s p e c t i v e l y . T h e p r i m a r y a c t i o n o f A i n t h e n e i g h b o r h o o d o f J ,

t h e r e f o r e , i s f l e x i o n ( d y h a s t h e l a r g e s t m a g n i t u d e a n d i s n e g a t i v e ) ,

t h e s e c o n d a ry a c t i o n i s a d d u c t i o n ( d x h a s t h e s e c o n d l a rg e s t m a g n i

t u d e a n d i s p o s i t i v e ), a n d t h e t e r t i a r y a c t i o n i s e x t e r n a l r o t a t i o n ( d z

h as t h e s m a l l e s t m a g n i t u d e a n d i s n e g a t i v e ). T h e t h r e e M A V c o m

p o n e n t s d x , d y , and d z a r e in t h e r at i o o f 3 : - 5 : - 2 , s o t h e r e l at i v e

t u r n i n g e ff e c t s o f A a bo u t t h e t h r e e j o i n t a x e s t h r o u g h J a r e a ls o i n

t h e r at i o o f 3 : - 5 : - 2 .

Commentary

I commend Dostal and associates for using the moment

arm vector (MAV) concept to study the actions of hip muscles. I support their efforts to demonstrate how the MAV

concept and the straight-line muscle model can contribute to

a thorough understanding of muscle function and m ovement

dysfunctions encountered by physical therapists. I hope my

comm ents further help the reader understand the m odel and

the implications of the study and contribute to development

of the model and its application to physical therapy.

The au thors describe the MAV concept and muscle model

in clear, concise language. The App endix and Figures contrib

ute to u nderstanding the concept. Several aspects of the model

warrant comment. The simulated actions of manv muscles

can be examined simultaneously in relation to three planesin a variety of hip positions. As a result, the relative m agnitude

and direction of each muscle's action in the three planes can

be calculated over a wide range of hip positions. The authors

demonstrated geometrical evidence that the three componentactions of most hip muscles change according to various

positions of the femur in relation to a fixed pelvis. Such

information supports the concept that most muscles have

multiple actions and, therefore, contribute to movements in

spiral and diagonal patterns, a concept that has gained wide

spread acceptance and application in physical therapy.

The method is limited, however, because the magnitude of

the direction of pull caused by one muscle cannot be com

pared with that of another muscle. For example, the rectus

femoris muscle has a component arm vector of -4.3 cm of

flexion in the sagittal plane (Tab. 1). The iliopsoas muscle has

a component arm vector of -1.8 cm of flexion. These numbers indicate that, within the MAV components of each

muscle, flexion s the primary direction of action, not that the

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1986; 66:351-359.PHYS THER.

AndrewsWilliam F Dostal, Gary L Soderberg and James GActions of Hip Muscles

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