TECHNICAL NOTE
MUSCLE
FIBER
ARCHITECTURE
JAXIES A. FRIEDERICH
IN THE HUMAN
LOWER
LIMB
and RICHARD A. BRAND*
Biomechanics Laboratory. Department of Orthopaedic Surgery, The University of Iowa, Iowa City, Iowa 52242, U.S.A.
INTRODUCTION Mathematical calculations of muscle forces often require an estimate of a given muscle’s capacity to generate force. A traditional way of expressing a muscle’s fora generating capacity is in terms of its ‘physiological cross-sectional area’ (degned by muscle volume or muscle mass divided by either gross musck length or muscle fiber length with or without accounting for pennation) (Brand et al.. 1981: Close, 1972; Crowninshield and Brand. IPRI; Crowninshield et a/., 1978; Fict. 19l& Haxton. 1944; lkai and Fukunaga. 1968; Morris, 1949; Pierrynowski. 1982 Spector er uf.. 1980). Sina no study reports systematically colkctcd muscle liber length in all lower limb muscles, including hip muscles, we conducted the following work. METHODS
We dissected the legs of IWO embalmed cadavers: a 37. year-old. 183 cm, 91 kg malt (specimen I). and a 63-yearold, 168 cm, 59 kg female (specimen 2). The length and estimated average fiber angle were measured with a scaled ruler (resolution in one millimeter increments) and a goniomcter respectively for each of 38 muscles(listed in Table I) before removal from the attachment sites with the body in an anatomic position (le.. supine with hips close to full extension and neutral abduction-adduction and rotation, knees extended, and feet in neutral position neither dorsi- nor plantar-flexed). For those few muscles wrapping around a joint so that a straight line between origin and insertion could not be measured the length of the excised muscle was measured. We excluded tendons in the measurements. If the origin or insertion of the muscle was spread over a broad surfaa (e.g.. gluteus medius), the muscle length was taken to be that kngth from an estimated antroid of origin or insertion. After excision. the lengths were remeasured and the volume was measured using water displaament. Muscle fiber kngths were determined by a modiIkation of the procedure used by Close (1964) and Spector cf of. (1980). Mu&s were soaked in normal saline for I-5 days to remove embalming chemicals. Two to hve muscle Iiber bundles approximately 5 to 20mm in diameter were randomly removed from diRerent parts of the muscle, measured, and placed in 20% nitric acid for 24 to 48 h. In broad muscles (e.g. gluteur medius) the muscle was divided into two or three sections from which two to five bundks were selected. After sufficient maaration. the fiber bundles were returned
Received in jincr//orm 27 February 1989. *Corresponding author.
to saline. Fiber bundles were then remeasured whole and compared to the pre-maaration length. We teased the fibers apart under a dissecting microscope, and measured their length with a scaled ruler (resolution in one millimeler increments) whik holding the ends taut. but without stretch. Ten to twenty fibers from each muscle bundle (two to five bundles for muscles where the bundks seemed to be of consistent length and four to ten bundles in broad muscks with variable bundle lengths) were measured. The average muscle fiber kngths (and standard deviations) for each muscle or muscle section were then computed (Tabk I). To compare our consistency (i.e.. standard deviations of 8ber kngths from a given musck in each cadaver) to that in the litcraturc. we used data reported by Wcber (1846) and by Wickiewicz et al. (1983) (Table 2). (Waber reported ranges. not standard deviations; to estimate standard deviation, we divided the dilkrence betwan the kngths of longest and shortest fibers by four, sina in a Gaussian distribution, 95% of the sample will lk within two standard deviations on each side of the mean.) Sina gross muscle length (but not fiber kngth) may be estimated in living subjects (Brand et al.. 1982) we c&dated the ratio of fiber length to musck length for those muscks which both WCand Wickicwicz et al. (H&3) studied. and then combined these ratios (Table 3). (Wickkwicz et ul. (1983) did not report data on the glutcal mm&s, the iliacus and psoas muscks, and the small hip rotator musclrs; therefore our comparisons exclude these muscles; neither did they report data on the characteristics of the cadavera from which the data were taken.) As a final comparison, the physiological cross-sectional areas (PCSAs) were calculated by dividing the muscle volume by the muscle fiber length (V/MFL) (Tabk 4). (Weber (1846) did not include fiber angle in his computation of PCSA. so it was necessary IO divide the PCSAs which Wickiewicz et al. (1983) reported by the cosine of the fiber angle for each muscle. This is not IO imply that angk of pennation is not important in the estimation of a musck’s physiologic function. Wckr also did not describe the characteristics of the single specimen he studkd.) The semitendinosus has a tendinous intersection near the middk of the belly of the muscle. and we measured sampks from both end* the two parts were summed when the PCSA was computed. Tbc PCSA of each muscle was finally divided by the average PCSA for all of the compared muscles in that cadaver. This ‘normalized’ PCSA allows for comparison between subjects and is similar IO the ‘tension fraction’ used by Brand er of. (198 I) to compare the data collected from IS cadaver arms. Using these normalized PCSAs. we computed a mean PCSA and itandard deviations for our two specimens, the three specimens of Wickiewin et al. (1983) and the Weber (1846) data (Table 4).
91
Technical Note
92
Table 1. Muscle length (ML). fiber length (MFL). standard deviation in fiber length. muscle volume. and computed PCSAs (V/MFL) for all muscles in specimens 1 and 2. The order is by functional group. Fiber lengths are remarkably similar in a given muscle
Specimen Hip muscles Add brev (I) Add brev (2) Add longus Add mag (I) Add mag (2) Add mag (3) Glut max I!) Glut max (2) GIUI max (3) Glut med (I) Glut med (2) GIUI med (3) Glut mitt (I) Glut min (2) Glut min (3) lliacus Psoas Inf gemellus Obt ext Obt int Pectineus Piriformis Quad femoris Sup gemellus
Muscle length (ML) (mm) I 2
110 145 185 125 220 225 I55 165 185 135 125 130 80 95
130 170 I65 125 220 235 160 160
I55 100
Mean Fiber length (MFL) (mm)
SD. (mm)
1
2
53.8 116.0 82.7 87.0 121.0 131.1 142.1 147.4 144.0 53.5 84.5 64.6 68.0 56. I 38.4 100.3 103.5 23.1 29.5 47.4 72.0 25.8 53.8 28.2
120 117 105.6 77.0 120.5 141.6 74.7 113.6 134.5 40.5 50.8 55.0 32.2 27.4 30.1 96.4 121.7 26.5 49.2 34.4 104.7 41.5
1
3.00 1.00 2.70 1.00 5.96 6.85 10.97 9.73 1.41 0.50 0.50 1.13 2.40 1.12 1.85 9.85 I.50 LO9 1.12 1.73 3.54 2.65 1.60 1.83
2 0 0
5.61 6.68 5.90 5.83 10.45 15.85 9.98 2.69 4.18 3.65 3.71 2.46 1.92 10.72 4.35 1.28
Volume (ml) 1 2
PCSA = V/MFL (cm) 2 1
62 62 188 222 222 222 288 288 288 137 137 137 46 46 46 234 266 IO 8 43 65 53 113 6
23 23 103 84 84 84 I09 109 109 53 53 53 24 24 24 85 45 4 24 32 13 38 4
11.52 5.34 22.73 25.52 18.35 16.95 20.20 19.59 20.00 25.00 16.21 21.21 6.76 8.20 II.98 23.33 25.70 4.33 2.71 9.07 9.03 20.54 21.00 2.13
60 20 60 105 75 45 25
27.34 3.74 42.96 2.90 46.33 23.21 8.00
1.92 1.97 9.75 10.91 6.97 5.93 14.59 9.68 8.10 13.09 10.43 9.64 7.45 8.76 7.97 8.82 3.70 1.51 4.88 9.30 1.24 9.16 1.45
MFL/ML 1 2
0.50
Fiber angle (degrees) 2 0 0
0.92 0.69 0.64 0.62 0.55
0.80 0.45 0.70 0.55 0.58 0.92 0.89 0.78 0.40 0.68 0.50 0.85 0.59 0.45 0.38 0.40 0.38 0.74 0.53 0.60 0.30 0.56
0;2
0
9.12 0.79 9.20 2.68 13.99 3.12 2.46
0.27 0.87 0.17 0.93 0.37 0.31 0.56
0.26 0.78 0.22 0.73 0.25 0.52 0.70
7 0 14 0 16 6 2.5
0.60
3.5 :.5
0.60
0.47 0.71 0.87 0.40 0.46 0.42 0.40
: 0 5 8 0 19 10.5
0.32 0.38 0.54 0.51 0.63 0.49 0.36 0.99 0.49
2: 6.5 7.5 0 7 25 0 9.5
2: 255 60 40 90 120 85 95 50
II0 I30 80 85 80 I80 240 42 loo 95 105 85 65
Hip and knee muscles Bit fern (Long) 293 Gracilis 270 Rectus fern 332 Sartorius 519 Semimembran 200 Semitendin 290 Ten fas lat 168
255 325 295 535 215 275 145
19.4 235.5 55.4 483.5 74.9 91.1 95.0
65.8 254.3 65.2 391.1 53.6 88.5 101.5
3.60 8.15 2.71 13.50 5.94 2.12 17.02
29.59 I.12 3.84 10.40
217 88 238 140 347 212 76
240 330 295 320
122.9 73.9 79.8 76.5
110.8 78.5 80.7 79.0
13.62 1.55 1.41 3.22
10.71 1.97 1.53 2.64
100 606 514 555
52 135 133 123
8.14 82.00 64.41 66.87
4.69 17.20 16.48 15.60
0.27 0.26 0.27
0.46 0.24 0.27 0.27
IS 2.5 13 7
235 230
210 205
41.9 76.9
35.8 44.2
2.26 3.95
2.49 4.94
212 110
61 38
50.60 14.30
17.04 8.60
0.18 0.33
0.17 0.22
6.5 17.5
290 270 250 265 252 250 265 190 290 370
278 325 175 205 195 225 250 105 250 305
17.0 87. I 46.2 46.9
68.4 74.3 84.8 29.0 34.6 43.4 46.0 65.2 21.7 29.8
3.88 2.55 1.31 0.83 3.13 0.95 0.85 2.08 0.96 3.94
‘2.82 5.24 2.65 0.92 3.55 1.31 1.77 4.2 I 1.14 1.25
130 65
58 16.88 7.46 30 I8 649 17 6:40 18.52 31 23 19.61 35 24.65 8 4.14 41 26.27 172 186.69
8.48 4.04 2.12 5.86 8.96 5.29 7.61 I.23 18.89 57.12
0.26 0.32 0.18 0.18 0.20 0.14 0.16 0.42 0.12 0.083
0.25 0.23 0.48 0.14 0.18 0.19 0.18 0.62 0.087 0.098
12 13 8 9 19 12 5.5 13
27.5
f*E 4:03 1.99 1.58 6.32
Knee muscles
Bit fern (Short) Vastus inter Vastus lat Vastus med
205 275 305 280
Knee and ankle Gastroc(med) Gastroc (!at)
muscles
Ankle muscles fib ant EXI dig comm Ext hall long Flexor dig Flex ha!! lonn Peronius bre; Peronius long Pemious tcrt Tib post Soleus
2: 42:6 79.8 35.4 30.8
;: 93 70 105 33 93 575
:;
Technical Note
93
Tabk 2 Fikr !engt!ts from our two cadavers, the three adavm of Wic!&wia et a!. (1983). and W&w’5 5tudy the statlndard deviation in our data (!ast two columns) and one-fourth of the ranp in kngth rqortcd by Wckr. For those musk in our specimens which were divided into two or three sections (Table I) we avcrapd fiber lengths. Fiber lengths between the studies arc remarkaMy similar
(18461 Var!abi!ity is measured by
This study I 2 Hip muscles Add brev Add long Add matpnts Pectineui Bit km (L) Gracilis. ’
I
Wickicwia* 2
Wcbcrt
Range/4
3
SD. 1
2
1.1
IO! 112 109 106 95 260
106 106 135.5 102 97 255
2: 11.2
z
93 105 106 105 78 271
65.2 391.1 53.6 144.0
61 482 70 160
68 464 54 154
63 419 64 -
12.8 435 80 197.0
3.1 12.2 5.0 0.0
2.7 13.5 5.9
10.4
2.8 29.6 1.1 17.0
122.9 73.9 79.8 76.5
110.8 78.5 80.7
145 64 66 72
133 78 67
140
15
z 64
132 65.6 -
4.5 20.7 -
13.6 3.3 -
10.7 2.4 -
Knee ami ankie mu&s Gastroc (M) Gastroc (L)
41.9 76.9
35.8 44.2
35 59
39 53
32 40
34.5 -
3.7 -
16.3 -
5.6 -
Ankle muscles Tib ant Ext dig Ext hall Flex dig FIex hall
11.0 81.1 46.2 46.9 50.2
68.4 74.3 84.8 29.0 34.6 43.4 46.0 21.7 29.8
70 94 80 26 37 46 44 24 20
93 82 103 2H 32 38 39 31 19
69 65 18
78.7 75.1 93 54.3 58.7 50 49.4
2.2 3.2 0.5 0.7 1.2 0.0 2.5 1.0 2.0
3.9 2.6 1.3 0.8 3.1
2.8 5.2 2.6 0.9 3.6 1.3 1.8 1.1 1.2
84.9 821 113.0 12.0 19.4 235.5
65.8 254.3
!kmimemb Semitend
55.4 483.5 74.9 162.4
Knee muscles Bit km (S) Vastus int Vastus lat Vastus mcd
Hip wtd knee muscles Rcctus fern saftoriu5
Pcron brcv Peron long Tib posl
35.7 42.6
so!cu5
30.8
35.4
118.8 105.6 112.9 104.1
79
115 108 131 102
27 33 :‘: 17 -
7.5
2::
26.4 2.7 12.0 3.5 3.6 8.2
A:: ::;
5.6 18.9 z 919
l Wickicwin et al. (1983). t W&X (I 846).In the Webcr study, the fiber lengths of the two heads of gastrocncmius were considered as one muscle. as were the vastus muscles.
RE!XJLTs Shtinkagc from maaration varied lrom 0% to 20% and was not consistent from muscle to muscle between the cadavcm Avera& shrinkap for all muscle bundles was 12.5% for ont spocimcn and 5.3% for the other. Within a &en murk the fiber kngths are remarkably similar. Only a few mu&s had standard deviations greater than 10% (Table I). There is even rcasonabk consistency of hbtr !engt!vs ktwecn the three data bases compared in Tabk 2, particularly considering variations in specimen rim. tcchniqwr, and o!rserven. T!rc ratios of musck length to muscle fiber kngth show cons!dembk variability between muscles. but remarkable consistency in a g!ven musck in various specimens (Table 3). Sina the ratio of muscle kngth to muscle fiber length is variabk from muscle to muscle. it is obvious that the PCSAs as cakulated by volume divided by muscle lentph wrsu5 vdume divida! by musck fiber length would be quite di&rcnt. DISCUSSION While musck fiber lengths arc us&l for many biomechanical studies, a number of problems occur in making
such estimates. The number of fibers measured is always small compared to the numkr present and sampling can potentially be a problem, shrinkage cannot be perfectly controlkd. and fibers from certain mu&s tended to be fragile. The first two probkms art inherent. l !t!mulh the errors are probab!y less than 20% (Brand ef al, 1981). Our samplinn of 20-100 fibers throunhout each musck likely red&s ;uch error. Additionally. Wcbcr’5 ( t 846)macros& pit diitions of !nmd!es (‘F!eischbundcl~ yie!dcd ranges similar to ours (Tabk 2). Furthetmorc, t!tc rmall standard deviations in fiber kngth in our data and the -By dose agreement our data with those of Wickkwia et a/. (19833, ruggests that such sampling errors are small. Shrinkag can occur after removal during maaration. Our cadavcra were fixed in kn6th in an lnatonwc position; WC detected no ‘shrinkage’ after excision. Maceration it a process in which the co!!agenous connective tissuesbetween fibers arc dissolved. We do not know the source OF the shrinkage which occurs with maantion. but it !s likely owing to some intracellular phmonmon. We lound the shrinkage during maceration uncontro!!ab!c and unprcdictabk. However. the shrinkage averaged only 12%. In reporting fiber lengths. one might correct for this shrinkage but it is generally much less than the differences in kngth occurring during excursion, and less than the variability between
of
Technical Note
94
Table 3. Average fiber length to muscle length ratios for our two specimensand the three specimens from the study by Wickiewicz et al. (1983). Ratios arc quite variable Mean
S.D.
0.70 0.50 0.53 0.83
0.14 0.08 0.12 0.15
Bit fern (L) Gracilis Rectus fern Sartorius Semimembran Semitendin
0.26 0.83 0.20 0.88 0.27 0.46
0.03 0.04 0.02 0.09 0.06 0.10
Knee muscles Bit fern (S) Vastus inter Vastus lat Vastus med
0.52 0.23 0.23 0.23
0.06 0.04 0.04 0.03
0.16 0.25
0.02 0.05
0.26
0.02 0.05 0.11 0.03 0.02 0.02
Hip
muscles Add brev Add long Add magnus Pectineus Hip
Knee
and knee muscles
and ankfc
Gastroc (Ml Gaslroc (L). Ankle
Acknowledgement:-This study was supported in part by NIH Grant AM14486 and a Grant from the Universitv of Iowa College of Medicine. We would also like IO thank- Dr Jerry Maynard for his help in specimen preparation and dissection techniques and Mrs. Rose Britton for her help in preparation of the manuscript.
REFERENCES
mus&s
muscles
Tib ant Ext di8 comm EXI hall long Flexor dig Flex hall long Pcroncus brcv Pcroneus long Tib post Solcus
The variability of the normalized PCSA suggeststhat it would be difficult to accurately predict the parameters needed to calculate the PCSA of a given muscle in a living subject based on current data. Data from many cadavera would be needed to devise and validate means IO predict PCSA in a living subject based on some anthropometric characteristics (e.g.. height, weight, lean body mass, etc.) A recent paper has demonstrated the sensitivity of muscle force predictions IO ditfcrences in PCSA (Brand et al.. 1986). It is therefore likely that while such predictions may provide information on the relative value of muscle forces in parametric studies, the absolute values of individual muscle forces must be viewed with some caution.
0.25
0.32 0.13 0.17 0.17 0.15 0.10 0.08
0.02 0.02
cadavera, and therefore might not add IO the meaningfulness of data for which WCcan obtain only estimates. Several muscles (the adductors in the first specimen) apparently were not well perfused with embalming fluid and the libers broke easily while being teased; we could isolate single libers. but could not be absolutely certain that they were whole When WChad reasonable doubt as to the intcgrity of the fibers, small bundles rather than individual fibers were dissected out and measured (i.e.. similar IO Weber. 1846). II seems likely that the bundle length is a reasonable approximation of fiber length. since in all muscles,except the semitcndinosus.the fibers reached from the (tendon or fascia of) origin to (tendon or fascia of) insertion. The fiber length to muscle length ratios of our data and those of Wickiewicz er a/. (1983) are remarkablv consistent (Table 3). Of greater importance to many resea&hers. however, is the PCSA. Brand er al. (1981) used a ‘normalized’ PCSA to compare data between fifteen cadaveric arms. When WCcalculated the normalized PCSA for our cadavcra. and those reported in the literature, we found reasonable consistency (average standard deviation 28.8%). but much fess so than for the fiber length to muscle length ratios. However, one would cxpec~a greater variability in this figure because muscle volume is highly variable. depending on body type. activity level, etc. This also suggests that the normalized PCSA (‘tension fraction’) may not be the best way to compare data between specimens.
Brand. P. W.. Beach. R. B. and Thompson, D. E. (1981) Relative tension and potential excursion of muscles in the forearm and hand. J. Hand Surg. 6.209-219. Brand. R. A.. Pcdersen, D. R. and Fricdcrich. J. A. (1986) The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J. 6iomerhanic.s 19, 589-596. Close. R. I. (1964) Dynamic propertics of fast and slow skelcta1 muscles of the rat during dcvclopmcnt. 1. Physbf. 173, 74. Close, R. 1. (1972) Dynamic propcrtics of mammalian skclcla1 muscles. Physiol. Rev. 52. 129-197. Crowninshicld. R. D. and Brand, R. A. (1981) A physiologically based criterion of muscle force prediction in locomolion. J. Biomechonics 14, 793-801. Crowninshicld. R. D.. Johnston, R. C.. Andrews. J. G. and Brand. R. A. (1978) A biomcchanical investigation of the human hip. J. Biomechonics Il. 75-85. Fick. R. (1910) Handhueh der Anor~mie des Menschen, Vol. 2. Gustav Fischer, Stuttgart. Haxton. H. A. (1944) Absolute muscle force in the ankle flexors of man. J. Physiol. 103, 267-273. Ikai. M. and Fukunaga. T. (1968) Calculation of muscle strength per unit cross-sectional area of human muscle by means of ultrasonic measurement. Int. 2. onyew. Physiol. 26. 26-32.
Morris, C. B. (1949) The measurement of the strength of muscle relative to the cross-section. Res. Q. Am. Ass. fflrh, phys.
Educ.
19-20,
295-303.
Pierrynowski, M. R. (1982) A physiological model for the solution of individual muscle forces during normal human walking Ph.D. Thesis, Simon Fraser University. Vancouver, British Columbia. Spector, S. A.. Gardiner. P. F.. Zernicke, R. F., Roy. R. R. and Edgerton. V. R. (1980) Muscle architecture and forcevelocity characteristics of cat solcus and medial gastrocncmiur Implication for motor control. 1. Neuraphysiol. 44, 951-960. Weber. E. (1846) Wagner’s ffondworcerhuch der Physinfogie. Braunschcig, Vicwcg. Wickicwicz, T. L.. Roy, R. R.. Powell. P. L. and Edgerton, V. R. (1983) Muscle architecture of the human lower limb. C/in. Orrhnp. Rel. Res. 179, 275-283.
Technical Note
95
Table 4. ‘Normalized’ (see text for explanation) PCSAs from our cadavers and those of Wickiewia er a/. (1983) and Weber (1846) and the mean and standard deviation for each muscle. These PCSAs do not include the compensation for cosine of the fiber angle to allow comparison to Weber’s data This study 2
I
I
Wickiewicz 2
Weber
All 6 specimens Mean SD.
3
Hip muscles
Add brev Add long Add magnus Pectineus
0.492 0.664 1.777 0.264
0.351 0.883 2.156 0.112
0.253 0.389 1.302 0.201
0.384 0.610 1.209 0.221
0.368 0.420 1.430 0.189
0.339 0.453 1.505 0.300
0.364 0.570 1.563 0.214
0.077 0.188 0.350 0.065
Bit fern (L)’ Gracilis Rectus fern Sartorius Semimembran Semitendin
0.799 0.109 I.255 0.085 1.354 0.680
0.826 0.072 0.833 0.243 1.266 0.282
1.062 0.110 0.984 0.136 1.224 0.408
0.854 0.134 0.825 0.110 1.087 0.256
0.778 0.137 0.936 0.116 1.556 -
0.486 0.176 I.235 0.135 I.128 0.311
0.954 0.123 1.011 0.138 1.269 0.387
0.195 0.035 0.191 0.055 1.170 0.173
Knee muscles Bit fern (S)’ Vastus inter* Vastus later* Vastus med.
0.238 2.400 I.882 1.954
0.424 1.557 1.492 1.412
2.565 1.807 1.438
0.639 2.505 1.633
1.724 2.210 1.409
0.260 6.340 -
5.496
0.770 -
Knee and ankle muscles Gastroc (M)’ Gastroc (L)*
1.478 0.418
1.542 0.778
1.930
2.331 -
3.396 -
2.448 -
2.387 -
0.544 -
0.493 0.218 0.190 0.187 0.541 0.573 0.720 0.768 5.454
0.768 0.336 0.192 0.530 0.811 0.479 0.689 1.710 5.225
0.822 0.285 0.142 0.408 0.421 0.317 0.810 1.646 4.340
0.459 0.378 0.087 0.302 0.308 0.273 1.029 0.872 -
0.946 0.631 0.168 0.400 0,452 0.473 0.789 2.461
0.576 0.198 0.104 0.236 0.574 0.285 0.593 0.772 3.596
0.677 0.158 0.147 0.344 0.517
0.196 0.346 0.044 0.126 0.173 0.125 0.150 0.694 0.853
Hip and knee muscles
-
Ankfemuscfcs Tib ant Ext dig Ext hall PIen dig flex hall Peron brev Peron long Tib post Soleus
-
~~ I:363 4.654
*In the Wickiewicz cr ul. (1983) study. the PCSAs of the two parts of the muscleswith two heads were added together. The same was done with the vas~usmuscfcsas a group and the two heads of gastrocnemius in the Weher (1846) study.
MUSCLE
FIBER
ARCHITECTURE
JAXIES A. FRIEDERICH
IN THE HUMAN
LOWER
LIMB
and RICHARD A. BRAND*
Biomechanics Laboratory. Department of Orthopaedic Surgery, The University of Iowa, Iowa City, Iowa 52242, U.S.A.
INTRODUCTION Mathematical calculations of muscle forces often require an estimate of a given muscle’s capacity to generate force. A traditional way of expressing a muscle’s fora generating capacity is in terms of its ‘physiological cross-sectional area’ (degned by muscle volume or muscle mass divided by either gross musck length or muscle fiber length with or without accounting for pennation) (Brand et al.. 1981: Close, 1972; Crowninshield and Brand. IPRI; Crowninshield et a/., 1978; Fict. 19l& Haxton. 1944; lkai and Fukunaga. 1968; Morris, 1949; Pierrynowski. 1982 Spector er uf.. 1980). Sina no study reports systematically colkctcd muscle liber length in all lower limb muscles, including hip muscles, we conducted the following work. METHODS
We dissected the legs of IWO embalmed cadavers: a 37. year-old. 183 cm, 91 kg malt (specimen I). and a 63-yearold, 168 cm, 59 kg female (specimen 2). The length and estimated average fiber angle were measured with a scaled ruler (resolution in one millimeter increments) and a goniomcter respectively for each of 38 muscles(listed in Table I) before removal from the attachment sites with the body in an anatomic position (le.. supine with hips close to full extension and neutral abduction-adduction and rotation, knees extended, and feet in neutral position neither dorsi- nor plantar-flexed). For those few muscles wrapping around a joint so that a straight line between origin and insertion could not be measured the length of the excised muscle was measured. We excluded tendons in the measurements. If the origin or insertion of the muscle was spread over a broad surfaa (e.g.. gluteus medius), the muscle length was taken to be that kngth from an estimated antroid of origin or insertion. After excision. the lengths were remeasured and the volume was measured using water displaament. Muscle fiber kngths were determined by a modiIkation of the procedure used by Close (1964) and Spector cf of. (1980). Mu&s were soaked in normal saline for I-5 days to remove embalming chemicals. Two to hve muscle Iiber bundles approximately 5 to 20mm in diameter were randomly removed from diRerent parts of the muscle, measured, and placed in 20% nitric acid for 24 to 48 h. In broad muscles (e.g. gluteur medius) the muscle was divided into two or three sections from which two to five bundks were selected. After sufficient maaration. the fiber bundles were returned
Received in jincr//orm 27 February 1989. *Corresponding author.
to saline. Fiber bundles were then remeasured whole and compared to the pre-maaration length. We teased the fibers apart under a dissecting microscope, and measured their length with a scaled ruler (resolution in one millimeler increments) whik holding the ends taut. but without stretch. Ten to twenty fibers from each muscle bundle (two to five bundles for muscles where the bundks seemed to be of consistent length and four to ten bundles in broad muscks with variable bundle lengths) were measured. The average muscle fiber kngths (and standard deviations) for each muscle or muscle section were then computed (Tabk I). To compare our consistency (i.e.. standard deviations of 8ber kngths from a given musck in each cadaver) to that in the litcraturc. we used data reported by Wcber (1846) and by Wickiewicz et al. (1983) (Table 2). (Waber reported ranges. not standard deviations; to estimate standard deviation, we divided the dilkrence betwan the kngths of longest and shortest fibers by four, sina in a Gaussian distribution, 95% of the sample will lk within two standard deviations on each side of the mean.) Sina gross muscle length (but not fiber kngth) may be estimated in living subjects (Brand et al.. 1982) we c&dated the ratio of fiber length to musck length for those muscks which both WCand Wickicwicz et al. (H&3) studied. and then combined these ratios (Table 3). (Wickkwicz et ul. (1983) did not report data on the glutcal mm&s, the iliacus and psoas muscks, and the small hip rotator musclrs; therefore our comparisons exclude these muscles; neither did they report data on the characteristics of the cadavera from which the data were taken.) As a final comparison, the physiological cross-sectional areas (PCSAs) were calculated by dividing the muscle volume by the muscle fiber length (V/MFL) (Tabk 4). (Weber (1846) did not include fiber angle in his computation of PCSA. so it was necessary IO divide the PCSAs which Wickiewicz et al. (1983) reported by the cosine of the fiber angle for each muscle. This is not IO imply that angk of pennation is not important in the estimation of a musck’s physiologic function. Wckr also did not describe the characteristics of the single specimen he studkd.) The semitendinosus has a tendinous intersection near the middk of the belly of the muscle. and we measured sampks from both end* the two parts were summed when the PCSA was computed. Tbc PCSA of each muscle was finally divided by the average PCSA for all of the compared muscles in that cadaver. This ‘normalized’ PCSA allows for comparison between subjects and is similar IO the ‘tension fraction’ used by Brand er of. (198 I) to compare the data collected from IS cadaver arms. Using these normalized PCSAs. we computed a mean PCSA and itandard deviations for our two specimens, the three specimens of Wickiewin et al. (1983) and the Weber (1846) data (Table 4).
91
Technical Note
92
Table 1. Muscle length (ML). fiber length (MFL). standard deviation in fiber length. muscle volume. and computed PCSAs (V/MFL) for all muscles in specimens 1 and 2. The order is by functional group. Fiber lengths are remarkably similar in a given muscle
Specimen Hip muscles Add brev (I) Add brev (2) Add longus Add mag (I) Add mag (2) Add mag (3) Glut max I!) Glut max (2) GIUI max (3) Glut med (I) Glut med (2) GIUI med (3) Glut mitt (I) Glut min (2) Glut min (3) lliacus Psoas Inf gemellus Obt ext Obt int Pectineus Piriformis Quad femoris Sup gemellus
Muscle length (ML) (mm) I 2
110 145 185 125 220 225 I55 165 185 135 125 130 80 95
130 170 I65 125 220 235 160 160
I55 100
Mean Fiber length (MFL) (mm)
SD. (mm)
1
2
53.8 116.0 82.7 87.0 121.0 131.1 142.1 147.4 144.0 53.5 84.5 64.6 68.0 56. I 38.4 100.3 103.5 23.1 29.5 47.4 72.0 25.8 53.8 28.2
120 117 105.6 77.0 120.5 141.6 74.7 113.6 134.5 40.5 50.8 55.0 32.2 27.4 30.1 96.4 121.7 26.5 49.2 34.4 104.7 41.5
1
3.00 1.00 2.70 1.00 5.96 6.85 10.97 9.73 1.41 0.50 0.50 1.13 2.40 1.12 1.85 9.85 I.50 LO9 1.12 1.73 3.54 2.65 1.60 1.83
2 0 0
5.61 6.68 5.90 5.83 10.45 15.85 9.98 2.69 4.18 3.65 3.71 2.46 1.92 10.72 4.35 1.28
Volume (ml) 1 2
PCSA = V/MFL (cm) 2 1
62 62 188 222 222 222 288 288 288 137 137 137 46 46 46 234 266 IO 8 43 65 53 113 6
23 23 103 84 84 84 I09 109 109 53 53 53 24 24 24 85 45 4 24 32 13 38 4
11.52 5.34 22.73 25.52 18.35 16.95 20.20 19.59 20.00 25.00 16.21 21.21 6.76 8.20 II.98 23.33 25.70 4.33 2.71 9.07 9.03 20.54 21.00 2.13
60 20 60 105 75 45 25
27.34 3.74 42.96 2.90 46.33 23.21 8.00
1.92 1.97 9.75 10.91 6.97 5.93 14.59 9.68 8.10 13.09 10.43 9.64 7.45 8.76 7.97 8.82 3.70 1.51 4.88 9.30 1.24 9.16 1.45
MFL/ML 1 2
0.50
Fiber angle (degrees) 2 0 0
0.92 0.69 0.64 0.62 0.55
0.80 0.45 0.70 0.55 0.58 0.92 0.89 0.78 0.40 0.68 0.50 0.85 0.59 0.45 0.38 0.40 0.38 0.74 0.53 0.60 0.30 0.56
0;2
0
9.12 0.79 9.20 2.68 13.99 3.12 2.46
0.27 0.87 0.17 0.93 0.37 0.31 0.56
0.26 0.78 0.22 0.73 0.25 0.52 0.70
7 0 14 0 16 6 2.5
0.60
3.5 :.5
0.60
0.47 0.71 0.87 0.40 0.46 0.42 0.40
: 0 5 8 0 19 10.5
0.32 0.38 0.54 0.51 0.63 0.49 0.36 0.99 0.49
2: 6.5 7.5 0 7 25 0 9.5
2: 255 60 40 90 120 85 95 50
II0 I30 80 85 80 I80 240 42 loo 95 105 85 65
Hip and knee muscles Bit fern (Long) 293 Gracilis 270 Rectus fern 332 Sartorius 519 Semimembran 200 Semitendin 290 Ten fas lat 168
255 325 295 535 215 275 145
19.4 235.5 55.4 483.5 74.9 91.1 95.0
65.8 254.3 65.2 391.1 53.6 88.5 101.5
3.60 8.15 2.71 13.50 5.94 2.12 17.02
29.59 I.12 3.84 10.40
217 88 238 140 347 212 76
240 330 295 320
122.9 73.9 79.8 76.5
110.8 78.5 80.7 79.0
13.62 1.55 1.41 3.22
10.71 1.97 1.53 2.64
100 606 514 555
52 135 133 123
8.14 82.00 64.41 66.87
4.69 17.20 16.48 15.60
0.27 0.26 0.27
0.46 0.24 0.27 0.27
IS 2.5 13 7
235 230
210 205
41.9 76.9
35.8 44.2
2.26 3.95
2.49 4.94
212 110
61 38
50.60 14.30
17.04 8.60
0.18 0.33
0.17 0.22
6.5 17.5
290 270 250 265 252 250 265 190 290 370
278 325 175 205 195 225 250 105 250 305
17.0 87. I 46.2 46.9
68.4 74.3 84.8 29.0 34.6 43.4 46.0 65.2 21.7 29.8
3.88 2.55 1.31 0.83 3.13 0.95 0.85 2.08 0.96 3.94
‘2.82 5.24 2.65 0.92 3.55 1.31 1.77 4.2 I 1.14 1.25
130 65
58 16.88 7.46 30 I8 649 17 6:40 18.52 31 23 19.61 35 24.65 8 4.14 41 26.27 172 186.69
8.48 4.04 2.12 5.86 8.96 5.29 7.61 I.23 18.89 57.12
0.26 0.32 0.18 0.18 0.20 0.14 0.16 0.42 0.12 0.083
0.25 0.23 0.48 0.14 0.18 0.19 0.18 0.62 0.087 0.098
12 13 8 9 19 12 5.5 13
27.5
f*E 4:03 1.99 1.58 6.32
Knee muscles
Bit fern (Short) Vastus inter Vastus lat Vastus med
205 275 305 280
Knee and ankle Gastroc(med) Gastroc (!at)
muscles
Ankle muscles fib ant EXI dig comm Ext hall long Flexor dig Flex ha!! lonn Peronius bre; Peronius long Pemious tcrt Tib post Soleus
2: 42:6 79.8 35.4 30.8
;: 93 70 105 33 93 575
:;
Technical Note
93
Tabk 2 Fikr !engt!ts from our two cadavers, the three adavm of Wic!&wia et a!. (1983). and W&w’5 5tudy the statlndard deviation in our data (!ast two columns) and one-fourth of the ranp in kngth rqortcd by Wckr. For those musk in our specimens which were divided into two or three sections (Table I) we avcrapd fiber lengths. Fiber lengths between the studies arc remarkaMy similar
(18461 Var!abi!ity is measured by
This study I 2 Hip muscles Add brev Add long Add matpnts Pectineui Bit km (L) Gracilis. ’
I
Wickicwia* 2
Wcbcrt
Range/4
3
SD. 1
2
1.1
IO! 112 109 106 95 260
106 106 135.5 102 97 255
2: 11.2
z
93 105 106 105 78 271
65.2 391.1 53.6 144.0
61 482 70 160
68 464 54 154
63 419 64 -
12.8 435 80 197.0
3.1 12.2 5.0 0.0
2.7 13.5 5.9
10.4
2.8 29.6 1.1 17.0
122.9 73.9 79.8 76.5
110.8 78.5 80.7
145 64 66 72
133 78 67
140
15
z 64
132 65.6 -
4.5 20.7 -
13.6 3.3 -
10.7 2.4 -
Knee ami ankie mu&s Gastroc (M) Gastroc (L)
41.9 76.9
35.8 44.2
35 59
39 53
32 40
34.5 -
3.7 -
16.3 -
5.6 -
Ankle muscles Tib ant Ext dig Ext hall Flex dig FIex hall
11.0 81.1 46.2 46.9 50.2
68.4 74.3 84.8 29.0 34.6 43.4 46.0 21.7 29.8
70 94 80 26 37 46 44 24 20
93 82 103 2H 32 38 39 31 19
69 65 18
78.7 75.1 93 54.3 58.7 50 49.4
2.2 3.2 0.5 0.7 1.2 0.0 2.5 1.0 2.0
3.9 2.6 1.3 0.8 3.1
2.8 5.2 2.6 0.9 3.6 1.3 1.8 1.1 1.2
84.9 821 113.0 12.0 19.4 235.5
65.8 254.3
!kmimemb Semitend
55.4 483.5 74.9 162.4
Knee muscles Bit km (S) Vastus int Vastus lat Vastus mcd
Hip wtd knee muscles Rcctus fern saftoriu5
Pcron brcv Peron long Tib posl
35.7 42.6
so!cu5
30.8
35.4
118.8 105.6 112.9 104.1
79
115 108 131 102
27 33 :‘: 17 -
7.5
2::
26.4 2.7 12.0 3.5 3.6 8.2
A:: ::;
5.6 18.9 z 919
l Wickicwin et al. (1983). t W&X (I 846).In the Webcr study, the fiber lengths of the two heads of gastrocncmius were considered as one muscle. as were the vastus muscles.
RE!XJLTs Shtinkagc from maaration varied lrom 0% to 20% and was not consistent from muscle to muscle between the cadavcm Avera& shrinkap for all muscle bundles was 12.5% for ont spocimcn and 5.3% for the other. Within a &en murk the fiber kngths are remarkably similar. Only a few mu&s had standard deviations greater than 10% (Table I). There is even rcasonabk consistency of hbtr !engt!vs ktwecn the three data bases compared in Tabk 2, particularly considering variations in specimen rim. tcchniqwr, and o!rserven. T!rc ratios of musck length to muscle fiber kngth show cons!dembk variability between muscles. but remarkable consistency in a g!ven musck in various specimens (Table 3). Sina the ratio of muscle kngth to muscle fiber length is variabk from muscle to muscle. it is obvious that the PCSAs as cakulated by volume divided by muscle lentph wrsu5 vdume divida! by musck fiber length would be quite di&rcnt. DISCUSSION While musck fiber lengths arc us&l for many biomechanical studies, a number of problems occur in making
such estimates. The number of fibers measured is always small compared to the numkr present and sampling can potentially be a problem, shrinkage cannot be perfectly controlkd. and fibers from certain mu&s tended to be fragile. The first two probkms art inherent. l !t!mulh the errors are probab!y less than 20% (Brand ef al, 1981). Our samplinn of 20-100 fibers throunhout each musck likely red&s ;uch error. Additionally. Wcbcr’5 ( t 846)macros& pit diitions of !nmd!es (‘F!eischbundcl~ yie!dcd ranges similar to ours (Tabk 2). Furthetmorc, t!tc rmall standard deviations in fiber kngth in our data and the -By dose agreement our data with those of Wickkwia et a/. (19833, ruggests that such sampling errors are small. Shrinkag can occur after removal during maaration. Our cadavcra were fixed in kn6th in an lnatonwc position; WC detected no ‘shrinkage’ after excision. Maceration it a process in which the co!!agenous connective tissuesbetween fibers arc dissolved. We do not know the source OF the shrinkage which occurs with maantion. but it !s likely owing to some intracellular phmonmon. We lound the shrinkage during maceration uncontro!!ab!c and unprcdictabk. However. the shrinkage averaged only 12%. In reporting fiber lengths. one might correct for this shrinkage but it is generally much less than the differences in kngth occurring during excursion, and less than the variability between
of
Technical Note
94
Table 3. Average fiber length to muscle length ratios for our two specimensand the three specimens from the study by Wickiewicz et al. (1983). Ratios arc quite variable Mean
S.D.
0.70 0.50 0.53 0.83
0.14 0.08 0.12 0.15
Bit fern (L) Gracilis Rectus fern Sartorius Semimembran Semitendin
0.26 0.83 0.20 0.88 0.27 0.46
0.03 0.04 0.02 0.09 0.06 0.10
Knee muscles Bit fern (S) Vastus inter Vastus lat Vastus med
0.52 0.23 0.23 0.23
0.06 0.04 0.04 0.03
0.16 0.25
0.02 0.05
0.26
0.02 0.05 0.11 0.03 0.02 0.02
Hip
muscles Add brev Add long Add magnus Pectineus Hip
Knee
and knee muscles
and ankfc
Gastroc (Ml Gaslroc (L). Ankle
Acknowledgement:-This study was supported in part by NIH Grant AM14486 and a Grant from the Universitv of Iowa College of Medicine. We would also like IO thank- Dr Jerry Maynard for his help in specimen preparation and dissection techniques and Mrs. Rose Britton for her help in preparation of the manuscript.
REFERENCES
mus&s
muscles
Tib ant Ext di8 comm EXI hall long Flexor dig Flex hall long Pcroncus brcv Pcroneus long Tib post Solcus
The variability of the normalized PCSA suggeststhat it would be difficult to accurately predict the parameters needed to calculate the PCSA of a given muscle in a living subject based on current data. Data from many cadavera would be needed to devise and validate means IO predict PCSA in a living subject based on some anthropometric characteristics (e.g.. height, weight, lean body mass, etc.) A recent paper has demonstrated the sensitivity of muscle force predictions IO ditfcrences in PCSA (Brand et al.. 1986). It is therefore likely that while such predictions may provide information on the relative value of muscle forces in parametric studies, the absolute values of individual muscle forces must be viewed with some caution.
0.25
0.32 0.13 0.17 0.17 0.15 0.10 0.08
0.02 0.02
cadavera, and therefore might not add IO the meaningfulness of data for which WCcan obtain only estimates. Several muscles (the adductors in the first specimen) apparently were not well perfused with embalming fluid and the libers broke easily while being teased; we could isolate single libers. but could not be absolutely certain that they were whole When WChad reasonable doubt as to the intcgrity of the fibers, small bundles rather than individual fibers were dissected out and measured (i.e.. similar IO Weber. 1846). II seems likely that the bundle length is a reasonable approximation of fiber length. since in all muscles,except the semitcndinosus.the fibers reached from the (tendon or fascia of) origin to (tendon or fascia of) insertion. The fiber length to muscle length ratios of our data and those of Wickiewicz er a/. (1983) are remarkablv consistent (Table 3). Of greater importance to many resea&hers. however, is the PCSA. Brand er al. (1981) used a ‘normalized’ PCSA to compare data between fifteen cadaveric arms. When WCcalculated the normalized PCSA for our cadavcra. and those reported in the literature, we found reasonable consistency (average standard deviation 28.8%). but much fess so than for the fiber length to muscle length ratios. However, one would cxpec~a greater variability in this figure because muscle volume is highly variable. depending on body type. activity level, etc. This also suggests that the normalized PCSA (‘tension fraction’) may not be the best way to compare data between specimens.
Brand. P. W.. Beach. R. B. and Thompson, D. E. (1981) Relative tension and potential excursion of muscles in the forearm and hand. J. Hand Surg. 6.209-219. Brand. R. A.. Pcdersen, D. R. and Fricdcrich. J. A. (1986) The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J. 6iomerhanic.s 19, 589-596. Close. R. I. (1964) Dynamic propertics of fast and slow skelcta1 muscles of the rat during dcvclopmcnt. 1. Physbf. 173, 74. Close, R. 1. (1972) Dynamic propcrtics of mammalian skclcla1 muscles. Physiol. Rev. 52. 129-197. Crowninshicld. R. D. and Brand, R. A. (1981) A physiologically based criterion of muscle force prediction in locomolion. J. Biomechonics 14, 793-801. Crowninshicld. R. D.. Johnston, R. C.. Andrews. J. G. and Brand. R. A. (1978) A biomcchanical investigation of the human hip. J. Biomechonics Il. 75-85. Fick. R. (1910) Handhueh der Anor~mie des Menschen, Vol. 2. Gustav Fischer, Stuttgart. Haxton. H. A. (1944) Absolute muscle force in the ankle flexors of man. J. Physiol. 103, 267-273. Ikai. M. and Fukunaga. T. (1968) Calculation of muscle strength per unit cross-sectional area of human muscle by means of ultrasonic measurement. Int. 2. onyew. Physiol. 26. 26-32.
Morris, C. B. (1949) The measurement of the strength of muscle relative to the cross-section. Res. Q. Am. Ass. fflrh, phys.
Educ.
19-20,
295-303.
Pierrynowski, M. R. (1982) A physiological model for the solution of individual muscle forces during normal human walking Ph.D. Thesis, Simon Fraser University. Vancouver, British Columbia. Spector, S. A.. Gardiner. P. F.. Zernicke, R. F., Roy. R. R. and Edgerton. V. R. (1980) Muscle architecture and forcevelocity characteristics of cat solcus and medial gastrocncmiur Implication for motor control. 1. Neuraphysiol. 44, 951-960. Weber. E. (1846) Wagner’s ffondworcerhuch der Physinfogie. Braunschcig, Vicwcg. Wickicwicz, T. L.. Roy, R. R.. Powell. P. L. and Edgerton, V. R. (1983) Muscle architecture of the human lower limb. C/in. Orrhnp. Rel. Res. 179, 275-283.
Technical Note
95
Table 4. ‘Normalized’ (see text for explanation) PCSAs from our cadavers and those of Wickiewia er a/. (1983) and Weber (1846) and the mean and standard deviation for each muscle. These PCSAs do not include the compensation for cosine of the fiber angle to allow comparison to Weber’s data This study 2
I
I
Wickiewicz 2
Weber
All 6 specimens Mean SD.
3
Hip muscles
Add brev Add long Add magnus Pectineus
0.492 0.664 1.777 0.264
0.351 0.883 2.156 0.112
0.253 0.389 1.302 0.201
0.384 0.610 1.209 0.221
0.368 0.420 1.430 0.189
0.339 0.453 1.505 0.300
0.364 0.570 1.563 0.214
0.077 0.188 0.350 0.065
Bit fern (L)’ Gracilis Rectus fern Sartorius Semimembran Semitendin
0.799 0.109 I.255 0.085 1.354 0.680
0.826 0.072 0.833 0.243 1.266 0.282
1.062 0.110 0.984 0.136 1.224 0.408
0.854 0.134 0.825 0.110 1.087 0.256
0.778 0.137 0.936 0.116 1.556 -
0.486 0.176 I.235 0.135 I.128 0.311
0.954 0.123 1.011 0.138 1.269 0.387
0.195 0.035 0.191 0.055 1.170 0.173
Knee muscles Bit fern (S)’ Vastus inter* Vastus later* Vastus med.
0.238 2.400 I.882 1.954
0.424 1.557 1.492 1.412
2.565 1.807 1.438
0.639 2.505 1.633
1.724 2.210 1.409
0.260 6.340 -
5.496
0.770 -
Knee and ankle muscles Gastroc (M)’ Gastroc (L)*
1.478 0.418
1.542 0.778
1.930
2.331 -
3.396 -
2.448 -
2.387 -
0.544 -
0.493 0.218 0.190 0.187 0.541 0.573 0.720 0.768 5.454
0.768 0.336 0.192 0.530 0.811 0.479 0.689 1.710 5.225
0.822 0.285 0.142 0.408 0.421 0.317 0.810 1.646 4.340
0.459 0.378 0.087 0.302 0.308 0.273 1.029 0.872 -
0.946 0.631 0.168 0.400 0,452 0.473 0.789 2.461
0.576 0.198 0.104 0.236 0.574 0.285 0.593 0.772 3.596
0.677 0.158 0.147 0.344 0.517
0.196 0.346 0.044 0.126 0.173 0.125 0.150 0.694 0.853
Hip and knee muscles
-
Ankfemuscfcs Tib ant Ext dig Ext hall PIen dig flex hall Peron brev Peron long Tib post Soleus
-
~~ I:363 4.654
*In the Wickiewicz cr ul. (1983) study. the PCSAs of the two parts of the muscleswith two heads were added together. The same was done with the vas~usmuscfcsas a group and the two heads of gastrocnemius in the Weher (1846) study.
