JOURNAL OF MORPHOLOGY 221:177-190 (1994)

Relationship Between Muscle Fiber Types and Sizes and Muscle Architectural Properties in the Mouse Hindlimb

THOMAS J. BURKHOLDER, BRIAN FINGADO, STEPHANIE BARON, AND RICHARD L. LIEBER Departments of Orthopaedics and AMESIBioenpineerinp. Biomedical Sciences Graduate Group, University of California and veterans Administration Medical Centers, Sun Diego, California 92161

ABSTRACT Skeletal muscle fiber and architectural properties both contrib- ute to the functional behavior of a muscle. This study uses discriminant analysis and mathematical modeling to identify the structurally and function- ally significant properties. The architectural properties of fiber length, muscle length, and pennation angle are found to be the most structurally significant parameters, whereas fiber length, muscle length, and fiber type distribution are found to be most functionally determining. Architectural speed and fiber type do not appear to be complimentary (i.e., the architectural determinant of speed, fiber length, is not associated with fibers of high intrinsic velocity). However, there does seem to be a synergistic relation between the two property classes and force production. Muscles with large physiological cross sectional areas (PCSAs) tend to contain a greater proportion of larger, faster fibers. Structurally or morphologically significant parameters are not always found to have a large functional effect. Pennation angle, though one of the most structurally significant variables, was found to have very little functional effect. Q 1994 Wiley-Liss, Inc.

Skeletal muscle contractile properties de- pend on muscle fiber size, muscle fiber physi- ological properties (i.e., fiber properties), and the arrangement and number of fibers within the muscle (i.e., muscle architecture). Fast- contracting fibers have an intrinsic contrac- tile speed (Vmm) that is about three times greater than slow-contracting muscle fibers (Close, '72). Differences in specific tension (i.e., force per unit fiber area) between fast and slow muscle fibers remains a matter of debate. For example, fast muscle fibers have been reported to have about the same specific tension (Bodine et al., '87; Lucas et a]., '87) or up to five times the specific tension (Burke, '81) compared to slow fibers. However, there is general agreement that architectural differ- ences between muscles can confer up to a 20-foid difference in tension and contractile speed between muscles (Gans, '82; Sacks and Roy, '82; Wickiewicz et al., '83; Powell et al., '84; Roy et al., '84a). Muscle contractile prop- erties can thus be altered by varying either fiber type or muscle architecture. However, whether or not architectural and fiber type distributions are complimentary has not been

determined in a large set of muscles within the same animal.

Many studies of human muscle function have inferred a relationship between fiber type distribution and torque production. For example, several investigators (Coyle et al., '79; Froese and Houston, '85; Thorstensson et al., '76; Suter et al., '93) calculated statisti- cally significant correlations between iso- kinetic knee extension torque and vastus lat- eralis fast fiber percentage. Yet the danger of inferring causation from correlation was pointed out by Schantz et al. ('831, who also documented a dependence of torque on muscle cross-sectional area without regard to fiber type percentage. These studies illus- trate the lack of consensus regarding the relative effects of muscle fiber type and archi- tecture on contractile performance.

We previously employed the statistical method of discriminant analysis in quantita- tive muscle architecture studies in the rabbit hindlimb (Lieber and Blevins, '89) and hu- man arm and hand (Lieber et al., '90, '92; Jacobson et al., '92) to determine those struc- tural features that best characterize func- tional groups. These studies demonstrated a

o 1994 WILEY-LISS, INC.

178 T.J. BURKHOLDER ET AL

remarkable degree of architectural specializa- tion between functional groups, which pre- sumably suits the muscle group to the func- tional task. Unfortunately, these studies did not consider the effect of muscle fiber type distribution along with architecture in deter- mining functional properties. Therefore, the purpose of this study was to measure architec- tural and fiber type properties simultaneously in paired mouse hindlimbs in order to deter- mine the relative influence of architecture and fiber type distribution in determining muscle contractile properties.

MATERIALS AND METHODS

Twenty-five muscles from each of 12 paired hindlimbs were dissected from adult female Swiss-Webster mice (Harlan Sprague Daw- ley, body mass = 24.6 * 2.0 g). One leg was used for morphometric analysis of fiber type and fiber size distribution; the contralateral limb was used for architectural measure- ments. Animals were sacrificed by COz as- phyxiation, skinned, and transected at the sacrum. One limb was placed immediately (within 30 minutes of sacrifice) in 4% para- formaldehyde with hip, knee, and ankle held at 90” and the hip in full abduction and fixed overnight. The other limb was fresh dis- sected, being kept moist with 0.9% saline. These muscles were placed hrectly into OCT mounting embedding medium (Miles Labora- tories, Naperville, IL) with the muscle fibers’ long axis as perpendicular to the surface of the mounting medium as possible, frozen in isopentane cooled by liquid nitrogen (-159”C), and stored at -80°C for subse- quent analysis. Dissection and freezing was typically completed within 3 hours of sacri- fice.

Fiber type determination Serial sections of 8 Frn thickness were

stained with hematoxylin and eosin (H&E) to view general fiber morphology, succinate dehydrogenase (SDH) to view fiber oxidative capacity, and myofibrillar ATPase after alka- line preincubation (pH = 10.2) to distin- guish between fast and slow contracting fi- bers (Brooke and Kaiser, ’70). Acidic preincubation (pH = 4.6) was used in pilot studies to determine the pH sensitivity of the mouse muscle and confirm reversal of dark and light fibers under acid and alkaline condi- tions. Fibers were then classified as type SO, FG, or FOG according to the scheme pre- sented by Peter et al. (’72) as previously

described in detail (Lieber et al., ’91). Also, a combined SDH and ATPase staining on a single section was used for fiber area determi- nation in order to identify all three fiber types on a single section. (This analysis as- sumed that there were no “FO” or “SG” fiber types. Pilot studies comparing the double-staining method with results obtained from serial sections staining all enzymes on 331 fibers demonstrated that this assump- tion was reasonable for 97% of the fibers studied). Based on the reported similarity of histomorphometric properties of the two com- partments of the semitendinosus (Roy et al., ’84b), analysis was performed only on the distal semitendinosus compartment.

Morphometric analysis Representative sections from each muscle

were viewed on a Nikon Microphot-SA micro- scope equipped with a color camera (Sony Model DXC-760MD, New York). The video signal was fed into a IBM 486-based com- puter with acquisition boards for frame grab- bing and image processing (Universal Imag- ing Corporation, Media, PA). The system software (Imagel, version 4.0) was used for calibration and thresholding of the video im- age acquired. Then, specific fiber images were manually edited to insure that only single muscle fibers were counted. Fiber area was determined from at least 50 muscle fibers of each type within each section except in the case where fewer than 50 fibers of a given type were present, in which case all fibers of that type were digitized (e.g., most peroneus brevis muscles contained only a few hundred fibers, of which fewer than about 12 were slow). Although some sections showed signifi- cant freezing artifacts, comparison of areas from these sections with undamaged muscles indicated that the artifacts did not greatly affect fiber size determination. To eliminate inter-observer variability, all image analysis was performed by the same individual. Sys- tem accuracy was calibrated against known size standards and shown to be accurate within 1%. In practice, however, given the variability in muscle fiber shape and optical density, the coefficient of variation for re- peated measurement of fiber area within the same section was about 6%. Fiber type per- centage within each section was determined by counting the fibers of each type in several microscope fields that covered the muscle and included at least 20% of the muscle cross- section was counted. Given a total spatial variation in fiber type percentage of about

MOUSE FIBER PROPERTIES AND ARCHITECTURE 179

15% (Mathieu et al., '79), this was considered to be about twice the area necessary to give an accurate estimate.

Skeletal muscle architecture Following fixation, limbs were rinsed twice

in phosphate buffered saline to remove re- sidual fixative and stored in buffer for later dissection. Individual muscles were dissected under 60x magnification (Wild Model M3, Wild, Inc., Heerbrug, Switzerland) to guaran- tee removal from origin to insertion. Indi- vidual muscles were blotted dry, and muscle mass (M) determined using an analytical bal- ance. Muscle length (Lm), defined as the dis- tance from the origin of the most proximal muscle fibers to the insertion of the most distal muscle fibers, was determined using a calibrated digital filar eyepiece (Lasico Model 112983, Los Angeles, CAI through the dissect- ing microscope. Pennation angle, defined as the angle between the internal tendon, or aponeurosis, and muscle fibers, was deter- mined using a goniometer under magnifica- tion. Individual muscles were partially di- gested in 15% HzS04 for 60 minutes. Small fiber bundles composed of 5-50 fibers were then teased from proximal, middle, and dis- tal muscle regions and mounted on slides for fiber length and sarcomere length determina- tion. Fiber dissection was performed at 60 x magnification, which enabled identification of single fibers running completely from ten- don of origin to tendon of insertion. Tapering fibers or fibers terminating in the mid-muscle portion were not observed (Loeb et al., '87; Ounjian et al., '911, except in the semitendi- nosus. (This is not to say that they did not exist; we simply selected for those regions that could be cleanly dissected from tendon plate to tendon plate.) Fiber length (Lf) was determined from individual fibers of each bundle using the filar eyepiece.

Mean fiber sarcomere length was mea- sured from three regions of each bundle via laser diffraction (Lieber et al., '84). All muscle lengths and fiber lengths were then normal- ized to a sarcomere length of 2.2 km to cor- rect for variability induced by differences in the angle of joint fixation. Physiological cross- sectional area (PCSA) was calculated as de- scribed by Sacks and Roy ('82) using the equation:

where M is muscle mass, 0 is pennation angle, p is fresh muscle density (0.001056 g/mm3, Mendez and Keys, '60), and Lf is fiber length.

Definition of functional groups In addition to comparisons between indi-

vidual muscles, comparisons between func- tional groups were performed by classifying muscles: hip adductors, hip extensors, knee extensors, ankle dorsiflexors, plantarflexors, or everters. Hip adductors included the adduc- tor magnus (AdM), adductor longus (AdL), and the anterior and posterior gracili (AG and PG; as the mouse has a distinct separa- tion of the gracilis into two partitions with a distinct insertion for each). Hip extensors included the semimembranosus (SM), the proximal and distal portions of the semitendi- nosus (PST and DST; each region was stud- ied as a separate muscle due to clear separa- tion of the two muscle bellies by tendon), and biceps femoris (BF). Knee extensors included the vastus medialis (VM), vastus lateralis (VL), vastus intermedius (VI), and rectus femoris (RF). Dorsiflexors included the tibi- alis anterior (TA), the extensor digitorum longus (EDL), and the extensor hallicus lon- gus (EHL). Plantarflexors consisted of the medial gastrocnemius (MG), the lateral gas- trocnemius (LG), the soleus (SOL), the plan- taris (PLA), the flexor hallicus longus (FHL), the flexor digitorum longus (FDL), and the tibialis posterior (TP). Ankle everters in- cluded the peroneus longus (PL), the pero- neus brevis (PB), and the peroneus tertius (PT). Although some muscles could be classi- fied into more than one category (e.g., the gastrocnemius acts as a knee flexor and ankle plantarflexor), we defined the groups based on the primary muscle action.

Statistical analysis Analysis of variance was used to compare

architectural and morphometric properties between groups (Statview 4.0, Abacus Con- cepts, Inc., Berkeley, CAI. Fisher's least squared difference (LSD) test was used to make paired comparisons between specific functional groups following significant one- way ANOVAs. Significance level was set to a = 0.05 and statistical power (1-p) calcu- lated for any comparison not exceeding the critical level of 0.05. Statistical power ranged from 10% (for FOG fiber area) to over 99% (for fiber length) with most values around 60%.

Discriminant analysis was then performed using the BMDP statistical software pro-

180 T.J. BURKHOLDER ET AL.

gram running on a VAX 11/780 (Dixon, ’83) as previously described (Lieber and Blevins, ’89). This program used an iterative method to determine the variables with the greatest discriminating power between functional groups, using a threshold F value of 4.000. The term “specialization” is used to indicate those parameters that vary systematically from group to group to indicate properties optimized to the performance of a particular function (e.g., knee extension), based on the assumption that muscles within a functional group are specialized for performance of that function.

Based on the assumption that no differ- ences exist between muscles on contralateral sides of the same animal (see above), morpho- metric data from one side were merged with architectural data obtained from the other to reduce the data set to 17 variables from 25 different muscles on six different animals (n = 2,382 variates).

Muscles in this study often contained ei- ther type FOG and FG fibers with no SO fibers or type FOG and SO fibers with no type FG fibers. Since discriminant analysis re- quires complete data sets, it was necessary to eliminate SO and FG fiber area data from the analysis. Thus, discriminant analysis was per- formed on a data set including the following variables: muscle mass, muscle length, fiber length, muscle length: fiber length ratio, pen- nation angle, physiological cross-sectional area, FOG fiber area, FOG fiber percentage, SO fiber percentage, total muscle area (mea- sured from the digitized cross section), fiber number (calculated by dividing total muscle area by the weighted average area of each fiber type), animal mass, tibia length, and femur length. Of the 150 muscles studied, seven were eliminated from discriminant analysis due to missing data.

Muscle modeling The importance of the discriminating pa-

rameters in determining muscle contractile properties was estimated using a mathemati- cal model. The model was designed to esti- mate contractile properties roughly. An arbi- trary muscle with variable architectural and fiber type properties was constructed (Fig. 1). Connective tissue, such as tendon and apo- neurosis, was considered to be inextensible. The projection area of a muscle was taken to be constant, based on the contractile and morphometric data of Zuurbier and Huijing (’92). Seven variables were determined to be discriminators between functional groups:

five independent and two dependent vari- ables. The independent variables were muscle length (Lm), fiber length (Lf), pennation angle (01, muscle mass (M), and fast fiber percent- age (F%), where F% included both FG and FOG fibers. In mice, fiber length and fascicle length are identical, so no distinction is neces- sary. However, in species with serial fibers (Loeb et al., ’87), fascicle length would be the appropriate model parameter. These indepen- dent variables were then used to calculate PCSA and slow fiber percentage. All of these variables were taken together to determine the whole muscle contractile properties for that model muscle.

Muscle projection area (A) was calculated as

A = 2 . L, . La sin p, (2)

where p is the included angle between the aponeurosis and the line of muscle action. Using the assumption of constant aponeuro- sis length, the aponeurosis angle can be calcu- lated for any given muscle length from the projection area of the muscle in its reference state. The reference state for each muscle was defined by the measured architectural properties. The law of sines then yields the relationship between fiber length, muscle length, and aponeurosis length as

(3)

where p represents the angle between the fibers and the muscle line of action. Equation 3 yields p and Lf from L,, La, and a. The fiber velocity function was taken directly from Zuurbier and Huijing (’92):

Lr La --=- Lnl sin r iso - ((I + - sin [PI sin [a] ’

The normalized force-length and force- velocity properties were obtained from rea- sonable approximations in the literature (Fig. 2). The force-length property was based on

Lrn 4 c.

Muscle Line of Anion

Fig. 1. Geometry of the mathematical model. L,, muscle length; Lap, aponeurosis length; Lf, fiber length; (I, fiber angle; p, aponeurosis angle; 8, pennation angle.

MOUSE FIBER PROPERTIES AND ARCHITECTURE 181

the relationship presented by Gordon et al. ('66); the force-velocity relationship was that presented by Katz ('39) with values for a and b obtained from the literature for mamma- lian muscle (Close, '72). The force-length re- lation plateau extended from sarcomere lengths of 2.0 to 2.2 ym. The shortening force-velocity relation was described by

while the lengthening relation was given by Vm, f v F = 1.8 - 0.8 V,, - 7 . 6 V . (6)

V,, was taken to be 17.6 Km/s for fast fibers, and 9.0 km/s for slow. Fast and slow fibers were considered to have the same spe- cific tension (but, see below on the effect of this assumption).

All independent variables were then sys- tematically varied over the entire physiologi- cal range observed. Therefore, the sensitivity analysis was performed in a physiologically meaningful context and not simply varied to theoretical extremes. As an example, fiber length was varied only from a low of 4.4 (as observed for the FDL muscle) to 17.1 (ob- served for the SM muscle) even though this characteristic could theoretically vary from just more than 0 to 24 (the maximum muscle

A 1 .o

a, g 0.8

? 2 0.2

0.6

's 0.4 -

Sarcomere Length (pm) B

slow force-vdococlty If relation 1

a, .Oo Fast force-velocilv relation

- ,$&. , . , ,;i:L d

-15 -10 -5 5 10 15 Sarcomere Velocity (pm/s)

Fig. 2. Assumed properties of sarcomeres. A Force length relation. B: Force velocity relation of fast and slow fiber types.

length). In this way, the influential param- eters were allowed to exert their effects only when physiologically reasonable.

RESULTS Architectural specialization

Significant specialization between func- tional groups is easily demonstrated since one-way ANOVAs reveals significant differ- ences in all architectural and morphometric properties (Tables 1 and 2, P < 0.01). In addition, for a given parameter, significant differences are almost always observed be- tween pairs of functional groups with only a few exceptions: dorsiflexor and ankle everter muscle lengths are not significantly different (P > 0.8, power > 80%). Knee extensor LfiL, ratios are similar to those of plantar- flexors (P > 0.6, power > 40%), and hip ex- tensor ratios are not significantly different from dorsiflexor LdL, ratios (P > 0.6, power > 50%). Hip adductor pennation angles are not Significantly different from hip extensor angles ( P > 0.5, power > 50%), nor are knee extensor and dorsiflexor (P > 0.4, power > 60%) or dorsiflexor and everter pen- nation angles (P > 0.3, power > 60%). Fi- nally, fast fiber area (Fig. 3) is similar be- tween hip extensors and shank muscles ( P > 0.4, power > 20%). Thus, with the few exceptions noted, most functional groups demonstrate remarkable specialization.

Architectural properties of muscles and functional groups are very similar to those reported for human (Wickiewicz et al., '831, cat (Sacks and Roy, ,821, rabbit (Lieber and Blevins, '89), and guinea pig (Powell et al., '84) muscles. It thus appears that architec- tural specialization is the norm across spe- cies with little regard for locomotion mode or relative activity level.

Fiber type size and distribution One-way ANOVA reveals significant differ-

ences in all fiber properties, with the excep- tion of FG%. Fisher's PLSD post-hoc analy- sis discloses fewer group to group differences. FG and SO fiber areas are found to be signifi- cantly larger in thigh muscles than shank muscles (P < 0.01). Antigravity muscles are found to have significantly more slow fibers than non-postural muscles (P < 0.01). It therefore appears that fiber type properties are less specialized or specific than architec- tural properties.

182 T.J. BURKHOLDER ET A L

TABLE 1. Architectural properties of muscles and functional groups (5S.D.)

Muscle mass Muscle length Fiber length PCSA Muscle (mg) Angle (") (mm) (mm) FL ratio (ss cm) Adductor Magnus Adductor Longus P Gracilis A Gracilis Hip adductors Biceps Femoris Semimembranosus D Semitendinosus P Semitendinosus Hip extensors Vastus Intermedius Vastus Lateralis Vastus Medialis Rectus Femoris Knee Extensors EDL ~~ ~

EHL TA Dorsiflexors FDL FHL L Gastrocnemius M Gastrocnemius Plantaris Soleus TP _ _ Plantar flexors Peronius Brevis Peronius Longus Peronius Tertius Ankle Everters

99.8 ? 8.0 42.3 c 37.7 10.5 f 2.7 19.5 f 7.8 43.0 f 40.1

177.5 f 15.3 21.4 f 6.6 56.4 2 10.2 56.4 t 10.2 77.9 ? 68.4 10.7 f 0.9 82.2 f 11.4 82.2 f 11.4 74.7 f 4.9 62.4 f 34.7 9.0 f 1.5 1.0 f 0.4

45.2 f 3.9 18.4 t 23.6 30.1 t 4.2 11.2 f 3.1 61.3 -t 13.6 73.6 ? 9.0 16.0 f 0.9

2.2 t 0.5 28.9 f 28.0 10.0 f 2.5 11.5 2 2.2 2.4 f 0.9 8.0 c 4.9

7.8 f 1.5

0 0

3.7 f 1.2 0

0.9 -c 1.8 0 0 0 0 0

8.5 f 1.0 7.2 ? 0.8 7.2 f 0.8

13.2 f 2.6 9.0 ? 2.8 8.3 -c 1.6 3.8 f 2.6

11.7 k 1.5 7.9 k 3.9 9.5 c 2.7

11.5 f 2.3 26.2 f 3.3 24.3 ? 2.1 14.3 k 2.1 8.5 z 2.7

13.9 f 8.5

8.3 f 2.4 1.7 ~t 1.5

3.2 ? 1.8

9.0 ? 3.2

6.3 ? 4.1

19.0 f 0.9 16.9 2 1.2 14.2 f 0.3 18.3 f 0.8 17.1 ? 2.2 19.0 5 2.0 18.6 -t 0.9 22.6 f 1.6 22.8 i 1.1 20.7 f 2.3 12.3 5 0.6 15.4 t 1.3 15.3 f 1.1 14.2 f 0.6 14.3 f 1.5 12.2 f 0.7 7.0 f 1.1

12.9 f 0.6 10.7 f 3.2 12.7 c 1.2 11.3 i 0.9 13.8 f 1.1 14.7 f 0.8 13.5 c 1.0 11.2 f 0.6 8.0 f 1.1

12.2 f 2.3 12.7 + 1.8 10.9 f 1.3 8.3 f 1.7

10.6 f 2.2

15.3 f 1.2 14.1 t 2.0 12.4 f 0.4 16.5 f 0.5 14.6 2 1.8 15.0 + 1.3 17.1 f 0.6 13.6 f 1.8 8.1 f 1.1

13.5 f 3.8 6.3 f 1.2 9.1 f 0.8 9.0 t 0.8 6.1 f 0.7 7.6 ? 1.7 6.2 f 2.2 5.6 -t 0.7 7.9 5 0.6 6.6 f 1.2 4.4 f 0.4 3.7 f 1.1 6.3 f 0.4 6.6 f 0.3 5.3 + 0.4 8.1 f 0.9 5.1 f 1.3 5.6 f 1.5 5.2 f 0.4 4.8 f 0.4 4.8 f 1.0 4.9 f 0.2

81% f 9% 84% ? 13% 88% f 2 4 90% i 3% 86% i 4 4 79% 2 7% 92% i 5% 619 ir 9% 36% i 4% 67% 2 25% 51% i 8% 59% i 4% 59% i 4% 43% i 5% 53% k 8% 51% f 18% 81% i 12% 61% i 4 6 646 i 16% 35% ? 3% 32% i 8% 46% i 4% 45% 2 3% 39% i 2% 72% ir 7 6 64% 2 13% 48% i 15% 41% i 6%

48% 2 9%

45% i 8% 59% i 13%

6.2 f 0.7 3.2 t 3.2 0.8 f 0.2 1.1 f 0.5 2.8 f 2.5

11.3 f 1.5 1.2 f 0.4 3.9 ? 0.3 6.7 ? 1.7 5.8 f 4.3 1.6 ir 0.3 8.5 f 0.9 8.6 f 1.0

11.4 f 1.3 7.5 f 4.2 1.8 f 1.6 0.2 ? 0.1 5.3 f 0.6 2.4 f 2.6 6.3 f 0.8 3.0 t 1.0 8.3 f 1.9 9.7 f 1.4 2.8 t 0.3 0.9 f 0.1 0.4 f 0.2 4.5 & 3.6 1.8 f 0.4 2.3 f 0.5 0.5 f 0.2 1.5 f 0.9

Relationship between architecture and fiber properties

Correlations between measured properties reveal the relationships between muscle ar- chitectural properties and muscle fiber prop- erties. No significant correlation between fi- ber length (the architectural determinant of muscle velocity) and fiber type percentage (related to the biochemical determinant of Vma) is seen. This indicates that architectur- ally fast muscles are not necessarily biochemi- cally fast contracting. In other words, fiber type distribution does not appear to comple- ment muscle fiber length.

Interestingly, a significant positive correla- tion is found between PCSA and FG% (r = 0.41, P < 0.0001), while a significant negative correlation is found between PCSA and the sum of FOG% plus SO% (r = -0.43, P < 0.0001). Because type FG fibers are typi- cally the largest (Fig. 3) and therefore the strongest these data indicate that high muscle force is accomplished both by the presence of type FG fibers and the arrangement of these fibers in such a way as to increase PCSA. However, the same cannot be said for the

relationship between the percentage of type FG fibers and muscle speed.

Muscle fiber length is negatively correlated with pennation angle (r = 0.55, P < 0.0001), as previously observed (Gans and Bock, '65; Sacks and Roy, '82; Lieber and Blevins, '891, which indicates that large pennation angles represent a strategy for fiber packing within muscle that maximizes force output (Gans and de Vree, '87).

Discriminant analysis Eight parameters are significant discrimi-

nators between functional groups: muscle mass, muscle length, fiber length, pennation angle, FOG fiber area, physiological cross- sectional area, FOG fiber percentage, and SO fiber percentage. Of these eight parameters, muscle length, fiber length, and pennation angle have F-values from the discriminant analysis (F = 14 to 17) that were over twice those of the rest of the parameters (F = 4 to 7), implying that they contain the best dis- criminating power between functional groups (Fig. 4). Note that they are all architectural properties.

TABL

E 2.

Fib

er p

rope

rtie

s of m

uscl

es a

nd fu

nctio

nal g

roup

s (2

S.D

.)

Mus

cle

Add

ucto

r Mag

nus

Add

ucto

r Lon

gus

P G

raci

lis

A G

raci

lis

Hip

Add

ucto

rs

Bic

eps F

emor

is

Sem

imem

bran

osus

D

Sem

itend

inos

us

P Se

mite

ndin

osus

H

ip E

xten

sors

V

astu

s Int

erm

ediu

s V

astu

s Lat

eral

is

Vas

tus M

edia

lis

Rec

tus

Fem

oris

K

nee E

xten

sors

ED

L EH

L TA

D

orsi

flex

ors

FDL

FHL

L

Gas

troc

nem

ius

M G

astr

ocne

miu

s Pl

anta

ris

Sole

us

TP

Pl

anta

r fle

xors

Pe

roni

us B

revi

s Pe

roni

us L

ongu

s Pe

roni

us T

erti

us

Ank

le E

vert

ers

FG fi

ber a

rea

(sq

Km

)

1,77

7.7 f 8

12.6

1,

651.

0 f 5

79.7

1,

450.

8 f 5

13.2

91

7.0 f 3

19.2

1,

449.

1 f 3

79.4

1,36

8.8 f 3

73.7

1,

252.

0 f 4

02.0

1,

252.

0 ?

402

.0

1,33

6.3 f 1

06.0

1,75

7.2 f 2

28.1

1,

353.

2 t 3

38.9

1,

937.

7 f 5

40.1

1,

465.

8 f 4

97.9

77

2.3 t 1

20.3

78

7.8 f 9

3.1

1,25

0.8 f 2

41.7

93

7.0 f 2

71.9

89

2.5 f 2

04.6

74

6.3 f 9

0.3

1,47

2.2 t 3

60.5

815.

0

1,13

6.7 -

c 17

0.9

1,15

3.2 f 3

39.8

1,

106.

7 t 2

92.1

672.

3 f 1

69.3

95

1.3 f 2

11.0

1.

036.

5 t 2

89.8

-,

- 739.

2 f 1

71.5

85

4.0 f 2

01.7

87

6.6 t 1

49.9

FOG

fibe

r are

a (s

q +m

)

957.

5 f 3

93.4

91

9.7 f 1

28.4

1,

049.

2 t 4

75.8

88

7.0 f 2

61.4

95

3.3 f 7

0.1

730.

3 f 1

50.3

64

2.8 f 2

02.2

69

7.2 t 1

20.2

69

7.2 f 1

20.2

69

1.9 f 3

6.2

1,12

2.0

-c 17

3.8

1,04

9.8 t 1

24.8

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184 T.J. BURKHOLDER ET AL.

W FGArea

0 FOGArea

0 SOArea Plantarflexors

Dorsif lexors

I

Knee Extensors

I Hip Extensors

I 1

0 500 1000 1500 2000 Fiber Area (pm 2)

Fig. 3. Fiber areas of functional groups (?S.D.). Note the FG fibers in each group are generally larger than the other fiber types within that same group.

LflL, ratio, animal properties (mass, fe- mur, and tibia lengths), muscle area, and fiber number are found not to be good dis- criminators at all. That Lf/L, ratio is not a good discriminator is not surprising, consid- ering that it can be calculated directly from muscle length and fiber length. A separate analysis forced LflL, ratio into the discrimi- nating equation and then fiber length was

not found to be a significant discriminator. Finally, the fact that 8 of the initial 14 vari- ables enter into the discriminating equation in spite of the stringent requirements for entry (F-to-enter = 4,000) demonstrates that a large number of factors vary between functional groups and it is not instructive to apply multiple univariate analyses to one variable at a time in order to extract muscle design parameters.

Fiber Length

Muscle Length

Pennation Angle

PCSA

FOG Fiber Area

SO Fiber %

Mbscle Mass

FOG Fiber %

5 5 1 0 1'5 20 F Value

Fig. 4. F values of variables identified by discriminant analysis.

MOUSE FIBER PROPERTIES AND ARCHITECTURE 185

The power of the discriminating equation can be evaluated by applying it retrospec- tively to the original data set. If, using the discriminating equations, muscles are placed into the correct functional group, the dis- criminant analysis can be considered success- ful and meaningful. Using the eight discrimi- nating parameters, it is possible to correctly classify 75% of the entire data set which is almost five times better than would be achieved by chance. The accuracy of the ret- rospective classification varies with func- tional group, ranging from a high of 83% for the hip adductors and knee extensors to a low of 67% for the ankle everters.

More detailed analysis of discriminating variables reveals that it is possible to identify muscles 57% correctly (range 41-78) based only on fiber length, muscle length, and pen- nation angle, suggesting that these three ar- chitectural parameters contain a majority of the discriminating information. Further, based only on fiber length and muscle length, it is possible to isolate the hip adductors and hip extensors from the remaining groups, suggesting that these two functional groups are quite different from the remaining four groups. This is most obvious based on inspec- tion of discriminating variables plotted in space (Fig. 5).

Mathematical model results Mathematical modeling reveals, as ex-

pected, that excursion and V,, are most strongly dependent on muscle length and fiber length, with only a slight dependence on pennation angle (Fig. 6). Peak force approxi- mations are strongly dependent on muscle mass and fiber length, with sight dependence on pennation angle, as would be expected from the formula for PCSA.

Considering a muscle of constant mass, it is possible to investigate the effect of simulta- neously varying fiber length, muscle length, and pennation angle. Increasing fiber length while holding all other parameters constant decreases peak tension and broadens the ac- tive range (Fig. 7A). This follows directly from the decrease in PCSA and the increased number of series sarcomeres associated with longer fibers. Increasing pennation angle also decreases PCSA slightly, and therefore peak isometric force, and shifts the length tension curve to slightly longer lengths because fi- bers can rotate more at longer muscle lengths.

The force-velocity relation is sensitive to fiber length (Fig. 7B). Increasing fiber length results in larger estimated V,, and less ap-

parent curvature. Pennation angle changes does not effect velocity.

Varying fiber type percentages has a very small effect on both muscle force and veloc- ity. The effect of decreasing the proportion of fast fibers is simply to increase the curvature of a muscle's force-velocity relation. Because the stress produced by a slow fiber at any given velocity is lower than that produced by a fast fiber, a muscle with a greater fraction of slow fibers will generate less force at any velocity than an architecturally identical muscle with more fast fibers. Because muscle force was modeled as the sum of slow fiber force and fast fiber force, decreasing the pro- portion of fast fibers does not change V,, until all fast fibers have been eliminated. This follows from the fact that even if 99.9% of the fibers are slow, and produce no force, the few remaining fast fibers are still active until their own V,,, giving the muscle the V,,, that would be associated with fast muscle. Of course this result neglects inertial effects, which would require those few fibers to produce enough force to move the whole muscle before exerting any external force.

Finally, the peak of the power-velocity rela- tion is independent of muscle or fiber length (Fig. 8). This indicates that the decrease in PCSA associated with longer fibers is compen- sated for by the increase in V,, resulting in near-constant peak power. Muscles of similar mass and fiber composition thus have similar power output. The dependence of power on fast fiber percentage is most interesting. As the percentage of fast fibers decreases, the power curve begins to show increased curva- ture with a sharp change of slope at the V,, associated with slow fibers (Fig. 9). This is because the estimated power curve repre- sents the sum of all the fibers within the muscle. In fact, for high percentages of slow fibers, it becomes increasingly obvious that the curve represents the sum of a power curve for a fast muscle and a power curve for a slow muscle.

DISCUSSION

The purpose of this study was to determine the relationship between architectural and fiber type properties in determining muscle contractile properties. The main result was that architectural specialization is not gener- ally complemented by fiber type specializa- tion to achieve a particular functional out- come. For example, one might expect a priori that muscles with long fibers would also have a high percentage of fast fibers because both

186 T.J. BURKHOLDER ET AL.

Fig. 5. Probability zones for muscle groups in muscle length, fiber length, and pennation angle space. Surfaces represent 2 1 SD (63% probability). Note clustering of hip adductors and extensors vs. knee extensors, dorsiflexors, plantarflexors, and everters. Black points with projections represent averages for each muscle, which are unlabeled for simplicity.

represent adaptation for high muscle veloc- ity. This was not the case, as shown by the lack of correlation between these two param- eters. This lack of correlation may be indica- tive of many conflicting influences acting on the muscle (e.g., contraction speed, use, and activation dynamics). If anything, the signifi- cant correlation between PCSA and percent- age FG fibers seems to indicate that FG fiber

type percentage in particular represents an adaptation for high force or power output, or ballistic movements.

Fiber length was the single best discrimina- tor between muscle groups, which is prob- ably a reflection of its functional importance as well as necessary size constraints of fitting a muscle onto either the thigh or shank. It is also important to note that several muscles

MOUSE FIBER PROPERTIES AND ARCHITECTURE

A B

187

Fiber Length (mm) Pennation Angle (")

lg51 -192.5

5 190

Fiber Length (mm) Pennation Angle (")

Fig. 6. Effect of fiber length (A$) and pennation angle (B,D) on maximum muscle excursion (A,B) and V,, (C,D).

from each group share similar origins and insertions, contributing to their similarity. This should not be taken to mean that simi- lar geometry causes the muscles to be simi- larly constructed. The space between origin and insertion can be filled as well with ten- don as with muscle, or with muscle organized in a variety of architectures. Functionally, increased fiber length results in increased muscle velocity, and decreased fiber length is correzated with (although not causal 00 in- creased muscle force. This result indicates that sarcomere number regulation during development and evolution represents a pow- erful determinant of muscle function. I t should be noted, however, that muscle prop- erties alone do not determine joint torque since muscle force is transmitted via a mo- ment arm to produce torque (Lieber and Boakes, '88). Long muscle fibers are gener- ally (McClearn, '85) but not always (Lieber and Brown, '93) associated with large mo- ment arms so that other factors than simple range of motion must account for variations in sarcomere number. Future studies are required to detail the nature of these factors.

That pennation angle is an important dis- criminator is somewhat surprising, in view of the almost negligible relationship between pennation angle and force or speed produc- tion (Fig. 6). Thus, pennation angle almost certainly represents a constraint for muscle placement (thigh vs. shank or anterior vs. posterior compartment) rather than muscle function. This result reinforces the concept that good discriminators are not necessarily functionally significant. In fact, in all of the discriminant analyses that we have per- formed on animal and human muscles (Li- eber and Blevins, '89; Lieber et al., '90; '92; Jacobson et al., '921, pennation angle has always emerged a good discriminator.

Although it was possible to define a normal range of architectural and fiber type proper- ties for each functional group, the differences between most groups were relatively small. That so many variables were required to distinguish correctly between plantarflexors, dorsiflexors, and everters gives credence to the belief that these are very similar types of muscles in terms of design. Similarly, the ease with which these three groups can be

188 T.J. BURKHOLDER ET AL

- Lf=Smm

.......... Lf=lO mm

......... Lf=l5 mm n . - - - - - - 201

.YlO

LD :: N In 7

A Excursion (mm)

- Lf=Smm a, 0

51.5 .......... Lf=lOmm LL . . -. - -. Lf= lSmm 8 .

., -. ........ ..................

B Velocity (mm/s)

Fig. 7. Effect of fiber length on length tension (A) and velocity tension (B) relations. Longer fibers increase speed and range at reduced force.

200

150

L g 100

I

0

a, 0 v, 50

a -

0

-50

distinguished from adductors and hip exten- sors using relatively few discriminators indi- cates that the hip muscles represent a much more distinct muscle design.

Mathematical modeling over the physiologi- cal range revealed a dominance of architec- tural effects over fiber type effects in deter- mining muscle function. It may be argued that this result was a necessary result of the model assumptions of identical specific ten- sions for fast and slow muscle fibers and identical shapes of the force-velocity relation. However, even a twofold difference in specific tension between slow and fast fibers would result in at most a 40% change in muscle force, whereas fiber length changes were shown to impart up to a 300% change in force and velocity.

Finally, these data have significant implica- tions with respect to studies that investigate the relationship between isokinetic torque and muscle fiber type composition (Coyle et al., '79; Froese and Houston, '85; Thorstens- son et al., '76; Suter et al., '93). The limita- tions of such studies are numerous: first, only one muscle is usually sampled (e.g., the vastus lateralis) for fiber type and fiber size characteristics, but the torque producing ca- pabilities of an entire muscle group is mea- sured for isokinetic torque. One may thus be comparing properties that have little to do

- Lf=5 mm .......... .... Lf=lO mm

Lf=14 mm - - - - - - -

.............................................

--.. .- -.

: I

0 0 N 8 m

Shortening Velocity (mm/s)

Fig. 8. Effect of fiber length on velocity power relation.

MOUSE FIBER PROPERTIES AND ARCHITECTURE

- F% =lo0

F% = 60 . . . .. . .. ..

F% = 20 - - - - - - -

I 0 0 0

51 z II :: 0

Shortening Velocity (mm/s)

Fig. 9. Effect of fast fiber percentage (F%) on velocity power relation. Note the increasing discontinuity in slope near V = 80, where slow fiber force goes to zero.

189

with one another. Second, the correlation between fast glycolytic fibers and large PCSA points out the danger of using a single param- eter to characterize a muscle. High isokinetic torques at a given velocity (or higher iso- kinetic torque at increasing velocity) may simply reflect the increased muscle force and power associated with increased PCSA. In fact, this was the very result presented by Schantz ('83), who demonstrated a signifi- cant correlation between isokinetic torque and quadriceps CSA as measured using mag- netic resonance imaging. Torque is the re- sult, not just of PCSA or fiber type or mo- ment arm, but of all these combined. These data point out the danger of implying causa- tion from correlation.

In summary, skeletal muscle function de- sign is based primarily on muscle architec- tural properties and is only slightly influ- enced by fiber properties. Muscle fiber size and type distributions probably result from activity patterns during development and are designed to provide efficient and complemen- tary contractile properties to a muscle's meta- bolic capacity. This can be inferred, for ex- ample, from the numerous quantitative histochemical studies that show a strong negative correlation between fiber oxidative capacity and fiber size but a much weaker

correlation between fiber type and fiber size (Jiang et al., '90, '91). Further studies are required to identify the factors responsible for determination of these architectural and fiber type and fiber size characteristics.

ACKNOWLEDGMENTS

The authors thank Dr. Sue Bodine and Dr. Dave Pierotti for helpful discussions. This work was supported by the Veterans Admin- istration and NIH grant AR35192.

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