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Departments of 1Physical Therapy and 5Rehabilitation, Lund University Hospital, SE-22185, and 6Department of Community Medicine, Lund University, SE-22100 Lund, Sweden; 2Faculty of Physical Education and Recreation Studies, University of Manitoba, Winnipeg, Canada, R3T 2N2; 3Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom; 4Copenhagen Muscle Research Centre, Department of Molecular Muscle Biology, DK-2100 Copenhagen, Denmark; and 7Department of Health Sciences, Luleå University of Technology, SE-96136 Boden, Sweden
Submitted 13 June 2002 ; accepted in final form 9 July 2003
| ABSTRACT |
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magnetic resonance imaging; skeletal; muscle contraction; muscle fibers; sex characteristics
50% of the TA power is used (25, 26). During rapid walking and sudden corrective movements, the TA activity is much higher; an EMG study has shown that almost all TA motor units are recruited during these movements (26). The DF are also important for balance control during perturbations in a standing position (5) and for controlling foot stability during the stance phase in normal walking (34). Against this background, it is conceivable that a reduction in the function of the DF can impair functional performance (10, 16, 49, 55). An increased knowledge of the strength, size, and fiber-type composition of the DF can therefore improve the understanding of the mechanisms underlying muscle dysfunction and aid in the design and evaluation of intervention therapy to alleviate the dysfunction.
Strength is largely determined by muscle size (see for example Refs. 13, 38). However, the relationship between DF strength and size has only been addressed in three studies (14, 15, 29); the correlation coefficients were very similar (r = 0.770.87), given the heterogeneity of the samples. These studies have shown that muscle size is a major determinant of DF strength, and
6076% of the variation in DF strength is explained by DF size, or more specifically by the muscle cross-sectional area (CSA) or muscle volume. Because a substantial portion, up to 40%, of DF strength cannot be explained by DF size alone, other factors must contribute. Differences in the fiber-type composition, i.e., the numbers, areas, and proportions of type I (slow-twitch) and type II (fast-twitch) fibers and relative myosin heavy chain (MHC) content, may explain some of the variation in strength. Several studies have shown a positive relationship between the percentage of type II fibers in the vastus lateralis muscle (VL) and quadriceps strength (6, 41, 48, 52). Other studies of the VL (7, 37), of the plantar flexors (53), and of the elbow flexors (7, 42) have found that the fiber-type composition and strength were not significantly correlated. No study has examined the relationship between the fiber-type composition and strength in the DF.
Men are generally stronger and have larger body size, i.e., body height and weight, and muscle mass, than women. To account for these size differences, strength has been expressed relative to body weight, fat-free mass, or muscle size measurements, for example muscle CSA; this is often referred to as specific strength (strength/muscle CSA). Specific strength for the DF, determined as isometric or isokinetic concentric strength per unit muscle, has been found to be similar for men and women (15, 29). These findings, consistent with studies of other muscle groups (38, 45), support the notion that differences in strength between the sexes are primarily due to differences in muscle size. The determinants of muscle size in men and women are not fully known. Both fiber number and fiber area contribute to muscle size, but to a varying degree (31). No study has determined the relationship between DF size and fiber-type composition of the TA, the main DF.
The aims of this study were to assess the relationships between DF strength, DF size, and TA fiber-type composition and to examine potential sex-related differences in 30 young, healthy, and moderately active men and women with similar physical activity patterns. We ascertained determinants of DF strength and then identified determinants of DF size. Throughout the study, we evaluated the extent by which sex influenced the determinants of DF strength and DF size. DF strength was assessed by measurements of isokinetic concentric (Con) and eccentric (Ecc) peak torque, and DF size was assessed from magnetic resonance images. The fiber-type composition of the TA was determined from multiple muscle biopsies. The hypotheses were that 1) DF size and TA fiber-type composition, height, and weight in both men and women can explain most of the variation in DF strength; 2) fiber-type composition of the TA, height, and weight explain most of the variation in DF size for both men and women; and 3) sex-related differences in DF strength and DF size are a reflection of differences in height and weight between men and women.
| MATERIALS AND METHODS |
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24 h/wk). None of the subjects were involved in specific training programs for strength or for athletic events. All measurements were done on the dominant leg. Leg dominance was determined to be the leg preferred for hopping or kicking a ball; all 30 subjects preferred the right leg. Data on the capillary supply and maximal enzyme activities obtained from biopsies of these 30 subjects have been presented previously (27, 40). Data on the contractile and noncontractile components of the DF by muscle by MRI have also been presented previously (22). Isokinetic strength measurements. DF strength measurements were obtained from the Biodex Multi-Joint System II isokinetic dynamometer (Biodex Medical Systems, Shirley, NY) with the Biodex Advantage software version 4.0. All isokinetic tests were done by one person (A. M. Holmbäck; for details, see Refs. 23, 24). After a 5-min warm-up on a cycle ergometer, each subject was seated on the Biodex chair, with the angles of the hip and knee joints at 80°flexion (0° neutral position) and 30° flexion (0° straight leg), respectively. Start and end-range settings on the isokinetic equipment were standardized for all subjects between 20° plantar flexion and 10° dorsiflexion. This range of motion was selected to ensure that all peak torque measurements for the 30 men and women always occurred within the range of motion. Mean values and standard deviations at the joint angles at which peak torque occurred during Con contractions at 30 and 90°/s were 10.5 ± 1.6° and 6.8 ± 2.8° plantar flexion, respectively. Corresponding values during Ecc contractions were 14.3 ± 5.7° plantar flexion at 30°/s and 13.2 ± 4.8° plantar flexion at 90°/s. There was no significant difference between the men and the women.
Before testing, familiarization with the equipment and testing procedures was done with the use of submaximal contractions. For the test procedures, three nonconsecutive maximal Con and Ecc contractions were performed at 30 and 90°/s. There was a 30-s rest between each maximal repetition, a 1-min rest between each angular velocity, and 2 min between the Con and the Ecc modes. Each subject was instructed to exert maximal voluntary effort by contracting as hard and as fast as possible during Con actions or to exert maximal voluntary effort by resisting the movement of the footplate during Ecc actions, but no verbal encouragement was given during the contractions. The highest of the three values (N · m) of the Con peak torque (PT) at 30°/s is called "PTCon30" and that at 90°/s "PTCon90"; the corresponding terms for the highest Ecc peak torques are "PTEcc30" and "PTEcc90." Peak torque variables for both Con and Ecc modes have high intrarater reliability: reported values of the intraclass correlation coefficient (ICC2.1) for the peak torque measurements exceeded 0.89, and the within-subjects coefficients of variation were between 3.6 and 9.2% (23, 24).
MRI measurements. A 1.5-T/64 MRI scanner (Siemens Magnetom Vision, Siemens Medical Systems, Erlangen, Germany) was used to quantify the contractile (cCSA) and noncontractile CSA of the relaxed DF. Proton T1-weighted spinecho axial plane imaging was used: repetition time 500 ms, echo time 12 ms, matrix 288 x 512, field of view 200 mm2, and slice thickness 5 mm. A scout image was obtained, and 20 transverse slices without interslice gaps were acquired. The slice with the largest DF anatomic CSA (aCSA; cm2) was selected, and a PC-based program (Ps2D, Pallas AB, Sweden) was used to determine the aCSA and cCSA (cm2) and the absolute (cm2) and relative CSA (%) of noncontractile tissue components of the DF compartment (for details, see Ref. 22). Measurements of contractile and noncontractile components, obtained from the same image, have high intrarater reliability: reported values of ICC1,1 for the measurements exceed 0.94. The within-subjects coefficient of variation was 0.7% for contractile components and 9.6% for noncontractile components (22). All MRI measurements were performed within 1 wk of the strength measurements. The image analyses were performed by one individual (A. M. Holmbäck), who was blinded to the identity of the subjects.
Specific strength. Specific strength, was estimated by dividing each of the four PT measurements by the contractile CSA (cCSA).
Muscle biopsy preparations and analyses. Muscle biopsies were obtained from the right TA and were taken to represent the fiber-type composition of the whole DF. The DF compartment is to a great extent (>65%) made up of the TA (47). A previous animal study has shown a similar fiber-type composition of the TA and extensor digitorum longus (32), but no study has in detail compared the fiber-type compositions of these two muscles in humans. All biopsies were taken by the same individual (J. Lexell) using the conchotome technique, close to the level of the largest DF aCSA determined from the MRI measurements. The biopsy procedure was performed within 1 wk after all the other measurements. One to four biopsies (5080 mg each) were taken from each subject, with the average being 2.7 ± 0.7. Each muscle biopsy was trimmed and mounted on cork disks, frozen in isopentane cooled with dry ice, and stored below 80°C.
For the determination of the relative amount of MHC, a total of 2030 serial cross sections (20 µm) were cut from each biopsy and placed in 100 µl of lysing buffer, heated for 5 min at 90°C (12). Five to 20 µl of the myosin-containing samples were loaded on SDS-PAGE gels containing 6% polyacrylamide (acrylamide:bis-acrylamide, 75:1) and 30% glycerol. To improve band resolution, 400 µl of 2-mercaptoethanol were added to the upper electrode buffer (per 500 ml of buffer) (4). Gels were run at 70 V for 42 h at 4°C (2). Subsequently, the gels were Coomassie stained, and three MHC isoform bands, corresponding to MHC1, MHC2a, and MHC2x, were resolved and quantified by use of a densitometric system (Cream 1-D, Kem-En-Tec Aps, Copenhagen, Denmark). In biopsies from 24 of 30 subjects, only MHC1 and MHC2a were found; in biopsies from the remaining 6 subjects (3 men, 4 women), very small amounts of MHC2x (<1.4%) were found.
For the morphological determination of the areas and proportions of the different fiber types, serial cryosections of 7 µm thick were cut from each biopsy and were stained for myofibrillar adenosine triphosphatase (mATPase) after pre-incubation at pH 10.4. Because the amount of MHC2x was extremely low, the differentiation of the type II subtypes was considered unnecessary. Fiber typing and morphometric measurements were made from eight to nine images from each subject, and an average of 690 ± 130 fibers (502991) was counted to estimate the proportion (%) of type I (Prop I) and type II (Prop II) fibers. To determine the mean fiber areas (µm2) for each subject (Area I and Area II for type I and type II fibers, respectively), an average of 180 ± 47 type I fibers (108273) and 81 ± 40 type II fibers (23194) were measured by use of Image Pro Plus version 3.0 (Media Cybernetics, Silver Spring, MD). All fiber typing and area measurements were done by one individual (M. M. Porter) who was blinded to the subjects' identity until completion of all measurements.
Several morphologically derived variables were also determined. The ratio of Area II to Area I was calculated to provide an index of the relative sizes of the two fiber types. The relative areas of type I fibers (Rel I) and type II fibers (Rel II) were calculated as the product of the proportion of that type and the corresponding mean area. Rel I and Rel II were then used to estimate the relative type I area [Rel I/(Rel I + Rel II)] and the mean fiber area (Rel I + Rel II); the relative type I area represents the proportional area of the muscle occupied by type I fibers. The total number of muscle fibers in the whole DF was estimated indirectly by dividing the cCSA for each individual by the mean fiber area for that individual.
Statistical analysis. Throughout, differences between the sexes were tested by using nonpaired t-tests. Differences between the men and women for PT at the two velocities and for the two contraction modes were tested by repeated-measures ANOVA. The relationship between the relative type I area and the relative MHC1 content was determined by a linear regression analysis.
To identify possible determinants of DF strength and of DF size, several variables were considered simultaneously with the use of multiple-regression analyses. The purpose of each analysis was to identify simple models that fitted the data: models that include few explanatory variables and that are of a simple mathematical form are called parsimonious models. More than one parsimonious model might be identified in an analysis. For each model, the data for men and women were analyzed together with sex treated as an additive effect. The adequacy of every fit was assessed by examining bivariate scatterplots, the overall F statistic from the ANOVA table, the plots of the observed values against the predicted values, and residual plots. Parsimonious models are reported together with the adjusted R2 values as assessments of the goodness-of-fit.
Possible determinants of DF PT (PTCon30, PTCon90, PTEcc30, and PTEcc90) were addressed in the first set of analyses. The following variables were considered as explanatory variables for the DF PT measurements: height, weight, cCSA, Prop I, Area I, and Area II. For each independent variable and each strength measurement, simple scatterplots were formed and relationships were assessed by correlation coefficients.
Five determinants of cCSA were considered in the second set of analyses: height, weight, Prop I, Area I, and Area II.
Because there was a significant difference in age between the men and the women, age was considered in the multivariate analyses. Furthermore, all the multiple-regression analyses that included cCSA were repeated with aCSA replacing cCSA. We also replaced height and weight by body mass index (BMI), and Prop I by MHC 1. These variables did not significantly influence the results and are therefore not reported. Transformations of the original covariates were also considered, for example, the square roots of Area I and Area II.
Values throughout are given as means ± SD. The percent differences for each variable are the relative amounts by which men exceeded women. Exact significance levels are given for values between 0.001 and 0.10, <0.001 is given for smaller values, whereas NS represents significance >0.10; statistical significance is represented by values <0.05. Throughout the analyses, SPSS versions 10.1 and 11.0 were used.
| RESULTS |
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The difference between the men and the women was significant for each DF PT measurement (P = 0.005 to P < 0.001; Table 2). The difference between the two velocities for Ecc PT was not significant for either sex but was significant for both sexes for Con PT, for which the values at 30°/s were significantly greater than those at 90°/s (P < 0.001). The differences between the men and the women were greater for Ecc PT than the differences for Con PT (P < 0.001).
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There was a significant difference between the men and the women for both aCSA and cCSA, whereas the absolute and relative noncontractile tissue components were not significantly different between the sexes (Table 3). The values of Ecc specific strength were significantly higher for the men than for the women (P < 0.01), but there were no differences between the sexes for Con specific strength (Table 4).
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Prop I, relative type I area, MHC1, MHC2a, and MHC2x did not differ significantly between the sexes (Table 5). The men had significantly larger mean areas of type I and type II fibers (Area I and Area II) and larger type II/type I fiber area ratio (Area II/Area I) than the women. Because Prop I was very similar for the men and the women, the differences between sexes for Rel I and Rel II were almost the same as the difference between sexes for Area I and Area II and are therefore not reported in Table 5. There was a significant relationship (r = 0.53; P = 0.002) between the relative type I area and the relative MHC1 content. The mean difference between the relative type I area and the relative MHC1 content was 3.4 ± 8.0%.
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The mean fiber area was significantly different (+24.5; P < 0.001) between the men and the women, whereas the estimated total number of fibers for the whole DF was not significantly different (7.5%; NS) between the men (219,611 ± 34,726) and the women (236,184 ± 33,685).
Determinants of strength. The relationships between the four DF PT measurements and cCSA are presented for men and women in scatterplots (Fig. 1, AD). In all cases, the relationships between cCSA and the four DF PT measurements were significant (r = 0.58 to r = 0.85; P = 0.025 to P < 0.001). There were significant relationships between each of the four DF PT measurements and height, weight, BMI, Area I, and Area II when the men and women were combined (r = 0.37 to r = 0.74; P = 0.044 to P < 0.001).
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There was also a significant relationship between PTCon30 and Prop I (r = 0.53; P = 0.044) and between PTEcc30 and Prop I (r = 0.67; P = 0.007) for the men, and between PTEcc30 and Area II (r = 0.53; P = 0.044) for the women.
The parsimonious models with the PT variables as the dependent variables are summarized in Table 6. The most dominant factor in determining the four PT measurements was cCSA (P < 0.001): cCSA was included in each model, sex and Prop I had a secondary effect, and the effects of the other explanatory variables were not significant. Sex had a significant effect in the models with Ecc PT as the dependent variable, but not in the models with Con PT. Prop I was significant for PTCon30 and PTEcc30. The four models explained 5381% of the variation in the PT measurements. For PTEcc30, 72% of the variation was explained by cCSA: sex and fiber-type characteristics explained an additional 9% of the variation. In all cases, variables other than cCSA contributed at most 9% of the variation.
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Determinants of muscle size. There were no significant relationships between cCSA and height, weight, Prop I, Area I, Area II, mean fiber area, and the total number of fibers for men, whereas for the women there were significant relationships between cCSA and the following four variables: weight (r = 0.61; P = 0.015), Area I (r = 0.57; P = 0.025), Area II (r = 0.53; P = 0.044), and mean fiber area (r = 0.67; P = 0.007).
A reasonably close fit (adjusted R2 = 0.57) was achieved with weight (P = 0.002) and Area I (P = 0.017) as predictors of cCSA in the parsimonious model with cCSA as the dependent variable. Sex was not included in the model. If Area I was replaced by Area II, then the fit was almost as good, because Area I and Area II are so closely related (for men and women combined, r = 0.81, P < 0.001).
| DISCUSSION |
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Strength, size, and fiber-type composition of the DF. Our data are comparable with other studies of the DF and other muscle groups: men are generally taller, heavier, and stronger and have larger muscle size than women. Data on the fiber-type composition of the DF of young healthy men and women with comparable physical activity patterns have not been presented previously. A few biopsy studies (18, 25, 43) and autopsy studies (21, 28) have assessed the fiber-type composition; mainly men were studied and the physical activity pattern of the subjects was not reported. The mean proportion of type I fibers in the present study was similar to values in previous studies; the mean proportion of type I fibers has ranged from 72 to 78% (18, 21, 25, 28, 43). No study has previously compared the MHC content for the TA of young healthy men and women with similar physical activity patterns. The proportion of type I fibers and the MHC1 content were very similar for the men and the women. Previous studies of the VL have found a slightly lower proportion of type I fibers in men than women (46), but these authors biopsied subjects with various training backgrounds.
The areas of both fiber types and the type II-to-type I fiber area ratio were significantly larger in the men than in the women. Similar values and sex differences have been found previously for the TA (18, 19, 20). The differences between fiber types and between men and women are larger than for other muscles such as the VL (46). This may be due to the different use of the TA compared with the VL and the lower proportion of type II fibers in the TA.
The MHC analysis showed virtually no MHC2x in these moderately active young men and women. Previous studies of other muscles in sedentary subjects have reported higher proportions of MHC2x (618%) (51). The TA is used in many regular daily activities, and during some of these activities all TA motor units are recruited. Physical activity and training are known to reduce the amount of MHC2x and increase either MHC1 or MHC2a, depending on the type of activity (51). The high proportion of type I fibers as well as the almost nonexisting levels of MHC2x in the TA of these moderately active young men and women therefore reflect the specific use of the TA.
Determinants of strength. The Con DF strength and cCSA measurements were strongly correlated for both men and women: r values ranged from 0.66 to 0.71 (P < 0.007). These results support previous studies that DF size (cCSA) is a strong predictor of DF strength (14, 15, 29). A similar degree of correlation between strength (isometric force or isokinetic Con strength) and size has also been found in other muscle groups: for VL, r values range from 0.51 to 0.70 (1, 38), for elbow flexors from 0.80 to 0.91 (13, 42), and for plantar flexors from 0.73 to 0.76 (3, 53). Even though cCSA was a strong predictor of DF strength in the present study, not all of the variation in DF strength could be explained by DF size.
Another predictor of DF strength explored here was the fiber-type composition. The multivariate statistical analysis, which included fiber-type composition, body size measurements (height, weight, and BMI), cCSA, and sex, showed that cCSA was indeed the strongest predictor of Con DF strength. A total of 5372% of the variation could be explained by cCSA (Table 6). For Con DF strength at the lower angular velocity (30°/s), a negative relationship with Prop I also predicted strength, but only to a minor extent; the higher the percentage of type II fibers, the greater was Con DF strength at 30°/s. The sex factor was not significant in explaining the variability of Con DF strength. Thus cCSA and fiber-type composition can explain a major part of the variation in Con DF strength, but other factors also contribute. Specific strength (strength/cCSA) in the Con mode did not differ between the men and the women, consistent with previous reports of DF specific strength (15, 29) and specific strength for other muscle groups (38, 45). This indicates that differences in Con DF strength between the sexes are primarily due to muscle size.
Ecc DF strength and cCSA were strongly correlated: r values ranged from 0.58 to 0.85 (P < 0.025). We are not aware of any studies reporting the relationship between Ecc DF strength and DF size. The multivariate analyses further confirmed that cCSA, together with fiber-type proportion and sex, could explain
80% of the variation in Ecc strength. Thus, in contrast to Con DF strength, sex was a significant factor: for the same amount of muscle, men produced more Ecc torque. Consequently, specific strength in the Ecc mode was significantly higher for the men than for the women. Sex differences in knee extensor and flexor specific strength have previously been reported (35): men had significantly higher specific strength in the Ecc mode, but also in the Con mode. In another study (8), knee extensor and flexor specific strength was similar for men and women in the Ecc mode, but significantly higher for men in the Con mode.
Explanations for these conflicting findings on sex-related differences in specific strength are unclear. Several factors may be responsible: for example, the diversity of muscle groups studied, the isokinetic methodologies used, the different techniques for determining specific strength, or the differences in activity level between the subjects. The methodologies to determine muscle size have also varied, for example using body weight (8) and dual-energy X-ray absorptiometry (35). Because we used a technique to determine DF size that corrected for the noncontractile tissues (MRI), specifically within the DF, this method of determining specific strength can be considered more precise than other methods. Another explanation for differences in specific Ecc strength between the sexes could be muscle activation in the Ecc mode. It appears almost impossible to maximally activate the muscle by voluntary commands during a maximum Ecc contraction (11, 54), and differences in activation between the sexes cannot therefore be excluded. In addition, sex differences in storage and utilization of elastic energy have been found (30, 33, 50), indicating that sex differences within the tendon-muscle complex could explain some of the variability of specific strength between men and women. Differences in activity level between the subjects have not always been controlled for, nor reported: we selected individuals on the basis of their activity level to ensure comparable patterns of physical activity and thereby minimized differences due to training status. Further studies are needed to confirm this sex difference in specific Ecc strength and its potential implications, for example, in running performance, the development of training programs, and the susceptibility to injuries in high-performance athletes.
Determinants of muscle size. The cCSA for the men was significantly greater than for the women. The cCSA was more variable for the women, because of two women having larger cCSA than the average value for the men. For the women, there were significant relationships between cCSA and weight, Area I, and Area II, but for the men no relationships were significant. The lower variance in cCSA for men compared with women may explain the lack of significant relationships, but specific sex differences could still be determinants of cCSA. Previous studies have shown a relationship between muscle size and fiber-type composition of the VL (31, 44). We have found no studies with a sufficiently large number of men and women with similar activity pattern examining fiber-type composition and muscle size of the DF. Thus it still remains to be determined whether there are specific differences between men and women with regard to the fiber-type composition and muscle size relationship.
Body weight and fiber areas explained 57% of the variation in DF size; from the multivariate analysis, sex was not a significant factor. Because over 40% of the variation in cCSA in the present study has not been explained, other factors must contribute to the size of the ankle dorsiflexor cCSA. In an autopsy study of 31 previously healthy men, age 1583 yr, it was found that the CSA of the VL was determined mainly by the total number of fibers and to a lesser extent by the size and/or the number of type II fibers (31). A study of the autopsied TA muscle of seven previously healthy right-handed young men has also shown that the difference in size between the left and the right TA muscle was due to a significantly higher number of muscle fibers in the left TA, with no difference in muscle fiber size (47). It is therefore likely that fiber number also contributes to muscle size. In the present study, the total number of muscle fibers was estimated. However, this estimate comes from the cCSA. Therefore, we cannot use the estimate as an independent variable in the multivariate analysis and cannot determine the contribution of total number of fibers to the cCSA.
Limitations of the study. Clearly, a greater sample size could have provided more detailed inferences. For example, for PTCon90 there is some evidence that a curvilinear relationship could have been appropriate, and so a nonlinear model might be required when a larger sample of subjects is taken from a more heterogeneous population. Moreover, two women having larger cCSA than the average value for the men may partly explain the relationship between cCSA and Area I and Area II in women but not in men. Studies of sex differences in muscle structure and function clearly require that the sample of men and women is as homogeneous as possible with regard to training background. In reality, we can never select subjects with exactly identical physical activity patterns, and therefore any differences between men and women can be the result of differences in exercise intensity.
Several conclusions can be made from this study: men were stronger and had greater DF cCSA than women; Con DF strength was to a large extent determined by the cCSA of DF; specific strength (strength/cCSA) in the Con mode did not differ between men and women, suggesting that sex-related differences in Con strength measurements were mainly due to muscle size; Ecc DF strength was also highly influenced by cCSA, with fiber-type proportion and sex having minor effects; specific strength in the Ecc mode was significantly higher for the men than for the women; and body weight and fiber areas explained >50% of the variation in cCSA. These results show that, for the DF, strength and muscle size are closely related and also that specific sex differences exist. The difference in Ecc specific strength between men and women is unclear and requires further study.
| DISCLOSURES |
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| ACKNOWLEDGMENTS |
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| FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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