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Original Research

Muscle Force per Cross-sectional Area is Inversely Related with Pennation Angle in Strength Trained Athletes

Ikegawa, Shigeki1; Funato, Kazuo2; Tsunoda, Naoya3; Kanehisa, Hiroaki4; Fukunaga, Tetsuo5; Kawakami, Yasuo5

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Journal of Strength and Conditioning Research: January 2008 - Volume 22 - Issue 1 - p 128-131
doi: 10.1519/JSC.0b013e31815f2fd3
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Force exerted by muscle is closely related to its cross-sectional area (2,3,11,18). However, the ratio of force to cross-sectional area (F/CSA) shows quite a few individual variation, the reason for which has been a matter of debate (1,4,6,7,13,17).

The F/CSA of elbow flexor muscles is negatively correlated with muscle force (1,12) and CSA (16). Bodybuilders show smaller F/CSA as compared with less trained individuals (1). Bodybuilders have larger muscle fiber pennation angles (PA) than untrained individuals (5), and Kawakami et al. (7) found a decrease of F/CSA of the triceps brachii with increasing PA after resistance training. These findings hint to the notion that the pennation angle is inversely related with F/CSA, which results in substantially small F/CSA in athletes with hypertrophied muscles, such as bodybuilders. This possibility has been proposed in a previous study (5,7,13), but not has been confirmed so far.

Bodybuilders train to acquire muscles to their dimensional limit, and weightlifters focus to increase muscle force production in their own weight-categorized classes. We expected that any difference in these strength-trained athletes' F/CSA is related with interindividual differences in PA, and we tested this hypothesis by measuring muscle force, cross-sectional area and muscle fiber pennation angles in elite bodybuilders and weightlifters.


Experimental Approach to the Problem

To test the above hypothesis, we carried out measurements of muscle size, pennation angles, and muscle force in highly-trained bodybuilders and weightlifters and investigated any differences between subjects. The latter athletes perform Olympic lifting which consists of “snatch” and “jerk.” Both of these actions involve extension of the elbow joint in a ballistic manner by a high-velocity contraction of the triceps muscle. Consequently, Olympic lifting mainly focuses on explosive power. On the contrary, bodybuilders repeat single joint actions such as elbow extension (French press) with much slower movements, aiming to gain muscle hypertrophy. We therefore tested differences between them with respect to muscle architecture and force-producing capability.


Thirty-two male bodybuilders (age, 29 ± 9.2 years; height, 170.1 ± 6.1 cm; mass, 76.6 ± 15.6 kg; means ± SD) and 20 male weightlifters (18.1 ± 3.6 yr, 167.3 ± 7.0 cm, 70.2 ± 19.7 kg) served as subjects. There is no significant difference in body weight and height between two groups. All bodybuilders were ranked at an elite level by their successful performance in domestic competitions, and all weightlifters were highly ranked at an intercollegiate level. Prior to experiment, written informed consent to participate in the study was obtained from each subject. This study was approved by the Department of Life Sciences ethics committee at the University of Tokyo.

Muscle Force

Maximal voluntary isometric muscle force of elbow extension was measured with a specially designed isokinetic dynamometer (DTM, SAKAI medical electronics, Tokyo). Maximal isometric force of elbow extension was measured with the elbow angle flexed by 80 degrees. The subject was seated on an experimental chair with his trunk and thigh secured by strap belts, and the upper arm rested and fixed with a strap belt on a horizontal table with the wrist attached to the lever arm of the dynamometer. The force was measured at the wrist for three to five exertions, and the maximal score was converted to muscle force, by multiplying the ratio of the ulna length to the triceps brachii moment arm, derived from a previous study (14).

Muscle CSA

The CSA of the triceps brachii muscles was measured by an ultrasonic apparatus (ALOKA SSD-1920 with a circular compound scanner). This ultrasonic system was specially designed for measuring only the cross-section of limb. The ultrasonic transducer could move automatically around the limb without touching it. The frequency of the ultrasonic wave was 5MHz. Each subject placed the limb perpendicularly along the central axis of a water tank. The scanner, circulated around the tank for 30s and made an image of cross-section of upper arm. The scanning point was at a site 60% of the upper arm length, distal from the acromion process of the scapula. The ultrasonic cross-sectional image of the upper arm was photographed by a 35 mm camera. From the printed image, boundaries of subcutaneous fat and muscles and those of muscles and a bone were manually traced, and CSA of the triceps brachii was calculated by planimetry. The accuracy and validity of measurements have been confirmed in a prior study (3).

Muscle Fiber Pennation Angles

The muscle fiber pennation angle (PA) was defined as the angle between the fascicle and the aponeurosis, i.e., the vertical inclination of fibers from the long axis of muscle. The pennation angle of the long head of triceps brachii was measured by a B-mode ultrasonic apparatus (ALOKA SSD-500) at the same site as that of the CSA measurement. The subjects stood with their arms relaxed in extended position. The center of probe of ultrasonic apparatus was set at the dermal surface of scanning point with water-soluble transmission gel. Before the measurement, the subject extended his elbow and exerted slight isometric force. The tester visually confirmed the muscle belly of the long head of triceps brachii. The angle between the echoes of the aponeulosis of the triceps and the echoes from interspaces among the fascicles were measured and defined as the muscle fiber pennation angle (PA). The reason for the same relative position over subjects was to obtain PA from the same relative position of the muscle, to exclude intra-muscle variability of PA (8,19). The accuracy and validity of measurements have been confirmed elsewhere (5).

Statistical Analyses

Values are presented by means ± SD. Differences between bodybuilders and weightlifters were tested by a student's t-test. When there was a significant relationship between parameters, a simple linear regression was calculated by using the least squares method, and a Pearson correlation coefficient was calculated. The probability level accepted for statistical significance was set at P ≤ 0.05.


The CSA was significantly greater in bodybuilders (36.8 ± 10.3 cm2) than in weightlifters (23.6 ± 5.9 cm2). The mean maximal isometric muscle force of bodybuilders was 4499 (±1157) N, which was significantly greater than 3553 (±725) N of weightlifters. The ratio of maximal isometric muscle force to CSA (F/CSA) of bodybuilders (127.7 ± 34.1 N/cm2) was, on the other hand, significantly smaller than weightlifters (153.5 ± 22.4 N/cm2). The mean PA of bodybuilders was significantly larger than that of weightlifters (Table 1).

Table 1
Table 1:
Group mean data for CSA, F, PA and F/CSA

There was a significant positive correlation between muscle force and CSA both for bodybuilders (r = 0.580, P < 0.001) and weightlifters (r = 0.823, P < 0.001) (Figure 1). Also, muscle CSA positively correlated with PA in both groups (r = 0.832, P < 0.001, and r = 0.682, P < 0.001, for bodybuilders and weightlifters respectively) (Figure 2). Furthermore, F/CSA was negatively correlated with PA in both groups (Figure 3).

Figure 1
Figure 1:
The relationship between elbow extension force (F) and cross-sectional areas (CSA) of the triceps brachii muscles. Individual values are plotted for bodybuilders (•) and weightlifters (○). There are significant positive relationships between these variables in both groups.
Figure 2
Figure 2:
The relationship between the pennation angle (PA) and muscle CSA. Individual values are plotted for bodybuilders (•) and weightlifters (○). There are significant positive relationships between these variables in both groups.
Figure 3
Figure 3:
The relationship between F/CSA and PA. Individual values are plotted for bodybuilders (•) and weightlifters (○). There are significant negative relationships between these variables in both groups.


In the present study, we measured muscle force, CSA, and fiber pennation angles in bodybuilders and weightlifters. Bodybuilders had larger force, CSA, and pennation angles, and smaller F/CSA compared with weightlifters. The F/CSA was negatively correlated to PA both in bodybuilders and weightlifters. The results strongly suggest that the larger pennation angle is associated with lower force generating capacity in strength trained athletes. But in the weightlifters, the ranges of both pennation angles and F/CSA were smaller in weightlifters, thus this negative effect is less pronounced in these athletes.

In the present study, PA of the triceps brachii was closely related to CSA. This is in agreement with previous studies that measured PA of the quadriceps femoris muscles (15) and triceps brachii muscles (5). Moreover, the present result is not consistent with the study of Rutherford and Jones (15) that reported no correlation between PA and CSA for the quardriceps femoris muscles. This might be due to a small variation in pennation angles in the vastus lateralis and intermedius (6-16°) in the their study compared with those of triceps brachii (13-55°) determined in the present study.

The physiological cross-sectional area (PCSA), which is the sum of CSA of all muscle fibers at right angles to their long axes, represents the number of sarcomeres in parallel, and accordingly, is related directly to the amount of tension that the muscle can generate (5,7). The PCSA of a pennate muscle is given by the following equation, i.e.,

where MV is muscle volume and FL is muscle-fiber length. Cosine of PA translates the line of action of each muscle fiber to the direction of tendon. If a muscle has greater PA, this would be disadvantageous for force transmission from muscle fibers to tendon. Therefore, it is quite possible that greater PA results in lower F/CSA, and in fact, Kawakami et al. (7) found a decreased F/CSA in the triceps brachii as a result of resistance training. Significant negative correlations between PA and F/CSA in both groups, and significantly larger PA in bodybuilders than in weightlifters strongly suggest the negative impact of larger PA on the observed difference in F/CSA. Maughan et al. (13) found a negative correlation between muscle CSA and F/CSA, and suggested architectural factors as a candidate of their finding. The present results provide experimental evidence for their speculation. We speculate that weightlifters train their muscles to the level at which muscle force is effectively produced, unlike bodybuilders whose primary objective is to increase muscle size. It is possible that inter-group difference was eminent for the triceps brachii muscles which are highly responsive to training with respect to muscle size and architecture (9).

In the present study, the ratio of muscle force to CSA of weightlifters was significantly higher than that of bodybuilders. Apart with the fact of a significant difference in F/CSA between the two groups (weightlifters higher than bodybuilders) which might be related to the explosive type training of weightlifters, both groups demonstrated negative correlations between F/CSA and PA. This result strongly suggests that higher pennation angles are associated with lower F/CSA in the present strength-trained athletes. Of the other contributors to the divergent F/CSA ratios, differences in the fiber type composition have been proposed. However, it has been reported that there is no effect of fiber type composition on F/CSA when isometric muscle force is used (10). An increase in the non-contractile connective tissues by training might be the source of possible explanations for a decreased F/CSA in bodybuilders. However, MacDougall et al. (10) reported that the proportion of connective and other noncontractile tissues was similar between bodybuilders and untrained subjects. Thus, the contribution of noncontractile tissues to the increase in muscle CSA, if any, would be of a minor effect.

It should be noted that only the long head of the triceps brachii muscles was tested for PA, neglecting architecture of the other two (medial and lateral) heads. It has been shown that PA of the medial head increases similarly to that of the long head in hypertrophied muscles (5). Although no information is available for the architectural feature of the lateral head, by considering the fact that the long and medial heads occupy most of the triceps volume (20), we feel it justified to conclude that PA significantly affects F/CSA for the triceps muscles. Another issue to note is that in this study, only isometric, single joint action was tested. Future study is warranted to clarify the relationship between muscle size, architecture and dynamic force- and power-producing capability.

In summary, we found greater isometric muscle force, CSA and PA in bodybuilders than in weightlifters. However, muscle force per CSA was smaller for bodybuilders, and it negatively correlated with CSA and PA in both groups. It was suggested that isometric muscle force per CSA is significantly influenced by muscle fiber pennation angles.

Practical Applications

Athletes who wish to gain muscle strength normally perform resistance training, often aiming muscle hypertrophy. Based on our findings, we suggested that the possibility of a decrease in isometric force per muscle mass due to excessive muscle hypertrophy such that observed in bodybuilders. For the athletes of sport events in which force exertion is an important issue, training regimens should be cautiously organized to optimally increase muscle strength.


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muscle force and cross-sectional area; pennation angle; triceps brachii

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