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Assessment of muscle volume and physiological cross-sectional area of the human triceps surae muscle in vivo
ARTICLE IN PRESS
Journal of Biomechanics 41 (2008) 2211–2218 www.elsevier.com/locate/jbiomech www.JBiomech.com
Assessment of muscle volume and physiological cross-sectional area of the human triceps surae muscle in vivo K. Albrachta, A. Arampatzisa,, V. Baltzopoulosb a
Institute of Biomechanics and Orthopaedics, German Sport University Cologne, Germany Institute for Biomedical and Clinical Research into Human Movement and Health, Manchester Metropolitan University, UK
b
Accepted 18 April 2008
Abstract The purpose of the present study was to investigate whether it is possible to predict the individual muscle volumes within the triceps surae (TS) muscle group by means of easily measurable parameters based on a theoretical consideration. A further objective was to verify the use of the available literature data to assess the contribution of each muscle of the group to the entire TS volume or physiological cross-sectional-area (PCSA). Therefore, magnetic resonance images of the right calf of 13 male subjects were acquired and each muscle of the TS was reconstructed. Muscle length (l m ), the maximum anatomical cross-sectional-area (ACSAmax ) and muscle volume were obtained from the 3D models. To assess the PCSA, fascicle length was determined by ultrasonography. In general, muscle volume can be expressed as a fraction of the product of ACSAmax and l m . The size of the fraction depends on muscle shape and its coefficient of variance among the examined population was considerable low (soleus 6%, gastrocnemius 4% and gastrocnemius lateralis 7%) in the present study. The product of ACSAmax and l m was, therefore, suitable to assess muscle volume (root mean squares, RMS 4–7%). Further, the soleus, gastrocnemius medialis and gastrocnemius lateralis accounted on average for about 52 3%, 32 2% and 16 2% of the total TS volume and 62 5%, 26 3% and 12 2% of the entire TS PCSA, respectively. The coefficient of variance of the relative portions were 5–10% for muscle volume and 8–17% for the PCSA. r 2008 Elsevier Ltd. All rights reserved. Keywords: MRI; Muscle reconstruction; Triceps surae muscle; Muscle volume; Volume distribution; PCSA distribution
1. Introduction The assessment of human muscle volume is essential when evaluating muscle performance and functional consequences of changes in muscle size and strength due to training, aging or immobilization (Aagaard et al., 2001; Kawakami et al., 2000; Thom et al., 2005). The maximum force-generating capacity of a muscle is proportional to the physiological cross-sectional-area (PCSA) (Haxton, 1944), which can be approximated from muscle volume and fascicle length (Alexander and Vernon, 1975; Powell et al., 1984). Furthermore, assuming homogeneous muscle density, muscle volume is a determinant of muscle mass, a parameter, which is needed to gain insight into the specific Corresponding author. Tel.: +49 221 4982 5620; fax: +49 221 4971598. E-mail address: [email protected] (A. Arampatzis).
0021-9290/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.04.020
muscle tension (Lynch et al., 1999), and to determine energy cost and muscle efficiency of certain contractions through modeling (Houdijk et al., 2006). For in vivo measurement of muscle volume, magnetic resonance imaging (MRI) is considered to be the most useful noninvasive imaging modality (Mitsiopoulos et al., 1998; Shellock, 1989). Despite recent improvements in image processing, a muscle reconstruction by MRI is still laborious and not widely applicable. Being essential for everyday activities such as walking (Winter, 1983) and stair negotiation (Riener et al., 2002) as well as in running (Winter, 1983) and sprinting (Stafilidis and Arampatzis, 2007), the triceps surae muscle group (TS) is frequently used in muscle modeling (Bobbert, 2001; Lichtwark and Wilson, 2007; Out et al., 1996). To estimate volume or PCSA of the individual TS muscles, data of muscle force-generating capacities or muscle volume derived from cadaveric studies are often applied to scale
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models of the muscle–tendon unit (Bobbert, 2001; Out et al., 1996). Using those data allow a better understanding of general principles of muscle function, but the comparability to individual muscle performance remains unclear. It is likely that data from cadaveric specimens do not accurately reflect absolute or relative sizes of muscles in young and healthy subjects (Tate et al., 2006). In addition, this approach implies that the distribution of muscle volume and PCSA is consistent within a muscle group among the population, although cadaveric studies (Friederich and Brand, 1990; Wickiewicz et al., 1983) are based usually on a few numbers of specimens. To our knowledge, there is no information available on whether the volume of the muscles within the TS can be estimated by less laborious measurements. Therefore, the aim of this study was to answer the question, whether it is possible to predict the individual muscle volumes within the TS by means of easily measurable parameters. A further goal was to verify the use of the available literature data to assess the contribution of each muscle of the group to the entire TS volume or PCSA. 2. Method
measurements, MRI as well as ultrasonography, were performed on the relaxed muscle and with the ankle and knee joints fixed at 90 and 180 , respectively (tibia perpendicular to the sole of the foot and the knee fully extended). The sonographic images were recorded along the mid-sagittal line of the gastrocnemius medialis muscle (GM), the GL and the SO at middistance between the proximal and distal tendon insertions using a B-mode, real-time ultrasonography (HDI-3000; ATL, Bothell, WA, USA) with a 3.8 cm linear array probe (7.5 MHz). In the sonographic images five evenly distributed points were digitized on each selected fascicle, the deeper and upper aponeurosis and a straight line was fitted through these five points in a least square sense (Fig. 1). The fascicle length was defined as the length between the two intersection points of the line corresponding to the fascicle and the lines corresponding to the upper and deeper aponeurosis. Transversal MRI scans were recorded, such that all three TS muscles were scanned from origin to insertion. The MRI was performed using a 0.2 Tesla open scanner (E-Scan, Esaote Biomedica, Genova, Italy) and a T1 weighted turbo 3D protocol with the following parameters: time to echo 16 ms; repetition time 38 ms; pixel spacing 0:625 0:625 mm, field of view 15:9 15:9 cm, slice thickness 2 mm and no gap between slices. Since the scanning range of the used imaging coil was restricted to 7 cm, either six or seven overlapping recordings of contiguous transversal images were acquired to capture the entire calf. In order to combine the different sequences and to define the transversal plane, three coplanar markers were placed every 6 cm on the leg (Fig. 2). In every second transversal plane image, the muscle boundaries were outlined manually using a piecewise
2.1. Theoretical consideration The general volume calculation of a solid (f ðz; x; yÞ) using Cartesian coordinates is defined as ZZZ f ðz; x; yÞ dz dx dy. (1) V¼ V
If the origin of the coordinate system is located at the insertion of the muscle (myotendinous junction) and if the longitudinal axis of the shank coincides with the z-direction, the anatomical cross-sectional-area (ACSA) RR at a certain location (z) of the shank is ACSAðzÞ ¼ AðzÞ f ðx; yÞ dx dy and the muscle volume (V m ) can be calculated as Z lm ACSAðzÞ dz Vm ¼ 0
¼ ACSA l m
(2)
with ACSA as the mean ACSA and l m as the muscle length, defined as the distance between the muscle’s proximal and distal end. When expressing the mean ACSA as a fraction of the maximum anatomical cross-sectionalarea (ACSAmax ) Eq. (2) can be rewritten as V m ¼ p ACSAmax l m
Fig. 1. Ultrasonographic image of the gastrocnemius medialis muscle. The straight lines correspond to the fascicle () and the upper and deeper aponeurosis (.).
(3)
with 0opp1. Eq. (3) shows that in general the muscle volume is a fraction of the product of ACSAmax and l m . The size of the fraction, i.e. the value of p depends on the muscle shape. If we assume that the shape of the three TS muscles is similar within the population, the assessment of muscle volume should be possible from ACSAmax and l m .
2.2. Data acquisition Thirteen male adults (height 180 36 cm, mass 76 6 kg and age 29 6 years) volunteered for this study. All subjects were university staff or students and were at most active in recreational sports. MRI was performed to assess muscle volume. To estimate PCSA, fascicle length was measured using ultrasonography. The PCSA distribution could only be determined for nine subjects, as difficulties in the ultrasound images prevented the analysis of gastrocnemius lateralis muscle (GL) architecture in one case and of soleus muscle (SO) architecture in three cases. Both
Fig. 2. Transversal magnet resonance image of the calf with the three markers placed on the skin and the outlined contours of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles.
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GL GM
w
SO
u SO
v
Fig. 3. (a) Segmented transversal contours of the soleus (SO) muscle. (b) B-Spline solid of the triceps surae muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) . linear boundary provided by the software program 3D Doctor (ABLE SOFTWARE CORP., Lexington, MA, USA). For the most proximal and distal portions of the muscle the images were analyzed every 2 mm. Finally, 60–100 contour curves were computed for each muscle (Fig. 3a), which were exported as 3D-coordinates and processed using Matlab (The MathWorks, Natick, MA, USA).
2.3. Reconstruction For each muscle a continuous B-Spline solid was created from the 3Dcoordinates of the transversal contours (Fig. 3) using a method based on the one proposed by Ng-Thow-Hing and Fiume (2002). To create the BSpline solid a parametrization was performed, such that u increases radially outward from the central axis of the solid to its contour boundaries, v traverses the perimeter around the central axis and w runs along the longitudinal iso-parametric lines from the bottom to the top of the stack (Fig. 4). The central axis is defined as a curve running through the centroid points of the contours. A second degree B-Spline basis functions and a chord length parametrization were used in the v and w domains. A first degree B-Spline basis function was used for the parameter u. Correspondence between adjacent contours was found using the shape context algorithm (Belongie et al., 2002), a robust and simple algorithm for finding correspondence between shapes, represented by a set of points. This algorithm could be utilized, as the muscle boundaries did not vary much from slice to slice.
2.4. Data analysis From the reconstructed muscle the following parameters were determined: muscle volume (V m ), muscle length (l m ), defined as the
Fig. 4. B-Spline solid of the soleus muscle. The parametrization was performed, such that u increases radially outward from the central axis of the solid to its contour boundaries, v traverses the perimeter around the axis and w runs along the longitudinal iso-parametric lines from the bottom of the stack to the top. distance between the muscle’s proximal and distal end, and the maximum anatomical cross-sectional-area (ACSAmax ). The PCSA was calculated as V m l 1 f (Lieber and Fride´n, 2000) using the fascicle length (l f ) determined by ultrasonography. The theoretical consideration (Eq. (3)) shows that in general muscle volume is a fraction of the product of ACSAmax and l m . We hypothesized that the size of the fraction, i.e. the shape of the muscle, is maintained across the population. To test whether this assumption is valid, we considered the intersubject variability of the ratio between muscle volume and the product of ACSAmax and l m (the shape factor p). Furthermore, we examined the intersubject variability for the ratios between muscle volume and either ACSAmax or l m . As a measure for the intersubject variability the coefficient of variance (CV) is used. To evaluate the accuracy of assessing muscle volumes, the volumes were predicted on the basis of Eq. (3) and the root mean squares (RMS) between the measured and predicted values were calculated and expressed relative to the mean of the measured values.
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To determine whether muscle volume or PCSA distribution is consistent across the subjects, we proceeded in an analogous manner. The intersubject variability was determined from the relative portion of each
Table 1 Muscle properties of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) determined in the present study lm (cm) SO GM GL
ACSAmax ðcm2 Þ
3:39 3:1a,b 29 4a,b 2:78 1:8b 18 3b 2:39 1:6 11 2
Vm ðcm3 Þ
PCSA ðcm2 Þ
lf (cm)
477 66a,b 131 31a,b 3:9 0:9a,b 285 45b 51 10b 5:7 0:7b 146 23 24 5 6:6 0:7
Values are means SD; l m : muscle length; ACSAmax : maximum anatomical cross-sectional-area; V m : muscle volume; PCSA: physiological cross-sectional-area; l f : fascicle length. a Significantly different from GM (po0:05). b Significantly different from GL (po0:05).
Table 2 The mean standard deviation and the coefficient of variance (CV) of the ratio between muscle volume and the product of ACSAmax and l m , the ratio between muscle volume and ACSAmax , the ratio between muscle volume and l m
SO GM GL
V m =ðACSAmax l m Þ
V m =ACSAmax
Mean
Mean (cm)
CV (%)
Mean ðcm2 Þ
CV (%)
16:73 1:31 16:44 1:36 13:60 1:37
8 8 10
14:17 2:03 10:62 1:99 6:35 1:25
14 19 20
CV (%)
0:496 0:029 6 0:592 0:026 4 0:569 0:039 7
V m =l m
V m : muscle volume of the individual muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL); l m : muscle length; ACSAmax : maximum anatomical cross-sectional-area.
individual TS muscle to the entire TS. The total TS volume and PCSA is defined as the sum of GM, GL and SO muscle volumes and PCSAs, respectively. Muscle volumes and PCSAs were predicted from the total TS volume or PCSA using the mean proportional distribution.
3. Results The SO showed the largest l m , ACSAmax , muscle volume and PCSA, followed by the GM and GL (Table 1). Fascicle length was largest in the GL (Table 1). Further the SO, GM and GL accounted on average for about 52 3%, 32 2% and 16 2% of the total TS volume and 62 5%, 26 3% and 12 2% of the entire TS PCSA, respectively. Within each component of the TS the CV was lowest (4–7%) for the ratio between muscle volume and the product of ACSAmax and l m (shape factor p) followed by the ratio between muscle volume and ACSAmax (8–10%) (Table 2). The CV for the ratio between muscle volume and l m (14–20%) was more than twofold higher than the other values (Table 2). According to these results, the RMS between the measured and predicted muscle volumes were lowest using the product of ACSAmax and l m (4–7%) and highest using l m (14–20%) (Fig. 5). The predicted muscle volumes (Fig. 5) were obtained utilizing a linear equation with no intercept term and with a slope corresponding either to the mean ratio between muscle volume and the product of ACSAmax and l m , the mean ratio between muscle volume and ACSAmax or the mean ratio between muscle volume and l m , which are presented in Table 2. The portions of the individual muscles relative to the entire TS showed lower CV for the muscle volume (5–10%) than for the PCSA (8–17%) (Table 3). The muscle volume
700 RMS 6%
muscle volume [cm3]
600
RMS 7%
RMS 14%
500 RMS 4%
400
RMS 8% RMS 19%
300 RMS 7%
200
RMS 10% RMS 20%
100
GL GM SO
0 0
200 400 600 800 1000 1200 1400 5 ACSAmax*lm [cm3]
GL GM SO 10
15
20
25
ACSAmax [cm2]
30
35
GL GM SO 40
20
25
30
35
40
45
lm [cm]
Fig. 5. The measured values for muscle volume (scatter plot) in comparison with the predicted values represented by the solid lines. The predicted muscle volumes were obtained utilizing a linear equation with no intercept term and with a slope corresponding to the mean ratio between the muscle volumes and (a) the product of maximum anatomical cross-sectional-area and muscle length (ACSAmax l m ), i.e. the shape factor p, (b) the maximum anatomical crosssectional-area (ACSAmax ), and (c) the muscle length (lm ) for the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles. The values for the ratios are presented in Table 2. The root mean square (RMS) is expressed relative to the mean of the measured values.
ARTICLE IN PRESS K. Albracht et al. / Journal of Biomechanics 41 (2008) 2211–2218 Table 3 The relative portion of muscle volume and physiological cross-sectional area (mean SD) for each muscle of the triceps surae muscle group (TS) to the entire TS V =V TS
SO GM GL
PCSA=PCSATS
Mean ð102 Þ
CV (%)
Mean ð102 Þ
CV (%)
51:82 2:83 31:81 2:23 16:36 1:70
5 7 10
62:08 4:90 25:79 3:14 12:14 2:05
8 12 17
700 individual muscle volume [cm3]
RMS 5% 600 500 RMS 7%
300 RMS 10%
200
SO GM GL
100 0 700
800
900
1000
1100
1200
1300
1400
TS muscle volume [cm3]
180 RMS 7%
individual muscle PCSA [cm2]
160 140 120 100
RMS 12%
80 60
RMS 16%
40
SO GM GL
20 0 140
160
180
200
220
240
260
280
300
as well as the PCSA of the SO showed the lowest CV followed by the ones of the GM and GL (Table 3). Using the mean relative portions from Table 3 to predict the muscle volumes and PCSAs of the individual muscles from the entire TS, the RMS between the predicted and the measured values ranges from 5% to 10% and 7% to 17%, respectively (Fig. 6).
4. Discussion
V: individual volume of the muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GM); V TS : volume of the triceps surae muscle group; PCSA: physiological cross-sectional-area of the individual muscles group; PCSATS : physiological cross-sectional-area of the triceps surae muscle group; CV: coefficient of variance.
400
2215
320
TS PCSA [cm2] Fig. 6. The measured values (scatter plot) for (a) muscle volume and (b) PCSAs in comparison with the predicted values represented by the solid lines. The predicted values were obtained utilizing a linear equation with no intercept term and with a slope corresponding the mean relative portions of either the soleus (SO), gastrocnemius medialis (GM) or gastrocnemius lateralis (GL) to the entire triceps surae (TS). The values of the relative portions are presented in Table 3. The root mean square (RMS) is expressed relative to the mean of the measured values.
The aim of the present investigation was to provide a method for reliably estimating (a) the individual muscle volumes within the TS by means of easily measurable parameters and (b) to investigate whether the distribution of muscle volume or PCSA within the TS muscles is maintained across the examined population. The present study showed a considerable low intersubject variability for the ratio between muscle volume and the product of ACSAmax and l m (4–7%, Table 2) indicating that the shape of each muscle seems to be similar across the examined population. The size of the ratio, i.e. the value of p, was significantly different between the SO (0:496 0:029) and both gastrocnemii muscles (GM: 0:592 0:038, GL: 0:569 0:038), whereas there was no significant difference between the GM and GL indicating that their shapes are similar. Due to the considerably low intersubject variability of the value p, the assessment of muscle volume from ACSAmax and l m using Eq. (3) was possible with an acceptable accuracy (RMS: 4–7%). As Fig. 5 shows there was certainly a good prediction of muscle volume from ACSAmax , suggesting that the ACSAmax alone reflects the whole volume. However, when estimating the muscle volume from the product of ACSAmax and l m using Eq. (3) and thus including the third dimension, the intersubject variability of the ratio as well as the error of the prediction was about 1–4% lower compared with predicting the muscle volumes only from ACSAmax (Fig. 6, Table 2). Both independent variables in Eq. (3), l m as well as ACSAmax , are easily assessible in comparison with the entire muscle reconstruction. The location of ACSAmax in relation to the shank length (distance between the tuberositas calcanei and the tibia plateau) is well defined, since the standard deviation of the location was 4% of shank length for all three muscles (Fig. 7). The ACSAmax was located at about the same site for the GM (79 4%) and GL (81 3%), whereas it was located significantly more distal for the SO (66 4%). The widths of the 95% confidence intervals were 4–5% of shank length. With a mean shank length of 43 2 cm this corresponds to about 2 cm. We can conclude that, only one MRI sequence (width 2 cm) for both gastrocnemii and one for the SO are required to identify the ACSAmax of all three muscles. Furthermore, l m can be determined by identifying the muscle’s proximal and distal end using ultrasonography or MRI.
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35 SO
ACSA [cm2]
30 25 20 15 10 5 0 35
GM
ACSA [cm2]
30 25 20 15 10 5 0 35
GL
ACSA [cm2]
30 25 20 15 10 5 0 0
20
40
60
80
100
120
normalized shank length [%] Fig. 7. Anatomical cross-sectional-areas (ACSA) of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles along the length of the shank. 0% corresponds to the tuberositas calcanei and 100% corresponds to the tibia plateau. The thin gray lines represent the position of the maximum ACSA among the examined population. Solid lines indicate the means and dashed lines the standard deviations.
To answer the question whether the proportional distribution of muscle volume or PCSA within the TS is consistent among the examined sample, the important finding was that the intersubject variability of muscle volumes and PCSAs of the three individual TS muscles relative to the entire TS were 5–10% and 7–15%, respectively. In comparison, the intersubject variability of the absolute volumes and PCSAs were on average about two times higher (Tables 1 and 3). When using the mean proportional distribution to predict the muscle volume or PCSA of each individual TS muscle, the prediction was best for the SO followed by the GM and GL (Fig. 6). For the GL the error of prediction was about twofold higher than for the SO. This result is not surprising, since the SO contribution to the entire TS volume and PCSA is highest, whereas the GL contribution is lowest. Consequently, a prediction of each TS muscle volume or PCSA using the mean proportional distribution should be possible at least for the SO and GM. One could argue that, the SO and the two gastrocnemii are functionally different and composed of different fiber types (Johnson et al., 1973) and, therefore, muscle volumes or PCSAs of the individual muscles increase or decrease non-uniformly due to training, aging
or immobilization. Recently it has been shown (Morse et al., 2005c) that aging does not influence the PCSA distribution and that the muscle volume distribution changes only by 2–3%. It seems that in people who are exposed to normal daily activities, the variation of a nonuniform adaptation between the three constituents of the TS has only a marginal influence on the proportional distribution. The above findings may have important implications for studies dealing with muscle hypertrophy or atrophy due to training, aging or immobilization. To assess changes in muscle size, many studies only consider the ACSA (Frontera et al., 2000; Kanehisa et al., 2003) instead of the entire volume or PCSA. However, a muscle can adapt in size by adding sarcomeres either in parallel or in series (Butterfield et al., 2005). Muscle volume is directly related to muscle mass and PCSA to the muscle force-generating capacity. Therefore, muscle volume as well as the PCSA might be more appropriate to investigate muscle hyper- or atrophy. Muscle atrophy at the TS assessed by MRI has been reported to be about 12% in response to unloading or disuse of various durations (Berg et al., 2007; Kubo et al., 2004) and between 17% and 29% with aging (Morse et al., 2005a, c; Thom et al., 2005). Morse et al. (2005b) found an increase of 12% in TS volume after a 12 month strength training program for elderly. We determined RMS values of about 4–7% and thus changes of such magnitude are detectable with the prediction equations (Eq. (3)) provided in this study. Combining this method with ultrasonography to measure fascicle length allows an approximation of PCSA. The proportional distribution of PCSA is commonly used to estimate maximum isometric force of the three individual TS muscles. Especially studies applying models to assess the performance of a muscle–tendon unit rely on such information (Bobbert, 2001; Out et al., 1996; Woittiez et al., 1983), which is obtained from cadaveric studies e.g. Wickiewicz et al. (1983) and Friederich and Brand (1990). The volume distribution is also essential in modeling, but to estimate energy consumption rather than force-generating capacity. However, in the literature the information about the distribution of muscle volume and PCSA among the three TS muscles is rare. The available data are mainly based on cadaveric studies with a small number of specimens. The results of the present study support the use of the assumption that distribution of muscle volume and PCSA is consistent within the TS at least for people who are exposed to normal daily activities. In comparison with the existing cadaveric measurements of muscle volume and PCSA for the TS (Friederich and Brand, 1990; Wickiewicz et al., 1983) our results for the relative muscle volume as well as for the relative PCSAs showed smaller values for both gastrocnemii together and higher values for the SO (differences: 6–13%). To determine PCSA we proposed to use the formula based on muscle volume and fascicle length which is commonly used in the literature (Friederich and Brand,
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1990; Fukunaga et al., 1992; Huijing, 1985; Wickiewicz et al., 1983). At the moment a direct in vivo measurement of PCSA is almost not feasible, even though the further development of diffusion tensor imaging seems to provide a more direct measurement of PCSA (Galba´n et al., 2004; Heemskerk et al., 2005). The calculation of PCSA is based on the assumption that fascicle length remains constant within the muscle, which can be assumed for both gastrocnemii (Maganaris et al., 1998; Muramatsu et al., 2002) and for the largest part, the posterior part, of the SO (Maganaris et al., 1998). Further, most of the studies on cadaveric specimens (Friederich and Brand, 1990; Huijing, 1985; Wickiewicz et al., 1983) used a fascicle length normalized to the optimum sarcomere length. In vivo it is difficult to determine the optimum fascicle length. Utilizing maximal voluntary contractions the GM likely operates at the ascending limb of the force–length relationship through the entire range of motion (Winter and Challis, 2008). Therefore, we determined fascicle length at rest in the anatomical neutral position. A previous study (Arampatzis et al., 2007) indicated that in this position fascicle length of the TS muscle is near its optimum length, because the force-generating response to the twitch was maximal in this particular position. However, the given suggestion using this method is that all individual muscles of the TS act at the same position of the force–length relationship, which is a limitation of the used methods. The chosen joint configuration should rather be considered as a reference position, which is likely to be near the optimum fascicle length. In summary, the present study demonstrated that the shape factor p is maintained among the investigated population and, therefore, muscle volume can be approximated using the values of ACSAmax and l m . Both parameters are easily assessible in comparison with an entire muscle reconstruction. Furthermore, the proportional distribution of muscle volume and PCSA within the TS was consistent across the subjects. Therefore, the results of the present study support the use of the assumption that the distribution of muscle volume and PCSA is consistent within the TS at least for people who are exposed to normal daily activities.
Conflict of interest statement The authors disclose any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
Acknowledgments We thank Professor Dr. Constantinos N. Maganaris for his suggestions and support with the ultrasonography of muscle architecture and Dr. Dimitrios E. Tsaopoulos for his assistance during the measurements.
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References Aagaard, P., Andersen, J.L., Dyhre-Poulsen, P., Leffers, A.M., Wagner, A., Magnusson, S.P., Halkjaer-Kristensen, J., Simonsen, E.B., 2001. A mechanism for increased contractile strength of human pennate muscle in response to strength training: changes in muscle architecture. Journal of Physiology 534 (Pt. 2), 613–623. Alexander, R., Vernon, A., 1975. The dimensions of the knee and ankle muskles and the force they exert. Journal of Human Movement Studies 1, 115–123. Arampatzis, A., Mademli, L., Monte, G.D., Walsh, M., 2007. Changes in fascicle length from rest to maximal voluntary contraction affect the assessment of voluntary activation. Journal of Biomechanics 40 (14), 3193–3200. Belongie, S., Malik, J., Puzicha, J., 2002. Shape matching and object recognition using shape contexts. PAMI 24 (4), 509–522. Berg, H.E., Eiken, O., Miklavcic, L., Mekjavic, I.B., 2007. Hip, thigh and calf muscle atrophy and bone loss after 5-week bedrest inactivity. European Journal of Applied Physiology 99 (3), 283–289. Bobbert, M.F., 2001. Dependence of human squat jump performance on the series elastic compliance of the triceps surae: a simulation study. Journal of Experimental Biology 204 (Pt. 3), 533–542. Butterfield, T.A., Leonard, T.R., Herzog, W., 2005. Differential serial sarcomere number adaptations in knee extensor muscles of rats is contraction type dependent. Journal of Applied Physiology 99 (4), 1352–1358. Friederich, J.A., Brand, R.A., 1990. Muscle fiber architecture in the human lower limb. Journal of Biomechanics 23 (1), 91–95. Frontera, W.R., Hughes, V.A., Fielding, R.A., Fiatarone, M.A., Evans, W.J., Roubenoff, R., 2000. Aging of skeletal muscle: a 12-yr longitudinal study. Journal of Applied Physiology 88 (4), 1321–1326. Fukunaga, T., Roy, R.R., Shellock, F.G., Hodgson, J.A., Day, M.K., Lee, P.L., Kwong-Fu, H., Edgerton, V.R., 1992. Physiological crosssectional area of human leg muscles based on magnetic resonance imaging. Journal of Orthopaedic Research 10 (6), 928–934. Galba´n, C.J., Maderwald, S., Uffmann, K., deGreiff, A., Ladd, M.E., 2004. Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf. European Journal of Applied Physiology 93 (3), 253–262. Haxton, H.A., 1944. Absolute muscle force in the ankle flexors of man. Journal of Physiology 103 (3), 267–273. Heemskerk, A.M., Strijkers, G.J., Vilanova, A., Drost, M.R., Nicolay, K., 2005. Determination of mouse skeletal muscle architecture using threedimensional diffusion tensor imaging. Magnetic Resonance in Medicine 53 (6), 1333–1340. Houdijk, H., Bobbert, M.F., deHaan, A., 2006. Evaluation of a Hill based muscle model for the energy cost and efficiency of muscular contraction. Journal of Biomechanics 39 (3), 536–543. Huijing, P.A., 1985. Architecture of the human gastrocnemius muscle and some functional consequences. Acta Anatomica (Basel) 123 (2), 101–107. Johnson, M.A., Polgar, J., Weightman, D., Appleton, D., 1973. Data on the distribution of fibre types in thirty-six human muscles an autopsy study. Journal of the Neurological Sciences 18 (1), 111–129. Kanehisa, H., Funato, K., Kuno, S., Fukunaga, T., Katsuta, S., 2003. Growth trend of the quadriceps femoris muscle in junior olympic weight lifters: an 18-month follow-up survey. European Journal of Applied Physiology 89 (3–4), 238–242. Kawakami, Y., Muraoka, Y., Kubo, K., Suzuki, Y., Fukunaga, T., 2000. Changes in muscle size and architecture following 20 days of bed rest. Journal of Gravitational Physiology 7 (3), 53–59. Kubo, K., Akima, H., Ushiyama, J., Tabata, I., Fukuoka, H., Kanehisa, H., Fukunaga, T., 2004. Effects of 20 days of bed rest on the viscoelastic properties of tendon structures in lower limb muscles. British Journal of Sports Medicine 38 (3), 324–330.
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Lichtwark, G.A., Wilson, A.M., 2007. Is achilles tendon compliance optimised for maximum muscle efficiency during locomotion? Journal of Biomechanics 40 (8), 1768–1775. Lieber, R.L., Fride´n, J., 2000. Functional and clinical significance of skeletal muscle architecture. Muscle & Nerve 23 (11), 1647–1666. Lynch, N., Metter, E., Lindle, R., Fozard, J., JD, T., Roy, T., Fleg, J., Hurley, B., 1999. Muscle quality. i. age-associated differences between arm and leg muscle groups. Journal of Applied Physiology 86 (1), 188–194. Maganaris, C.N., Baltzopoulos, V., Sargeant, A.J., 1998. In vivo measurements of the triceps surae complex architecture in man: implications for muscle function. Journal of Physiology 512 (Pt. 2), 603–614. Mitsiopoulos, N., Baumgartner, R., Heymsfield, S., Lyons, W., Gallagher, D., Ross, R., 1998. Cadaver validation of skeletal muscle measurement by magnetic resonance imaging and computerized tomography. Journal of Applied Physiology 85 (1), 115–122. Morse, C.I., Thom, J.M., Birch, K.M., Narici, M.V., 2005a. Changes in triceps surae muscle architecture with sarcopenia. Acta Physiologica Scandinavica 183 (3), 291–298. Morse, C.I., Thom, J.M., Mian, O.S., Muirhead, A., Birch, K.M., Narici, M.V., 2005b. Muscle strength, volume and activation following 12month resistance training in 70-year-old males. European Journal of Applied Physiology 95 (2–3), 197–204. Morse, C.I., Thom, J.M., Reeves, N.D., Birch, K.M., Narici, M.V., 2005c. In vivo physiological cross-sectional area and specific force are reduced in the gastrocnemius of elderly men. Journal of Applied Physiology 99 (3), 1050–1055. Muramatsu, T., Muraoka, T., Kawakami, Y., Fukunaga, T., 2002. Intramuscular variability of the architecture in human medial gastrocnemius muscle in vivo and its functional implications. Advanced Exercise and Sports Physiol 8 (1), 17–21. Ng-Thow-Hing, V., Fiume, E., 2002. Application-specific muscle representations. In: Proceedings of Graphics and Interface, pp. 107–115. Out, L., Vrijkotte, T.G., van Soest, A.J., Bobbert, M.F., 1996. Influence of the parameters of a human triceps surae muscle model on the isometric
torque-angle relationship. Journal of Biomechanical Engineering 118 (1), 17–25. Powell, P.L., Roy, R.R., Kanim, P., Bello, M.A., Edgerton, V.R., 1984. Predictability of skeletal muscle tension from architectural determinations in guinea pig hindlimbs. Journal of Applied Physiology 57 (6), 1715–1721. Riener, R., Rabuffetti, M., Frigo, C., 2002. Stair ascent and descent at different inclinations. Gait & Posture 15 (1), 32–44. Shellock, F., 1989. Biological effects and safety aspects of magnetic resonance imaging. Magnetic Resonance Quarrterly 5 (4), 243–261. Stafilidis, S., Arampatzis, A., 2007. Track compliance does not affect sprinting performance. Journal of Sports Science 25 (13), 1479–1490. Tate, C.M., Williams, G.N., Barrance, P.J., Buchanan, T.S., 2006. Lower extremity muscle morphology in young athletes: an MRI-based analysis. Medicine and Science in Sports and Exercise 38 (1), 122–128. Thom, J.M., Morse, C.I., Birch, K.M., Narici, M.V., 2005. Triceps surae muscle power, volume, and quality in older versus younger healthy men. Journal of Gerontology Series A—Biological Sciences and Medical Sciences 60 (9), 1111–1117. Wickiewicz, T.L., Roy, R.R., Powell, P.L., Edgerton, V.R., 1983. Muscle architecture of the human lower limb. Clinical Orthopaedics and Related Research (179), 275–283. Winter, D.A., 1983. Moments of force and mechanical power in jogging. Journal of Biomechanics 16 (1), 91–97. Winter, S.L., Challis, J.H., 2008. Reconstruction of the human gastrocnemius force–length curve in vivo: part 2, experimental results. Journal of Applied Biomechanics, in press, http://www.humankinetics.com/ JAB/viewarticle.cfm?jid=xm2Cb48qxj2L77kPxn8V87dDxp8D76c6xm 8K3J2Dxk8N4&aid=15674&site=xml2Cb48qxj2L77kPxn8V87dDxp 8D76c6xm8K3J2Dxk8N4&view=abs. Woittiez, R.D., Rozental, R.H., Huijing, P.A., 1983. The functional significance of architecture of the human triceps surae muscle. In: Winter, D.A., Norman, R.W., Wells, R.P., Hayes, K.C., Patla, E. (Eds.), Biomechanics IX-A. Human Kinetics Publishers, Inc., Champaign, IL, USA, pp. 21–26.
Journal of Biomechanics 41 (2008) 2211–2218 www.elsevier.com/locate/jbiomech www.JBiomech.com
Assessment of muscle volume and physiological cross-sectional area of the human triceps surae muscle in vivo K. Albrachta, A. Arampatzisa,, V. Baltzopoulosb a
Institute of Biomechanics and Orthopaedics, German Sport University Cologne, Germany Institute for Biomedical and Clinical Research into Human Movement and Health, Manchester Metropolitan University, UK
b
Accepted 18 April 2008
Abstract The purpose of the present study was to investigate whether it is possible to predict the individual muscle volumes within the triceps surae (TS) muscle group by means of easily measurable parameters based on a theoretical consideration. A further objective was to verify the use of the available literature data to assess the contribution of each muscle of the group to the entire TS volume or physiological cross-sectional-area (PCSA). Therefore, magnetic resonance images of the right calf of 13 male subjects were acquired and each muscle of the TS was reconstructed. Muscle length (l m ), the maximum anatomical cross-sectional-area (ACSAmax ) and muscle volume were obtained from the 3D models. To assess the PCSA, fascicle length was determined by ultrasonography. In general, muscle volume can be expressed as a fraction of the product of ACSAmax and l m . The size of the fraction depends on muscle shape and its coefficient of variance among the examined population was considerable low (soleus 6%, gastrocnemius 4% and gastrocnemius lateralis 7%) in the present study. The product of ACSAmax and l m was, therefore, suitable to assess muscle volume (root mean squares, RMS 4–7%). Further, the soleus, gastrocnemius medialis and gastrocnemius lateralis accounted on average for about 52 3%, 32 2% and 16 2% of the total TS volume and 62 5%, 26 3% and 12 2% of the entire TS PCSA, respectively. The coefficient of variance of the relative portions were 5–10% for muscle volume and 8–17% for the PCSA. r 2008 Elsevier Ltd. All rights reserved. Keywords: MRI; Muscle reconstruction; Triceps surae muscle; Muscle volume; Volume distribution; PCSA distribution
1. Introduction The assessment of human muscle volume is essential when evaluating muscle performance and functional consequences of changes in muscle size and strength due to training, aging or immobilization (Aagaard et al., 2001; Kawakami et al., 2000; Thom et al., 2005). The maximum force-generating capacity of a muscle is proportional to the physiological cross-sectional-area (PCSA) (Haxton, 1944), which can be approximated from muscle volume and fascicle length (Alexander and Vernon, 1975; Powell et al., 1984). Furthermore, assuming homogeneous muscle density, muscle volume is a determinant of muscle mass, a parameter, which is needed to gain insight into the specific Corresponding author. Tel.: +49 221 4982 5620; fax: +49 221 4971598. E-mail address: [email protected] (A. Arampatzis).
0021-9290/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.04.020
muscle tension (Lynch et al., 1999), and to determine energy cost and muscle efficiency of certain contractions through modeling (Houdijk et al., 2006). For in vivo measurement of muscle volume, magnetic resonance imaging (MRI) is considered to be the most useful noninvasive imaging modality (Mitsiopoulos et al., 1998; Shellock, 1989). Despite recent improvements in image processing, a muscle reconstruction by MRI is still laborious and not widely applicable. Being essential for everyday activities such as walking (Winter, 1983) and stair negotiation (Riener et al., 2002) as well as in running (Winter, 1983) and sprinting (Stafilidis and Arampatzis, 2007), the triceps surae muscle group (TS) is frequently used in muscle modeling (Bobbert, 2001; Lichtwark and Wilson, 2007; Out et al., 1996). To estimate volume or PCSA of the individual TS muscles, data of muscle force-generating capacities or muscle volume derived from cadaveric studies are often applied to scale
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models of the muscle–tendon unit (Bobbert, 2001; Out et al., 1996). Using those data allow a better understanding of general principles of muscle function, but the comparability to individual muscle performance remains unclear. It is likely that data from cadaveric specimens do not accurately reflect absolute or relative sizes of muscles in young and healthy subjects (Tate et al., 2006). In addition, this approach implies that the distribution of muscle volume and PCSA is consistent within a muscle group among the population, although cadaveric studies (Friederich and Brand, 1990; Wickiewicz et al., 1983) are based usually on a few numbers of specimens. To our knowledge, there is no information available on whether the volume of the muscles within the TS can be estimated by less laborious measurements. Therefore, the aim of this study was to answer the question, whether it is possible to predict the individual muscle volumes within the TS by means of easily measurable parameters. A further goal was to verify the use of the available literature data to assess the contribution of each muscle of the group to the entire TS volume or PCSA. 2. Method
measurements, MRI as well as ultrasonography, were performed on the relaxed muscle and with the ankle and knee joints fixed at 90 and 180 , respectively (tibia perpendicular to the sole of the foot and the knee fully extended). The sonographic images were recorded along the mid-sagittal line of the gastrocnemius medialis muscle (GM), the GL and the SO at middistance between the proximal and distal tendon insertions using a B-mode, real-time ultrasonography (HDI-3000; ATL, Bothell, WA, USA) with a 3.8 cm linear array probe (7.5 MHz). In the sonographic images five evenly distributed points were digitized on each selected fascicle, the deeper and upper aponeurosis and a straight line was fitted through these five points in a least square sense (Fig. 1). The fascicle length was defined as the length between the two intersection points of the line corresponding to the fascicle and the lines corresponding to the upper and deeper aponeurosis. Transversal MRI scans were recorded, such that all three TS muscles were scanned from origin to insertion. The MRI was performed using a 0.2 Tesla open scanner (E-Scan, Esaote Biomedica, Genova, Italy) and a T1 weighted turbo 3D protocol with the following parameters: time to echo 16 ms; repetition time 38 ms; pixel spacing 0:625 0:625 mm, field of view 15:9 15:9 cm, slice thickness 2 mm and no gap between slices. Since the scanning range of the used imaging coil was restricted to 7 cm, either six or seven overlapping recordings of contiguous transversal images were acquired to capture the entire calf. In order to combine the different sequences and to define the transversal plane, three coplanar markers were placed every 6 cm on the leg (Fig. 2). In every second transversal plane image, the muscle boundaries were outlined manually using a piecewise
2.1. Theoretical consideration The general volume calculation of a solid (f ðz; x; yÞ) using Cartesian coordinates is defined as ZZZ f ðz; x; yÞ dz dx dy. (1) V¼ V
If the origin of the coordinate system is located at the insertion of the muscle (myotendinous junction) and if the longitudinal axis of the shank coincides with the z-direction, the anatomical cross-sectional-area (ACSA) RR at a certain location (z) of the shank is ACSAðzÞ ¼ AðzÞ f ðx; yÞ dx dy and the muscle volume (V m ) can be calculated as Z lm ACSAðzÞ dz Vm ¼ 0
¼ ACSA l m
(2)
with ACSA as the mean ACSA and l m as the muscle length, defined as the distance between the muscle’s proximal and distal end. When expressing the mean ACSA as a fraction of the maximum anatomical cross-sectionalarea (ACSAmax ) Eq. (2) can be rewritten as V m ¼ p ACSAmax l m
Fig. 1. Ultrasonographic image of the gastrocnemius medialis muscle. The straight lines correspond to the fascicle () and the upper and deeper aponeurosis (.).
(3)
with 0opp1. Eq. (3) shows that in general the muscle volume is a fraction of the product of ACSAmax and l m . The size of the fraction, i.e. the value of p depends on the muscle shape. If we assume that the shape of the three TS muscles is similar within the population, the assessment of muscle volume should be possible from ACSAmax and l m .
2.2. Data acquisition Thirteen male adults (height 180 36 cm, mass 76 6 kg and age 29 6 years) volunteered for this study. All subjects were university staff or students and were at most active in recreational sports. MRI was performed to assess muscle volume. To estimate PCSA, fascicle length was measured using ultrasonography. The PCSA distribution could only be determined for nine subjects, as difficulties in the ultrasound images prevented the analysis of gastrocnemius lateralis muscle (GL) architecture in one case and of soleus muscle (SO) architecture in three cases. Both
Fig. 2. Transversal magnet resonance image of the calf with the three markers placed on the skin and the outlined contours of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles.
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GL GM
w
SO
u SO
v
Fig. 3. (a) Segmented transversal contours of the soleus (SO) muscle. (b) B-Spline solid of the triceps surae muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) . linear boundary provided by the software program 3D Doctor (ABLE SOFTWARE CORP., Lexington, MA, USA). For the most proximal and distal portions of the muscle the images were analyzed every 2 mm. Finally, 60–100 contour curves were computed for each muscle (Fig. 3a), which were exported as 3D-coordinates and processed using Matlab (The MathWorks, Natick, MA, USA).
2.3. Reconstruction For each muscle a continuous B-Spline solid was created from the 3Dcoordinates of the transversal contours (Fig. 3) using a method based on the one proposed by Ng-Thow-Hing and Fiume (2002). To create the BSpline solid a parametrization was performed, such that u increases radially outward from the central axis of the solid to its contour boundaries, v traverses the perimeter around the central axis and w runs along the longitudinal iso-parametric lines from the bottom to the top of the stack (Fig. 4). The central axis is defined as a curve running through the centroid points of the contours. A second degree B-Spline basis functions and a chord length parametrization were used in the v and w domains. A first degree B-Spline basis function was used for the parameter u. Correspondence between adjacent contours was found using the shape context algorithm (Belongie et al., 2002), a robust and simple algorithm for finding correspondence between shapes, represented by a set of points. This algorithm could be utilized, as the muscle boundaries did not vary much from slice to slice.
2.4. Data analysis From the reconstructed muscle the following parameters were determined: muscle volume (V m ), muscle length (l m ), defined as the
Fig. 4. B-Spline solid of the soleus muscle. The parametrization was performed, such that u increases radially outward from the central axis of the solid to its contour boundaries, v traverses the perimeter around the axis and w runs along the longitudinal iso-parametric lines from the bottom of the stack to the top. distance between the muscle’s proximal and distal end, and the maximum anatomical cross-sectional-area (ACSAmax ). The PCSA was calculated as V m l 1 f (Lieber and Fride´n, 2000) using the fascicle length (l f ) determined by ultrasonography. The theoretical consideration (Eq. (3)) shows that in general muscle volume is a fraction of the product of ACSAmax and l m . We hypothesized that the size of the fraction, i.e. the shape of the muscle, is maintained across the population. To test whether this assumption is valid, we considered the intersubject variability of the ratio between muscle volume and the product of ACSAmax and l m (the shape factor p). Furthermore, we examined the intersubject variability for the ratios between muscle volume and either ACSAmax or l m . As a measure for the intersubject variability the coefficient of variance (CV) is used. To evaluate the accuracy of assessing muscle volumes, the volumes were predicted on the basis of Eq. (3) and the root mean squares (RMS) between the measured and predicted values were calculated and expressed relative to the mean of the measured values.
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To determine whether muscle volume or PCSA distribution is consistent across the subjects, we proceeded in an analogous manner. The intersubject variability was determined from the relative portion of each
Table 1 Muscle properties of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) determined in the present study lm (cm) SO GM GL
ACSAmax ðcm2 Þ
3:39 3:1a,b 29 4a,b 2:78 1:8b 18 3b 2:39 1:6 11 2
Vm ðcm3 Þ
PCSA ðcm2 Þ
lf (cm)
477 66a,b 131 31a,b 3:9 0:9a,b 285 45b 51 10b 5:7 0:7b 146 23 24 5 6:6 0:7
Values are means SD; l m : muscle length; ACSAmax : maximum anatomical cross-sectional-area; V m : muscle volume; PCSA: physiological cross-sectional-area; l f : fascicle length. a Significantly different from GM (po0:05). b Significantly different from GL (po0:05).
Table 2 The mean standard deviation and the coefficient of variance (CV) of the ratio between muscle volume and the product of ACSAmax and l m , the ratio between muscle volume and ACSAmax , the ratio between muscle volume and l m
SO GM GL
V m =ðACSAmax l m Þ
V m =ACSAmax
Mean
Mean (cm)
CV (%)
Mean ðcm2 Þ
CV (%)
16:73 1:31 16:44 1:36 13:60 1:37
8 8 10
14:17 2:03 10:62 1:99 6:35 1:25
14 19 20
CV (%)
0:496 0:029 6 0:592 0:026 4 0:569 0:039 7
V m =l m
V m : muscle volume of the individual muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL); l m : muscle length; ACSAmax : maximum anatomical cross-sectional-area.
individual TS muscle to the entire TS. The total TS volume and PCSA is defined as the sum of GM, GL and SO muscle volumes and PCSAs, respectively. Muscle volumes and PCSAs were predicted from the total TS volume or PCSA using the mean proportional distribution.
3. Results The SO showed the largest l m , ACSAmax , muscle volume and PCSA, followed by the GM and GL (Table 1). Fascicle length was largest in the GL (Table 1). Further the SO, GM and GL accounted on average for about 52 3%, 32 2% and 16 2% of the total TS volume and 62 5%, 26 3% and 12 2% of the entire TS PCSA, respectively. Within each component of the TS the CV was lowest (4–7%) for the ratio between muscle volume and the product of ACSAmax and l m (shape factor p) followed by the ratio between muscle volume and ACSAmax (8–10%) (Table 2). The CV for the ratio between muscle volume and l m (14–20%) was more than twofold higher than the other values (Table 2). According to these results, the RMS between the measured and predicted muscle volumes were lowest using the product of ACSAmax and l m (4–7%) and highest using l m (14–20%) (Fig. 5). The predicted muscle volumes (Fig. 5) were obtained utilizing a linear equation with no intercept term and with a slope corresponding either to the mean ratio between muscle volume and the product of ACSAmax and l m , the mean ratio between muscle volume and ACSAmax or the mean ratio between muscle volume and l m , which are presented in Table 2. The portions of the individual muscles relative to the entire TS showed lower CV for the muscle volume (5–10%) than for the PCSA (8–17%) (Table 3). The muscle volume
700 RMS 6%
muscle volume [cm3]
600
RMS 7%
RMS 14%
500 RMS 4%
400
RMS 8% RMS 19%
300 RMS 7%
200
RMS 10% RMS 20%
100
GL GM SO
0 0
200 400 600 800 1000 1200 1400 5 ACSAmax*lm [cm3]
GL GM SO 10
15
20
25
ACSAmax [cm2]
30
35
GL GM SO 40
20
25
30
35
40
45
lm [cm]
Fig. 5. The measured values for muscle volume (scatter plot) in comparison with the predicted values represented by the solid lines. The predicted muscle volumes were obtained utilizing a linear equation with no intercept term and with a slope corresponding to the mean ratio between the muscle volumes and (a) the product of maximum anatomical cross-sectional-area and muscle length (ACSAmax l m ), i.e. the shape factor p, (b) the maximum anatomical crosssectional-area (ACSAmax ), and (c) the muscle length (lm ) for the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles. The values for the ratios are presented in Table 2. The root mean square (RMS) is expressed relative to the mean of the measured values.
ARTICLE IN PRESS K. Albracht et al. / Journal of Biomechanics 41 (2008) 2211–2218 Table 3 The relative portion of muscle volume and physiological cross-sectional area (mean SD) for each muscle of the triceps surae muscle group (TS) to the entire TS V =V TS
SO GM GL
PCSA=PCSATS
Mean ð102 Þ
CV (%)
Mean ð102 Þ
CV (%)
51:82 2:83 31:81 2:23 16:36 1:70
5 7 10
62:08 4:90 25:79 3:14 12:14 2:05
8 12 17
700 individual muscle volume [cm3]
RMS 5% 600 500 RMS 7%
300 RMS 10%
200
SO GM GL
100 0 700
800
900
1000
1100
1200
1300
1400
TS muscle volume [cm3]
180 RMS 7%
individual muscle PCSA [cm2]
160 140 120 100
RMS 12%
80 60
RMS 16%
40
SO GM GL
20 0 140
160
180
200
220
240
260
280
300
as well as the PCSA of the SO showed the lowest CV followed by the ones of the GM and GL (Table 3). Using the mean relative portions from Table 3 to predict the muscle volumes and PCSAs of the individual muscles from the entire TS, the RMS between the predicted and the measured values ranges from 5% to 10% and 7% to 17%, respectively (Fig. 6).
4. Discussion
V: individual volume of the muscles: soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GM); V TS : volume of the triceps surae muscle group; PCSA: physiological cross-sectional-area of the individual muscles group; PCSATS : physiological cross-sectional-area of the triceps surae muscle group; CV: coefficient of variance.
400
2215
320
TS PCSA [cm2] Fig. 6. The measured values (scatter plot) for (a) muscle volume and (b) PCSAs in comparison with the predicted values represented by the solid lines. The predicted values were obtained utilizing a linear equation with no intercept term and with a slope corresponding the mean relative portions of either the soleus (SO), gastrocnemius medialis (GM) or gastrocnemius lateralis (GL) to the entire triceps surae (TS). The values of the relative portions are presented in Table 3. The root mean square (RMS) is expressed relative to the mean of the measured values.
The aim of the present investigation was to provide a method for reliably estimating (a) the individual muscle volumes within the TS by means of easily measurable parameters and (b) to investigate whether the distribution of muscle volume or PCSA within the TS muscles is maintained across the examined population. The present study showed a considerable low intersubject variability for the ratio between muscle volume and the product of ACSAmax and l m (4–7%, Table 2) indicating that the shape of each muscle seems to be similar across the examined population. The size of the ratio, i.e. the value of p, was significantly different between the SO (0:496 0:029) and both gastrocnemii muscles (GM: 0:592 0:038, GL: 0:569 0:038), whereas there was no significant difference between the GM and GL indicating that their shapes are similar. Due to the considerably low intersubject variability of the value p, the assessment of muscle volume from ACSAmax and l m using Eq. (3) was possible with an acceptable accuracy (RMS: 4–7%). As Fig. 5 shows there was certainly a good prediction of muscle volume from ACSAmax , suggesting that the ACSAmax alone reflects the whole volume. However, when estimating the muscle volume from the product of ACSAmax and l m using Eq. (3) and thus including the third dimension, the intersubject variability of the ratio as well as the error of the prediction was about 1–4% lower compared with predicting the muscle volumes only from ACSAmax (Fig. 6, Table 2). Both independent variables in Eq. (3), l m as well as ACSAmax , are easily assessible in comparison with the entire muscle reconstruction. The location of ACSAmax in relation to the shank length (distance between the tuberositas calcanei and the tibia plateau) is well defined, since the standard deviation of the location was 4% of shank length for all three muscles (Fig. 7). The ACSAmax was located at about the same site for the GM (79 4%) and GL (81 3%), whereas it was located significantly more distal for the SO (66 4%). The widths of the 95% confidence intervals were 4–5% of shank length. With a mean shank length of 43 2 cm this corresponds to about 2 cm. We can conclude that, only one MRI sequence (width 2 cm) for both gastrocnemii and one for the SO are required to identify the ACSAmax of all three muscles. Furthermore, l m can be determined by identifying the muscle’s proximal and distal end using ultrasonography or MRI.
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35 SO
ACSA [cm2]
30 25 20 15 10 5 0 35
GM
ACSA [cm2]
30 25 20 15 10 5 0 35
GL
ACSA [cm2]
30 25 20 15 10 5 0 0
20
40
60
80
100
120
normalized shank length [%] Fig. 7. Anatomical cross-sectional-areas (ACSA) of the soleus (SO), gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) muscles along the length of the shank. 0% corresponds to the tuberositas calcanei and 100% corresponds to the tibia plateau. The thin gray lines represent the position of the maximum ACSA among the examined population. Solid lines indicate the means and dashed lines the standard deviations.
To answer the question whether the proportional distribution of muscle volume or PCSA within the TS is consistent among the examined sample, the important finding was that the intersubject variability of muscle volumes and PCSAs of the three individual TS muscles relative to the entire TS were 5–10% and 7–15%, respectively. In comparison, the intersubject variability of the absolute volumes and PCSAs were on average about two times higher (Tables 1 and 3). When using the mean proportional distribution to predict the muscle volume or PCSA of each individual TS muscle, the prediction was best for the SO followed by the GM and GL (Fig. 6). For the GL the error of prediction was about twofold higher than for the SO. This result is not surprising, since the SO contribution to the entire TS volume and PCSA is highest, whereas the GL contribution is lowest. Consequently, a prediction of each TS muscle volume or PCSA using the mean proportional distribution should be possible at least for the SO and GM. One could argue that, the SO and the two gastrocnemii are functionally different and composed of different fiber types (Johnson et al., 1973) and, therefore, muscle volumes or PCSAs of the individual muscles increase or decrease non-uniformly due to training, aging
or immobilization. Recently it has been shown (Morse et al., 2005c) that aging does not influence the PCSA distribution and that the muscle volume distribution changes only by 2–3%. It seems that in people who are exposed to normal daily activities, the variation of a nonuniform adaptation between the three constituents of the TS has only a marginal influence on the proportional distribution. The above findings may have important implications for studies dealing with muscle hypertrophy or atrophy due to training, aging or immobilization. To assess changes in muscle size, many studies only consider the ACSA (Frontera et al., 2000; Kanehisa et al., 2003) instead of the entire volume or PCSA. However, a muscle can adapt in size by adding sarcomeres either in parallel or in series (Butterfield et al., 2005). Muscle volume is directly related to muscle mass and PCSA to the muscle force-generating capacity. Therefore, muscle volume as well as the PCSA might be more appropriate to investigate muscle hyper- or atrophy. Muscle atrophy at the TS assessed by MRI has been reported to be about 12% in response to unloading or disuse of various durations (Berg et al., 2007; Kubo et al., 2004) and between 17% and 29% with aging (Morse et al., 2005a, c; Thom et al., 2005). Morse et al. (2005b) found an increase of 12% in TS volume after a 12 month strength training program for elderly. We determined RMS values of about 4–7% and thus changes of such magnitude are detectable with the prediction equations (Eq. (3)) provided in this study. Combining this method with ultrasonography to measure fascicle length allows an approximation of PCSA. The proportional distribution of PCSA is commonly used to estimate maximum isometric force of the three individual TS muscles. Especially studies applying models to assess the performance of a muscle–tendon unit rely on such information (Bobbert, 2001; Out et al., 1996; Woittiez et al., 1983), which is obtained from cadaveric studies e.g. Wickiewicz et al. (1983) and Friederich and Brand (1990). The volume distribution is also essential in modeling, but to estimate energy consumption rather than force-generating capacity. However, in the literature the information about the distribution of muscle volume and PCSA among the three TS muscles is rare. The available data are mainly based on cadaveric studies with a small number of specimens. The results of the present study support the use of the assumption that distribution of muscle volume and PCSA is consistent within the TS at least for people who are exposed to normal daily activities. In comparison with the existing cadaveric measurements of muscle volume and PCSA for the TS (Friederich and Brand, 1990; Wickiewicz et al., 1983) our results for the relative muscle volume as well as for the relative PCSAs showed smaller values for both gastrocnemii together and higher values for the SO (differences: 6–13%). To determine PCSA we proposed to use the formula based on muscle volume and fascicle length which is commonly used in the literature (Friederich and Brand,
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1990; Fukunaga et al., 1992; Huijing, 1985; Wickiewicz et al., 1983). At the moment a direct in vivo measurement of PCSA is almost not feasible, even though the further development of diffusion tensor imaging seems to provide a more direct measurement of PCSA (Galba´n et al., 2004; Heemskerk et al., 2005). The calculation of PCSA is based on the assumption that fascicle length remains constant within the muscle, which can be assumed for both gastrocnemii (Maganaris et al., 1998; Muramatsu et al., 2002) and for the largest part, the posterior part, of the SO (Maganaris et al., 1998). Further, most of the studies on cadaveric specimens (Friederich and Brand, 1990; Huijing, 1985; Wickiewicz et al., 1983) used a fascicle length normalized to the optimum sarcomere length. In vivo it is difficult to determine the optimum fascicle length. Utilizing maximal voluntary contractions the GM likely operates at the ascending limb of the force–length relationship through the entire range of motion (Winter and Challis, 2008). Therefore, we determined fascicle length at rest in the anatomical neutral position. A previous study (Arampatzis et al., 2007) indicated that in this position fascicle length of the TS muscle is near its optimum length, because the force-generating response to the twitch was maximal in this particular position. However, the given suggestion using this method is that all individual muscles of the TS act at the same position of the force–length relationship, which is a limitation of the used methods. The chosen joint configuration should rather be considered as a reference position, which is likely to be near the optimum fascicle length. In summary, the present study demonstrated that the shape factor p is maintained among the investigated population and, therefore, muscle volume can be approximated using the values of ACSAmax and l m . Both parameters are easily assessible in comparison with an entire muscle reconstruction. Furthermore, the proportional distribution of muscle volume and PCSA within the TS was consistent across the subjects. Therefore, the results of the present study support the use of the assumption that the distribution of muscle volume and PCSA is consistent within the TS at least for people who are exposed to normal daily activities.
Conflict of interest statement The authors disclose any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
Acknowledgments We thank Professor Dr. Constantinos N. Maganaris for his suggestions and support with the ultrasonography of muscle architecture and Dr. Dimitrios E. Tsaopoulos for his assistance during the measurements.
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