Supplementary information on methods 
 
“The force-length-velocity potential of the human soleus muscle is related to the 
energetic cost of running” 
by Sebastian Bohm, Falk Mersmann, Alessandro Santuz & Adamantios Arampatzis 
Journal:  
Proceedings of the Royal Society B 
DOI: 
 
http://dx.doi.org/10.1098/rspb.2019.2560 
 
Determination of the ankle joint moments during MVC 
The resultant moments at the ankle joint were calculated by means of an established inverse dynamics 
approach [1], which takes the effects of gravitational and passive moments and any misalignment 
between ankle joint axis and dynamometer axis into account. The required kinematic data were recorded 
during the MVCs on the basis of anatomically referenced reflective markers (medial and lateral malleoli 
and epicondyle, calcaneal tuberosity, 2nd metatarsal and greater trochanter) using a Vicon motion 
capture system (Version 1.8, Vicon Motion Systems, Oxford, UK). The ankle joint angle-specific 
moments due to gravity and passive moments were measured during an additional ankle joint rotation 
driven by the dynamometer at 5 °/s with the participants completely relaxed. Thus, moments due to 
gravity and passive moments in a certain joint angle were attributed to the measured moment during 
the MVCs in the same joint angle configuration [1]. Furthermore, the contribution of the antagonistic 
muscles to the different measured ankle joint moments [2] was considered by establishing an individual 
relationship of EMG amplitude of the tibialis anterior muscle, agonistic moment as well as ankle joint 
angle. For this reason, EMG activity was measured at rest and during two submaximal isometric 
dorsiflexion contractions that displayed slightly lower and higher EMG magnitude as during the 
maximum plantar flexions [2] in three different joint angles (i.e. dorsiflexion, neutral position and plantar 
flexion) within the assessed range of motion. The relationship was described by the following regression 
equation:  
𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑀𝑀𝐸𝐸𝑐𝑐𝑡𝑡𝑡𝑡.  𝑐𝑐𝑎𝑎𝑐𝑐.  ∙ (𝑎𝑎 + 𝑏𝑏 ∙ 𝛼𝛼𝑐𝑐𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 + 𝑐𝑐 ∙ 𝛼𝛼𝑐𝑐𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎²)  
 
(eq. 1) 
where Mcoact is the antagonistic joint moment during the maximum plantar flexion, EMGtib. ant. is the 
respective tibialis anterior EMG activity during the MVCs, αankle the ankle joint angle measured via the 
Vicon system and a, b and c the individual regression coefficients. This means that for each joint angle 
the relationship between moment and EMG activity was assumed to be linear because of the small 
differences of the EMG magnitude of the two submaximal isometric dorsal flexion contractions [2]. The 
joint angle-moment relationship presented by the three different measured angles was than formulated 
by a quadratic function to account for the force-length dependence of the muscle. EMG activity of the 
tibialis anterior and soleus muscle was measured using a wireless EMG system (Myon m320RX, Myon 
AG, Baar, Switzerland) and two bipolar surface electrodes (2 cm inter-electrode distance) that were 
placed on the muscle at an acquisition frequency of 1000 Hz, synchronized with the kinematic data.  
 
 
Determination of the Achilles tendon lever arm 
The Achilles tendon lever arm was individually determined by means of the tendon excursion method 
[3,4]. In this method, the lever arm of the Achilles tendon is calculated as the ratio of the m. 
gastrocnemius medialis myotendinous junction displacement obtained by ultrasonography to the 
corresponding angular excursion of the ankle joint during a passive joint rotation by the dynamometer 
(5 °/s). The lever arm values were further corrected for the alignment of the tendon occurring during 
contractions using the factor provided by Maganaris et al. (1998) [5]. 
 
Fascicle length determination from the ultrasound images  
The procedure included an approximation of the deeper and upper aponeurosis by a best linear fit 
through three manually placed and frame-by-frame adjusted marks. By means of the bwtraceboundary 
function of the Matlab Image Processing toolbox the algorithm then identified the shape and orientation 
of image brightness features between both aponeuroses in each frame, which are indicative for the 
hyperechoic perimysial connective tissue parts aligned with the muscle fascicles (fig. 1A in main 
manuscript). The feature identification criteria were set to: minimal length of 23 pixels (i.e. 0.4 cm, from 
the bottom left to the top right), area to length ratio of 8.5, angle between feature and deeper aponeurosis 
between 10° and 80° and 80% of the pixels on a line between the start and end point of a feature had 
to be white [6]. Every frame was visually controlled for adequate feature placement and manually 
corrected if necessary. Based on the identified features, a linear averaged reference fascicle was 
calculated (fig. 1A in main manuscript). Reliability of the tracking approach was confirmed and reported 
in two previous studies [6,7]. 
 
EMG processing  
Raw EMG signals from the running and MVC trials were processed by a fourth-order high-pass 
Butterworth zero-phase filter with a 50 Hz cut-off frequency then a full-wave rectification and a low-
pass zero-phase filter with a 20 Hz cut-off frequency for creating a linear envelope of the signal [8,9]. 
 
 
References 
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The force-length-velocity potential of the human soleus muscle is related to the energetic cost of running.
Bohm, Sebastian,Mersmann, Falk,Santuz, Alessandro,Arampatzis, Adamantios