Assessment and modelling of the activation‐dependent shift in optimal length of the human soleus muscle in vivo

Previous in vitro and in situ studies have reported a shift in optimal muscle fibre length for force generation (L0) towards longer length at decreasing activation levels (also referred to as length‐dependent activation), yet the relevance for in vivo human muscle contractions with a variable activation pattern remains largely unclear. By a combination of dynamometry, ultrasound and electromyography (EMG), we experimentally obtained muscle force–fascicle length curves of the human soleus at 100%, 60% and 30% EMGmax levels from 15 participants aiming to investigate activation‐dependent shifts in L0 in vivo. The results showed a significant increase in L0 of 6.5 ± 6.0% from 100% to 60% EMGmax and of 9.1 ± 7.2% from 100% to 30% EMGmax (both P < 0.001), respectively, providing evidence of a moderate in vivo activation dependence of the soleus force–length relationship. Based on the experimental results, an approximation model of an activation‐dependent force–length relationship was defined for each individual separately and for the collective data of all participants, both with sufficiently high accuracy (R2 of 0.899 ± 0.056 and R2 = 0.858). This individual approximation approach and the general approximation model outcome are freely accessible and may be used to integrate activation‐dependent shifts in L0 in experimental and musculoskeletal modelling studies to improve muscle force predictions.


Introduction
The force-length relationship of skeletal muscle is a key determinant for muscle force generation (Blix, 1892;Ramsey & Street, 1940).Although isometric force at intermediate muscle length is maximal (i.e.optimal length for force generation, L 0 ), it is reduced in short and long length as a result of the amount of effective overlap between the myosin and actin proteins (Gordon et al., 1966).However, a particular characteristic of the force-length relationship is a shift in L 0 towards longer length at decreasing activation levels (Rack & Westbury, 1969), i.e. activation-dependent shift in L 0 (also referred to as length-dependent activation; Rassier et al., 1999), which is not predicted by actin-myosin overlap alone.A length-dependent calcium sensitivity is considered to be a main factor of the activation-dependent shift in L 0 (de Tombe et al., 2010;MacIntosh, 2017), although additional calcium sensitivity-independent mechanisms were also suggested (Hessel et al., 2019;Holt & Azizi, 2014;Holt & Williams, 2018;MacDougall et al., 2020;Winters, 1995).For example, an activation-dependent magnitude of residual force depression (i.e.active force is depressed after muscle shortening compared to the isometric force at that same length; Abbott & Aubert, 1952;Rassier & Herzog, 2004) as a result of fibre shortening against the compliant tendon during a fixed-end contraction may contribute to activation-dependent shifts in L 0 (Holt & Williams, 2018).From a functional perspective, the activation dependence of L 0 dictates that force generation for a given muscle length during a movement with variable activation is not constant but is scaled by the activation-dependent shift in the force-length curve.However, this feature of skeletal muscle is not captured by current experimental investigations of the force-length relationship and muscle models.
Activation-dependent shifts in L 0 are a consistent finding of in vitro and in situ preparations (Hessel et al., 2019;Holt & Azizi, 2014, 2016;MacDougall et al., 2020;Morgan, 1990;Rack & Westbury, 1969;Stephenson & Wendt, 1984).However, it has been argued that the activation methods used in the in vitro and in situ experiments may not appropriately represent the physiological in vivo muscle activation conditions (i.e.too large electrical stimulation frequency ranges and potentially unphysiological calcium concentrations) and therefore the activation-dependent shift in L 0 might actually be rather small during in vivo contractions (de Brito Fontana & Herzog, 2016).Indeed, in vivo studies on humans are sparse and inconsistent.Although the results of the study by Hessel et al. (2021) suggest a substantial shift in L 0 from maximal to submaximal electromyographic (EMG) activity levels (up to 20%) for the human soleus and gastrocnemius lateralis muscle, de Brito Fontana & Herzog (2016) reported only slight and variable rightward shifts in L 0 (∼5%) over the full range of EMG activity levels for the vastus lateralis with no statistically significance.Hessel et al. (2021) determined the force-fascicle length relationship of the soleus and gastrocnemius lateralis muscle simultaneously at an extended knee joint position where the measured ankle joint moment is a result of all three muscles of the triceps surae (soleus, gastrocnemius medialis and lateralis; Hessel et al., 2021).This approach does not allow differentiation of the contribution of the monoarticular soleus and the biarticular gastrocnemii muscles on the measured ankle joint moment, which may introduce artifacts in the assessed force-length relationship of both muscles.On the other hand, de Brito Fontana & Herzog (2016) investigated the force-length relationship of the monoarticular vastus lateralis muscle at a flexed hip joint angle to minimize the contribution of the biarticular rectus femoris on the measured knee extension moment.Furthermore, inaccuracies in the muscle's lever arm determination (Bakenecker et al., 2019;Holzer et al., 2020), as well as unavoidable misalignments between the rotation axis of the joint and dynamometer during contractions (Arampatzis et al., 2004(Arampatzis et al., , 2005) ) and the contribution of the antagonistic muscles to the joint moment (Baratta et al., 1988;Mademli et al., 2004) that were not considered in the earlier studies, may additionally affect the activation-dependent shift in L 0 .The few and conflicting findings demonstrate that the activation dependence in L 0 in human in vivo muscle contractions is not well understood and potentially less distinct compared to the in vitro and in situ observations.
An activation-dependent shift in L 0 would have important functional implications.During functional daily life movements, muscles are activated with a variable activation pattern and mostly submaximal.Consequently, the force-length potential (i.e.fraction of maximum active force according to the force-length curve in each activation level) would not be constant for a given muscle fascicle length as a result of the activation-dependent shift in L 0 .When operating on the ascending limb of the force-length curve at maximal activation, the same fascicle length would actually correspond to a lower aspect of the force-length curve at submaximal activation and therefore the force-length potential would be comparably less.This would be the opposite when fascicles operate on the descending limb of the force-length curve at maximal activation.The effect of the activation dependence of L 0 on estimates of force or the force-length potential is currently not considered in experimental studies on the force-length properties of human muscles.Here, the measured operating muscle fascicle length during the movement of interest is usually mapped on a single force-length curve determined at maximal activation despite the fact that the activation level is mostly submaximal during the movement (Austin et al., 2010;Bohm et al., 2019;Brennan et al., 2019;Monte et al., 2020;Nikolaidou et al., 2017;Rubenson et al., 2012).Furthermore, most common muscle models used in musculoskeletal studies and popular software systems (e.g.OpenSim or AnyBody) do not account for the activation dependence of L 0 (Thelen, 2003;Zajac, 1989).Although some earlier models implemented a generic activation-dependent shift in L 0 (Hatze, 1978;Winters, 1995), these are based on in vitro animal input data and thus their validity with regard to human muscles in vivo is unclear.An approximation of the activation-dependent shift in L 0 in human muscle based on in vivo evidence could therefore provide an important improvement of muscle force predictions, which are essential to musculoskeletal modelling and simulations in the context of basic, clinical and application research, as well as the design of assistive devices and exoskeletons controlled by EMG activity or muscle fascicle length.
The main purpose of the present study was to gain a better understanding of the activation dependence of L 0 of human muscle in vivo.By experimentally determining the soleus fascicle force-length curves at maximum and two submaximal EMG activity levels, we investigated activation-dependent shifts in L 0 of the human soleus.We focused on the soleus muscle because it is the greatest plantar flexor (Albracht et al., 2008) and main contributor to propulsion of the body and thereby crucial for the mechanics and energetics of human locomotion (Bohm et al., 2021(Bohm et al., , 2023;;Dorn et al., 2012;Hamner & Delp, 2013;Hamner et al., 2010;Liu et al., 2008).Based on earlier in vivo reports, we hypothesized a moderate rightward shift in the soleus L 0 towards longer length at submaximal EMG activity levels.The second objective was to develop an approximation model that allows to consider the effect of the activation dependence of L 0 on the force-length J Physiol 602.7 relationship using the EMG activity and fascicle length as input variables.

Ethical approval
The ethics committee of the university approved the study (HU-KSBF-EK_2022_0032) and the participants provided their written informed consent in accordance with the Declaration of Helsinki.

Participants and experimental protocol
Fifteen physically active adults were included in the present investigation (height 178 ± 10 cm, mass 76 ± 13 kg, age 26 ± 5 years, five females, mean ± SD).None of the participants reported a history of neuromuscular or skeletal impairments in the 6 months prior to the recordings.
Following a standardized warm-up (15 submaximal and three maximal contractions), participants performed voluntary isometric plantar flexion contractions in 10 different ankle joint angles with the knee in flexed position and the ankle joint moment, soleus fascicle length and soleus EMG activity were measured (Fig. 1).The ankle joint angles were equally-distributed from 10°plantar flexion (dynamometer angle) to the individual maximum dorsiflexion angle and set in a randomized order, allowing to measure over the full joint moment-fascicle length range (Fig. 1B).In each ankle joint angle, the participants first performed a maximum voluntary contraction for ∼5 s.The respective EMG activity of the soleus muscle was processed directly (details below) and the average of a 0.5 s time window around the highest ankle joint moment was defined as maximum EMG activity (EMG max , Fig. 1C).Corresponding joint moments and fascicle lengths were processed accordingly.Participants then performed two submaximal voluntary contractions in the same joint angles when the actual EMG activity was displayed to the participants as percentage of EMG max on a monitor to guide for the two targeted EMG activity levels of 60% EMG max and 30% EMG max .Prior to the recordings, the participants were asked to test the submaximal contraction intensity at the two targeted EMG activity levels in each angle, respectively.No difficulties in achieving and maintaining the targeted EMG activity level by the participants were observed.The submaximal contractions were held for ∼10-14 s, and the EMG activity, joint moment and fascicle length values were averaged over the time interval of 1 s that was closest to the target EMG activity (i.e.60% EMG max or 30% EMG max ) throughout the contraction (Fig. 1C).The ankle joint angles during both submaximal contractions were adjusted to the angle during the peak moment of the maximum voluntary contraction (based on kinematic analysis).A rest of at least 3 min was given between contractions.The measured ankle joint moment, soleus fascicle length and soleus EMG activity were then used to determine activation-specific force-fascicle length curves.

Ankle joint moments
For the plantar flexion contractions, the participants were placed in prone position on the bench of a dynamometer (System 3; Biodex Medical, Inc., Shirley, NY, USA) (Fig. 1A).The right ankle joint was oriented to the dynamometer axis and the knee was fixed in flexed position (∼120 °) to restrict the contribution of the biarticular gastrocnemii muscles to the plantar flexion moment (Hof & van den Berg, 1977;Maganaris, 2001;Rubenson et al., 2012) (Fig. 1A).The resultant moments at the ankle joint were calculated by means of an inverse dynamics approach taking unavoidable misalignments between ankle joint axis and dynamometer axis during contraction as well as gravitational and passive moments into account (Arampatzis et al., 2005).The required kinematic data were recorded based on anatomically referenced reflective markers (medial and lateral malleolus and epicondyles, calcaneal tuberosity, second metatarsal and greater trochanter) and a motion capture system (Vicon, version 2.1; Vicon Motion Systems, Oxford, UK) integrating nine cameras operating at 250 Hz (Fig. 1A).Ankle joint angle-specific gravitational and passive moments as well as angle-specific gravitational moments from the dynamometer's foot adapter were taken into account by recording an additional trial, where the passive ankle joint was rotated by the dynamometer at 5°s -1 at full muscle relaxation (Arampatzis et al., 2005).Furthermore, we used the EMG-based approach reported by Mademli et al. (2004) to determine the contribution of the antagonistic muscles during the plantar flexion contractions, under consideration of the force-length dependence of the antagonists (Bohm et al., 2019).

Soleus muscle fascicle length
Soleus muscle fascicle length during the plantar flexion contractions was synchronously captured by B-mode ultrasonography at 30 Hz (Aloka Prosound Alpha 7; Hitachi, Tokyo, Japan) using a 6 cm linear array probe (UST-5713T; 13.3 MHz).The probe was placed over the medial aspect of the soleus muscle belly with a custom neoprene/plastic cast (Fig. 1A).A standoff gel pad was used to ensure proper signal transmission (Sonokit soft; Sonogel, Bad Camberg, Germany).The fascicle length was analysed from the ultrasound images using an advanced version of our earlier semi-automatic tracking algorithm (Marzilger et al., 2018).The procedure included an automatic frame-by-frame identification of the deeper and upper aponeurosis using the 'canny edge detection algorithm' implemented in Matlab, R2019a (Mathworks, Natick, MA, USA).Image brightness features between both aponeuroses were then identified by means of the Matlab 'bwtraceboundary' function and the 'canny edge detection algorithm' (Fig. 1A).
Every frame was visually controlled for adequate feature and aponeurosis placement and manually corrected if necessary.Based on multiple fascicle features, a linear weighted averaged reference fascicle was calculated to determine a representative fascicle length (Fig. 1A).The raw fascicle length data were filtered using a low-pass second order Butterworth filter with a cut-off frequency of 6 Hz.

Electromyographic activity
During the maximal and submaximal isometric plantar flexion contractions, the soleus muscle EMG activity was captured at a sampling frequency of 1000 Hz using a cable EMG system (Biovision, Wehrheim, Germany) and two bipolar surface electrodes (H124SG; Medtronic plc, Dublin, Ireland).After skin preparation, the two electrodes were placed on the medial belly of the soleus muscle with an inter-electrode distance of 2 cm and the ground electrode on the medial malleoli according to the Seniam guidelines (http://www.seniam.org).The raw EMG data were processed using a second order high-pass Butterworth filter with a cut-off frequency of 6 Hz, a full-wave rectification and then a second order low-pass Butterworth filter with a cut-off frequency of 3 Hz (Fig. 1B).

Activation-specific force-length relationship
The force acting on the Achilles tendon during the plantar flexion contractions was calculated as quotient of the ankle joint moment and the individual Achilles tendon lever arm.The lever arm was determined by the ultrasound-based tendon excursion method (Fath et al., 2010;Holzer et al., 2020).During a passive ankle joint rotation at 5°s -1 using the Biodex, the displacement of the musculus gastrocnemius medialis-Achilles tendon junction was captured by ultrasound and the lever arm was calculated as the quotient of junction displacement and corresponding angular excursion.The quotient was calculated over the interval of 5°dorsiflexion to 15°p lantar flexion, where tendon deformation is very small (De Monte et al., 2006).The individual values were then corrected for the alignment of the tendon during contractions (Maganaris et al., 1998).
For each muscle contraction at the different EMG activity levels (100%, 60% and 30% EMG max ), the assessed forces applied to the tendon and corresponding soleus muscle fascicle length were used to calculate individual force-fascicle length relationships using a second-order polynomial fit.The activation-specific L 0 and respective peak force were then derived from the fit, respectively.In three participants, only nine ankle joint angles could be included as a result of measurement artifacts.

Approximation model of the activation-dependent force-length relationship
A force-length-EMG activity relationship for the full spectrum of EMG activity levels and fascicle lengths was approximated for each participant separately.The individually measured soleus fascicle lengths and forces at the three different EMG activity levels were first normalized to the optimal fascicle length and corresponding maximum force determined from the individual 100% EMG max force-length curve (i.e.L 0 max and F max 100% ).The normalized fascicle lengths and forces were used as inputs to the Matlab optimization function 'fmincon' aiming to define constrained activation-specific parabolic force-length curves by minimizing the quadratic errors of the fit.Descending forces from 100% EMG max to 0% EMG max activity level in the fascicle lengths region 0.5 to 1.5 L 0 max and a given predefined L 0 in all three EMG activity levels based on the experimental data were used as constraints.Note that single curve fitting (experimental part) might not fulfill these conditions per se and could have caused contortions in the approximation or unreasonable shifts in L 0 .Accordingly, maximum forces and shapes of the parabolas might slightly deviate from the experimental curves.The chosen fascicle length region should reflect the regions where active force is generated (Zajac, 1989).The three parabolas were then evaluated at 200 equidistant data points and used as inputs to the Matlab function 'scatteredinterpolant' that interpolated the force between the different levels of EMG activity linearly.The evaluation of the model output allows to approximate the individual soleus isometric muscle force and force-length potential (i.e.fraction of the maximum active force according to the force-length curve at each EMG activity level) for any given normalized fascicle length and EMG activity under consideration of the activation dependence (i.e.individual approximation).The same approximation approach was also applied to the data of all fifteen participants together, aiming to obtain a group-level estimate of the force-length relationship (i.e.average approximation).The Matlab code and approximation outcome is provided in the Supporting information, including an example data set.The flow chart in Fig. 2 illustrates the steps taken to develop the approximation model.Using the individual approximation model outcome, we calculated the individual approximated force-length potential as a function of fascicle length and EMG activity (mesh grid from 0.6 to 1.4 L/L 0 max and 0 to 1 EMG/EMG max ) for each participant.We compared this with the corresponding individual force-length potential not changing across EMG levels, i.e. constant L 0 across EMG activity levels based on the individual force-length potential at EMG max .The resulting differences of the force-length potential were then averaged across participants and displayed by a contour plot in order to examine the effect of an activation-dependent shift in the force-length relationship on the force-length potential.Furthermore, we used the average approximation model outcome to calculate an average activation-dependent force-length potential as a function of normalized fascicle length and EMG activity.For each participant, we then calculated the absolute mean differences between the individual approximated force-length potential (based on the individual measured data) and the average force-length potential (based on all participants data).The resulting force-length potentials were again averaged and examined by a contour plot to examine the difference between the average and the individual approximation for each participant.

Statistical analysis
A linear mixed model (random effects) with the factor EMG activity level (100% EMG max , 60% EMG max and 30% EMG max ) was used to test its effect on L 0 .In the case of a main effect of EMG activity level, pairwise comparisons were performed with P value adjustment following the Benjamini-Hochberg procedure controlling for the false discovery rate (adjusted P values are reported).Normal distribution of the normalized residuals was given according to the Shapiro-Wilk test.The level of significance was set to α = 0.05 and the statistical analyses were performed using RStudio, version 2022.07.1 (RStudio Inc., Boston, MA, USA) and the 'nlme' and 'emmeans' packages.R 2 was calculated to describe the goodness of the quadratic fit to the measured normalized fascicle length and normalized forces at each EMG activity level as a measure of the accuracy of the individual and average approximation of the activation-specific force-length relationships.Descriptive data are presented as the mean ± SD.

Results
Soleus muscle forces and fascicle lengths for the 100%, 60% and 30% EMG max activity levels with the respective fitted force-length curves for one representative participant are shown in Fig. 3.
Figure 4 shows the average force-fascicle length curves for the 100% EMG max , 60% EMG max and 30% EMG max levels.Compared to the 100% EMG max force-length curve, the curves of the 60% EMG max and 30% EMG max showed a slight but consistent shift to the right.There was a significant main effect of EMG activity level on L 0 (P < 0.001) (Fig. 4B).The post hoc test showed a significant increase of 6.5 ± 6.0% (mean ± SD) of L 0 from 100% EMG max to 60% EMG max (P < 0.001) and of 9.1 ± 7.2% from 100% EMG max to 30% EMG max (P < 0.001), whereas the increase of 2.4 ± 2.8% from 60% EMG max to 30% EMG max was not significant (P = 0.062) (Fig. 4).The peak force in the 100% EMG max , 60% EMG max and 30% EMG max condition was 2894 ± 739 N, 1604 ± 271 N and 749 ± 140 N, respectively.
The approximation of the individual activation-specific force-length curves showed a high goodness of fit with an average R 2 of 0.899 ± 0.056 (range 0.965 to 0.762; for a representative example, see Fig. 5A).Furthermore, using the data of all participants in the model, the average activation-specific force-length curves were approximated with a high accuracy of R 2 = 0.858 as well (Fig. 5C).The contour plots of the approximated force-length potential as a function of normalized EMG activity (to EMG max ) and normalized fascicle length (to L 0 max ) for one representative individual (Fig. 5B) and the average group data (Fig. 5D) demonstrate how the measured shift in L 0 influences the approximated force-length potential for a given EMG activity and fascicle length.As a result of the activation-dependent shift, the approximated force-length potential is less at a given short length and higher at a given long length at the submaximal EMG activity levels compared to the force-length potential at maximum EMG activity as indicated by the rightward progression of the isolines of a certain force-length potential from high to low EMG activity (Fig. 5B and D).
The comparison between the individual approximation of the activation-dependent force-length potential and the force-length potential without consideration of the activation dependence showed mean differences below 10% for a broad range of normalized EMG activity levels and fascicle lengths (Fig. 6A).Differences were higher for low EMG activity levels and short and long fascicle lengths with average differences of −17% to +15% at the displayed boundaries of 0.6 and 1.4 L 0 max and activation level of 0% EMG max , respectively (Fig. 6A).The average approximation of the force-length potential compared to the individual approximation showed slight absolute mean differences, yet they were mostly below 5% in the examined range (Fig. 6B).Higher absolute mean differences were only found at longer fascicle lengths (>1.3 L 0 max ).The observed differences between average and individual approximation were always less than the differences when not considering the activation dependence (Fig. 6A vs. B).

Discussion
In the present study, we experimentally determined force-fascicle length curves of the human soleus muscle at 100% EMG max , 60% EMG max and 30% EMG max levels to investigate activation-dependent shifts in L 0 in vivo.We found a moderate rightward shift in the force-fascicle relationship with a significantly greater L 0 at decreasing EMG activity levels, providing evidence of an in vivo activation dependence of the force-length relationship of the human soleus muscle.Based on the experimental results, we developed an approximation model of the activation-dependent force-length relationship for each individual separately and using the collective data of all participants, and both models allowed an estimation with high accuracy.This approach enables to consider the activation dependence of L 0 in future investigations of muscle force-length properties.
The experimentally determined L 0 max of the soleus muscle (i.e.41.4 mm) was comparable to previous experimental studies using the ultrasound methodology (range 38-45 mm; Bohm et al., 2019;Bohm et al., 2023;Bohm et al., 2021;Maganaris, 2001;Rubenson et al., 2012).During the submaximal contractions, however, L 0 shifted slightly towards longer lengths by 6.5% from 100% EMG max to 60% EMG max and by 9.1% from 100% EMG max to 30% EMG max .This demonstrates an activation dependence of L 0 of the human soleus muscle during voluntary contractions in vivo.Previous in vitro and in situ studies mostly reported greater activation-dependent shifts in L 0 as we found here (Hessel et al., 2019;MacDougall et al., 2020;Morgan, 1990;Rack & Westbury, 1969;Stephenson & Wendt, 1984), sometimes up to 30% (Holt & Azizi, 2016;Holt & Williams, 2018) and even 70% (Holt & Azizi, 2014).Large electrical stimulation frequency ranges or potentially non-physiological calcium concentrations used for the muscle activation in the in vitro and in situ experiments may not adequately represent the calcium levels of voluntary activation in vivo (de Brito Fontana & Herzog, 2016).Therefore, the phenomenon of the activation dependence of L 0 may actually be less pronounced under physiological in vivo conditions.Regarding in vivo investigations in humans, the reported results are inconsistent.Hessel et al. (2021) reported a sub-stantial activation dependence for the soleus and gastrocnemius lateralis muscle in vivo (up to 20%), thus being markedly greater compared to the moderate shift in L 0 of 9.1% in the present study.Moreover, at their submaximal 30% EMG max and 22% EMG max levels, they did not find a descending part in the soleus muscle force-length curve.In the study by Hessel et al. (2021), the force-fascicle length relationship of the soleus and gastrocnemius lateralis muscle was investigated at an extended knee joint position, where all three muscles of the triceps surae (soleus, gastrocnemius medialis and lateralis) contribute to the measured ankle joint moment.Therefore, by means of this experimental design, it was not possible to quantify the specific contribution of the monoarticular soleus and the contribution of the biarticular gastrocnemii muscles.In the present study, the soleus muscle was isolated as a result of the marked knee flexion of >110°, where the contribution of the gastrocnemii to the ankle joint moment is negligible (Hof & van den Berg, 1977;Maganaris, 2001;Rubenson et al., 2012).This might explain the discrepancy of the magnitude of the activation-dependent shift of L 0 for the soleus muscle between the two studies.de Brito Fontana & Herzog (2016) investigated the human vastus lateralis muscle in vivo and found small and variable rightward shifts in L 0 in a range of ∼5% at decreasing EMG activity levels without statistical significance, suggesting a minor effect of the activation dependence for this muscle in Experimentally-determined force-fascicle length curves (mean ± SD, n = 15) of the soleus muscle for the maximal (100% EMG max ) and two submaximal (60% EMG max and 30% EMG max ) EMG activity levels (A).Force is normalized to the maximal force obtained from the maximal isometric plantar flexion contractions (F max ) and fascicle length to the corresponding optimal fascicle length (L 0 max ).With decreasing activation level, the optimal length (L 0 ) showed a shift towards longer lengths (B, box plots show median, upper and lower quartiles, and whiskers extend to the most extreme data points not considered outliers; dots present individual data, n = 15).* Significant main effect of EMG activity level (P < 0.001).# Significantly greater than 100% EMG max level (both P < 0.001).

S. Bohm and others
J Physiol 602.7 vivo.In addition to methodological discrepancies in the determination of the force-fascicle length relationship, the activation dependence of L 0 of different muscles and individuals might also be influenced by physiological factors such as fibre type composition (Konhilas et al., 2002) and magnitude of fibre shortening as a result of tendon stiffness (Holt & Williams, 2018).Activation-dependent shifts in L 0 are commonly assigned to a length-dependent calcium sensitivity (de Tombe et al., 2010;MacIntosh, 2017).Recently, force depression as a result of initial fascicle shortening against the compliant tendon during fixed-end (isometric) contractions were suggested as a further factor for activation-dependent shifts in L 0 .Force depression has been shown to increase with greater shortening magnitude (Herzog & Leonard, 1997;Maréchal & Plaghki, 1979) and with higher activation levels (De Ruiter et al., 1998).In the present study, the EMG activity in each level was similar as predefined by the protocol.Therefore, for a given EMG activity level, force depression could theoretically influence the activation-specific force-length curve only when the shortening magnitude would be different across the contractions at the different ankle joint angles (i.e.length portions of the force-length curve).When testing for differences of the fascicle shortening magnitudes between the 10 different contractions at the different ankle joint angles within each EMG activity level (resting fascicle length to length at target EMG activity), we did not find any statistically significant differences.The similar EMG activity and fascicle shortening within the three investigated EMG activity levels indicate that a potential force depression across the contractions at the different joint angles would be consistent and thus will not affect the position of L 0 on the activation-specific force-length curves.However, between the three EMG activity levels, both fascicle shortening (100% EMG max : 16.63 ± 1.08 mm, 60% EMG max : 13.56 ± 1.48 mm and 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Fascicle length (L/L 0 max ) .Activation-dependent force-length potential A, isolines show the mean percentual differences between the individual approximated soleus force-length potential and the force-length potential without a shift in L 0 as a function of normalized EMG activity (to EMG max ) and normalized fascicle length (to L 0 max ).As a result of the activation-dependent shift in L 0 , the percentual differences displayed by the isolines in the force-length potentials increase with decreasing EMG activity levels and shorter and longer fascicle lengths, indicating the evolvement of the effect of the activation dependence of L 0 on the force-length potential throughout the physiological spectrum of EMG activity levels.B, isolines show the absolute percentual differences of the soleus force-length potential between the averageand the individual approximation models averaged across participants.
30% EMG max : 11.71 ± 1.24 mm) and EMG activity, were not similar, which predicts a different magnitude of force depression and hence potential effects on L 0 .Recent human in vivo evidence suggest that force depression in the tibialis anterior muscle during a fixed-end contraction is ∼3-5% (Raiteri et al., 2023).To assess the potential contribution of force depression to our observed activation-dependent shift in L 0 of the soleus muscle, we assumed a force depression of 5.00%, 3.34% and 1.67% for our 100%, 60% and 30% EMG max levels.Taking these values into account for each of the 10 contractions in the three EMG activity levels, we subsequently recalculated the force-length curves and respective L 0 of the three EMG activity levels.The difference in force depression between the three EMG activity levels did not change the activation-specific shift in L 0 , indicating a negligible effect on the activation-dependent shift in L 0 in our results.Activation dependence of L 0 can influence the muscles force generating potential during dynamic movements with a variable activation pattern.We found a significant, yet moderate activation-dependent shift in L 0 of the soleus muscle in vivo.Using the approximation model, we showed that, at a given fascicle length, the activation dependence of L 0 may influence the force-length potential of the soleus muscle during submaximal activation levels (Fig. 6A).For example, at an activity level of 0.4 EMG/EMG max and a fascicle length of 0.8 L/L 0 max , the force-length potential under consideration of the activation dependence of L 0 was ∼10% lower compared to the force-length potential without its consideration.At the same EMG activity but longer length of 1.2 L/L 0 max , the force-length potential that includes the activation dependence was ∼6% higher.Earlier studies have shown that the human soleus muscle operates on the ascending limb close to L 0 during the stance phase of walking and running and thus at a high force-length potential (i.e.>0.90), which was based on a force-length curve determined at EMG max activity (Bohm et al., 2019(Bohm et al., , 2023;;Rubenson et al., 2012).However, the corresponding EMG activity during gaits was not maximal.Using the overall approximation model outcome that integrates the activation dependence of L 0 , it can be predicted that the soleus fascicles operate lower on the ascending limb of the activation-specific force-length curve and that the soleus force-length potential is consequently less, depending on the actual EMG activity level.At the highest running speeds, the normalized EMG activity of soleus is higher than 0.8 EMG/EMG max over a large part of the stance period and, during the same time, the fascicles operate around 0.85-0.95L/L 0 max (Bohm et al., 2023), indicating that the effect of the activation dependence in the relevant time of force generation would be below 2%.However, during walking the soleus EMG activity around the peak is only in a range of 0.3-0.4EMG/EMG max J Physiol 602.7 (Kharazi et al., 2021) with the normalized fascicle length being in a range comparable to that during running (Rubenson et al., 2012), which predicts a greater reduction of the force-length potential in magnitude of ∼6-7%.This example shows that the activation dependence of the force-length relationship influences the soleus force-length potential during functional movements and gives a reason for its integration in studies experimentally investigating the muscle force-length potential in vivo or in musculoskeletal models for muscle force predictions and its related various research and application fields (e.g.such as for the design of powered prostheses and exoskeletons).However, one might consider that the effect of the activation dependence of L 0 on the force-length potential, at least for the soleus muscle, is moderate as indicated by the approximation model outcome.
We developed an individual and an average approximation model to enable a consideration of the activation-dependent shift in L 0 in the determination of the force or force-length potential during dynamic movements.The approximation for each individual showed a high agreement between the estimated and measured activation-specific force-length curves (R 2 = 0.899).Accordingly, this approach allows, for the first time, an approximation of an individual force-length potential that accounts for the activation dependence of L 0 for any submaximal EMG activity level and fascicle length with very good accuracy.By the method proposed here (i.e.measurement of three activation-specific force-length curves and the approximation model), the individual activation-dependent force-length relationship can be determined, which enables a biologically better founded force-length potential.The Matlab code used for the individual approximation model is available in the Supporting information and may also be used for other muscles.Furthermore, the average approximation based on all participants showed a quite high agreement between the predicted and measured activation-specific force-length curves as well (R 2 = 0.858).The comparison of the individual and the average approximation of the soleus muscle force-length potential showed absolute mean differences lower than 5% for the investigated range of fascicle lengths and EMG activity levels.Most importantly, the observed differences in the force-length potential between average and individual approximation were always smaller than the differences to the force-length potential without considering the activation dependence of L 0 at all.The output of the average approximation model is accessible via the Supporting information and can be used with measured normalized fascicle lengths and EMG activities as inputs for the consideration of the activation-dependent shift of L 0 in in vivo experimental investigations, substantially reducing measurement and analysis efforts and, in musculoskeletal models, enhancing the accuracy of the muscle force predictions.
In conclusion, the present study provides experimental evidence of a moderate activation-dependent shift in L 0 of the human soleus muscle in vivo that may influence the operating force-length potential during dynamic movements.An individual and an average approximation model with high accuracy was formulated based on the experimental data, enabling the consideration of the activation dependence of L 0 in future experimental investigations of muscle force-length properties and musculoskeletal modelling.
Figure 1.Experimental procedureA maximum (100% EMG max ) and two submaximal isometric plantar flexion contractions (60% EMG max and 30% EMG max ) were performed in different ankle joint angles and the ankle joint moments, soleus muscle fascicle length (fas.) and electromyographic activity (EMG) were recorded (A).The different ankle joint angles throughout the full range of motion were used to measure the full joint moment-fascicle length range (B, negative angles indicate plantar flexion and dots the measured fascicle lengths and ankle angles during contraction).The processed EMG activity around the maximum joint moment was used as a reference value to target the EMG activity of the 60% EMG max and 30% EMG max(C, raw EMG in grey and processed EMG in black, vertical  lines indicate averaging windows).[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 2 .
Figure 2. Flow chart Flow chart to illustrate the process of developing the individual and average approximation model.[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 3 .
Figure 3. Exemplary soleus muscle force-fascicle length curvesSoleus muscle force-fascicle length curves for the investigated EMG activity levels (i.e.100%, 60% and 30% EMG max ) based on the measured activation-specific muscle forces and fascicle lengths for a representative participant.

FascicleFigure 4 .
Figure 4. Experimentally-determined force-fascicle length curves and optimal fascicle length of the soleus muscleExperimentally-determined force-fascicle length curves (mean ± SD, n = 15) of the soleus muscle for the maximal (100% EMG max ) and two submaximal (60% EMG max and 30% EMG max ) EMG activity levels (A).Force is normalized to the maximal force obtained from the maximal isometric plantar flexion contractions (F max ) and fascicle length to the corresponding optimal fascicle length (L 0 max ).With decreasing activation level, the optimal length (L 0 ) showed a shift towards longer lengths (B, box plots show median, upper and lower quartiles, and whiskers extend to the most extreme data points not considered outliers; dots present individual data, n = 15).* Significant main effect of EMG activity level (P < 0.001).# Significantly greater than 100% EMG max level (both P < 0.001).

Figure 5 .
Figure 5. Activation-dependent force-length relationships Approximation of the activation-dependent force-length relationships for one representative individual (A) and including the data of all participants (C, n = 15).The isolines in the corresponding contour plots (B and D) show the approximated force-length potential (fraction of the maximum active force according to the force-length curve at each EMG activity level) by the individual and average approximation model as a function of the full spectrum of normalized EMG activity (to EMG max ) and normalized fascicle length (to L 0 max ).Because of the activation-dependent shift in the force-length relationship, the approximated force-length potential also shifts for any given fascicle length at submaximal EMG activity levels compared to the potential at maximum EMG activity, i.e. rightward progression of isolines with decreasing EMG activity (individual approximation in (B) and average approximation in (D)).