Force enhancement and force depression in a modified muscle model used for muscle activation prediction

Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx

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Force enhancement and force depression in a modified muscle model used for muscle activation prediction Natalia Kosterina a, Ruoli Wang a, Anders Eriksson a, Elena M. Gutierrez-Farewik a,b,⇑ a b

KTH Mechanics, Osquars backe 18, 100 44 Stockholm, Sweden Karolinska Institutet, Department of Women’s and Children’s Health, Sweden

a r t i c l e

i n f o

Article history: Received 27 June 2012 Received in revised form 22 February 2013 Accepted 25 February 2013 Available online xxxx Keywords: Muscle model Force depression Force enhancement Activation modification Musculoskeletal system Heel-raise Squat Electromyography

a b s t r a c t This article introduces history-dependent effects in a skeletal muscle model applied to dynamic simulations of musculoskeletal system motion. Force depression and force enhancement induced by active muscle shortening and lengthening, respectively, represent muscle history effects. A muscle model depending on the preceding contractile events together with the current parameters was developed for OpenSim software, and applied in simulations of standing heel-raise and squat movements. Muscle activations were computed using joint kinematics and ground reaction forces recorded from the motion capture of seven individuals. In the muscle-actuated simulations, a modification was applied to the computed activation, and was compared to the measured electromyography data. For the studied movements, the history gives a small but visible effect to the muscular force trace, but some parameter values must be identified before the exact magnitude can be analysed. The muscle model modification improves the existing muscle models and gives a more accurate description of underlying forces and activations in musculoskeletal system movement simulations. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Musculoskeletal modelling is widely used for motion analysis and movement prediction. An accurate muscle model is an essential factor for reliable musculoskeletal system simulation of dynamic tasks. Forward dynamics simulations allow examination of muscle properties that cannot be measured. Among the developed musculo-skeletal models, very few studies consider muscle history phenomena in dynamic simulations (Ettema, 2002; McGowan et al., 2010) despite the need to investigate the influence of history-dependent effects (Winters, 1995). The existing muscle models are limited due to complexity of the underlying processes and gaps in knowledge. Based on previous research (Kosterina et al., 2008, 2009, 2011) improvements to a common muscle model by adding a history dependence during active length variations have been suggested. Residual force enhancement (FE) induced by active stretching and force depression (FD) induced by active shortening are complex phenomena, but can be relatively well predicted by a simple formula as these history effects can be

⇑ Corresponding author at: KTH Mechanics, Osquars backe 18, 100 44 Stockholm, Sweden. Tel.: +46 87907719. E-mail address: [email protected] (E.M. Gutierrez-Farewik). URL: http://www.mech.kth.se/mech/info_staff.jsp?ID=200 (E.M. Gutierrez-Farewik).

described by the mechanical work accumulated or performed during the movements (Kosterina et al., 2008, 2009). Force history effect induced by muscle length variation has been studied by many groups during the last six decades, (Abbott and Aubert, 1952; Herzog and Leonard, 1997; Lee and Herzog, 2003; Lou et al., 1998; Marechal and Plaghki, 1979; Morgan et al., 2000; Power et al., 2012; Sugi and Tsuchiya, 1988). A study of voluntary contractions of large human muscles in vivo has shown that the activation reduces along with FE after stretch contractions (Seiberl et al., 2012), which shows that the motor control system can adjust according to the history effect. Activation modification was observed along with the force modification in intact muscle contraction, (Altenburg et al., 2008; Hahn et al., 2007; Oskouei and Herzog, 2006). Both manifestations of the history effect, i.e. force and activation modifications, are essential although the reported conclusions diverge (Pinniger and Cresswell, 2007; Seiberl et al., 2012; Tilp et al., 2009). The correct relation between force and activation modifications during voluntary contractions would further describe the muscle history effect. Regarding the quantitative significance of FD and FE, these phenomena have been suggested to lead to alterations in the neural activation and changes in muscle activation rather than producing smaller or larger forces (Seiberl et al., 2012). Oskouei and Herzog (2006) found that less activation was required to obtain a certain submaximal force level after muscle stretch and proposed that muscle history phenomena are related to metabolic cost of the contractions.

1050-6411/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jelekin.2013.02.008

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008

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N. Kosterina et al. / Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx

Muscles’ characteristic force–length and force-shortening velocity relationships play important roles in the mechanics of muscle behaviour and are measured and estimated using various techniques. Ultrasonography and magnetic resonance imaging allow fairly accurate estimations of muscle length (Maganaris, 2001), and the musculotendon complex length can be estimated from anatomical and joint kinematic data (Fukunaga et al., 2001). However, muscle forces in situ have only been measured in human adductor pollicis muscle (Lee and Herzog, 2002; Ruiter et al., 1998). Muscle force measurements in vivo are invasive and restricted to superficial structures such as Achilles’ tendon (Finni et al., 1998) and intact tendons (Schuind et al., 1992). To estimate muscle force, the torque created from a muscle group can be measured in vivo (Altenburg et al., 2008; Hahn et al., 2007; Lee et al., 1999) and the load sharing problem solved, though the solution will depend on the optimization design and criteria (Kaphle and Eriksson, 2008). Due to the measurement limitations, a musculoskeletal model can be validated, at least in part, by several methods, e.g., by comparing muscle forces calculated from inverse dynamics with dynamometric measurements for a muscle group (McGowan et al., 2010). Another method consists of comparing calculated muscle activation with the recorded electromyography signal (EMG) (Lloyd and Besier, 2003). Computed activation is an approach to describe muscle excitation, alluding to which muscles are involved and to which extent. The EMG signal measures the stimulation directly under the electrode placement, regardless of the resulting muscle activation. Despite the differences between activation and stimulation, these quantities are commonly used interchangeably in musculo-skeletal modelling. Hatze (1977) proposed an equation describing how muscle force and activation are related. A modified form of this relation by Thelen et al. (2003) is:

F ¼ ðA  F lv ðl; _lÞ þ F passive ðlÞÞ  cosðaÞ;

ð1Þ

where F is a steady-state muscle force, A the activation, Flv the active force–length–velocity surface, Fpassive the passive force, a the pennation angle at the steady-state muscle length l for a given muscle, and _l denotes time derivative of length. Muscle activation, A, can be calculated for an existing muscle model using experimental data by solving A from a computed force F⁄ under given l, _l and muscle architecture, using Eq. (1). A procedure of this type is used in OpenSim (Delp et al., 2007) to compute a muscle force F⁄ from kinematics, and then ultimately an activation A. This inverse calculation of activation from kinematics and external forces implicitly assumes an equation of the form in Eq. (1), regardless of history. The calculation is performed for each considered muscle. History effects from previous muscular work can be added to the force calculated from the activation according to, Kosterina et al. (2009):

F þ ¼ F þ dF mod ;

Amod

2. Methods Seven healthy adults (six females and one male, age 29 ± 3 years, weight 56.1 ± 6.9 kg, height 1.63 ± 0.04 m) participated in this study. The subjects participated with informed consent; they were physically active, but none of them participated in any competitive exercise training. The study was approved by the local Ethics Committee. 2.1. Experimental setup A maximum voluntary isometric contraction (MVIC) test was performed for EMG scaling. The subjects sat upright in an isometric dynamometer chair with the hip, knee and ankle fixed at 90°, 60° and 90° (neutral), respectively (Örtqvist et al., 2007). The calf and the foot were tightly fastened to restrict joint motion. The isometric condition was defined as a fixed-end contraction where the muscle–tendon complex was held at constant length. Surface EMG signals (Motion Laboratory System, Baton Rouge, LA) were recorded for the subjects for the rectus femoris (RecFem), tibialis

ð2Þ

with F+ the total force consisting of the activated force F from Eq. (1) and a history-dependent modification dFmod. When this modified force is used in an inverse dynamics setting, this demands a corresponding modification of the calculation of activation from the computed force. As the force modification dFmod at a certain time instance is completely defined by history, only the remainder of a needed force F⁄ must be created by the activation. Using Eq. (1), one can find the modified activation as:

   F  dF mod 1 ¼ ;  F passive ðlÞ  cosðaÞ F lv ðl; _lÞ

The situation considered in the present work is shown in Fig. 1. The basis for the figure is that a force F⁄ (any of the forces in the studied system) is needed to create the recorded kinematics, symbolically represented by L⁄. Without consideration of history, as in OpenSIM, an activation would be calculated by CMC, which is the inverse of Eq. (1) — or Eq. (3) with dFmod = 0. When considering the force modification, only the force Fmod = F⁄  dFmod need be created by the activation, and the modified activation Amod is calculated from Eq. (3). This activation Amod used in Eq. (1) creates the force Fmod to which is added dFmod leading to the total force F⁄ consistent with kinematics. As will be further detailed below, the modified activation Amod can be seen as a subtraction of a quantity dAmod from the A calculated by the included CMC algorithm. Our study hypotheses were that (i) introducing the history effect in a musculoskeletal system improves the modelling of movement, that (ii) the motor control activation in human movement considers the history effect, and that and (iii) activation Amod conforms to EMG data better than the OpenSim output A, which would tend to verify (i). The present work thereby introduces a method to test a musculoskeletal system modelling in the open-source software OpenSim. A series of experiments on human movement was conducted to test the effects of this modified muscle model, using the model for all muscles in a studied subject, keeping track of the force history of all muscles, and using an evaluation of activation based on Eq. (3), rather than on the inverse of Eq. (1).

ð3Þ

which creates the force F⁄ by using the expressions in Eqs. (1) and (2).

Fig. 1. Schematic diagram of activation calculations. Kinematics of a movement symbolically represented by L⁄ demand a muscular force F⁄ in each muscle. OpenSim calculates the corresponding activation A without consideration of history effects, through the CMC algorithm, representing the inverse of Eq. (1). When considering the history effect dFmod, a modified activation Amod creates the force Fmod which with dFmod sums up to F⁄. The present work aims to calculate the difference dAmod, defined by Amod = A  dAmod.

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008

N. Kosterina et al. / Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx

anterior (TibAnt), medial head of the gastrocnemius muscle (MedGas) and soleus (Sol) bilaterally according to the SENIAM protocol (http://www.seniam.org). A series of tasks was chosen to place a high load on the five mentioned muscles. The participants performed a dynamic task after the MVIC test: 3 cycles of standing heel-raise (rise up and down on toes) with a 3 s delay in the upper position, and 3 cycles of squats. The subjects were examined using an 8–camera motion capture system (Vicon MX40, Oxford, UK) and two force-plates (Kister, Winterthur, Switzerland). Sixty-four reflective markers (9 mm) were placed bilaterally on bony landmarks based on a conventional full-body marker set (Vicon Plug-in-Gait), plus a multisegment foot model marker set (Stebbins et al., 2006). One subject performed an additional series of squats both slowly and quickly, and both with and without an additional load of 40 kg, held at the shoulders.

2.2. Data processing During experiments, EMG was sampled at 1000 Hz. Data were filtered using a bidirectional second order Butterworth filter with a cutoff frequency of 3 Hz in Matlab (version R2011a, The MathWorks, Natick, USA). EMG for each muscle was normalized from zero to one based on the minimum and maximum values for that muscle during the MVIC and the performed movements.

2.3. Musculoskeletal model A generic musculoskeletal model with 14 segments, 23 degreesof-freedom and 96 musculotendon actuators was used to generate the simulation in OpenSim 2.4 (Delp et al., 2007). The head, arms, and torso were modelled as a single rigid body which articulated with the pelvis via a ball-and-socket back joint. Each hip was modelled as a ball-and-socket joint, each knee as a hinge joint, each ankle, subtalar and metatarsophalangeal joint as a revolute joint (Anderson and Pandy, 1999; Delp et al., 1990). A subject-specific simulation of heel-raise and squat was generated. The model was scaled to each subject based on the experimental marker set placed on anatomical landmarks. The inverse kinematics algorithms solved for joint kinematics that minimized the differences between experimental marker and virtual marker positions. Dynamic inconsistency between the measuredground reaction forces and the kinematics was resolved by applying small external forces and torques (i.e. residuals) to the torso and making small adjustments to the model mass properties and kinematics (Delp et al., 2007). Constraints on muscle activation were pre-defined based on the EMG records for the relevant muscles, primarily to maintain the load-sharing between synergetic muscles. The range of the activations was outlined as filtered normalized EMG signal ±10% of its maximum value. Computed muscle control (CMC) (Thelen et al., 2003) with the pre-defined constraints on these muscles’ activations was used to find a set of actuator activations, A, implicitly using the A  F relation of Eq. (1). The constraints are required to track the kinematics and to be generally consistent with experimental EMG patterns. Static optimization was used in CMC to determine the muscle forces and to minimize a cost function at every timestep t for the set of N muscles:

JðtÞ ¼

N X V i ½Ai ðtÞ2 ; i¼1

where Vi is the volume of muscle i and Ai(t) is the activation of muscle i (Happee, 1994; Thelen and Anderson, 2006).

3

2.4. Muscle model modification The muscle force modification in Eq. (2) during and after nonisometric contractions is expressed with a simple formula:

dF mod ¼ K hist  W  A;

ð4Þ

where Khist is the history coefficient, and W is the mechanical work performed by or on the muscle during the dynamic movement (described by the sign of W). Due to lack of information about the history coefficient for the studied human muscles, Khist was varied in order to test the benefit of implementing the muscle force modification. Considering that force enhancement and force depression reaches up to 30% of maximum isometric force (Lee and Herzog, 2003; Ruiter et al., 1998), the value Khist = 10 m1 was assumed to be appropriate for all muscles. The force modification described by Kosterina et al. (2009) was studied for fully active muscle. We scaled the force modification to muscle activation A in order to eliminate the history effect when the muscle is destimulated (Julian and Morgan, 1979; Morgan et al., 2000). The modified activation was calculated according to Eq. (3) and appeared as:

Amod ¼ A  dAmod ¼ A 

dF mod : cosðaÞ  F lv

ð5Þ

The mechanical work was evaluated at a current time by a numerical integration over the passed time range of the force multiplied by shortening velocity:

W¼

X

F  _l  Dt;

ð6Þ

where F and _l are quantities in the time series of intervals Dt. The same modification was used for all muscles, using the individual work histories. This means that Eqs. (4)–(6) were used for each muscle independently. The new functionality was added to the generalOpenSim software using an application programming interface (API). A plug-in was written in C++ using dynamically linked libraries to calculate Fmod and Amod using built-in classes and objects. The plug-in was then used in the graphical user interface for simulated dynamical motions. 2.5. Data analysis To test the accuracy of the muscle model modification, simulated quantities were compared to experimental data. EMG data was compared to both muscle activation (A) and modified activation (Amod). The differences between the datasets (EMG – A and EMG – Amod) were calculated. The root-mean squared errors were extracted (RMSE). The RMSE quantity was calculated for every attempt, then mean and standard deviations for the groups of individual attempts were computed for both squat and heel-raise movements. 3. Results Heel-raise and squat data were analysed. Due to technical problems, squat data for two of the tested subjects could not be analysed, so the results are based on n = 7 subjects for heel-raise and n = 5 subjects for squat. Two pairs of muscles with the highest normalized forces during the specified movements were chosen. These muscles during a heel-raise were MedGas and Sol, and during squat TibAnt and RecFem. The muscle activations during a heel-raise and a squat are plotted along with the EMG signal in Figs. 2a and 4a. The RMSE between EMG and A, and between EMG and Amod are presented in Figs. 2b and 4b. The modified activation Amod was closer to the

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008

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N. Kosterina et al. / Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx

speculate that metabolic cost of contractions changes depending on the preceding muscle history, with e.g. decrease of metabolic cost during eccentric contractions and compensation for force depression during concentric contractions. In this study, CMC analysis was used to evaluate the set of muscular forces necessary for reproducing recorded movements, therefore it was assumed F  F⁄ and only activation modification dAmod was considered, Eq. (5), Fig. 1. In fact, both modifications of activation and force must be included and future studies should be aimed at defining a correlation between dA and dF. These could be represented in a new formula giving a more accurate description for skeletal muscle model:

EMG signal than the OpenSim output A for MedGas, Sol and TibAnt muscles but not for RecFem. The muscle force F (calculated with A and Eq. (1)) was plotted along with the modified muscle force F+ = F + dFmod, Fig. 3. The force modification appeared negative or positive depending on the preceding muscle length variation. Quantitatively, the modification was up to 15% of the force value. Different conditions of squat performance were compared in a pilot-study. A subject was asked to squat slowly and quickly, then do the same with two 20 kg loads held at the shoulders. Force traces for RecFem muscles are presented in Fig. 5. EMG signal, activation and force modification appeared larger for quick and loaded squats than for slow and unloaded, correspondingly. The results from the additional motion analysis illustrate that force modification is practically non-existent in slow motion with low loads, but present when motion is loaded or fast. The plug-in used for additional analysis, i.e. for calculating of modified muscle activation and force, takes approximately 10% of time used by CMC analysis.

F þ ð1  cÞ  dF mod ¼ ððA  c  dAmod Þ  F lv ðl; _lÞ þ F passive ðlÞÞ  cosðaÞ; ð7Þ where c 2 [0, 1] defines a balance between dFmod, Eq. (4), and dAmod, Eq. (5), induced by active muscle length variations and motor control. In the current study the value c = 1 was assumed, i.e. the brain has full control of the force generation and adjusts the activation level so that the force is not influenced by the length variations. An example of c = 0 is when the central nervous system does not consider the history effect, for instance when in vitro stimulation at a constant activation is performed. Referring to studies wherein both activation and force were modified after active stretch (Oskouei and Herzog, 2006; Seiberl et al., 2012), one may speculate that coefficient c might possess any value between 0 and 1 depending on the extent to which the brain predicts and responds to the active muscle length variation leading to the history effect. This speculation could thus indicate the degree to which the motor control system is familiar with the movement performed. The amount of FD and FE in most published studies has been associated with the shortening magnitude, (Abbott and Aubert, 1952; Bullimore et al., 2007; Herzog and Leonard, 1997; Lou et al., 1998; Schachar et al., 2004) or speed of shortening (Herzog and Leonard, 1997; Lee and Herzog, 2003; Marechal and Plaghki, 1979; Morgan et al., 2000; Sugi and Tsuchiya, 1988). However, a strong association between FD and the mechanical work performed by the muscle has been identified (Herzog et al., 2000; Josephson and Stokes, 1999; Kosterina et al., 2008, 2009). There is, on the other hand, no generally accepted predictor of FE. Bullimore et al. (2007) and Hisey et al. (2009) have found that, starting from a certain stretch magnitude, FE does not depend on the lengthening parameters but on the current muscle length. Kosterina et al. (2009) observed a linear relation between FE and

4. Discussion The main consequence of this study is the improvement of a skeletal muscle model by adding the history effect to the muscle activation using the possibility to add new functionality to the open-source software OpenSim. The modified activation was closer to experimentally observed activation in three out of four studied muscles. The major function of a muscle is to transform an electrical signal into length variation through contractile force generation. The computed muscle control, CMC, (Thelen and Anderson, 2006) makes it possible to compute activation that results in force F, which in turn can be modified by adding a history component dFmod, Eq. (4). However, force F + dFmod would lead to a new movement, so activation modification was introduced instead, Fig. 1. Since muscle memory has mainly been investigated in electrically stimulated muscles and muscle fibres in vitro, modification of activation has not been described in detail. Recent studies of voluntary contractions of human muscles (Altenburg et al., 2008; Oskouei and Herzog, 2006; Seiberl et al., 2012) have shown presence of activation modification along with the force modification. Considering muscle history phenomena, the brain adjusts the signal according to a desired motion. Thus muscle activation decreases after lengthening and increases after shortening. One may

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Fig. 2. Simulation of muscle excitation compared to EMG signal during one heel-raise cycle with 3 s delay in the upper position. The results are given for MedGas and Sol muscles. (a) Example of normalized EMG signal – thin grey line, muscle activation – dashed black line, modified muscle activation – solid thick black line. (b) Root mean squared residuals between muscle activation and EMG signal (triangles) and modified muscle activation and EMG signal (circles), mean ± std, n = 7.

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008

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N. Kosterina et al. / Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx MedGas

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Fig. 3. Simulation of muscle force (dashed black line) and modified muscle force (solid black line) are plotted above, traces of normalized muscle length plotted below. (a) Example of heel-raise cycle with 3 s delay in the upper position, the results are given for MedGas and Sol muscles. (b) Example of squat, the results are given for RecFem and TibAnt muscles. The force modification (grey line) is negative during shortening–stretch cycles (MedGas, Sol, TibAnt) and positive during stretch–shortening cycle (RecFem).

the mechanical work for a subrange of physiological stretch magnitudes. Even though the relationship between FE and mechanical work throughout a wide range of motion is not precisely known, the same function for FE and FD have been incorporated here, as was also done in several other muscle models (Ettema and Meijer, 2000; Forcinito et al., 1998). For computing the force modification, there is one constant required, Khist, Eq. (4), but there are no data for tested human muscles. In a previous study, Kosterina et al. (2009) derived a value of the history coefficient for mouse muscles, 3 m1 for extensor digitorum longus and 4 m1 for soleus muscle. Herzog et al. (2000) obtained Khist = 10 m1 for cat soleus muscle. Assuming that force modification is linearly related with W  A, Khist = 10 m1 was chosen among tested values of the scaling coefficient. The decision was based on the amount of force modification which lies in a range between 30% and 20% of maximum isometric force, MVIC (Lee and Herzog, 2003; Ruiter et al., 1998), and the tested movements do not actually demand a

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substantial effort. A more correct value for Khist in human muscle demands further work and may differ for different muscles. This parameter can be obtained from in vitro experiments, and most likely will be a muscle-specific characteristic but not necessarily person-specific (Kosterina et al., 2009). The modified activation Amod matches measured EMG signal better than A for Sol and MedGas during a heel-raise (Fig. 2) and TibAnt during a squat, but not for RecFem (Fig. 4). The inconstancy of the error tendencies (Figs. 2b and 4b) is probably due to the optimization procedure in OpenSim. A closer look at the muscle activation A in Figs. 2a and 4a shows that its peak is always below the EMG peak. For this reason, Amod after stretch is inferior to A. It is noted that the optimization of load-sharing in OpenSim presently does not consider the history effect, which is not a negligible source of error. Stronger control constraints for muscle activations based on EMG signal might invalidate this irregularity but the intention was to give more freedom for the activation and identify the trend of the modification.

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Fig. 4. Simulation of muscle excitation compared to EMG signal during one squat. The results are given for TibAnt and RecFem muscles. (a) Example of EMG signal – thin grey line, muscle activation – dashed black line, modified muscle activation – solid thick black line. (b) Root mean squared residuals between muscle activation and EMG signal (triangles) and modified muscle activation and EMG signal (circles), mean ± std, n = 5.

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008

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N. Kosterina et al. / Journal of Electromyography and Kinesiology xxx (2013) xxx–xxx

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effect after quick ramps (Kosterina et al., 2008, 2009). This can be explained by accompanied increase of muscle activation in fast movements which scales the influence of the modification component, Eq. (4). The observation may have important implications in, for instance, sports or collision simulations.

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Skeletal muscle model modification representing muscle force depression induced by active shortening and force enhancement induced by active lengthening was introduced in simulations of musculoskeletal system motion by a simple formula. Though current techniques and limited experimental data do not enable us to validate the result fully, the added formulation improved the description of skeletal muscle force and showed the importance of the modification in demanding tasks. Conflict of interest statement

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Fig. 5. Simulation of RecFem muscle force during one squat cycle. Muscle force F – dashed black line, modified muscle force Fmod – solid black line, force modification dFmod – grey line.

The diversity is also explained by muscle length variations during the movement. The muscle force was plotted with probable modified forces, and the results show that dFmod increases force for RecFem but decreases for MedGas, Sol and TibAnt, Fig. 3. In the studied motions, Sol, MedGas and TibAnt muscles perform shortening–stretch cycles, while RecFem muscle does the opposite: it first stretches and then shortens during a squat. Force modification reflects this variation: muscle shortening induces FD, and muscle lengthening induces FE; dFmod P 0 during stretch–shortening and dFmod 6 0 during shortening–stretch contraction. The modification tends to change the force in the expected direction, but the technique does not allow us to measure muscle forces and validate the improvement. Moreover, Eq. (7) should be used in inverse dynamics and CMC analysis to keep an equilibrium between the forces and kinematics. The question of additivity of history effects induced by stretching and shortening was raised several times. Herzog and Leonard (2000) and Lee et al. (2001) have shown that FD and FE are additive in shortening–stretch cycles, but FE disappears in stretch–shortening cycle. Contradicting results are shown for soleus and extensor digitorum longus (EDL) muscles, where FE and FD seem to be additive for EDL but not for soleus muscle Kosterina et al. (2009), Fig. 3). Bullimore et al. (2008) have shown a remaining FE effect after shortening when performing equal distances of stretch and shortening on frog muscle fibres. The last experimental setup is rather similar to the present study, where muscles stretch and lengthen on the same amount during cyclic movements and there is a time delay between the length ramps. Therefore, the hypothesis that shortening following stretch eliminates initial FE was neglected. The force modification introduced in musculoskeletal modelling may be most relevant in sport and impact biomechanics since the effect of muscle history increases with speed of motion and load. While it is difficult to specify the absolute value of the history correction, the magnitude of force modification was somewhat low in the tested motions. The additional analysis was included to illustrate that force modification may be negligible in slow, unloaded movements, but non-negligible in fast motions with high loads. It is interesting that fast movements lead to larger force modification, but maximally stimulated muscles demonstrate smaller history

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Natalia Kosterina received her PhD degree in Engineering Mechanics in 2012 from the Royal Institute of Technology, Sweden, and Masters degree in Applied Math and Mechanics from Saint-Petersburg State University, Russia. Her doctoral research area was numerical simulation of muscular force generation, particularly investigation of muscle history effect and implementation of this phenomenon in muscle and musculoskeletal models.

Ruoli Wang received her PhD degree in 2012 in Engineering Mechanics from the Royal Institute of Technology, Stockholm, Sweden, and has a Master’s degree from Southeast University, China. Her research interests include applying gait analysis, analytical biomechanics theory and computational modelling and simulation to understand human movement, in particular, focusing in the consequences of lower limb musculoskeletal impairments and injuries.

Anders Eriksson is a professor of Structural Mechanics at the Royal Institute of Technology in Stockholm, Sweden. His research background is primarily related to numerical simulations of complex load-carrying systems, with applications in both engineering and biological systems. His research in biomechanical systems has been concerned with muscle physiological models, with the biological–mechanical coupling in tissues, and with optimization of human movements in numerical contexts. Sports mechanics is frequently used as example problems.

Elena Gutierrez-Farewik (‘Lanie’) is an associate professor of Biomechanics at KTH Mechanics, the Royal Institute of Technology in Stockholm, Sweden. She is also affiliated with the Motion Analysis Laboratory at the Karolinska Institutet and University Hospital. She has a PhD in orthopedics and a master’s degree in biomedical engineering. Her research interests are in analysis and simulation of human movement, particularly in persons with motion disorders.

Please cite this article in press as: Kosterina N et al. Force enhancement and force depression in a modified muscle model used for muscle activation prediction. J Electromyogr Kinesiol (2013), http://dx.doi.org/10.1016/j.jelekin.2013.02.008