Voluntary EMGtoforce estimation with a multiscale physiological muscle model
 Mitsuhiro Hayashibe^{1}Email author and
 David Guiraud^{1}
https://doi.org/10.1186/1475925X1286
© Hayashibe and Guiraud; licensee BioMed Central Ltd. 2013
Received: 8 January 2013
Accepted: 21 August 2013
Published: 4 September 2013
Abstract
Background
EMGtoforce estimation based on muscle models, for voluntary contraction has many applications in human motion analysis. The socalled Hill model is recognized as a standard model for this practical use. However, it is a phenomenological model whereby muscle activation, forcelength and forcevelocity properties are considered independently. Perreault reported Hill modeling errors were large for different firing frequencies, level of activation and speed of contraction. It may be due to the lack of coupling between activation and forcevelocity properties. In this paper, we discuss EMGforce estimation with a multiscale physiology based model, which has a link to underlying crossbridge dynamics. Differently from the Hill model, the proposed method provides dual dynamics of recruitment and calcium activation.
Methods
The ankle torque was measured for the plantar flexion along with EMG measurements of the medial gastrocnemius (GAS) and soleus (SOL). In addition to Hill representation of the passive elements, three models of the contractile parts have been compared. Using common EMG signals during isometric contraction in four ablebodied subjects, torque was estimated by the linear Hill model, the nonlinear Hill model and the multiscale physiological model that refers to Huxley theory. The comparison was made in normalized scale versus the case in maximum voluntary contraction.
Results
The estimation results obtained with the multiscale model showed the best performances both in fastshort and slowlong term contraction in randomized tests for all the four subjects. The RMS errors were improved with the nonlinear Hill model compared to linear Hill, however it showed limitations to account for the different speed of contractions. Average error was 16.9% with the linear Hill model, 9.3% with the modified Hill model. In contrast, the error in the multiscale model was 6.1% while maintaining a uniform estimation performance in both fast and slow contractions schemes.
Conclusions
We introduced a novel approach that allows EMGforce estimation based on a multiscale physiology model integrating Hill approach for the passive elements and microscopic crossbridge representations for the contractile element. The experimental evaluation highlights estimation improvements especially a larger range of contraction conditions with integration of the neural activation frequency property and forcevelocity relationship through crossbridge dynamics consideration.
Keywords
Introduction
Any human movement is produced by muscular and skeletal systems controlled by the nervous system. Mechanism of the human body dynamics has been revealed by many biomechanical researches. The general neuromusculoskeletal model of the whole body and its dynamics computation package have been developed and reported[1]. However, the detailed neuromuscular activation system should still be closely analyzed and modeled from microscopic to macroscopic scales. Macroscopic modeling, such as the Hilltype muscle model, is a phenomenological model. Conversely, microscopic modeling is based on muscle physiology, more specifically the dynamics of actinmyosin, allowing it to display a richer response.
Neuromuscular modeling is important for neuroscience to understand how limb movements are smoothly and effectively controlled[2, 3]. It is also valuable for clinical applications to be used for quantitative analysis on abnormal muscle activation patterns such as spasticity induced by stroke or cerebral palsy[4]. Moreover, neuroprosthetic control such as functional electrical stimulation (FES) for paralyzed muscles[5, 6] can be improved through neuromuscular modeling to optimize the muscle activation control.
Surface electromyography (EMG) is widely used to assess the muscle status in a wide range of clinical fields. The signal generated during a contraction is the summation of the signals of all different recruited motor units (MU) at a given time. Each MU receives information from the central nervous system in the form of action potentials, which are transmitted from the alpha motor neuron to the muscle fibers via the neuromuscular junction. During voluntary contraction, the EMG signal can be seen as the interference pattern of all active MUs, with each MU firing at its own mean frequency with its own timing[7]. The contributions of individual MU cannot be easily recovered from the EMG signal. However, EMG signals still contain precious information about muscle activation and could thus represents the entry of a muscle model. Indeed, the important advantage of EMG usage is that it can account for a subject’s individual activation pattern to estimate muscle force. Moreover, as the EMG signals can be considered for each individual groups of antagonist muscles with their own muscle models, cocontraction can be captured and deeply investigated through the computation of individual force and stiffness. On the contrary, numerical optimization techniques typically do not account for muscular cocontraction.
EMGbased models were already used in many studies to estimate torques around joints[8] or in musculoskeletal models[9, 10]. Most of the muscle models used in such studies are based on phenomenological models derived from Hill’s study[11] and summarized by Zajac[12]. The Hilltype model is attractive in biomechanical simulations because of the computational simplicity and easy to calibrate using experimentally measurable variables. It tends to produce accurate estimation results, however in limited ranges of function.
However, recent work[13] performed the validation of Hill model under functionally wider relevant conditions. The authors concluded that the modeling errors were substantial for different firing frequencies and greatest at low motor unit firing rates that are most relevant in normal movement conditions both in voluntary and FES muscle contractions. They pointed out that this could be due to the Hill model assumption whereby muscle activation, forcelength and forcevelocity properties are considered independently. In their discussion, it was suggested that more physiological coupling between activation and forcevelocity properties can be demonstrated in crossbridge models incorporating dependence between physiologically based activation and crossbridge attachment[13]. The important finding is that Hill modeling errors were large for different firing frequencies and greatest at low motor unit firing rates. In[13], classical linear Hill model was used. Especially for solving the problem of the mismatch at low muscle activation level, a nonlinear conversion was proposed[14] and used by other researchers[9]. This can solve partially the problem, however, there is a still the problem to correspond to the estimations in different contraction speeds. Besides, in Hilltype modeling, the cut off frequency should be carefully chosen depending on the type of task because the envelope of the estimated force is almost defined by the lowpass filtering of the activation. Thus, we aim at proposing multiscale muscle model, which can have more physiological coupling between activation and forcevelocity properties by incorporating microscopic crossbride and dual dynamics pathway for the recruitment / activation level and the calcium triggering the contraction cycle. However, the whole passive structure is based on Hill model as only the contractile element differs.
The first microscopic muscle model was proposed by Huxley[15]. He detailed the interaction of the crossbridges in a sarcomere in order to explain the force generation. The distinctions between microscopic and macroscopic levels are not absolute; thus a sarcomere model can be used to represent a whole muscle, which is assumed to be a homogeneous assembly of identical sarcomeres. Conversely, the Hill model, which was originally developed for whole muscles, has been used to represent the dynamics of individual sarcomeres within a fiber[16]. The distributionmoment approach of Zahalak[17] is a model for sarcomeres or whole muscle, which is extracted via a formal mathematical Gaussian approximation from Huxley crossbridge model. This model fills a gap between microscopic and macroscopic levels. Based on Huxley and Hilltype models, BestelSorine[18] proposed an explanation of how the beating of cardiac muscle may take place, through chemical control input connected to the calcium dynamics of cells in muscles. This chemical input triggers the contractile element model.
Complete Huxley type physiological model have a greater repertoire of response, but are computationally complex. BestelSorine representation provides an efficient tradeoff between complexity and power of the model expression. It consists in an explicit computation of the first two moments reprenting stiffness and force of the contractile element, triggered by the chemical input as regard the contraction start and stop. Starting with this concept, we first adapted it to the striated muscle model to represent muscle responses under FES[19]. The multiscale muscle model was applied for voluntary contraction in a preliminary work[20]. In this study, we aim at developing EMGbased muscle model to study voluntary muscle contraction with this multiscale modeling approach compared to Hill approaches, both linear and nonlinear. Indeed, in Hill approach, the dependency on cutoff frequency choice prevents from good performances in a wide range of contraction types. The multiscale approach should improve the performances in particular regarding fast and slow contraction patterns. In addition, we consider that it is of interest to apply the same type of EMGtoforce estimation with a physiologically detailed model and not only with a phenomenological Hill model because the internal biophysical dynamics could shed new light on neuromuscular activation. Using common data sets of isometric muscle contractions, the force estimation results are compared between Hill model approaches and newly proposed approach.
Methods
Hilltype muscle model
The transformation from EMG to muscle activation is a dominant process because the estimated muscle force is assumed to be proportional to the muscle activation.
EMG processing
 1.
highpass filtering of raw EMG using zerolag 4th order Butterworth filter (30 Hz) to remove motion artifacts
 2.
wave rectification
 3.
lowpass filtering with a 2 Hz cutoff frequency using zerolag 2nd order Butterworth filter
 4.
normalization with the peak of maximum voluntary contraction (MVC)
There is an alternative method instead of the lowpass filtering of the third step. It is referred to as the mean absolute value (MAV) method. A moving average filter is applied within a fixed time window, which is equivalent to lowpass filtering. The recommendations of the SENIAM project indicate a time window of 0.25 to 0.5 seconds[21]. It corresponds to the choice of cutoff frequency of the lowpass filter of 2 to 4 Hz. This critical parameter choice depends on the task dynamics. Indeed, this choice of cut off frequency is a trade off between how fast the fluctuations in amplitude can be and how reliable the estimate of the amplitude is. A low cut off frequency gives a more reliable estimate of the amplitude, but cannot capture fast changes, while higher cut off frequency results in noisier output but captures fast contractions. The cut off frequency mentioned in the SENIAM recommendations is 2 Hz for slow motions, and 6 Hz for fast motions[21]. In Hilltype model, this cut off frequency should be carefully set depending on the type of task because the envelope of the estimated force is almost determined by this lowpass filtering step. The normalized EMG is processed with the following activation dynamics, which mainly captures the delay from muscle activation to mechanical output.
Activation dynamics
where d is the electromechanical delay and γ, β_{1} and β_{2} are the coefficients that define the secondorder dynamics. To obtain a positive stable solution, a set of constraints are employed, i.e. β_{1}=C_{1}+C_{2},β_{2}=C_{1}C_{2} where C_{1}<1,C_{2}<1. In addition, the gain of this filter should be maintained by ensuring γ−β_{1}−β_{2}=1 as described in[8].
Nonlinearization of muscle activation for nonlinear Hill model
Many researchers assume that the above p(t) is a reasonable approximation of muscle activation. However, a nonlinear relationship has been reported between individual muscle EMG and the joint moment for some muscles, especially at lower forces[14]. In studies on single motor units, multiple APs cause succesive twitch responses. If the time between APs decreases, twitches start to merge and the muscle force increases steadily. However, at high frequency we reach maximal contraction, where force development saturates even if the frequency increases. This induces a nonlinear relationship between the frequency and force for single motor units[8].
where A is a constant parameter for the nonlinear shape factor allowed to vary between 3 and 0, with A=−3 being highly exponential and A=0 being linear.
Hilltype contraction dynamics
where ε_{ c } is the strain of the contractile element, f_{ l }(ε_{ c }) and${f}_{v}\left({\stackrel{\u0307}{\epsilon}}_{c}\right)$ are the normalized forcelength and forcevelocity relationships, respectively. F^{ m } is the maximum isometric muscle force.
where L_{c 0} is the length of contractile element at rest position and V_{ sh } is a constant parameter. The b and V_{ sh } parameters were obtained from[23, 24]. At each time step, the fiber velocity should be solved and the muscle fiber length is computed by forward integration using RungeKutta algorithm[8]. Since the value of ε_{ c } changed, the calculation should continue iteratively until the end of the input time series of a(t).
Muscle model parameters
Parameter  Unit  Value  

b    0.5  
V _{ sh }    0.3  
L_{c 0}(G A S)  cm  5.1  
Hill  L_{t 0}(G A S)  cm  40 
Pennation ϕ(GAS)  Degrees  14  
Common  F_{ m }(GAS)  N  1600 
parameters  L_{c 0}(S O L)  cm  3.0 
L_{t 0}(S O L)  cm  26.8  
Pennation ϕ(SOL)  Degrees  30  
F_{ m } (SOL)  N  2830  
k _{ t }  N/m m  180  
A (subject1)    1.7  
Nonlinear  A (subject2)    1.2 
Hill  A (subject3)    1.7 
A (subject4)    1.5  
U _{ c }  1/s  5  
Physiological  U _{ r }  1/s  10 
model  k _{ m }  N/m  F_{ m }×20 
Physiological muscle model
We breifly describe the main points of the multiscale physiological muscle model. It integrates the characteristics both of macroscopic and microscopic muscle dynamics. The details of this modeling are given in[19]. This model was originally designed to represent the muscle response under FES and is applied to voluntary muscular force estimation based on EMG in this paper.
Generation of chemical input
Thus, the chemical threshold consists basically in extracting the contraction time duration of the muscle and to indicating if the muscle is in contraction or not. The level of activation itself is managed by recruitment rate which is classically used in EMG usage for Hill model. Thus, especially for the low activation state, even if the chemical input is inaccurately determined, its effect is low since the recruitment activation p(t) is very low during this period. And for the higher activation state, the contraction period is accurately captured by this method. As long as the threshold is taken little above the baseline, the threshold is less sensitive as long as it gives the picture of contraction/relaxation state. The parameters for chemical input generation was obtained from[18, 28].
Sarcomere scale
All the sarcomeres are assumed to be identical, and the deformation of both sarcomere and muscle is proportional. If S is the sarcomere length, we can write (S−S_{0})/S_{0}=(L_{ c }−L_{c 0})/L_{c 0}=ε_{ c }.
Huxley proposed that a crossbridge between actin filaments and myosin heads could exist in two biochemical states, i.e. attached and detached states as in Figure2(B). Filaments sliding is the result of interactions between the myosin crossbridges and the thin actin filaments. The crossbridges reversibly bind to actin and produce a mechanical impulse, which in turn results in force transmission along the filaments. M and A in the figure represents the myosin head and actin binding site respectively.
where h is the maximum elongation of the myosin spring, x is the distance and y the normalized distance between the actin binding site and the myosin head:$y=\frac{x}{h}$. n(y,t) is a distribution function representing the fraction of attached cross bridges relative to the normalized relative position y. To ensure a one way displacement, this attachment is considered possible only when y is between 0 and 1.${S}_{0}{\stackrel{\u0307}{\epsilon}}_{C}$ represents the velocity of the actin filament relative to the myosin filament. f and g denote the rate functions of attachment and detachment, respectively.
Contrary to Zahalak approximation, we do not make any assumption on the distribution, rather the chosen f and g functions allows for a straightforward computation of the stiffness and the force generated by the contractile element. It provides a computational effective model that however relies on Huxley theory.
Myofiber and muscle scale
where k_{ m }=S_{0}N k_{0}f_{ l }(ε_{ c })/L_{c 0},F_{ m }=N k_{0}h f_{ l }(ε_{ c })/2. k_{0} (Nm ^{−1}) is the maximum stiffness obtained when all the available bridges are attached.
Recruitment rate is thus mixed with the dynamics of the contraction relaxation cycle providing a wider range of mechanical responses than Hill approaches. Compared to Zahalak approximation, we provide a two input model with intricate dynamics due to both internal muscle dynamics and recruitment rate dynamics in a straightforward way.
Computation of the whole dynamics
For the macroscopic representation, the same configuration with Hill models as in Figure2(A) is used including the muscle tendon parameters. The contractile element is replaced with the above nonlinear differential equations.
${S}_{{\stackrel{\u0307}{\epsilon}}_{c}}$ is the sign of${\stackrel{\u0307}{\epsilon}}_{c}$. From the condition: k_{ t }L_{c 0}/c o s ϕ+k_{ c }L_{c 0}−F_{ c }>0,${S}_{{\stackrel{\u0307}{\epsilon}}_{c}}$ can be obtained from the sign of these terms:${k}_{t}{L}_{0}\stackrel{\u0307}{\epsilon}/\mathrm{cos\varphi}+{F}_{c}u\alpha {F}_{m}{\Pi}_{c}\left(t\right){U}_{c}$. Then we can compute${\stackrel{\u0307}{k}}_{c}$ and${\stackrel{\u0307}{F}}_{c}$ with (14). The internal state vector of this system should be set as$\mathbf{x}=\left[\phantom{\rule{0.3em}{0ex}}\begin{array}{lll}{k}_{c}& {F}_{c}& {\epsilon}_{c}\end{array}\right]$.
Experimental measurement and data processing
Four healthy volunteers (2 males and 2 females, age =30.8±1.3 years, mass =66.5±16.0 kg, and stature =1.7±0.13 m) participated in the study after signing an informed consent form. The study was approved by the Agence française de sécurité sanitaire des produits de santé (Afssaps) committee for persons’ protection managed by CHRU Montpellier (2011A0103338), dedicated to the study of the lower limb biomechanics within ANR SoHuSim project.
In this preliminary test, we focused on the isometric condition and tried to compare the output force on a normalized scale against the output during MVC. The common parameters between three approaches were set at the same value as summarized in Table1. In order to maintain similar conditions, the common macroscopic model as in Figure2(A) was used for all the three approaches. Only the dynamics representation of the contractile element was replaced. A was the only parameter identified for each subject. A was obtained by minimizing the root mean square difference between the measured and the model estimation at MVC. Other muscle parameters except A are taken from literatures as explained in the model section.
The estimated muscle force is multiplied by the moment arm in order to obtain the torque. The moment arm was estimated from the Hawkins data[29] from the joint angle in the measured condition. The moment arms for MG and SOL are 0.0515 [m] and 0.0464 [m], respectively. The contribution ratio was calculated using the values reported by Delp[25]. This was obtained as the maximum force by the moment arm considering the pennation angle. The resulting ratio is MG 0.41 vs SOL 0.59. The SUM in the estimation result is plotted using the ratio as the sum of the two muscles.
The generated input command u(t) and activation rate α were given to the contractile element of the physiological model and the active stiffness k_{ c } and the muscle force F_{ c } were computed using Eq. 14. The same value for F_{ m } for the three approaches were used. k_{ m } is proportional to F_{ m } from the condition in Eq. 14. It was multipied by 20 times, as shown in Table1, based on the knowledge that the muscle active stiffness reaches the tendon stiffness at approximately maximum contraction[30]. However, this muscle stiffness parameter does not influence much the force output in isometric condition.
Results
The predicted joint torque based on EMG signals was compared with the directly measured torque of the ankle joint for the plantar flexion. The comparison was made against the case in MVC in normalized scale. Thus, we avoided the situation effected by the subjectspecific difference regarding muscle strength, which is significant for torque estimation in absolute scale.
RMS errors between the measured and estimated results in 30% and 70% of MVC
Nonlinear Hill  Full physiology  

Subject  30%  70%  30%  70% 
1  0.0852  0.089  0.0365  0.0848 
2  0.047  0.106  0.0307  0.0871 
RMS errors between the measured and estimated results in random contraction
Method  Error type  Subject1  Subject2  Subject3  Subject4  Mean±SD 

RMS (whole)  0.117  0.153  0.195  0.212  0.169±0.043  
Linear  RMS (slowlong)  0.133  0.186  0.233  0.252  0.201±0.053 
Hill  RMS (fastshort)  0.0508  0.0435  0.0706  0.0909  0.064±0.021 
Peak error (fast)  0.188  0.050  0.30  0.338  0.219±0.129  
RMS (whole)  0.063  0.0681  0.126  0.116  0.093±0.032  
Nonlinear  RMS (slowlong)  0.0585  0.0795  0.0986  0.136  0.093±0.033 
Hill  RMS (fastshort)  0.0806  0.0318  0.167  0.0682  0.087±0.057 
Peak error (fast)  0.274  0.0583  0.317  0.057  0.176±0.138  
RMS (whole)  0.0499  0.0373  0.0531  0.102  0.061±0.028  
Physiological  RMS (slowlong)  0.0427  0.0418  0.0558  0.103  0.061±0.029 
model  RMS (fastshort)  0.0742  0.0242  0.0472  0.101  0.062±0.033 
Peak error (fast)  0.0354  0.013  0.0536  0.131  0.058±0.051 
Discussion
Hilltype muscle is a phenomenological model based on experimental facts with no link to the microscopic physiology. First, even if the estimation performances are equivalent, it is meaningful to understand and capture the muscle dynamics with a more detailed representation. Indeed, the same kind of force estimation could be obtained with the newly proposed physiological model using voluntary EMG signals.
Second, previous work by Perreault[13] reported that Hill modeling errors were large for different firing frequencies and greatest at low MU firing rates. The classical linear Hill model was used. They suggested that more physiological coupling between activation and forcevelocity properties may help to deal with these issues[13]. Thus, the aim of introducing new approach based on a physiologically detailed model[19] was to develop EMGforce estimation with natural velocity dependency incorporating microscopic crossbridge dynamics on top of recruitment dynamics.
In general, the estimation accuracy of the proposed method is better than that of the linear and nonlinear Hilltype approach as in the obtained result regarding RMS errors. In addition, uniform accuracy was obtained for different types of contractions in the proposed method. In particular, the proposed model is able to properly deal with both slow and fast contraction speeds. When considering the Hill model results, Figure6(A,B) shows largest errors for the estimation of fastshort contractions. The reason of this error could be explained as follows: the signal measured in EMG is the summation of the APs of all different MUs. Even in the fastshort contraction, the amplitude of EMG itself does not reflect differences except duration with the same level as for slowlong contraction. However, the resulting fastshort contraction force is actually much less than that of slowlong contraction. This means that there is sometimes hysteresis regarding the neural command. In Hill approach, muscle activation a(t) is proportional to the resulting force. It therefore does not include the effect of the time hysteresis in contraction[13], thus Hill model can not accurately represent both short and longterm contractions simultaneously with only one choice of cutoff frequency in EMG lowpass filtering. In the proposed approach, the derivative of the contraction force is directly given by the neural command and it brings time hysteresis in force generation. It is interesting to note that this kind of uniform accuracy for different types of contractions was appeared along with the introduction of crossbridge dynamics.
In addition, it is known that there is a nonlinear relationship between frequency during contraction and force for single MUs[14]. In modified Hill model, this frequency dependency is offset only by the nonlinear conversion. This nonlinearization was recently proposed to modify the classical Hill model. This process was originally not introduced in the socalled Hill model. In fact, this modification brings much better estimation, especially at lower forces. However, even with the modification, it is not a time function so it still can not correspond to the different muscle contraction speeds. In Hilltype approach, neural activation p(t) is dominantly imposed by lowpass filtering with a 2–10 Hz cutoff frequency. The choice of cutoff frequency is very sensitive to the dynamics of p(t). p(t) is more or less proportional to the resulting force. Therefore, it is advised that the choice of cut off frequency should be carefully selected depending on the type of task in Hilltype modeling. In this study, a 2 Hz cutoff frequency was used according to the SENIAM recommendation. Sometimes by changing the cutoff frequency for different types of contraction, better results can be obtained with Hilltype model. However, in any case, the expected motion by subject is unknown in advance for practical use of EMGforce estimation, so it is difficult to have an appropriate cutoff frequency in advance. Moreover it assumes that the subject stays in the same kind of motion dynamics, that is not always the case. In the proposed model, the nonlinear activation property coming from forcevelocity dependency is internally integrated in the model dynamics.
Furthermore, the physiological model satisfies the well established properties observed for the muscle’s behavior: i) the forcelength relation is included in the definition of Eq. 13, ii) the forcevelocity relationship can be expressed in isotonic and tetanic conditions. Before isotonic contraction could occur, the muscle contracts in isometric conditions until the force generated by the muscle balances the imposed one. Isotonic contraction then becomes possible. Assuming${\stackrel{\u0307}{F}}_{c}=0$ in Eq. 14, the following equation may be formulated:${F}_{c}=(\alpha {F}_{m}{U}_{c}+{k}_{c}{L}_{c0}{\stackrel{\u0307}{\epsilon}}_{c})/({U}_{c}+\left{\stackrel{\u0307}{\epsilon}}_{c}\right)$.
This correspondence can be found in Eq. 5. It can be verified that our physiological muscle model integrates the forcevelocity relation naturally when considering the actinmyosin cross bridge. Finally, this improvement in estimation accuracy is in line with the suggestion put forward in a previous work[13] on introducing crossbridge model.
Future study will be focused on simulations with multiple sets of the proposed model corresponding to multiple MUs in one muscle considering size principal, fast/slow fibers. However, for the application of voluntary EMGforce estimation, we should keep the simplicity as Hilltype model. Future work will also focus on increasing the number of experimental tests and we should develop an algorithm to statistically determine if a muscle is turned on/off regarding the chemical thresholding. In addition, the further interpretation of neuromuscular system both in voluntary and FES activations should be pursued. We have already performed the study on the identification and validation of the physiological model in invivo rabbit experiment[31] and in paraplegic subjects including nonisometric situation under FES[32]. In order to be applied to a broader range of clinical situations, further investigations in isokinetic and isotonic cases should be carried out.
Conclusion
In this paper we presented a method that allows estimation of muscle force from EMG signals with a multiscale physiology based model with a link to underlying microscopic filament dynamics. The experimental results highlight the feasibility of the torque estimation and its comparison with Hilltype models using the same EMG signals. This is the first report on EMGforce estimation based on a multiscale physiology model integrating Hilltype and microscopic cross bridge representations. The proposed method features:

a novel physiologically detailed model for EMGforce estimation in the place of a phenomenological Hilltype muscle model,

the estimation improvement especially for different types of contraction incorporating dual dynamics of recruitment and microscopic crossbridge formation toward coupled activationvelocity relationship.
Declarations
Acknowledgements
This work was supported by French National ANR SoHuSim project (http://sohusim.gforge.inria.fr/).
Authors’ Affiliations
References
 Delp SL, Anderson FC, al E: OpenSim: Opensource software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng 2007, 54(11):1940–1950.View ArticleGoogle Scholar
 Flash T, Hogan N: The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 1985, 5(7):1688–1703.Google Scholar
 Kawato M, Maeda Y, Uno Y, Suzuki R: Trajectory formation of arm movement by cascade neural network model based on minimum torquechange criterion. Biol Cybern 1990, 62(4):275–288. 10.1007/BF00201442View ArticleGoogle Scholar
 Smaga S: Tremor. Am Fam Physician 2003, 68: 1545–1552.Google Scholar
 Kobetic R, Triolo RJ, Uhlir JP, Bieri C, Wibowo M, Polando G, Marsolais EB, Davis JA: Implanted functional electrical stimulation system for mobility in paraplegia:a followup case report. IEEE Trans Rehabil Eng 1999, 7(4):390–398. 10.1109/86.808942View ArticleGoogle Scholar
 Guiraud D, Stieglitz T, Koch KP, Divoux JL, Rabischong P: An implantable neuroprosthesis for standing and walking in paraplegia: 5year patient followup. J Neural Eng 2006, 3: 268–275. 10.1088/17412560/3/4/003View ArticleGoogle Scholar
 Stegeman DF, Blok JH, Hermens HJ, Roeleveld K: Surface EMG models: properties and applications. J Electromyogr Kinesiol 2000, 10: 313–326. 10.1016/S10506411(00)000237View ArticleGoogle Scholar
 Buchanan TS, Lloyd DG, Manal K, Bessier TF: Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command. J Appl Biomech 2004, 20: 367–395.Google Scholar
 Lloyd DG, Bessier TF: An emgdriven musculoskeletal model to estimate muscle forces and knee joint moment in vivo. J Biomech 2003, 36: 765–776. 10.1016/S00219290(03)000101View ArticleGoogle Scholar
 Koo TKK, Mak AFT: Feasibility of using emg driven neuromusculoskeletal model for prediction of dynamic movement of the elbow. J Electromyogr Kinesiol 2005, 15: 12–26. 10.1016/j.jelekin.2004.06.007View ArticleGoogle Scholar
 Hill AV: The heat of shortening and the dynamic constants in muscle. Proc R S Ser B; London 1938, 126: 136–195. 10.1098/rspb.1938.0050View ArticleGoogle Scholar
 Zajac FE: Muscle and tendon: properties, models, scaling and application to biomechanics and motor control. CRC Critic Rev Biomed Eng 1989, 17: 359–411.Google Scholar
 Perreault E, Heckman C, Sandercock T: Hill muscle model errors during movement are greatest within the physiologically relevant range of motor unit firing rates. J Biomech 2003, 36: 211–218. 10.1016/S00219290(02)003329View ArticleGoogle Scholar
 Manal K, Buchanan TS: A oneparameter neural activation to muscle activation model. J Biomech 2003, 36: 1197–1202. 10.1016/S00219290(03)001520View ArticleGoogle Scholar
 Huxley AF: Muscle structure and theories of contraction. Prog Biophys Biophys Chem 1957, 7: 255–318.Google Scholar
 Leeuwen JL: Optimum power output and structural design of sarcomeres. J Theor Biol 1991, 19: 229–256.View ArticleGoogle Scholar
 Zahalak GI: A distributionmoment approximation for kinetic theories of muscular contraction. Math Biosci 1981, 55: 89–114. 10.1016/00255564(81)900146View ArticleGoogle Scholar
 Bestel J, Clement F, Sorine M: A biomechanical model of muscle contraction. Proc Int Conf Med Image Comput ComputAssist Intervent MICCAI 2001, Lect Notes Comput Sci 2001, 2208: 1159–1161.Google Scholar
 Makssoud HE, Guiraud D, Poignet P, Hayashibe M, Wieber PB, Yoshida K, Azevedo C: Multiscale modeling of skeletal muscle propertiesexperimental validations in isometric conditions. Biol Cybern 2011, 105(2):121–138. 10.1007/s0042201104457View ArticleGoogle Scholar
 Hayashibe M, Guiraud D, Poignet P: EMGtoforce estimation with fullscale physiology based muscle model. Proc IEEE/Int Conf Intell Robots Syst 2009, 1621–1626.Google Scholar
 Hermens HJ, Freriks B, Merletti R, Stegeman D, Blok J, Rau G, DisselhorstKlug C, Hagg G: European recommendations for surface electromyography, results of the seniam project. Enschede, The Netherlands: Roessingh Research and Development; 1999.Google Scholar
 Lichtwark GA, Wilson AM: Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running. J Theor Biol 2008, 252(4):662–673. http://www.ncbi.nlm.nih.gov/pubmed/18374362 10.1016/j.jtbi.2008.01.018MathSciNetView ArticleGoogle Scholar
 Stroeve S: Learning combined feedback and feedforward control of a musculoskeletal system. Biol Cybern 1996, 75: 73–83. 10.1007/BF00238741View ArticleGoogle Scholar
 Stroeve S: Impedance characteristics of a neuromusculoskeletal model of the human arm I: posture control. Biol Cybern 1999, 81: 475–494. 10.1007/s004220050577View ArticleGoogle Scholar
 Delp SL: Surgery simulation: a computer graphics system to analyze and design musculoskeletal reconstructions of the lower limb. PhD thesis, Dissertation, Stanford University, CA, USA; 1990Google Scholar
 Keener J, Sneyd J: Mathematical Physiology, II: Systems Physiology. Series 8, Vol. 2. New York: Springer; 2009.Google Scholar
 Hatze H: A general myocybernetic control model of skeletal muscle. Biol Cybern 1978, 28: 143–157. 10.1007/BF00337136View ArticleGoogle Scholar
 Bestel J: Modele Differentiel de la Contraction Musculaire controlee application au system cardiovasculaire. PhD thesis, Dissertation, Universite de Paris IX, France; 2000Google Scholar
 Hawkins D, Hull M: A method for determining lower extremity muscletendon lengths during flexion/extension movements. J Biomech 1990, 23: 487–494. 10.1016/00219290(90)90304LView ArticleGoogle Scholar
 Cook C, McDonagh M: Measurement of muscle and tendon stiffness in man. Eur J Appl Physiol Occup Physiol 1996, 72(4):380–382. 10.1007/BF00599700View ArticleGoogle Scholar
 Hayashibe M, Guiraud D, Poignet P: In vivo identification of skeletal muscle dynamics with nonlinear Kalman filter: comparison between EKF and SPKF. ISRN Rehabil 2013. 2013: Article ID 610709Google Scholar
 Benoussaad M, Poignet P, Hayashibe M, Azevedo C, Fattal C, Guiraud D: Experimental parameter identification of a multiscale musculoskeletal model controlled by electrical stimulation: application to patients with spinal cord injury. Med Biol Eng Comput 2013, 51(6):617–631. 10.1007/s115170131032yView ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.