Application of EMG generation simulation technology in analyzing aging muscle remodeling
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https://www.eduzhai.net American Journal of Biomedical En gineer in g 2013, 3(3): 77-83 DOI: 10.5923/j.ajbe.20130303.05 Simulation Techniques of EMG Generation to Analyze Remodeling of Aging Muscles Mohammad A. Ahad1,*, Mohammed Ferdjallah2 1Department of Electrical Engineering, Georgia Southern University, Statesboro, GA 30458, USA 2School of Engineering Technology, ECPI University, 5555 Greenwich Road, Virginia Beach, VA 23462 Abstract Surface Electro myography (EM G) signals are expected to be different in young and elderly due to the physiological changes that occur during the aging process. Clinical studies can only provide snap shots of the pathological changes that may occur in the aging muscle. The main objective of this paper is to demonstrate the clinical EM G findings of muscle remodeling during aging through modeling and simu lation analysis without the need for extensive and lengthy clin ical studies. The hypothesis of this study is that the shift in the EM G spectrum of aging muscles is due to a decrease in fast muscle fibers. In this art icle, an EM G-generation algorith m was designed by considering the physiologic behavior of type-I and type-II motor units during voluntary contractions. A modified mult ilayer muscle model was used to generate monopolar surface EM G signals. The muscle model simu lates EM G s ignals of the Tibialis Anterio r muscle for both young and elderly subjects using published physiological data. Thus, the designed muscle model is limited to axial muscles. To demonstrate the hypothesis of this study, simulated EM G s ignals were generated for young (26-44 years) and elderly populations (65-83 years). The simu lated EM G parameters such as root mean squared (RMS) and average rectified voltage (ARV) and spectrum parameters such as mean frequency (MNF) and median frequency (MDF) were co mpared between young and elderly Tibialis Anterior muscles and also compared with published experimental values. Our simu lated results not only illustrate the remodeling of muscles during aging but also provide theoretical findings that are comparable to clin ical and experimental findings. Keywords Modeling, Aging, Fiber Type Distribution, Average Rectified Vo ltage, Median Frequency 1. Introduction As humans grow older, their skeletal muscles loose the strength and the capacity to generate force due to skeletal muscle mass reductions.This is known as sarcopenia[1, 2].Most researchers reported that age related muscle atrophy results from fiber atrophy rather than a loss of muscle fibers[3, 4, 5, 6, 7]. In addition to the decrease in skeletal muscle mass due to the atrophy of the muscle fibers, the muscles of elderly subjects (65-83 years of age) contain less contractile tissues (Type-II) and more noncontractile tissues (Type-I) when co mpared with the skeletal muscle of younger subjects (26-44 years of age). In recent reviews, it is also found that the size of Type-I fibers does not change substantially with age, but Type-II fibers undergo selective atrophy[2, 8, 9]. However, in voluntary contractions, it is also necessary to consider motor unit remodeling during aging process. Z. Erim et al described three novel observations regarding the firing behaviorof aged motor u n its . * Corresponding author: firstname.lastname@example.org (Mohammad A. Ahad) Published online at https://www.eduzhai.net Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved 1) A decreasein the fluctuations of firing frequency in the muscle of elderly that are observed among the firingrates of motor units in the young. 2) The linear relationship observedbetween the firing rate and recruitment threshold of young subjectsis also seen in the elderly. 3) The progressive decrease observed in the firingrates of concurrently active motor units in constant-force contractionsin the young is not seen in the elderly. In addition to these findings, EM G of the muscles of elderly has decreased average firing rates decreased number of motor units a shift in recru it ment thresholds toward lowerforce Taken as a whole, thesefindings indicate significant age-related modifications in thecontrol properties of human motorunits.Although the number of motor units decreases, the muscle fibers belonging to the deceased motor unit are often reinnervated by other existing motor units[8, 11].Therefore, although there is a reduction in the number of motor un its, some motor units specially the low force type-I units become larger due to reinervation.Thus, EM G signals fro m young and elderly are expected to be significantly different due to pathological changes and changes in motor unit functioning strategy during aging. 78 M ohammad A. Ahad et al.: Simulation Techniques of EM G Generation to Analyze Remodeling of Aging M uscles Most of the work done previously on EM G signal simu lation was concerned with single fiber action potential modeling using a simplified transfer function of the mediu m [12, 13,14]. In 2001, Farina et al  proposed a new model of EM G signal generation and detection by describing the volume conductor as an inhomogeneous and anisotropic med iu m constituted by muscle, fat and skin tissue. Not too many researchers worked on the development of the motor unit pool in a muscle mostly because there was lack of informat ion about the motor unit physiology. Several researchers [16, 17, 18] later presented more realistic EM G models than others but did not incorporate the effect of different types of fibers, which influence the EM G generation significantly especially when neuro muscular properties changes due to aging or diseases. An EM G generation algorithm has been developed in this study using two separate models.The first model describes an extracellular single fiber action potential calculat ion and hence motor unit action potential, wh ich is the summation of all the single fiber action potential in a motor unit.The second model is a motor unit pool model which is a mathematical description o f brain-muscle interaction.This model describes the nature of motor unit recruit ment and their discharge rate during isometric voluntary contractions.The techniques followed in this study to develop the motor unit pool model algorith m using the most up to date motor unit physiology will facilitate the application of this model in several areas of b io medical research.The main objective of this paper is to demonstrate the clinical findings regarding muscle remodeling during aging through modeling and simulation analysis. Preliminary results of this paper was reported in. 2. Methods 2.1. Single Fi ber Action Potenti al Using Multi-layer Model Air Skin Fat M uscle z Longitudinal Figure 1. Four layer EMG model The difference between most of the single fiber action potential generation technique lies in the representation of the memb rane current in different mathemat ical forms.In this study, line source model which considers the transme mbrane current im as discrete point sources along the axis of the muscle fiber for a fin ite fiber was utilized to derive the analytical solution of e xt racellula r action potential. Figure 1 shows a four-layer concentric cylindrical model that represents a large inner cylinder of muscular an isotropic tissue, an intermediate layer of subcutaneous fat and an outer layer of skin, both as an isotropic mediu m.The potential in the anisotropic muscle med iu m can be expressed using the Laplace equation as: ∂2 ∂x2 + ∂2 ∂y 2 + P ∂2 ∂z 2 φmuscle ( x, y, z) = im (1) where P = σ z σr However, for the fat and skin mediu m σ z = σ r . Thus Laplace equations for fat and skin layer can be written as: ∂2 ∂x 2 + ∂2 ∂y 2 + ∂2 ∂z 2 ϕ fat (x, y, z ) = 0 (2) ∂2 ∂x 2 + ∂2 ∂y 2 + ∂2 ∂z 2 ϕ skin (x, y, z ) = 0 (3) Equations (1), (2) and (3) can be solved using boundary conditions at the interfaces which are the equations of continuity of currents in the y direction and of the fields in the z and x directions. For finite length single fiber that lies in the muscle layer parallel to the surface of the skin, the solution of equation (1) using line source model can be solved as: ϕ(r, z) = a 2σ r z2 ∫ z1 im(s) dz′ σ z r 2 + (z − z′)2 (4) σr which is the convolution of transmembrane current (im) and volume conductor weighting factor.To account for the fin ite dimensions of muscle fibers and volu me conductor distortions, the excitation and the extinction of the action potential are described as current sources at the neuromuscular endplate and fiber endings.These compensating current sources are calculated such as the total current is zero over the active part of the fiber. The comb ined transfer function of the fat and skin layer was derived by Farina et al. The t ransfer function of the fat and skin layer is given by: ( ( )) ( ( )) H (ωx ,ωz ) = (1+ Rc )cosh ωy t f + ts 2 + (1− Rc )cosh ω y t f − ts (5) Where ωx = 2πfx and ω z = 2πf z are the spatial angular frequency in x (perpendicular to the fiber) and z (parallel to the fiber) directions, ωy = ω 2 x + ω 2 z in the direction of distance between muscle and electrode, Rc is the conductivity ratio between skin and fat, t f and ts are thickness of fat and skin respectively.The solution of potential distribution in the space domain can be obtained by taking the two dimensional inverse Fourier t ransform.So the American Journal of Biomedical Engineer ing 2013, 3(3): 77-83 79 final single fiber act ion potential φsfap equation will be the inverse Fourier t ransform of the product of H and Φ (r,ω) where Φ (r,ω) is the Fourier t ransform of φ(r,z). ϕsfap = F −1(Φ(r,ω).H ) 2.2. Motor Neuron Pool Model A motor unit pool model predicts the number of motor units that is recruited fro m a pool of motor units in a muscle as a function of force and recru it ment threshold.It also describes the pattern of recruiting as the force increases up to the maximu m voluntary contraction.The most consistent finding in the motor unit physiology is that motor unit properties have skewed nature of distribution. Thus, it can be stated that most of the motor units will have smaller diameters and very few will have bigger diameters and this relationship can be expressed by the following equation: ln(R) i di = dmine n (6) where, di = diameter of the ith motor unit dmin= diameter of the smallest motor unit R = rat io of the biggest and the smallest motor unit dia meter n = nu mber of motor units Within muscle the ratio of the d iameter of smaller and the bigger motor units can vary up to 1:10.Type-II motor units are the larger units in a muscle. The variation in innervation ratios, which is the number of fibers that belongs to a motor unit, is one of the most significant factors that contribute to differences in motor unit force. Such a distribution can also be represented as an e xponential form as[22, 24]: yi = aeln(nR).i (7) where:yi is the innervation number of motor unit i a is the innervation number for the smallest unit R is the ratio of the innvervation numbers for the largest and the smallest units n is the total number of motor units Figure 2 shows the number of motor units that innervate the different fiber types. Although the Tibialis Anterior muscle of young is comprised of 70% type-I and 30% type-II fibers, 396 or 92% motor units are of type-I and only 8% of them are type-II in a pool of 435 motor units . 2.2.1. Motor Unit Recru it ment According to the size principle proposed by Hennman, starting with the smallest motor units, progressively larger units are recruited with increasing strength of muscle contraction. The recruit ment sequence thus begins with slow type I motor units and progress to type II units. An indiv idual motor unit is not active until the leve l of muscle contraction or the excitatory input current to the motoneurons is above some minimal level, which is termed its recruit ment threshold. In accordance with the ‘size principle’, the earlier recruited motor units will have smaller recruit ment threshold and later recruited motor units will have larger threshold.As suggested by Fuglevand, a Poisson distribution of recruit ment thresholds similar to the distribution of motor unit territories reflects the distribution of thresholds of the motor units and the size principle suggested by Henneman. Fo r ease of simulat ion procedure, the recruit ment thresholds are assigned in the unit of percentage of maximal voluntary contraction (M VC), and thus the exponential equation that describes the Poisson distribution of recru it ment thresholds is similar to the Equation (6) and (7). Fi gure 2. Number of different t ypes of motor unit s in Tibialis ant erior 2.2.2. Motor Unit Firing Motor unit firing or the rate coding is one of the two neural methods that the nervous system adopts during contraction of the muscle.Motor units have been found to modulate their firing rates in unison and simu ltaneously.The firing rate of motor unit is not constant, even during constant force contractions rather it fluctuates.The firing rates of earlier recruited motor units are greater than those of later recruited motor units at any given force value[16, 17]. Motor unit firing frequency is characterized by four parameters, namely, minimu m firing frequency, peak firing frequency, force and firing frequency relationship and interpulse interval (IPI) of the firing action potentials. 2.3. Simulation Procedure In a muscle, type-I and type-II motor units are distributed randomly.For simu lation, muscle cross sectional surface is divided into number of small square areas using grid where one side of a square is equal to the maximu m fiber diameter and total number of squares are equal to total nu mber of fibers in that muscle.As different types of fibers are distributed randomly inside muscle, each square area is numbered rando mly as ‘1’ or ‘2’ for type-I and type-II fiber respectively.Total number of ‘1’s and ‘2’s represent total number of type-I and type-II fibers in a muscle.A circular motor unit center point is randomly selected inside this cross 80 M ohammad A. Ahad et al.: Simulation Techniques of EM G Generation to Analyze Remodeling of Aging M uscles sectional surface.Figure 3 shows the random distribution of different types of motor units inside a muscle.Motor units diameter and their innervation numbers were assigned using the Equation (6) and (7) respectively. Fiber diameters in a motor unit were assigned randomly fro m the min imu m and the maximu m fiber diameter of a part icular muscle. that level for another one second.Recruit ment level is set at 80%M VC, wh ich means that all motor units in the muscle will be activated when the contraction reaches at 80% of MVC.In other wo rds, at 80% of M VC the highest threshold motor unit will be recru ited.Thus the range for the recruit ment threshold has been set fro m 1 to 80. 3. Results Figure 3. Type I (light) and type II (dark) distribution Because of the random motor unit distribution effects, all simu lations have been performed 50 times.Figure 4 shows the IPI variat ion and train of pulses for five different motor units in a motor unit pool of 200.Figure 5 shows the generated EM G signal for the young at 100% M VC.The frequency spectrums for both of these signals are shown in Figure 6 (a) and (b) for visual co mparison.The simulated EM G parameters such as root mean squared (RMS) and average rectified voltage (A RV) and spectrum parameters such as mean (M NF) and median frequency (M DF) are compared between young and elderly in Figure 6(c), (d), (e) and (f) respectively. Tibialis Anterior muscle g roup has been selected for the simu lation of EM G generation for both young and elderly for voluntary contraction.Elderly are vulnerab le to falling due to the lack of balance control.Thus Tibialis Anterior muscle has always been an object of interest for the clinicians and gerontologists.The physiological data, such as number of motor units, number of fibers per motor unit, percentage of fiber types and their diameter for both the young and the elderly are collected fro m published data[26, 27, 28]. Motor unit firing and recruit ment properties for young and elderly have been reported by Connelly D.M et al.It has been found that, even in aging muscle, recruit ment order follows the size principle during voluntary contractions[26, 30]. The force-firing rate curve is acquired fro m. M inimu m firing rate in the elderly is 4.18 Hz whereas this rate is 8.14 Hz in the Tibialis Anterior muscle of young.The slope of the linear firing frequency vs. threshold curve for the young is 0.3 and for the elderly is 0.27. As stated earlier, variation in the inter pulse interval (IPI) of the firing frequencies is less in the elderly than in the young people.The covariance of the IPI variation is estimated as 0.25 for young and 0.20 for elderly. Simu lations have been performed for both young and elderly for 5% to 100% of the maximu m voluntary contraction.Only a monopolar electrode, which is situated 10mm away fro m the center of the endplate zone, has been simu lated for EM G generation for both populations.Also in simu lation, only muscle with fat and skin has been considered.A ramp voluntary contraction has been applied as a force or excitation fo r the motor neuron pool model, wh ich increases to the level of simulated %M VC in one second and stays at Figure 4. Train of MUAPs and IPI variation in a motor unit pool of 200 at 100% MVC Figure 5. signal for young at 100%MVC American Journal of Biomedical Engineer ing 2013, 3(3): 77-83 81 (a) (b) (c) (d) (e ) (f) Figure 6. a) Frequency spectrum of young Tibialis Anterior at 100%MVC, b) frequency spectrum of elderly Tibialis anterior at 100%MVC, c) comparison of average rectified voltage (ARV) between young and elderly at 100%MVC, d) comparison of root-mean-squared value (RMS) between young and elderly at 100%MVC, e) comparison of mean frequency between young and elderly and f) comparison of median frequency between young and elderly at 100%MVC To verify the simulat ion results, experimental work of Yamada et al on young and elderly is adopted.Although the exact physiological parameters of the subjects were not known, the different physiological para mete rs for young (20 year old) and elderly (80 year o ld) are for the average young and old subjects that were adopted from the published data described earlier.Figure 7(a) illustrates the simulated median frequency and the experimentally found med ian frequency for both young and elderly subjects at the maximu m voluntary contraction.Statistical analysis shows that simu lated and experimental results are not significantly different (p < 0.05, two tailed, paired).Similarly, average rectified value for both young and elderly are co mpared in Figure 7(b ) for simu lated and experimental results.These results also show that there is no significant difference (p <0.05) between simulated and the experimental results.The 82 M ohammad A. Ahad et al.: Simulation Techniques of EM G Generation to Analyze Remodeling of Aging M uscles results of this study not only illustrate the remodeling of muscle during aging but also provide theoretical findings that are comparable to clinical findings. 4. Discussion Since impairment of skeletal muscle function leads to disability and loss of independence, it is important to understand the basic cellular mechanis m underlying muscle dysfunction in the elderly.Th is knowledge is essential to optimize rehabilitation and preventive strategies for this population, which by the year of 2030 will increase by 107 for the age group of 65 years and 133% for the age group of 85 years as predicted by the US Census Bureau. This means that the number of people requiring institutionalizat ion for d isabilit ies will increase substantially. Aging has different effects on different muscle limbs: h igher in the lower limbs than the upper.Although we did not consider the effects of aging on different muscles, this can be done easily by incorporating mode co mplex muscle model. (a) modeling.We attempted to model the muscle considering a ll its physiological aspects.Although it may not be possible to compare direct ly the results of this study to experimental work, due to differences in physiological properties of the muscle under study, our simu lated EM G values are in good agreement with published data. Simu lated EM G signals and its spectrum are qu ite distinctive for young and elderly mainly because elderly has fewer fast type-II fibers, which has smaller durat ion of the action potential than the type-I.For a constant-force contraction, the major factors that affect the motor unit action potential are the conduction velocity of the muscle fibers.The conduction velocity of the muscle fiber is proportional to its diameter.Therefo re, muscles with larger diameter fibers, such as those generally belonging to type-II motor units, will have greater average conduction velocities which, in turn, will shift the frequency spectrum towards the high frequency range and consequently increase the value of the median frequency.On the other hand, in the EMG of elderly, the magnitude of the lower frequency contents in the range of 30-40Hz is larger than that of the young.The muscles of elderly has more type-I motor units of bigger size due to the re-enervation of the muscle fibers, wh ich fires more frequently than the type-II motor units that is seen in larger amount in the muscle of young.Thus the magnitude of the frequency content in the range of 30-40 Hz, wh ich is the average peak firing frequency of type-I motor units, is higher in the Tib ialis Anterior muscle of elderly. In addition, the amount of subcutaneous (fatty) tissue between the electrode and the active fibers determines the amount of spatial filtering to wh ich the signal is subjected.The greater the thickness of the tissue, the greater is the low-pass filtering.Thus, additional subcutaneous tissue reduces the value of the med ian frequency.Moreover it is important to note that, electrode location and orientation, electrode configuration are also important factors influencing the EM G spectrum. 5. Conclusions (b) Figure 7. Comparison between simulated and experimental data at 100%MVC. a) mean frequency and b) average rectified voltage (ARV) During aging, remodeling of motor units and muscle physiological changes occur which are the reasons of significant changes of EM G signal in young and elderly healthy muscle.That is why, consideration of different fiber types and their changes during aging are crucial in the EM G In this study, a unique algorithm has been presented which incorporates motor units as two different types of motor units rather than assigning the same dia meter for a ll the motor unit fibers that was used in the earlier EM G simu lation.Excitation input currents to the population of motor units are simulated in the form of voluntary iso metric contraction to the muscle, and all the muscle input output relationships are described in the form of vo luntary contraction as input and generated EM G signals as output.The objective of this study has been met and the results of simulat ion are comparable to clinical finding.Therefo re, the potential contribution of the models designed in this paper can be used to show the detail of muscle remodeling throughout the aging process whereas, clin ical studies can only provide snap shots of the pathological changes that may occur during aging.For computational limitations, we used a simp lified analytical American Journal of Biomedical Engineer ing 2013, 3(3): 77-83 83 muscle model; a nu merical model wou ld certain ly enhance the accuracy of the results presented in this study.  D. Farina, R. M erletti, “A Novel Approach for Precise Simualtion of the EMG Signal Detected by Surface Electrode,” IEEE Trans Biomed Eng, vol. 48, pp. 637-646, Jun. 2001 REFERENCES  M .A. Rogers, W.J. Evans,Changes in skeletal muscle with aging: Effects of exercise training, Exerc Sport Sci Rev, vol. 21, pp. 65-102, 1993.  W.R. Frontera, V.A. Hughes, R. A. Fielding, A ging of skeletal muscle: A 12 year longitudinal study, Journal for Applied Physiology,vol. 88,pp. 1321-1326, Apr. 2000.  W. F. Brown, M J. Strong, R. Snow,M ethods for estimating numbers of motor units in biceps-brachialis muscles and losses of motor units with aging, Muscle& Nerve, vol. 11,pp. 423-432, M ay. 1988.  J. Lesell, C.C. Taylor, Variability in muscle fiber areas in whole human Quadriceps M uscle: Effects of increasing age, Journal of Anatomy,vol. 174,pp. 239-249, Feb. 1991.  J.A. Kent-Braun, A.V. Ng, K. Young,Skeletal muscle contractile and noncontractile components in young and older women and men, Journal for Applied Physiology, vol. 88, pp. 662-668, Feb. 2000.  A.J. Fuglevand, D.A. Winter, A.E. Patla, M odels of recruitment and rate codingorganization in motor unit pool, J. Neurophysiol, vol. 70, pp. 2470-2488, Dec. 1993.  D.W. Stashuk,Simulation of electromyographic signal, J. Electromyogr. Kinesil, vol. 3, pp. 157-173, M ar. 1993.  J. Duchene, J.Y. Hogrel, A model of EM G generation, IEEE Tran. Of Biomedical Eng, vol 47, pp. 192-201, Feb, 2000.  M . Ahad, T. Orth, N. Islam, M . Ferdjallah, (2012) Simulation of EM G signals for aging muscle, proceeding ofIEEE Southeast Conf, pp. 1-5, Orlando, FL.  S. Andreassen, A. Rosenfalck,Relationship of intracellular and extracellular action potentials of skeletal muscle fibers, CRC Critical Reviews in Bioengineering, vol. 6, pp. 267-306, 1981.  D. Farina, A. Rainoldi,Compensation of the effect of subcutaneous tissue layers on surface EM G: A simulation study, Med Engg Phys, vol. 22. pp. 487-496, 1999.  R.M . Enoka, A.J. Fuglevand.,M otor unit physiology: some unresolved issues, M uscle Nerve, vol. 34, pp. 4-17, Jan. 2001.  P.G. Arabadjis, R.R. Heffner, D.R. Jr,  K. Kanda, K. Hashizume, Factors causing difference in force Pendergast,M orphologic and functional alterations in A ging output among motor units in the rat medial gastrocnemius Rat M uscle, Journal of Neuropathol Exp Neurol, vol. 49,pp. 600-609, Nov. 1990. muscle, J. Physiol. (Lond), vol. 448, pp.677-695, 1992.  R.M . Enoka, M orphologicai featuresand activation patterns  M . Brown,Change in fiber size, not number, in aging skeletal of motor units, Journal of Clinical Neurophysiolo,oy, vol. 12, muscle, Age Ageing, vol. 16, pp. 244-248, Apr.1987. pp. 538-559, Nov. 1995.  G.N. Williams, M .J. Higgins, M .D. Lewek, Aging skeletal muscle: Physiologic changes and the effects of training, Physical Therapy, vol. 82, pp. 62-68, Jan. 2002.  M .M. Porter, A.A. Vandervoort, J. Lexell, A ging of human muscle: structure, function and adaptability, Scand J Med Sci Sports, vol. 5, pp. 129-142, Jun. 1995.  Z. Erim, M . F. Beg, D. T. Burke, and Carlo J. de Luca, Effects of aging on motor-unit control properties,J Neurophysiol,vol. 82, pp. 2081-2091, Nov. 1999.  M .L. Campbell, A.J. M cComas, F. Petito,Physiological changes in ageing muscles, Journal of Neurol Neurosurg Psychiatry, vol. 36, pp. 174-182, Apr. 1973.  S.D. Nandedkar, E. Stalberg, “Simulation of Single M uscle Fiber action Potentials,” Med Biol Eng Computing, vol. 21, pp. 158-165, 1983.  TJJM Gootzen, D.F. Stegeman, A. Van Oosterom, “Finite Limb Dimensions and Finite M uscle Length in a M odel for the Generation of Electromyographic Signals,” Electroenceph Clin Neurophysiol, vol. 81:152-162, Apr. 1991.  G. Kim, M . Ferdjallahand F. D. M cKenzie, An empirical muscle intracellular action potential model with multiple erlang probability density functions based on a modified newton method, Biomedical Eng and Computational Biology, vol. 5, pp. 33-42, 2013  E. Henneman, Functional organization of motoneuron pools: the size principle, Integration in the Nervous System, edited by H. Asunuma and V.J. Wilson. Tokyo: Igaku Shion, pp. 13-25, 1979.  M .M. Porter, S. Stuart, J. Lexell, Capilary supply of the tibialis anterior muscle in young and healthy and moderately active men and women, J. appl. Phyisiol, vol. 92, pp. 1451-1457, Apr. 2002.  F. Jakobson, K. Borg, L. Edstrom, L. Grimby, Use of motor units in relation of muscle fiber type and size in men, Muscle & Nerve, vol. 11, pp. 1211-1218, Dec. 1988.  C.J. M cNeil, T.J. Doherty, D.W. Stashuk and C.L. Rice, M otor unit number estimates in the tibialis anterior muscle of young, old, and very old men, M uscle Nerve, vol. 31, pp. 461-467, Apr. 2005.  D.M . Connelly, C.L. Rice, M .R. Roos, M otor unit firing rates and contractile properties in tibialis anterior of young and old men, J. applied Physiol, vol. 87, pp. 843-852, Aug. 1999.  J. Duchateau, K. Hainaut, Effects of immobilization on contractile properties, recruitment and firing rates of human motor units, Journal of Physiol (Lond), vol. 422, pp. 55-65, M ar. 1990.  H. Yamada et al, Effect of aging on EM G variables during fatiguing isometric contraction, Journal Human Ergol, vol. 29, pp. 7-14, M ar. 2000.
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