Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm.

The mechanical properties of the human arm are regulated to maintain stability across many tasks. The static mechanics of the arm can be characterized by estimates of endpoint stiffness, considered especially relevant for the maintenance of posture. At a fixed posture, endpoint stiffness can be regulated by changes in muscle activation, but which activation-dependent muscle properties contribute to this global measure of limb mechanics remains unclear. We evaluated the role of muscle properties in the regulation of endpoint stiffness by incorporating scalable models of muscle stiffness into a three-dimensional musculoskeletal model of the human arm. Two classes of muscle models were tested: one characterizing short-range stiffness and two estimating stiffness from the slope of the force-length curve. All models were compared with previously collected experimental data describing how endpoint stiffness varies with changes in voluntary force. Importantly, muscle properties were not fit to the experimental data but scaled only by the geometry of individual muscles in the model. We found that force-dependent variations in endpoint stiffness were accurately described by the short-range stiffness of active arm muscles. Over the wide range of evaluated arm postures and voluntary forces, the musculoskeletal model incorporating short-range stiffness accounted for 98 ± 2, 91 ± 4, and 82 ± 12% of the variance in stiffness orientation, shape, and area, respectively, across all simulated subjects. In contrast, estimates based on muscle force-length curves were less accurate in all measures, especially stiffness area. These results suggest that muscle short-range stiffness is a major contributor to endpoint stiffness of the human arm. Furthermore, the developed model provides an important tool for assessing how the nervous system may regulate endpoint stiffness via changes in muscle activation.

[1]  D. McCloskey,et al.  Maintenance of constant arm position or force: reflex and volitional components in man. , 1987, The Journal of physiology.

[2]  Philippe Mailly,et al.  34th Annual Meeting of Society for Neuroscience , 2004 .

[3]  R. Trumbower,et al.  Interactions between limb and environmental mechanics influence stretch reflex sensitivity in the human arm. , 2010, Journal of neurophysiology.

[4]  Eric J Perreault,et al.  In situ estimation of tendon material properties: differences between muscles of the feline hindlimb. , 2009, Journal of biomechanics.

[5]  Francisco J. Valero Cuevas,et al.  Reported anatomical variability naturally leads to multimodal distributions of Denavit-Hartenberg parameters for the human thumb , 2006, IEEE Transactions on Biomedical Engineering.

[6]  Neville Hogan,et al.  The mechanics of multi-joint posture and movement control , 1985, Biological Cybernetics.

[7]  Ian E. Brown,et al.  A Reductionist Approach to Creating and Using Neuromusculoskeletal Models , 2000 .

[8]  S. Delp,et al.  Moment-generating capacity of upper limb muscles in healthy adults. , 2007, Journal of biomechanics.

[9]  J Cholewicki,et al.  EMG assisted optimization: a hybrid approach for estimating muscle forces in an indeterminate biomechanical model. , 1994, Journal of biomechanics.

[10]  Keng Peng Tee,et al.  A model of force and impedance in human arm movements , 2004, Biological Cybernetics.

[11]  L. Selen,et al.  Impedance Control Reduces Instability That Arises from Motor Noise , 2009, The Journal of Neuroscience.

[12]  S. Delp,et al.  Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions. , 2002, Journal of biomechanics.

[13]  H. Gomi,et al.  Task-Dependent Viscoelasticity of Human Multijoint Arm and Its Spatial Characteristics for Interaction with Environments , 1998, The Journal of Neuroscience.

[14]  H. Gomi,et al.  Multijoint muscle regulation mechanisms examined by measured human arm stiffness and EMG signals. , 1999, Journal of neurophysiology.

[15]  S. Grillner The role of muscle stiffness in meeting the changing postural and locomotor requirements for force development by the ankle extensors. , 1972, Acta physiologica Scandinavica.

[16]  D. R. Fish,et al.  Sources of goniometric error at the elbow. , 1985, Physical therapy.

[17]  F. Zajac Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. , 1989, Critical reviews in biomedical engineering.

[18]  M. Kawato,et al.  Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics , 2003, Experimental Brain Research.

[19]  A. Huxley,et al.  The variation in isometric tension with sarcomere length in vertebrate muscle fibres , 1966, The Journal of physiology.

[20]  Wendy M Murray,et al.  Variability in surgical technique for brachioradialis tendon transfer. Evidence and implications. , 2006, The Journal of bone and joint surgery. American volume.

[21]  Keng Peng Tee,et al.  Concurrent adaptation of force and impedance in the redundant muscle system , 2010, Biological Cybernetics.

[22]  G. C. Joyce,et al.  The forces generated at the human elbow joint in response to imposed sinusoidal movements of the forearm , 1974, The Journal of physiology.

[23]  N Hogan,et al.  Dynamics of Pushing , 2001, Journal of motor behavior.

[24]  K. An,et al.  Monte Carlo simulation of a planar shoulder model , 1997, Medical and Biological Engineering and Computing.

[25]  Sybert H. Stroeve,et al.  Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control , 1999, Biological Cybernetics.

[26]  Rieko Osu,et al.  The central nervous system stabilizes unstable dynamics by learning optimal impedance , 2001, Nature.

[27]  Scott L. Delp,et al.  A Model of the Upper Extremity for Simulating Musculoskeletal Surgery and Analyzing Neuromuscular Control , 2005, Annals of Biomedical Engineering.

[28]  J E Grohmann Comparison of two methods of goniometry. , 1983, Physical therapy.

[29]  I. Hunter,et al.  Dynamics of human ankle stiffness: variation with mean ankle torque. , 1982, Journal of biomechanics.

[30]  P. Crago,et al.  Effects of voluntary force generation on the elastic components of endpoint stiffness , 2001, Experimental Brain Research.

[31]  Nathan E. Bunderson,et al.  Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion. , 2008, Journal of biomechanics.

[32]  Eric J Perreault,et al.  Motor unit composition has little effect on the short-range stiffness of feline medial gastrocnemius muscle. , 2007, Journal of applied physiology.

[33]  B Roszek,et al.  Decreasing stimulation frequency-dependent length-force characteristics of rat muscle. , 1994, Journal of applied physiology.

[34]  G. C. Joyce,et al.  The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements , 1969, The Journal of physiology.

[35]  R. F. Ker,et al.  Mechanical properties of various mammalian tendons , 1986 .

[36]  John Ross Computing in Science , 1992 .

[37]  Rieko Osu,et al.  Endpoint Stiffness of the Arm Is Directionally Tuned to Instability in the Environment , 2007, The Journal of Neuroscience.

[38]  T. Milner,et al.  Inability to activate muscles maximally during cocontraction and the effect on joint stiffness , 2004, Experimental Brain Research.

[39]  R. Crowninshield,et al.  A physiologically based criterion of muscle force prediction in locomotion. , 1981, Journal of biomechanics.

[40]  E. Bizzi,et al.  Postural force fields of the human arm and their role in generating multijoint movements , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[41]  Dale D. Murphy,et al.  Evidence and Implications , 2006 .

[42]  D. Lloyd,et al.  An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. , 2003, Journal of biomechanics.

[43]  S. Cannon,et al.  The mechanical behavior of active human skeletal muscle in small oscillations. , 1982, Journal of biomechanics.

[44]  E. Bizzi,et al.  Neural, mechanical, and geometric factors subserving arm posture in humans , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[45]  M G Pandy,et al.  Static and dynamic optimization solutions for gait are practically equivalent. , 2001, Journal of biomechanics.

[46]  P. Rack,et al.  The effects of length and stimulus rate on tension in the isometric cat soleus muscle , 1969, The Journal of physiology.

[47]  G. Lewis,et al.  Interactions with compliant loads alter stretch reflex gains but not intermuscular coordination. , 2008, Journal of neurophysiology.

[48]  R. Blickhan,et al.  Stabilizing function of skeletal muscles: an analytical investigation. , 1999, Journal of theoretical biology.

[49]  K. An,et al.  Shoulder muscle moment arms during horizontal flexion and elevation. , 1997, Journal of shoulder and elbow surgery.

[50]  J. Misiaszek Control of frontal plane motion of the hindlimbs in the unrestrained walking cat. , 2006, Journal of neurophysiology.

[51]  Scott L. Delp,et al.  A computational framework for simulating and analyzing human and animal movement , 2000, Comput. Sci. Eng..

[52]  Frans C. T. van der Helm,et al.  Bifurcation and stability analysis in musculoskeletal systems: a study in human stance , 2004, Biological Cybernetics.

[53]  Y. Koike,et al.  A myokinetic arm model for estimating joint torque and stiffness from EMG signals during maintained posture. , 2009, Journal of neurophysiology.

[54]  S. Delp,et al.  The isometric functional capacity of muscles that cross the elbow. , 2000, Journal of biomechanics.

[55]  J J Collins,et al.  The redundant nature of locomotor optimization laws. , 1995, Journal of biomechanics.

[56]  D. Morgan Separation of active and passive components of short-range stiffness of muscle. , 1977, The American journal of physiology.

[57]  D J Ostry,et al.  Are complex control signals required for human arm movement? , 1998, Journal of neurophysiology.

[58]  S. Delp,et al.  Upper limb muscle volumes in adult subjects. , 2007, Journal of biomechanics.

[59]  T. Flash,et al.  Human arm stiffness characteristics during the maintenance of posture , 1990, Experimental Brain Research.

[60]  I. Hunter,et al.  Dynamics of human ankle stiffness: variation with displacement amplitude. , 1982, Journal of biomechanics.

[61]  Stan C. A. M. Gielen,et al.  A comparison of models explaining muscle activation patterns for isometric contractions , 1999, Biological Cybernetics.

[62]  W. Rymer,et al.  Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance , 1994, IEEE Transactions on Biomedical Engineering.

[63]  A Hufschmidt,et al.  Short‐range elasticity and resting tension of relaxed human lower leg muscles. , 1987, The Journal of physiology.

[64]  R. Stein,et al.  Identification of intrinsic and reflex contributions to human ankle stiffness dynamics , 1997, IEEE Transactions on Biomedical Engineering.

[65]  Scott L. Delp,et al.  Moment-generating capacity of upper limb muscles , 2006 .

[66]  P. Rack,et al.  The short range stiffness of active mammalian muscle and its effect on mechanical properties , 1974, The Journal of physiology.

[67]  E. Bizzi,et al.  The control of stable postures in the multijoint arm , 1996, Experimental Brain Research.

[68]  Kamran Iqbal,et al.  Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback. , 2004, Journal of biomechanical engineering.

[69]  E. Perreault,et al.  Modeling short-range stiffness of feline lower hindlimb muscles. , 2008, Journal of biomechanics.

[70]  Toshio Tsuji,et al.  Human hand impedance characteristics during maintained posture , 1995, Biological Cybernetics.

[71]  V. Edgerton,et al.  Muscle architecture and force-velocity characteristics of cat soleus and medial gastrocnemius: implications for motor control. , 1980, Journal of neurophysiology.

[72]  D. Ostry,et al.  Learning to control arm stiffness under static conditions. , 2004, Journal of neurophysiology.