In vivo estimation of the short-range stiffness of cross-bridges from joint rotation

Short-range stiffness (SRS) is a mechanical property of muscles that is characterized by a disproportionally high stiffness within a short length range during both lengthening and shortening movements. SRS is attributed to the cross-bridges and is beneficial for stabilizing a joint during, e.g., postural conditions. Thus far, SRS has been estimated mainly on isolated mammalian muscles. In this study we presented a method to estimate SRS in vivo in the human wrist joint.SRS was estimated at joint level in the angular domain (N m/rad) for both flexion and extension rotations of the human wrist in nine healthy subjects. Wrist rotations of 0.15 rad at 3 rad/s were imposed at eight levels of voluntary contraction ranging from 0 to 2.1 N m by means of a single axis manipulator.Flexion and extension SRS of the wrist joint was estimated consistently and accurately using a dynamic nonlinear model that was fitted onto the recorded wrist torque. SRS increased monotonically with torque in a way consistent with previous studies on isolated muscles.It is concluded that in vivo measurement of joint SRS represents the population of coupled cross-bridges in wrist flexor and extensor muscles. In its current form, the presented technique can be used for clinical applications in many neurological and muscular diseases where altered joint torque and (dissociated) joint stiffness are important clinical parameters.     

Perturbation velocity affects linearly estimated neuromechanical wrist joint properties

The dynamic behavior of the wrist joint is governed by nonlinear properties, yet applied mathematical models, used to describe the measured input-output (perturbation-response) relationship, are commonly linear. Consequently, the linearly estimated model parameters will depend on properties of the applied perturbation properties (such perturbation amplitude and velocity). We aimed to systematically address the effects of perturbation velocity on linearly estimated neuromechanical parameters.Using a single axis manipulator ramp and hold perturbations were applied to the wrist joint. Effects of perturbation velocity (0.5, 1 and 3 rad/s) were investigated at multiple background torque levels (0, 0.5 and 1 N·m). With increasing perturbation velocity, estimated joint stiffness remained constant, while damping and reflex gain decreased. This variation in model parameters is dependent on background torque levels, i.e. muscle contraction.These observations support the future development of nonlinear models that are capable of describing wrist joint behavior over a larger range of loading conditions, exceeding the restricted range of operation that is required for linearization.     

Effect of altering starting length and activation timing of muscle on fiber strain and muscle damage.

Muscle strain injuries are some of the most frequent injuries in sports and command a great deal of attention in an effort to understand their etiology. These injuries may be the culmination of a series of subcellular events accumulated through repetitive lengthening (eccentric) contractions during exercise, and they may be influenced by a variety of variables including fiber strain magnitude, peak joint torque, and starting muscle length. To assess the influence of these variables on muscle injury magnitude in vivo, we measured fiber dynamics and joint torque production during repeated stretch-shortening cycles in the rabbit tibialis anterior muscle, at short and long muscle lengths, while varying the timing of activation before muscle stretch. We found that a muscle subjected to repeated stretch-shortening cycles of constant muscle-tendon unit excursion exhibits significantly different joint torque and fiber strains when the timing of activation or starting muscle length is changed. In particular, measures of fiber strain and muscle injury were significantly increased by altering activation timing and increasing the starting length of the muscle. However, we observed differential effects on peak joint torque during the cyclic stretch-shortening exercise, as increasing the starting length of the muscle did not increase torque production. We conclude that altering activation timing and muscle length before stretch may influence muscle injury by significantly increasing fiber strain magnitude and that fiber dynamics is a more important variable than muscle-tendon unit dynamics and torque production in influencing the magnitude of muscle injury.     

Passive tension and stiffness of vertebrate skeletal and insect flight muscles: the contribution of weak cross-bridges and elastic filaments.

Tension and dynamic stiffness of passive rabbit psoas, rabbit semitendinosus, and waterbug indirect flight muscles were investigated to study the contribution of weak-binding cross-bridges and elastic filaments (titin and minititin) to the passive mechanical behavior of these muscles. Experimentally, a functional dissection of the relative contribution of actomyosin cross-bridges and titin and minititin was achieved by 1) comparing mechanically skinned muscle fibers before and after selective removal of actin filaments with a noncalcium-requiring gelsolin fragment (FX-45), and 2) studying passive tension and stiffness as a function of sarcomere length, ionic strength, temperature, and the inhibitory effect of a carboxyl-terminal fragment of smooth muscle caldesmon. Our data show that weak bridges exist in both rabbit skeletal muscle and insect flight muscle at physiological ionic strength and room temperature. In rabbit psoas fibers, weak bridge stiffness appears to vary with both thin-thick filament overlap and with the magnitude of passive tension. Plots of passive tension versus passive stiffness are multiphasic and strikingly similar for these three muscles of distinct sarcomere proportions and elastic proteins. The tension-stiffness plot appears to be a powerful tool in discerning changes in the mechanical behavior of the elastic filaments. The stress-strain and stiffness-strain curves of all three muscles can be merged into one, by normalizing strain rate and strain amplitude of the extensible segment of titin and minititin, further supporting the segmental extension model of resting tension development.     

Smooth muscle myosin: regulation and properties

The relationship of the biochemical states to the mechanical events in contraction of smooth muscle cross-bridges is reviewed. These studies use direct measurements of the kinetics of Pi and ADP release. The rate of release of Pi from thiophosphorylated cycling cross-bridges held isometric was biphasic with turnovers of 1.8 s-1 and 0.3 s-1, reflecting properties and forces directly acting on cross-bridges through mechanisms such as positive strain and inhibition by high-affinity MgADP binding. Fluorescent transients reporting release of an ADP analogue 3'-deac-edaADP were significantly faster in phasic than in tonic smooth muscles. Thiophosphorylation of myosin regulatory light chains (RLCs) increased and positive strain decreased the release rate around twofold. The rates of ADP release from rigor cross-bridges and the steady-state Pi release from cycling isometric cross-bridges are similar, indicating that the ADP-release step or an isomerization preceding it may limit the ATPase rate. Thus ADP release in phasic and tonic smooth muscles is a regulated step with strain- and dephosphorylation-dependence. High affinity of cross-bridges for ADP and slow ADP release prolong the fraction of the duty cycle occupied by strongly bound AM.ADP state(s) and contribute to the high economy of force that is characteristic of smooth muscle. RLC thiophosphorylation led to structural changes in smooth muscle cross-bridges consistent with our findings that thiophosphorylation and strain modulate product release.     

Mechanism of thixotropic behavior at relaxed joints in the rat

When a relaxed joint is subjected to a small sinusoidal torque, the amplitude of the steady-state displacement response is increased up to severalfold by a transient larger perturbation. The original state, in which the relaxed joint is unexpectedly stiff, is restored by several seconds of inactivity. This thixotropic phenomenon has previously been observed in a variety of human joints. We have now investigated the mechanism of thixotropic behavior at relaxed joints in rats anesthetized with pentobarbital sodium, by using a series of preparations including the intact ankle joint, a blood-perfused soleus muscle preparation, an isolated soleus muscle, and ankle joint isolated by severing all muscular attachments. Thixotropic behavior was observed in all intact, isolated muscle, and isolated joint preparations. The contribution of the joint to thixotropic behavior was comparable to, and at times exceeded, the contribution of muscle. We also analyzed the short-range stiffness properties of relaxed, blood-perfused soleus muscles and found them to be similar to thixotropy with respect to range of action (0.2-0.3% of muscle length), elastic modulus (approximately 4 kg/cm2), and time course for redevelopment (time constant = 2.5 s at 34 degrees C). Thus thixotropic behavior at a relaxed joint may be attributed both to the joint structures and to short-range stiffness of muscles acting at the joint.     

Interplay between passive tension and strong and weak binding cross- bridges in insect indirect flight muscle. A functional dissection by gelsolin-mediated thin filament removal

The interplay between passive and active mechanical properties of indirect flight muscle of the waterbug (Lethocerus) was investigated. A functional dissection of the relative contribution of cross-bridges, actin filaments, and C filaments to tension and stiffness of passive, activated, and rigor fibers was carried out by comparing mechanical properties at different ionic strengths of sarcomeres with and without thin filaments. Selective thin filament removal was accomplished by treatment with the actin-severving protein gelsolin. Thin filament, removal had no effect on passive tension, indicating that the C filament and the actin filament are mechanically independent and that passive tension is developed by the C filament in response to sarcomere stretch. Passive tension increased steeply with sarcomere length until an elastic limit was reached at only 6-7% sarcomere extension, which corresponds to an extension of 350% of the C filament. The passive tension-length relation of insect flight muscle was analyzed using a segmental extension model of passive tension development (Wang, K, R. McCarter, J. Wright, B. Jennate, and R Ramirez-Mitchell. 1991. Proc. Natl. Acad. Sci. USA. 88:7101-7109). Thin filament removal greatly depressed high frequency passive stiffness (2.2 kHz) and eliminated the ionic strength sensitivity of passive stiffness. It is likely that the passive stiffness component that is removed by gelsolin is derived from weak-binding cross-bridges, while the component that remains is derived from the C filament. Our results indicate that a significant number of weak-binding cross-bridges exist in passive insect muscle at room temperature and at an ionic strength of 195 mM. Analysis of rigor muscle indicated that while rigor tension is entirely actin based, rigor stiffness contains a component that resists gelsolin treatment and is therefore likely to be C filament based. Active tension and active stiffness of unextracted fibers were directly proportional to passive tension before activation. Similarly, passive stiffness due to weak bridges also increased linearly with passive tension, up to a limit. These correlations lead us to propose a stress-activation model for insect flight muscle in which passive tension is a prerequisite for the formation of both weak-binding and strong-binding cross-bridges.     

Mechanomyogram amplitude vs. isometric ankle plantarflexion torque of human medial gastrocnemius muscle at different ankle joint angles

The purpose of this study was to investigate the influence of changes in ankle joint angle on the mechanomyogram (MMG) amplitude of the human medial gastrocnemius (MG) muscle during voluntary isometric plantarflexion contractions. Ten healthy individuals were asked to perform voluntary isometric contractions at six different contraction intensities (from 10% to 100%) and at three different ankle joint angles (plantarflexion of 26°; plantarflexion of 10°; dorsiflexion of 3°). MMG signals were recorded from the surface over the MG muscle, using a 3-axis accelerometer. The relations between root mean square (RMS) MMG and isometric plantarflexion torque at different ankle joint angles were characterized to evaluate the effects of altered muscle mechanical properties on RMS MMG.We found that the relation between RMS MMG and plantarflexion torque is changed at different ankle joint angles: RMS MMG increases monotonically with increasing the plantarflexion torque but decreases as the ankle joint became dorsiflexed. Moreover, RMS MMG shows a negative correlation with muscle length, with passive torque, and with maximum voluntary torque, which were all changed significantly at different ankle joint angles.Our findings demonstrate the potential effects of changing muscle mechanical properties on muscle vibration amplitude. Future studies are required to explore the major sources of this muscle vibration from the perspective of muscle mechanics and muscle activation level, attributable to changes in the neural command.     

Elastic Energy Storage and Radial Forces in the Myofilament Lattice Depend on Sarcomere Length

We most often consider muscle as a motor generating force in the direction of shortening, but less often consider its roles as a spring or a brake. Here we develop a fully three-dimensional spatially explicit model of muscle to isolate the locations of forces and energies that are difficult to separate experimentally. We show the strain energy in the thick and thin filaments is less than one third the strain energy in attached cross-bridges. This result suggests the cross-bridges act as springs, storing energy within muscle in addition to generating the force which powers muscle. Comparing model estimates of energy consumed to elastic energy stored, we show that the ratio of these two properties changes with sarcomere length. The model predicts storage of a greater fraction of energy at short sarcomere lengths, suggesting a mechanism by which muscle function shifts as force production declines, from motor to spring. Additionally, we investigate the force that muscle produces in the radial or transverse direction, orthogonal to the direction of shortening. We confirm prior experimental estimates that place radial forces on the same order of magnitude as axial forces, although we find that radial forces and axial forces vary differently with changes in sarcomere length.     

Behavior of human muscle fascicles during shortening and lengthening contractions in vivo.

The aim of the present study was to investigate the behavior of human muscle fascicles during dynamic contractions. Eight subjects performed maximal isometric dorsiflexion contractions at six ankle joint angles and maximal isokinetic concentric and eccentric contractions at five angular velocities. Tibialis anterior muscle architecture was measured in vivo by use of B-mode ultrasonography. During maximal isometric contraction, fascicle length was shorter and pennation angle larger compared with values at rest (P < 0.01). During isokinetic concentric contractions from 0 to 4.36 rad/s, fascicle length measured at a constant ankle joint angle increased curvilinearly from 49.5 to 69.7 mm (41%; P < 0.01), whereas pennation angle decreased curvilinearly from 14.8 to 9.8 degrees (34%; P < 0.01). During eccentric muscle actions, fascicles contracted quasi-isometrically, independent of angular velocity. The behavior of muscle fascicles during shortening contractions was believed to reflect the degree of stretch applied to the series elastic component, which decreases with increasing contraction velocity. The quasi-isometric behavior of fascicles during eccentric muscle actions suggests that the series elastic component acts as a mechanical buffer during active lengthening.     

The integration of lateral gastrocnemius muscle function and kinematics in running turkeys

Animals commonly move over a range of speeds, and encounter considerable variation in habitat structure, such as inclines. Hindlimb kinematics and muscle function in diverse groups of vertebrates are affected by these changes in behavior and habitat structure, providing a fruitful source of variation for studying the integration of kinematics and muscle function. While it has been observed in a variety of vertebrates that muscle length change can be minimal during locomotion, it is unclear how, and to what degree, in vivo muscle length change patterns are integrated with kinematics. We tested the hypothesis that the length of the turkey lateral gastrocnemius (LG), a biarticular muscle that has moments at the ankle and knee, is not solely affected by changes in joint kinematics. We recorded in vivo muscle length changes (using sonomicrometry) and hindlimb movements (using high-speed video) of wild turkeys running on various inclines, and at different speeds. We quantified the relationship between joint angle (knee and ankle separately) and muscle length in freshly euthanized specimens, and then applied an empirically derived correction for changes in pennation angle and tendon strain during locomotion to improve the accuracy of our predicted lengths. We estimated muscle length at four points during each stride and then compared these values with those measured directly. Other than during swing, the predicted changes in muscle length calculated from the changes in joint kinematics did not correspond with our measured values of LG length. Therefore, the lengths at which the LG operates in turkeys are not determined entirely by kinematics. In addition to strain in series elastic components, we hypothesize that heterogeneous strain within muscles, interactions between muscles and muscle pennation angle all contribute to the nonlinear relationship between muscle length changes and kinematics.     

A parametric model of muscle moment arm as a function of joint angle: Application to the dorsiflexor muscle group in mice

A parametric model was developed to describe the relationship between muscle moment arm and joint angle. The model was applied to the dorsiflexor muscle group in mice, for which the moment arm was determined as a function of ankle angle. The moment arm was calculated from the torque measured about the ankle upon application of a known force along the line of action of the dorsiflexor muscle group. The dependence of the dorsiflexor moment arm on ankle angle was modeled as r=R sin(a+Δ), where r is the moment arm calculated from the measured torque and a is the joint angle. A least-squares curve fit yielded values for R, the maximum moment arm, and Δ, the angle at which the maximum moment arm occurs as offset from 90°. Parametric models were developed for two strains of mice, and no differences were found between the moment arms determined for each strain. Values for the maximum moment arm, R, for the two different strains were 0.99 and 1.14 mm, in agreement with the limited data available from the literature. While in some cases moment arm data may be better fitted by a polynomial, use of the parametric model provides a moment arm relationship with meaningful anatomical constants, allowing for the direct comparison of moment arm characteristics between different strains and species.     

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics.

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2: Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control uponelastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body systemvariational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and jointmodeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,whileallowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from aHill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,aneffective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models themuscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated byutilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies,models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone andtendon.     

Position dependence of ankle joint dynamics--I. Passive mechanics

System identification techniques were used to examine the position dependence of passive ankle joint mechanics. The relaxed ankle was stochastically perturbed about different angles in the range of motion (ROM). The linear dynamic relation between ankle position and torque was identified and modelled as a second-order underdamped system, having inertial (I), viscous (B) and elastic (K) parameters. Mean joint torque changed as the ankle was rotated through the ROM; it was small at mid-range and became much larger toward either extreme. While I remained constant both B and K changed as a function of ankle angle. At the extremes of the ROM, K was much larger than previously assumed and the relation between stiffness and the passive torque generated when the ankle was placed at different mean positions was linear. These results show that large variations in joint mechanics are possible even in the absence of voluntary muscle contraction. Moreover, these changes appear to be related to the torque generated when passive joint structures are stretched.     

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Analysis of a muscular control system in human movements

In this work, we have studied a muscular control system under experimental conditions for analyzing the dynamic behavior of individual muscles and theoretical considerations for elucidating its control strategy. Movement of human limbs is achieved by joint torques and each torque is specified as the sum of torques generated by muscle forces. The behavior of individual muscles is controlled by the neural input which is estimated by means of an electromyogram (EMG). In this study, the EMGs for a flexor and an extensor are measured in elbow joint movements and the dynamic behavior of individual muscles is analyzed. As a result, it is verified that both a flexor and an extensor are activated throughout the entire movement and that the activation of muscles is controlled above a specific limit independent of the hand-held load. Subsequently, a system model for simulating elbow joint movements is developed which includes the muscle dynamic relationship between the neural input and the isometric force. The minimum limit of muscle activation that has been confirmed in experiments is provided as a constraint of the neural input and the criterion is defined by a derivative of the isometric force of individual muscles. The optimal trajectories formulated under these conditions are quantitatively compared with the experimentally observed trajectories, and the control strategy of a muscular control system is studied. Finally, a muscular control system in multi-joint arm movements is discussed with regard to the comparative analysis between observed and optimal trajectories. Received: 7 April 1999 / Accepted in revised form: 27 July 1999     

Intrinsic and extrinsic contributions to the passive moment at the metacarpophalangeal joint

The purpose of this investigation was to determine whether the passive range of motion at the finger joints is restricted more by intrinsic tissues (cross a single joint) or by extrinsic tissues (cross multiple joints). The passive moment at the metacarpophalangeal (MP) joint of the index finger was modeled as the sum of intrinsic and extrinsic components. The intrinsic component was modeled only as a function of MP joint angle. The extrinsic component was modeled as a function of MP joint angle and wrist angle. With the wrist fixed in seven different positions the passive moment at the MP joint of eight subjects was recorded as the finger was rotated through its range at a constant rate. The moment-angle data were fit by the model and the extrinsic and intrinsic components were calculated for a range of MP joint angles and wrist positions. With the MP joint near its extension limit, the median percent extrinsic contribution was 94% with the wrist extended 60° and 14% with the wrist flexed 60°. These percentages were 40 and 88%, respectively, with the MP joint near its flexion limit. Our findings indicate that at most wrist angles the extrinsic tissues offer greater restraint at the limits of MP joint extension and flexion than the intrinsic tissues. The intrinsic tissues predominate when the wrist is flexed or extended enough to slacken the extrinsic tissues. Additional characteristics of intrinsic and extrinsic tissues can be deduced by examining the parameter values calculated by the model.     

Elastic properties of relaxed, activated, and rigor muscle fibers measured with microsecond resolution.

Tension responses due to small and rapid length changes (completed within 40 microseconds) were obtained from skinned single-fiber segments (4- to 7-mm length) of the iliofibularis muscle of the frog incubated in relaxing, rigor, and activating solution. The fibers were skinned by freeze-drying. The first 500 microseconds of the responses for all three conditions could be described with a linear model, in which the fiber is regarded as a rod composed of infinitesimally small identical segments, containing an undamped elastic element, two damped elastic elements and a mass in series. An additional damped elastic element was needed to describe tension responses of activated fibers up to the first 5 ms. Consequently phase 1 and phase 2 of activated fibers can be described with four apparent elastic constants and three time constants. The results indicate that fully activated fibers and fibers in rigor have similar elastic properties within the first 500 microseconds of tension responses. This points either to an equal number of attached cross-bridges in rigor and activated fibers or to a different number of attached cross-bridges in rigor and activated fibers and nonlinear characteristics in rigor cross-bridges. Mass-shift measurements obtained from equatorial x-ray diffraction patterns support the latter possibility.     

Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.