Postural dependence of muscle actions: implications for neural control

Abstract

The neural control of reaching entails the specification of a precise pattern of muscle activation distributed across the many muscles of the arm. Musculoskeletal geometry limits the possible solutions to this problem. Insight into the nature of this constraint was obtained by quantifying the postural variation in the mechanical actions of six human shoulder muscles. Estimates of muscle mechanical actions were obtained by electrically stimulating muscles to the point of contraction and recording the resulting forces and torques with a six-degree-of-freedom force-torque transducer. In a given experiment, data were obtained for up to 29 different arm postures. The mechanical actions of each muscle varied systematically with arm posture, regardless of the frame of reference used to define these actions. The nature of this dependence suggests that a relatively simple strategy can be used by the nervous system to account for the changing mechanical actions of arm muscles.

Fig. 1.

Experimental apparatus (A), angles defining arm posture (B), and a free-body diagram of the forces and torques exerted on the upper arm (C).A, A six-degree-of-freedom force–torque sensor was rigidly coupled to an upper extremity orthosis at one end and a stereotaxic frame at the other. Two coordinate frames are illustrated: an x, y, z, frame that was fixed to the arm/sensor, and an x′, y′,z′ frame (inset) that was fixed in space. In this posture, the axes of the two frames were parallel. Thez- and x-axes were aligned with the long axes of the upper arm and forearm segments of the orthosis, respectively; the y-axis was orthogonal to the plane containing these two axes. B, Three angles were used to define upper arm posture: η, a rotation about the verticalz′-axis; θ, a rotation in a vertical plane passing through the upper arm (measured relative to the verticalz′-axis), and ζ, a rotation about the long axis of the humerus. C, A cylinder representing the upper arm is depicted along with the forces (F_x,F_y, F_z) and torques (T_x, T_y,T_z) recorded at the transducer and the corresponding torques at the shoulder (M_x,M_y, M_z). The shoulder, elbow, and length of the upper arm are labeledS, E, and La, respectively.

Fig. 2.

Graphical representation of the calculation of shoulder torques and the method used to evaluate the constancy of torque direction. A, The left andcenter plots show 1.5 sec of force (F_x, F_y) and torque (T_x, T_y,T_z) traces recorded at the transducer during the stimulation of MD at a single arm posture. Data from five consecutive trials aligned at stimulation onset are shown. These traces were averaged and combined using Equation 4 (see Materials and Methods) to obtain the traces on the right, representing the components of torque at the shoulder (M_x, M_y,M_z) in an arm-fixed frame of reference. Force units are Newtons (N), and torque units are Newton-meters (N-m). B, A three-dimensional torque trace obtained from AD during the ramp period of stimulation. The SD of the torque direction during this period had to be within the bounds of the 10° cone depicted here to be included in subsequent analyses.

Fig. 3.

SD (in degrees) of the angles defining torque direction for each of the six muscles. Data from all retained data sets are shown.

Fig. 4.

Shoulder torque vectors resulting from the stimulation of AD. Data were obtained from Subject A in one experimental session. Three separate views are shown, obtained by plotting the individual components of shoulder torque (M_x, M_y,M_y) against each other. Each vector is an average of five stimulations at a single arm posture. Data from 28 different arm postures are shown. Torques are defined in an arm-fixed frame of reference; units are Newton-meters (N-m).

Fig. 5.

Normalized shoulder torque vectors forAD, MD, and PD. The data in each plot were obtained from Subject C in one experimental session. Data are plotted in the same format as those in the top two panels of Figure 4.

Fig. 6.

Normalized shoulder torque vectors forLaD, CPec, and SPec. The data in each plot were obtained from Subject C in one experimental session. Date are plotted in the same format as in Figure 5.

Fig. 7.

Dependence of torque direction (ALPHA) on humeral rotation [ROT(ζ)] for each of the six muscles. α is the angle in theM_x/M_yplane relative to the −M_x (ABD)-axis. Negative values of humeral rotation indicate external rotation; positive values indicate internal rotation. Each symbolrepresents a different subject.

Fig. 8.

Dependence of torque direction (BETA) on humeral rotation [ROT (ζ)] for each of the six muscles. β is the angle relative to theM_x/M_yplane. Negative values of humeral rotation indicate external rotation; positive values indicate internal rotation. Each symbolrepresents a different subject.

Fig. 9.

Dependence of torque direction (ALPHA) on humeral rotation [ROT (ζ)] and upper arm azimuth (η) for each of the six muscles. Data are the same as those presented in the top plots of Figures 5and 6 (Subject C). α is the angle in theM_x/M_yplane, relative to the −M_x (ABD)-axis. Negative values of humeral rotation indicate external rotation; positive values indicate internal rotation. The diameters of the individual circles are proportional to values of upper arm azimuth, with the largest circles corresponding to the most lateral elbow locations.

Fig. 10.

Dependence of torque direction (ALPHA and BETA) on the angles defining arm posture (ROT (ζ), AZ (η),EL (θ)) for the body-fixed frame of reference. Data from the AD of Subject C are shown; these are the same data that appear (in the arm-fixed frame of reference) in the extreme left plots of Figure 5. For the scatterplots, α is the angle in the M_x′/M_y′plane, relative to the -M_x′(ABD)-axis, and β is the angle relative to theM_x′/M_y′ plane. Negative values of humeral rotation indicate external rotation; positive values indicate internal rotation.

Fig. 11.

Predicted torque direction vectors for anterior deltoid (AD, top) and the sternocostal head of pectoralis major (SPec, bottom), viewed in the body-fixed frame of reference. Vectors from 28 different arm postures are shown, representing three values each of upper arm azimuth, elevation, and humeral rotation and one additional posture. For the 27 postures, η ranged from −15 to −75°, θ ranged from 15 to 75°, and ζ ranged from −15 to 75°. Also included in each panel is a vector representing upper arm vertical (the 28th vector). Vectors are colored for upper arm elevation (θ), withyellow vectors representing 0 or 15°,orange representing 45°, and redrepresenting 75°. All vectors originate at the right shoulder of a mannequin, and the mannequins faceforward. The M_x′-axis also points forward, the−M_y′-axis points to the leftof the page (the mannequins’ right), and theM_z′-axis points upward.