Modeling tongue surface contours from Cine-MRI images.

This study demonstrated that a simple mechanical model of global tongue movement in parallel sagittal planes could be used to quantify tongue motion during speech. The goal was to represent simply the differences in 2D tongue surface shapes and positions during speech movements and in subphonemic speech events such as coarticulation and left-to-right asymmetries. The study used tagged Magnetic Resonance Images to capture motion of the tongue during speech. Measurements were made in three sagittal planes (left, midline, right) during movement from consonants (/k/, /s/) to vowels (/i/, /a/, /u/). MR image-sequences were collected during the C-to-V movement. The image-sequence had seven time-phases (frames), each 56 ms in duration. A global model was used to represent the surface motion. The motions were decomposed into translation, rotation, homogeneous stretch, and in-plane shear. The largest C-to-V shape deformation was from /k/ to /a/. It was composed primarily of vertical compression, horizontal expansion, and downward translation. Coarticulatory effects included a trade-off in which tongue shape accommodation was used to reduce the distance traveled between the C and V. Left-to-right motion asymmetries may have increased rate of motion by reducing the amount of mass to be moved.

Modeling the motion of the internal tongue from tagged cine-MRI images.

A new technique, tagged Cine-Magnetic Resonance Imaging (tMRI), was used to develop a mechanical model that represented local, homogeneous, internal tongue deformation during speech. The goal was to infer muscle activity within the tongue from tissue deformations seen on tMRI. Measurements were made in three sagittal slices (left, middle, right) during production of the syllable /ka/. Each slice was superimposed with a grid of tag lines, and the approximately 40 tag line intersections were tracked at 7 time-phases during the syllable. A local model, similar to a finite element analysis, represented planar stretch and shear between the consonant and vowel at 110 probed locations within the tongue. Principal strains were calculated at these locations and revealed internal compression and extension patterns from which inferences could be drawn about the activities of the Verticalis, Hyoglossus, and Superior Longitudinal muscles, among others.

Using joint geometry to determine the motion of the cricoarytenoid joint.

Facet surfaces of the cricoarytenoid joints from two cadaver larynges were digitized. The data were used to compute the optimal axis of rotation for each of the joints in the sense that the computed axis minimized the variance of the joint gap over the full range of joint motion. The optimal axis corresponded to a rocking motion of the arytenoid on the corresponding cricoid. This motion was consistent with experimental data from digitized recordings of vocal fold movement. Using the rigid laryngoscopic view, a similarity in vocal process movement, over the range in motion, between the rocking axis and the vertical axis described in the literature was found, resolving the controversy between two conflicting views of motion of the vocal processes.

Muscle coordination of maximum-speed pedaling.

A simulation based on a forward dynamical musculoskeletal model was computed from an optimal control algorithm to understand uni- and bi-articular muscle coordination of maximum-speed startup pedaling. The muscle excitations, pedal reaction forces, and crank and pedal kinematics of the simulation agreed with measurements from subjects. Over the crank cycle, uniarticular hip and knee extensor muscles provide 55% of the propulsive energy, even though 27% of the amount they produce in the downstroke is absorbed in the upstroke. Only 44% of the energy produced by these muscles during downstroke is delivered to the crank directly. The other 56% is delivered to the limb segments, and then transferred to the crank by the ankle plantarflexors. The plantarflexors, especially soleus, also prevent knee hyperextension, by slowing the knee extension being produced during downstroke by the other muscles, including hamstrings. Hamstrings and rectus femoris make smooth pedaling possible by propelling the crank through the stroke transitions. Other simulations showed that pedaling can be performed well by partitioning all the muscles in a leg into two pairs of phase-controlled alternating functional groups, with each group also alternating with its contralateral counterpart. In this scheme, the uniarticular hip/knee extensor muscles (one group) are excited during downstroke, and the uniarticular hip/knee flexor muscles (the alternating group) during upstroke. The ankle dorsiflexor and rectus femoris muscles (one group of the other pair) are excited near the transition from upstroke to downstroke, and the ankle plantarflexors and hamstrings muscles (the alternating group) during the downstroke to upstroke transition. We conclude that these alternating functional muscle groups might represent a centrally generated primitive for not only pedaling but also other locomotor tasks as well.

Simulation of distal tendon transfer of the biceps brachii and the brachialis muscles.

Rupture of the distal tendons of the biceps brachii and the brachialis often consists of a clean avulsion of the end of the tendons from their tuberosities. In most of the reattachment procedures these tendons are reinserted to the same tuberosities. The purpose of this study was to examine the kinetic activity in the upper limb when the insertion locations of the two prime elbow flexors are altered. The right upper limb was modeled as a two-bar linkage moving in the vertical plane of the scapula. Our Hill-type musculo-tendon actuation system was modeled in terms of five muscles moving in three-dimensional space. The prime elbow flexors, i.e. the biceps brachii and the brachialis, were excited maximally, while the other muscles were left passive and were included as such in the analysis. The limb kinetics was studied in four different insertion locations of the biceps brachii and the brachialis. Data on the elbow kinematics, the muscle tensions histories, the muscle length-tension and velocity-tension relationships and the joint constraint forces were produced. The results indicate that when the new insertions of the biceps brachii and the brachialis are located further away from the elbow joint axis, the moments of these muscles about the joint axis increase. However, the shortening velocities of these muscles are increased as well, which results in a reduced tension. In addition, the magnitudes of the compressive force, the tangential forces and the torsional and bending moments are reduced. These results suggest that, whenever surgically possible, reinsertion of ruptured distal tendons of the biceps brachii and the brachialis more distally to the location of their tuberosities should be beneficial.

An optimal control model for maximum-height human jumping.

To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).

Spinal cord circuits: are they mirrors of musculoskeletal mechanics?

Over the past decade, research at three different levels of sensorimotor control has revealed a degree of complexity that challenges traditional hypotheses regarding servocontrol of individual muscles: (a) The connectivity of spinal circuits is much more divergent and convergent than expected. (b) The normal and reflex-induced recruitment of individual muscles and compartments of muscles is more finely controlled than was noted previously. (c) The mechanical interactions among linked skeletal segments and their often multiarticular muscles are neither simple nor intuitively obvious. We have developed a mathematical model of the cat hind limb that permits us to examine the influence of individual muscles on posture and gait. We have used linear quadratic control theory to predict the optimal distribution of feedback from a hypothetical set of proprioceptors, given different assumptions about the behavioral goals of the animal. The changes in these predictions that result from changes in the structure and control objectives of the model may provide insights into the functions actually performed by the various circuits in the spinal cord.

Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion.

Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.

Hindlimb muscular activity, kinetics and kinematics of cats jumping to their maximum achievable heights.

Cats were trained to jump from a force platform to their maximum achievable heights. Vertical ground reaction forces developed by individual hindlimbs showed that the propulsion phase consists of two epochs. During the initial "preparatory phase' the cat can traverse many different paths. Irrespective of the path traversed, however, the cat always attains the same position, velocity and momentum at the end of this phase. Starting from this dynamic state the cat during the subsequent "launching phase' (about 150 ms long) generates significant propulsion as its hindlimbs develop force with identical, stereotypic profiles. Cinematographic data, electromyographic data, and computed torques about the hip, knee and ankle joints indicate that during the jump proximal extensor musculature is activated before distal musculature. During terminal experiments when the hindlimb was set at positions corresponding to those in the jump, isometric torques produced by tetanic stimulation of groups of extensor and flexor muscles were compared with computed torques developed by the same cat during previous jumps. These comparisons suggest that extensor muscles of the hindlimb are fully activated during the maximal vertical jump.