Thomas J. Burkholder

HUMAN WRIST MOTORS: BIOMECHANICAL DESIGN AND APPLICATION TO TENDON TRANSFERS

Moment arm, muscle architecture, and tendon compliance in cadaveric human forearms were determined and used to model the wrist torque-joint angle relation (i.e. wrist torque profile). Instantaneous moment arms were calculated by differentiating tendon excursion with respect to joint rotation. Maximum isometric tension of each wrist muscle-tendon unit was predicted based on muscle physiological cross-sectional area. Muscle forces were subsequently adjusted for sarcomere length changes resulting from joint rotation and tendon strain. Torque profiles were then calculated for each prime wrist motor (i.e. muscle-tendon unit operating through the corresponding moment arm). Influences of moment arm, muscle force, and tendon compliance on the torque profile of each motor were quantified. Wrist extensor motor torque varied considerably throughout the range of motion. The contours of the extensor torque profiles were determined primarily by the moment arm-joint angle relations. In contrast, wrist flexor motors produced near-maximal torque over the entire range of motion. Flexor torque profiles were less influenced by moment arm and more dependent on muscle force variations with wrist rotation and with tendon strain. These data indicate that interactions between the joint, muscle, and tendon yield a unique torque profile for each wrist motor. This information has significant implications for biomechanical modeling and surgical tendon transfer.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion.

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

Sarcomere Length changes after flexor carpi ulnaris to extensor digitorum communis tendon transfer

Sarcomere length was measured intraoperatively on five patients undergoing tendon transfer of the flexor carpi ulnaris (FCU) to the extensor digitorum communis (EDC) for radial nerve palsy. The most significant result was that the absolute sarcomere length and sarcomere length operating range of the FCU increased after transfer into the EDC (p < .001). Preoperatively, with the wrist fully extended and fingers flexed, FCU sarcomere length was 4.22 +/- .24 microns and decreased to 3.19 +/- .05 microns as the wrist was fully flexed. This represented an overall sarcomere length range of 1.03 microns. After the tendon transfer using standard recommended techniques, all sarcomere lengths were significantly longer (p < .001). Specifically, sarcomeres were 0.74 +/- .14 microns longer with the muscle in its fully lengthened position (4.96 +/- .43 microns with the wrist and digits flexed) and 0.31 +/- .16 microns longer with the FCU in the fully shortened position (3.50 +/- .06 microns with the wrist and digits extended). At these sarcomere lengths, the FCU muscle was predicted to develop relatively high force only during movement involving synergistic wrist flexion and finger extension. Under the conditions of the procedures performed, the transferred FCU muscle was predicted to produce maximum force over the range of about 30 degrees of wrist flexion and 0 degree of finger flexion to 70 degrees of wrist extension and 90 degrees of finger flexion. While this is acceptable, a more desirable result was predicted to occur if the muscle was transferred at a longer length. In this latter case, greater stretch of the FCU during transfer (increasing sarcomere length to about 5 microns) was predicted to improve the transfer. The more highly stretched FCU was predicted to result in maximum force as the wrist and fingers progressed from about 60 degrees of wrist extension and 0 degree of finger flexion to 80 degrees of wrist extension and 70 degrees of finger flexion. These results quantify the relationship between the passive tension chosen for transfer, sarcomere length, and the estimated active tension that can be generated by the muscle. The results also demonstrate the feasibility of using intraoperative laser diffraction during tendon transfer as a guide for optimal placement of the transferred muscle.

Uniaxial strain system to investigate strain rate regulation in vitro

Cells are able to sense and respond to mechanical strain both in vivo and in vitro, and though the ability of strain to stimulate intracellular biochemical events is well established, the influence of the rate at which these strains are applied has not been extensively investigated. In order to study the role of strain as well as strain rate, an in vitro device has been developed and validated for applying cyclic uniaxial strains to cells cultured on a silicone sheet substrate. The stepper motor driven system provides strains up to 50% in increments as small as 12 nm (0.25 μstrain) at strain rates from μstrain/day to 300%/s. Computer control allows all displacement parameters to be easily modified and provides precise control, while the low profile design and planar culture surface allows the cells to be visualized during all phases of cell culture and strain application. Displacement parameters were verified using a linear variable displacement transformer to track linear motion, while strain analysis of...

Evidence that mechanosensors with distinct biomechanical properties allow for specificity in mechanotransduction.

Various cell types can sense and convert mechanical forces into biochemical signaling events through a process called mechanotransduction, and this process is often highly specific to the types of mechanical forces applied. However, the mechanism(s) that allow for specificity in mechanotransduction remain undefined. Thus, the goal of this study was to gain insight into how cells distinguish among specific types of mechanical information. To accomplish this goal, we determined if skeletal myoblasts can distinguish among differences in strain, strain rate, and strain-time integral (STI). Our results demonstrate that mechanically induced signaling through the c-jun N-terminal kinase 2 [JNK2] is elicited via a mechanism that depends on an interaction between the magnitude of strain and strain rate and is independent of STI. In contrast to JNK2, mechanically induced signaling through the ribosomal S6 kinase [p70(389)] is not strain rate sensitive, but instead involves a magnitude of strain and STI dependent mechanisms. Mathematical modeling also indicated that mechanically induced signaling through JNK2 and p70(389) can be isolated to separate viscous and elastic mechanosensory elements, respectively. Based on these results, we propose that skeletal myoblasts contain multiple mechanosensory elements with distinct biomechanical properties and that these distinct biomechanical properties provide a mechanism for specificity in mechanotransduction.

Stepwise regression is an alternative to splines for fitting noisy data

In this study, we compared numerical methods that are used to fit noisy data. Comparisons included polynominal regression, stepwise polynomial regression and quintic spline approximation. The advantages and limitations of each method are discussed in terms of curve fit quality, computational speed and ease, and solution compactness. Overall, the spline approximation and stepwise polynomial regression provide the best fits to the data. Stepwise regression provides the added utility of providing a simple, unconstrained function which can be easily implemented in simulation studies.

Directional constraint of endpoint force emerges from hindlimb anatomy

SUMMARY Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

Limited expression of slow tonic myosin heavy chain in human cranial muscles

Recent reports of slow tonic myosin heavy chain (MHCst) in human masticatory and laryngeal muscles suggest that MHCst may have a wider distribution in humans than previously thought. Because of the novelty of this finding, we sought to confirm the presence of MHCst in human masticatory and laryngeal muscles by reacting tissue from these muscles and controls from extraocular, intrafusal, cardiac, appendicular, and developmental muscle with antibodies (Abs) ALD‐58 and S46, considered highly specific for MHCst. At Ab dilutions producing minimal reaction to muscle fibers positive for MHCI, only extraocular, intrafusal, and fetal tongue tissue reacted with Ab S46 had strong immunoreaction in an appreciable number of muscle fibers. In immunoblots, Ab S46, but not Ab ALD‐58, labeled adult extraocular muscles; no other muscles were labeled with either Ab. We conclude that, in humans, Ab S46 has greater specificity for MHCst than does Ab ALD‐58. We suggest that reports of MHCst in human masticatory and laryngeal muscles reflect false‐positive identification of MHCst due to cross‐reactivity of Ab ALD‐58 with another MHC isoform. Muscle Nerve, 2007

Permeability of C2C12 myotube membranes is influenced by stretch velocity

Mechanical signals are critical to the growth and maintenance of skeletal muscle, but the mechanism by which these signals are transduced by the cell remains unknown. This work examined the hypothesis that stretch conditions influence membrane permeability consistent with a role for membrane permeability in mechanotransduction. C2C12 myotubes were grown in conditions that encourage uniform alignment and subjected to uniform mechanical deformation in the presence of fluorescein labeled dextran to evaluate membrane permeability as a function of stretch amplitude and velocity. Within a physiologically relevant range of conditions, a complex interaction between the two aspects of stretch was observed, with velocity contributing most strongly at large stretch amplitudes. This suggests that membrane viscosity could contribute to mechanotransduction.

Changes in growth-related kinases in head, neck and limb muscles with age.

Sarcopenia coincides with declines in several systemic processes that signal through the MAP kinase and Akt-mTOR-p70S6k cascades typically associated with muscle growth. Effects of aging on these pathways have primarily been examined in limb muscles, which experience substantial activity and neural changes in addition to systemic hormonal and metabolic changes. Head and neck muscles are reported to undergo reduced sarcopenia and disuse with age relative to limb muscles, suggesting muscle activity may contribute to maintaining mass with age. However many head and neck muscles derive from embryonic branchial arches, rather than the somites from which limb muscles originate, suggesting that developmental origin may be important. This study compares the expression and phosphorylation of MAP kinase and mTOR networks in head, neck, tongue, and limb muscles from 8- and 26-month old F344 rats to test the hypothesis that physical activity and developmental origin contribute to preservation of muscle mass with age. Phosphorylation of p38 was exaggerated in aged branchial arch muscles. Phosphorylation of ERK and p70S6k T421/S424 declined with age only in the biceps brachii. Expression of p70S6k declined in all head and neck, tongue and limb muscles although no change in phosphorylation of p70S6k on T389 could be resolved. A systemic change that results in a loss of p70S6k protein expression may reduce the capacity to respond to acute hypertrophic stimuli, while the exaggerated p38 signaling in branchial arch muscles may reflect more active muscle remodeling.