Mechanics of the anterior drawer test at the ankle: the effects of ligament viscoelasticity

The anterior drawer test at the human ankle joint is a routine clinical examination. The relationship between the mechanical response of this joint and the flexion angle was elucidated by a recent mathematical model, using purely elastic mechanical characteristics for the ligament fibres. The objective of the present work was to assess the effect of ligament viscoelasticity on the force response of the ankle joint for anterior displacements of the foot relative to the tibia, at different ankle flexion positions. A viscoelastic model of the ligaments from the literature was included in the recently proposed mathematical model. Drawer tests were simulated at several flexion angles and for increasing velocities of the imposed anterior displacement. The stiffness of the model ankle joint increased only modestly with velocity. The response force found for a 6mm displacement at 20 degrees plantarflexion increased by only 13% for a one hundred-fold increase in velocity from 0.1 to 10 mm/s. The flexion angle was confirmed as the most influential parameter in the mechanical response of the ankle to anterior drawer test.     

Influence of tool rotation on 3D surface topography at the nanometric scale

The influence of the tool rotation on the 3D surface topography produced by the nano-cutting process is investigated using molecular dynamics simulations. The least square mean method is utilized to model the evaluation criteria for the surface roughness parameters. The effects of the tool rotation on the cutting force and the chip formation at the nano-metric scale are also evaluated. It is found that the chip formation produced with tool rotation is dominated by the ploughing and the shearing forces. With increase of the adopted rotation velocity, the cutting force is sharply increased and the smaller elastic recovery of the machined surface is observed. The 3D surface roughness parameters at the nano-metric scale are significantly influenced by the tool rotation velocity and the feed speed, and the surface quality can be improved by decreasing the tool rotation velocity and the feed speed.     

Orientation of tendons in vivo with active and passive knee muscles

Tendon orientations in knee models are often taken from cadaver studies. The aim of this study was to investigate the effect of muscle activation on tendon orientation in vivo. Magnetic resonance imaging (MRI) images of the knee were made during relaxation and isometric knee extensions and flexions with 0 degrees , 15 degrees and 30 degrees of knee joint flexion. For six tendons, the orientation angles in sagittal and frontal plane were calculated. In the sagittal plane, muscle activation pulled the patellar tendon to a more vertical orientation and the semitendinosus and sartorius tendons to a more posterior orientation. In the frontal plane, the semitendinosus had a less lateral orientation, the biceps femoris a more medial orientation and the patellar tendon less medial orientation in loaded compared to unloaded conditions. The knee joint angle also influenced the tendon orientations. In the sagittal plane, the patellar tendon had a more anterior orientation near full extension and the biceps femoris had an anterior orientation with 0 degrees and 15 degrees flexions and neutral with 30 degrees flexions. Within 0 degrees to 30 degrees of flexion, the biceps femoris cannot produce a posterior shear force and the anterior angle of the patellar tendon is always larger than the hamstring tendons. Therefore, co-contraction of the hamstring and quadriceps is unlikely to reduce anterior shear forces in knee angles up to 30 degrees . Finally, inter-individual variation in tendon angles was large. This suggests that the amount of shear force produced and the potential to counteract shear forces by co-contraction is subject-specific.     

Micropipette suction for measuring piconewton forces of adhesion and tether formation from neutrophil membranes.

A new method for measuring piconewton-scale forces that employs micropipette suction is presented here. Spherical cells or beads are used directly as force transducers, and forces as small as 10-20 pN can be imposed. When the transducer is stationary in the pipette, the force is simply the product of the suction pressure and the cross-sectional area of the pipette minus a small correction for the narrow gap that exists between the transducer and the pipette wall. When the transducer is moving along the pipette, the force on it is corrected by a factor that is proportional to the ratio of its velocity relative to its drag-free velocity. With this technique, the minimum force required to form a membrane tether from neutrophils is determined (45 pN), and the length of the microvilli on the surface of neutrophils is inferred. The strength of this technique is in its simplicity and its ability to measure forces between cells without requiring a separate theory or a calibration against an external standard and without requiring the use of a solid surface.     

In vivo muscular force analysis during the isometric flexion on a monkey's elbow

An experimental method has been developed to analyse muscular forces and torques in vivo during isometric flexion of the elbow in small monkeys (Macaca fascicularis). A mini-transducer was built with a view to measure forces in situ, without cutting tendons. The positions of tendon insertions were measured on anatomical parts, then integrated in a series of calculations aiming of deducing the lever arms of forces to be included in a torque equilibrium relationship. Muscle activity of the three main flexors was measured for five angles of isometric flexion between 70 degrees and 110 degrees, 0 degrees corresponding to the full extended forearm. The analysed signals were selected using physiological and biomechanical criteria. Then, results corresponding to force participation, and torque participations, were worked out; they are presented and discussed in the present paper.     

MD simulation of tool wear behaviour based on changes of tool rake and flank angle caused by diamond tool position adjustment

A new method for adjusting the tool rake and flank angles by changing the position of the tools was used to explore the behaviour of wear using MD simulation. In this paper, a new improved tool was used and found to have lower wear compared to conventional tools. Simulations under the same cutting conditions were carried out using a tool swinging to six different rake angles of six different adjustment angles. Further analysis of the influence of different adjustment angles on the wear behaviour of the tool by cutting force, friction coefficient, temperature, radial distribution function and wear rate was conducted. The highest normal force was observed with the tool swung to ?15°, and the tangential force did not produce any significant changes. The friction coefficients were also not observed as a linear change with the increasing angle of adjustment. At the same time, the particularities and differences at ?15° were illustrated, from the most intuitive tool flank wear images. Finally, the causes of this phenomenon were further explained in terms of temperature and radial distribution function and the correctness of this phenomenon was proved, which is different from previous researches.     

Application and validation of a three-dimensional mathematical model of the human masticatory system in vivo.

A previously described three-dimensional mathematical model of the human masticatory system, predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces, was validated in in vivo experiments. The morphological input parameters to the model for individual subjects were collected using MRI scanning of the jaw system. Experimental measurements included recording of maximum voluntary bite force (magnitude and direction) and surface EMG from the temporalis and masseter muscles. For bite forces with an angle of 0, 10 and 20 degrees relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0.9 and 1.2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity. The average measured and predicted muscle recruitment patterns showed no striking differences. Nevertheless, some systematic differences, dependent on the bite force direction, were found between the predicted and the measured maximum possible bite forces. In a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied. The results suggest that they were caused primarily by an improper determination of the joint force directions.     

Age and contraction type influence motor output variability in rapid discrete tasks.

The purpose of this study was to examine the ability to control knee-extension force during discrete isometric (IC), concentric (CC), and eccentric contractions (EC) in 24 young (mean age +/- SD = 25.3 +/- 2.8 yr) and 24 old (mean age +/- SD = 73.3 +/- 5.5 yr) healthy and active individuals. Subjects were to match a parabola with a time to peak force of 200 ms during IC, CC, and EC at six target levels of force [20, 35, 50, 65, 80, and 90% of the maximum voluntary contraction (MVC)]. ICs were performed at 90 degrees of knee flexion, whereas CCs and ECs ranged from 90 to 80 degrees of knee flexion (0 degrees is full extension) at a slow velocity (25 degrees /s). Results showed that subjects produced similar MVC forces for the three types of contractions. Young subjects produced greater MVC forces than old subjects, and within each age group, men produced greater force than women. The variability (standard deviation) of peak force and impulse in absolute values was greater for young compared with old subjects. When variability was normalized to the force produced [coefficient of variation (CV)], however, old subjects exhibited greater CV than young subjects for peak force and impulse. Both the standard deviation and CV of time to peak force and impulse duration were greater for the old adults. In general, ECs were more variable than ICs and CCs, and old adults exhibited greater CV compared with young adults during rapid, discrete ICs, CCs, and particularly ECs of the quadriceps.     

Improved accuracy and reliability of sweepback angle, pitch angle and hand velocity calculations in swimming.

The estimation of forces in swimming using the quasi-static approach (Schleihauf, In: J. Terauds, J.P. Clarys (Eds.), Swimming III, International Series on Sports Sciences. Vol. 8, University Park Press, Baltimore, 1979, 70-109) has been popular in recent years as propulsion is an important determinant of performance. The aim of this study was to establish the accuracy and reliability of current and newly proposed procedures for the reconstruction of hand velocity, sweepback angle and pitch angle from underwater three-dimensional video analysis. A full-scale mechanical arm capable of simulating a controlled and highly repeatable underwater phase of the front-crawl stroke was filmed for a set of five trials. A seven-point model of the arm and hand was then digitised at 25 Hz. Hand velocity, sweepback angle and pitch angle were calculated using the procedures of Schleihauf (1979), Berger et al. J. Biomech. 28 (1995) 125-133 and a newly proposed procedure (Lauder). Statistical comparisons were made between procedures to establish their relative accuracy and reliability throughout the stroke. The mean absolute error in measurement of hand velocity between points on the hand was very small (+/- 0.04 and +/- 0.06 m s(-1) in the x and z directions, respectively). The mean errors in sweepback angle and pitch angle were, respectively, 9.3 degrees and 7.6 degrees (Berger), 10.1 degrees and 8.1 degrees (Schleihauf and 10.7 degrees and 7.0 degrees (Lauder). Agreement between procedures showed the standard error between Schleihauf and Lauder to be the least (Schleihauf and Lauder, 0.4 degrees; Berger and Schleihauf, 1.3 degrees; Berger and Lauder; 1.6 degrees). The use of four points in the reconstruction of the orientation of the hand (Schleihauf and Lauder procedures) was shown to be less sensitive to errors in the digitising procedure. The reconstruction procedure proposed in this study (Lauder). further reduced the sensitivity to digitising error in the reconstruction of sweepback and pitch angles in swimming.     

Muscular force production after concentric contraction

The steady-state force following active shortening does not reach the maximum isometric force associated with the final length. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this shortening-induced force depression. The muscles were pre-stimulated at fixed length, shortened and then held isometrically to give maximum post-shortening forces, before de-stimulation. The shortening magnitude was 0.18, 0.36 or 0.72mm (about 2-7% of optimal length), time of shortening was chosen as 0.03, 0.06 and 0.12s, and final length as +0.72, 0 and -0.72mm, related to optimal length. The mechanical work during active shortening was evaluated by integrating the product of force and shortening velocity over the shortening period. The results show a positive correlation between the force depression and the mechanical work, whereas the force depression was not correlated to the velocity of shortening. Depression of the passive force component was also observed following all stimulations. Experiments show that the fully stimulated redevelopment of isometric force following concentric contraction follows a time function similar to the creation of force when isometric muscle is initially stimulated. The conclusion is that the isometric force development after active shortening can be well described by an asymptotic force which is decided by the produced work, and the initial isometric time constant.     

Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.     

In vivo estimation of contraction velocity of human vastus lateralis muscle during "isokinetic" action.

To determine the shortening velocities of fascicles of the vastus lateralis muscle (VL) during isokinetic knee extension, six male subjects were requested to extend the knee with maximal effort at angular velocities of 30 and 150 degrees /s. By using an ultrasonic apparatus, longitudinal images of the VL were produced every 30 ms during knee extension, and the fascicle length and angle of pennation were obtained from these images. The shortening fascicle length with extension of the knee (from 98 to 13 degrees of knee angle; full extension = 0 degrees ) was greater (43 mm) at 30 degrees /s than at 150 degrees /s (35 mm). Even when the angular velocity remained constant during the isokinetic range of motion, the fascicle velocity was found to change from 39 to 77 mm/s at 150 degrees /s and from 6 to 19 mm/s at 30 degrees /s. The force exerted by a fascicle changed with the length of the fascicle at changing angular velocities. The peak values of fascicle force and velocity were observed at approximately 90 mm of fascicle length. In conclusion, even if the angular velocity of knee extension is kept constant, the shortening velocity of a fascicle is dependent on the force applied to the muscle-tendon complex, and the phenomenon is considered to be caused mainly by the elongation of the elastic element (tendinous tissue).     

Efficiency as a predictor of human jaw design in the sagittal plane

The effects of changing the direction of the bite force and of the mandibular joint reaction have been studied with a mathematical model assisted by a computer using the technique of linear programming. We conclude the following: In the sagittal plane the long axes of lower molars are each tilted in the direction that most efficiently converts muscle force into work at the bite point rather than in the direction that would maximize static bite force. These genetically determined angles are referred to as the most 'work efficient' angles. Collectively they lead to the appearance of the curve of Spee associated with the postcanines. Given the most work efficient angle of the first molar, the model indicates for bite forces generated in this direction the joint reaction is least when tilted forward from the vertical at between 20 degrees and 30 degrees. The joint reaction is normal to the articular surface of the condyle which is itself tilted forward 20-30 degrees from the occlusal plane. We conclude the condyle and articular eminence are remodelled to the angle that minimizes the joint reaction. The direction of the bite force may be controlled via neuronal circuitry connecting mechanoreceptors of the periodontal ligament with motor nerves supplying the jaw-closing muscles. The height of the occlusal plane in the molar region has little effect on jaw efficiency.     

In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion

Three orthogonal components of the tibiofemoral and patellofemoral forces were measured simultaneously for knees with intact cruciate ligaments (nine knees), following anterior cruciate ligament resection (six knees), and subsequent posterior cruciate ligament resection (six knees). The knees were loaded using an experimental protocol that modeled static double-leg squat. The mean compressive tibial force increased with flexion angle. The mean anteroposterior tibial shear force acted posteriorly on the tibia below 50 deg flexion and anteriorly above 55 deg. Mediolateral shear forces were low compared to the other force components and tended to be directed medially on both the patella and tibia. The mean value of the ratio of the resultant tibial force divided by the quadriceps force decreased with increasing flexion angle and was between 0.6 and 0.7 above 70 deg flexion. The mean value of the ratio of the resultant tibiofemoral contact force divided by the resultant patellofemoral contact force decreased with increasing flexion and was between 0.8 and 1.0 above 55 deg flexion. Cruciate ligament resection resulted in no significant changes in the patellar contact forces. Following resection of the anterior cruciate ligament, the tibial anteroposterior shear force was directed anteriorly over all flexion angles tested. Subsequent resection of the posterior cruciate ligament resulted in an approximately 10 percent increase in the quadriceps tendon and tibial compressive force.     

Phase transition in force during ramp stretches of skeletal muscle.

Active glycerinated rabbit psoas fibers were stretched at constant velocity (0.1-3.0 lengths/s) under sarcomere length control. As observed by previous investigators, force rose in two phases: an initial rapid increase over a small stretch (phase I), and a slower, more modest rise over the remainder of the stretch (phase II). The transition between the two phases occurred at a critical stretch (LC) of 7.7 +/- 0.1 nm/half-sarcomere that is independent of velocity. The force at critical stretch (PC) increased with velocity up to 1 length/s, then was constant at 3.26 +/- 0.06 times isometric force. The decay of the force response to a small step stretch was much faster during stretch than in isometric fibers. The addition of 3 mM vanadate reduced isometric tension to 0.08 +/- 0.01 times control isometric tension (P0), but only reduced PC to 0.82 +/- 0.06 times P0, demonstrating that prepowerstroke states contribute to force rise during stretch. The data can be explained by a model in which actin-attached cross-bridges in a prepowerstroke state are stretched into regions of high force and detach very rapidly when stretched beyond this region. The prepowerstroke state acts as a mechanical rectifier, producing large forces during stretch but small forces during shortening.     

Energetic costs of producing muscle work and force in a cyclical human bouncing task

Muscles expend energy to perform active work during locomotion, but they may also expend significant energy to produce force, for example when tendons perform much of the work passively. The relative contributions of work and force to overall energy expenditure are unknown. We therefore measured the mechanics and energetics of a cyclical bouncing task, designed to control for work and force. We hypothesized that near bouncing resonance, little work would be performed actively by muscle, but the cyclical production of force would cost substantial metabolic energy. Human subjects (n = 9) bounced vertically about the ankles at inversely proportional frequencies (1-4 Hz) and amplitudes (15-4 mm), such that the overall rate of work performed on the body remained approximately constant (0.30 ± 0.06 W/kg), but the forces varied considerably. We used parameter identification to estimate series elasticity of the triceps surae tendon, as well as the work performed actively by muscle and passively by tendon. Net metabolic energy expenditure for bouncing at 1 Hz was 1.15 ± 0.31 W/kg, attributable mainly to active muscle work with an efficiency of 24 ± 3%. But at 3 Hz (near resonance), most of the work was performed passively, so that active muscle work could account for only 40% of the net metabolic rate of 0.76 ± 0.28 W/kg. Near resonance, a cost for cyclical force that increased with both amplitude and frequency of force accounted for at least as much of the total energy expenditure as a cost for work. Series elasticity reduces the need for active work, but energy must still be expended for force production.     

An EMG-assisted model of loads on the lumbar spine during asymmetric trunk extensions

An EMG-assisted, low-back, lifting model is presented which simulates spinal loading as a function of dynamic, asymmetric, lifting exertions. The purpose of this study has been to develop a model which overcomes the limitations of previous models including static or isokinetic mechanics, inaccurate predictions of muscle coactivity, static interpretation of myoelectric activity, and physiologically unrealistic or variable muscle force per unit area. The present model predicts individual muscle forces from processed EMG data, normalized as a function of trunk angle and asymmetry, and modified to account for muscle length and velocity artifacts. The normalized EMGs are combined with muscle cross-sectional area and intrinsic strength capacity as determined on a per subject basis, to represent tensile force amplitudes. Dynamic internal and external force vectors are employed to predict trunk moments, spinal compression, lateral and anterior shear forces. Data from 20 subjects performing a total of 2160 exertions showed good agreement between predicted and measured values under all trunk angle, asymmetry, velocity, and acceleration conditions. The design represents a significant step toward accurate, fully dynamic modeling of the low-back in multiple dimensions. The benefits of such a model are the insights provided into the effects of motion induced, muscle co-activity on spinal loading in multiple dimensions.     

Reduction in range of movement can increase maximum voluntary eccentric forces for the human knee extensor muscles

Using the KinCom 500H isokinetic dynamometer the first part of this study measured the characteristics of the force velocity relationship curve for the human knee extensors between -1.57 (eccentric) and 3.67 (concentric) rads x s(-1) (-90 and 210 degrees s(1)) for both legs in 4 subjects. A significant increase in force generation was seen in eccentric activity at 0.52 rads x s(-1) (30 degrees s(-1)) but not at 1.57 rads x s(-1) (90 degrees s(-1)) compared to maximum voluntary isometric force (P < 0.005). This increase was, however, lower than would be expected from the classical force-velocity relationship. The second part of the study examined whether restricting the range of movement was able to further increase the eccentric forces. In a further 6 subjects, the eccentric contractions were repeated during either an 80 degrees (15-95 degrees flexion) and a 50 degrees (45-95 degrees flexion) range of movement. Significant increases in force were seen over the shorter range of movement at 0.52 rads x s(-1) (30 degrees s(-1)) (P = 0.006) and 1.57 rads x s(-1) (90 degrees s(-1)) (P < 0.001).     

The entrainment of sediments by the turbulent flow of water

This paper attempts to clarify the role of fluid turbulence in the entrainment process of particles from the flat bed of an alluvial channel. A 6 mm diameter sphere, placed in an array of similar particles on the bed of a laboratory flume, was connected to a 3-component force transducer. Dynamic measurements of longitudinal, lift and lateral force components were made with the particle at a number of positions above the bed. Detailed measurements of velocity and turbulence were also made. The velocity and force spectral measurements showed similarities in the longitudinal (streamwise) direction but the lift force component spectra were significantly different.An analytical model of the entrainment process is proposed, in which the impulse required to lift a sediment particle from the channel bed may be calculated. The experimental data has been used to evaluate the constants in the analytical expressions, and a relationship between the forces and turbulence intensity established. The analysis shows that the impulse required to entrain a particle may be expressed as a function of a dimensionless entrainment parameter, the turbulence intensity, and the initial angle of repose of the particle.     

In vivo 3-dimensional measurement of the force exerted on a tooth during clenching

We have developed a three-dimensional (3D) force-measuring device for teeth and used it to measure functional forces in vivo. It comprises an inner part forming a metal core (abutment), a 3D piezoelectric force transducer, and an outer part forming a metal crown, all joined together with a steel screw. The force transducer can measure +/- 500 N along the z-axis and +/- 150 N along the x- and y-axes. We evaluated the relationship between output and load and the effects of hysteresis and temperature on the output. The transducer had high linearity (r>0.9999), low hysteresis (1.7% at maximum), and high thermal stability (0.05% per degree) along each axis. The measuring device was mounted on the maxillary left second molar of a healthy male subject; the tooth had been endodontically treated (neurovascular bundle removed) and prepared for metal abutment and a crown. The 3D load calculated from the outputs of the transducer was expressed as a vector of the coordinates based on the Frankfort horizontal (x-y) and sagittal (y-z) planes. The force measured during maximum voluntary clenching was about 170 N; the force vector was directed from the crown to the root medially at an angle of about 10 degrees from the y-z plane and posteriorly at an angle of about 3 degrees from the x-z plane. This transducer will enable measurement of forces applied to different types of prosthetic appliances and has the potential to provide important basic in vivo data for analysis using computer simulation.