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Muscle volume is a major determinant of joint torque in humans.

Muscle force (MF) is linearly related to physiological cross-sectional area (CSA), which is obtained from muscle volume (MV) divided by fibre length. Taking into account the fact that joint torque (TQ) is determined by MF multiplied by the moment arm, the maximal TQ would be a function of MV. This proposition was tested in the present study by investigating the relationship between MV and TQ for elbow flexor (EF) and extensor (EE) muscles of 26 males. The MVs of EF and EE were determined from a series of muscle CSA by magnetic resonance imaging (MRI), and pennation angle (theta) and FL by ultrasonography (US). Maximal isometric TQ was measured at right angle of elbow joint for EF and EE. There was a highly significant correlation between MV and TQ both for EF and EE (r=0.95 and 0.96 respectively) compared with that between muscle CSA and TQ, suggesting the dependence of TQ on MV. Furthermore, prediction equations for MV (MVULT) from muscle thickness (MT) measured by US was developed with reference to MVMRI by the MRI on 26 subjects, and the equations were applied to estimate MV of healthy university students (CON; 160 males) and sports athletes (ATH; 99 males). There were significant linear relationships between MVULT and TQ both for EF (r=0.783) and EE (r=0.695) for all subjects (n=259). The MVULT was significantly higher in ATH (by 32% for EF and 33% for EE, respectively) than in CON. Similarly, significantly greater TQ was observed in ATH (by 35% for EF, 37% for EE, respectively). The theta for EE showed no difference between both groups (17.8 degrees for CON and 17.5 degrees for ATH). On the other hand, the TQ to MV ratio were identical for CON and ATH. The results reveal that the muscle volume of the upper arm is a major determinant of joint torque (TQ), regardless of athletic training.

Adult↗

Knee flexion to extension peak torque ratios and low-back injuries in highly active individuals.

The purpose of this study was to investigate for possible relationships between knee flexion to extension peak torque ratios (F1/Ext(rat)) and low-back injuries in highly active males and females. Forty-eight male (age 25.9 +/- 4.5 years) and 41 female (age 27.3 +/- 2.6 years) competitive rowers, and 20 male (age 26.6 +/- 6.0 years) professional ballet dancers volunteered for the study. Each subject performed a test of lumbar and knee flexor flexibility, isokinetic dynamometry and completed a self-administered questionnaire. Flexibility was assessed by using the sit-and-reach test. Knee flexion to extension peak torques were bilaterally monitored at the angular velocities of 1.04 and 4.19 rad x s(-1). The questionnaire was designed to obtain information regarding the number of days off action (e.g., training, competition, and rehearsals), due to low-back injuries, for the 12-month period prior to testing. Results revealed significant negative correlation coefficients between knee F1/Ext(rat), obtained at 1.04 rad x s(-1), and days off physical activity for oarsmen (r = - 0.69; p < 0.01), oarswomen (r = -0.62; p < 0.01) and male dancers (r = -0.57; p < 0.05). No such correlations were found for either knee F1/ Ext(rat) obtained at the angular velocity of 4.19 rad x s(-1) or between the sit-and-reach test results and low-back injuries. A sub-group of 22 female rowers was re-tested after a 6-8 month period, during which a special hamstring strength training programme was introduced. The main conclusions were: a) the lower the F1/Ext(rat) the greater the degree of low-back injury, b) at least in female rowers, 6-8 months of hamstring strength training can contribute to a reduction of the incidence of low-back injury, and c) isokinetic assessment of quadriceps and hamstrings obtained at lower compared to higher angular velocities is more prognostic of low back injury.

Adult↗

Chaotic attitude oscillations of a satellite filled with a rotating ellipsoidal mass of liquid subject to gravity-gradient torques.

The Hamiltonian equations of a liquid-filled satellite subject to gravity-gradient torques in terms of the generalized Deprit variables are established for applying the Melnikov theory formally. The heteroclinic orbits of the torque-free symmetric liquid-filled satellite are found. A criterion for the heteroclinic transversal intersections at the onset of chaotic attitude is formulated using Melnikov's integral. The results from the Melnikov theory are crosschecked with simulation.

Acceleration↗

The "Tip-Edge" torquing mechanism: a mathematical validation.

The Tip-Edge (TP Orthodontics, LaPorte, Ind) bracket is unique among orthodontic brackets because it can be used in combination with rectangular archwire to torque teeth, not through activation of the archwire itself but through the action of auxiliary springs that are active in the tip plane. The purpose of this report is to describe the way in which a tipping couple generates a secondary torquing couple and the resulting path traced by the root apex and to express those actions mathematically. The magnitude of forces applied by the auxiliary spring to the tooth apex is calculated on the basis of an experiment.

Adolescent↗

The maximum number of torque-generating units in the flagellar motor of Escherichia coli is at least 11.

Torque is generated in the rotary motor at the base of the bacterial flagellum by ion translocating stator units anchored to the peptidoglycan cell wall. Stator units are composed of the proteins MotA and MotB in proton-driven motors, and they are composed of PomA and PomB in sodium-driven motors. Strains of Escherichia coli lacking functional stator proteins produce flagella that do not rotate, and induced expression of the missing proteins leads to restoration of motor rotation in discrete speed increments, a process known as "resurrection." Early work suggested a maximum of eight units. More recent indications that WT motors may contain more than eight units, based on recovery of disrupted motors, are inconclusive. Here we demonstrate conclusively that the maximum number of units in a motor is at least 11. Using back-focal-plane interferometry of 1-mum polystyrene beads attached to flagella, we observed at least 11 distinct speed increments during resurrection with three different combinations of stator proteins in E. coli. The average torques generated by a single unit and a fully induced motor were lower than previous estimates. Speed increments at high numbers of units are smaller than those at low numbers, indicating that not all units in a fully induced motor are equivalent.

Bacterial Proteins↗

Changes in the relationship between joint angle and torque production associated with the repeated bout effect.

A single bout of eccentric exercise induces a protective adaptation against damage from a repeated bout. The aim of this study was to determine whether this repeated bout effect is due to a change in the length-tension relationship. Twelve individuals performed an initial bout of six sets of 10 eccentric quadriceps contractions and then performed a repeated bout 2 weeks later. Eccentric contractions were performed on an isokinetic dynamometer at 1.04 rad x s(-1) with a target intensity of 90% of isometric strength at 70 degrees of knee flexion. Isometric strength and pain were recorded before and after both eccentric bouts and on each of the next 3 days. Isometric strength was tested at 30 degrees, 50 degrees, 70 degrees, 90 degrees and 110 degrees of knee flexion. On the days following the initial bout, there was a significant loss of isometric strength at all knee flexion angles except 110 degrees (bout x angle: P < 0.01). On day 2, strength averaged 86% of baseline for 30-90 degrees and 102% of baseline for 110 degrees. Strength loss and pain after the initial bout was contrasted by minimal changes after the repeated bout (pain: P < 0.001; strength: P < 0.01). The repeated bout effect was associated with a rightward shift in the length-tension curve; before the repeated bout, isometric strength was 6.8% lower at 30 degrees and 13.6% higher at 110 degrees compared with values before the initial bout (bout x angle: P < 0.05). Assuming that torque production at 110 degrees occurs on the descending limb of the length-tension curve, the increase in torque at 110 degrees may be explained by a longitudinal addition of sarcomeres. The addition of sarcomeres would limit sarcomere strain for subsequent eccentric contractions and may explain the repeated bout effect observed here.

Adult↗

Torque Production Using Hand Cranks in a Simulated Gear-Operated Valve Opening Task.

Hand cranks are used in a variety of industries to actuate valves and in other gear-operated applications. In order to evaluate these types of operations and their compatibility with operator strength capabilities, a rotational dynamometer was used to measure torque production capability of operators using a hand crank at different heights and angles (with respect to the coronal plane). The tests were conducted for both clockwise and counterclockwise rotations using the dominant arm of each test participant. A total of 18 tests were completed by each of five male right-handed test participants. A 0° declination angle, counterclockwise operation, and both 40.65 cm and 60.96 cm heights were found to be associated with the greatest torque production capabilities.

gear operation↗

Classification of the intention to generate a shoulder versus elbow torque by means of a time-frequency synthesized spatial patterns BCI algorithm.

In this paper, we attempt to determine a subject's intention of generating torque at the shoulder or elbow, two neighboring joints, using scalp electroencephalogram signals from 163 electrodes for a brain-computer interface (BCI) application. To achieve this goal, we have applied a time-frequency synthesized spatial patterns (TFSP) BCI algorithm with a presorting procedure. Using this method, we were able to achieve an average recognition rate of 89% in four healthy subjects, which is comparable to the highest rates reported in the literature but now for tasks with much closer spatial representations on the motor cortex. This result demonstrates, for the first time, that the TFSP BCI method can be applied to separate intentions between generating static shoulder versus elbow torque. Furthermore, in this study, the potential application of this BCI algorithm for brain-injured patients was tested in one chronic hemiparetic stroke subject. A recognition rate of 76% was obtained, suggesting that this BCI method can provide a potential control signal for neural prostheses or other movement coordination improving devices for patients following brain injury.

Adult↗

Anterior tooth morphology and its effect on torque.

This study was undertaken to determine the variation in crown-root angle (CRA) of the upper incisors and canines as well as the variation in their labial contour. In addition, the influence of the variability of the labial contour and of different bracket heights on torque was evaluated. Proximal radiographs were taken of 160 extracted maxillary teeth (81 incisors and 79 canines). They were digitized and analysed with Jasc Paint Shop Pro 7TM and Mathcad 2001 Professional. The incisal edge, the centre of the cemento-enamel junction (CEJ), and the root apex were digitized to define the crown and root long axis. For all teeth the CRA was measured. At several heights of the labial surface a tangent was determined, enabling measurement of the inclination of the labial surface. The CRA had great variability, ranging from 167 to 195 degrees for the canines (mean value 183 degrees) and from 171 to 195 degrees for the incisors (average 184 degrees). The mean inclinations of the labial surfaces for the incisors varied greatly. Between 4 and 4.5 mm from the incisal edge the standard deviations (SD) were the smallest and between 2 and 4.5 mm from the incisal edge the labial surface angle differed by approximately 10 degrees. For the canines the mean inclinations of the buccal surface also varied. This angle differed by around 10 degrees between 2 and 4.5 mm from the incisal edge, but the SD were much larger than for the incisors. It can be concluded that placement of a bracket on a tooth at varying heights, still within a clinically acceptable range, results in important differences in the amount of root torque.

Cuspid↗

Voltage-generated torque drives the motor of the ATP synthase.

The mechanism by which ion-flux through the membrane-bound motor module (F0) induces rotational torque, driving the rotation of the gamma subunit, was probed with a Na+-translocating hybrid ATP synthase. The ATP-dependent occlusion of 1 (22)Na+ per ATP synthase persisted after modification of the c subunit ring with dicyclohexylcarbodiimide (DCCD), when 22Na+ was added first and ATP second, but not if the order of addition was reversed. These results support the model of ATP-driven rotation of the c subunit oligomer (rotor) versus subunit a (stator) that stops when either a 22Na+-loaded or a DCCD-modified rotor subunit reaches the Na+-impermeable stator. The ATP synthase with a Na+-permeable stator catalyzed 22Na+out/Na+in-exchange after reconstitution into proteoliposomes, which was not significantly affected by DCCD modification of the c subunit oligomer, but was abolished by the additional presence of ATP or by a membrane potential (DeltaPsi) of 90 mV. We propose that in the idling mode of the motor, Na+ ions are shuttled across the membrane by limited back and forth movements of the rotor against the stator. This motional flexibility is arrested if either ATP or DeltaPsi induces the switch from idling into a directed rotation. The Propionigenium modestum ATP synthase catalyzed ATP formation with DeltaPsi of 60-125 mV but not with DeltapNa+ of 195 mV. These results demonstrate that electric forces are essential for ATP synthesis and lead to a new concept of rotary-torque generation in the ATP synthase motor.

Adenosine Triphosphate↗

Effects of position and speed on joint torques and knee shear after ACL injury.

PURPOSE: The purpose of this study was to assess the effect of joint position and movement speed on hip (HT) and knee (KT) extensor torque, HT/KT ratio (HKR), and anterior tibial shear (S) in presurgical-ACL deficient (PRE; N = 15), post-ACL reconstructed (POST; N = 15), and uninjured controls (CON; N = 15). METHODS: Measurements were recorded on a semirecumbent variable resistance, closed-chain dynamometer. Tests were conducted at 1 and 1.5 Hz and maximum speed at 33% and 50% 1RM. HT, KT, and S were recorded during the extension phase of the cycle (85 degrees -25 degrees of knee flexion). RESULTS: KT was greatest when the knee was more flexed, whereas HT dominated when it was more extended. This suggests that the hamstrings, as a component of the hip extensors, may generate considerable propulsive force during knee extension, which may help counter anterior tibial shear. S increased whereas KT decreased, suggesting that the quadriceps continue to generate shear force despite the decreasing mechanical advantage producing KT. Increasing knee extension speed significantly decreased S in the POST and CON groups. The correlations between KT and S changed from significantly negative to significantly positive as the knee extended from 85 degrees to 25 degrees in the POST and CON groups. This may be related to the orientation of the patellar tendon, relative to the tibial longitudinal axis that shifts from a posterior to anterior direction, as the knee extends. CONCLUSIONS: Joint position and movement speeds affect the magnitude of hip and knee torques and anterior tibial shear. Reducing the magnitude of S during heavy loads may be a normal phenomenon, and POST surgical subjects may retain or regain this function by 1 yr after surgery.

Adult↗

Direct measurement of torque in an optical trap and its application to double-strand DNA.

We present a method that offers the possibility to directly apply and measure torque on particles in an optical trap. It can be used to rotationally manipulate biopolymers attached to appropriate particles. A flat object is trapped and oriented in the focus of a linearly polarized laser light. The direction and power of the orientational trap are controlled by the polarization state of the light. As a demonstration of the capabilities of the method, we examined the torsional stiffness of dsDNA (lambda-DNA) in its linear torsional regime by directly measuring the torque generated by the molecule.

DNA↗

The relationship between electrical stimulus and joint torque: a dynamic model.

The knowledge of the behavior of electrically activated muscles is an important requisite for the development of functional electrical stimulation (FES) systems to restore mobility to persons with paralysis. The aim of this work was to develop a model capable of relating electrical parameters to dynamic joint torque for FES applications. The knee extensor muscles, stimulated using surface electrodes, were used for the experimental preparation. Both healthy subjects and people with paraplegia were tested. The dynamics of the lower limb were represented by a nonlinear second order model, which took account of the gravitational and inertial characteristics of the anatomical segments as well as the damping and stiffness properties of the knee joint. The viscous-elastic parameters of the system were identified experimentally through free pendular movements of the leg. Leg movements induced by quadriceps stimulation were acquired too, using a motion analysis system. Results showed that, for the considered experimental conditions, a simple one-pole transfer function is able to model the relationship between stimulus pulsewidth (PW) and active muscle torque. The time constant of the pole was found to depend on the stimulus pattern (ramp or step) while gain was directly dependent on stimulation frequency.

Bias↗

Noninvasive measurement of torque development in the rat foot: measurement setup and results from stimulation of the sciatic nerve with polyimide-based cuff electrodes.

In neural rehabilitation, selective activation of muscles after electrical stimulation is mandatory for control of paralyzed limbs. For an evaluation of electrode selectivity, a setup to noninvasively measure the force development after electrical stimulation in the rat foot was developed. The setup was designed in accordance to the anatomical features of the rat model to test the isometric torque development at given ankle positions in an intact leg. In this paper, the setup design and development is presented and discussed. In a first study, the selectivity of small nerve cuffs with 12 electrodes implanted around the rat sciatic nerve was investigated. Special attention was drawn to the performance of the torque measurement setup in comparison to electrophysiological data obtained from compound muscle action potential recordings. Using one cuff around the nerve, electrical stimulation on different electrode tripoles led to plantarflexion and dorsiflexion of the foot without an a priori alignment of the cuff.

Animals↗

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators.

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.

Algorithms↗

Effects of body size, body density, gender and growth on underwater torque.

Two forces act on a human body motionless in water: weight (W) and buoyancy (B). They are applied to the center of mass (CM) and to the center of volume (CV) of the subject, respectively. CM and CV do not coincide; this generates a torque that is a measure of the tendency of the upper part of the body to rise, rotating around its center of mass. To quantify this tendency, Pendergast & Craig defined 'underwater torque' (T') as the product of the net force with which the feet of a subject lying horizontally in water tend to sink, times the distance between the feet and the center of volume of the lungs. In this paper we have investigated: (a) the relationships between T' and body weight (BW), height (H), body surface area (BS), body density (BD) and leg density (LD) in a group of 30 subjects (group A, 14 females and 16 males, age range 16-50 years); and (b) the effect of gender and growth on T' in a group of 110 subjects (group B, 67 girls and 43 boys, age range 12-17 years). In group A, T' was found to be linearly related with BW (r=0.833, P<0.001), H (r=0.803, P<0.001), BS (r=0.866, P<0.001), BD (r=0.617, P<0.001) and LD (r=0.549, P<0.005). A multiple linear regression analysis showed that BS and BD explained about 85% of the variability of T' (r2=0.85). In group B, T' was found to increase linearly with age (r=0.47, P<0.01), the increasing rate being three times higher in boys compared with girls. As a consequence, the T' ratio between boys and girls increased with age, from 1.69 at 13 years to 2.04 at 16 years.

Adolescent↗

Bone tissue responses to surface-modified zirconia implants: A histomorphometric and removal torque study in the rabbit.

BACKGROUND: Zirconia ceramics are biocompatible and have mechanical properties that make them suitable as materials for dental implants. Little is known about how surface modification influences the stability and bone tissue response to zirconia implants. PURPOSE: The objective of the investigation was to histologically and biomechanically evaluate the bone tissue response to zirconia implants with two different surface modifications in comparison with machined, nonmodified zirconia implants and oxidized titanium implants. MATERIALS AND METHODS: Threaded zirconia implants with a diameter of 3.75 mm with either a machined surface (Zr-Ctr) or one of two surface modifications (Zr-A and Zr-B) were manufactured. Oxidized titanium (Ti-Ox) implants 3.75 mm in diameter were also used. The implants were characterized with regard to surface topography using an interferometer. Twelve rabbits received 96 implants using a rotational scheme, two in each tibia and two in each femur. The implants in six rabbits were subjected to removal torque (RTQ) tests after a healing period of 6 weeks. The implants in the remaining six animals were removed en bloc for light microscopic analysis. Back-scatter scanning electron microscopic (BS-SEM) analyses were used to evaluate the state of the bone-implant interface at the modified zirconia implants after RTQ testing. RESULTS: The Ti-Ox and Zr-A implants showed the highest surface roughness, followed by the Zr-B implants and, finally, the Zr-Ctr implants. The nonmodified ZrO2 implants showed statistically significant lower RTQs than all other implants. No significant differences in bone-implant contact or bone area filling the threads were observed. BS-SEM showed intact surface layers of the surface-modified implants after RTQ testing and revealed fracture of the interface bone rather than a separation. CONCLUSION: The present study showed a strong bone tissue response to surface-modified zirconia implants after 6 weeks of healing in rabbit bone. The modified zirconia implants showed a resistance to torque forces similar to that of oxidized implants and a four- to fivefold increase compared with machined zirconia implants. The findings suggest that surface-modified zirconia implants can reach firm stability in bone.

Animals↗

Reflex activation patterns in relation to multidirectional ankle torque in decerebrate cats.

Cutaneous reflexes have been described primarily according to their actions in the flexion/extension plane. It is shown here, by measuring electromyography and isometric force in decerebrate cats, that ankle muscles are activated in relation to their actions in the abduction/adduction plane during sural nerve (SNR) and crossed-extension (XER) reflexes. Ankle adductors (tibialis posterior, extensor digitorum longus, and flexors digitorum and hallucis longus) were active in XER, but not in SNR. Muscles producing ankle abduction (medial and lateral gastrocnemii and peroneus longus and brevis) were consistently more strongly activated in SNR than in XER. This differential pattern of muscle activation results in greater abduction torque at the ankle in SNR than in XER. These data demonstrate reflex organization in relation to the multidirectional torque generated by individual muscles.

Animals↗