General Muscle Torque Generator Model for a Two Degree-of-Freedom Shoulder Joint.

Muscle torque generators (MTGs) have been developed as an alternative to muscle-force models, reducing the muscle-force model complexity to a single torque at the joint. Current MTGs can only be applied to single Degree-of-freedom (DoF) joints, leading to complications in modeling joints with multiple-DoFs such as the shoulder. This study aimed to develop an MTG model that accounts for the coupling between 2-DoF at the shoulder joint: shoulder plane of elevation (horizontal abduction/adduction) and shoulder elevation (flexion/extension). Three different 2-DoF MTG equations were developed to model the coupling between these two movements. Net joint torques at the shoulder were determined for 20 participants (10 females and 10 males) in isometric, isokinetic, and passive tests. Curve and surface polynomial fitting were used to find the best general fit for the experimental data in terms of the different degrees of coupling. The models were validated against experimental isokinetic torque data. It was determined that implicit coupling that used interpolation between single-DoF MTGs resulted in the lowest root-mean-square percent error of 8.5%. The work demonstrated that general MTG models can predict torque results that are dependent on multiple-DoFs of the shoulder.

A novel equation that incorporates the linear and hyperbolic nature of the force-velocity relationship in lower and upper limb exercises.

The purpose of this study is to provide a force-velocity (F-V) equation that combines a linear and a hyperbolic region, and to compare its derived results to those obtained from linear equations. A total of 10 cross-training athletes and 14 recreationally resistance-trained young men were assessed in the unilateral leg press (LP) and bilateral bench press (BP) exercises, respectively. F-V data were recorded using a force plate and a linear encoder. Estimated maximum isometric force (F0), maximum muscle power (Pmax), and maximum unloaded velocity (V0) were calculated using a hybrid (linear and hyperbolic) equation and three different linear equations: one derived from the hybrid equation (linearhyb), one applied to data from 0 to 100% of F0 (linear0-100), and one applied to data from 45 to 100% of F0 (linear45-100). The hybrid equation presented the best fit to the recorded data (R2 = 0.996 and 0.998). Compared to the results derived from the hybrid equation in the LP, significant differences were observed in F0 derived from linear0-100; V0 derived from linearhyb, linear0-100 and linear45-100; and Pmax derived from linearhyb and linear45-100 (all p < 0.05). For the BP, compared to the hybrid equation, significant differences were found in F0 derived from linear0-100; and V0 and Pmax derived from linearhyb, linear0-100 and linear45-100 (all p < 0.05). An F-V equation combining a linear and a hyperbolic region showed to fit adequately recorded F-V data from ~ 20 to 100% of F0, and overcame the limitations shown by linear equations while providing relevant results.

Comparisons of Knee Extensor Functional Demand During Gait by Age, Physical Activity Level, and the Impact of Acute Exercise and Walking Speed.

The link between age-related changes in muscle strength and gait is unclear. We tested if knee extensor functional demand differs by age and physical activity status and if functional demand increases with walking speed or after exercise. Gait and knee extensor muscle torque were collected from young adults and highly and less active older adults before and after treadmill walking. Functional demand was the ratio of knee moments during gait to knee extensor muscle torques estimated from participant-specific torque-velocity curves. Functional demand at the peak knee flexion moment was greater in less active older adults than young adults (29.3% [14.3%] vs 24.6% [12.1%]) and increased with walking speed (32.0% [13.9%] vs 22.8% [10.4%]). Functional demand at both knee extension moments increased ∼2% to 3% after exercise. The low functional demand found in this study suggests that healthy adults maintain a reserve of knee extensor strength.

Strength and size relationships of the quadriceps and hamstrings with special reference to reciprocal muscle balance.

PURPOSE: This study examined the association of muscle size and strength for the quadriceps and hamstrings, the relationship between the size of these muscles, and whether the H:Q size ratio influenced reciprocal strength balance-widely regarded as a risk factor for hamstrings injury. METHODS: Knee extensor and flexor isometric, concentric and eccentric (50 and 350° s(-1)) strength were measured in 31 healthy, recreationally active young men. Muscle volume was measured with magnetic resonance imaging. RESULTS: The knee flexors achieved higher concentric and eccentric torques (normalised to isometric values) than the extensors. Muscle volume explained a significant part of the inter-individual differences in strength in both extensors (isometric 71%, concentric 30-31%) and flexors (isometric 38%, concentric 50-55%). Notably, muscle size was related to knee flexor eccentric strength (r = 0.69-0.76; R (2) = 48-58%) but not extensor eccentric strength. Quadriceps and hamstrings volumes were moderately correlated (r = 0.64), with the majority of the variance in the size of one muscle (59%) not explained by the size of the other muscle. The hamstrings-to-quadriceps (H:Q) volume ratio was correlated with the isometric (r = 0.45) and functional strength ratios (350° s(-1), r = 0.56; 50° s(-1), r = 0.34). CONCLUSIONS: Muscle size exhibited a differential influence on knee extensor and flexor eccentric strength. Quadriceps and hamstrings muscle size was related, and the H:Q size ratio contributed to their strength ratios. Muscle size imbalances contribute to functional imbalances and these findings support the use of hamstrings strength training with an emphasis on hypertrophic adaptations for reducing injury risk.

Relative differences in strength and power from slow to fast isokinetic velocities may reflect dynapenia.

INTRODUCTION: We compared absolute and normalized values for peak torque (PT), mean power (MP), rate of velocity development, and electromyography (EMG) amplitude during maximal isometric and concentric isokinetic leg extension muscle actions, as well as the %decrease in PT and %increase in MP from 1.05 to 3.14 rad·s(-1) in younger versus older men. METHODS: Measurements were performed twice for reliability. Isokinetic measurements were normalized to the isometric muscle actions. RESULTS: Absolute isometric PT, isokinetic PT and MP, and EMG amplitudes at 1.05 and 3.14 rad·s(-1) were greater in the younger men, although normalizing to isometric PT eliminated the age differences. The older men exhibited greater %decrease in PT (37.2% vs. 31.3%) and lower %increase in MP (87.6% vs. 126.4%) regardless of normalization. CONCLUSIONS: Normalization eliminated absolute differences in isokinetic strength and power, but the relative differences from slow to fast velocities may reflect dynapenia characterized by age-related decreases in fast-twitch fiber function.

Ten-year longitudinal changes in muscle power, force, and velocity in young, middle-aged, and older adults.

BACKGROUND: Maximum muscle power (Pmax ) is a biomarker of physical performance in all ages. No longitudinal studies have assessed the effects of aging on Pmax obtained from the torque-velocity (T-V) relationship, which should be considered the 'gold standard'. This study evaluated the longitudinal changes in the T-V relationship and Pmax of the knee-extensor muscles in young, middle-aged, and older adults after 10 years of follow-up. METHODS: Four hundred eighty-nine subjects (311 men and 178 women; aged 19-68 years) were tested at baseline and after a 10-year follow-up. Anthropometric data, daily protein intake, physical activity level (PAL), and knee-extension muscle function (isometric, isokinetic, and isotonic) were evaluated. A novel hybrid equation combining a linear and a hyperbolic (Hill-type) region was used to obtain the T-V relationship and Pmax of the participants, who were grouped by sex and age (young: 20-40 years; middle-aged: 40-60 years; and old: ≥60 years). Linear mixed-effect models were used to assess effects of time, sex, and age on T-V parameters, Pmax , and body mass index (BMI). Additional analyses were performed to adjust for changes in daily protein intake and PAL. RESULTS: Pmax decreased in young men (-0.6% per year; P < 0.001), middle-aged men and women (-1.1% to -1.4% per year; P < 0.001), and older men and women (-2.2% to -2.4% per year; P ≤ 0.053). These changes were mainly related to decrements in torque at Pmax at early age and to decrements in both torque and velocity at Pmax at older age. BMI increased among young and middle-aged adults (0.2% to 0.5% per year; P < 0.001), which led to greater declines in relative Pmax in those groups. S/T0 , that is, the linear slope of the T-V relationship relative to maximal torque, exhibited a significant decline over time (-0.10%T0 ·rad·s-1 per year; P < 0.001), which was significant among middle-aged men and old men and women (all P < 0.05). Annual changes in PAL index were significantly associated to annual changes in Pmax (P = 0.017), so the overall decline in Pmax was slightly attenuated in the adjusted model (-5.26 vs. -5.05 W per year; both P < 0.001). CONCLUSIONS: Pmax decreased in young, middle-aged, and older adults after a 10-year follow-up. The early declines in Pmax seemed to coincide with declines in force, whereas the progressive decline at later age was associated with declines in both force and velocity. A progressively blunted ability to produce force, especially at moderate to high movement velocities, should be considered a specific hallmark of aging.

Neural and muscular contributions to the age-related loss in power of the knee extensors in men and women.

The mechanisms for the loss in limb muscle power in old (60-79 years) and very old (≥80 years) adults and whether the mechanisms differ between men and women are not well-understood. We compared maximal power of the knee extensor muscles between young, old, and very old men and women and identified the neural and muscular factors contributing to the age-related loss of power. 31 young (22.9±3.0 years, 15 women), 83 old (70.4±4.9 years, 39 women), and 16 very old adults (85.8±4.2 years, 9 women) performed maximal isokinetic contractions at 14 different velocities (30-450°/s) to identify peak power. Voluntary activation (VA) and contractile properties were assessed with transcranial magnetic stimulation to the motor cortex and electrical stimulation of the femoral nerve. The age-related loss in power was ~6.5 W·year-1 for men (R2=0.62, p<0.001), which was a greater rate of decline (p=0.002) than the ~4.2 W·year-1 for women (R2=0.77, p<0.001). Contractile properties were the most closely associated variables with power output for both sexes, such as the rate of torque development of the potentiated twitch (men: R2=0.69, p<0.001; women: R2=0.57, p<0.001). VA was weakly associated with power in women (R2=0.13, p=0.012) but not men (p=0.191), whereas neuromuscular activation (EMG amplitude) during the maximal power contraction was not associated with power in men (p=0.347) or women (p=0.106). These data suggest that the age-related loss in power of the knee extensor muscles is due primarily to factors within the muscle for both sexes, although neural factors may play a minor role in older women.

Comparison of linear, hyperbolic and double-hyperbolic models to assess the force-velocity relationship in multi-joint exercises.

AbstractThis study assessed the validity of linear, hyperbolic and double-hyperbolic models to fit measured force-velocity (F-V) data in multi-joint exercises and the influence of muscle excitation on the F-V relationship. The force-joint angle and F-V relationships were assessed in 10 cross-training athletes and 14 recreationally resistance-trained subjects in the unilateral leg press (LP) and bilateral bench press (BP) exercises, respectively. A force plate and a linear encoder were installed to register external force and velocity, respectively. Muscle excitation was assessed by surface EMG recording of the quadriceps femoris, biceps femoris and gluteus maximus muscles during the unilateral LP. Linear, Hill's (hyperbolic) and Edman's (double-hyperbolic) equations were fitted to the measured F-V data and compared. Measured F-V data were best fitted by double-hyperbolic models in both exercises (p < 0.05). F-V data deviated from the rectangular hyperbola above a breakpoint located at 90% of measured isometric force (F0) and from the linearity at ≤45% of F0 (both p < 0.05). Hyperbolic equations overestimated F0 values by 13 ± 11% and 6 ± 6% in the LP and BP, respectively (p < 0.05). No differences were found between muscle excitation levels below and above the breakpoint (p > 0.05). Large associations between variables obtained from linear and double-hyperbolic models were noted for F0, maximum muscle power, and velocity between 25% and 100% of F0 (r = 0.70-0.99; all p < 0.05). The F-V relationship in multi-joint exercises was double-hyperbolic, which was unrelated with lower muscle excitation levels. However, linear models may be valid to assess F0, maximal muscle power and velocity between 25% and 100% of F0.

On the Shape of the Force-Velocity Relationship in Skeletal Muscles: The Linear, the Hyperbolic, and the Double-Hyperbolic.

The shape of the force-velocity (F-V) relationship has important implications for different aspects of muscle physiology, such as muscle efficiency and fatigue, the understanding of the pathophysiology of several myopathies or the mechanisms of muscle contraction per se, and may be of relevance for other fields, such as the development of robotics and prosthetic applications featuring natural muscle-like properties. However, different opinions regarding the shape of the F-V relationship and the underlying mechanisms exist in the literature. In this review, we summarize relevant evidence on the shape of the F-V relationship obtained over the last century. Studies performed at multiple scales ranging from the sarcomere to the organism level have described the concentric F-V relationship as linear, hyperbolic or double-hyperbolic. While the F-V relationship has most frequently been described as a rectangular hyperbola, a large number of studies have found deviations from the hyperbolic function at both ends of the F-V relation. Indeed, current evidence suggests that the F-V relation in skeletal muscles follows a double-hyperbolic pattern, with a breakpoint located at very high forces/low velocities, which may be a direct consequence of the kinetic properties of myofilament cross-bridge formation. Deviations at low forces/high velocities, by contrast, may be related to a recently discovered, calcium-independent regulatory mechanism of muscle contraction, which may also explain the low metabolic cost of very fast muscle shortening contractions. Controversial results have also been reported regarding the eccentric F-V relationship, with studies in prepared muscle specimens suggesting that maximum eccentric force is substantially greater than isometric force, whereas in vivo studies in humans show only a modest increase, no change, or even a decrease in force in lengthening contractions. This review discusses possible reasons reported in the literature for these discrepant findings, including the testing procedures (familiarization, pre-load condition, and temperature) and a potential neural inhibition at higher lengthening velocities. Finally, some unresolved questions and recommendations for F-V testing in humans are reported at the end of this document.

Shear stress transmission model for the flagellar rotary motor.

Most bacteria that swim are propelled by flagellar filaments, which are driven by a rotary motor powered by proton flux. The mechanism of the flagellar motor is discussed by reforming the model proposed by the present authors in 2005. It is shown that the mean strength of Coulomb field produced by a proton passing the channel is very strong in the Mot assembly so that the Mot assembly can be a shear force generator and induce the flagellar rotation. The model gives clear calculation results in agreement with experimental observations, e g., for the characteristic torque-velocity relationship of the flagellar rotation.

Proposed model for the flagellar rotary motor with shear stress transmission.

Most bacteria that swim are propelled by flagellar filaments, which are driven by a rotary motor powered by proton flux. The motor consists of the rotor and the stator. The stator consists of about 8 MotA-Mot B complex. There seems to be no definite information about the structure between the rotor and the stator, and it is examined whether the experimental data can be explained based upon the following assumptions. (a) There is viscoelastic medium between the rotor and the stator. (b) MotA-MotB complex has an electric dipole moment and produces shear stress in the electric field by a proton in the channel. Calculation results based upon these assumptions are in good agreement with the following experimental observations. (1) One revolution of the flagellar rotation consists of a constant number of steps. (2) The rotation velocity of the rotor is proportional to the trans-membrane potential difference. (3) When the rotational velocity of a flagellum is changed by adjusting the viscosity of the outer fluid, the torque for the cell to rotate a flagellum is practically constant but sharply decreases when the rotational velocity increases over a critical value. (4) The rotation direction remains the same when the sign of the electrochemical potential gradient is reversed. (5) The cell produces constant torque to rotate the flagellum even when the cell is rotated by externally applied torque. (6) A simple switch mechanism is proposed for chemotaxis.