Functional torque-velocity and power-velocity characteristics of elite athletes

Technical limitations of some isokinetic dynamometers have called into question the validity of some data on human muscle mechanics. The Biodex dynamometer has been shown to minimize the impact artefact while permitting automatic gravity correction. This dynamometer was used to study quadriceps muscle torque and power generation in elite power (n = 6) and elite endurance (n = 7) athletes over 12 randomly assigned isokinetic velocities from 30 degrees.s-1 to 300 degrees.s-1. The angle at peak torque varied as a negative, linear function of angular velocity, with the average angle across test velocities being 59.5 degrees (SD 10.2 degrees). Power athletes developed greater peak torque at each angular velocity (P less than 0.05) and experienced a 39.7% decrement in torque over the velocity range tested. Endurance athletes encountered a 38.8% decline in peak torque. Torques measured at 60 degrees of knee flexion followed a similar trend in both groups; however the greatest torques were recorded at 60 degrees.s-1 rather than at 30 degrees.s-1. Leg extensor muscle power increased monotonically with angular velocity in both power (r2 = 0.728) and endurance athletes (r2 = 0.839); however these curves diverged significantly so that the power athletes produced progressively more power with each velocity increment. These inter group differences probably reflected a combination of natural selection and training adaptation.     

Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.     

Ageing and isokinetic plantar flexion

Isokinetic torques (Cybex II) of the plantar flexors in 25 healthy men were compared at 5 angular velocities (30, 60, 90, 120 and 180 degrees X s-1). The purposes were to compare plantar flexion torques in young and old subjects, and to determine whether the expected decrease was significantly associated with age, physical activity, or aerobic fitness. Four groups were studied: young (21.7 +/- 2.0 years) and older (63.3 +/- 2.8 years), active and sedentary. Measurements of height, weight, % body fat, VO2max, and daily leisure energy expenditure (questionnaire) were determined for each subject. Statistical measures of analysis of variance were used to determine significant differences among groups; product moment correlation and stepwise regression analysis were used to describe the degree of association between the dependent variable of plantar flexion torque and the independent variables at each velocity. A decline in torque was observed as the isokinetic velocity of angular motion increased. Age alone was a significant determinant of plantar flexion torque, whereas at the slowest speed, when VO2max was used as an explanatory variable, age was not a significant determinant of torque. At 30 degrees X s-1 47% of the variance in torque was explained by VO2max while at 180 degrees X s-1 49% of the variance was explained by age.     

A new dynamometer measuring concentric and eccentric muscle strength in accelerated, decelerated, or isokinetic movements. Validity and reproducibility

A new computerized dynamometer (the SPARK System) is described. The system can measure concentric and eccentric muscle strength (torque) during linear or nonlinear acceleration or deceleration, isokinetic movements up to 400 degrees.s-1, and isometric torque. Studies were performed to assess: I. validity and reproducibility of torque measurements; II. control of lever arm position; III. control of different velocity patterns; IV. control of velocity during subject testing; and, V. intra-individual reproducibility. No significant difference was found between torque values computed by the system and known torque values (p greater than 0.05). No difference was present between programmed and external measurement of the lever arm position. Accelerating, decelerating and isokinetic velocity patterns were highly reproducible, with differences in elapsed time among 10 trials being never greater than 0.001 s. Velocity during concentric and eccentric isokinetic quadriceps contractions at 30 degrees.s-1, 120 degrees.s-1 and 270 degrees.s-1 never varied by more than 3 degrees.s-1 among subjects (N = 21). Over three days of testing, the overall error for concentric and eccentric quadriceps contraction peak torque values for 5 angular velocities between 30 degrees.s-1 and 270 degrees.s-1 ranged from 5.8% to 9.0% and 5.8% to 9.6% respectively (N = 25). The results indicate that the SPARK System provides valid and reproducible torque measurements and strict control of velocity. In addition, the intra-individual error is in accordance with those reported for other similar devices.     

Torque-velocity relationships for the knee extensors in women in their 3rd and 7th decades

Maximal isokinetic knee extensor strength was measured as torque in 17 young (mean age +/- SD, 21 +/- 3 years) and 16 elderly (68 +/- 5 years) women at 30 degrees (0.52 rad) before full extension, at angular velocities from 0 to 5.24 rad s-1, in 7 increments of 0.87 rad s-1. The elderly women were significantly weaker than the young women at all angular velocities. The rate of loss of absolute torque with increasing velocity was similar for both age groups, but when torque was standardised as a percentage of the individual's maximum, the elderly group showed a significantly greater rate of loss than the younger group. Quick-release from an isometric effort did not increase the recorded torques at 4.36 rad s-1 compared with the free-running method in either age group. The age differences are compatible with lower ratio of type II to type I fibre are in the older group.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

Measurements of human strength can be important during analyses of physical activities. Such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity. However, the available strength varies substantially with joint position and velocity. When examining dynamic activities, strength measurements should account for these variations. A model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity. The model is based on well-known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb. Isometric, concentric and eccentric maximum voluntary contractions were collected during hip extension, hip flexion, knee extension, knee flexion, ankle plantar flexion and dorsiflexion. Model parameters are reported for each of these exertion directions by gender and age group. This model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques.     

Eccentric and concentric torque-velocity characteristics of the quadriceps femoris in man

The primary purpose of this investigation was to study the eccentric and concentric torque-velocity characteristics of the quadriceps femoris in man using a recently developed combined isometric, concentric and eccentric controlled velocity dynamometer (the SPARK System). A secondary purpose was to compare the method error associated with maximal voluntary concentric and eccentric torque output over a range of testing velocities. 21 males (21-32 years) performed on two separate days maximal voluntary isometric, concentric and eccentric contractions of the quadriceps femoris at 4 isokinetic lever arm velocities of 0 degree.s-1 (isometric), 30 degrees.s-1, 120 degrees.s-1 and 270 degrees.s-1. Eccentric peak torque and angle-specific torques (measured every 10 degrees from 30 degrees to 70 degrees) did not significantly change from 0 degrees.s-1 to 270 degrees.s-1 (p greater than 0.005) with the exception of angle-specific 40 degrees torque, which significantly increased; p less than 0.05). The mean method error was significantly higher for the eccentric tests (10.6% +/- 1.6%) than for the concentric tests (8.1% +/- 1.7%) (p less than 0.05). The mean method error decreased slightly with increasing concentric velocity (p greater than 0.05), and increased slightly with increasing eccentric velocity (p greater than 0.05). A tension restricting neural mechanism, if active during maximal eccentric contractions, could possibly account for the large difference seen between the present eccentric torque-velocity results and the classic results obtained from isolated animal muscle.     

Isokinetic strength and joint mobility asymmetries in oarside experienced oarsmen

The purpose of the present study was to investigate oarside and nonoarside lower extremity asymmetries in isokinetic strength and joint mobility of port and starboard oarsmen. Peak torques of right and left extensors and flexors were measured on isokinetic dynamometer at angular velocities of 60 and 180°·s-1 in 12 starboard (n = 12; training age 5.55 ± 0.52 years) and 14 port (n = 14; training age 6.09 ± 0.95 years) well-trained male rowers. Mobility of the hip, knee, and ankle joints was measured using the Myrin flexometer, a modification of the Leighton flexometer. The findings indicate that ports had a significantly higher peak torque in oarside right knee extensors at 60°·s-1 (p < 0.001) and 180°·s-1 (p < 0.01) compared to in the nonoarside left knee extensors. In a respective manner, starboards had a higher peak torque in left knee extensors at 60°·s-1 (p < 0.05) and 180°·s-1 (p < 0.05) compared to the right side. Right flexors peak torque was significantly higher in ports compared to that in starboards at 60°·s-1 (p < 0.05) and 180°·s-1 (p < 0.01). No significant difference between port and starboards in left knee flexors at either angular velocity was found. Both port and starboards exhibited a significantly higher hip (p < 0.01) mobility in oarside compared to in nonoarside. We conclude that sweep rowers develop a significantly higher flexion knee peak torque and hip mobility depending on oarside. Strength and mobility abnormalities may provide information for training and rehabilitation. Strengthening and stretching training programs to compensate for potential strength and mobility imbalance and thereby reducing the occurrence of injuries may be designed.     

Modelling the maximum voluntary joint torque/angular velocity relationship in human movement

The force exerted by a muscle is a function of the activation level and the maximum (tetanic) muscle force. In "maximum" voluntary knee extensions muscle activation is lower for eccentric muscle velocities than for concentric velocities. The aim of this study was to model this "differential activation" in order to calculate the maximum voluntary knee extensor torque as a function of knee angular velocity. Torque data were collected on two subjects during maximal eccentric-concentric knee extensions using an isovelocity dynamometer with crank angular velocities ranging from 50 to 450 degrees s(-1). The theoretical tetanic torque/angular velocity relationship was modelled using a four parameter function comprising two rectangular hyperbolas while the activation/angular velocity relationship was modelled using a three parameter function that rose from submaximal activation for eccentric velocities to full activation for high concentric velocities. The product of these two functions gave a seven parameter function which was fitted to the joint torque/angular velocity data, giving unbiased root mean square differences of 1.9% and 3.3% of the maximum torques achieved. Differential activation accounts for the non-hyperbolic behaviour of the torque/angular velocity data for low concentric velocities. The maximum voluntary knee extensor torque that can be exerted may be modelled accurately as the product of functions defining the maximum torque and the maximum voluntary activation level. Failure to include differential activation considerations when modelling maximal movements will lead to errors in the estimation of joint torque in the eccentric phase and low velocity concentric phase.     

Eccentric and concentric torque-velocity relationships during arm flexion and extension Influence of strength level

Forty men were tested with a computerized dynamometer for concentric and eccentric torques during arm flexion and extension at 0.52, 1.57, and 2.09 rad.s-1. Based on the summed concentric and eccentric torque scores, subjects were placed into a high strength (HS) or low strength (LS) group. The eccentric and concentric segments of the torque-velocity curves (TVCs) were generated using peak torque and constant-angle torque (CAT) at 1.57 and 2.36 rad. Angle of peak torque was also recorded. Compared to LS, HS had significantly greater estimated lean body mass (+10.2 kg) and approximately 25% greater average torque output. Reliability of the peak torque scores on 2 days in 20 subjects was r greater than or equal to 0.85. The difference between observed torques and the mathematically computed criterion torque scores averaged 1% for three validation loads that ranged from 11.4 to 90.4 kg. Statistical analysis revealed that torque output in LS plateaued at low concentric velocities and was also flattened with increasing eccentric velocities. Conversely, torque output for HS increased with decreasing concentric velocities and increased with increasing eccentric velocities. The method of plotting the TVCs for peak or CAT did not influence the pattern of TVC. Eccentric flexion peak torque occurred at a significantly shorter muscle length (1.88 rad) than concentric torque (2.12 rad). This difference was also present for extension; it was 1.88 rad for eccentric and 2.03 rad for concentric torque.(ABSTRACT TRUNCATED AT 250 WORDS)     

Use of a Kin-Com dynamometer to study the stretch-shortening cycle during plantar flexion

The aim of this study was to evaluate the Kin-Com II dynamometer in the study of the stretch-shortening cycle (a concentric muscle action preceded by an eccentric muscle action). Measurements were made of plantar flexion at different angular velocities (120 degrees.s-1 and 240 degrees.s-1) with the knee at two different angles (0 degree and 90 degrees). Ten healthy women ranging in age from 22 to 41 years were studied. Torque values were recorded simultaneously with surface electromyograms (EMG): maximal voluntary concentric torque values were recorded and, after a short rest, the torque values of the concentric action which followed immediately after an eccentric action of the same velocity, both with maximal effort. Mean values were taken at different ankle positions and also averaged over different ranges. A concentric action preceded by an eccentric action generated a torque value on an average about 100% larger than a concentric action alone. The EMG activity was lower or unchanged. It was concluded that the present method could be useful in the study of the stretch-shortening cycle in plantar flexion and in the testing of the behaviour of the elastic components in people with disabilities in the lower limbs.     

Isokinetic elbow flexion and coactivation following eccentric training.

The influence of an eccentric training on torque/angular velocity relationships and coactivation level during maximal voluntary isokinetic elbow flexion was examined. Seventeen subjects divided into two groups (Eccentric Group EG, n = 9 Control Group CG, n = 8) performed on an isokinetic dynamometer, before and after training, maximal isokinetic elbow flexions at eight angular velocities (from - 120 degrees s(-1) under eccentric conditions to 240 degrees s(-1) under concentric conditions), and held maximal and submaximal isometric actions. Under all conditions, the myoelectric activities (EMG) of the biceps and the triceps brachii muscles were recorded and quantified as the RMS value. Eccentric training of the EG consisted of 5x6 eccentric muscle actions at 100 and 120% of one maximal repetition (IRM) for 21 sessions and lasted 7 weeks. In the EG after training, torque was significantly increased at all angular velocities tested (ranging from 11.4% at 30 degrees (s-1) to 45.5% at - 120 degrees s(-1)) (p < 0.05). These changes were accompanied by an increase in the RMS activities of the BB muscle under eccentric conditions (from - 120 to - 30 degrees (s-1)) and at the highest concentric angular velocities (180 and 24 degrees s(-1)) (p < 0.05). The RMS activity of the TB muscle was not affected by the angular velocity in either group for all action modes. The influence of eccentric training on the torque gains under eccentric conditions and for the highest velocities was attributed essentially to neural adaptations.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

Comparing different approaches for determining joint torque parameters from isovelocity dynamometer measurements

Strength, or maximum joint torque, is a fundamental factor governing human movement, and is regularly assessed for clinical and rehabilitative purposes as well as for research into human performance. This study aimed to identify the most appropriate protocol for fitting a maximum voluntary torque function to experimental joint torque data. Three participants performed maximum isometric and concentric-eccentric knee extension trials on an isovelocity dynamometer and a separate experimental protocol was used to estimate maximum knee extension angular velocity. A nine parameter maximum voluntary torque function, which included angle, angular velocity and neural inhibition effects, was fitted to the experimental torque data and three aspects of this fitting protocol were investigated. Using an independent experimental estimate of maximum knee extension angular velocity gave lower variability in the high concentric velocity region of the maximum torque function compared to using dynamometer measurements alone. A weighted root mean square difference (RMSD) score function, that forced the majority (73-92%) of experimental data beneath the maximum torque function, was found to best account for the one-sided noise in experimental torques resulting from sub-maximal effort by the participants. The suggested protocol (an appropriately weighted RMSD score function and an independent estimate of maximum knee extension angular velocity) gave a weighted RMSD of between 11 and 13 Nm (4-5% of maximum isometric torque). It is recommended that this protocol be used in generating maximum voluntary joint torque functions in all torque-based modelling of dynamic human movement.     

Isokinetic Identification of Knee Joint Torques before and after Anterior Cruciate Ligament Reconstruction

The aim of this study was to evaluate the serial change of isokinetic muscle strength of the knees before and after anterior cruciate ligament reconstruction (ACLR) in physically active males and to estimate the time of return to full physical fitness. Extension and flexion torques were measured for the injured and healthy limbs at two angular velocities approximately 1.5 months before the surgery and 3, 6, and 12 months after ACLR. Significant differences (p ≤ 0.05) in peak knee extension and flexion torques, hamstring/quadriceps (H/Q) strength ratios, uninvolved/involved limb peak torque ratios, and the normalized work of these muscles between the four stages of rehabilitation were identified. Significant differences between extension peak torques for the injured and healthy limbs were also detected at all stages. The obtained results showed that 12 months of rehabilitation were insufficient for the involved knee joint to recover its strength to the level of strength of the uninvolved knee joint. The results helped to evaluate the progress of the rehabilitation and to implement necessary modifications optimizing the rehabilitation training program. The results of the study may also be used as referential data for physically active males of similar age.     

Effect of hip joint angle on concentric knee extension torque

This study tested the hypothesis that the effect of hip joint angle on concentric knee extension torque depends on knee joint angle during a single knee extension task. Twelve men performed concentric knee extensions in fully extended and 80° flexed hip positions with maximal effort. The angular velocities were set at 30° s⁻¹ and 180° s⁻¹. The peak torque and torques attained at 30°, 50°, 70° and 90° (anatomical position = 0°) of the knee joint were compared between the two hip positions. Muscle activations of the vastus lateralis, medialis, rectus femoris and biceps femoris were determined using surface electromyography. The peak torque was significantly greater in the flexed than in the extended hip position irrespective of angular velocity. The torques at 70° and 90° of the knee joint at both angular velocities and at 50° at 180° s⁻¹ were significantly greater in the flexed than in the extended hip position, whereas corresponding differences were not found at 30° (at either angular velocity) and 50° (at 30° s⁻¹) of the knee joint. No effect of hip position on muscle activation was observed in any muscle. These results supported our hypothesis and may be related to the force–length and force–velocity characteristics of the rectus femoris.     

Reproducibility of isokinetic leg strength and endurance characteristics of adult men and women

Day-to-day variability and single-measurement reliability of selected isokinetic knee extension-flexion strength and endurance indices were assessed in 10 adult men and 8 adult women. On three occasions separated by at least 5 days, the subjects completed 4 reciprocal maximal voluntary contractions (MVC) at different angular velocities (1.05 rad.s-1 and 3.14 rad.s-1). The men also completed a muscular endurance test consisting of 30 reciprocal, MVC at 3.14 rad.s-1. Coefficient of variation, intra-class correlation coefficient and standard error of single-measurement scores support the continued use of gravity corrected peak torque (PT) and average peak torque (APT) as indices of isokinetic leg strength. Similarly, gravity corrected APT and total work should be the recommended indices of isokinetic leg muscular endurance in men. The results suggest that these isokinetic indices must be assessed using multiple day-to-day trial protocols adequately to describe performance capacity. Composite indices such as the ratio of Knee flexion to extension PT and fatigue measurements offer considerably reduced reliability and a greater potential for misinterpretation. The reliability of knee extension indices generally exceeds that of flexion indices. Similar variability and reproducibility of responses were observed between men and women and between reciprocal contractions performed at angular velocities of 1.05 rad.s-1 and 3.14 rad.s-1.     

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).     

Torque-velocity characteristics and muscle fiber type in human vastus lateralis

The relationship between torque-velocity characteristics of the knee extensors during isokinetic contractions and muscle fiber type of the vastus lateralis, determined from two muscle biopsy samples, was investigated in 12 male and 18 female subjects. Peak torque, corrected for the effect of gravity and impact artifact, was classified as corrected peak torque. The torque measured 30 degrees from full extension and, corrected for gravity, was classified as corrected torque at 30 degrees. No significant correlations were found between the percentage of fast-twitch fibers (%FT) or the relative area of FT fibers (%FTA) and corrected peak torque values for any of the velocities tested or the knee angles where corrected peak torques were measured. However, significant inverse relationships were determined for corrected torque at 30 degrees at all but the fastest velocity (270 degrees/s) and both %FT and %FTA for the male subjects. These results reveal that muscle fiber type of the vastus lateralis, based on duplicate muscle samples, is not related to the peak torque actually generated by the knee extensors but may influence the shape of the torque output for maximal contractions sustained over the entire range of motion.     

The function of gastrocnemius as a knee flexor at selected knee and ankle angles.

The gastrocnemius has been viewed as an important contributor at the knee joint as a joint flexor and stabilizer across all the knee and ankle joint angles. The purpose of this study was to investigate the influence of knee and ankle joint angles on the knee flexor function of the gastrocnemius. Seventeen participants were tested on a Biodex dynamometer with the gastrocnemius muscle selectively stimulated at a standardized level of electrical current. The results indicated that both ankle and knee joint angle influence the knee joint flexion moment produced by the gastrocnemius. Further analysis revealed that the flexion moment was greatest with the knee joint straight (180 degrees ) across all ankle joint angles. The greatest reduction in knee flexion moment occurred between 180 and 165 degrees of knee angle. No significant difference was observed in the knee flexion moment between 165 degrees and 115 degrees knee flexion, and little knee flexion moment was observed at knee angles of 90 degrees and 75 degrees. The dramatic reduction of moment between 180 degrees and 165 degrees knee angle is possibly due to the change of moment arm while the little moment production during extreme flexion (90 degrees and 75 degrees ) may be due to the reduction of muscle length.