A novel method of studying fascicle architecture in relaxed and contracted muscles

A muscle’s architecture, described by geometric variables such as fascicle pennation angles or lengths, plays a crucial role in its functionality. Usually, single parameters are used to estimate force vectors or lengthening rates, thereby assuming that they represent the architecture properly and are constant during contraction. To describe muscle architecture in more detail and compare relaxed and contracted states, we developed and validated a new approach. The m. soleus of the laboratory rat was shock-frozen while relaxed and under isometric contraction, reconstructed three-dimensionally from histological sections, and fascicle lengths, curvatures and pennation angles, as well as the shape of the aponeuroses were analysed. Remarkable differences in volume distribution and the shapes of the aponeuroses as well as locally varying changes in the fascicle architecture were observed. While the mean pennation angle increased by only 2° due to contraction, local changes of up to 4° were observed. Fascicle curvature increased in the distal but remained unchanged in the proximal parts. Our approach may help to identify functional subunits within the muscle, i.e., regions with homogeneous architectural properties. Our results are discussed regarding the input parameters essential for realistic muscle modelling and challenge maximum isometric force estimations that are based on the physiological cross-sectional area or the Hill-model.     

Behavior of human muscle fascicles during shortening and lengthening contractions in vivo.

The aim of the present study was to investigate the behavior of human muscle fascicles during dynamic contractions. Eight subjects performed maximal isometric dorsiflexion contractions at six ankle joint angles and maximal isokinetic concentric and eccentric contractions at five angular velocities. Tibialis anterior muscle architecture was measured in vivo by use of B-mode ultrasonography. During maximal isometric contraction, fascicle length was shorter and pennation angle larger compared with values at rest (P < 0.01). During isokinetic concentric contractions from 0 to 4.36 rad/s, fascicle length measured at a constant ankle joint angle increased curvilinearly from 49.5 to 69.7 mm (41%; P < 0.01), whereas pennation angle decreased curvilinearly from 14.8 to 9.8 degrees (34%; P < 0.01). During eccentric muscle actions, fascicles contracted quasi-isometrically, independent of angular velocity. The behavior of muscle fascicles during shortening contractions was believed to reflect the degree of stretch applied to the series elastic component, which decreases with increasing contraction velocity. The quasi-isometric behavior of fascicles during eccentric muscle actions suggests that the series elastic component acts as a mechanical buffer during active lengthening.     

Determination of fascicle length and pennation in a contracting human muscle in vivo

Fukunaga, Tetsuo, Yoshiho Ichinose, Masamitsu Ito, YasuoKawakami, and Senshi Fukashiro. Determination of fascicle lengthand pennation in a contracting human muscle in vivo.J. Appl. Physiol. 82(1): 354-358, 1997.We have developed a technique to determine fascicle length inhuman vastus lateralis muscle in vivo by using ultrasonography. Whenthe subjects had the knee fully extended passively from a position of110° flexion (relaxed condition), the fascicle length decreasedfrom 133 to 97 mm on average. During static contractions at 10% ofmaximal voluntary contraction strength (tensed condition), fascicleshortening was more pronounced (from 126 to 67 mm), especially when theknee was closer to full extension. Similarly, as the knee was extended, the angle of pennation (fascicle angle, defined as the angle between fascicles and aponeurosis) increased (relaxed, from 14 to 18°; tensed, from 14 to 21°), and a greater increase in the pennation angle was observed in the tensed than in the relaxed condition when theknee was close to extension (<40°). We conclude that there aredifferences in fascicle lengths and pennation angles when the muscle isin a relaxed and isometrically tensed conditions and that thedifferences are affected by joint angles, at least at thesubmaximal contraction level.

     

The effect of leg flexion angle on the mechanomyographic responses to isometric muscle actions

The purpose of this investigation was to examine the effect of leg flexion angle on the relationship between mechanomyographic (MMG) amplitude and isometric torque production. Adult males (n = 9) performed isometric muscle actions of the leg extensors at 25, 50, 75, and 100 percent maximal voluntary contraction (%MVC) on a calibrated CYBEX 6000 dynamometer at 25, 50, and 75° below full extension. A piezoelectric MMG recording device was placed over the mid-portion of the rectus femoris. At 25° of leg flexion, the MMG amplitude increased to 100%MVC. At 50 and 75° of leg flexion, however, MMG amplitude increased to 75%MVC, and then did not change significantly (P > 0.05) between 75 and 100%MVC. These findings indicate that the MMG amplitude-isometric torque relationship is joint angle specific and may be the result of leg flexion angle differences in: (1) muscle stiffness, or (2) motor unit activation strategies. Accepted: 2 March 1998     

Inevitable joint angular rotation affects muscle architecture during isometric contraction

The purpose of this study was to quantify the influence of inevitable ankle joint motion during an isometric contraction on the measured change of the gastrocnemius medialis muscle (GM) architecture in vivo during the loading and the unloading phase. Sitting on a dynamometer subjects performed isometric maximal voluntary contractions as well as contractions induced by electrostimulation. Synchronous joint angular motion, plantarflexion moment, foot’s centre of pressure and real-time ultrasonography of muscle architecture changes of the GM were obtained. During the contraction the ankle joint position altered and significantly affected the change in muscle architecture. At maximal tendon force (1094 ± 323 N), the measured fascicle length overestimated the change in fascicle length due to the tendon force by 1.53 cm, while the measured pennation angle overestimated the change in pennation angle due to the tendon force by 5.5°. At the same tendon force the measured fascicle length and pennation angle were significantly different between loading and unloading conditions. After correcting the values for the change in ankle joint angle no differences between the loading and the unloading phase at the same tendon force were found. Concerning the estimation of GM fascicle length–force and pennation angle–force curves during the loading and unloading phase of an isometric contraction, these findings indicate that not accounting for ankle joint motion will produce unreliable results.     

Effect of hip flexion angle on stiffness of the adductor longus muscle during isometric hip flexion

This study examined the effect of hip flexion angle on the stiffness of the adductor longus (AL) muscle during isometric hip flexion. Seventeen men were recruited. Ten participants performed submaximal voluntary contraction at 0%, 25%, 50%, and 75% of maximal voluntary contraction (MVC) during isometric hip flexion after performing MVC at 0°, 40°, and 80° of hip flexion. Seven participants performed submaximal voluntary tasks during isometric hip extension in addition to hip flexion task. The shear modulus of the AL muscle was used as the index of muscle stiffness, and was measured using ultrasound shear-wave elastography during the tasks at each contraction intensity for each hip flexion angle. During hip flexion, the shear modulus of the AL muscle was higher at 0° than at 40° and 80° of hip flexion at each contraction intensity (p < 0.016). Conversely, a significant effect was not found among hip flexion angle during hip extension at 75% of MVC (p = 0.867). These results suggest that mechanical stress of the AL muscle may be higher at 0° of hip flexion during isometric hip flexion.     

In vivo determination of fascicle curvature in contracting human skeletal muscles.

Fascicle curvature of human medial gastrocnemius muscle (MG) was determined in vivo by ultrasonography during isometric contractions at three (distal, central, and proximal) locations (n = 7) and at three ankle angles (n = 7). The curvature significantly (P < 0.05) increased from rest to maximum voluntary contraction (MVC) (0.4-5.2 m(-1)). In addition, the curvature at MVC became larger in the order dorsiflexed, neutral, plantar flexed (P < 0.05). Thus both contraction levels and muscle length affected the curvature. Intramuscular differences in neither the curvature nor the fascicle length were found. The direction of curving was consistent along the muscle: fascicles were concave in the proximal side. Fascicle length estimated from the pennation angle and muscle thickness, under the assumption that the fascicle was straight, was underestimated by ~6%. In addition, the curvature was significantly correlated to pennation angle and muscle thickness. These findings are particularly important for understanding the mechanical functions of human skeletal muscle in vivo.     

Finite element modeling reveals complex strain mechanics in the aponeuroses of contracting skeletal muscle

A finite element model was used to investigate the counter-intuitive experimental observation that some regions of the aponeuroses of a loaded and contracting muscle may shorten rather than undergo an expected lengthening. The model confirms the experimental findings and suggests that pennation angle plays a significant role in determining whether regions of the aponeuroses stretch or shorten. A smaller pennation angles (25°) was accompanied by aponeurosis lengthening whereas a larger pennation angle (47°) was accompanied by mixed strain effects depending upon location along the length of the aponeurosis. This can be explained by the Poisson effect during muscle contraction and a Mohr’s circle analogy. Constant volume constraint requires that fiber cross sectional dimensions increase when a fiber shortens. The opposing influences of these two strains upon the aponeurosis combine in proportion to the pennation angle. Lower pennation angles emphasize the influence of fiber shortening upon the aponeurosis and thus favor aponeurosis compression, whereas higher pennation angles increase the influence of cross sectional changes and therefore favor aponeurosis stretch. The distance separating the aponeuroses was also found to depend upon pennation angle during simulated contractions. Smaller pennation angles favored increased aponeurosis separation larger pennation angles favored decreased separation. These findings caution that measures of the mechanical properties of aponeuroses in intact muscle may be affected by contributions from adjacent muscle fibers and that the influence of muscle fibers on aponeurosis strain will depend upon the fiber pennation angle.     

Ultrasonographic quantification of architectural response in tibialis anterior to neuromuscular electrical stimulation

While muscle contraction in voluntary efforts has been widely investigated, little is known about contraction during neuromuscular electrical stimulation (NMES). The aim of this study was to quantify in vivo muscle architecture of agonist and antagonist muscles at the ankle joint during NMES. Muscle fascicle lengths and pennation angles of the tibialis anterior (TA) and lateral gastrocnemius muscles were assessed via ultrasonography in 8 healthy young males. Measures were obtained during maximal NMES and torque-matched voluntary dorsiflexion contractions. In the TA, NMES induced a shorter fascicle length (67.2 ± 8.1 mm vs 74.6 ± 11.4 mm; p = 0.04) and a greater pennation angle (11.0 ± 2.4° vs 9.3 ± 2.5°; p = 0.03) compared with voluntary torque-matched dorsiflexion contractions. Architectural responses in the antagonist lateral gastrocnemius muscle did not significantly differ from rest or between voluntary and electrically induced contractions (p > 0.05). Contraction of the antagonist muscle was not a contributing factor to a greater fascicle shortening and increased pennation angle in the TA during NMES. TA architectural response during NMES likely arose from the contribution of muscle synergists during voluntary contractions coupled with a potentially localized contractile activity under the stimulation electrodes during NMES induced contractions.     

Functional and clinical significance of the architecture of human skeletal muscles

The architectural properties of the triceps surae muscle were studied in vivo in groups of healthy subjects (eight men) and patients with locomotor function disorders (four men and four women) with the ankle joint positioned at a plantar flexion 0° and the knee set at 90° (neutral position). In this position, using ultrasonic scanning, longitudinal ultrasonic images of the medial gastrocnemius (MG), lateral gastrocnemius (LG), and soleus (Sol) muscles were obtained when the subject was relaxed (the passive state) or performed isometric plantar flexion (50% of the maximum voluntary contraction (MVC), the active state). The fascicle lengths, fascicle angles, and muscle thickness were determined. In the passive state, the fascicle lengths of the MG, LG, and Sol muscles in the group of healthy subjects were 33, 35, and 30 mm and the pennation angle, 25°, 19°, and 25°; in the group of patients with motor disorders, 38, 39, and 29 mm and 21°, 19°, and 24°, respectively. The MG, LG, and Sol thicknesses in the group of healthy subjects were 15, 13, and 12 mm, and in the group of patients with motor disorders, 14, 12, and 14 mm, respectively. In the active state (50% of the MVC), the MG, LG, and Sol fiber lengths in the group of healthy subjects shortened by 31, 24, and 18%; the fiber pennation angle increased by 60, 41, and 41%, respectively. In the group of patients with motor disorders, the fiber lengths shortened by 28, 14, and 18% and the fiber pennation angle decreased by 28, 26, and 36%, respectively. The MG, LG, and Sol thicknesses in the group of healthy subjects increased by 9, 22, and 18%, while in the group of patients with motor disorders the thickness decreased by 4% in the MG and increased by 11 and 4% in the LG and Sol muscles, respectively. Different fiber lengths and pennation angles and their changes upon contraction might be related to differences in the force-producing capabilities of the muscles and the viscoelastic properties of muscle tendons and aponeuroses.     

Isometric torque–angle relationships of the elbow flexors and extensors in the transverse plane

Maximal voluntary isometric torque–angle relationships of elbow extensors and flexors in the transverse plane (humerus elevation angle of 90°) were measured at two different horizontal adduction angles of the humerus compared to thorax: 20° and 45°. For both elbow flexors and extensors, the torque–angle relationship was insensitive to this 25° horizontal adduction of the humerus. The peak in torque–angle relationship of elbow extensors was found at 55° (0° is full extension). This is closer to full elbow extension than reported by researchers who investigated this relationship in the sagittal plane. Using actual elbow angles during contraction, as we did in this study, instead of angles set by the dynamometer, as others have done, can partly explain this difference.We also measured electromyographic activity of the biceps and triceps muscles with pairs of surface electrodes and found that electromyographic activity level of the agonistic muscles was correlated to measured net torque (elbow flexion torque: Pearson’s r = 0.21 and extension torque: Pearson’s r = 0.53). We conclude that the isometric torque–angle relationship of the elbow extensors found in this study provides a good representation of the force–length relationship and the moment arm–angle relationship of the elbow extensors, but angle dependency of neural input gives an overestimation of the steepness.     

Predictability of in vivo changes in pennation angle of human tibialis anterior muscle from rest to maximum isometric dorsiflexion

The aim of this study was to assess the predictability of in vivo, ultrasound-based changes in human tibialis anterior (TA) pennation angle from rest to maximum isometric dorsiflexion (MVC) using a planimetric model assuming constant thickness between aponeuroses and straight muscle fibres. Sagittal sonographs of TA were taken in six males at ankle angles of -15 degrees (dorsiflexion direction), 0 degrees (neutral position), + 15 (plantarflexion direction) and + 30 degrees both at rest and during dorsiflexor MVC trials performed on an isokinetic dynamometer. At all four ankle angles scans were taken from the TA proximal, central and distal regions. TA architecture did not differ (P > 0.05) neither between its two unipennate parts nor along the scanned regions over its length at a given ankle angle and state of contraction. Comparing MVC with rest at any given ankle angle, pennation angle was larger (62-71%, P < 0.01), fibre length smaller (37-40%, P < 0.01) and muscle thickness unchanged (P > 0.05). The model used estimated accurately (P > 0.05) changes in TA pennation angle occurring in the transition from rest to MVC and therefore its use is encouraged for estimating the isometric TA ankle moment and force generating capacity using musculoskeletal modelling.     

Can pennation angles be predicted from EMGs for the primary ankle plantar and dorsiflexors during isometric contractions?

Ultrasonography was used to measure pennation angle and electromyography (EMG) to record muscle activity of the human tibialis anterior (TA), lateral gastrocnemius (LG), medial gastrocnemius (MG), and soleus (SOL) muscles during graded isometric ankle plantar and dorsiflexion contractions done on a Biodex dynamometer. Data from 8 male and 8 female subjects were collected in increments of approximately 25% of maximum voluntary contraction (MVC) ranging from rest to MVC. A significant positive linear relationship (p<0.05) between normalized EMG and pennation angle for all muscles was observed when subject specific pennation angles at rest and MVC were included in the analysis. These were included to account for gender differences and inter-subject variability in pennation angle. The coefficient of determination, R(2), ranged between 0.76 for the TA and 0.87 for the SOL. The EMG-pennation angle relationships have ramifications for use in EMG-driven models of muscle force. The regression equations can be used to characterize fiber pennation angle more accurately and to determine how it changes with contraction intensity, thus providing improved estimates of muscle force when using musculoskeletal models.     

Architectural specialization of the intrinsic thoracic limb musculature of the American badger (Taxidea taxus)

Evaluation of the relationships between muscle structure and digging function in fossorial species is limited. Badgers and other fossorial specialists are expected to have massive forelimb muscles with long fascicles capable of substantial shortening for high power and applying high out‐force to the substrate. To explore this hypothesis, we quantified muscle architecture in the thoracic limb of the American badger (Taxidea taxus) and estimated the force, power, and joint torque of its intrinsic musculature in relation to the use of scratch‐digging behavior. Architectural properties measured were muscle mass, belly length, fascicle length, pennation angle, and physiological cross‐sectional area. Badgers possess hypertrophied shoulder flexors/humeral retractors, elbow extensors, and digital flexors. The triceps brachii is particularly massive and has long fascicles with little pennation, muscle architecture consistent with substantial shortening capability, and high power. A unique feature of badgers is that, in addition to elbow joint extension, two biarticular heads (long and medial) of the triceps are capable of applying high torques to the shoulder joint to facilitate retraction of the forelimb throughout the power stroke. The massive and complex digital flexors show relatively greater pennation and shorter fascicle lengths than the triceps brachii, as well as compartmentalization of muscle heads to accentuate both force production and range of shortening during flexion of the carpus and digits. Muscles of most functional groups exhibit some degree of specialization for high force production and are important for stabilizing the shoulder, elbow, and carpal joints against high limb forces generated during powerful digging motions. Overall, our findings support the hypothesis and indicate that forelimb muscle architecture is consistent with specializations for scratch‐digging. Quantified muscle properties in the American badger serve as a comparator to evaluate the range of diversity in muscle structure and contractile function that exists in mammals specialized for fossorial habits. J. Morphol. 2013. © 2012 Wiley Periodicals, Inc.     

Motor unit firing patterns of lower leg muscles during isometric plantar flexion with flexed knee joint position

The ankle flexor and extensor muscles are essential for pedal movements associated with car driving. Neuromuscular activation of lower leg muscles is influenced by the posture during a given task, such as the flexed knee joint angle during car driving. This study aimed to investigate the influence of flexion of the knee joint on recruitment threshold-dependent motor unit activity in lower leg muscles during isometric contraction. Twenty healthy participants performed plantar flexor and dorsiflexor isometric ramp contractions at 30 % of the maximal voluntary contraction (MVC) with extended (0°) and flexed (130°) knee joint angles. High-density surface electromyograms were recorded from medial gastrocnemius (MG), soleus (SOL), and tibialis anterior (TA) muscles and decomposed to extract individual motor units. The torque-dependent change (Δpps /Δ%MVC) of the motor unit activity of MG (recruited at 15 %MVC) and SOL (recruited at 5 %MVC) muscles was higher with a flexed compared with an extended knee joint (p < 0.05). The torque-dependent change of TA MU did not different between the knee joint angles. The motor units within certain limited recruitment thresholds recruited to exert plantar flexion torque can be excited to compensate for the loss of MG muscle torque output with a flexed knee joint.     

Changes in fascicle lengths and pennation angles do not contribute to residual force enhancement/depression in voluntary contractions

Force enhancement following muscle stretching and force depression following muscle shortening are well-accepted properties of skeletal muscle contraction. However, the factors contributing to force enhancement/depression remain a matter of debate. In addition to factors on the fiber or sarcomere level, fiber length and angle of pennation affect the force during voluntary isometric contractions in whole muscles. Therefore, we hypothesized that differences in fiber lengths and angles of pennation between force-enhanced/depressed and reference states may contribute to force enhancement/depression during voluntary contractions. The purpose of this study was to test this hypothesis. Twelve subjects participated in this study, and force enhancement/depression was measured in human tibialis anterior. Fiber lengths and angles of pennation were quantified using ultrasound imaging. Neither fiber lengths nor angles of pennation were found to differ between the isometric reference contractions and any of the force-enhanced or force-depressed conditions. Therefore, we rejected our hypothesis and concluded that differences in fiber lengths or angles of pennation do not contribute to the observed force enhancement/depression in human tibialis anterior, and speculate that this result is likely true for other muscles too.     

MMG and EMG responses of the superficial quadriceps femoris muscles.

Eighteen adults performed isometric muscle actions of the leg extensors at 25, 50, 75, and 100% maximal voluntary contraction (%MVC) at leg flexion angles of 25, 50, and 75 degrees. The results indicated that isometric torque production increased as leg flexion angle increased (75 degrees > 50 degrees > 25 degrees). For each muscle tested (rectus femoris, vastus lateralis, and vastus medialis), the EMG amplitude increased up to 100%MVC at each leg flexion angle (25, 50, and 75 degrees). The MMG amplitude for each muscle, however, increased up to 100%MVC at 25 and 50 degrees of leg flexion, but plateaued from 75 to 100%MVC at 75 degrees of leg flexion. We hypothesize that the varied patterns for the MMG amplitude-isometric torque relationships were due to leg flexion angle differences in: (1) muscle stiffness, (2) intramuscular fluid pressure, or (3) motor unit firing frequency.     

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).     

Differences in stretch reflex responses of elbow flexor muscles during shortening, lengthening and isometric contractions

Stretch reflexes were evoked in elbow flexor muscles undergoing three different muscle contractions, i.e. isotonic shortening (SHO) and lengthening (LEN), and isometric (ISO) contractions. The intermuscle relationships for the magnitude of the stretch reflex component in the eletromyographic (EMG) activities of two main elbow flexor muscles, i.e. the biceps brachii (BB) and the brachioradialis (BRD), were compared among the three types of contractions. The subjects were requested to move their forearms sinusoidally (0.1 Hz) against a constant pre-load between elbow joint angles of 10° (0° = full extension) and 80° during SHO and LEN, and to keep an angle of 45° during the ISO. The perturbations were applied at the elbow angle of 45° in pseudo-random order. The EMG signals were rectified and averaged over a period of 100 ms before and 400 ms after the onset of the perturbation 40–50 times. From the ensemble averaged EMG waveform, the background activity (BGA), short (20–50 ms) and long latency (M2, 50–80, M3, 80–100 ms) reflex and voluntary activity (100–150 ms) components were measured. The results showed that both BGA and reflex EMG activity of the two elbow flexor muscles were markedly decreased during the lengthening contraction compared to the SHO and ISO contractions. Furthermore, the changes of reflex EMG components in the BRD muscle were more pronounced than those in the BB muscle, i.e. the ratios of M2 and M3 magnitudes between BRD and BB (BRD:BB) were significantly reduced during the LEN contractions. These results would suggest that the gain of long latency stretch reflex EMG activities in synergistic muscles might be modulated independently according to the model of muscle contraction. Accepted: 1 September 1997     

In vivo fascicle length measurements via B-mode ultrasound imaging with single vs dual transducer arrangements

Ultrasonography is a useful technique to study muscle contractions in vivo, however larger muscles like vastus lateralis may be difficult to visualise with smaller, commonly used transducers. Fascicle length is often estimated using linear trigonometry to extrapolate fascicle length to regions where the fascicle is not visible. However, this approach has not been compared to measurements made with a larger field of view for dynamic muscle contractions. Here we compared two different single-transducer extrapolation methods to measure VL muscle fascicle length to a direct measurement made using two synchronised, in-series transducers. The first method used pennation angle and muscle thickness to extrapolate fascicle length outside the image (extrapolate method). The second method determined fascicle length based on the extrapolated intercept between a fascicle and the aponeurosis (intercept method). Nine participants performed maximal effort, isometric, knee extension contractions on a dynamometer at 10° increments from 50 to 100° of knee flexion. Fascicle length and torque were simultaneously recorded for offline analysis. The dual transducer method showed similar patterns of fascicle length change (overall mean coefficient of multiple correlation was 0.76 and 0.71 compared to extrapolate and intercept methods respectively), but reached different absolute lengths during the contractions. This had the effect of producing force–length curves of the same shape, but each curve was shifted in terms of absolute length. We concluded that dual transducers are beneficial for studies that examine absolute fascicle lengths, whereas either of the single transducer methods may produce similar results for normalised length changes, and repeated measures experimental designs.