Hydrodynamic calculations on the movements of cilia and flagella. II. Opalina.

Two different theoretical models are used to represent the propulsive mechanisms of Opalina. One model uses the concept of an envelope over all the cilia, while the other considers an array of elongated rods, similar to the model used in part 1. The envelope model shows a correlation between the motion of the cilium tip and the type of metachronism exhibited by the organism but under-predicts the velocities of propulsion. Calculations of the velocity profile, force and bending moment are carried out on the three-dimensional beat of a cilium of Opalina ranarum using the cilia sublayer model. The mean velocity profile is found to be twisted in form: in a clockwise direction at the top of the cilia sublayer relative to the effective stroke. Calculations of the force and rate of working emphasize the approximately equal duration of the effective and recovery strokes. Overall the sublayer model is found to be a more informative and useful approach than the envelope model which is limited to small amplitude motions.     

An active porous medium model for ciliary propulsion

The velocity profile in the cilia sublayer on dense ciliated cell surfaces is calculated by using an active porous medium model. Calculations using the beat patterns observed on Opalina and in cilia lining the airways of the lung predict maximum velocities similar to those observed in nature.     

The differences in sagittal plane whole-body angular momentum during gait between patients with hemiparesis and healthy people

Regulation of whole-body angular momentum (WBAM) is essential for maintaining dynamic balance during gait. Patients with hemiparesis frequently fall toward the anterior direction; however, whether this is due to impaired WBAM control in the sagittal plane during gait remains unknown. The present study aimed to investigate the differences in WBAM in the sagittal plane during gait between patients with hemiparesis and healthy individuals. Thirty-three chronic stroke patients with hemiparesis and twenty-two age- and gender-matched healthy controls walked along a 7-m walkway while gait data were recorded using a motion analysis system and force plates. WBAM and joint moment were calculated in the sagittal plane during each gait cycle. The range of WBAM in the sagittal plane in the second half of the paretic gait cycle was significantly larger than that in the first and second halves of the right gait cycle in the controls (P = 0.015 and P = 0.011). Furthermore, multiple regression analysis revealed the slower walking speed (P < 0.001) and larger knee extension moment on the non-paretic side (P = 0.003) contributed to the larger range of WBAM in the sagittal plane in the second half of the paretic gait cycle. Our findings suggest that dynamic stability in the sagittal plane is impaired in the second half of the paretic gait cycle. In addition, the large knee extension moment on the non-paretic side might play a role in the dynamic instability in the sagittal plane during gait in patients with hemiparesis.     

The forces applied by cilia depend linearly on their frequency due to constant geometry of the effective stroke

Mucus propelling cilia are excitable by many stimulants, and have been shown to increase their beating frequency up to threefold, by physiological extracellular stimulants, such as adenosine-triphosphate, acetylcholine, and others. This is thought to represent the evolutionary adaptation of mucociliary systems to the need of rapid and efficient cleansing the airways of foreign particles. However, the mucus transport velocity depends not only on the beat frequency of the cilia, but on their beat pattern as well, especially in the case of mucus bearing cilia that beat in a complex, three-dimensional fashion. In this study, we directly measured the force applied by live ciliary tissues with an atomic force microscope, and found that it increases linearly with the beating frequency. This implies that the arc swept by the cilia during their effective stroke remains unchanged during frequency increase, thus leading to a linear dependence of transport velocity on the beat frequency. Combining the atomic force microscope measurements with optical measurements, we have indications that the recovery stroke is performed on a less inclined plane, leading to an effective shortening of the overall path traveled by the cilia tip during this nontransporting phase of their beat pattern. This effect is observed to be independent of the type of stimulant (temperature or chemical), chemical (adenosine-triphosphate or acetylcholine), or concentration (1 μM-100 μM), indicating that this behavior may result from internal details of the cilium mechanical structure.     

Age-related changes in multifinger synergies in accurate moment of force production tasks.

The purpose of this investigation was to document and quantify age-related differences in the coordination of fingers during a task that required production of an accurate time profile of the total moment of force by the four fingers of a hand. We hypothesized that elderly subjects would show a decreased ability to stabilize a time profile of the total moment of force, leading to larger indexes of moment variability compared with young subjects. The subjects followed a trapezoidal template on a computer screen by producing a time profile of the total moment of force while pressing down on force sensors with the four fingers of the right (dominant) hand. To quantify synergies, we used the framework of the uncontrolled manifold hypothesis. The elderly subjects produced larger total force, larger variance of both total force and total moment of force, and larger involvement of fingers that produced moment of force against the required moment direction (antagonist moment). This was particularly prominent during supination efforts. Young subjects showed covariation of commands to fingers across trials that stabilized the moment of total force (moment-stabilizing synergy), while elderly subjects failed to do so. Both subject groups showed similar indexes of covariation of commands to the fingers that stabilized the time profile of the total force. The lack of moment-stabilizing synergies may be causally related to the documented impairment of hand function with age.     

Deformation and flow of membrane into tethers extracted from neuronal growth cones.

Membrane tethers are extracted at constant velocity from neuronal growth cones using a force generated by a laser tweezers trap. A thermodynamic analysis shows that as the tether is extended, energy is stored in the tether as bending and adhesion energies and in the cell body as "nonlocal" bending. It is postulated that energy is dissipated by three viscous mechanisms including membrane flow, slip between the two monolayers that form the bilayer, and slip between membrane and cytoskeleton. The analysis predicts and the experiments show a linear relation between tether force and tether velocity. Calculations based on the analytical results and the experimental measurements of a tether radius of approximately 0.2 micron and a tether force at zero velocity of approximately 8 pN give a bending modulus for the tether of 2.7 x 10(-19) N.m and an extraordinarily small "apparent surface tension" in the growth cone of 0.003 mN/m, where the apparent surface tension is the sum of the far-field, in-plane tension and the energy of adhesion. Treatments with cytochalasin B and D, ethanol, and nocodazole affect the apparent surface tension but not bending. ATP depletion affects neither, whereas large concentrations of DMSO affect both. Under conditions of flow, data are presented to show that the dominant viscous mechanism comes from the slip that occurs when the membrane flows over the cytoskeleton. ATP depletion and the treatment with DMSO cause a dramatic drop in the effective viscosity. If it is postulated that the slip between membrane and cytoskeleton occurs in a film of water, then this water film has a mean thickness of only approximately 10 A.     

A continuous dynamic beam model for swimming fish

When a fish swims in water, muscle contraction, controlled by the nervous system, interacts with the body tissues and the surrounding fluid to yield the observed movement pattern of the body. A continuous dynamic beam model describing the bending moment balance on the body for such an interaction during swimming has been established. In the model a linear visco-elastic assumption is made for the passive behaviour of internal tissues, skin and backbone, and the unsteady fluid force acting on the swimming body is calculated by the 3D waving plate theory. The body bending moment distribution due to the various components, in isolation and acting together, is analysed. The analysis is based on the saithe (Pollachius virens), a carangiform swimmer. The fluid reaction needs a bending moment of increasing amplitude towards the tail and near-standing wave behaviour on the rear-half of the body. The inertial movement of the fish results from a wave of bending moment with increasing amplitude along the body and a higher propagation speed than that of body bending. In particular, the fluid reaction, mainly designed for propulsion, can provide a considerable force to balance the local momentum change of the body and thereby reduce the power required from the muscle. The wave of passive visco-elastic bending moment, with an amplitude distribution peaking a little before the mid-point of the fish, travels with a speed close to that of body bending. The calculated muscle bending moment from the whole dynamic system has a wave speed almost the same as that observed for EMG-onset and a starting instant close to that of muscle activation, suggesting a consistent matching between the muscle activation pattern and the dynamic response of the system in steady swimming. A faster wave of muscle activation, with a variable phase relation between the strain and activation cycle, appears to be designed to fit the fluid reaction and, to a lesser extent, the body inertia, and is limited by the passive internal tissues. Higher active stress is required from caudal muscle, as predicted from experimental studies on fish muscle. In general, the active force development by muscle does not coincide with the propulsive force generation on the tail. The stiffer backbone may play a role in transmitting force and deformation to maintain and adjust the movement of the body and tail in water.     

Torsion and Antero-Posterior Bending in the In Vivo Human Tibia Loading Regimes during Walking and Running

Bending, in addition to compression, is recognized to be a common loading pattern in long bones in animals. However, due to the technical difficulty of measuring bone deformation in humans, our current understanding of bone loading patterns in humans is very limited. In the present study, we hypothesized that bending and torsion are important loading regimes in the human tibia. In vivo tibia segment deformation in humans was assessed during walking and running utilizing a novel optical approach. Results suggest that the proximal tibia primarily bends to the posterior (bending angle: 0.15°–1.30°) and medial aspect (bending angle: 0.38°–0.90°) and that it twists externally (torsion angle: 0.67°–1.66°) in relation to the distal tibia during the stance phase of overground walking at a speed between 2.5 and 6.1 km/h. Peak posterior bending and peak torsion occurred during the first and second half of stance phase, respectively. The peak-to-peak antero-posterior (AP) bending angles increased linearly with vertical ground reaction force and speed. Similarly, peak-to-peak torsion angles increased with the vertical free moment in four of the five test subjects and with the speed in three of the test subjects. There was no correlation between peak-to-peak medio-lateral (ML) bending angles and ground reaction force or speed. On the treadmill, peak-to-peak AP bending angles increased with walking and running speed, but peak-to-peak torsion angles and peak-to-peak ML bending angles remained constant during walking. Peak-to-peak AP bending angle during treadmill running was speed-dependent and larger than that observed during walking. In contrast, peak-to-peak tibia torsion angle was smaller during treadmill running than during walking. To conclude, bending and torsion of substantial magnitude were observed in the human tibia during walking and running. A systematic distribution of peak amplitude was found during the first and second parts of the stance phase.     

Scaling of chew cycle duration in primates

The biomechanical determinants of the scaling of chew cycle duration are important components of models of primate feeding systems at all levels, from the neuromechanical to the ecological. Chew cycle durations were estimated in 35 species of primates and analyzed in conjunction with data on morphological variables of the feeding system estimating moment of inertia of the mandible and force production capacity of the chewing muscles. Data on scaling of primate chew cycle duration were compared with the predictions of simple pendulum and forced mass-spring system models of the feeding system. The gravity-driven pendulum model best predicts the observed cycle duration scaling but is rejected as biomechanically unrealistic. The forced mass-spring model predicts larger increases in chew cycle duration with size than observed, but provides reasonable predictions of cycle duration scaling. We hypothesize that intrinsic properties of the muscles predict spring-like behavior of the jaw elevator muscles during opening and fast close phases of the jaw cycle and that modulation of stiffness by the central nervous system leads to spring-like properties during the slow close/power stroke phase. Strepsirrhines show no predictable relationship between chew cycle duration and jaw length. Anthropoids have longer chew cycle durations than nonprimate mammals with similar mandible lengths, possibly due to their enlarged symphyses, which increase the moment of inertia of the mandible. Deviations from general scaling trends suggest that both scaling of the jaw muscles and the inertial properties of the mandible are important in determining the scaling of chew cycle duration in primates.     

TURNING MANEUVERS IN STELLER SEA LIONS (EUMATOPIAS JUBATUS)

Steller sea lions are highly maneuverable marine mammals (expressed as minimum turning radius). Video recordings of turns ( n = 195) are analyzed from kinematic measurements for three captive animals. Speed-time plots of 180° turns have a typical "V-shape." The sea lions decelerated during the first half of the turn, reached a minimum speed in the middle of the curved trajectory and reaccelerated by adduction of the pectoral flippers. The initial deceleration was greater than that for passive gliding due to pectoral flipper braking and/or change in body contour from a stiff, straight streamlined form. Centripetal force and thrust were determined from the body acceleration. Most thrust was produced during the power phase of the pectoral flipper stroke cycle. Contrary to previous findings on otariids, little or no thrust was generated during initial abduction of the pectoral flippers and during the final drag-based paddling phase of the stroke cycle. Peak thrust force at the center of gravity occurs halfway through the power phase and the centripetal force is maximal at the beginning of the power stroke. Performance is modulated by changes in the duration and intensity of movements without changing their sequence. Turning radius, maximum velocity, maximum acceleration and turning duration were 0.3 body lengths, 3.5 m/s, 5 m/s², and 1.6 s, respectively. The relative maneuverability based on velocity and length specific minimum turning radius is comparable to other otariids, superior to cetaceans but inferior to many fish.     

Contractile events in the cilia of Paramecium, Opalina, Mytilus, and Phragmatopoma.

The motion of the abnormal cilia of Opalina and Mytilus can be described by the recently developed model for ciliary motion, provided the activation of the contractility during the effective stroke is reduced by three- to fivefold compared with that in the recovery stroke. The stiffness of the Mytilus cilium during the effective stroke is found several hundred times larger than that predicted by the model, however. The stiffness of the cilia of Paramecium, Opalina, Phragmatopoma, and of Mytilus in the recovery phase, is predicted approximately correctly by the model. The activation of contractility in Mytilus and Phragmatopoma cilia increases with the viscosity of the medium, as the velocity of the ciliary motion slows down. This leads to the equivalent of a force-velocity relation. The velocity of propagation of the bend in the cilia during the recovery stroke is shown to be dependent only on the elastic properties of the ciliary shaft, and to be independent of the contractile activiey.     

The Contractile Mechanism in Cilia

A detailed analysis is made of the motion and the forces in the cilium of Sabellaria over the complete cycle. The results indicate that the stiffness of the cilium is directly related to the moments produced by the internal contractile elements. A sliding filament model is developed to generate the complete cycle of motion. The activation of the force-producing elements, the peripheral fibers, occurs over their entire length at once during the effective stroke. In the recovery stroke the sliding of peripheral fibers relative to each other produces activation. The peripheral fibers contribute to the stiffness of the cilium in the sliding filament model only when they are not free to slide because of cross-linkage. The model describes successfully the motion of a variety of types of cilia.     

Peripheral doublet microtubules and wave generation in eukaryotic flagella

The shape and propagation of waves produced by eukaryotic flagella depend on the three-dimensional arrangement and physical-chemical properties of peripheral substructures. The modeling analysis presented here, which assumes force-moment equilibrium and neglects the viscous resistances of the medium, shows how substructural arrangements characteristic of 9+0, 9+1, and 9+2 axonemes can yield their characteristic wave patterns. When flexural stiffnesses are equal along all axonemal radii, any non-uniform doublet shearing pattern propagated distally at constant rate, with successive pairs $\text{1}\text{9}$ cycle out of phase, should generate helical waves. When stiffnesses differ greatly on different radii, but the stiffness pattern is the same for all cross-sections, any such shearing pattern should yield planar waves resembling sine-generated curves.Propagated axonemal bending results from the active bending moment produced by local shearing of doublet pairs. Uniformly twisting the doublets about the axonemal axis cannot directly alter the magnitude of the active bending moment. If dynein cross-bridges are activated by shear displacement between peripheral doublets, then the resulting distribution of the active bending moment will be appropriate for balancing the elastic moment in a propagated bending wave.     

CHROMOSOME VELOCITY DURING MITOSIS AS A FUNCTION OF CHROMOSOME SIZE AND POSITION

Chromosome velocity has been studied in living Melanoplus differentialis spermatocytes by phase contrast cinemicrography. Melanoplus chromosomes (and bivalents) differ in length by as much as 1:3.5. As expected, no size-dependent velocity differences were detected in anaphase, and this is also shown to be true for the less predictable movements during prometaphase congression. The size of the X chromosome can change during observation following x-irradiation, but this is equally without influence on velocity. However, an effect of position on velocity is found in both prometaphase and in anaphase: the chromosomes furthest from the central interpolar axis move 25 per cent faster than more central chromosomes. A simple mechanical model relating frictional resistance and mitotic forces to chromosome velocity is discussed in detail. Calculations from the model suggest that a significant difference in the force acting on a large, as compared with a small chromosome is necessary to account for the observed similarity in velocity. Therefore, it is concluded that the mitotic forces are so organized or regulated that velocity is, within limits, independent of load. The implications of velocity-load independence in relation to the molecular origin of mitotic forces are discussed.     

Functional significance of the mandibular symphysis.

The purpose of this investigation was to relate the morphology of connective tissues in the mandibular symphysis to the behavioral and experimental evidence for mobility and mechanical stress at the symphysis. The anatomy of the symphysis was examined histologically in 6 mammalian orders encompassing 22 species. Behavioral and experimental evidence of stress during the power stroke of the chewing cycle correspond with stresses at the symphysis implied by the location and orientation of symphyseal connective tissues. These stresses are: (1) dorsoventral shear of the symphysis due to the transfer of force from balancing to chewing sides, (2) bending of the symphysis causing tension along the inferior and compression along superior borders due to torsion on the dentaries from the jaw closing muscles, and (3) antero-posterior shear of the symphysis due to an anteriorly directed stress on the chewing side. Interspecific comparisons suggest that leaf eaters can resist greater dorsoventral shear than fruit or insect eaters, but no correlations exist between diet and bending or antero-posterior shear. This suggests that chewing leaves requires larger biting forces.     

Model study on the strain and stress distributions in the vicinity of an arterial stenosis

By the evaluation of the strain and stress distributions in the vicinity of a stenosis, it is suggested that the bending moment generated by the axial force acting on a stenosis is one of the causes of the post-stenotic dilatation. The conditions which enhance this bending moment are investigated and it is expected that the present mechanism is specially effective for the artery where the ratio of wall thickness to radius is very small. Lastly, the concrete numerical value of this bending moment is evaluated and it is shown that the bending moment generated by this mechanism is large enough to cause the post-stenotic dilatation.     

Longer moment arm results in smaller joint moment development, power and work outputs in fast motions

Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.     

Effect of velocity and added resistance on selected coordination and force parameters in front crawl

The effect of (a) increasing velocity and (b) added resistance was examined on the stroke (stroke length, stroke rate [SR]), coordination (index of coordination [IdC], propulsive phases), and force (impulse and peaks) parameters of 7 national-level front crawl swimmers (17.14 ± 2.73 years of swimming; 57.67 ± 1.62 seconds in the 100-m freestyle). The additional resistance was provided by a specially designed parachute. Parachute swimming (PA) and free-swimming (F) conditions were compared at 5 velocities per condition. Video footage was used to calculate the stroke and coordination parameters, and sensors allowed the determination of force parameters. The results showed that (a) an increase in velocity (V) led to increases in SR, IdC, propulsive phase duration, and peak propulsive force (p < 0.05), but no significant change in force impulse per cycle, whatever the condition (PA or F); and (b) in PA conditions, significant increases in the IdC, propulsive phase duration, and force impulse and a decrease in SR were recorded at high velocities (p < 0.05). These results indicated that, in the F condition, swimmers adapted to the change in velocity by modifying stroke and coordination rather than force parameters, whereas the PA condition enhanced the continuity of propulsive action and force development. Added resistance, that is, "parachute training," can be used for specific strength training purposes as long as swimming is performed near maximum velocity.     

Flow-pressure drop measurement and calculation in a tapered femoral artery of a dog

This study describes the in vivo measurement of pressure drop and flow during the cardiac cycle in the femoral artery of a dog, and the computer simulation of the experiment based on the use of the measured flow, vessel dimensions and blood viscosity. In view of the experimental uncertainty in obtaining the accurate velocity profile at the wall region, the velocity pulse at the center was measured and numerical calculations were performed for the center Une instantaneous velocity and within the two limits of spatial distribution of inlet flow conditions: uniform and parabolic. Temporal and spatial variations of flow parameters, i.e., velocity profile, shear rate, non-Newtonian viscosity, wall shear stress, and pressure drop were calculated. There existed both positive and negative shear rates during a pulse cycle, i.e., the arterial wall experiences zero shear three times during a cardiac cycle. For the parabolic inlet condition, the taper of the artery not only increased the magnitude of the positive and negative shear rates, but caused a steep gradient in shear rate, a phenomenon which in turn affects wall shear stress and pressure. In contrast, for the uniform inlet condition, the flow through the tapered artery was predominantly the developing type, which resulted in reduction in magnitude of wall shear rate along the axial direction.     

The bending stiffness of shoes is beneficial to running energetics if it does not disturb the natural MTP joint flexion

A local minimum for running energetics has been reported for a specific bending stiffness, implying that shoe stiffness assists in running propulsion. However, the determinant of the metabolic optimum remains unknown. Highly stiff shoes significantly increase the moment arm of the ground reaction force (GRF) and reduce the leverage effect of joint torque at ground push-off. Inspired by previous findings, we hypothesized that the restriction of the natural metatarsophalangeal (MTP) flexion caused by stiffened shoes and the corresponding joint torque changes may reduce the benefit of shoe bending stiffness to running energetics. We proposed the critical stiffness, k_cr, which is defined as the ratio of the MTP joint (MTPJ) torque to the maximal MTPJ flexion angle, as a possible threshold of the elastic benefit of shoe stiffness. 19 subjects participated in a running test while wearing insoles with five different bending stiffness levels. Joint angles, GRFs, and metabolic costs were measured and analyzed as functions of the shoe stiffness. No significant changes were found in the take-off velocity of the center of mass (CoM), but the horizontal ground push-offs were significantly reduced at different shoe stiffness levels, indicating that complementary changes in the lower-limb joint torques were introduced to maintain steady running. Slight increases in the ankle, knee, and hip joint angular impulses were observed at stiffness levels exceeding the critical stiffness, whereas the angular impulse at the MTPJ was significantly reduced. These results indicate that the shoe bending stiffness is beneficial to running energetics if it does not disturb the natural MTPJ flexion.