Tongues, tentacles and trunks: the biomechanics of movement in muscular-hydrostats

Muscular-hydrostats, muscular organs which lack typical systems of skeletal support, include the tongues of mammals and lizards, the arms and tentacles of cephalopod molluscs and the trunks of elephants. In this paper the means by which such organs produce elongation, shortening, bending and torsion are discussed. The most important biomechanical feature of muscular-hydrostats is that their volume is constant, so that any decrease in one dimension will cause a compensatory increase in at least one other dimension. Elongation of a muscular-hydrostat is produced by contraction of transverse, circular or radial muscles which decrease the cross-section. Shortening is produced by contraction of longitudinal muscles. The relation between length and width of a constant volume structure allows amplification of muscle force or displacement in muscular-hydrostats and other hydrostatic systems. Bending requires simultaneous contraction of longitudinal and antagonistic circular, transverse or radial muscles. In bending, one muscle mass acts as an effector of movement while the alternate muscle mass provides support for that movement. Torsion is produced by contraction of muscles which wrap the muscular-hydrostat in a helical fashion.     

Computer simulation of bend propagation by axoplasmic microtubules

The generation of bending waves by microtubules in squid nerve axoplasm has been modelled using appropriately modified versions of computer programs developed previously for simulation of flagellar bending waves. The results confirm that a constant longitudinal force directed along the axis of the microtubule is sufficient to cause the generation of regular oscillations and propagated bending waves when the forward gliding movement of the microtubule is obstructed. No control mechanism is required to modulate the active force-generating system. In order to obtain bending waves similar to those observed experimentally, it was necessary to use a model for the force-generating system in which the active force decreases with increasing sliding velocity. If the elastic bending resistance of axoplasmic microtubules is similar to that of microtubules in sperm terminal filaments, the longitudinal force per unit length generated by the axoplasmic microtubules must be of the same order of magnitude as the force generated by dynein arms along the doublet microtubules of eukaryotic flagella.     

On the estimate of the two dominant axes of the knee using an instrumented spatial linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.     

Scaling of form and function in the xenarthran femur: a 100-fold increase in body mass is mitigated by repositioning of the third trochanter

How animals cope with increases in body size is a key issue in biology. Here, we consider scaling of xenarthrans, particularly how femoral form and function varies to accommodate the size range between the 3 kg armadillo and its giant relative the 300 kg glyptodont. It has already been noted that femoral morphology differs between these animals and suggested that this reflects a novel adaptation to size increase in glyptodont. We test this idea by applying a finite element analysis of coronal plane forces to femoral models of these animals, simulating the stance phase in the hind limb; where the femur is subject to bending owing to longitudinal compressive as well as abduction loads on the greater trochanter. We use these models to examine the hypothesis that muscles attaching on the third trochanter (T3) can reduce this bending in the loaded femur and that the T3 forces are more effective at reducing bending in glyptodont where the T3 is situated at the level of the knee. The analysis uses traditional finite element methods to produce strain maps and examine strains at 200 points on the femur. The coordinates of these points before and after loading are also used to carry out geometric morphometric (GM) analyses of the gross deformation of the model in different loading scenarios. The results show that longitudinal compressive and abductor muscle loading increases bending in the coronal plane, and that loads applied to the T3 reduce that bending. In the glyptodont model, the T3 loads are more effective and can more readily compensate for the bending owing to longitudinal and abductor loads. This study also demonstrates the usefulness of GM methods in interpreting the results of finite element analyses.     

Characterization of in vivo strain in the rat tibia during external application of a four-point bending load.

This paper describes a technique for characterizing strains and stresses induced in vivo in the rat tibia during application of an external four-point bending load. An external load was applied through the muscle and soft tissue with a four-point bending device, to induce strain in a 11 mm section of the right tibiae of ten adult female Sprague-Dawley rats. Induced strains were measured in vivo on the lateral surface of the tibia. Inter-rat difference, leg positioning and strain gage placement were evaluated as sources of variability of applied strains. Beam bending theory was used to predict externally induced in vivo strains. Finite element analysis was used to quantify the magnitude of shear stresses induced by this type of loading. There was a linear relationship between applied load and induced in vivo strains. In vivo strains induced by external loading were linearly correlated (R2 = 0.87) with the strains calculated using beam bending theory. The finite element analysis predicted shear stresses at less than 10% of the longitudinal stresses resulting from four-point bending. Strains predicted along the tibia by finite element analysis and beam bending theory were well-correlated. Inter-rat variability due to tibia size and shape difference was the most important source of variation in induced strain (CV = 21.6%). Leg positioning was less important (CV = 9.5%).     

Mechano-sensitive orientation of cortical microtubules during gravitropism in azuki bean epicotyls

The orientation of cortical microtubules (cMT) during gravitropism was studied in epidermal cells of azuki epicotyls. The relative proportion of cells with longitudinal cMT increased in the upper epidermis, and those with transverse cMT increased in the lower epidermis. When epicotyls were kept straight during gravistimulation, no change in cMT orientation occurred in either the upper and lower epidermis. When epicotyls were forced to bend downward, cells with transverse cMT increased in the upper epidermis, and those with longitudinal cMT increased in the lower epidermis. When epicotyls were loaded with naphthylphthalamic acid, an inhibitor of auxin transport, both gravitropic bending and change in cMT orientation were inhibited. However, when a change in cMT orientation was induced by forced downward bending, cells with longitudinal cMT increased in the compressed (lower) side and those with transverse cMT increased in the extended (upper) side. It was suggested that cMT orientation was controlled by the bending of the epicotyl and not by a gravity signal per se. Loading with Gd³⁺, an inhibitor of the stretch-activated channel, did not inhibit gravitropic bending. However, it inhibited cMT reorientation induced by gravitropic bending and by forced bending. Involvement of the stretch-activated channel in mechano-sensitive orientation of cMT was suggested.     

Cochlear outer hair cell bending in an external electric field.

We have used a high-resolution motion analysis system to reinvestigate shape changes in isolated guinea pig cochlear outer hair cells (OHCs) evoked by low-frequency (2-3 Hz) external electric stimulation. This phenomenon of electromotility is presumed to result from voltage-dependent structural changes in the lateral plasma membrane of the OHC. In addition to well-known longitudinal movements, OHCs were found to display bending movements when the alternating external electric field gradients were oriented perpendicular to the cylindrical cell body. The peak-to-peak amplitude of the bending movement was found to be as large as 0.7 microm. The specific sulfhydryl reagents, p-chloromercuriphenylsulfonic acid and p-hydroxymercuriphenylsulfonic acid, that suppress electrically evoked longitudinal OHCs movements, also inhibit the bending movements, indicating that these two movements share the same underlying mechanism. The OHC bending is likely to result from an electrical charge separation that produces depolarization of the lateral plasma membrane on one side of the cell and hyperpolarization on the other side. In the cochlea, OHC bending could produce radial distortions in the sensory epithelium and influence the micromechanics of the organ of Corti.     

The cyclic reorientation of cortical microtubules on walls with a crossed polylamellate structure: effects of plant hormones and an inhibitor of protein kinases on the progression of the cycle

Summary The outer tangential wall (OTW) of epidermal cells of azuki bean epicotyls has a crossed polylamellate structure, in which lamellae of longitudinal cellulose microfibrils alternate with lamellae of transverse cellulose microfibrils. This implies that the cyclic reorientation of cortical microtubules (MTs) from longitudinal to transverse and from transverse to longitudinal occurs on the OTW. Treatment with a solution that contained no auxin caused the accumulation of cells with longitudinal MTs, suggesting that auxin is required for the reorientation of MTs from longitudinal to transverse during the reorientation cycle. Treatment with 6-dimethylaminopurine (DMAP), an inhibitor of protein kinases that promoted the reorientation of MTs from transverse to longitudinal, resulted in the accumulation of cells with longitudinal MTs. Subsequent treatment with auxin caused a marked increase in the percentage of cells with transverse MTs and then a decrease in the percentage, indicating that the reorientation of MTs from longitudinal to transverse and then from transverse to longitudinal occurred during treatment with auxin. The percentage of cells with transverse MTs decreased more slowly in segments that had been pretreated with gibberellin A₃ (GA) than in segments that had been pretreated without GA, suggesting that GA, in cooperation with auxin, caused the suppression of the reorientation of MTs from transverse to longitudinal.Abbreviations BL brassinolide - BSA bovine serum albumin - GA gibberellin A₃ - DMAP 6-dimethylaminopurine - DMSO dimethylsulfoxide - FITC fluorescein isothiocyanate - IAA indoleacetic acid - MT microtubule - OTW outer tangential wall - PBS phosphate-buffered saline Dedicated to Professor Eldon H. Newcomb in recognition of his contributions to cell biology     

基于图像分析技术的红细胞膜力学特性多参数动态测定的研究

探索以图像分析技术,在无扰、在位、实时的情况下,对单个活态红细胞的多个力学参量：弯曲模量KC、剪切模量μ及切向与弯曲模量之比ε等进行非侵入性连续动态测定的新方法。以该技术对红细胞在不同外部条件（温度、氧分压、渗透压）下的力学参量进行动态监测,不但揭示出有关变量条件对细胞各个力学参量的影响。还证明了本技术适于对细胞的各种生理和病理过程进行连续监测。     

Dynamic reconstruction of the fish locomotor wave

Theoretical modeling substantiates the bionic solution of an optimal wave propulsor for water transport, which must have the amplitude and phase characteristics of the fish bending locomotor waves. Use is made of a computer model of multilink chain bending waves where arbitrary distributions can be set for amplitudes and phases of separate segments. With the linear increase in the amplitude of segmental oscillations, a numerical experiment determines the optimal phasing whereby each segment provides a maximal longitudinal component of the motive force. Two versions of hydrodynamic interaction of the segments with water are compared, implying (i) linear and (ii) quadratic drag: the optimal phasing of the transverse and longitudinal oscillations proves to be (i) orthogonal and (ii) nearly orthogonal. The computed bending wave shapes corresponding to dynamic optimization are consistent with the experimental data.     

Elastic Properties of the Sea Urchin Sperm Flagellum

The theory of flexural vibrations in thin rods, applied to the movement of flagella, has been extended to include an investigation of the influence of the boundary conditions on the theoretical waveforms. It was found that for flagella which are flexible enough, the flexibility can be estimated solely from the wavelength of the wave traveling in it. This can be expected to hold for those flagella which do not possess a fibrous sheath. The bending moment in flagella in which the ampitude of the wave is maintained as the wave travels distally is almost completely produced by active contractile elements. This means that the active bending moment can be estimated from the radius of curvature of the flagellum and the stiffness. The above findings were applied to the case of the sea urchin sperm flagellum. One finds that the stiffness of the flagellum is caused mainly by the nine longitudinal fibers which must have a Young's modulus of slightly less than 10⁸dyne/cm². The longitudinal fibers need to develop a tension of 1.6 × 10⁸dyne/cm² to account for the bending moment in the flagellum. These two figures are in line with those found for muscle fibers.     

Micro-biomechanics vs macro-biomechanics in cortical bone. A micromechanical investigation of femurs deformed by bending

Previous studies have shown that longitudinal and transverse lamellae in compact bone signal the presence of tensile and compressive forces, respectively. On this basis an investigation has been carried out to ascertain the distribution of lamellae in femoral shafts that have been deformed by bending. To do this, a series of undecalcified plane-parallel sections 100 microns thick were prepared, and the proportion of transversely oriented collagen and crystallites in the lamellae was measured, using circularly polarized light as an illuminating source and a Quantimet 720 image-analyzing computer. It has been concluded that the distribution of the two types of lamellae is in accordance with the need to compensate for the deformity produced by the bending of the bones, and that an obvious relationship exists between the macroscopic features of the femurs and their modified microscopic structures.     

Structural differences between "dark" and "bright" isolated human osteonic lamellae

This investigation presents new insights into the structure of human secondary lamellae. Lamellar specimens that appear dark and bright on alternate osteon transverse sections under circularly polarizing light were isolated using a new technique, and examined by polarizing light microscopy, synchrotron X-ray diffraction, and confocal microscopy. A distribution of unidirectional collagen bundles and of two overlapping oblique bundles appears on circularly polarizing light microscopy images in relation to the angle between the specimen and the crossed Nicols' planes. The unidirectional collagen bundles observed at 45 degrees run parallel to the osteon axis in the dark lamellar specimens and perpendicular to it in the bright ones. Small and wide-angle micro-focus X-ray diffraction indicates that the dark lamellae are structurally quite homogeneous, with collagen fibers and apatite crystals preferentially oriented parallel to the osteon axis. Bright lamellar specimens exhibit different orientation patterns with the dominant ones bidirectional at +/-45 degrees with respect to the osteon axis. Accordingly, confocal microscopy evidences the presence of longitudinal bundles in dark lamellar specimens and oblique bundles in the bright ones. Radial bundles are evidenced in both lamellar types. The alternate osteon structure is described by a rather continuous multidirectional pattern, in which dark and bright lamellae display different mechanical and possibly biological functions.     

Shear effects on failure of hollow trees

It is shown that bending stresses in a non-cracked hollow trunk can never explain failure. Consequently, stem breakage due to bending stress cannot be primary failure. It is shown by field studies and simple theoretical assessments that the initiation of a longitudinal shear crack is primarily responsible for failure. Due to cracking, the bending stresses increase and failure by bending happens as secondary failure. As a result, bending theory of a non-cracked closed circular pipe is inappropriate to describe failure of hollow trees. In the appendix is shown the reason for high shear stresses at the tree base and why the shear stresses increase more due to hollowness than to bending stresses.     

Biomechanical analysis of the Rolled (RLD) leaf phenotype of maize

The pleiotropic effects of the Rld1-O/+ mutation of Zea mays (Poaceae) on leaf phenotype include a suppression of normal transverse unrolling, a reversed top/bottom epidermal polarity, and an apparently straighter longitudinal shape. According to engineering shell theory, there might be mechanical coupling between transverse and longitudinal habit, i.e., the leaf rolling itself might produce the longitudinal straightening. We tested this possibility with quantitative curvature measurements and mechanical uncoupling experiments. The contributions of elastic bending under self weight, mechanical coupling, and rest state of leaf parts to the longitudinal and transverse habit were assessed in Rld1-O/+ mutants and a population of sibling +/+ segregants. Elastic bending and curvature coupling are shown to be relatively unimportant. The Rld1-O/+ mutation is shown to alter not only the unrolling process, but also the developmental longitudinal curving in the growing leaf, leading to a straighter midrib and a rolled lamina. The Rld1-O/+ mutant is thus a suitable model to study the relation between tissue polarity and differential curvature development in the maize leaf. Since on the abaxial side of the leaf, more abundant sclerenchyma is found in +/+ than in Rld1-O/+, a gradient in sclerification may contribute to the development of midrib curvature.     

Analysis of flagellar bending in hamster spermatozoa: characterization of an effective stroke

The mechanism by which flagella generate the propulsive force for movement of hamster spermatozoa was analyzed quantitatively. Tracing points positioned 30, 60, 90, and 120 microm from the head-midpiece junction on the flagellum revealed that they all had zigzag trajectories. These points departed from and returned to the line that crossed the direction of progression. They moved along the concave side (but not the convex side) of the flagellar envelope that was drawn by tracing the trajectory of the entire flagellum. To clarify this asymmetry, the bending rate was analyzed by measuring the curvatures of points 30, 60, 90, and 120 microm from the head-midpiece junction. The bending rate was not constant through the cycle of flagellar bending. The rate was higher when bending was in the direction described by the curve of the hook-shaped head (defined as a principal bend [P-bend]) to the opposite side (R-bend). We measured a lower bending rate in the principal direction (R-bend to P-bend). To identify the point at which the propulsive force is generated efficiently within the cycle of flagellar bending, we calculated the propulsive force generated at each point on the flagellum. The value of the propulsive force was positive whenever the flagellum bent from an R-bend to a P-bend (when the bending rate was lowest). By contrast, the propulsive force value was zero or negative when the flagellum bent in the other direction (when the bending rate was higher). These results indicate that flagellar bending in hamster spermatozoa produces alternate effective and ineffective strokes during propulsion.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

A Model Describing Bending in Flagella

In Part I of this paper, we present a modelto account for the force generationproducing bending, and the formation of awaveform in sperm flagella. The model isbased on the observation that dimers, andhence microtubules, possess dipole moments.The electric field these dipoles produce isthe source for storing mechanical work indynein arms. The mechanical work is thenreleased and act on the doublets to producea distally directed force with the resultthat bending occurs. The model described isconsistent with experimental observationsreported in the literature. The flexuralrigidity of a dynein arm is alsocalculated. In Part II of this paper, theconsequences of the bending mechanism arediscussed. It is shown that the sum offorces from dynein arms acting distallyalong doublet microtubules in a flagellumis essentially zero when all dyneins areattached thus resulting in the rigor state.The waveform in a flagellum occurs if oneof the sets of bending moments is zero,that is, a row of dyneins are detached oversome distance along the flagellum. Thedirection of the bend in the waveform isdetermined by which set of dynein arms aredetached with respect to the verticalmedian plane of the flagellum. Thepropagation of a bending wave is the resultof a moving region in which alternate sidesfrom the vertical median plane haveinactive dynein arms. The processes bywhich this moving region occurs and therelationship of the above results to thepropulsion of the flagellum are notconsidered.     

Balken orientation in three coleopteran cuticles

The cuticles of three beetles of differing habit have been examined, and the disposition of the Balken (fibre bundles) found to be appropriate to functional requirements. Crossed Balken are present in the body generally, but longitudinal orientation of Balken provides suitable reinforcement where bending stresses may be expected to be high, as in the femur of the hind limbs of Cybister and G eotrupes , and in the horns of Golofa .     

Analysis of simulated single ligament transection on the mechanical behaviour of a lumbar functional spinal unit.

The influence of the different lumbar spinal ligaments on intersegmental rotation is not fully understood. In order to explore this effect, a finite element model of the functional spinal unit L3/L4 was loaded with pure moments in the three main anatomic planes. The two extremes--minimum and maximum--ligament stiffness values reported in the literature were applied. After virtual transection of each of the spinal ligaments in turn, the intersegmental rotation and forces in the remaining ligaments were calculated. On flexion, the highest force was found for the posterior longitudinal ligament; on extension and lateral bending for the anterior longitudinal ligament; and on axial rotation for the facet capsular ligament. The strongest influence on intersegmental rotation is exerted by the interspinous ligament on flexion, by the anterior longitudinal ligament on extension and lateral bending, and by the facet capsular ligaments on axial rotation. Ligament stiffness has a strong influence on intersegmental rotation and forces in the ligaments, so that finite element models of spinal segments must be validated by experimental data. This study should help to elucidate the role of the various ligaments.