An elastic rod model for anguilliform swimming

We develop a model for anguilliform (eel-like) swimming as an elastic rod actuated via time-dependent intrinsic curvature and subject to hydrodynamic drag forces, the latter as proposed by Taylor (in Proc Roy Proc Lond A 214:158–183, 1952). We employ a eometrically exact theory and discretize the resulting nonlinear partial differential evolution both to perform numerical simulations, and to compare with previous models consisting of chains of rigid links or masses connected by springs, dampers, and prescribed force generators representing muscles. We show that muscle activations driven by motoneuronal spike trains via calcium dynamics produce intrinsic curvatures corresponding to near-sinusoidal body shapes in longitudinally-uniform rods, but that passive elasticity causes Taylor’s assumption of prescribed shape to fail, leading to time-periodic motions and lower speeds than those predicted Taylor (in Proc Roy Proc Lond A 214:158–183, 1952). We investigate the effects of bending stiffness, body geometry, and activation patterns on swimming speed, turning behavior, and acceleration to steady swimming. We show that laterally-uniform activation yields stable straight swimming and laterally differential activation levels lead to stable turns, and we argue that tapered bodies with reduced caudal (tail-end) activation (to produce uniform intrinsic curvature) swim faster than ones with uniform activation.     

A Viscoelastic Traction Layer Model of Muco-Ciliary Transport

A new mathematical model of the transport of mucus and periciliary liquid (PCL) in the airways by cilia is presented. Mucus is represented by a linearly viscoelastic fluid, the mat of cilia is modelled as an ‘active porous medium.’ The propulsive effect of the cilia is modelled by a time-dependent force acting in a shear-thinned ‘traction layer’ between the mucus and the PCL. The effects of surface and interface tension are modelled by constraining the mucus free surface and mucus–PCL interface to be flat. It is assumed that the epithelium is impermeable to fluid. Using Fourier series, the system is converted into ODEs and solved numerically. We calculate values for mean mucus speed close to those observed by Matsui et~al. [{J. Clin. Invest.}, 102(6):1125–1131, 1998], (∽40 μms^-1). We obtain more detail regarding the dynamics of the flow and the nonlinear relationships between physical parameters in healthy and diseased states than in previously published models. Pressure gradients in the PCL caused by interface and surface tension are vital to ensuring efficient transport of mucus, and the role of the mucus–PCL interface appears to be to support such pressure gradients, ensuring efficient transport. Mean transport of PCL is found to be very small, consistent with previous analyses, providing insight into theories regarding the normal tonicity of PCL. An erratum to this article can be found at     

Mapping motor neuron activity to overt behavior in the leech

As an initial step in constructing a quantitative biomechanical model of the medicinal leech (Hirudo medicinalis), we determined the passive properties of its body wall over the physiological range of dimensions. The major results of this study were:

1. The ellipsoidal cross section of resting leeches is maintained by tonic muscle activation as well as forces inherent in the structure of the body wall (i.e., residual stress).
2. The forces required for longitudinal and circumferential stretch to maximum physiological dimensions were similar in magnitude. Cutting out pieces of body wall did not affect the passive longitudinal or circumferential properties of body wall away from the edges of the cut.
3. The strain (i.e., the percentage change in dimension) of different body segments when subject to the same force was identical, despite differences in muscle crosssections.
4. Serotonin, a known modulator of tension in leech muscles, affected passive forces at all physiological muscle lengths. This suggests that the longitudinal muscle is responsible for at least part of the passive tension of the body wall.
5. We propose a simple viscoelastic model of the body wall. This model captures the dynamics of the passive responses of the leech body wall to imposed step changes in length. Using steady-state passive tensions predicted by the viscoelastic model we estimate the forces required to maintain the leech at any given length over the physiological range.

     

Expression of titin isoforms in red and white muscle fibres of carp (Cyprinus carpio L.) exposed to different sarcomere strains during swimming

Titin (also known as connectin) is a striated-muscle-specific protein that spans the distance between the Z- and M-lines of the sarcomere. The elastic segment of the titin molecule in the I-band is thought to be responsible for developing passive tension and for maintaining the central position of thick filaments in contracting sarcomeres. Different muscle types express isoforms of titin that differ in their molecular mass. To help to elucidate the relation between the occurrence of titin isoforms and the functional properties of different fibre types, we investigated the presence of different titin isoforms in red and white fibres of the axial muscles of carp. Gel electrophoresis of single fibres revealed that the molecular mass of titin was larger in red than in white fibres. Fibres from anterior and posterior axial muscles were also compared. For both white and red fibres the molecular mass of titin in posterior muscle fibres was larger than in anterior muscle fibres. Thus, the same fibre type can express different titin isoforms depending on its location along the body axis. The contribution of titin to passive tension and stiffness of red anterior and posterior fibres was also determined. Single fibres were skinned and the sarcomere length dependencies of passive tension and passive stiffness were determined. Measurements were made before and after extracting thin and thick filaments using relaxing solutions with 0.6 mol · l⁻¹ KCl and 1 mol · l⁻¹ KI. Tension and stiffness measured before extraction were assumed to result from both titin and intermediate filaments, and tension after extraction from only intermediate filaments. Compared to mammalian skeletal muscle, intermediate filaments developed high levels of tension and stiffness in both posterior and anterior fibres. The passive tension-sarcomere length curve of titin increased more steeply in red anterior fibres than in red posterior fibres and the curve reached a plateau at a shorter sarcomere length. Thus, the smaller titin isoform of anterior fibres results in more passive tension and stiffness for a given sarcomere strain. During continuous swimming, red fibres are exposed to larger changes in sarcomere strain than white fibres, and posterior fibres to larger changes in strain than anterior fibres. We propose that sarcomere strain is one of the functional parameters that modulates the expression of different titin isoforms in axial muscle fibres of carp. Accepted: 7 May 1997     

Sinusoidal swimming in fishes: the role of season,density of large zooplankton,fish length,time of the day,weather condition and solar radiation

The sinusoidal swimming of fish, previously interpreted as foraging behaviour, was studied with respect to season, density of large zooplankton, fish length, time of the day, weather condition and solar radiation in Římov Reservoir, Czech Republic, using a bottom-mounted, split-beam transducer (7°, nominal angle; frequency 120 kHz). The proportion of sinusoidally swimming fish increased from April to August while this behaviour was absent in October. The occurrence of sinusoidal swimming showed an apparent pattern throughout the day; it increased sharply around sunrise, was highest within 5–6 h around solar noon, and sharply decreased around sunset. Significantly less frequent occurrence of sinusoidal swimming was recorded during cloudy days compared to sunny days. The vast majority of records came from fish of standard length ranging from 100 to 400 mm, which represents the typical size range of common bream Abramis brama and roach Rutilus rutilus of age >1+, the main zooplanktivores in the reservoir. The presence of these larger fish in the open water of the reservoir, as well as the presence of sinusoidal swimming, apparently correlates with the presence of large zooplankton (Daphnia, Leptodora and Cyclops vicinus) in the epilimnion. The increase of sinusoidal swimming between April, June and finally August resulted in an increase of zooplankton component in fish guts. It appears that high values of solar radiation, and stable calm weather during high pressure periods, result in optimal optical conditions for sinusoidal swimming, making this foraging behaviour more efficient and widely used in fishes exploiting the zooplankton production in the reservoir.     

Modelling the mechanical properties of cardiac muscle

A model of passive and active cardiac muscle mechanics is presented, suitable for use in continuum mechanics models of the whole heart. The model is based on an extensive review of experimental data from a variety of preparations (intact trabeculae, skinned fibres and myofibrils) and species (mainly rat and ferret) at temperatures from 20 to 27°C. Experimental tests include isometric tension development, isotonic loading, quick-release/restretch, length step and sinusoidal perturbations. We show that all of these experiments can be interpreted with a four state variable model which includes (i) the passive elasticity of myocardial tissue, (ii) the rapid binding of Ca²⁺ to troponin C and its slower tension-dependent release, (iii) the kinetics of tropomyosin movement and availability of crossbridge binding sites and the length dependence of this process and (iv) the kinetics of crossbridge tension development under perturbations of myofilament length.     

Modification of leech behavior following foraging for artificial blood

In this study we examined whether the foraging for artificial blood affected the behavioral responsiveness of leeches to electrical stimulation of the body wall. After foraging for artificial blood, electrical stimulation of the posterior end of the leech significantly increased the percentage of stimulation trials that elicited locomotory activity—swimming and crawling—compared to the behaviors elicited when leeches did not forage or foraged for normal saline. On the other hand, shortening always dominated the behavioral profile of the leech to anterior stimulation even after foraging for artificial blood. In intact anterior end-isolated nerve cord preparations, we also found that application of artificial blood to the intact anterior end was sufficient to modify motor responsiveness to DP nerve stimulation. Full strength artificial blood had an overall negative effect on the likelihood of DP nerve stimulation initiating swimming and on the average length of elicited swim episodes compared to when pond water surrounded the anterior end. Application of a 10% solution of artificial blood to the anterior end led to an increase in the likelihood of DP nerve stimulation eliciting swimming.     

Analysis of impulse adaptation in motoneurons

Animal locomotion results from muscle contraction and relaxation cycles that are generated within the central nervous system and then are relayed to the periphery by motoneurons. Thus, motoneuron function is an essential element for understanding control of animal locomotion. This paper presents motoneuron input–output relationships, including impulse adaptation, in the medicinal leech. We found that although frequency-current graphs generated by passing 1-s current pulses in neuron somata were non-linear, peak and steady-state graphs of frequency against membrane potential were linear, with slopes of 5.2 and 2.9 Hz/mV, respectively. Systems analysis of impulse frequency adaptation revealed a static threshold nonlinearity at −43 mV (impulse threshold) and a single time constant (τ = 88 ms). This simple model accurately predicts motoneuron impulse frequency when tested by intracellular injection of sinusoidal current. We investigated electrical coupling within motoneurons by modeling these as three-compartment structures. This model, combined with the membrane potential–impulse frequency relationship, accurately predicted motoneuron impulse frequency from intracellular records of soma potentials obtained during fictive swimming. A corollary result was that the product of soma-to-neurite and neurite-to-soma coupling coefficients in leech motoneurons is large, 0.85, implying that the soma and neurite are electrically compact.     

Effect of body mass and water temperature on the standard metabolic rate of juvenile yellow perch, Perca flavescens (Mitchill)

Fish respiration rates that are presumed to represent standard metabolic rates (SMR) may sometimes include an unspecified energy expenditure associated with activity and digestion. This situation may introduce a bias in bioenergetics models because standard metabolism, digestion, and activity may not be affected by the same environmental conditions. The aim of this study was to (1) develop a SMR model for juvenile yellow perch, Perca flavescens (Mitchill), that represent the minimum energy expenditure required to maintain life and (2) compare the results of this study with published perch metabolic rates and bioenergetics models. SMR was estimated for yellow perch over a range of body␣mass (4.4–24.7 g) and water temperature (12–20°C). The intercept of the relationship between fish respiration and swimming velocity obtained during forced swimming experiments was used to determine SMR. SMR estimated by the present study were comparable to values presented by two published studies on Eurasian perch, Perca fluviatilis L. However, estimated SMR were 4.1–20.9 times lower than values of a third respirometry study and predictions of bioenergetics models for perch. The present study suggests that published SMR models may sometimes include a significant fraction of energy expenditures (39.2–75.9%) associated with digestion and activity. This may complicate the implementation and the interpretation of fish bioenergetics models. The present study indicates that the intercept of respiration-velocity relationships and long-term respiration rates during starvation experiments may provide similar and reliable SMR values.     

Relationship Between Medium Salinity, Body Density, Buoyancy and Swimming in Artemia franciscana Larvae: Constraints on Water Column Use?

Body density measurements were carried out on larval Artemia franciscana that had been held for 24 h at either 33 or 100‰ after hatching. Body density was low (1.0308–1.0342 g ml⁻¹) by comparison with marine crustacean zooplankters or benthic freshwater crustaceans, and very stable, being only 0.3% higher in 100‰ than in 33‰. Vertical and horizontal swimming in 2nd instar larvae was studied at 8.5, 17, 34, 50, 100, 150 and 250‰ at 23 °C. At 8.5–50‰ downwards swimming was always significantly faster than upwards swimming, but in 100‰ downwards swimming was much slower than upwards swimming, indicating substantial positive buoyancy. At 150 and 250‰ downwards swimming was impossible. Horizontal swimming speed was unaffected by salinity over the range 8.5–100‰, but could not be studied at 150 and 250‰ as larvae could not leave the surface film. An asymptotic relationship between salinity and viscosity was found over the range 8.5–250‰. Calculations indicate a rise from 1.197 to 1.513 cp between 8.5 and 100‰, but this does not significantly impede horizontal locomotion. It appears that water column use by early stage Artemia larvae, that use a pair of 2nd antennae for rowing-type locomotion, is constrained by the increasing positive buoyancy associated with living at salinities above that corresponding to neutral buoyancy (approximately 48‰).     

Serotonin modulates muscle function in the medicinal leech Hirudo verbana

The body wall muscles of sanguivorous leeches power mechanically diverse behaviours: suction feeding, crawling and swimming. These require longitudinal muscle to exert force over an extremely large length range, from 145 to 46 per cent of the mean segmental swimming length. Previous data, however, suggest that leech body wall muscle has limited capacity for force production when elongated. Serotonin (5-HT) alters the passive properties of the body wall and stimulates feeding. We hypothesized that 5-HT may also have a role in allowing force production in elongated muscle by changing the shape of the length-tension relationship (LTR). LTRs were measured from longitudinal muscle strips in vitro in physiological saline with and without the presence of 10 μM 5-HT. The LTR was much broader than previously measured for leech muscle. Rather than shifting the LTR, 5-HT reduced passive muscle tonus and increased active stress at all lengths. In addition to modulating leech behaviour and passive mechanical properties, 5-HT probably enhances muscle force and work production during locomotion and feeding.     

Searching for Spatial Patterns in a Pollinator–Plant–Herbivore Mathematical Model

This paper deals with the spatio-temporal dynamics of a pollinator–plant–herbivore mathematical model. The full model consists of three nonlinear reaction–diffusion–advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases. The first one is a model for a mutualistic interaction (pollinator–plant), later on a sort of predator–prey (plant–herbivore) interaction model is studied. In both cases, the interaction term is described by a Holling response of type II. Finally, by considering that the plant population is the unique feeding source for the herbivores, a mathematical model for the three interacting populations is considered. By incorporating a constant diffusion term into the equations for the pollinators and herbivores, we numerically study the spatiotemporal dynamics of the first two mentioned models. For the full model, a constant diffusion and advection terms are included in the equation for the pollinators. For the resulting model, we sketch the proof of the existence, positiveness, and boundedness of solution for an initial and boundary values problem. In order to see the separated effect of the diffusion and advection terms on the final population distributions, a set of numerical simulations are included. We used homogeneous Dirichlet and Neumann boundary conditions.     

Effects of passive tension on unloaded shortening speed of frog single muscle fibers.

Experiments were performed to determine the influence of sarcomere length and passive tension on the velocity of unloaded shortening (Vu) as measured by the slack test technique. Slack test results were obtained from intact twitch fibers isolated from the frog (Rana temporaria). Measurements were made both in the absence and presence of passive tension using two different protocols. In one, all releases were initiated from the same sarcomere length and passive tension level; in the other, all releases ended at the same sarcomere length. In the absence of passive tension, no difference was observed between the results from the two slack test protocols. When passive tension was present, performing all releases from the same initial sarcomere length and passive tension level resulted in linear step size-slack time relationships in which the slopes (Vu) were independent of length over a sarcomere length range extending to 3.1 microns, and the intercepts increased with increasing sarcomere length. Performing all releases to the same final sarcomere length in the presence of passive tension produced nonlinear step size-slack time relationships. The results presented here show that, in the presence of significant levels of passive tension, the traditional interpretation of the slope of the slack test plot as the constant unloaded shortening velocity is only correct when all length steps are initiated from the same initial sarcomere length and level of passive tension.     

A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm

 Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits. Received: 21 November 2000 / Revised version: 9 August 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 92B99, 70K40, 70K05 Key words or phrases: Intracranial saccular aneurysm – Bruit – Spectrum – Nonlinear dynamics – Transients – Vortex shedding – Fung model     

Sexual dimorphism in <Emphasis Type="Italic">Sebastes owstoni</Emphasis> (Scorpaenidae) from the Sea of Japan

Morphological and genetic differences between red and yellow morphotypes of Sebastes owstoni were investigated, utilizing 277 males [84.0–194.3 mm in standard length (SL)] and 542 females (92.3–251.5 mm SL) from the Sea of Japan. All males smaller than 120 mm SL were characterized by red body color. The frequency of specimens with yellow body color thereafter increased gradually with SL, all specimens larger than 170 mm SL being yellow. The specimens with yellow body color were observed throughout the year. All females smaller than 170 mm SL were characterized by red body color, the frequency of specimens with yellow body color tending to slightly increase with SL. However, most females had red body color, except for 16 specimens (177.7–241.5 mm SL) that were yellow, growth-related color change from red to yellow being uncommon. Morphological analysis of 49 males (107.6–193.3 mm SL) and 68 females (108.7–241.5 mm SL) showed the head length, orbit diameter, lower jaw length, and predorsal length to be relatively greater, but the distance between the pelvic and anal fins less, in males. A discriminant analysis using Mahalanobis distances resulted in 100% correct assignment of specimens to sex, regardless of SL and body color. In addition, no genetic differences were apparent between red and yellow individuals in mitochondrial DNA sequence analyses from the threonine tRNA to the first half of the control region (498 bp). Accordingly, the differences in body color, maximum size, and the five morphometric characters listed above were considered to represent sexual dimorphism. That evidenced by body color was considered to appear after that shown by morphometric characters, some exceptions in the former occurring in females. This is the first report of permanent sexual dimorphism in body color in Sebastes.     

A new flounder,monolene helenensis (pleuronectiformes: Bothidae) from the eastern tropical atlantic

Monolene helenensis sp. nov. is described on the basis of seven specimens collected from the eastern tropical Atlantic Ocean. This new bothid flounder differs from all known congeners by the following combination of characters: 108–116 dorsal and 89–92 anal fin rays, 101–111 lateral line scales, 7–10+10–15=18–25 gill rakers, 10–12+37–38=48–50 vertebrae, body depth 2.58–2.77 in standard length, ocular side pectoral fin length 1.34–1.59, in head length and upper half of pectoral fin blackish.     

A new armored searobin <Emphasis Type="Italic">Paraheminodus longirostralis</Emphasis> (Teleostei: Peristediidae) from New Caledonia

A new species of armored searobin, Paraheminodus longirostralis, is described from five specimens collected from New Caledonia at depths of 412–467 m. It is distinguishable from its three known congeners in having 34 bony plates in the upper lateral row, a forward-directed spine on each plate between the 23rd–26th and 31st–32nd plates in the upper lateral row, 6–7 + 1 + 20–21 = 27–28 gill rakers, an elongate body posterior to the anus (49.9–52.1% standard length), an elongate rostral projection (53.0–59.3% head length), short upper jaw (42.1–43.4% head length), an elongate pectoral fin (70.6–79.4% head length), and long preopercular spine (39.2–57.7% head length).     

Auditory brainstem responses to airborne sounds in the aquatic frog Xenopus laevis: correlation with middle ear characteristics

In this study we recorded auditory brainstem responses to airborne sounds to determine the hearing sensitivity of Xenopus laevis frogs and correlated their hearing profiles with middle ear characteristics. In newly metamorphosed frogs (body mass 0.5–0.76 gm, snout-vent length 17–20 mm) best hearing sensitivities were measured in the 2.4–2.8 kHz range, whereas optimal hearing sensitivity of older adults (body mass 18–90 gm; snout-vent length 57–100 mm) ranged from 1.0 to 1.2 kHz. Middle ear volumes reconstructed from serial sections showed approximate volume of 0.002 cc and 0.04–0.07 cc in newly metamorphosed and older frogs, respectively. This inverse frequency–volume relationship is consistent with the properties of an acoustic resonator indicating that differences in best hearing sensitivity are at least in part correlated to variation in middle ear volumes for airborne sounds. These results are consistent with peak frequency vibrational velocity profiles of Xenopus tympanic disk that have been shown to be dependent on underlying middle ear volumes and corroborate the occurrence of peak amplitudes of otoacoustic emissions in the 1.0–1.2 kHz region in adult Xenopus frogs.     

Tissue elastance influences airway smooth muscle shortening: comparison of mechanical properties among different species

We have observed striking differences in the mechanical properties of airway smooth muscle preparations among different species. In this study, we provide a novel analysis on the influence of tissue elastance on smooth muscle shortening using previously published data from our laboratory. We have found that isolated human airways exhibit substantial passive tension in contrast to airways from the dog and pig, which exhibit little passive tension (<5% of maximal active force versus approximately 60% for human bronchi). In the dog and pig, airway preparations shorten up to 70% from Lmax (the length at which maximal active force occurs), whereas human airways shorten by only approximately 12% from Lmax. Isolated airways from the rabbit exhibit relatively low passive tension (approximately 22% Fmax) and shorten by 60% from Lmax. Morphologic evaluation of airway cross sections revealed that 25-35% of the airway wall is muscle in canine, porcine, and rabbit airways in contrast to approximately 9% in human airway preparations. We postulate that the large passive tension needed to stretch the muscle to Lmax reflects the high connective tissue content surrounding the smooth muscle, which limits shortening during smooth muscle contraction by imposing an elastic load, as well as by causing radial constraint.     

Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers

Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like) swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.