Optimization of the mechanical performance of a two-duct semicircular duct system--part 1: dynamics and duct dimensions

The classical representation of the semicircular duct system consists of three separate duct circuits. The ducts are, however, in reality, hydrodynamically interconnected. Muller & Verhagen (1988a,b) derived equations for the mechanical behaviour of an interconnected system with three ducts (anterior, posterior and horizontal). An analytical solution of these equations would, however, be too complex to provide surveyable formulae. A system of two interconnected ducts avoids this complexity whilst keeping the essentials of the coupling of ducts intact. The solution of the equation of motion leads to expressions for time constants and maximal endolymph excursions which are functions of morphological parameters, viz. the ratios of radii (gamma) and lengths (lambda) of the common vestibular part (crus commune or utriculus) and the ducts. The system possesses two short time constants which are shown to have similar values. The maximum endolymph displacements in the two ducts after a steplike stimulus are the products of the respective initial velocities and combinations of time constants. The initial velocities depend strongly on the position of the labyrinth with respect to the excitating rotation vector. Measured data of gamma and lambda are compared with the theoretical results. For gamma, excellent agreement was found. lambda is treated elsewhere.     

Population dynamics of clock-controlled biological species: models and why circadian rhythms are circadian

The endolymph flow inside the semicircular ducts is analytically investigated by considering a system of two hydrodynamically interconnected ducts. Rotation of this system adds an amount of motion (momentum) to parts of it. This results in an endolymph flow in generally all vestibular parts. The "external impulses" are the impulses which emerge by rotation of exclusively a particular vestibular part. The real impulses can be calculated from a set of equations which contain the external impulses. Analytical expressions are derived for the initial velocities in the ducts and for the maximum endolymph displacements. These formulae contain the external impulses and the ratios of: (1) the radii of crus commune and ducts (gamma), (2) the lengths of crus commune and ducts (lambda). It was proven that an interconnected system composed of two ducts, and also a system composed of two such semicircular duct systems, behaves as a pure rotation transducer (like a single duct does), also when it is rotated excentrically. Duct systems with polygonal and circular geometries were used to evaluate whether an optimal value of lambda would exist (gamma was already considered elsewhere). Optimum values of lambda in a range of about 0.10-0.52 were found. This rather wide range of values agrees with values from measurements. Optimization of an interconnected duct system appeared to be equal to optimization of a system composed of separate ducts.     

Optimization of the mechanical performance of a two-duct semicircular duct system--part 3: the positioning of the ducts in the head

In the majority of vertebrates, the horizontal duct of the vestibular system lies approximately in the yawing plane of the head. The positioning of the vertical ducts, however, is not in the pitch- and roll planes but the vertical ducts generally lie under an angle of about 30-45 degrees relative to the medial plane. Using the equations for a hydrodynamically interconnected two-duct system, optimal positions of the vertical and horizontal ducts in different vertebrate groups can be derived. It was stated that the mean response of the vertical ducts should be optimized. This leads to a symmetrical positioning of the vertical ducts with respect to the medial plane. In all observed vertebrate groups, a solution of mu =(pi-alpha)/2 is found (mu is the angle of the vertical ducts relative to the medial plane, alpha is the angle between the vertical duct planes). For alpha=90 degrees, this provides an equal sensitivity for pitch- and roll- movements. For alpha>90 degrees, a larger sensitivity for pitch movements is obtained, at the expense of a lower sensitivity for roll movements. It is argued that the angle alpha between the vertical ducts may vary from 90 to 120 degrees. In most vertebrates, the centre of mass is stabilized by e.g. fins, tri- or quadrupedal stability, a crawling body or upside-down resting positions (e.g. bats). Birds are generally biped, so in walking they are also rather sensitive to roll. These features are related to labyrinth positioning in the head.     

Possible functional properties of the labyrinth in Brachiosaurus brancai]

The dimensions of the semicircular canals and the respective ampullae of a complete labyrinth caste of Brachiosaurus Brancai were determined. Using the equation of motion and the dimensions of the semicircular canals the behaviour of the endolymph displacement of the Brachiosaurus labyrinth was calculated. The time constants of the system were found to be between the values 4 sec and 13 sec for T1 and 0.2 sec and 0.5 sec for T2. From these results it was concluded, that the head movements of the animal occurred in a range between 0.02 and 0.1 cps.     

The membranous labyrinth and its innervation inChaetodon trifasciatus (Pisces,Teleostei, Chaetodontidae)

Synopsis In the butterflyfishChaetodon trifasciatus, the labyrinth is characterized by its elevated form and especially the size of the vertical canals, the almost circular form of the horizontal canal and its posterior opening not directly in the utriculus but in the common pillar of the two vertical canals. There is an almost complete separation between utriculus and sacculus which are only linked by a virtual pore. The lagena, which is medially situated to the posterior part of the sacculus, is separated from it by an incomplete vertical wall. There are two maculae neglectae, the anterior macula being situated in the pore separating utriculus from sacculus and filling this pore, the posterior in a gutter of the floor of the utriculus. A long and narrow endolymphatic canal, originating from the sacculus close to the communication with the utriculus, follows the common pillar of the two vertical canals and widens into an endolymphatic sac at the top of the membranous labyrinth. The innervation of the labyrinth is made by the acoustic ganglion, which is connected to the brain by two roots and elongated into three parts: the anterior part innervates the anterior and horizontal cristae and the utricular and saccular maculae; the middle part innervates the macula sacculae and the macula neglecta 1; the posterior part innervates the macula neglecta II, the macula lagenae and the posterior crista. The important size of the vertical canals and the almost circular form of the horizontal canal may reflect very precise locomotory aptitudes.     

Numerical modeling of the cupular displacement and motion of otoconia particles in a semicircular canal

Balance is achieved and maintained by a balance system called a labyrinth that is composed of three semicircular canals and the otolith organs that sense linear gravity and acceleration. Within each semicircular canal, there is a gelatinous structure called the cupula, which is deformed under the influence of the surrounding endolymph. One of the balance disorders is benign paroxysmal positional vertigo, and one of the pathological conditions that have been identified as possible causes of this syndrome is canalithiasis—disturbance of the endolymph flow and cupular displacement caused by the free-moving otoconia particles within the lumen of the canal. Analysis of phenomena occurring within the semicircular canal can help to explain some balance-related disorders and the response of the vestibular system to external perturbations under various pathological conditions. Numerical simulations allow a study of the influence of a wide range of factors, without the need to perform experiments and clinical examinations. In case of canalithiasis, an accurate explanation and tracking of the motion of otoconia particles in vivo is obviously nearly impossible. In this study, a numerical model was developed to predict the motion of otoconia particles within the semicircular canal and the effect of the endolymph flow and particles on the deformation of the cupula.     

Histomorphometrical study of the submandibular gland ductal system in the rat

The duct system of murine submandibular gland is composed, in contrast with other mammals, by four types of ducts, among which the granular duct is unique for rodents. The granular duct shows a typical secretory structure with a clear intersex morphological diversity on which we carried out a morphometrical study in order to determine the relative area of each duct in rats in comparison with the rest of ducts and the whole gland. Our results, in both sexes, show that the duct with the broadest surface is the granular duct, followed by the excretory, striated and the intercalated ducts. In addition, we found a significant intersex difference between the relative surface of the granular and the excretory ducts, being bigger in males than in females. Finally, in both sexes, there is a greater variation in the data related to the excretory ducts than to the other ducts.     

Function of transient receptor potential cation channel subfamily V member 4 (TRPV4) as a mechanical transducer in flow-sensitive segments of renal collecting duct system

The TRPV4 Ca(2+)-permeable channel is sensitive to mechanical stimuli. In the current study we have employed immunocytochemical staining in kidney slices and functional assessments (Ca(2+) imaging) in isolated, split-opened, tubule segments to define TRPV4 sites of expression and flow-dependent function in the collecting duct system. Staining patterns revealed strong expression of TRPV4 along the entire collecting duct system with highest levels at the apical (luminal)/subapical region of the principal cells (PCs), the dominant cell type, with more diffuse staining in intercalated cells (ICs). Using fluorescence Ca(2+) imaging and the selective TRPV4 agonist, GSK1016790A, we demonstrated functional TRPV4 channels in PCs and ICs of split-opened cortical collecting ducts and connecting tubules. The agonist was ineffective in inducing a rise in [Ca(2+)](i) in the absence of extracellular Ca(2+) or in tubules from TRPV4-deficient animals. Most importantly, a 10-fold elevation in luminal (apical) fluid flow induced a rapid and sustained influx of Ca(2+) that was abolished by the TRPV channel inhibitor, ruthenium red, or in tubules isolated from TRPV4 deficient animals. We concluded that TRPV4 is highly expressed along the entire collecting duct system where it appears to function as a sensor/transducer of flow-induce mechanical stresses.     

Immunocytochemical localization of a renal glycoprotein (gpCDI) synthesized by cultured collecting duct cells

A sulfated, proline-rich glycoprotein (gpCDI, apparent molecular weight 200,000 in column chromatography and 150,000 in SDS-PAGE) was isolated from cultured renal collecting duct epithelium by centrifugation. Triton X100 extraction and DEAE-cellulose ion exchange chromatography. A DEAE-cellulose ion exchange chromatography fraction with the enriched gpCDI was used for immunization of guinea pigs. The antiserum was prepared for antigen localization by indirect immunofluorescence in collecting duct cell cultures and in tissue sections of neonatal and adult rabbit kidneys. In the cultured collecting duct epithelium, antibody staining of the epithelium and structures of the extracellular matrix was age dependent. Cultures of dedifferentiated collecting duct monolayers revealed positive reaction in the cytoplasm. In neonatal and adult rabbit kidneys, the antibody was localized in the entire collecting duct system but not in the collecting duct ampullae of the newborn kidney. Staining of the cytoplasm was found only in medullary collecting ducts of the neonatal kidney; other portions revealed staining mostly at the basal circumference of the tubule and at the luminal cell borders. Apart from collecting ducts, no other tubular segments were reactive. The cortical and the medullary interstitium contained fluorescent fibres which were concentrated around vascular structures. A possible relation between gpCDI and collagenous compounds is discussed. Bowman's capsule reacted positively, whereas staining of the mesangial matrix was weak. The localization of the antigen, as revealed by indirect immunofluorescence, suggests that gpCDI occurs both in intracellular and extracellular (interstitial) location. Two main points are emphasized: Firstly gpCDI is considered an important constituent in different stages of collecting duct development, and secondly, the staining pattern of the antibody varies with the different portions of both young and adult kidney collecting ducts; this staining heterogeneity may correspond with the known regional differences of collecting duct functions.     

A computational framework to simulate the endolymph flow due to vestibular rehabilitation maneuvers assessed from accelerometer data

Vertiginous symptoms are one of the most common symptoms in the world, therefore investing in new ways and therapies to avoid the sense of insecurity during the vertigo episodes is of great interest. The classical maneuvers used during vestibular rehabilitation consist in moving the head in specific ways, but it is not fully understood why those steps solve the problem. To better understand this mechanism, a three-dimensional computational model of the semicircular ducts of the inner ear was built using the finite element method, with the simulation of the fluid flow being obtained using particle methods. To simulate the exact movements performed during rehabilitation, data from an accelerometer were used as input for the boundary conditions in the model. It is shown that the developed model responds to the input data as expected, and the results successfully show the fluid flow of the endolymph behaving coherently as a function of accelerometer data. Numerical results at specific time steps are compared with the corresponding head movement, and both particle velocity and position follow the pattern that would be expected, confirming that the model is working as expected. The vestibular model built is an important starting point to simulate the classical maneuvers of the vestibular rehabilitation allowing to understand what happens in the endolymph during the rehabilitation process, which ultimately may be used to improve the maneuvers and the quality of life of patients suffering from vertigo.     

Position and bony structures of the vestibular apparatus in the guinea pig]

The study of the inner ear of the guinea pig intended to give an explanation to what extent there are differences discernible in relation to the human labyrinth. Additional histological research should clarify the question, if structural differences exist in the osseous labyrinth capsule of the same animal. It has turned out that in normal headbearing the position of the semicircular canals deviates from the human vestibular apparatus. The semicircular canals are nearly vertical to each other, but in comparison to the human labyrinth they are shifted around the longitudinal axis of the utriculus caudal by ca. 30 degrees. In general the position of the vestibulo-cochlear organ is fixed to a great extent by the inclined course of the petrosal pyramid. This different position of the semicircular canals in man and animal is supposed to be due to the phylogenetic evolution and the adjustment to upright walk. Size and extension of the single semicircular canals are very different within the same animal. These differences in size indicate causalities of form and function. The relations in the build of the osseous labyrinth are extremely complicated. Compared to the other corporal regions the static parts of the petrosal pyramid are exceptional massive and of remarkable hard consistency. In the inner capsule of the ear there are three different bone strata to be seen. The characteristic lamel structure is most solid nearest to the semicircular canals. The fetal characteristics in the maturing process of the petrosal bone were traced a long while in the postnatal life. The typical building of the labyrinthal bone structures contributes to the mechanical stability of the capsule.     

Anatomo-stereologic characteristics of the mucous membrane of the major duodenal papilla

In 55 men and 60 women who had had not any pathology in their biliary-pancreato-duodenal system during life, microrelief of the mucous membrane in the major duodenal papilla has been studied by means of light and scanning electron microscopy. It is defined by variants of fusion of the common bile duct and the pancreatic duct in the papilla. Three main variants of the ducts fusion are defined and, respectively, three main varieties of the structure of the mucous membrane folds. When the ducts flow into the same orifice separately, the mucous membrane relief is even, parvigranular and there are no fold-valves. In the common major duodenal papilla, the architectonics of the mucous membrane resembles the valve that acts as a block-outlet mechanism.     

Immunocytochemical localization of a renal glycoprotein (gp CD I) synthesized by cultured collecting duct cells

Summary A sulfated, proline-rich glycoprotein (gp_CDI, apparent molecular weight 200,000 in column chromatography and 150,000 in SDS-PAGE) was isolated from cultured renal collecting duct epithelium by centrifugation, Triton X100 extraction and DEAE-cellulose ion exchange chromatography. A DEAE-cellulose ion exchange chromatography fraction with the enriched gp_CDI was used for immunization of guinea pigs. The antiserum was prepared for antigen localization by indirect immunofluorescence in collecting duct cell cultures and in tissue sections of neonatal and adult rabbit kidneys. In the cultured collecting duct epithelium, antibody staining of the epithelium and structures of the extracellular matrix was age dependent. Cultures of dedifferentiated collecting duct monolayers revealed positive reaction in the cytoplasm. In neonatal and adult rabbit kidneys, the antibody was localized in the entire collecting duct system but not in the collecting duct ampullae of the newborn kidney. Staining of the cytoplasm was found only in medullary collecting ducts of the neonatal kidney; other portions revealed staining mostly at the basal circumference of the tubule and at the luminal cell borders. Apart from collecting ducts, no other tubular segments were reactive. The cortical and the medullary interstitium contained fluorescent fibres which were concentrated around vascular structures. A possible relation between gp_CDI and collagenous compounds is discussed. Bowman's capsule reacted positively, whereas staining of the mesangial matrix was weak. The localization of the antigen, as revealed by indirect immunofluorescence, suggests that gp_CDI occurs both in intracellular and extracellular (interstitial) location. Two main points are emphasized: Firstly, gp_CDI is considered an important constituent in different stages of collecting duct development, and secondly, the staining pattern of the antibody varies with the different portions of both young and adult kidney collecting ducts; this staining heterogeneity may correspond with the known regional differences of collecting duct functions.     

Development of the duct system during exocrine pancreas differentiation in the grass snake Natrix natrix (Lepidosauria,Serpentes)

We analyzed the development of the pancreatic ducts in grass snake Natrix natrix L. embryos with special focus on the three‐dimensional (3D)‐structure of the duct network, ultrastructural differentiation of ducts with attention to cell types and lumen formation. Our results indicated that the system of ducts in the embryonic pancreas of the grass snake can be divided into extralobular, intralobular, and intercalated ducts, similarly as in other vertebrate species. However, the pattern of branching was different from that in other vertebrates, which was related to the specific topography of the snake's internal organs. The process of duct remodeling in Natrix embryos began when the duct walls started to change from multilayered to single‐layered and ended together with tube formation. It began in the dorsal pancreatic bud and proceeded toward the caudal direction. The lumen of pancreatic ducts differentiated by cavitation because a population of centrally located cells was cleared through cell death resembling anoikis. During embryonic development in the pancreatic duct walls of the grass snake four types of cells were present, that is, principal, endocrine, goblet, and basal cells, which is different from other vertebrate species. The principal cells were electron‐dense, contained indented nuclei with abundant heterochromatin, microvilli and cilia, and were connected by interdigitations of lateral membranes and junctional complexes. The endocrine cells were electron‐translucent and some of them included endocrine granules. The goblet cells were filled with large granules with nonhomogeneous, moderately electron‐dense material. The basal cells were small, electron‐dense, and did not reach the duct lumen.     

Ducts of the labral glands of Leptestheria dahalacensis (Crustacea: Branchiopoda: Spinicaudata)

Inside the labrum of Leptestheria dahalacensis are situated three types of large epidermal gland cells, whose ducts open onto the outer dorsal surface of the labrum. SEM revealed that the thin ducts of the A-type gland cells open out behind the epipharynx at the end of small, conically shaped protuberances, the two paired ducts of the B-type gland cells lead into the distal portion of the labrum, and the external opening of the single duct of the C-type gland cells lies on the dorsal lobe of the labrum. The ducts of the three different gland cell types have the same fundamental constitution, but vary in diameter. Each secretory unit consists of a pair of gland cells (A, B, or C) and a secretory duct. The duct is formed by ring-shaped folding of one anteroposteriorly elongated epidermal cell (duct cell), whose ends adhere closely to one another. A further ring-folded epidermal cell (accessory cell), but flattened in shape, is interposed, like a sleeve-connection, between the gland cells and the duct cell. The reservoirs of gland cells open into the lumen of the duct. Discontinuous deposits of highly electron-dense matter are present on the plasma membrane of the accessory cell delimiting the initial part of the duct lumen, while the plasma membrane of the duct cell facing the lumen is cuticularized. The cytoplasm of the accessory cell, on examination by TEM, appears quite similar to that of the duct cell, except for the different distribution and greater abundance of microtubules. Similarly organized tricellular tegumental glands also commonly occur in other Crustacea, both Malacostraca and non-Malacostraca. Possible functions of secretions from the three different types of gland cells present in the labrum of L. dahalacensis are discussed.