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Structure-function relationships in the pulmonary arterial tree.

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are independent of vessel diameter, and although the actual arterial tree is quite heterogeneous, the diameter of each route, through which the blood flows, tapers from the arterial inlet to essentially the same terminal arteriolar diameter. In the model the average route is represented as a tapered tube through which the blood flow decreases with distance from the inlet because of the diversion of flow at the many bifurcations along the route. The taper and flow diversion are expressed in terms of morphometric parameters obtained using various methods for summarizing morphometric data. To help put the model parameter values in perspective, we applied one such method to morphometric data obtained from perfused dog lungs. Model simulations demonstrate the sensitivity of model pressure-flow relationships to variations in the morphometric parameters. Comparisons of simulations with experimental data also raise questions as to the "hemodynamically" appropriate ways to summarize morphometric data.

Algorithms↗

Detailed flow patterns in the nasal cavity.

The human nasal cavity filters and conditions inspired air while providing olfactory function. Detailed experimental study of nasal airflow patterns has been limited because of the complex geometry of the nasal cavity. In this work, particle image velocimetry was used to determine two-dimensional instantaneous velocity vector fields in parallel planes throughout a model of the nasal cavity that was subjected to a nonoscillatory flow rate of 125 ml/s. The model, which was fabricated from 26 computed tomography scans by using rapid prototyping techniques, is a scaled replica of a human right nasal cavity. The resulting vector plots show that the flow is laminar and regions of highest velocity are in the nasal valve and in the inferior airway. The relatively low flow in the olfactory region appears to protect the olfactory bulb from particulate pollutants. Low flows were also observed in the nasal meatuses, whose primary function has been the subject of debate. Comparison of sequentially recorded data suggests a steady flow.

Adult↗

Analysis of tracheal mechanics and applications.

We have developed a mathematical model for a tracheal ring that consists of a "horseshoe" of cartilage with its tips joined by a membrane. The ring is subjected to a uniform transmural pressure (Ptm) difference. The model was used to calculate the cross-sectional area (A) of the trachea. Whereas the mechanics of the deformation of the cartilage were analyzed using elastica theory, the posterior membrane was treated as a simple membrane that is inextensible under changes in Ptm. The membrane can be specified to be of any length less than baseline and thus can represent a posterior membrane under tension. The cartilage can have specifiable nonuniform unstressed curvature as well as nonuniform bending stiffness. We have investigated the effect on the tracheal A-Ptm curve of posterior membrane length and tensile force in the membrane, cartilage shape and elasticity, and localized weakening of the cartilage. The model predictions are in good agreement with magnetic resonance imaging data from rabbit tracheas and show that the shape of the horseshoe as well as the posterior membrane force are important determinants of tracheal compliance.

Cartilage↗

Local particle deposition patterns may play a key role in the development of lung cancer.

The apparent discrepancy between the reported preferential occurrence of bronchial carcinomas in central bronchial airways and current dose estimates for inhaled particles suggests that experimentally observed local accumulations of particles within bronchial airway bifurcations may play a crucial role in lung cancer induction. Here, we computed three-dimensional particle deposition patterns in lobar-segmental airway bifurcations and quantified the resulting inhomogeneous deposition patterns in terms of deposition enhancement factors, which are defined as the ratio of local to average deposition densities. Our results revealed that a small fraction of epithelial cells located at carinal ridges can receive massive doses that may be even a few hundred times higher than the average dose for the whole airway. This lends further credence to the hypothesis that the apparent site selectivity of neoplastic lesions may indeed be caused by the enhanced deposition of toxic particulate matter at bronchial airway bifurcations.

Aerosols↗

Localized compliance of small airways in excised rat lungs using microfocal X-ray computed tomography.

Airway compliance is a key factor in understanding lung mechanics and is used as a clinical diagnostic index. Understanding such mechanics in small airways physiologically and clinically is critical. We have determined the "morphometric change" and "localized compliance" of small airways under "near"-physiological conditions; namely, the airways were embedded in parenchyma without dehydration and fixation. Previously, we developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomography system (Sera et al. J Biomech 36: 1587-1594, 2003). In this study, we used this technique to analyze changes in diameter and length of the same small airways ( approximately 150 microm ID) and then evaluated the localized compliance as a function of airway generation (Z). For smaller (<300-microm-diameter) airways, diameter was 36% larger at end-tidal inspiration and 89% larger at total lung capacity; length was 18% larger at end-tidal inspiration and 43% larger at total lung capacity than at functional residual capacity. Diameter, especially at smaller airways, did not behave linearly with V(1/3) (where V is volume). With increasing lung pressure, diameter changed dramatically at a particular pressure and length changed approximately linearly during inflation and deflation. Percentage of airway volume for smaller airways did not behave linearly with that of lung volume. Smaller airways were generally more compliant than larger airways with increasing Z and exhibited hysteresis in their diameter behavior. Airways at higher Z deformed at a lower pressure than those at lower Z. These results indicated that smaller airways did not behave homogeneously.

Animals↗

A fractal analysis of the radial distribution of bronchial capillaries around large airways.

We analyzed published measurements of the bronchial circulation and airway wall (Anderson JC, Bernard SL, Luchtel DL, Babb AL, and Hlastala MP. Respir Physiol Neurobiol 132: 329-339, 2002) and determined that the radial distribution of bronchial capillary cross-sectional area was fractal. We limited our analysis to bronchial capillaries, diameter < or =10 mum, that resided between the epithelial basement membrane and adventitia-alveolar boundary, the airway wall tissue. Thirteen different radial distributions of capillary-to-tissue area were constructed simply by changing the number of annuli (i.e., the annular size) used to form each distribution. For the 13 distributions created, these annuli ranged in size from to of the size of the airway wall area. Radial distributions were excluded from the fractal analysis if the sectioning procedure resulted in an annulus with a radial thickness less than the diameter of a capillary. To determine the fractal dimension for a given airway, the coefficient of variation (CV) for each distribution was calculated, and ln(CV) was plotted against the logarithm of the relative piece area. For airways with diameter >2.4 mm, this relationship was linear, which indicated the radial distribution of bronchial capillary cross-sectional area was fractal with an average fractal dimension of 1.27. The radial distribution of bronchial capillary cross-sectional area was not fractal around airways with diameter <1.5 mm. We speculated on how the fractal nature of this circulation impacts the distribution of bronchial blood flow and the efficiency of mass transport during health and disease. A fractal analysis can be used as a tool to quantify and summarize investigations of the bronchial circulation.

Anatomy, Cross-Sectional↗

Length and curvature of the dog diaphragm.

Transdiaphragmatic pressure is a result of both tension in the muscles of the diaphragm and curvature of the muscles. As lung volume increases, the pressure-generating capability of the diaphragm decreases. Whether decrease in curvature contributes to the loss in transdiaphragmatic pressure and, if so, under what conditions it contributes are unknown. Here we report data on muscle length and curvature in the supine dog. Radiopaque markers were attached along muscle bundles in the midcostal region of the diaphragm in six beagle dogs of approximately 8 kg, and marker locations were obtained from biplanar images at functional residual capacity (FRC), during spontaneous inspiratory efforts against a closed airway at lung volumes from FRC to total lung capacity, and during bilateral maximal phrenic nerve stimulation at the same lung volumes. Muscle length and curvature were obtained from these data. During spontaneous inspiratory efforts, muscle shortened by 15-40% of length at FRC, but curvature remained unchanged. During phrenic nerve stimulation, muscle shortened by 30 to nearly 50%, and, for shortening exceeding 52%, curvature appeared to decrease sharply. We conclude that diaphragm curvature is nearly constant during spontaneous breathing maneuvers in normal animals. However, we speculate that it is possible, if lung compliance were increased and the chest wall and the diameter of the diaphragm ring of insertion were enlarged, as in the case of chronic obstructive pulmonary disease, that decrease in diaphragm curvature could contribute to loss of diaphragm function.

Animals↗

Maximizing quantitative accuracy of lung airway lumen and wall measures obtained from X-ray CT imaging.

To objectively quantify airway geometry from three-dimensional computed tomographic (CT) images, an idealized (circular cross section) airway model is parameterized by airway luminal caliber, wall thickness, and tilt angle. Using a two-dimensional CT slice, an initial guess for the airway center, and the full-width-half-maximum principle, we form an estimate of inner and outer airway wall locations. We then fit ellipses to the inner and outer airway walls via a direct least squares fit and use the major and minor axes of the ellipses to estimate the tilt and in-plane rotation angles. Convolving the airway model, initialized with these estimates, with the three-dimensional scanner point-spread function forms the predicted image. The difference between predicted and actual images is minimized by refining the model parameter estimates via a multidimensional, unconstrained, nonlinear minimization routine. When optimization converges, airway model parameters estimate the airway inner and outer radii and tilt angle. Results using a Plexiglas phantom show that tilt angle is estimated to within +/-4 degrees and both inner and outer radii to within one-half pixel when a "standard" CT reconstruction kernel is used. By opening up the ability to measure airways that are not oriented perpendicular to the scanning plane, this method allows evaluation of a greater sampling of airways in a two-dimensional CT slice than previously possible. In addition, by combining the tilt-angle compensation with the deconvolution method, we provide significant improvement over the previous full-width-half-maximum method for assessing location of the luminal edge but not the outer edge of the airway wall.

Algorithms↗

Commutative saccadic generator is sufficient to control a 3-D ocular plant with pulleys.

One-dimensional models of oculomotor control rely on the fact that, when rotations around only one axis are considered, angular velocity is the derivative of orientation. However, when rotations around arbitrary axes [3-dimensional (3-D) rotations] are considered, this property does not hold, because 3-D rotations are noncommutative. The noncommutativity of rotations has prompted a long debate over whether or not the oculomotor system has to account for this property of rotations by employing noncommutative operators. Recently, Raphan presented a model of the ocular plant that incorporates the orbital pulleys discovered, and qualitatively modeled, by Miller and colleagues. Using one simulation, Raphan showed that the pulley model could produce realistic saccades even when the neural controller is commutative. However, no proof was offered that the good behavior of the Raphan-Miller pulley model holds for saccades different from those simulated. We demonstrate mathematically that the Raphan-Miller pulley model always produces movements that have an accurate dynamic behavior. This is possible because, if the pulleys are properly placed, the oculomotor plant (extraocular muscles, orbital pulleys, and eyeball) in a sense appears commutative to the neural controller. We demonstrate this finding by studying the effect that the pulleys have on the different components of the innervation signal provided by the brain to the extraocular muscles. Because the pulleys make the axes of action of the extraocular muscles dependent on eye orientation, the effect of the innervation signals varies correspondingly as a function of eye orientation. In particular, the Pulse of innervation, which in classical models of the saccadic system encoded eye velocity, here encodes a different signal, which is very close to the derivative of eye orientation. In contrast, the Step of innervation always encodes orientation, whether or not the plant contains pulleys. Thus the Step can be produced by simply integrating the Pulse. Particular care will be given to describing how the pulleys can have this differential effect on the Pulse and the Step. We will show that, if orbital pulleys are properly located, the neural control of saccades can be greatly simplified. Furthermore, the neural implementation of Listing's Law is simplified: eye orientation will lie in Listing's Plane as long as the Pulse is generated in that plane. These results also have implications for the surgical treatment of strabismus.

Algorithms↗

Cloning, ontogenesis, and localization of an atypical uncoupling protein 4 in Xenopus laevis.

Uncoupling protein 1 (UCP1) is the first UCP described. It belongs to the family of mitochondrial carrier proteins and is expressed mainly in brown adipose tissue. Recently, the family of the UCPs has rapidly been growing due to the successive cloning of UCP2, UCP3, UCP4, and UCP5, also called brain mitochondrial carrier protein 1. Phylogenetic studies suggest that UCP1/UCP2/UCP3 on one hand and UCP4/UCP5 on the other hand belong to separate subfamilies. In this study, we report the cloning from a frog Xenopus laevis (Xl) oocyte cDNA library of a novel UCP that was shown, by sequence homology, to belong to the family of ancestral UCP4. This cloning provides a milestone in the gap between Drosophila melanogaster or Caenorhabditis elegans on one hand and mammalian UCP4 on the other. Xl UCP4 is already expressed in the oocyte, being the first UCP described in germ cell lineage. During development, it segregates in the neural cord, and, in the adult, in situ hybridization shows its expression in the neurons and also in the choroid plexus of the brain. By RT-PCR analysis, it was found that Xl UCP4 is present in all the subdivisions of the brain and also that it differs from mammalian UCP4 by a very high relative level of expression in peripheral tissues such as the liver and kidney. The peripheral tissue distribution of Xl UCP4 reinforces the hypothesis that UCP4 might be the ancestral UCP from which other UCPs diverged from.

Amino Acid Sequence↗

Modelling of components of the human middle ear and simulation of their dynamic behaviour.

In order to get a better insight into the function of the human middle ear it is necessary to simulate its dynamic behaviour by means of the finite-element method. Three-dimensional measurements of the surfaces of the tympanic membrane and of the auditory ossicles malleus, incus and stapes are carried out and geometrical models are created. On the basis of these data, finite-element models are constructed and the dynamic behaviour of the combinations tympanic membrane with malleus in its elastic suspensions and stapes with annular ligament is simulated. Natural frequencies and mode shapes are computed by modal analysis. These investigations showed that the ossicles can be treated as rigid bodies only in a restricted frequency range from 0 to 3.5 kHz.

Computer Simulation↗

Identification of parameters for the middle ear model.

This paper presents a method of parameter identification for a finite-element model of the human middle ear. The parameter values are estimated using a characterization of the difference in natural frequencies and mode shapes of the tympanic membrane between the model and the specimens. Experimental results were obtained from temporal bone specimens under sound excitation (300-3,000 Hz). The first 3 modes of the tympanic membrane could be observed with a laser scanning vibrometer and were used to estimate the stiffness parameters for the orthotropic finite-element model of the eardrum. A further point of discussion is the parameter sensitivity and its implication for the identification process.

Acoustic Stimulation↗

Vibro-acoustic modelling of the outer and middle ear using the finite-element method.

In this study, a computer-based method called finite-element analysis is used to predict the forced-frequency response of the ear, with and without an ossicular replacement prosthesis (PORP 0362, Xomed Surgical Products). The method allows visualisation of the dynamical behaviour of the tympanic membrane (TM) and of the ossicles. The finite-element model is fully three-dimensional and includes both ligaments and muscles, and accounts for damping caused by the TM, ligaments, incudostapedial joint and the fluids of the inner ear. For validation, comparison is made with experimental measurements of umbo displacement taken from the literature. The translation and rotation (both anterior-posterior and inferior-superior) of the stapedial footplate are investigated. It is predicted that the translatory motion of the footplate decreases with increasing frequency, except when the frequency of the acoustic signal matches the natural frequencies of the ossicular chain or outer ear canal. The tilting motion of the stapedial footplate is also predicted to depend on frequency of excitation. The presence of a prosthesis changes the dynamical response considerably by shifting the natural frequencies of the ossicular chain. Ratios of stapes motion with and without the prostheses are plotted as a function of frequency allowing this effect to be clearly observed.

Ear, External↗

Determination of the shape and inertia properties of the human auditory ossicles.

This paper describes a method to accurately determine the shape of the human middle ear ossicles. If the density and the shape of a body are known, the inertia properties can be calculated using commercially available software. The inertia properties have been calculated for the stapes and for the incudomalleal unit. Different rectangular views of the stapes and the incudomalleal unit are shown to depict the position of the center of gravity and the position of the principal axes of inertia.

Ear Ossicles↗

Cochlear model with three-dimensional fluid, inner sulcus and feed-forward mechanism.

A three-dimensional model of the guinea pig cochlea using the phase-integral method is presented. This model incorporates the viscous fluid effects in the cochlea, dimensional and material property variation along the cochlear duct and the active feed-forward mechanism of the outer hair cells. Two degrees of freedom of the basilar membrane are considered, which results in two traveling waves propagating along the duct for a given frequency. Basilar membrane response with the active feed-forward mechanism compares favorably with published experimental measurements.

Acoustic Stimulation↗

Migration, matrix production and lamellar bone formation of human osteoblast-like cells in porous titanium implants.

The goal of this study was to characterize growth, mineralization and bone formation of osteoblast-like cells in titanium pore channels of defined diameter. Titanium implants with continuous drill channels of diameters of 300, 400, 500, 600 and 1,000 microm were inserted into human osteoblast-like cell cultures. The ingrowth of the cells into the drill channels was investigated by transmitted-light microscopy and scanning electron microscopy. Immunofluorescence and histological analysis of 15-channel sections of each diameter were used to investigate the growth behavior and the matrix protein patterns. Mineralization was evidenced by Alizarin red staining and high-resolution microradiography. The ingrowth of human osteoblast-like cells in the drill channels occurred in a sequence of four characteristic stages. In stage 1, osteoblast precursor cells adhered to the wall of the channel and migrated three-dimensionally into the channel by forming foot-like protoplasmic processes. For all 15 sample drill channels that were investigated, the cell ingrowth over 20 days amounted on average to 793 microm (+/- 179) into 600-microm-diameter channels, where they migrated significantly faster than in all the other channels. In stage 2, approximately on day 5-7, the osteoblast-like cells began to anchor on the substrate wall by matrix proteins and to build up a dense network of matrix proteins in the drill channel. The mineralization of the extracellular matrix, while depending on cell stimulation, was initiated in stage 3, on average after 4 weeks. In drill channels of a diameter of 1,000 microm the cell growth was incomplete and no mineralization was found by radiological assessment. Starting in week 6, in the drill channels of diameters ranging from 300 to 600 microm, the network of extracellular matrix proteins and osteoblast-like cells began to form an osteon-like structure. Neither the highly developed migration behavior of osteoblastic cells nor the reorganization from a fiber-like matrix to a lamellar structure have so far been described for cell cultures.

Bone Matrix↗

Neuronal labeling in the rat brain and spinal cord from the ovary using viral transneuronal tracing technique.

In the present investigations the viral transneuronal labeling method, which is able to reveal hierarchial chains of central nervous system (CNS) neurons, was applied to identify sites in the CNS connected with the ovary and presumably involved in the control of ovarian functions. Pseudorabies virus was injected into the ovaries of rats and a few days later (at various times after the injection) the spinal cord and brain were examined for virus-infected neurons from the ovary. The virus-labeled nerve cells were identified by immunocytochemistry using polyclonal antiviral antibody. Virus-labeled neurons were detected both in the spinal cord and the brain. In the spinal cord such elements were observed in the intermediolateral cell column, in the dorsal horn close to the marginal zone and in the central autonomic nucleus. In the medulla oblongata and pons, neurons of several nuclei and cell groups (area postrema, nucleus of the solitary tract, dorsal vagal complex, nucleus ambiguus, paragigantocellular nucleus, parapyramidal nucleus, A1, A5 and A7 cell groups, caudal raphe nuclei, locus ceruleus, subceruleus nucleus, Barrington's nucleus, Kölliker-Fuse nucleus) were found to be transneuronally labeled. In the mesencephalon, the ventrolateral part of the periaqueductal gray matter contained virus-labeled neurons. In the diencephalon, a very intensive cell body labeling was observed in the hypothalamic paraventricular nucleus and a few virus-infected neurons could be detected in the lateral and dorsal hypothalamus, in the arcuate nucleus, zona incerta, perifornical area and in the anterior hypothalamus. Concerning the telencephalic structures, virus-labeled cells were found in the bed nucleus of the stria terminalis and in the central amygdala nucleus. These findings provide the first neuromorphological evidence for the existence of a multisynaptic neuronal pathway between the ovary and the CNS, and give a detailed account of the structures involved in this pathway.

Animals↗

Developing a physical model of the human cochlea using micro-fabrication methods.

Advances in micro-machining technology have provided the opportunity to explore possibilities of creating life-sized physical models of the cochlea. The physical model of the cochlea consists of two fluid-filled channels separated by an elastic partition. The partition is micro-machined from silicon and uses a 36-mm linearly tapered polyimide plate with a width of 100 microm at the basal end and 500 microm at the apex to represent the basilar membrane. Thicknesses from 1 to 5 microm have been fabricated. Discrete aluminum fibers (1.5 microm in width) are machined to create direction-dependent properties. A 0.5 x 0.5 mm opening represents the helicotrema. The fluid channels are machined from plexiglas using conventional machining methods. A magnet-coil system excites the fluid channel. Measurements on a model with thickness 4.75 microm show a velocity gain of 4 and phase of 3.5 pi radians at a location 23 mm from the base. Mathematical modeling using a 3-D formulation confirm the general characteristics of the measured response.

Auditory Perception↗