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PubMed1993

Branching airway network models for analyzing high-frequency lung input impedance.

The input impedance of the lung (Zin) at high frequencies (> 100 Hz) is a complex function of the airway geometry and the mechanical properties of the airway walls. To investigate how the purely geometrical factors influence Zin, we measured Zin between 16 and 1,520 Hz in six dried dog lungs with the forced oscillation technique. In each of the lungs we found three resonances, at 36 +/- 5, 648 +/- 100, and 1,289 +/- 150 Hz, and at least two antiresonances (relative maxima in the real part of Zin), at 372 +/- 60 and 1,105 +/- 110 Hz. These data were fit with models featuring a detailed asymmetric branching network of the airways obtained from morphometric data published by Horsfield et al. (J. Appl. Physiol. 52: 21-26, 1982). On the basis of low-frequency (< 100 Hz) data alone, we first established a model of the acini, which was then attached to the end of the airway branching model. With a single scaling factor for the radius and length of the airways, the fit was unsatisfactory. Using sensitivity analysis techniques we determined which candidate variables of the structural model could influence Zin in a manner to improve the fit. We found that a two-parameter model accounting for separate central and peripheral airway diameter scaling provided a reasonable fit to Zin. On average the model required central diameter scaling close to unity (0.94 +/- 0.09), and the peripheral diameter scaling factor was 0.87 +/- 0.38. Over a range of parameter values that we believed were physiologically reasonable (i.e., scaling factors between 0.5 and 1.5), a single set of parameter values was found in all lungs. These results suggest that structurally based inverse models of Zin that include multiple antiresonances may provide information about airway geometry.

Airway Resistance↗
PubMed1997

On the asymmetry of bifurcations in the bronchial tree.

The branching pattern of the conducting airways is significantly asymmetrical in the human, and even more so in other species. Although this asymmetry is believed to have an important effect on air flow and other transport processes in the bronchial tree, both experimental and theoretical studies have predominantly employed symmetrical model bifurcations. In this paper, published morphometric data for four species (human, dog, rat and hamster) is used to calculate the frequencies with which different degrees of asymmetry occur, and to examine the relationships between four of its manifestations, asymmetry of the cross-sectional areas, the lengths, the branching angles and the flow rates of the daughter branches. The observed characteristics are compared with some of the theoretical 'branching laws' which have been proposed. Quantification of the correlations between the different manifestations of asymmetry allows the geometrical characteristics to be specified for a range of realistic asymmetrical bifurcations, for use in either theoretical or experimental studies of transport in the bronchial tree.

Animals↗
PubMed2001

Accuracy requirements for image-guided spinal pedicle screw placement.

STUDY DESIGN: Accuracy requirement analysis for image-guided pedicle screw placement. OBJECTIVES: To derive theoretical accuracy requirements for image-guided spinal pedicle screw placement. SUMMARY OF BACKGROUND DATA: Underlying causes of inaccuracy in image-guided surgical systems and methods for quantifying this inaccuracy have been studied. However, accuracy requirements for specific spinal surgical procedures have not been delineated. In particular, the accuracy requirements for image-guided spinal pedicle screw placement have not been previously reported. METHODS: A geometric model was developed relating spinal pedicle anatomy to accuracy requirements for image-guided surgery. This model was used to derive error tolerances for pedicle screw placement when using clinically relevant screw diameters in the cervical (3.5 mm), thoracic (5.0 mm), and thoracolumbar spine (6.5 mm). The error tolerances were represented as the permissible rotational and translational deviations from the ideal screw trajectory that would avoid pedicle wall perforation. The relevant dimensions of the pedicle model were extracted from existing morphometric data. RESULTS: As anticipated, accuracy requirements were greatest at spinal levels where the relevant screw diameter approximated the dimensions of the pedicle. These requirements were highest for T5, followed in descending order by T4, T7, T6, T3, T12, L1, T8, T11, C4, L2, C3, T10, C5, T2, T9, C6, L3, C2, T1, C7, L4, and L5. Maximum permissible translational/rotational error tolerances ranged from 0.0 mm/0.0 degrees at T5 to 3.8 mm/12.7 degrees at L5. CONCLUSIONS: These results, obtained by mathematical analysis, demonstrate that extremely high accuracy is necessary to place pedicle screws at certain levels of the spine without perforating the pedicle wall. These accuracy requirements exceed the accuracy of current image-guided surgical systems, based on clinical utility errors reported in the literature. In actual use, however, these systems have been shown to improve the accuracy of pedicle screw placement. This dichotomy indicates that other factors, such as the surgeon's visual and tactile feedback, may be operative.

Biomechanical Phenomena↗
PubMed2004

Predictive value of Kushida index and acoustic pharyngometry for the evaluation of upper airway in subjects with or without obstructive sleep apnea.

Acoustic pharyngometry is a relatively new noninvasive method that quantifies geometrically complexed pharyngeal dimensions. Our study aimed to investigate the predictability and usefulness of acoustic pharyngometry in diagnosis of obstructive sleep apnea (OSA), and we developed a prospective clinical trial in 16 subjects without apnea and 54 subjects with apnea. All seventy subjects received polysomnography (PSG) to assess the sleep architecture, including breathing and the degree of apnea hypopnea index. Acoustic pharyngometry was performed in four body positions (sitting, supine, right and left lateral) while awake with tidal breathing in addition to morphometric measurements (Kushida index) of oral cavity. This study shows that the cross-sectional area and volume of the upper airway is smaller in the supine position than any other positions. As well, the oropharyngeal junction area of the supine position is the most predictive parameter to discriminate between subjects with or without OSA. Acoustic pharyngometry can be a clinically useful tool for localizing the narrowed portion of the upper airway and predicting obstructive sleep apnea.

Acoustics↗
PubMed2001

Thin-plate spline analysis of mandibular growth.

The analysis of mandibular growth changes around the pubertal spurt in humans has several important implications for the diagnosis and orthopedic correction of skeletal disharmonies. The purpose of this study was to evaluate mandibular shape and size growth changes around the pubertal spurt in a longitudinal sample of subjects with normal occlusion by means of an appropriate morphometric technique (thin-plate spline analysis). Ten mandibular landmarks were identified on lateral cephalograms of 29 subjects at 6 different developmental phases. The 6 phases corresponded to 6 different maturational stages in cervical vertebrae during accelerative and decelerative phases of the pubertal growth curve of the mandible. Differences in shape between average mandibular configurations at the 6 developmental stages were visualized by means of thin-plate spline analysis and subjected to permutation test. Centroid size was used as the measure of the geometric size of each mandibular specimen. Differences in size at the 6 developmental phases were tested statistically. The results of graphical analysis indicated a statistically significant change in mandibular shape only for the growth interval from stage 3 to stage 4 in cervical vertebral maturation. Significant increases in centroid size were found at all developmental phases, with evidence of a prepubertal minimum and of a pubertal maximum. The existence of a pubertal peak in human mandibular growth, therefore, is confirmed by thin-plate spline analysis. Significant morphological changes in the mandible during the growth interval from stage 3 to stage 4 in cervical vertebral maturation may be described as an upward-forward direction of condylar growth determining an overall "shrinkage" of the mandibular configuration along the measurement of total mandibular length. This biological mechanism is particularly efficient in compensating for major increments in mandibular size at the adolescent spurt.

Adolescent↗
PubMed1988

Stochastic morphological model of the rat lung.

The laboratory rat is often used as a human surrogate in aerosol inhalation studies. Here we present a new stochastic model for the rat lung analogous to that for the human lung. Morphometric data on the tracheobronchial geometry of the rat lung provided by the Lovelace Inhalation Toxicology Research Institute were analyzed. The results of this statistical analysis reveal significant differences in diameters and branching angles between major and minor daughter tubes starting from the same bifurcation. As a consequence of the more monopodial airway branching in the rat lung compared to the more dichotomous structure of the human lung, we recommend classifying the rat lung airways by their diameters and not by generation numbers. The distributions of the geometric airway parameters and the correlations among them will be used for Monte Carlo deposition calculations.

Animals↗
PubMed2002

Modeling combined transport of water and test macromolecules across the glomerular capillary barrier: dynamics of the permselectivity.

The structure, function, and composition of the basement membrane of the glomerular capillaries of the mammalian kidney have been extensively studied, in light of the membrane's important physiological role in glomerular filtration of macromolecules and of its frequent involvement in renal diseases. An analytical mathematical model, based on the fiber matrix theory, was developed to describe the dynamics of the permselective function of the glomerular capillary barrier using mainly its hemodynamic and morphometric variables. The glomerular basement membrane was represented as a homogeneous three-dimensional meshwork of fibers of uniform length (L(f)), radius (R(f)), and packing density (N(fv)) and characterized by a local Darcy permeability (a measure of the intrinsic hydraulic conductance of the glomerular basement membrane). The model was appropriate for simulating in vivo fractional clearance data of neutral test macromolecules from an experimental rat model. We believe that the L(f) and R(f) best-fit numerical values, characterizing a glomerular basement membrane geometrical arrangement, may represent diagnostic measures for renal function in health and disease. That is, these parameters may signify new insights for the diagnosis of some human nephropathies and possibly may explain the beneficial effects and/or sites of action of some pharmacological modifiers (e.g., angiotensin converting enzyme inhibitors).

Algorithms↗
PubMed1999

Technical Advance: Confocal measurement of the three-dimensional size and shape of plant parenchyma cells in a developing fruit tissue.

Parenchyma cells from the inner mesocarp of a grape berry (Vitis vinifera L. cv. Chardonnay) were visualised in three-dimensions within a whole mount of cleared, stained tissue using confocal laser scanning microscopy and digital image reconstruction. The whole berry was fixed, bisected longitudinally, cleared in methyl salicylate, stained with safranin O and mounted in methyl salicylate. Optical slices were collected at 1.0 µm intervals to a depth of 150 µm. Neighbouring z-series were joined post-collection to double the field-of-view. Attenuation at depth of the fluorescent signal from cell walls was quantified and corrected. Axial distortion due to refractive index mismatch between the immersion and mounting media was calibrated using yellow-green fluorescent microspheres and corrected. Transmission electron microscopy was used to correct fluorescent measurements of cell wall thickness. Digital image reconstructions of wall-enclosed spaces enabled cells to be rendered as geometric solids of measurable surface area and volume. Cell volumes within the inner mesocarp tissue of a single grape berry exhibited a 14-fold range, with polysigmoidal distribution and groupings around specific size classes. Cell shape was irregular and the planes of contact were rarely flat or simple. Variability in cell shape was indicated by the range in surface area to volume ratios, from 0.080 to 0.198 µm-1. Structural detail at the internal surface of the cell wall was apparent. The technique is applicable to a wide range of morphometric analyses in plant cell biology, particularly developmental studies, and reveals details of cell size and shape that were previously unattainable.

Journal Article↗
PubMed2004

Stochastic model of particle clearance in human bronchial airways.

A stochastic bronchial clearance model, based on a stochastic morphometric model of the human bronchial tree, has been developed, which simulates the combined action of fast and slow bronchial clearance mechanisms by Monte Carlo methods. To model fast bronchial clearance, mucus velocities in individual airways were based on a correlation between mucus velocity and airway diameter, considering conservation of mucus flow. In addition, mucus transport was assumed to be delayed at bronchial bifurcation zones. The size dependence of the slow bronchial clearance phase was considered by a linear relationship between the slow bronchial clearance fraction, f(s), and the geometric particle diameter, derived from bolus inhalation experiments. Potential variations of f(s) from proximal to distal airway generations were simulated by five different scenarios, which allocated slow bronchial clearance to successively peripheral bronchial regions. Alveolar clearance, which contributes only to longterm particle retention, was modeled by transfer rates supplied by the ICRP respiratory tract model. To test the different components of the clearance model, modeling predictions were compared with experimental retention data from bolus inhalation experiments, using various particle sizes and bolus front depths, as well as from slow inhalation experiments, with a flow rate of only 0.045 L sec(-1). The overall good agreement between modeling results and experimental data indicate that the present model correctly predicts bronchial clearance, suggesting that slow bronchial clearance mechanisms are most effective in smaller bronchial airways.

Biological Transport↗
PubMed1989

[Computerized reconstruction of the spatial organization of enamel rods].

Morphometric reliefs on the enamel of the lower incisor of albino rats in correspondence with the prism compaction area during the first third of the ameloblastic modulation phase have been carried out. The reliefs were done on the longitudinal and median fracture plane and on the transversal fracture plane 8 mm from the cervical ansa. Measurements of the diameters of the honeycomb pits were carried out during the deposition phase, following removal of the ameloblastic coat. The data obtained were fed into an Apple Macintosh 512K/800 computer to obtain the geometric reconstruction of an isolated prism, the relations between each portion of the prism and the respective pits and a graphic example of the architectural organization of the enamel. It was shown that each prism consists of three distinct portion, just as there are three types of honeycomb pit. The external orifice of each pit is complementary to the interdigitant portion of the Tomes process, so the study of the pits may be used to evaluate the spatial orientation of the rods and not the morphology of their section. Cross-over between rows of contiguous rods occurs throughout the thickness of the internal enamel layer. The enamel possesses a particularly suitable structure for the transformation of surface type tangential forces into stresses or prevalently compression type.

Amelogenesis↗
PubMedDate not supplied

A probabilistic ribbon model for shape analysis of the cerebral sulci: application to the central sulcus.

PURPOSE: An approach for quantifying the shapes of the cerebral sulci is presented, utilizing a probabilistic geometric model, and it is applied to the central sulcus. METHOD: The geometric structure of the central sulcus is determined from a set of outlines on cross-sectional images and is used by a procedure that automatically labels the major crest lines, i.e., curves of locally maximal curvature, along the sulcus. An automated procedure then determines a parametric representation of the central sulcus that is consistent across individuals, in that it assigns the same parametric coordinates to corresponding regions of the sulcus. RESULTS: The method is applied to the central sulci from 20 subjects. The use of this shape representation in cortical morphometric analysis applications is demonstrated, in particular in obtaining local depth and curvature measurements of a sulcus as well as in determining average shapes and variability. CONCLUSION: With this method, we were able to build parametric representations of the sulcal ribbons by preserving anatomical homologies.

Anatomy, Cross-Sectional↗
PubMed1996

Morphometric variation in Plio-Pleistocene hominid distal humeri.

The magnitude and meaning of morphological variation among Plio-Pleistocene hominid distal humeri have been recurrent points of disagreement among paleoanthropologists. Some researchers have found noteworthy differences among fossil humeri that they believe merit taxonomic separation, while others question the possibility of accurately sorting these fossils into different species and/or functional groups. Size and shape differences among fossil distal humeri are evaluated here to determine whether the magnitude and patterns of these differences can be observed within large-bodied, living hominoids. Specimens analyzed in this study have been assigned to various taxa (Australopithecus afarensis, A. africanus, A. anamensis, Paranthropus, and early Homo) and include AL 288-1m, AL 288-1s, AL 137-48a, AL 322-1, Gomboré IB 7594, TM 1517, KNM-ER 739, KNM-ER 1504, KMN-KP 271 (Kanapoi), and Stw 431. Five extant hominoid populations are sampled to provide a standard by which to consider differences found between the fossils, including two modern human groups (Native American and African American), one group of Pan troglodytes, and two subspecies of Gorilla gorilla (G.g. beringei, G.g. gorilla). All possible pairwise d values (average Euclidena distances) are calculated within each of the reference populations using an exact randomization procedure. This is done using both raw linear measurements as well as scale-free shape data created as ratios of each measurement to the geometric mean. Differences between each pair of fossil humeri are evaluated by comparing their d values to the distribution of d values found within each of the reference populations. Principal coordinate analysis and an unweighted pair group method with arithmetic averages (UPGMA) cluster analysis are utilized to further assess similarities and differences among the fossils. Finally, canonical variates analysis and discriminant analysis are employed using all hominoid samples in order to control for correlations among variables and to identify those variables that discriminate among groups; possible affinities of individual fossils with specific extant species are also examined. The largest size differences, those between the small Hadar specimens and the two largest fossils (KNM-ER 739, IB 7594), can be accommodated easily within the ranges of variation of the two Gorilla samples, but are extreme relative to the other reference samples. The d values between most of the fossils based on shape data, with the notable exception of those associated with KNM-ER 739 and KNM-ER 1504, can be sampled safely within all five reference samples. Subsequent analyses further support the inference that KNM-ER 739 and KNM-ER 1504 are different from the other hominid humeri and possess a unique total morphometric pattern. In overall shape, the distal humeri of the other fossils (non-Koobi Fora) are most similar to living chimpanzees. The distal humerus of Paranthropus from Kromdraai (TM 1517e) is most similar to one of the Hadar specimens of A. afarensis (AL 137-48a), whereas the first specimen of A. africanus from Sterkfontein (Stw 431) is not closely linked to any of the other australopithecines. The A. anamensis humerus from Kanapoi exhibits no special affinities to A. afarensis or to modern humans.

Animals↗
PubMed2005

Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels.

Studies of the origin of pulmonary blood flow heterogeneity have highlighted the significant role of vessel branching structure on flow distribution. To enable more detailed investigation of structure-function relationships in the pulmonary circulation, an anatomically based finite element model of the arterial and venous networks has been developed to more accurately reflect the geometry found in vivo. Geometric models of the arterial and venous tree structures are created using a combination of multidetector row X-ray computed tomography imaging to define around 2,500 vessels from each tree, a volume-filling branching algorithm to generate the remaining accompanying conducting vessels, and an empirically based algorithm to generate the supernumerary vessel geometry. The explicit generation of supernumerary vessels is a unique feature of the computational model. Analysis of branching properties and geometric parameters demonstrates close correlation between the model geometry and anatomical measures of human pulmonary blood vessels. A total of 12 Strahler orders for the arterial system and 10 Strahler orders for the venous system are generated, down to the equivalent level of the terminal bronchioles in the bronchial tree. A simple Poiseuille flow solution, assuming rigid vessels, is obtained within the arterial geometry of the left lung, demonstrating a large amount of heterogeneity in the flow distribution, especially with inclusion of supernumerary vessels. This model has been constructed to accurately represent available morphometric data derived from the complex asymmetric branching structure of the human pulmonary vasculature in a form that will be suitable for application in functional simulations.

Adult↗
PubMed1984

The shift of Schlemm's canal during the remodelling of the chamber angle in the developing rat eye.

A morphometric analysis of the pre- and postnatal development of the tissue components of the chamber angle was performed in the rat. One eye of each of five weight-matched littermates was evaluated by light microscopy at the following time points: prenatal days 18, 21; day 0 (= day of birth); postnatal days 5, 10, 15, 20, 40, 60. Composite photomicrographs of the entire chamber angle area at a magnification of 5776 X were prepared from each eye under investigation. Developmental stages were analysed by direct measurements between selected anatomical reference points and by computerised calculations that were obtained from geometrical constructions on the photomicrographs. A statistical analysis was performed on the correlation of measurements and calculations with the entire investigated time period. This way, a modification of the allometric growth analysis was developed. Our data indicate that Schlemm's canal undergoes a distinct forward shift from a position next to the peripheral retina towards the chamber angle recess. This forward shift is paralleled by a considerable growth of the ciliary body. In contrast, an arrest of growth of tissues between the end of Descemet's membrane and the anterior end of Schlemm's canal is observed. Thus, with the anterior chamber angle components remaining constant and the posterior ones growing in the meridional diameter, a forward and internal shift of Schlemm's canal results.

Animals↗
PubMed1975

Pattern formation in ciliary organelle systems of ciliated protozoa.

Genetic, morphometric, and microsurgical investigations of the pattern of ciliary organells in ciliate protozoa support the view that ther are two types of developmental process responsible for the positioning of these organelles. The first is exemplified by the propagation of ciliary rows through localized addition of new ciliary units along the axis of the row, a process which is responsible for the maintenance of the pre-existing number of rows in clonal lineages over a large number of fissions. The second is illustrated by two examples: (1) Ciliary units are distributed among ciliary rows of Euplotes minuta according to an invariant geometrical pattern that is independent both of the total number of units and of the number of rows. (2) Microsurgical alteration of the topographical contours of a related ciliate, Paraurostyla weissei, brings about a shift in the sites of formation of certain specific ciliary rudiments to new positions that are determined in relation to the newly constructed form. The two modes of pattern formation in ciliates are discussed from both genetic and developmental viewpoints. The localized positional mechanisms within the ciliary rows allow for a 'configurational heredity' shich is, however, subject to constraints of nuclear genic control both of the stable range of number of rows and of the positioning mechanism itself. The large-scale systems of pattern determination are probably more closely related to the field properties of developing multicellular organisms. In ciliates such systems are almost certainly located in the cell membrane or in the relatively fixed cytoplasmic layer just beneath the membrane.

Animals↗
PubMed1995

Fractal and integer-dimensional geometric analysis of pigmented skin lesions.

Accurate in vivo diagnosis of pigmented skin lesions is required to identify and excise malignant melanomas but to avoid unnecessary excision of benign lesions; the published rates of clinical diagnostic accuracy are about 65%. This study investigates whether fractal geometric analysis of pigmented skin lesions can improve the rate of diagnostic accuracy. Forty-two pigmented skin lesions (15 malignant melanomas, 21 melanocytic naevi, and 6 basal cell papillomas) on patients attending a dermatology clinic were photographed, excised, and sent for histopathological examination. The fractal dimension of the boundary of the lesions was measured using a box-counting method implemented on a microcomputer-based image analysis system. Euclidean geometric parameters were also measured. The fractal dimension of all the lesions was greater than the topological dimension (one), indicating that there is a fractal element to their structure. Using all measured parameters together, multivariate linear discriminant analysis produced a confusion matrix in which 45% of the lesions were assigned to the correct diagnostic group with a kappa statistic of 0.33. There was no significant difference between the fractal dimension of melanocytic naevi and that of malignant melanomas (p = 0.18). Although pigmented skin lesions have a fractal element to their structure, the fractal dimension of their boundaries is not a useful morphometric discriminant between the diagnostic groups of malignant melanomas and benign melanocytic naevi.

Algorithms↗
PubMed1995

An important role of tachykinins in ozone-induced airway hyperresponsiveness.

We investigated the role of tachykinins in ozone-induced airway hyperresponsiveness (AHR) in guinea pigs. Airway responsiveness was assessed by determining the provocative concentration (PC200) of a histamine aerosol. Ozone exposure (3.0 ppm for 2 h) caused significant AHR. For vehicle-pretreated animals, the geometric mean pre- and post-ozone PC200 values were 0.87 mg/ml (GSEM 1.33) and 0.11 mg/ml (GSEM 1.17), respectively. Tachykinin depletion by capsaicin (50 mg/kg) prevented this AHR, whereas it did not alter pre-ozone airway responsiveness. The PC200 was 0.36 mg/kg (GSEM 1.64) before ozone and 0.24 mg/kg (GSEM 1.72) after ozone for this group. Ozone also caused a significant increase in neutrophils in bronchoalveolar lavage fluid (BALF) compared with BALF from a normal control group (1.71 +/- 0.69 versus 0.07 +/- 0.02 x 10(5)/ml, respectively). Capsaicin pretreatment attenuated this neutrophil influx (0.23 +/- 0.16 x 10(5)/ml). Morphometric assessment revealed edema of the bronchiolar wall after ozone exposure, which was not observed in the capsaicin group. BAL and morphometry revealed that the degree of ozone-induced epithelial desquamation was similar in both groups. These results suggest that tachykinins may be responsible for ozone-induced AHR, possibly via neurogenic inflammation.

Animals↗
PubMed1991

Atherometric system. A suitable methodology to characterize atherosclerotic lesions in any artery or group of patients.

The atherometric system (AS) is a set of methods and procedures derived from a group of interdependent and strongly interrelated variables, resulting from certain biophysical (rheological, geometrical, hemodynamic) and mathematical considerations and reasonings. The variables of the AS are divided into two groups: the arterial and the organ-related variables. Each of them is subdivided into (a) descriptive variables, since correct use of them and their different combinations will enable proper examination of all pathomorphological and pathophysiological alterations to arteries and to atherosclerotically affected organs and (b) weighting indices which yield accurate prediction of the atherosclerotic process, its severity and consequences. The AS is a tool for medical and biological investigations in relation with any vascular disease due to atherosclerosis. It is useful for etiological, pathogenetical, pathomorphological, morphometrical, pathophysiological, biochemical, and epidemiological studies. Also it has proved its facilities for experimental studies with a view to elucidating possible effects of therapeutic action and effectiveness of pharmaceuticals to which anti-atherogenetic or anti-atherosclerotic activities are attributed.

Arterial Occlusive Diseases↗