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

2005 ◽  
Vol 98 (3) ◽  
pp. 850-855 ◽  
Author(s):  
Joseph C. Anderson ◽  
Albert L. Babb ◽  
Michael P. Hlastala
Keyword(s):  
Fractal Dimension ◽  
Radial Distribution ◽  
Fractal Analysis ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Airway Wall ◽  
Cross Sectional ◽  
Wall Area ◽  
Bronchial Circulation ◽  
Epithelial Basement Membrane

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 ≤10 μm, 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.

scholarly journals Computed tomographic measures of airway morphology in smokers and never-smoking normals

2014 ◽  
Vol 116 (6) ◽  
pp. 668-673 ◽  
Author(s):  
G. R. Washko ◽  
A. A. Diaz ◽  
V. Kim ◽  
R. G. Barr ◽  
M. T. Dransfield ◽  
...  
Keyword(s):  
Chronic Obstructive Pulmonary Disease ◽  
Chronic Obstructive ◽  
Sectional Area ◽  
Airway Wall ◽  
Cross Sectional ◽  
Obstructive Pulmonary Disease ◽  
Wall Area ◽  
Computed Tomographic ◽  
Airway Morphology ◽  
Central Airway

Bronchial wall area percent (WA% = 100 × wall area/total bronchial cross sectional area) is a standard computed tomographic (CT) measure of central airway morphology utilized in smokers with chronic obstructive pulmonary disease (COPD). Although it provides significant clinical correlations, the range of reported WA% is narrow. This suggests limited macroscopic change in response to smoking or that remodeling proportionally affects the airway wall and lumen dimensions such that their ratio is preserved. The objective of this study is to assess central airway wall area (WA), lumen area (Ai), and total bronchial area (Ao) from CT scans of 5,179 smokers and 92 never smoking normal subjects. In smokers, WA, Ai, and Ao were positively correlated with forced expiratory volume in 1 s (FEV1) expressed as a percent of predicted (FEV1%), and the WA% was negatively correlated with FEV1% ( P < 0.0001 for all comparisons). Importantly, smokers with lower FEV1% tended to have airways of smaller cross-sectional area with lower WA. The increases in the WA% across GOLD stages of chronic obstructive pulmonary disease (COPD) can therefore not be due to increases in WA. The data suggest two possible origins for the WA% increases: 1) central airway remodeling resulting in overall reductions in airway caliber in excess of the decreased WA or 2) those with COPD had smaller native airways before they began smoking. In both cases, these observations provide an explanation for the limited range of values of WA% across stages of COPD.

Conservation of bronchiolar wall area during constriction and dilation of human airways

1997 ◽  
Vol 82 (3) ◽  
pp. 954-958 ◽  
Author(s):  
R. W. Mitchell ◽  
E. Rühlmann ◽  
H. Magnussen ◽  
N. M. Muñoz ◽  
A. R. Leff ◽  
...  
Keyword(s):  
Smooth Muscle ◽  
Smooth Muscle Contraction ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Wall Area ◽  
Total Cross Sectional Area ◽  
Human Airways ◽  
Contraction And Relaxation

Mitchell, R. W., E. Rühlmann, H. Magnussen, N. M. Muñoz, A. R. Leff, and K. F. Rabe. Conservation of bronchiolar wall area during constriction and dilation of human airways. J. Appl. Physiol. 82(3): 954–958, 1997.—We assessed the effect of smooth muscle contraction and relaxation on airway lumen subtended by the internal perimeter ( A i) and total cross-sectional area ( A o) of human bronchial explants in the absence of the potential lung tethering forces of alveolar tissue to test the hypothesis that bronchoconstriction results in a comparable change of A iand A o. Luminal area (i.e., A i) and A owere measured by using computerized videomicrometry, and bronchial wall area was calculated accordingly. Images on videotape were captured; areas were outlined, and data were expressed as internal pixel number by using imaging software. Bronchial rings were dissected in 1.0- to 1.5-mm sections from macroscopically unaffected areas of lungs from patients undergoing resection for carcinoma, placed in microplate wells containing buffered saline, and allowed to equilibrate for 1 h. Baseline, A o[5.21 ± 0.354 (SE) mm2], and A i(0.604 ± 0.057 mm2) were measured before contraction of the airway smooth muscle (ASM) with carbachol. Mean A inarrowed by 0.257 ± 0.052 mm2in response to 10 μM carbachol ( P = 0.001 vs. baseline). Similarly, A onarrowed by 0.272 ± 0.110 mm2in response to carbachol ( P = 0.038 vs. baseline; P = 0.849 vs. change in A i). Similar parallel changes in cross-sectional area for A iand A owere observed for relaxation of ASM from inherent tone of other bronchial rings in response to 10 μM isoproterenol. We demonstrate a unique characteristic of human ASM; i.e., both luminal and total cross-sectional area of human airways change similarly on contraction and relaxation in vitro, resulting in a conservation of bronchiolar wall area with bronchoconstriction and dilation.

Anatomy and Properties of Japanese Hardwoods I. Variation of Fibre Dimensions and Tissue Proportions and their Relation to Basic Density

IAWA Journal ◽  
1991 ◽  
Vol 12 (4) ◽  
pp. 419-424 ◽  
Author(s):  
Shinji Fujiwara ◽  
Kazuhiko Sameshima ◽  
Kenichi Kuroda ◽  
Norio Takamura
Keyword(s):  
Wall Thickness ◽  
Fibre Length ◽  
Basic Density ◽  
Cross Sectional Area ◽  
Wall Material ◽  
Sectional Area ◽  
Cross Sectional ◽  
Wall Area ◽  
Fibre Wall ◽  
Area Percentage

Variations of tissue proportions and fibre dimensions (fibre length, fibre cross sectional area, fibre wall thickness, fibre wall area, percentage of fibre wall area) of 50 Japanese hardwoods are compared. The fibre cross sectional area showed large variations as compared to fibre length. There is no significant correlation between fibre cross sectional area and fibre wall thickness.The multiple regression analysis showed that fibre wall thickness, percentage of fibre wall material and ray volume are the parameters most closely correlated with basic density.

Pelvic Canal Narrowing Caused by Triple Pelvic Osteotomy in the Dog

1994 ◽  
Vol 07 (03) ◽  
pp. 110-113 ◽  
Author(s):  
D. L. Holmberg ◽  
M. B. Hurtig ◽  
H. R. Sukhiani
Keyword(s):  
Postoperative Complications ◽  
Pelvic Osteotomy ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Canal Width ◽  
Operative Complications ◽  
Post Operative Complications

SummaryDuring a triple pelvic osteotomy, rotation of the free acetabular segment causes the pubic remnant on the acetabulum to rotate into the pelvic canal. The resulting narrowing may cause complications by impingement on the organs within the pelvic canal. Triple pelvic osteotomies were performed on ten cadaver pelves with pubic remnants equal to 0, 25, and 50% of the hemi-pubic length and angles of acetabular rotation of 20, 30, and 40 degrees. All combinations of pubic remnant lengths and angles of acetabular rotation caused a significant reduction in pelvic canal-width and cross-sectional area, when compared to the inact pelvis. Zero, 25, and 50% pubic remnants result in 15, 35, and 50% reductions in pelvic canal width respectively. Overrotation of the acetabulum should be avoided and the pubic remnant on the acetabular segment should be minimized to reduce postoperative complications due to pelvic canal narrowing.When performing triple pelvic osteotomies, the length of the pubic remnant on the acetabular segment and the angle of acetabular rotation both significantly narrow the pelvic canal. To reduce post-operative complications, due to narrowing of the pelvic canal, overrotation of the acetabulum should be avoided and the length of the pubic remnant should be minimized.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Changes in the parameters of nasal breathing and parameters of the upper respiratory tract during orthognathic operations in patients with II and III skeletal class of jaw anomalies

2020 ◽  
pp. 22-27
Author(s):  
S.Sh. Gammadaeva ◽  
M.I. Misirkhanova ◽  
A.Yu. Drobyshev
Keyword(s):  
Respiratory Tract ◽  
Nasal Cavity ◽  
Nasal Septum ◽  
Cross Sectional Area ◽  
Upper Respiratory Tract ◽  
Sectional Area ◽  
Nasal Breathing ◽  
Cross Sectional ◽  
Skeletal Class ◽  
Upper Respiratory

The study analyzed the functional parameters of nasal breathing, linear parameters of the nasal aperture, nasal cavity and nasopharynx, volumetric parameters of the upper airways in patients with II and III skeletal class of jaw anomalies before and after orthognathic surgery. The respiratory function of the nose was assessed using a rhinomanometric complex. According to rhinoresistometry data, nasal resistance and hydraulic diameter were assessed. According to the data of acoustic rhinometry, the minimum cross-sectional area along the internal valve, the minimum cross-sectional area on the head of the inferior turbinate and nasal septum and related parameters were estimated. According to the CBCT data, the state of the nasal septum, the inferior turbinates, the nasal aperture, the state of the nasal cavity, and the linear values of the upper respiratory tract (nasopharynx) were analyzed. The patients were divided into 4 groups according to the classification of the patency of the nasal passages by

Unequal Probability Scheme for Fruit Count in a Guava Tree

2016 ◽  
Vol 3 (4) ◽  
Author(s):  
R. C. BHARATI
Keyword(s):  
Cross Sectional Area ◽  
Equal Probability ◽  
Sampling Scheme ◽  
Research Station ◽  
Sectional Area ◽  
Cross Sectional ◽  
Unequal Probability ◽  
Selection Probabilities ◽  
Horticultural Research ◽  
Number Of Branches

Data on fruit count corresponding to primary, secondary and tertiary branches of a randomly selected guava CV. Allahabad Safeda were recorded from the guava orchard of Horticultural Research Station, Birauli. The proposed sampling scheme in which the selection probabilities are based on length of braches between two forking points was compared with equal probability(PE), probability proportional to the number of branches(PPN), probability proportional to the cross sectional area (PPA) and probability proportional to volume (PPV) method of sampling and found to be more efficient.

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