Mathematical model of pressure-related changes in stenosis cross-sectional area during the cardiac cycle

1992 ◽  
Author(s):  
Maria Siebes
Keyword(s):  
Mathematical Model ◽  
Cardiac Cycle ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional

scholarly journals Formation of Annual Ring Eccentricity in Coarse Roots within the Root Cage of Pinus ponderosa Growing on Slopes

Plants ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 181 ◽  
Author(s):  
Antonio Montagnoli ◽  
Bruno Lasserre ◽  
Gabriella Sferra ◽  
Donato Chiatante ◽  
Gabriella Stefania Scippa ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Root System ◽  
Pinus Ponderosa ◽  
Cross Sectional Area ◽  
Root Segment ◽  
Mechanical Forces ◽  
Sectional Area ◽  
Coarse Roots ◽  
Cross Sectional ◽  
Branching Point

The coarse roots of Pinus ponderosa included in the cage are the ones most involved in tree stability. This study explored the variations in traits, such as volume, cross-sectional area, and radius length of cage roots, and used those data to develop a mathematical model to better understand the type of forces occurring for each shallow lateral root segment belonging to different quadrants of the three-dimensional (3D) root system architecture. The pattern and intensity of these forces were modelled along the root segment from the branching point to the cage edge. Data of root cage volume in the upper 30 cm of soil showed a higher value in the downslope and windward quadrant while, at a deeper soil depth (>30 cm), we found higher values in both upslope and leeward quadrants. The analysis of radius length and the cross-sectional area of the shallow lateral roots revealed the presence of a considerable degree of eccentricity of the annual rings at the branching point and at the cage edge. This eccentricity is due to the formation of compression wood, and the eccentricity changes from the top portion at the branching point to the bottom portion at the cage edge, which we hypothesize may be a response to the variation in mechanical forces occurring in the various zones of the cage. This hypothesis is supported by a mathematical model that shows how the pattern and intensity of different types of mechanical forces are present within the various quadrants of the same root system from the taproot to the cage edge.

Tensile strength of partially filled FFF printed parts: meta modelling

2017 ◽  
Vol 23 (3) ◽  
pp. 524-533 ◽  
Author(s):  
Shahrain Mahmood ◽  
A.J. Qureshi ◽  
Kheng Lim Goh ◽  
Didier Talamona
Keyword(s):  
Mathematical Model ◽  
Tensile Strength ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Fused Filament Fabrication ◽  
Cross Sectional ◽  
Content Type ◽  
Test Pieces ◽  
Solid Part ◽  
The Cross

Purpose This paper aims to investigate the tensile strength of partially filled fused filament fabrication (FFF) printed parts with respect of cross-sectional geometry of partially filled test pieces. It was reported in the authors’ earlier work that the ultimate tensile strength (UTS) is inversely proportional to the cross-sectional area of a specimen, whereas the number of shells and infill density are directly proportional to the UTS with all other parameters being held constant. Here, the authors present an in-depth evaluation of the phenomenon and a parametric model that can provide useful estimates of the UTS of the printed part by accounting for the dimensions of the solid floor/roof layers, shells and infills. Design/methodology/approach It was found that partially filled FFF printed parts consist of hollow sections. Because of these voids, the conventional method of determining the UTS via the gross cross-sectional area given by A = b × h, where b and h are the width and thickness of the printed part, respectively, cannot be used. A mathematical model of a more accurate representation of the cross-sectional area of a partially filled part was formulated. Additionally, the model was extended to predict the dimensions as well as the lateral distortion of the respective features within a printed part using input values from the experimental data. Findings The result from this investigation shows that to calculate the UTS of a partially filled FFF part, the calculation based on the conventional approach is not sufficient. A new meta-model is proposed which takes into account the geometry of the internal features to give an estimate of the strength of a partially filled printed part that is closer to the value of the strength of the material that is used for fabricating the part. Originality/value This paper investigates the tensile strength of a partially filled FFF printed part. The results have shown that the tensile strength of a partially filled part can be similar to that of a solid part, at a lower cost: shorter printing time and lower material usage. By taking into account the geometries within a printed part, the cross-sectional area can be accurately represented. The mathematical model which was developed would aid end-users to predict the tensile strength for a given set of input values of the process parameters.

Left Ventricular Function: Correlation With Deformation of the Myocardium

1978 ◽  
Vol 100 (2) ◽  
pp. 99-104 ◽  
Author(s):  
C. A. Phillips ◽  
E. S. Grood ◽  
R. E. Mates ◽  
H. L. Falsetti
Keyword(s):  
Cardiac Cycle ◽  
Volume Overload ◽  
Left Ventricular ◽  
Area Ratio ◽  
Equatorial Region ◽  
Cross Sectional Area ◽  
Tissue Deformation ◽  
Sectional Area ◽  
Cross Sectional ◽  
Congestive Cardiomyopathy

The amount of local tissue deformation at the equatorial region of the left ventricle is quantitated by the ratio of the instantaneous cross-sectional area of a tissue element to the cross-sectional area at end-diastole. The area ratio, AR, was computed for the circumferential and longitudinal, apex to base, direction throughout the cardiac cycle from catheterization and cineangiographic data on 36 patients. The patients were divided into four groups: normal left ventricualr function—15, compensated volume overload—6, decompensated volume overload—9, and congestive cardiomyopathy—6. The peak longitudinal area ratio was elevated in the compensated group (P <0.001) and not statistically significant from normal in the decompensated group. A larger fraction of the cardiac cycle was required to reach the peak longitudinal (p <0.01) and circumferential (p <0.05) area ratio in the compensated group. The volume overload compensatory process apparently involves a change in the relative magnitude and timing of tissue deformation. The hypo-contractile ventricle was characterized by a reduction in the sum of the logitudinal and circumferential area ratios, which for all six patients in the congestive cardiomyopathy group, had a value less than any of the other thirty patients.

Analysis of Coronary Sinus Motion and Cross-Sectional Area Using Cine MRI

2010 ◽  
Author(s):  
Pierre Watson ◽  
Jonathan Suever ◽  
John Oshinski
Keyword(s):  
Magnetic Resonance ◽  
Coronary Sinus ◽  
Cardiac Cycle ◽  
Cross Sectional Area ◽  
Cine Mri ◽  
Sectional Area ◽  
Cross Sectional ◽  
Coronary Veins ◽  
Coronary Magnetic Resonance

To quantify periods of low motion of the coronary veins during the cardiac cycle. Coronary magnetic resonance venograms (cMRV) require that images be acquired during periods of low motion.

scholarly journals MODELING OF REDUCTION IN THE CROSS-SECTIONAL AREA OF STEEL REINFORCEMENT IN CONCRETE UNDER THE ACTION OF CORROSIVE ENVIRONMENT

2017 ◽  
Vol 21 (1) ◽  
pp. 43-49 ◽  
Author(s):  
G. A. Smolyago ◽  
A. V. Dronov ◽  
N. V. Frolov
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Steel Reinforcement ◽  
Cross Sectional Area ◽  
Testing Time ◽  
Corrosive Environment ◽  
Sectional Area ◽  
Cross Sectional ◽  
Rc Structures ◽  
The Cross

Process of depassivation of steel in concrete under the action of chloride corrosive environment is considered. Method of durable testing of bended reinforced concrete structures during corrosive period is described. Results of experimental research in steel reinforcement corrosion in reinforced concrete beams under the action of corrosive environment are described in the article. The diagram of corrosive potential changes during the testing time is given in the article. Measurements of corrosion potential were carried out by the corrosion analyzing instrument. Analysis of corrosive potential changes during the testing time was carried out. Main properties and features of chloride corrosion process and damages are considered. Corrosive pits on the surface of the reinforcement bars were studied. Measurements of depth and diameter of the corrosive pits were carried out. Stress-strain diagrams of steel after the corrosive period were obtained. Mathematical model of reduction in the cross-sectional area of steel reinforcement in concrete under the action of corrosive chloride environment is suggested. This model allows to consider effect of concrete cover thickness on depth of corrosion. Comparison of experimental results and theoretical calculations reveals high accuracy of corrosion damage definition by given mathematical model. The ways to use the model are suggested. The given model allows to consider corrosive damages of steel rebars by definition of cross-section area losses and may be used in calculations of strength and deformations of RC structures. It’s possible to use the model for prediction of the remaining strength life of RC structures.

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.

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