Pressure, Flow and Vessel Wall Stress Distribution in the Entrance Region of an Artery: A Mathematical Model Study

1989 ◽  
pp. 109-121
Author(s):  
Ren-Jing Cen ◽  
Ned H. C. Hwang
Keyword(s):  
Mathematical Model ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Wall Stress ◽  
Entrance Region ◽  
Pressure Flow ◽  
Model Study

A Mathematical Model of Blood Flow in a Catheterized artery with multiple stenoses

2020 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
B. Basu Mallik ◽  
Saktipada Nanda
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Stress Distribution ◽  
Flow Resistance ◽  
Wall Stress ◽  
Symmetric Flow ◽  
Catheterized Artery ◽  
Impedance Wall ◽  
Analytical Expressions ◽  
Insight Into

A mathematical model is developed in this investigation for studying the axi-symmetric flow of blood through a catheterized artery with multiple stenoses. Consideration of Newtonian character of blood is described following the report of Young (1968) and Srivastava (2009) with the appropriate constitutive equation governing the flow. The boundary conditions appropriate to the problem under study are the standard no slip conditions at the artery and the catheter wall. Analytical expressions for impedance (flow resistance), the wall stress distribution in the stenotic region and the shear stress at the stenosis throat in their non dimensional form are derived by using the model. The derived expressions are computed numerically and the results are presented graphically for different values of the rheological and other parameters. The study provides an insight into the effects of catheter radius and stenosis height on impedance, wall stress distribution in the stenotic region and the shear stress at the stenotic throat.

Influence of Material Model and Aortic Root Motion in Finite Element Analysis of Two Exemplary Cases of Proximal Aortic Dissection

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Dhananjay Radhakrishnan Subramaniam ◽  
Ephraim Gutmark ◽  
Niels Andersen ◽  
Dorte Nielsen ◽  
Kristian Mortensen ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Peak Stress ◽  
Wall Stress ◽  
Material Model ◽  
Element Analysis ◽  
Type A Dissection ◽  
The Subject

Abstract The risk of type-A dissection is increased in subjects with connective tissue disorders and dilatation of the proximal aorta. The location and extents of vessel wall tears in these patients could be potentially missed during prospective imaging studies. The objective of this study is to estimate the distribution of systolic wall stress in two exemplary cases of proximal dissection using finite element analysis (FEA) and evaluate the sensitivity of the distribution to the choice of anisotropic material model and root motion. FEA was performed for predissection aortas, without prior knowledge of the origin and extents of vessel wall tear. The stress distribution was evaluated along the wall tear in the postdissection aortas. The stress distribution was compared for the Fung and Holzapfel models with and without root motion. For the subject with spiral dissection, peak stress coincided with the origin of the tear in the sinotubular junction. For the case with root dissection, maximum stress was obtained at the distal end of the tear. The FEA predicted tear pressure was 20% higher for the subject with root dissection as compared to the case with spiral dissection. The predicted tear pressure was higher (9–11%) for root motions up to 10 mm. The Holzapfel model predicted a tear pressure that was lower (8–15%) than the Fung model. The FEA results showed that both material response and root motion could potentially influence the predicted dissection pressure of the proximal aorta at least for conditions tested in this study.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

Role of tapering in aortic wave reflection: hydraulic and mathematical model study

2000 ◽  
Vol 33 (3) ◽  
pp. 299-306 ◽  
Author(s):  
Patrick Segers ◽  
Pascal Verdonck
Keyword(s):  
Mathematical Model ◽  
Wave Reflection ◽  
Model Study

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

scholarly journals Mathematical model study on the damage of the liquid phase to productivity in the gas reservoir with a bottom water zone

Petroleum ◽  
2018 ◽  
Vol 4 (2) ◽  
pp. 209-214 ◽  
Author(s):  
Xiaoliang Huang ◽  
Xiao Guo ◽  
Xinqian Lu ◽  
Xiang Zhou ◽  
Zhilin Qi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Liquid Phase ◽  
Bottom Water ◽  
Gas Reservoir ◽  
Water Zone ◽  
Model Study

In vivo porcine left atrial wall stress: Effect of ventricular tachypacing on spatial and temporal stress distribution

2011 ◽  
Vol 44 (16) ◽  
pp. 2755-2760 ◽  
Author(s):  
Elena S. Di Martino ◽  
Chiara Bellini ◽  
David S. Schwartzman
Keyword(s):  
Stress Distribution ◽  
Left Atrial ◽  
Wall Stress ◽  
Stress Effect ◽  
Atrial Wall ◽  
Left Atrial Wall

Abstract 482: Attachment Site Curvature of Thoracic Endografts is Correlated to Adjacent Aortic Wall Stress and Stress Distribution

2014 ◽  
Vol 34 (suppl_1) ◽  
Author(s):  
Nathan Couper ◽  
Michael Richards ◽  
Ankur Chandra
Keyword(s):  
Stress Distribution ◽  
Aortic Root ◽  
Mean Curvature ◽  
Aortic Wall ◽  
Attachment Site ◽  
Wall Stress ◽  
Patient Specific ◽  
Clinical Tool ◽  
Element Analysis ◽  
Clinical Series

INTRODUCTION: TEVAR has been seen to cause acute and chronic stent-induced tears of the adjacent aortic wall after treatment in 10-25% of cases with increasing frequency as the stent is placed closer to the aortic valve. The underlying cause for these tears and the ability to predict their occurrence is poorly understood. We hypothesize the cause of these tears is related to stent-induced changes in the adjacent aortic wall which could be quantified and predicted through finite element analysis (FEA) of stent-aorta interface. METHODS: Abaqus TM was used to resolve the FEA model of the stent-aorta interface in three configurations. The maximum principal stress in the vessel wall was averaged over the volume around the stent attachment point and the curvature of the stent was calculated at both the distal and proximal ends. (Figure 1). RESULTS: As the curvature of the attachment site increased, an increase in adjacent aortic wall stress was noted. These ranged from mean curvature (1/m) of 0.1 with wall stress of 49kPa for the distal attachment, position #2 to mean curvature of 6.7 and wall stress of 82kPa for the distal attachment site in position #3. There was an increase in maximum stress distribution as the TEVAR approached the aortic root of 104kPa, 109kPa, and 112kPa for positions 1-3 repectively. CONCLUSIONS: An increase in adjacent aortic wall stress and stress distribution was noted as TEVAR were placed closer to the aortic root which corresponds to the increase in stent-induced aortic tears observed in clinical series. This approach provides the basis for a predictive clinical tool to allow for patient-specific TEVAR planning with associated aortic wall stress analysis to minimize adjacent aortic trauma and assist in future stent design.

P5631The impact of plaque type on strut embedment/protrusion and shear stress distribution in bioresorbable scaffold

2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
E Tenekecioglu ◽  
R Torii ◽  
Y Katagiri ◽  
J Dijkstra ◽  
R Modolo ◽  
...  
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Cross Section ◽  
Vessel Wall ◽  
Shear Stress Distribution ◽  
Local Flow ◽  
Bioresorbable Scaffold ◽  
Plaque Type ◽  
The Impact ◽  
Section Level

Abstract Background and aim Scaffold design and plaque characteristics influence implantation outcomes and local flow dynamics in treated coronary segments. Our aim is to assess the impact of strut embedment/protrusion of bioresorbable scaffold on local shear stress distribution in different atherosclerotic plaque types. Method Fifteen Absorb everolimus-eluting Bioresorbable Vascular Scaffolds were implanted in human epicardial coronary arteries. Optical coherence tomography (OCT) was performed post-scaffold implantation and strut embedment/protrusion were analyzed using a dedicated software. OCT data was fused with angiography to reconstruct three-dimensional coronary anatomy. Blood flow simulation was performed and wall shear stress (WSS) was estimated in each scaffolded surface and the relationship between strut embedment/protrusion and WSS was evaluated. Results There were 9083 struts analysed. Ninety-seven percent of the struts (n=8840) were well apposed and 243 (3%) were malapposed. At cross-section level (n=1289), strut embedment was significantly increased in fibroatheromatous plaques (76±48μm) and decreased in fibro-calcific plaques (35±52 μm). Compatible with strut embedment, WSS was significantly higher in lipid-rich fibroatheromatous plaques (1.50±0.81Pa), whereas significantly decreased in fibro-calcified plaques (1.05±0.91Pa). After categorization of WSS as low (<1.0 Pa) and normal/high WSS (≥1.0 Pa), the percent of low-WSS in the plaque subgroups were 30.1%, 31.1%, 25.4% and 36.2% for non-diseased vessel wall, fibrous plaque, fibro-atheromatous plaque and fibro-calcific plaque, respectively (p-overall<0.001). Table 1. Cross-section level Embedment/Protrusion and WSS according to the plaque type Plaque type Embedment depth (μm) Protrusion distance (μm) WSS (Pa) Non-atherosclerotic intimal thickening/normal vessel wall (n=2275) 47±34*Δ¥ 123±34¶Ξπ 1.44±0.9解 Fibrous (n=4191) 53±40*#& 118±38¶Ψ‡ 1.24±0.78αθ∞ Fibroatheromatous (n=2027) 76±48#ΦΔ 94.6±46Ω†Ψπ 1.50±0.81Σ§α Fibro-calcific (n=590) 35±52&Φ¥ 139±50‡†Ξ 1.05±0.91∞£Σ For embedment: *p=0.09, #p<0.001, &p<0.001, Φp<0.0001, Δp<0.0001, ¥p<0.0001. For protrusion: ¶p=0.74, Ξp<0.0001, πp<0.0001, Ψp<0.0001, ‡p<0.0001, †p<0.0001. For WSS: θp<0.001, §p=0.06, £p<0.0001, αp<0.0001, ∞p<0.0001, Ωp<0.0001. n=total strut number in each plaque type, p-values come from mixed-effects regression analysis. Conclusion The composition of the underlying plaque influences strut embedment which seems to have effect on WSS. The struts deeply embedded in lipid-rich fibroatheromas plaques resulted in higher WSS compared to the other plaque types.

scholarly journals Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

2020 ◽  
Vol 6 ◽  
Author(s):  
Theo J. C. Faes ◽  
Romain Meer ◽  
Guy R. Heyndrickx ◽  
Peter L. M. Kerkhof
Keyword(s):  
Mathematical Model ◽  
Fractional Flow Reserve ◽  
Coronary Stenosis ◽  
Fractional Flow ◽  
Flow Reserve ◽  
Model Study
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