Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Governing Equations and Simulation Setup
2.2. Non-Newtonian Blood Rheological Models
2.3. Grid Generation and Mesh Convergence
2.4. Statistical Analysis
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
U | fluid velocity |
p | fluid pressure |
ρ | fluid density |
τ | stress tensor |
D | rate-of-deformation tensor |
shear rate | |
μ | dynamic viscosity |
WSS | wall shear stress |
TAWSS | time evarage wall shear stress |
OSI | oscillatory shear index |
RRT | relative residence time |
IL | local non-Newtonian importance factor |
IG | global non-Newtonian importance factor |
NNEF | non-Newtonian effect factor |
C | Carreau |
CY | Carreau–Yasuda |
Cs | Casson |
Cs-m | Casson modified |
Cr | Cross |
Cr-m | Cross modified |
Cr-s | Cross simplified |
HB | Herschel–Bulkley |
KL | Kuang–Luo |
N | Newtonian |
PE | Powell–Eyring |
PE-m | Powell–Eyring modified |
P | power-law |
P-g | power-law generalized |
Q | Quemada |
WS | Walburn–Schneck |
VIF | variance-inflation filtering |
PCA | principal components analysis |
IGPS | global non-Newtonian importance factor at peak systole |
IGLD | global non-Newtonian importance factor at late diastole |
ILPSmax | maximum of local non-Newtonian importance factor at peak systole |
ILEDdec | decile of local non-Newtonian importance factor at early diastole |
ILEDmax | maximum of local non-Newtonian importance factor at early diastole |
ILLDmax | maximum of local non-Newtonian importance factor at late diastole |
NNEFPSmin | minimum of non-Newtonian effect factor at peak systole |
NNEFLDmin | minimum of non-Newtonian effect factor at late diastole |
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# | Name (Abbreviation) | Equation | Parameter Values | References |
---|---|---|---|---|
1 | Carreau (C) | [5,25,27,28] | ||
2 | Carreau–Yasuda (CY) | [13,25,29,30] | ||
3 | Casson (Cs) | [25,36] | ||
4 | Casson modified (Cs-m) | [37,38] | ||
5 | Cross (Cr) | [15,25,31,32] | ||
6 | Cross modified (Cr-m) | [25,31,33,34] | ||
7 | Cross simplified (Cr-s) | [25,31] | ||
8 | Herschel–Bulkley (HB) | [2,47] | ||
9 | Kuang–Luo (KL) | [6,31,39] | ||
10 | Newtonian (N) | [42,56] | ||
11 | Powell–Eyring (PE) | [25,48] | ||
12 | Powell–Eyring modified (PE-m) | [25] | ||
13 | Power-law (P) | [38,39,43,45,46] | ||
14 | Power-law generalized (P-g) | [5,6] | ||
15 | Quemada (Q) | [31,40,41] | ||
16 | Walburn–Schneck (WS) | [31,42,43] |
Mesh | # of Elements | # of Nodes | BL Levels | BL Min (mm) |
---|---|---|---|---|
Coarse | 282450 | 299194 | 5 | 0.2688 |
Medium | 660000 | 683789 | 10 | 0.0770 |
Fine | 1229952 | 1263617 | 14 | 0.0338 |
Extra fine | 2464640 | 2515452 | 19 | 0.0129 |
Mesh | TAWSS Result (Pa)/Error (%) | OSI Result/Error (%) | Outlet Velocity Result (m/s)/Error (%) | Volume Pressure Integral Result (Pa·m3)/Error (%) | ||||
---|---|---|---|---|---|---|---|---|
Coarse | 0.7905 | 6.65% | 0.2117 | 5.96% | 0.0548 | 2.81% | 1.4225 | −6.44% |
Medium | 0.7623 | 2.85% | 0.2043 | 2.25% | 0.0541 | 1.50% | 1.4578 | −4.12% |
Fine | 0.7433 | 0.28% | 0.2010 | 0.60% | 0.0535 | 0.38% | 1.5312 | −0.70% |
Extra fine | 0.7412 | - | 0.1998 | - | 0.0533 | - | 1.5205 | - |
Cluster | Variable | Cluster Mean | p-Value |
---|---|---|---|
CL1 | IGLD | 0.914 | 0.001 |
CL2 | ILLDmax | 1.424 | 0.031 |
CL3 | IGLD | −0.864 | 0.024 |
N | NNEFLDmin | 2.640 | 0.006 |
P-g | ILPSmax | 3.473 | <0.001 |
Cr-s | IGPS | 3.085 | 0.001 |
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Tzirakis, K.; Kamarianakis, Y.; Kontopodis, N.; Ioannou, C.V. Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation. Symmetry 2023, 15, 630. https://doi.org/10.3390/sym15030630
Tzirakis K, Kamarianakis Y, Kontopodis N, Ioannou CV. Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation. Symmetry. 2023; 15(3):630. https://doi.org/10.3390/sym15030630
Chicago/Turabian StyleTzirakis, Konstantinos, Yiannis Kamarianakis, Nikolaos Kontopodis, and Christos V. Ioannou. 2023. "Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation" Symmetry 15, no. 3: 630. https://doi.org/10.3390/sym15030630
APA StyleTzirakis, K., Kamarianakis, Y., Kontopodis, N., & Ioannou, C. V. (2023). Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation. Symmetry, 15(3), 630. https://doi.org/10.3390/sym15030630