BLOOD FLOW THROUGH CAROTID ARTERY FLUID FLOW THROUGH

BLOOD FLOW THROUGH CAROTID ARTERY: FLUID FLOW THROUGH HOLLOW TUBE Dana Fraij ME 599 M Sensitivity Analysis and Uncertainty Quantification and Propagation

BACKGROUND • Research based on analyzing how geometry affects the progression of carotid artery disease. • Physical changes caused by disease can affect blood flow in artery. • Common carotid artery modeled as a hollow tube.

ASSUMPTIONS • Newtonian fluid • Laminar Flow • No slip at the vascular wall • Steady flow • Cylindrical shape • Uniform cross section • Rigid wall • Fully developed flow

MATHEMATICAL MODEL • Hagen-Poiseuille Equation • Volumetric Flow: • Maximum Velocity: • Maximum Shear at Wall:

VARIABLES • Parameters for left common carotid artery • Constants: • Length: 12. 4 cm +- 1. 4 cm • Input: • Pressure: maximum (systolic) 100– 140 minimum (diastolic) 60– 90 mm. Hg • Diameter: 5. 78 +- 0. 57 mm • Viscosity: 3. 2*10^-3 Pa. s • Output • Volumetric flow • Maximum velocity • Maximum shear rate at the wall

CENTERED PARAMETER STUDY

PRESSURE RESULTS FLOW VELOCITY SHEAR

DIAMETER FLOW VELOCITY SHEAR

VISCOSITY FLOW VELOCITY SHEAR

PARAMETER STEP FLOW

PARAMETER STEP VELOCITY

PARAMETER STEP SHEAR

LHS STUDY

UQ PRESSURE FLOW VELOCITY SHEAR

UQ DIAMETER FLOW VELOCITY SHEAR

UQ VISCOSITY FLOW VELOCITY SHEAR

UQ SCATTER PLOTS

UQ INPUT PRESSURE CORRELATION

UQ INPUT DIAMETER CORRELATION

UQ INPUT VISCOSITY CORRELATION

UQ OUTPUT FLOW CORRELATION

UQ OUTPUT VELOCITY CORRELATION

UQ OUTPUT SHEAR CORRELATION

CONCLUSION • Pressure affects shear • Diameter affects volumetric flow • Viscosity does not have a huge impact on the output variables

REFERENCES • https: //www. ncbi. nlm. nih. gov/pubmed/17203830 • http: //lhtc. epfl. ch/webdav/site/lhtc/shared/import/migration/2%20 VISCOSITY. pdf • https: //edisciplinas. usp. br/pluginfile. php/97576/mod_resource/content/1/Physicsofth e. Human. Body-Herman-01. pdf • http: //jnis. bmj. com/content/8/5/536. long

RESULTS ADDED