Sensitivity Analysis of Simulated Blood Flow in Cerebral Aneurysms - PowerPoint PPT Presentation

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Why simulate? Better resolution than any measurement methods available. Minimal disturbance to the patient. Easily change physical parameters. Increased computational power yields greater accuracy. Assist medical personnel in making prognoses and determening treatment. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Uncertainties There are many sources of errors present: Poor resolution of medical images. Little exact patient specific data available. Several simplifications and assumptions are made on the model. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Uncertainties There are many sources of errors present: Poor resolution of medical images. Little exact patient specific data available. Several simplifications and assumptions are made on the model. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Uncertainties There are many sources of errors present: Poor resolution of medical images. Little exact patient specific data available. Several simplifications and assumptions are made on the model. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Uncertainties There are many sources of errors present: Poor resolution of medical images. Little exact patient specific data available. Several simplifications and assumptions are made on the model. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Aim of this study Assess qualitative and quantitative effects of several common simplifications and assumptions. Viscosity Geometry Boundary conditions Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Aneurysms Numerical Methods Blood Qualitative Analysis Why simulate? Quantitative Analysis Uncertainties Conclusion Aim of this study Aim of this study Assess qualitative and quantitative effects of several common simplifications and assumptions. Viscosity Geometry Boundary conditions Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Layout Background And Motivation 1 Numerical Methods 2 Qualitative Analysis 3 Quantitative Analysis 4 Conclusion 5 Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Main assumptions Rigid walls. Body forces such as gravity are negligible. Incompressibility. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Main assumptions Rigid walls. Body forces such as gravity are negligible. Incompressibility. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Main assumptions Rigid walls. Body forces such as gravity are negligible. Incompressibility. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion The Navier-Stokes equations ∂ u ∂ t + u · ∇ u = ∇ · 2 νǫ ( u ) − 1  ρ ∇ p        ∇ · u = 0 for x ∈ Ω u ( x , 0 ) = 0       p ( x , 0 ) = 0  u = 0 for x ∈ Γ w u = u 0 for x ∈ Γ I p = p 0 for x ∈ Γ O Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion The Navier-Stokes equations ∂ u ∂ t + u · ∇ u = ∇ · 2 νǫ ( u ) − 1  ρ ∇ p        ∇ · u = 0 for x ∈ Ω u ( x , 0 ) = 0       p ( x , 0 ) = 0  u = 0 for x ∈ Γ w u = u 0 for x ∈ Γ I p = p 0 for x ∈ Γ O Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion The Navier-Stokes equations ∂ u ∂ t + u · ∇ u = ∇ · 2 νǫ ( u ) − 1  ρ ∇ p        ∇ · u = 0 for x ∈ Ω u ( x , 0 ) = 0       p ( x , 0 ) = 0  u = 0 for x ∈ Γ w u = u 0 for x ∈ Γ I p = p 0 for x ∈ Γ O Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion The Navier-Stokes equations ∂ u ∂ t + u · ∇ u = ∇ · 2 νǫ ( u ) − 1  ρ ∇ p        ∇ · u = 0 for x ∈ Ω u ( x , 0 ) = 0       p ( x , 0 ) = 0  u = 0 for x ∈ Γ w u = u 0 for x ∈ Γ I p = p 0 for x ∈ Γ O Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Problem = ∇ · 2 νǫ ( u ) − 1 � ∂ u ∂ t + u · ∇ u ρ ∇ p for x ∈ Ω . ∇ · u = 0 Several difficulties: Nonlinear. Combination of a hyperbolic and a parabolic term. Two unknowns. Exact solutions exist only to simple problems. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Problem = ∇ · 2 νǫ ( u ) − 1 � ∂ u ∂ t + u · ∇ u ρ ∇ p for x ∈ Ω . ∇ · u = 0 Several difficulties: Nonlinear. Combination of a hyperbolic and a parabolic term. Two unknowns. Exact solutions exist only to simple problems. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Problem = ∇ · 2 νǫ ( u ) − 1 � ∂ u ∂ t + u · ∇ u ρ ∇ p for x ∈ Ω . ∇ · u = 0 Several difficulties: Nonlinear. Combination of a hyperbolic and a parabolic term. Two unknowns. Exact solutions exist only to simple problems. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Problem = ∇ · 2 νǫ ( u ) − 1 � ∂ u ∂ t + u · ∇ u ρ ∇ p for x ∈ Ω . ∇ · u = 0 Several difficulties: Nonlinear. Combination of a hyperbolic and a parabolic term. Two unknowns. Exact solutions exist only to simple problems. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Implementation The Incremental Pressure Correction Scheme was used. Implementation done using the finite element method, and the software library FEniCS. Source code modified from a previous project ( nsbench ). Meshes are built using tetrahedral cells. The solution is approximated by using polynomials at each cell. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Implementation The Incremental Pressure Correction Scheme was used. Implementation done using the finite element method, and the software library FEniCS. Source code modified from a previous project ( nsbench ). Meshes are built using tetrahedral cells. The solution is approximated by using polynomials at each cell. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Implementation The Incremental Pressure Correction Scheme was used. Implementation done using the finite element method, and the software library FEniCS. Source code modified from a previous project ( nsbench ). Meshes are built using tetrahedral cells. The solution is approximated by using polynomials at each cell. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Implementation The Incremental Pressure Correction Scheme was used. Implementation done using the finite element method, and the software library FEniCS. Source code modified from a previous project ( nsbench ). Meshes are built using tetrahedral cells. The solution is approximated by using polynomials at each cell. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Implementation The Incremental Pressure Correction Scheme was used. Implementation done using the finite element method, and the software library FEniCS. Source code modified from a previous project ( nsbench ). Meshes are built using tetrahedral cells. The solution is approximated by using polynomials at each cell. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion An exact solution Fully developed, steady state flow in a straight channel/cylinder. Yields the exact solutions for velocity and WSS: u = r 2 − a 2 dp 4 µ dx � a dp � � � τ w = � � 2 dx � � where dp dx is determined from the average flow velocity applied at the inlet. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion An exact solution Fully developed, steady state flow in a straight channel/cylinder. Yields the exact solutions for velocity and WSS: u = r 2 − a 2 dp 4 µ dx � a dp � � � τ w = � � 2 dx � � where dp dx is determined from the average flow velocity applied at the inlet. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Method A common set of parameters, modelling the middle cerebral artery (MCA). Tests were performed in both 2D and 3D. A range of different time steps were tested. Comparisons were made between a quadratic and a linear approximation to the velocity. The exact solution of the WSS was used as reference. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Method A common set of parameters, modelling the middle cerebral artery (MCA). Tests were performed in both 2D and 3D. A range of different time steps were tested. Comparisons were made between a quadratic and a linear approximation to the velocity. The exact solution of the WSS was used as reference. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Method A common set of parameters, modelling the middle cerebral artery (MCA). Tests were performed in both 2D and 3D. A range of different time steps were tested. Comparisons were made between a quadratic and a linear approximation to the velocity. The exact solution of the WSS was used as reference. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Method A common set of parameters, modelling the middle cerebral artery (MCA). Tests were performed in both 2D and 3D. A range of different time steps were tested. Comparisons were made between a quadratic and a linear approximation to the velocity. The exact solution of the WSS was used as reference. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Method A common set of parameters, modelling the middle cerebral artery (MCA). Tests were performed in both 2D and 3D. A range of different time steps were tested. Comparisons were made between a quadratic and a linear approximation to the velocity. The exact solution of the WSS was used as reference. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Resulting choices A timestep of 0.00125s was chosen. A linear approximation of the velocity was preferred to a quadratic approximation. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods The Mathematical Model Qualitative Analysis Implementation Quantitative Analysis Verification of implementation Conclusion Resulting choices A timestep of 0.00125s was chosen. A linear approximation of the velocity was preferred to a quadratic approximation. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Layout Background And Motivation 1 Numerical Methods 2 Qualitative Analysis 3 Quantitative Analysis 4 Conclusion 5 Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Method A single aneurysm was studied. The effects of three uncertainties were measured: Geometric effects Non-Newtonian effects Effects of different hematocrit levels Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Method A single aneurysm was studied. The effects of three uncertainties were measured: Geometric effects Non-Newtonian effects Effects of different hematocrit levels Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Method A single aneurysm was studied. The effects of three uncertainties were measured: Geometric effects Non-Newtonian effects Effects of different hematocrit levels Segmented out an aneurysm from CT-images using VMTK. (a) Cross section (b) Isosurface (c) Zoom-in Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Method Three different meshes were created, all with about 1,300,000 cells. A pulsatile flow profile was set at inlet, with a heart rate of 75bpm. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Simulation Simulation of blood flow through aneurysm at 75 bpm. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Simulation Simulation of blood flow through aneurysm, at 1/5th of the speed. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Results None of the three changes studied seem to have any significant effect on the overall flow pattern within the aneurysm. Locally, the effects on the velocity could be quite large. Areas of high flow velocity were less affected by the changes than areas of low velocity. Areas of high WSS were less affected by the changes than areas of low WSS. The effects were most prominent at systole. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Results None of the three changes studied seem to have any significant effect on the overall flow pattern within the aneurysm. Locally, the effects on the velocity could be quite large. Areas of high flow velocity were less affected by the changes than areas of low velocity. Areas of high WSS were less affected by the changes than areas of low WSS. The effects were most prominent at systole. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Results None of the three changes studied seem to have any significant effect on the overall flow pattern within the aneurysm. Locally, the effects on the velocity could be quite large. Areas of high flow velocity were less affected by the changes than areas of low velocity. Areas of high WSS were less affected by the changes than areas of low WSS. The effects were most prominent at systole. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Results None of the three changes studied seem to have any significant effect on the overall flow pattern within the aneurysm. Locally, the effects on the velocity could be quite large. Areas of high flow velocity were less affected by the changes than areas of low velocity. Areas of high WSS were less affected by the changes than areas of low WSS. The effects were most prominent at systole. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Method Qualitative Analysis Simulation Quantitative Analysis Results Conclusion Results None of the three changes studied seem to have any significant effect on the overall flow pattern within the aneurysm. Locally, the effects on the velocity could be quite large. Areas of high flow velocity were less affected by the changes than areas of low velocity. Areas of high WSS were less affected by the changes than areas of low WSS. The effects were most prominent at systole. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Layout Background And Motivation 1 Numerical Methods 2 Qualitative Analysis 3 Quantitative Analysis 4 Conclusion 5 Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion The aneurysms (a) M1 (b) M2 (c) M3 (d) M5 (e) M8 (f) M9 (g) M11 (h) M12 (i) M15 (j) M16 (k) M18 (l) M20 Large variation in sizes and types. Used in a previous study at Simula. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects studied The four different effects which sensitivity analysis has been performed on are Neglecting the shear thinning (non-Newtonian) behaviour of blood. An increase in the hematocrit level from 38% to 40%. Increasing the inlet flux by 33%. Applying a different set of outlet boundary conditions for the pressure. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects studied The four different effects which sensitivity analysis has been performed on are Neglecting the shear thinning (non-Newtonian) behaviour of blood. An increase in the hematocrit level from 38% to 40%. Increasing the inlet flux by 33%. Applying a different set of outlet boundary conditions for the pressure. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects studied The four different effects which sensitivity analysis has been performed on are Neglecting the shear thinning (non-Newtonian) behaviour of blood. An increase in the hematocrit level from 38% to 40%. Increasing the inlet flux by 33%. Applying a different set of outlet boundary conditions for the pressure. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects studied The four different effects which sensitivity analysis has been performed on are Neglecting the shear thinning (non-Newtonian) behaviour of blood. An increase in the hematocrit level from 38% to 40%. Increasing the inlet flux by 33%. Applying a different set of outlet boundary conditions for the pressure. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Non-Newtonian effects Method: Comparing a Casson viscosity model to a reference Newtonian viscosity model with the same asymptotic viscosity at the limit of infinite shear rate. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Non-Newtonian effects - Results Large differences between the aneurysms: Aneurysms with a high average shear rate shows little non-Newtonian effects. Differences seems to be largest at diastole and early systole. Largest change in average WSS: 2.24%. Largest change in maximum WSS: -7.14%. Including non-Newtonian effects predicts a significantly lower maximum WSS (mean=-2.31%, P=0.0091). Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Non-Newtonian effects - Results Large differences between the aneurysms: Aneurysms with a high average shear rate shows little non-Newtonian effects. Differences seems to be largest at diastole and early systole. Largest change in average WSS: 2.24%. Largest change in maximum WSS: -7.14%. Including non-Newtonian effects predicts a significantly lower maximum WSS (mean=-2.31%, P=0.0091). Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Non-Newtonian effects - Results Large differences between the aneurysms: Aneurysms with a high average shear rate shows little non-Newtonian effects. Differences seems to be largest at diastole and early systole. Largest change in average WSS: 2.24%. Largest change in maximum WSS: -7.14%. Including non-Newtonian effects predicts a significantly lower maximum WSS (mean=-2.31%, P=0.0091). Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Non-Newtonian effects - Results Large differences between the aneurysms: Aneurysms with a high average shear rate shows little non-Newtonian effects. Differences seems to be largest at diastole and early systole. Largest change in average WSS: 2.24%. Largest change in maximum WSS: -7.14%. Including non-Newtonian effects predicts a significantly lower maximum WSS (mean=-2.31%, P=0.0091). Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased hematocrit Physiological motivation: The increase of two percentage points is an average increase seen in women going through menopause. The average age of menopause for women is 51.7 years, and the average age of aneurysm rupture is 52 years. This triggers a hypothesis of a correlation. Method: Using the Casson viscosity model (which incorporates the hematocrit level) the hematocrit is increased from 38% to 40%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased hematocrit - Results Large differences between the aneurysms. Changes in average WSS range from -3.2% to 5.2%. Significantly higher average WSS is predicted (mean=1.56, P=0.026). Changes in maximum WSS range from -12.7% to 5.7%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased hematocrit - Results Large differences between the aneurysms. Changes in average WSS range from -3.2% to 5.2%. Significantly higher average WSS is predicted (mean=1.56, P=0.026). Changes in maximum WSS range from -12.7% to 5.7%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased hematocrit - Results Large differences between the aneurysms. Changes in average WSS range from -3.2% to 5.2%. Significantly higher average WSS is predicted (mean=1.56, P=0.026). Changes in maximum WSS range from -12.7% to 5.7%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased hematocrit - Results Large differences between the aneurysms. Changes in average WSS range from -3.2% to 5.2%. Significantly higher average WSS is predicted (mean=1.56, P=0.026). Changes in maximum WSS range from -12.7% to 5.7%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow Method: Adjusting the inlet spatial peak velocity from an average of 535mm/s to 695mm/s. This corresponds to an increase in inlet flux of 33%. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow - Results The changes in WSS deviate highly from an expected linear relation between inlet flux and WSS. Measured average WSS and maximum WSS is increased by an average of 72.8% and 73.6% respectively. The changes in WSS seems greater within the aneurysm than in the surrounding arteries. All changes are highly significant. All aneurysms showed the same tendencies. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow - Results The changes in WSS deviate highly from an expected linear relation between inlet flux and WSS. Measured average WSS and maximum WSS is increased by an average of 72.8% and 73.6% respectively. The changes in WSS seems greater within the aneurysm than in the surrounding arteries. All changes are highly significant. All aneurysms showed the same tendencies. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow - Results The changes in WSS deviate highly from an expected linear relation between inlet flux and WSS. Measured average WSS and maximum WSS is increased by an average of 72.8% and 73.6% respectively. The changes in WSS seems greater within the aneurysm than in the surrounding arteries. All changes are highly significant. All aneurysms showed the same tendencies. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow - Results The changes in WSS deviate highly from an expected linear relation between inlet flux and WSS. Measured average WSS and maximum WSS is increased by an average of 72.8% and 73.6% respectively. The changes in WSS seems greater within the aneurysm than in the surrounding arteries. All changes are highly significant. All aneurysms showed the same tendencies. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of increased inflow - Results The changes in WSS deviate highly from an expected linear relation between inlet flux and WSS. Measured average WSS and maximum WSS is increased by an average of 72.8% and 73.6% respectively. The changes in WSS seems greater within the aneurysm than in the surrounding arteries. All changes are highly significant. All aneurysms showed the same tendencies. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition Method: Changing the outlet boundary conditions for pressure from a resistance boundary condition to a zero-pressure boundary condition. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition - Results Differences in outlet flux of up to 231.6%. Significant changes in flow pattern in and after the bifurcation. Largest change in average WSS: 36.15%. Largest change in maximum WSS: 56.92%. Very large variation in the prediction of WSS. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition - Results Differences in outlet flux of up to 231.6%. Significant changes in flow pattern in and after the bifurcation. Largest change in average WSS: 36.15%. Largest change in maximum WSS: 56.92%. Very large variation in the prediction of WSS. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition - Results Differences in outlet flux of up to 231.6%. Significant changes in flow pattern in and after the bifurcation. Largest change in average WSS: 36.15%. Largest change in maximum WSS: 56.92%. Very large variation in the prediction of WSS. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition - Results Differences in outlet flux of up to 231.6%. Significant changes in flow pattern in and after the bifurcation. Largest change in average WSS: 36.15%. Largest change in maximum WSS: 56.92%. Very large variation in the prediction of WSS. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Non-Newtonian effects Numerical Methods Effects of increased hematocrit Qualitative Analysis Effects of increased inflow Quantitative Analysis Effects of a different outlet boundary condition Conclusion Effects of a different outlet boundary condition - Results Differences in outlet flux of up to 231.6%. Significant changes in flow pattern in and after the bifurcation. Largest change in average WSS: 36.15%. Largest change in maximum WSS: 56.92%. Very large variation in the prediction of WSS. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Qualitative Analysis Quantitative Analysis Conclusion Layout Background And Motivation 1 Numerical Methods 2 Qualitative Analysis 3 Quantitative Analysis 4 Conclusion 5 Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms

Background And Motivation Numerical Methods Qualitative Analysis Quantitative Analysis Conclusion Uncertainties regarding boundary conditions are far more important than uncertainties in flow parameters. Patient specific boundary data is absolutely necessary to accurately simulate cerebral blood flow accurately. Simulations might still be relevant even without patient specific boundary data. Non-Newtonian effects may safely be neglected if the boundary data is unknown or uncertain. The WSS is unexpectedly sensitive to changes in inlet flux. Øyvind Evju SA of Simulated Blood Flow in Cerebral Aneurysms