Modeling of Subject Arterial Segments Using 3D Fluid Structure Interaction and 1D-0D Arterial Tree Network Boundary Condition

Constant wall thickness and

linear-elastic wall properties

Modeling of Subject Arterial Segments Using

3D Fluid Structure Interaction and 1D-0D

Arterial Tree Network Boundary Condition

Magnus Andersson, Jonas Lantz and Matts Karlsson

Department of Management and Engineering, Linköping University, Linköping, Sweden

The 6

international symposium on Biomechanics in Vascular Biology and

Cardiovascular Disease, April 14-15, 2011, Rotterdam, The Netherlands.

Contact:

Magnus.Andersson@liu.se

INTRODUCTION

In recent years it has been possible to simulate 3D blood flow trough

Computational Fluid Dynamics (CFD) including the dilatation effect in elastic

arteries using Fluid-Structure Interaction (FSI) to better match in vivo data. Outlet boundary condition (BC) models have been shown crucial and difficult to

implement accurately in order to capture realistic pressure reflection arising from the distal vascular bed.

Qin

11% of Qin is forced

into each renal

METHODS

3D - FSI

REFERENCES

[1] Heiberg E. et al, Time resolved three-dimensional automated segmentation of the left ventricle, Computers in Cardiology, Vol. 32, pp.599-602, 2005.

[2] Reymond P. et al, Validation of a one-dimensional model of the systemic arterial tree, Am. J. Physiol. Heart Circ. Physion.,

297:H208-H222, 2009.

MRI acquisition

Subject specific MRI and PC-MRI scanning was utilized to acquire geometry and flow data respectively.

Segmentation

The MRI images were segmented using an in-house software (Segment,

http://segment.heiberg.se,[1]) to obtain a 3D surface of the vessel lumen.

Mesh

The surfaces was meshed with a high quality

hexahedral elements using ANSYS ICEM CFD 12.0 (ANSYS Inc, Canonsburg, PA, USA).

This work focus on a full scaled FSI simulation at an arterial section obtained from Magnetic Resonance Imaging (MRI) data. The outlet BC at the iliac arteries is

connected with a 1D-0D systemic arterial network. This 3D-(0D-1D) connection can provide the essential features of the peripheral flow , the 1D-0D coupling allow for investigation of cardiovascular diseases including stenoses and/or hypertension.

RESULTS

CONCLUSIONS

Prediction of the flow impedance at the iliac root boundaries for

Typical 1D vascular stiffness High (2x) 1D vascular stiffness 1D-0D Approximated iliac flow profiles

Normal BP Hypertension Iliac pressure profiles 2-way iterative scheme 3D-FSI Simulation Solid Mechanics Fluid Dynamics

Segment wall stiffness

Typical: 2.6 MPa

Hypertension: 3.9 MPa

3D-FSI model

The FSI use a 2-way interactively scheme, ANSYS Multifield, for

solving the pressure/displacement interaction at the shared interface.

Peripheral arterial segments are terminated with a three-element windkessel (WK3) model.

1D-0D model

The arterial tree network is based on transmission-line theory represented by a complex flow impedance model for the pressure-flow relationship.

The arterial topology was extracted from literature [2] where only the central arteries was considered.

0 0.3 0.6 0.9 0 50 100 150 Time (s) V o lu m e F lo w ( m l/ s )

Iliacs Pressure vs Flow Profiles

0 0.3 0.6 0.9 75 90 140 180 0 0.3 0.6 0.9 75 90 140 180 0 0.3 0.6 0.9 75 90 140 180 0 0.3 0.6 0.9 75 90 140 180 P re s s u re ( m m H g ) RI Hypertension LI Hypertension RI Normal Pressure LI Normal Pressure RI Volume Flow LI Volume Flow

Instantaneous wall shear stress (WSS) at three different times in the cardiac cycle, max

acceleration, peak systole and max deceleration, is presented for normal BP and hypertension.

The average WSS over one cardiac cycle was

evaluated, revealing close similarities for both

results.

Normal BP

Hyper-tension

Wall Shear Stress

Max acc. Peak systole Time average Max dec.

This method allows for a better insight of large scale vascular

networks effect of the local 3D flow features and also gives a better representation of the peripheral flow compared to a pure 0D

(lumped parameter/Windkessel) model. PC-MRI will provide data for validation of velocity profiles in the 3D model. Future work

includes a hyperelastic material model for 3D geometry as well a MRI-based subject specific 1D vascular topology to be combined with the 3D model.

Reduced PC-MRI flow profile Iliac pressure vs. flow profiles

0 0.3 0.6 0.9 0 50 100 150 V o lu m e F lo w ( m l/ s ) Time (s) Max Acceleration Peak Systole Max Deceleration

Two cases are studied, normal and

high blood pressure(BP), for different vascular stiffness.

Segment wall stiffness is increase by 50 % at hypertension.