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 6th international symposium on Biomechanics in Vascular Biology and Cardiovascular Disease, April 14-15, 2011, Rotterdam, The Netherlands.

Contact: Magnus.Andersson@liu.se

WK3

R1

R2

C

Elastic support ofsurrounding tissue

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

SegmentationThe MRI images were segmented using an in-house software (Segment, http://segment.heiberg.se,[1]) to obtaina 3D surface of the vessel lumen.

MeshThe 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

Deformation at peak systole for normal BP

1D-0D ArterialTree Network

Rightiliac (RI)

Left iliac (LI)

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-wayiterativescheme

3D-FSI Simulation

Solid Mechanics

Fluid Dynamics

Segment wall stiffnessTypical: 2.6 MPaHypertension: 3.9 MPa

3D-FSI modelThe 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 modelThe 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

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Time (s)V

olu

me F

low

(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

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0 0.3 0.6 0.9

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90

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Pre

ssu

re (

mm

Hg

)

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

Maxacc.

Peaksystole

Timeaverage

Maxdec.

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

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50

100

150

Vo

lum

e F

low

(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.