Flow Investigation Behind the End-To-Side Anastomosisfluids.fs.cvut.cz/akce/konference/istp_2005/full/165.pdfbasic idea on flow behind the end-to-side anastomosis; to describe the

ISTP-16, 2005, PRAGUE 16TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA

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Abstract The goal of this work was to describe the velocity field behind the distal end-to-side bypass junction in dependence on the connection angle both experimentally and numerically.

1 Introduction In our current civilization, diseases of the

cardiovascular system are the major cause of mortality and morbidity among people in their productive age and among seniors. A complex medical approach has significantly improved the conditions of people who suffer from these diseases, with surgery as one of the most important fundaments of this approach. Without concentrating on any further details, bypassing is the most usual method in which a clogged or damaged artery is bypassed with material of a biological or synthetic type. In order to ensure long-term permeability of such a reconstruction, it is necessary to meet a number of conditions, including optimum hemodynamic characteristics of the reconstruction.

The long-term project is solved in author’s workplace and its objective is to optimise the shape of anastomosis (end-to-side), which is used for the bypass anastomosis, and thus to minimize the negative impact of the flow dynamics on the vascular walls and blood, thanks to which the bypass failure risk can be successfully reduced.

This project continues a set of previous projects, some of which investigated unsteady flow by laser doppler anemometry (LDA) method [1,2,3,4,5], the others dealt with using

particle image velocimetry (PIV) method for investigation of flow in cardiovascular models [6,8,9,10,11] etc.

We present the first results of this project in this paper. The PIV experimental measurement is of special importance in this project.

The aim of this work was to measure the flow field in symmetry plane by PIV method for steady conditions; to create the methodology of measurement by PIV method in the model of bypass anastomosis; to create the methodology of manipulation with measured data and to design a practical system of data storage which enables to compare flow characteristics for different flow regimes and for different models.

One of the most important flow characteristics, which has influence on pathological phenomenon, is wall shear stress (WSS) and thus the possibility of evaluation of WSS values from PIV measurement was verified.

If the optimal bypass junction shape was searched in an experiment, many models would have to be constructed and each model would have to be checked in a great number of measurements. In order to choose the optimum models and to reduce the number of experiments a numerical solution is planned. Therefore numerical computations in the models similar to the experiment models were carried out in order to verify the selected type, the location and sufficient accuracy of appropriate boundary conditions which ensure a good agreement when comparing resultant flow characteristics obtained from numerical solution

FLOW INVESTIGATION BEHIND THE END-TO-SIDE ANASTOMOSIS

Jan Matěcha, Hana Netřebská, Martin Bíca, Jan Tůma, Josef Adamec Czech Technical University in Prague, Faculty of Mechanical Engineering,

Division of Fluid Dynamics and Thermodynamics Corresponding author: [email protected], +420 224 352 710, +420 224 310 292

Keywords: hemodynamics, by-pass, PIV, experiment, numerical simulation

mailto:[email protected]

J. Matecha, H. Netrebska, M. Bica, J. Tuma, J. Adamec

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and experiment. The next aim was: to get a basic idea on flow behind the end-to-side anastomosis; to describe the influence of graft angle and different flow regimes on flow characteristics and to identify interesting places because of planning following experiments.

2 Experiment - 2D PIV The experimental equipment (fig. 1) for

measurement by 2D PIV method in symmetry plane of bypass junction (fig. 2) was made. The liquid was pumped into a tank with overflow because of constant pressure gradient. The liquid was conducted from the tank through the ultrasound flowmeter and the valve, which changed total flow rate, into the branch and then into the model of bypass. The second ultrasound flow meter and valve were placed in the graft-branch and it enabled to divide flow between host artery and graft and to simulate different rate of stenosis patency. In order to provide developed laminar profile in graft and in host artery in the place of junction, the one-meter long straight pipes were placed upstream the bypass model.

The bypass models were made from plexiglas with connection angles 20°, 30°, 45°, 60° and 90°. The host artery and graft diameter was 10mm. Solution of sodium-iodine (58% NaI, ρ = 1730 kg/m3, η = 0,00254 Ns/m2, t = 24°C) was used as a working fluid.

NaI solution was used because its refractive index is the same as refractive index of plexiglas and thus the optical distortions between model and working fluid were minimalized. Due to higher price of NaI the whole circuit volume was minimalized. Fluorescent particles with diameter 1-20 µm were used as seeding particles. This type of particles was used because it allows filtering reflexes from laser in the boundary of model and liquid. If these particles are illuminated with ND-YAG laser (λ=532 nm) and if the screen for camera (which transmits only the light with the wave length higher than λ=580 nm) is used then it is possible to scan only the light emitted from the particles and thus to filter out the reflections.

The construction enables fixed holding of cameras, laser and models in optimal position for measurements, their rotation and shifting

Fig. 1 Experimental equipment scheme. Fig.3 Scheme of measure place.

Fig. 2 Scheme of bypass.


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with regard to the model (fig. 3). The accuracy of PIV measurement is dependent on precise setup of whole system and precise position of PIV component [7]. The camera, which was placed perpendicular to the laser sheet, was fixed on guideway which enables camera movement along the host artery axis.

The PIV system from Dantec Dynamics which comprises these components: a pair of cameras Dantec HiSense, 1 024k x 1 280k pixel CCD, frequency 4.5 Hz for double frame mode and 9Hz for single frame mode; a pair of pulsed lasers Nd:YAG New Wave Geminy 15 Hz-120 mJ, with optics; PIV processor Dantec FlowMap 1500, 2 x 1Gb buffer, PC DELL Precision 2 x P4 Xeon 2 800 MHz was used.

The flow field was measured in symmetry plane of the model for steady conditions (Re=500;1400). Six areas were measured along the host artery (length of measured area was approximately 60mm). The image of model with a scale which was placed under the model was saved for every camera position. Thanks to this scale, a coordinate system for every camera position was set up so that the images had one coordinate system and it was possible to connect them for evaluation.

100 of double-images were measured for every measured area. The instant flow fields were evaluated from these double-images (in Flow Manager software from Dantec Dynamics) by following analysis sequence:

- subtract mean image map - mask image - adaptive correlation - mask vectors - peak validation - moving-average validation.

The statistics (tab. 2) was evaluated from the instant flow fields. The set of statistics was exported from Flow Manager to MATLAB with the help of command "Link to MATLAB" and saved. The matrixes of all statistics values are stored together with axis vectors X and Y which contain coordinate values.

The corresponding set of statistics (for one measured regime) was connected in one matrix in MATLAB for next evaluation. The Matrixes of evaluated data (fig. 4 - I) have different size

(different number of columns and rows) dependent on concrete setting of analysis sequence and overlap each other in the direction of host artery axis.

First, the final matrix was created (fig. 4 - VI) with required number of columns and rows with corresponding final X and Y vectors. The values from statistics (fig. 4 - I) (without overlap) were interpolated into the final matrix with the help of MATLAB command interp2. Whole sequence was carried out simultaneously for all matrixes (U,V, StdU, STdV, K).

The connected set of statistics was stored in one structured variable (tab. 1) of field type where index of field is the order of the measured regime. The data storage in one structured variable enables easy evaluation and comparison of flow characteristics for different models and regimes.

A(i). - structured variable of field type alfa - graft angle Q - total flow rate Q1 - flow rate in graft X, Y - coordinates in host artery U, V - velocity in X, Y direction StdU, StdV - standard deviation for U, V velocity K - Correlation coefficient

Tab.1 Structured variable saved dates.

Fig.4 Scheme of data manipulation.


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WSS is one of the important flow characteristics which are necessary to evaluate in hemodynamics. If WSS values obtained from PIV measurement are evaluated several problems appear, on the one hand due to the principle of measurement (the PIV method evaluates particles shift which don’t need to

follow precisely the flow stream near the wall) on the other hand due to the optical access close to wall (optical distortion and laser reflections appear in boundary of model and fluid which worsen the optical access). Hence, as a first step gradient of mean velocity in r direction was evaluated in place of model wall.

The velocity profile in r direction (fig. 5 B) is selected from the whole flow field (fig. 5 A). Several values are selected from this profile (fig. 5 C,D) and these values are fitted with polynomial with the help of MATLAB command fit. It is not possible to determine precisely the boundary between liquid and wall because of the magnitude of scanned area, optical access and because of used optical device resolution. This boundary is found on the base of the non-slip condition principle (value of r is found for v=0). In this place gradient of polynomial is calculated (fig. 5 E). Whole process is repeated for different profiles along the host artery axis so that the behaviour of mean velocity gradient on the wall was

Mean value ∑=

=µN

1iiu u

N1 ,

Variance ( )∑=

µ−−

=σN

1i

2ui

2u u

1N1 ,

Standard deviation 2uu σ=σ ,

Covariance

( )( )∑=

µ−µ−−

=N

1iviui vu

1N1}V,U{Cov ,

Correlation coefficient { }vu

V,UCovkσσ

=

Tab.2 Evaluated flow characteristics from Flow Manager.

Fig.5 Scheme of mean velocity profile gradient calculation from PIV data.


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obtained. These values were multiplied with dynamic viscosity for comparison with WSS from numerical simulation.

3 Numeric simulation The numerical solution was found with the

help of the CFD FLUENT. The numerical model geometry was derived from the geometry of the experiment and was slightly simplified against the experiment. It consists of two tubes with inner diameter d = 10mm. The length of graft to junction was 700 mm. The length of POS was 100 mm and it was closed in order to simulate the stenosis. The length of DOS was 700 mm. 3D computation grid was generated using the pre-processor Gambit with hexahedron elements of about 800 000 cells. Simulations were performed for several models with different angle connection (60°; 45°; 30°; 20°). The first calculation was stationary until it converged, next calculation was unsteady with the time step ratio 1.10-3 s. Numeric simulations were calculated for (Re=500;1400). The 58% solution of sodium-iodine (NaI) (ρ = 1730 kg/m3, η = 0,00254 Ns/m2, t = 24 °C) was used as a working fluid (both for experimental and numerical solution). The solver was set up to double precision segregated implicit. The mathematical model was selected as the laminar model. The boundary conditions were set on the input to the graft – velocity inlet, on input to the host artery – wall and on the output – pressure outlet.

The problems with calculation stability appeared in models with very fine computation grid because of the nonlinearity of the equation set being solved by FLUENT. Divergence appeared also when setting very low under-relaxation factors.

Following flow characteristic were evaluated and compared from calculated results for different graft angles and flow rates: flow field, WSS. The scripts for data export (velocity profile, WSS) were made which serve as input data for MATLAB. With the help of these scripts data from CFD were compared with data from the experiment.

4 Results The flow in model of bypass anastomosis

is complex. The models, both experimental and numerical, were created so that developed laminar flow was in graft in junction place.

The complex flow structures begin to create in the junction place.

The region of stream with maximum velocity, which is in graft in the center of the pipe due to developed laminar flow, is seen in figure 6. This stream divides along the symmetry plane after impact on the wall (floor) and begins to climb on sides of host artery and creates the external envelope of the flow (fig. 7). The flow is formed into two symmetric helixes. The flow in the downstream direction gradually approaches to developed laminar flow.

Fig. 6 The path lines from center of graft (from CFD).

Fig. 7 The velocity field in bypass with connection angle 45º (from CFD).


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The fluid from the slower stream (it is nearer the wall in the graft) gets into the center of this envelope.

The fluid from region near the toe flows into host artery and begins to create two symmetric helical vortices in envelope of faster flow (fig. 8). Small area with recirculation is formed in the region close to junction. This region is smaller for smaller graft angles until it disappears. The presence of this region was identified by experimental measurements too.

The fluid from region near the heel (fig. 9) impacts on the floor first, divides also into two symmetric helixes and copies the surface near the host artery wall. Both parts of fluid come together near behind the toe. From this place these layers shift between envelope of fast flow

and previous layer into the center of the pipe where helical vortex structures create together.

Very small part of this flow returns in POS direction after impact on the floor and behind the input laminar flow creates vortex structure consisting of two vortices which rotate in reverse direction. First vortex is more intensive (fig. 11) and the second is weaker (fig. 10) toward the POS. The part of this flow returns into the main stream along the host artery sides.

Good agreement between the experiments and numeric simulations of flow in bypass was shown on velocity profile characteristics (fig. 14, 15). The deviation of these profiles in symmetry plane can be caused by several factors. Inaccuracy of making models was caused by milling and there was a problem with

Fig. 8 . The path lines from area close to toe (from CFD).

Fig. 9 The path lines from area close to heel (from CFD).

Fig. 10 Detail of vortex structure in POS direction in of bypass with connection angle 45º (from CFD)

Fig. 11 Detail of vortex structure in POS direction in symmetry plane of bypass with connection angle 45º (from CFD).


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an alignment. This caused different formation of the flow especially different formation of secondary flow. Choice of type, location and selected accuracy of boundary conditions were another problem.

The use of pressure boundary condition was difficult because there was a minimal difference of pressure. Therefore velocity inlet boundary condition was used. The velocity in bypass was derived from measured mass flow data. Because of ultrasound meter (which was used) accuracy some differences existed between experimental reality and measured data.

Laser sheet has non-zero thickness and therefore CCD camera records signal from seeding particles which are not in symmetry plane only. But signal was measured from near area too. It can cause inaccuracy of measured data.

Selected laminar computational model was a source of inaccuracy because the definition of the type of flow in the place behind the connection is not possible to determine explicitly if there is only laminar flow due to secondary flow.

Fig. 14 Comparison of velocity profiles from CFD (Un) with velocity profiles from PIV ( Ue) in distance x=0,5 and 10 mm for angle connection 60º

Fig. 15 Comparison of velocity profiles from CFD (Un) with velocity profiles from PIV ( Ue) in distance x=0,5 and 10 mm for angle connection 45 º

Fig. 12 The flow field in cross-section in x=10mm (angle connection 45º) from CFD.

Fig. 13 The flow field in cross-section in x=20mm (angle connection 45º) from CFD.


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The influence of the graft angle on flow

field is seen in figures 16 and 17 which show the flow fields in symmetry plane measured by PIV. In the region in host artery (fig. 16 A) the flow field in the host artery axis direction has monotonic decreasing character for the small graft angle. The areas with higher and lower velocity appear in this region with increasing angle at the projection of flow field into symmetry plane. It is caused by increasing secondary flow with increasing graft angle which can be seen from the numerical simulation.

The next evaluated variable is velocity

fluctuations which are evaluated from data measured by PIV method (tab. 1). The area with low fluctuation is in the region where the liquid flows from the graft into the host artery and further in graft direction (fig. 18 A). On the boundaries of this area there are areas with slightly increased value of fluctuation (fig. 18 B). The area with the highest value of fluctuations is in figure 18 marked as C. This area is featureless for smaller angles. The total value of fluctuation is rising with rising angle.

Fig. 19 Standard deviation of velocity U by angle connection 60 from PIV.

Fig. 17 Flow field for graft angle 20 from PIV. Fig. 16 Flow field for graft angle 60 from PIV.

A

Fig. 18 Standard deviation of velocity V by angle connection 60 from PIV.

A

B

C


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The behaviors of WSS evaluated from CFD in symmetry plane for different graft angles are shown in figure 20 and 21. The magnitude of WSS behind the graft junction rises. Maximum value of WSS is approximately in distance of one diameter from junction. It shifts downstream for bigger graft angles and upstream for smaller graft angles. The maximum value of WSS rises with rising graft angle. The character of the behavior of WSS is

similar for floor and opposite the floor. For floor, maximum values are approximately three to four times bigger. The values of velocity profile gradient on the floor, multiplied with dynamic viscosity of working fluid, evaluated from PIV data, are shown in figure 22 for several models and several measured regimes. The character of behavior of these values is similar to WSS evaluated from CFD. The figure 22 shows that the maximum value of WSS increases with increasing flow rate. In case that flow rate in graft is 75% from the total flow rate the maximum values of WSS decrease which can be seen in behavior of WSS for angles 45° and 60°.

Fig.22 Behaviours of mean velocity gradients multiplied by dynamic viscosity for different graft angles and different flow regimes from PIV.

Fig. 21 Wall shear stress on line down from CFD. Fig. 20 Wall shear stress on line up from CFD

Fig. 23 Wall shear stress for angle α = 45° from numerical simulation.


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5 Conclusion

2D PIV measurement was measured in symmetry plane of the model for steady conditions (Re=500; 1400). The length of measured area was approximately 60 mm. The bypass models were made from plexiglass with connection angles 20°, 30°, 45°, 60° and 90°. The host artery and graft diameter were 10 mm. Solution of sodium-iodine was used as a working fluid. Fluorescent particles diameter 1-20 µm were used as seeding particles.

The numerical calculations were carried out for connection angles and regimes as an experiment. Within the framework of the project submitted in this article the calculations on calculation grids with different density were carried out. The influence of the grids on flow characteristic was shown. On the base of this experience suitable calculation grids will be made and additional simulations will be carried out. The simulations of pulsated inlet boundary conditions are also planned to be carried out. The conditions will be set with the help of user define function (UDF) into CFD Fluent.

The definition of the type of flow in the place behind the connection is not possible to determine explicitly if there is only laminar flow due to secondary flow. The scripts for data export were made (velocity profile WSS) which serve as input data for MATLAB. With the help of the scripts the CFD data are compared with data from the experiment.

Methodology for processing of measured data was created and working system for data saving which enables prompt processing and comparing flow characteristics of individual flow regimes in various models was also designed. A set of scripts were created in mathematical software MATLAB for this system. These scripts are prepared for using in evaluation of additional experiments.

The flow field in bypass model was described on the base of results from CFD and PIV. The velocity fields, fluctuation velocity fields for different angles of connection and different flow regimes were evaluated from PIV data. The behaviour of velocity profile gradients on the wall were evaluated in mathematical

software MATLAB. The influence of connection angle on velocity field and velocity fluctuation field was evaluated. |The behaviour of WSS in the symmetry plane was evaluated from CFD calculations. Velocity profiles in the symmetry plane obtained from CFD and PIV data were compared. The agreement of the resultant flow characteristics obtained from CFD and the experiment showed that choice of type, location and selected accuracy of boundary conditions were sufficient. More perfect coincidence is assumed when using grid with more computation cells.

One of the problems when evaluating WSS is velocity evaluating near the wall. At methods which obtain velocity profile on detecting the motion of the seeding particles (e.g. PIV, LDA, UVP), the particles near the wall need not to follow the flow (e.g. the particles get stuck on the wall). Considerable deformation of optical access between measuring point and the sensor near the wall often appears when measuring by optical methods which can be caused by different refraction indexes of models, working fluid and vicinity. When using PIV method the reflections of laser beam appear on boundary between working fluid and the model. These reflections cover signal of seeding particles and thus the measured data near the wall are devaluated. This problem was solved by using fluorescent particles and by filter which transmits only the light with the wave length higher than λ=580 nm. Gradient of velocity profile at the wall was evaluated as equivalent to WSS. The gradient was obtained by fitting a curve with several values of velocity measured near the wall. The results have correspondent qualitative character when comparing with the results from CFD and even with the results which could be found in literature. The calibration measurement by CTA method is planned in order to verify the methodology of WSS evaluation by PIV method.

On the basis of performed experiments and obtained experiences, flow characteristics measurements of connection model by stereo PIV method for obtaining 3D flow field, the measurement at pulsated flow for obtaining flow field in the whole period, extending of


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bypass model with part with stenosis placed in the connection vicinity, are prepared.

Acknowledgements

This research has been supported by grant of GA ČR 101/05/0675 Theoretical and Experimental Optimalization of Vascular Reconstruction in the View of Hemodynamics

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Flow Investigation Behind the End-To-Side Anastomosisfluids.fs.cvut.cz/akce/konference/istp_2005/full/165.pdfbasic idea on flow behind the end-to-side anastomosis; to describe the

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