Abstract. 1 Introduction

Transcription

1 A numerical study of the flow disturbance caused by an intravascular Doppler catheter in a blood vessel Giulio Lorenzini D.I.E.N.C.A. - Dipartimento diingegneria Energetica Nucleare e del Controllo Ambientale, Universita' degli Studi di Bologna, Viale Risorgimento, 2, Bologna, Italy giulio. lorenzini@mail. ing. unibo. it Abstract In this paper, the flow disturbance caused by the presence of an intravascular Doppler catheter inside coronary arteries has been studied. Numerical investigations have been carried out on 2-D models of cylindrical blood vessels with a concentric catheter tube. The CFD package CFX 4.1 was used to calculate the flow patterns inside the blood vessels. Computer simulations have been performed for a range of coronary vessel sizes, flow rates and inlet velocity profiles. Predicted results have shown that the propagation of the flow disturbance and its magnitude were greater in larger blood vessels and for higher blood flow rates. 1 Introduction The use of intravascular Doppler catheters has become a very popular medical technique in the study of blood flow inside coronary arteries affected by various types of pathologies. However, it has been argued that the reliability of the velocity measurements obtained with this method may be influenced by the flow disturbance created by the presence of the catheter itself inside the blood stream [1,2]. Tadaoka et

2 104 Advances in Fluid Mechanics II al. [3], for example, have assessed the validity of the Doppler catheter velocimetry in an experimental model of a coronary artery and found that measured velocities were always lower than the known velocities for these vessels. Yamagishi et al. [4] have admitted that this method is simple and convenient; however, they found that flow measurements were inaccurate in areas of disturbed flow and incapable of detecting true peak velocities. The objective of this work is to gain a better understanding of the disturbance phenomenon produced by the presence of the catheter inside the blood flow. The investigation was carried out using a CFD model of the blood vessel-catheter tube flow and was aimed at assessing the influence of (i) the blood vessel size, (ii) the value of the blood flow rate and (iii) the inlet velocity profile on the propagation of the disturbance and, comparing the magnitudes of the disturbance at the flow measurement location for all the different cases considered. In this paper, the numerical model is described in its details in the method section; predicted results are presented and discussed in the results and discussion section; conclusive remarks and recommendations for future work are given in the conclusion section. 2 Method For this initial study, a simplified geometrical configuration has been used for the analysis of the disturbance caused by the catheter on the velocity profiles of the coronary vessels. Similarly, simplifying assumptions were adopted for the boundary conditions. A portion of a cylindrical straight coronary vessel having a constant cross section has been considered. Inside the blood vessel a portion of a concentric, cylindrical straight catheter tube having a constant cross section was located. The flow was assumed steady and laminar and the fluid newtonian, isothermal and incompressible. The study focused on the parametric analysis of the velocity distribution of blood inside the domain for different coronary vessel diameters, mass flow rate values and velocity profiles at the inlet plane. Three values of the vessel diameter, d, have been considered (2, 4 and 6 mm), for three values of flow rate,/, (20, 135 and 250 ml/min) and two different inlet velocity profiles ( and parabolic). The above chosen values for the blood vessel diameter and for the flow rates are typical for coronary arteries. A summary of the analysis parameters considered is reported in TABLE 1.

3 Advances in Fluid Mechanics II 105 TABLE 1 Summary of the analysis parameters Blood Vessel Diameter (mm) Flow Rate (ml/min) Inlet Velocity Profile parabolic For every blood vessel diameter considered, the effects produced by all three different flow rates and by both inlet velocity profiles have been studied. Therefore, 18 cases have been studied in total. The catheter diameter, equal to 1 mm, the length of the portion of catheter considered, equal to 30 mm, and the total length of the blood vessel, equal to 480 mm, were the same in these 18 cases. The length of the blood vessel was chosen to ensure that the flow at the outlet was fully developed in all cases. 2.1 Numerical model The numerical simulations of the above described 18 cases have been performed using the general purpose CFD software CFX 4.1 (AEA Tech., Harwell, UK). This is based on the Finite Volume Method and solves the full Navier-Stokes equations in body-fitted multi-block structured grids. The numerical modelling work was carried out in 4 phases: 1) pre-processing; 2) front-end generation; 3) flow solving; 4) post-processing. The pre-processing has been performed using CFX-MESHBUILD and it can be divided into three steps: a) geometry definition; b) boundary condition assignment; c) grid generation.

4 106 Advances in Fluid Mechanics II The geometry construction began with the assignment of the x-y coordinates of the key points for the definition of the analysed geometry, 12 points for this study. Five faces have then been created with the selected points and grouped together. The group has then been extruded in the z direction creating in this way a "fictitious" third dimension, which was "one cell thick". The final geometry topology was composed of 5 blocks. As an example of the generated geometries, an enlargement of the 6 mm diameter geometry is reported in Fig. 1. Once the geometry was built, the boundary conditions of the problem had to be assigned by means of a "set patch" operation. WALL patches have been set at the catheter surfaces and at the blood vessel internal walls; the three outlet patches have been set to be PRESSURE boundaries; the two inlet patches have been set to be INLET patches with velocity profile or MASS FLOW BOUNDARY patches with a parabolic velocity profile; the surfaces perpendicular to the 2-D model were assigned to be SYMMETRY planes. See Fig. 2 for details. The last part of the pre-processing phase was the generation of the grid subdivisions. The grid was set to be finer in the proximity of the catheter tube, both in the x and y directions, and expanded gradually from it with an expansion factor of 1.05 in the axial direction and 1.1 in the radial direction. A total number of 140 subdivisions in the x direction was used; in the y direction the catheter tip was divided in 10 equal intervals, while the remaining top and bottom parts have been subdivided in 28, 20 or 8 intervals for a d of 6, 4 or 2 mm, respectively. The total numbers of cells used per each d are summarised in TABLE 2. Details of the grid near the catheter tip for a model with d = 6 mm are shown in Fig. 3. TABLE 2 Total number of cells for each d d = 2 mm 2080 d= 4 mm 3760 d= 6 mm 4880 The simulation parameters have been specified in the command file. Among them were the different values of the inlet velocity of blood for the velocity profile or the values of the inlet flow rate for the parabolic velocity profile. Moreover, blood was assumed to be a newtonian fluid even if it is not: however, a study of this property was not the aim of this work. The blood flow was also specified to be laminar, Re varying between about 19 (d=6 mm; f=20 ml/min) and about

5 Advances in Fluid Mechanics II (d=2 mm; f=250 ml/min).velocity data were extracted from the output data using a fortran user routine (USRTRN). To run the software, geometry file, command file and fortran routine were linked with the flow solver CFX-F3D. Velocity patterns were visualised using CFX- VIEW. Plots of the velocity data at different x locations were produced using Excel 5.0 for Windows. Figure 1: Geometry details of the numerical model (d = 6 mm). Wall Mass Flow Boundary/Inlet, Wall Wall Wall Press u re Boundary Mass Flow Boundary/Inlet Wall Figure 2: Patch detail in a rescaled model (d = 6 mm) Figure 3: Grid detail in the proximity of the catheter region.

6 108 Advances in Fluid Mechanics II 3 Results and discussion The first part of the parametric study has assessed the extent of the propagation of the disturbance along the x-axis. This was done by finding at which x the disturbance due to the presence of the catheter could be considered insignificant. Velocity profiles were analysed for the different inlet flow rates, the blood vessel diameters and the inlet velocity profiles. The undisturbed lengths, /, for the 18 cases examined are given in TABLE 3. As can be seen, the propagation of the disturbance increases with the flow rate of one order of magnitude when the flow rate goes from 20 to 250 ml/min. As far as the influence of the blood vessel diameter is concerned, it can be noted that for given values of the flow rate and inlet profile, the propagation of the disturbance increases with the diameter. This is maximum in the case of a/= 135 ml/min and increases by a factor 2 when going from d = 2 mm to d = 6 mm; a smaller increase is present also in the other cases. The analysis of the effect of the inlet velocity profile on the propagation of the disturbance is contradictory in some cases. In fact, while for/= 20 and/= 135 ml/min the propagation of the disturbance is larger when the inlet velocity profile is uniform (), for y^ 250 ml/min the effect is inverted. However, the flow inlet profile used in this study was not physiologically realistic and therefore the latter results were considered of secondary importance. To estimate the magnitude of the flow disturbance due to the presence of the catheter, the velocity distributions were investigated at the x location of 6 mm downstream the catheter tip. This location is intermediate ( between 2 and 10 mm ) for typical intravascular Doppler catheter measurements. Results are plotted in Fig. 4 where fully developed velocity profiles are compared to the disturbed profile at x = 6 mm. No significant change was seen between the parabolic and the inlet velocity profile cases and, therefore, only the inlet velocity profile cases are shown. In agreement with what was previously observed, the magnitude of the disturbance increases with the blood vessel diameter. A typical "M" shape velocity profile at the chosen x location was generally seen for the disturbed flow sections. This was not very evident for the six cases with f= 20 ml/min, but became more pronounced for the cases with/= 135 ml/min and even more accentuated for the cases with/= 250 ml/min.

7 Advances in Fluid Mechanics II 109 TABLE 3 Undisturbed lengths (mm) for the 18 cases studied /=20 ml/min 526 d= 2 mm d = 2 mm d= 2 mm i d = 4 mm 63.5 /=135 ml/min d = 4 mm /=250 ml/min d= 4 mm d=6 mm d= 6 mm Plug I = d=6 mm (a) (b)

8 110 Advances in Fluid Mechanics II (c) (d) (e) (0 (g) (h)

9 Advances in Fluid Mechanics II 111 Figure 4: Comparison between the velocity profile at x = 6 mm and at x = 450 mm downstream the catheter tip. (a)/= 20 ml/min ; d = 2 mm; (b)/= 135 ml/min ; d= 2 mm; (c)/= 250 ml/min ;rf=2 mm; (d)/= 20 ml/min ;rf=4 mm; (e)/= 135 ml/min ; d- 4 mm; (f)/= 250 ml/min ; 6/=4 mm; (g)/= 20 ml/min ;rf=6 mm; (h)/= 135 ml/min \d=6 mm; (i)/= 250 ml/min ; d- 6 mm; 4 Conclusions In this paper, the effect of a catheter on the blood flow inside a coronary artery has been investigated. In its initial stage, this work has focused on simplified geometry and flow boundary conditions for which basic considerations can be made. Simulations were performed using the software CFX 4.1. The geometry, the boundary conditions and the grid were defined with the pre-processor CFX-MESHBUILD. Results have shown that the flow disturbance due to the presence of the catheter inside the blood vessel propagates more extensively for higher blood flow rate and larger blood vessel diameters. The effect of different velocity profiles on the flow disturbance was found to be insignificant. These results were found to be in general agreement with other experimental and numerical studies, such as those carried by Tadaoka et al. [3] and by Yamagishi et al. [4]. In this paper ml/min has been used to specify blood flow rate rather than cm-vs, being the former more typical in blood flow studies ((1/60) is the conversion factor). Further numerical research will be required for non-concentric catheters and pulsatile flow inlet conditions.

10 112 Advances in Fluid Mechanics II Acknowledgements This paper was written during the time that the Author spent in the Department of Mechanical Engineering and Aeronautics (MEAD) of City University, London, UK, as a Visiting Researcher. A special acknowledgement is due to Dr. Francesca ludicello (Research Fellow, MEAD, City University) for her conscientious and competent technical support, for her extraordinary ability as a supervisor and for the constant moral support to the Author. An acknowledgement also due to Ms. Chantelle Taylor (Undergraduate Student, MEAD, City University) for her caring and patient help with the plotting of the results. References [1] Moraes, R., Evans, D.H., "Effects of non uniform insonation by catheter-tipped Doppler transducers on velocity estimation", Ultrasound in Med. & Biol., Vol. 21, No. 6, pp , [2] Spencer, K.T., Lang, R.M., Neumann, A., Borow, K.M., Shroff, S.G., "Doppler and electromagnetic comparisons of instantaneous aortic flow characteristics in primates", Circulation Research, Vol. 68, No. 5, pp ,1991. [3] Tadaoka, S., Kagiyama, M., Hiramatsu, O., Ogasawara, Y., Tsujioka, K., "Accuracy of 20 MHz Doppler catheter coronary artery velocimetry for measurements of coronary blood flow velocity", Cathet. Cardiovasc. Diagn., Vol. 19, pp , [4] Yamagishi, M., Hotta, D., Tamai, J., Nakatani, S., Miyatake, K., "Validity of catheter-tip Doppler techniques in assessment of coronary flow velocity and application of spectrum analysis method", Am. J. Cardiol., Vol. 67, pp , 1991.