flow visualisation through model abdominal aortic...
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Fourth Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion The University of Adelaide, South Australia, Australia 7-9 December 2005
Flow Visualisation through Model Abdominal Aortic Aneurysm
R. Cowling and J. Soria
Laboratory for Turbulence Research in Aerospace and Combustion Department of Mechanical Engineering, Monash University, VIC. 3800, AUSTRALIA
ABSTRACT Flow characteristics in Abdominal Aortic Aneurysms have been investigated using Planar Laser Induced Fluorescence (PLIF) for both steady and pulsatile flow conditions. For the pulsatile flow investigations a simple artificial waveform was used. Under steady flow conditions two zones were identified, the first being the bulk fluid through the core of the expansion, and the second being a recirculation zone occupying the majority of the expansion. As Reynolds number increased interaction in the form of a Kelvin-Helmholtz instability was observed between the two zones. Under pulsatile flow conditions the Kelvin-Helmholtz instabilities observed in the steady flow case are amplified and significant vorticity is observed at the distal end of the bulge during parts of the pulsatile flow cycle. 1. INTRODUCTION Following the large scale growth of interest in bio fluids engineering, conventional research on pulsatile flows within pipes or channels is being translated to pulsatile flows within the human body (arterial in vivo flows). The primary impetus for research in this area is to gain an understanding of the characteristics of pulsatile flow within arteries in order to develop treatments for conditions which alter vascular flow. Some examples of such medical conditions are stenosis (constriction tubes) and abdominal aortic aneurysms (sudden expansion). The abdominal aorta is one of the primary arteries of the body that supplies the lower half of the body with blood. The diameter of the abdominal aorta ordinarily lies between 15-20mm [1]. This diameter can dilate into a balloon like bulge referred to as an abdominal aortic aneurysm (AAA). At present there is not a complete census on the definition for AAA for diagnosis purposes, however the disorder is generally diagnosed if the aortic diameter is 30mm or more [2]. Studies indicate that AAA’s occur in 4%-8% of men and 1%-3% of women [3], those most at risk being males over the age of 60. The principal health danger of an AAA is rupture, which in up to 85% of victims is fatal [4], making AAA rupture the 15th leading cause of death in the United States of America [3]. The available treatment options used by physicians include either surgical intervention or continued surveillance; surgical intervention is sought when the cumulative risk for rupture exceeds risk of repair, within the context of overall life expectancy. Currently this risk is primarily gauged on aneurysm diameter; the intrinsic risks associated with surgery are deemed to be outweighed by risk of rupture once the lesion maximum diameter exceeds 50mm. Rupture risk based solely on maximal lesion diameter is a crude criterion at best, as it neglects other factors which could alter the aorta’s fluid flow dynamic and mechanical properties, such as, the bulge shape and wall thickness. The fallibility of this method can be further illustrated with the knowledge that
in some cases aneurysm with a maximal diameter of less than 40mm have been seen to rupture [3]. A better method of determining risk of rupture would be to undertake a biomechanical analysis of the stress state within the arterial wall. Internal stresses exist in the walls due to the flow of blood. Blood exerts both normal and shear forces on the wall inner surface. From a mechanical engineering point of view, aneurysm rupture is analogous to a material failure, whereby the aneurysm ruptures when the stress within the aortic wall exceeds the material limits of the wall. To date, researchers have focused on determining stress states within the aortic walls, and investigating the relationship between the bulge shape and maximal diameter of the aneurysm and the structures present in the flow. This research has been conducted using both computer simulations [1] and experimental models both in vivo and in vitro, in the case of in-vitro models complicated continuous flow loops were employed [5],6] Quantitative steady flow experimental investigations into aortic aneurysm hemodynamics have been conducted using DPIV analysis [7] and laser Doppler velocimetry (LDV) [6]. LDV was used to investigate the relationship between Reynolds number and a transition to turbulence in a pursuit of a critical Reynolds number [6,8]. During these investigations it was revealed that flow within the bulge section can become unstable and exhibit random velocity fluctuations even with controlled steady flow conditions [6,8]. Budwig [8] (1993) characterised this critical Reynolds number to lie between 2000 and 2500. Peattie et al [5], investigated flow fields and flow induced wall shear stress distributions in in vitro models of AAA of varying diameter whilst using a physiological realistic pulsatile flow. The data suggested a strong correlation between the size of the aneurysm and the intensity and frequency of turbulence within the aneurysm, observing the fact that larger aneurysms may be subject to more frequent and intense turbulence than smaller aneurysms. During the last half of the previous century links have been made with regions of atherosclerosis (cardio vascular disease) and/or thrombogenesis (formation of blood clots) with regions of ‘disturbed flow’. In a medical context disturbed flow is defined as regions where recirculation, stagnation, vortex formation or even turbulence can develop [1]. Examples of disturbed flow include flow near arterial branches, curves, contractions or as in the case of this study, aneurysms. As yet studies have still not determined the exact mechanism(s) how the ‘disturbed flow’ conditions contribute to the development of atherosclerosis and/or formation of a mural thrombus (partial clot), but there are several leading theories relating to the effects of disturbed flow (abnormal shear stress distribution/evolution) on the endothelial cell lining. This paper details a preliminary study of the nature of the flow within an axisymmetric AAA model. Initially an investigation into the nature of steady flow through the model over a
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Reynolds numbers range of 500-2500 was undertaken. This testing range is representative of the Reynolds number range present in physiological flow through the abdominal aorta at rest conditions (60 beats/min). Following the steady flow experiments, two pulsatile flows with different frequencies of pulsing will be investigated. 2. EXPERIMENTAL TECHNIQUE 2.1 Models The abdominal aortic aneurysm is modeled by the simplified geometry shown in the schematic in figure 1. Secondary aortic bifurcations were deliberately disregarded to isolate the flow dynamics within the aneurysm itself. The model consists of an acrylic block with a 20 mm bore (d) and an axisymmetric bulge described by the formula representing an ellipse with major (A) and minor axis dimensions (D) 88 mm and 50 mm respectively. A 0.5mm dye hole was located one bore diameter upstream of the expansion. The bore size of 20mm was selected to match the diameter of a normal healthy aorta, and the 50 mm maximal expansion represents the diameter where surgical intervention is sought [9]. The bulge length (L/d=4) was designed to match the typical length of fusiform (spindle shaped) AAA’s [1].
Figure 1. Cross section of Symmetric AAA test model, solid circle shows location of the dye hole 2.2 Flow Parameterisation For pulsatile luminal flow within biological systems, two dimensionless parameters are typically used to characterise the flow conditions, namely the Reynolds number (Re) and the Womersley number (α). The Reynolds number is defined as:
νdU
Re md =
The Womersley number is generally interpreted as the ratio of unsteady force to viscous force or the unsteady nature of fluid flow in response to an unsteady pressure gradient and is defined as:
νωα
2d
=
In this study d is the reference length scale in this case the normal aortic diameter, ω is the frequency of the pulsatile waveform and ν the kinematic viscosity of the working fluid. Within biological systems the Womersley number is used to simplify the characterisation of pulsatile flows in order to formulate both qualitative and quantitative descriptions of physiological processes that are caused by altered flow, such as atherosclerosis. Large Womersley numbers represent a pulsatile flow with large acceleration and deceleration. 2.3 Experimental Apparatus Ku (1997) [10] illustrated several features of vascular flows that can be considered secondary in importance. These include
wall elasticity, and both the non-Newtonian and non-homogeneous properties of blood, which can be safely ignored in arteries with diameter greater than 0.5 mm. As such, water was chosen as the working fluid. The experiments were carried out in the Laboratory for Turbulence Research in Aerospace and Combustion at Monash University within an acrylic quiescent tank 1000 mm long, 500 mm wide and 500 mm deep, filled with filtered water.
The model assembly was positioned in the centre of the end wall of the tank. In each experiment jets were formed by discharging water from a circular cylinder of inner diameter Dp = 50 mm into the model assembly using a stepper motor actuated piston moving within a cylindrical cavity. A diagram is shown in Figure 2.
1. Solo PIV Nd:YAG Laser 2. Riser Tube 3. Image Plane 4. Piston Assembly 5. Lead screw 6. Stepper Motor
1
64
5x
r
Figure 2. Schematic of Exp
Steady flow was forced through the mvelocity piston stroke. Pulsatile fprogramming the stepper motor veltime-periodic function developed byFigure 3, superimposed over a longstroke. Production of a physiologicathe abdominal aorta was found to be the apparatus in its current configurat
00.5
11.5
0 0.25 0.5
t/T
U/U
m
Figure 3. Normalised artificial profile Although the pulsatile motion studiedresemblance to in-vivo flow in the abperiodic acceleration and deceleratiocondition. Using a control volumebetween the piston and model acontinuity equation, the mean velocion the piston speed was calculatepulsatile waveforms were used the firresting conditions) and the second α=conditions) [1]. 2.3 Flow visualisation Planar Laser Induced Fluorescence (the characterisation of the flow fieldflow visualisations were recorded us
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camera with a 55mm telecentric lens with a red filter to minimise noise, mounted on rails with three degrees of freedom. The fluorescent dye used for these experiments was Kiton Red 620, which fluoresces orange (corresponding to a wavelength of 620nm) when illuminated by light with a wavelength of 532nm, in this case a dual cavity Nd:YAG laser. Dye was supplied using a device that provides a constant effusion velocity for liquids [11] known as a Mariotte bottle. The Mariotte bottle was fitted with a micro valve to precisely adjust the flow rate of the dye. The dye was injected through the dye port one diameter upstream of the elliptical expansion. The flow rate had to be carefully monitored to ensure there was minimal disturbance to the flow. 3. RESULTS AND DISCUSSION 3.1 Steady Flow Conditions Under steady flow conditions (Figure 4) two zones were identified; the bulk flow zone through the core of the model, and a recirculation zone forming on the outer surfaces of the bulge. At the bottom of the Re range investigated, this stable (constant growth) recirculation encompassed the entire width of the bulge (Figure 4a). Minimal interaction was observed between the bulk flow and the recirculation. As the Re increased, thinner, more compact, faster rotating dye streak lines were observed in the recirculation zone suggesting an increase in recirculation strength. The beginning of the development of an instability in the shear layer at the distal end of the expansion was observed at Re=1500 (Figure 4b). Despite the presence of this instability only one vortical structure remained identifiable in the recirculation region; however some vortex distortion was noted. It is suggested that this distortion of the vortex may be linked to the development of the shear layer instability; further work is warranted to examine mechanisms for this to occur. From an incompressible 1-D Bernoulli analysis it can be shown that the instability is developing in regions were the flow is accelerating due to the negative (converging) area change. Clear interaction between the two zones was first observed at Re=2000 (Figure 4c). The aforementioned instability appears to have a significant effect on the structure of the recirculation zone with multiple structures of various length scales observed within the recirculation region. Mild asymmetry is also observed. However, caution must be exercised when making observations regarding symmetry of the flow as dye was only injected in one half of the model section. A tendency for intermittent bursts of increased amplification in the flapping of the shear layer was observed for 2000<Re<2500; similar tendencies were reported in [6]. Moving on to the Re=2500 condition, increasing interaction between the bulk flow zone and the recirculation zone was observed. The recirculation zone consisted of multiple structures of different length scales. The presence of smaller scale structures in this mix of varying length scale structures suggests that turbulent transition may have occurred. Asbury et al. [6] observed that a transition occurred under steady flow conditions in a similar model between 2000≤Re≤2500. Further support to the theory of a turbulent transition is the observed asymmetry, suggesting possible three dimensionality within the flow. Caution must be exercised when interpreting momentum transport (vorticity) from observation of scalar transport, as there are differences in the diffusivity term within their respective transport equations [12]. With this in mind, dye was injected as close as possible to the region of interest.
3.2 Pulsatile flow conditions As found by Yu [7] the observed pulsatile flow patterns were markedly different from their steady flow counterparts. The Re range in the pulsatile flow was 1500-2500. For the α=16.9 case significant instabilities were evident in the shear layer (figure 5) resulting in asymmetry along the centreline of the model. Flow within the expansion consisted of 2D and 3D structures of varying length scales. As with the steady flow entrance conditions, an increase in the instability in the shear layer was observed as the cross-sectional area of the bulge was reduced. After increasing the frequency of pulsation to α=22.5, development of Kelvin-Helmholtz instabilities in the shear layer was identified by the characteristic crested wave rollup. This Kelvin-Helmholtz instability induced the rollup of several vortices which were convected downstream and ultimately impinged upon the wall and fragmented. These fragmented vortices then contribute to the recirculating flow around the extremes of the expansion. A time-lapse sequence of images illustrating this observed phenomena can be seen in Figure 6. Studies have suggested areas of ‘disturbed flow’ such as recirculation regions may have significant physiological implications on the function of the protective endothelial lining of the vessel wall. It is put forward by the author that as the bulk entrance flow accelerates the recirculating region is pulled downstream out the distal end of the bulge by the pressure gradient produced by the accelerating bulk fluid. However, in order to ascertain if this is occurring, phase matched measurements coupled with pressure measurements are warranted to determine the temporal pressure evolution throughout the pulsatile cycle. It is suggested that this vortical impingement could impart significant shear stresses on the wall and then as the flow recirculates oscillating shear stresses may be produced along the wall surface. 4. CONCLUSION A study of the flow characteristics within an in vitro AAA model under steady and pulsatile conditions has been conducted. In steady flow, two zones were identified; the first being a bulk flow zone through the core of the model and second being a recirculation zone occupying the top and bottom regions of the expansion. At Reynolds numbers below 1500 minimal interaction was observed between these zones. At Re=1500, development of an instability at the distal end of the bulge was observed. Further increases of the Re saw an amplification of this instability. Under pulsatile flow conditions asymmetry was produced, the instabilities observed in the steady flow case were amplified and developed into a Kelvin-Helmholtz instability. Significant vortical activity is observed at the distal end of the bulge during parts of the pulsatile flow cycle. REFERENCES: [1] Egelhoff, C.J., Budwig , R.S., Elger D.F., Khraishi T.A., Johansen, K.H.,1999" Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions” J. Biomechanics,32,1319-1329. [2] Sakalihasan, N., Limet, R. and Defawe, O.D., 2005, “Abdominal Aortic Aneursym”, Lancet, vol 365, 1577-1589. [3] Singh K., Bonaa K.H., Jacobsen B.K., Bjork L., Solberg S., 2001, “Prevalence of and risk factors for abdominal aortic aneurysms in a population-based study - The Tromso Study”;American Journal of Epidemiology, 154, 236 –244.
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[4] Knimeyer, H.W., Kessler T., Reber P.U., Ris, H.B., Hakki H., 2000, “Treatment of ruptured abdominal aortic aneurysm, a permanent challenge or a waste of resources? Prediction of outcome using a multi-organ-dysfunction score.” European Journal of Vascular Endovascular Surgery, 19 pp190-196. [5] Peattie, R.A., Riehle, T. J., Bluth, E.I., 2004, “Pulsatile flow in fusiform models of abdominal aortic aneurysms: Flow fields, velocity patterns and flow-induced wall stresses”, ASME Journal of Biomechanical Engineering, 126, 438-446. [6] Asbury, C.L., Ruberti, J.W., Bluth, E.I. and Peattie, R.A., 1995, “Experimental investigation of steady flow in rigid models of abdominal aortic aneurysms”, Annals of Biomed. Eng, 23, pp. 23-29. [7] Yu, S.C.M., 1999, “Steady and pulsatile flow studies in abdominal aortic aneurysm models using particle image velocimetry”, International Journal of Heat and Fluid Flow, 21, pp. 74-83. [8] Budwig, R., Elger, D., Hooper, H., Slippy, J., 1993. “Steady flow in abdominal aortic aneurysm models”. ASME Journal of Biomechanical Engineering 115, 418-423. [9] Johansen, K.H.,1982, “Aneursyms”, Scientific American, vol 247, pp. 110-125. [10] Ku, D.N., 1997, “Blood flow in arteries”, Annual review of Fluid Mechanics, 29, pp. 399-434. [11] Maroto, J., de Dois, J. and de las Nieves, F., 2002, “Use of a Mariotte bottle for the experimental study of the transition from laminar to turbulent flow”, American Journal of Physics, Vol. 70, No. 7, pp. 698-701. [12] Lim, T. T., 2000, Flow-Visualisation: Techniques and Examples, edited by T.T. Lim and A.J. Smits, published by Imperial College Press.
Figure 4: Steady flow
Rem=2000 α=16.9
Figure 5: Pulsatile flow
T+0 secs
T+0.125 secs
4a) Re=500
T+0.250 secs
4b) Re=1500
T+0.375 secs
4c) Re=2000
Figure 6: Pulsatile flow Rem=2000 α=22.5
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