Experimental study of hemodynamics in the circle of willis
Model preparation
In previous studies, various techniques were used to measure the geometry of the CoW,
including CTA imaging, MRI and direct measure of cerebral vessels. Due to individual
differences, the dimensions of each artery segment are varied from case to case. In
this study, average length and diameter from previous studies were used in this study
to achieve a universal model 33,36,44,47,52]. The dimensions of each segment are listed in Table 1 and a physical model based on these dimensions was constructed. To simplify the model,
each vessel is represented by a single silicon tube of constant radius. This simplification
is acceptable because the length of every segment is relatively short and the conicity
index is relatively small at cerebral artery site.
Table 1. Diameters and length of vessels.
To simulate the different degrees of ICA stenosis, a set of connectors with different
flow tunnel diameter was prepared. All connectors were made by copper cylinders of
a length of 20 mm and an outer diameter of 4.5 mm. Flow tunnels with different diameters
were drilled at the centre of the cross section along the axial direction to simulate
different degrees of stenosis of ICA. The degree of stenosis is defined as the ratio
of inner diameter of stenosed artery over original inner diameter. L-ICA occlusion
was simulated by clamping the tube using a hemostat.
Physiological flow system
The schematic diagram of the patented (ZL 200910021375.5) test rig is shown in Figure
2. A linear actuator (LMS 50, PBA System Pte. Ltd., Singapore) controlled by a programmable
servo (Cornet COR 5/230, Elmo Motion Control Ltd., Israel) was used to drive the piston
to generate pulsatile pressure waveforms. Function as mitral valve and aortic valve
to prevent back flow, two one-way valves were connected to reservoir tank and compliance
chamber, respectively. The effect of artery compliance was simulated by imposing an
air chamber which air volume is adjustable. A flow distributor after the compliance
chamber separated the flow into four branches and connected to the four afferent arteries
of the CoW model.
Figure 2. Schematic of experimental test rig.
A physiological pulsatile pressure waveform for the bilateral ICA and VA were applied
as inlet boundary condition (Figure 3). The systolic pressure, diastolic pressure and average pressure are 16.1 kPa (120.7
mmHg), 10.97 kPa (82 mmHg) and 12.7 kPa (95 mmHg), respectively 44,45,53]. The inlet pressure was measured by using dynamic pressure transducer (ATM231, Sensoren
Transmitter Systeme GmbH, Sindelfingen, Germany). Six micro pressure transducers (XCQ-062,
Kulite Semiconductor Products Inc., Ridgefield, NJ, USA) were installed at six bifurcation
sites of the model, include the the bifurcation at the junction of bilateral PCA and
PCoA, the bifurcation at the junction of bilateral MCA and PCoA and the bifurcation
at the junction of bilateral ACA and ACoA. Pressure signals at these sites were recorded
by a data acquisition system (Vision XP, LDS Test and Measurement GmbH, Ismaning,
Germany).
Figure 3. Inlet pressure waveform.
Adjustable resistors were connected to the end of efferent arteries. Six beakers were
placed at ends of the efferent arteries, and volume of fluid flows out from each efferent
artery was measured periodically, to calculate the total mean volume flow rates and
the flow rate of each efferent artery. The fluid collecting system simultaneously
collected outflows from the CoW and distributes the fluid into six beakers so that
the mean flow rate can be measured. The total flow rate of the complete CoW was set
at physiological level of 760 ml·min-1, and the flow rate ratio between VAs and ICAs was 30:70. The cardiac cycle was set
to 0.8 s (75 beats·min-1).
All devices were turned on 30 minutes before data collection for warm up and reach
a stable condition. Measurements were collected for 100 consecutive cardiac cycles,
and were repeated three times for each cases mentioned above. In the complete CoW,
the pressure waveforms measured over 100 cycles in L-ICA was within 0.1% for peak
systolic pressure and peak diastolic pressure respectively, shows an excellent repeatability
between cycles. The average pressure difference between L-ICA and R-ICA of the complete
CoW at systolic peak is less than 0.8%.
Working fluid
Blood is a non-Newtonian multiphase fluid with shear thinning properties. However,
most researchers have considered blood as a Newtonian fluid except when they study
the blood flow in medium to large arteries 54,55]. In this study, blood was assumed as Newtonian fluid. The working fluid applied here
is a 40% aqueous solution of glycerin (volume ratio), the viscosity and density of
which is 3.5 mPa·s (DV-III+, Brookfield, USA) and 1056 kg·m-3, respectively.
Experimental methods
To investigate the blood flow distribution in the CoW under different ICA stenosis
degrees, a series of pathological variations were considered, including:
1) Complete circle;
2) Different stenosis degrees of L-ICA (40%, 50%, 60%, 75%, and 87.5%) and L-ICA complete
occlusion;
3) L-ICA occlusion coexist with the absence of communication arteries (R-PCoA, ACoA
and L-PCoA).
Flow rates of above conditions were recorded and analysed.
To investigate the collateral mechanism of the CoW, pressure at both ends of each
communicating artery (ACoA, L-PCoA and R-PCoA) under different L-ICA stenosis degrees
was recorded, and this also provide indication of the flow direction.