Pulsatility index as a parameter for clinical diagnostics of vascular disease Idit Avrahami1, Dikla Kersh2, Alex Liberzon2 *1 Department of Mechanical Engineering and Mechatronics, Ariel University, Israel,
[email protected] 2
School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
Abstract Arterial wall shear stress (WSS) parameters are widely used as prediction criteria for the initiation and development of atherosclerosis and arterial pathologies. However, clinical measurements of local WSS require complicated and expensive techniques and therefore traditional clinical evaluation of arterial condition relay mainly on flowrate and heart rate measurements. In this manuscript we show that heart rate and flowrate measurements are not sufficient for prediction of local WSS parameters and we suggest a third parameter based on the local pulsatility index (PI). The study includes experimental measurements of the flow profiles and WSS parameters of 16 different physiological flow waveforms in a straight arterial model. For each case, the phase-averaged velocity profiles were measured using digital particle image velocimetry techniques and were used to estimate WSS parameters utilizing the Womersley pulsating flow model. The results show that heart rate and flowrate parameters were not sufficient for prediction local WSS parameters for the 16 cases, while PI parameter exhibited well one-to-one correlation with WSS oscillatory index (OSI) and with the frequency of negative WSS occurrence (P[%]). In addition it provide a lowest limit for the peak-to-peak WSS ratios (min/max) for varying conditions. Therefore, PI was found to be an essential parameter for the complete description of the local WSS quantities for arterial flow.
Keywords wall shear stress, pulsatility index, digital particle image velocimetry, Womersley model
1
Introduction
Hemodynamics dysfunction has been strongly correlated with cardiovascular diseases and disorders, with majority of pathologies related to low, oscillatory, turbulent or negative nearwall shear stresses (WSS) (Caro et al. 1971; Ku et al. 1985; Nerem 1992; Malek et al. 1999; Resnick et al. 2003; Boussel et al. 2008; Peiffer et al. 2013). Arterial WSS are known as a main regulator of endothelial cell function and vascular structure (Reneman et al. 2006; Gonzales et al. 2008). Moreover, it was proved that Nitric oxide (NO) production is reduced in reverse flow and that negative WSS lead to vascular dysfunction, including intimal hyperplasia, cell activation and platelet adhesion (Lu and Kassab 2004). Particularly, in advanced congestive heart failure, the combination of reduced cardiac output (CO) compensated by increased heart rate (HR) promotes retrograde flow and negative shear stress over a major part of the cardiac cycle (Gharib and Beizaie 2003). However, clinical evaluations of time-dependent WSS in-vivo require complicated and expensive 4D MRI or Ultrasound techniques (Reneman, Arts et al. 2006; Leguy et al. 2009; Harloff et al. 2010). These techniques require accurate measurement very close to the wall, and therefore are often inaccurate and far from being a part of routine cardiovascular exams. The routine exams usually include measurements of flowrate and HR, and can be correlated with the hemodynamic parameters of Reynolds number and Womersley number. For example, Finol et al. (2002) found that the maximal values of non-dimensional mean WSS and non-dimensional WSS gradient increase with the Reynolds number, while others showed a strong correlation between Womersley number and WSS (Niebauer and Cooke 1996). Increased HR is considered a major risk factor for cardiovascular disease (Palatini and Julius 2004; Fox et al. 2008), and when medically treated, was found to reduce heart failure (Böhm et al. 2010). Yet, for the same HR and flowrate, the local time-dependent flow waveform, and thus local WSS parameters, may change drastically. For example, the aortic wave steepening downstream the aorta, caused by wave reflection and diameter reduction (Yomosa 1987; Nichols and O'Rourke 1998) result in different time-dependent flow waveforms at different locations. In addition, due to the loss of flow to the renal track, infrarenal positions show a higher level of retrograde flow and negative WSS than suprarenal positions (Oyre et al. 1997; Gharib and Beizaie 2003). This yields completely different WSS parameters along the same aortic trunk. Moore et al. (Moore et al. 1994) demonstrated already in 1994 that local oscillating WSS in the infrarenal aorta tend to develop atherosclerosis while regions of relatively high wall shear stress tend to be spared. Therefore, HR and flowrate are not sufficient parameters to predict local WSS. In this study we suggest using a pulsatility parameter in addition to flowrate and HR as a part of clinical practice, to better predict local WSS parameters in the main arteries. Pulsatility index (PI), first introduced by Gosling and King (1974), is a measure of the variability of blood velocity in a vessel, typically based on Doppler Ultrasound measured
waveform. It is equal to the difference between the peak systolic and minimum diastolic velocities divided by the mean velocity during the cardiac cycle. Pulsatility index is quantifying the pulsatility or oscillations of the flow waveform and it has been shown to be well correlated with arterial stenosis (Evans et al. 1980). This manuscript describes the experimental methods in which the relation of HR, flowrate and PI to the important WSS parameters has been found. We utilize optical imaging methods to the well-controlled pulsating flow of different waveforms to shed light on the significance of the proposed relations.
2
Materials and Methods
2.1
Experimental method
A custom-design flow test rig was developed to create well-controlled pulsatile flows. The measurements used digital particle image velocimetry (DPIV) technique to extract time-dependent velocity profiles (see Figure 1 for schematic description), as detailed below.
Figure 1: A setup scheme of the phase-averaged DPIV measurement systems. The computer
controlled waveform pressure signal was continuously monitored as shown in the inset and the DPIV system was triggered at each cycle using the pressure sensor output and the prescribed threshold.
The pulsating flow is created in an elastic tube (made of Tygon B-44-4X, Saint Gobain, inner diameter of 3/4” and wall thickness of 1/8”, L/d ≥ 40, elasticity modulus of 12 MPa, estimated distensibility 1.36 × 10−6 Pa−1) by a set of three DC voltage driven computer controlled gear pumps. In order to allow high quality optical measurements, the tube was placed in a 800 × 300 × 200 mm glass tank filled with a refractive index matched liquid (60%w
glycerin-water solution). A 40%w glycerin-water solution was used as blood
mimicking fluid. The flow was monitored using pressure transducers (EW-68075-02, Cole Parmer) and magnetic flow meter (MAG 1100, Danfoss). We created a set of physiological like flow waveforms in the following range of the flow parameters: Reynolds number between
Re= 60 ÷ 900, Womersley number α= 6 ÷ 11 and PI = 1.5 ÷ 9. We implemented digital particle image velocimetry (DPIV) technique using a dual Nd:YAG laser (532 nm, 120 mJ/pulse, Solo 120XT, New Wave Research), a highresolution CCD camera (12 bit, 4008×2672 pixels, TSI Inc.). Silver-coated hollow glass spheres (14 µm, 1.05 g/cm3, TSI Inc.,) were used as seeding particles. More than 100 images were acquired at each of the 7 phases of the pulse period, triggered by the pressure transducer. Phase averaged velocity was estimated using a commercial software
(Insight3G,
TSI
Inc.)
and
verified
with
an
open
source
software
(www.openpiv.net) (Taylor et al. 2010).
2.2
Wall shear stress related properties
Wall shear stresses were estimated by utilizing the Womersley solution for pulsating flow in a rigid tube (Womersley 1955a). The flowrate waveform Q(t) has been calculated by integrating the measured velocity profiles. The Fourier coefficients of the signal were calculated using fast Fourier transform (k = 32, N = 100): N − `1
Qk = ∑ Qn e
−j
2πk N
,
(1)
n =0
where Qn is the nth component of the flow rate waveform in its Fourier representation. Velocity profiles are estimated from the Fourier representation of the flow rate waveform according to the inverse Womersley relations:
⎧ ⎫ ⎛ 3 / 2 ⎛ 3 / 2 r ⎞ ⎞ 3/ 2 3/ 2 ⎪⎪ N −`1 Q ⎜ j α n J 0 j α n − j αJ 0 ⎜ j α n ⎟ ⎟ ⎪ R ⎠ ⎟ − jωnt ⎪ ⎝ u (r , t ) = Re ⎨ ∑ n2 ⎜ e ⎬ ⎜ ⎟ j 3 / 2α n J 0 j 3 / 2α n − 2 J1 j 3 / 2α n ⎪ n = 0 πR ⎜ ⎪ ⎟ ⎪⎩ ⎪⎭ ⎝ ⎠
(
)
(
where Jo and J1
ωn and ν
(
)
(2)
are the zero and first order Bessel functions respectively, ω is the
pulsation frequency, j = αn = R
)
th − 1 and α n is the n
Womersley number defined as
R is the inner radius of the pipe. Finally, WSS can be estimated directly from
the obtained Womersley velocity profiles at different phases. The flow waveforms were characterized using three non-dimensional Reynolds, Womersley and Pulsatility Index (PI) numbers:
Re = Re max = U max D /ν
α = R ω /ν
(3)
PI = (Qmax − Qmin ) / Qmean where Umax is the maximal time averaged velocity, D is the tube inner diameter and ν is the kinematic viscosity of the fluid. High PI values characterize severe reverse flow phases.
The following WSS related properties are considered in the present study:
min/ max = P[%] =
τ max τ min
t τ
