S/D (systolic end-diastolic flow rate ratio), PI (pulsatility index), and RI (resistance index) are the three most commonly parameters in ultrasound doppler measurement. Specifically, the three indicators for arterial vascular evaluation can be used for carotid artery or umbilical artery assessment. In addition to the three indicators mentioned above, sometimes, specific blood flow velocity values are measured. For example, the peak systolic flow velocity at the stenosis location, which is used to estimate the degree of carotid artery stenosis and the blood flow of internal fistula in hemodialysis patients. The estimate is used to assess the maturity and patency of the internal fistula. However, the objective existence of measurement errors cannot be avoided in any measurement. Let’s talk about what operations may bring errors to the measurement briefly.
First of all, all measurement sources come from the doppler frequency shift formula
Fd =2*F0*V*cos(a)/c
Where Fd is the doppler frequency shift (or frequency deviation), F0 is the ultrasonic emission frequency, V is the flow velocity, a is the angle between the Doppler scan line and the flow direction (ie doppler correction angle), and c is the speed of sound. After the ultrasound system detects the Doppler signal, it obtains a spectrogram through spectrum analysis, and estimates the maximum flow velocity and average flow velocity at each moment on the spectrogram. This is also the basis of all doppler measurements. Therefore, before understanding Doppler measurement, it is necessary to understand how the maximum flow velocity curve and the average flow velocity curve come from.
It has different moving speeds for the blood cells in the area covered by the Doppler sampling gate with different moving speeds, which will generate Doppler signals with different Doppler frequency shifts. We intercept a section of Doppler signal from the received Doppler signal. Although this section of signal is random and irregular in waveform, it can be assumed to be superimposed by signals of different intensities and different frequencies. The so-called spectrum analysis is to perform Fourier analysis on a section of Doppler signal, so as to estimate the intensity of different frequency signal components. The frequency here corresponds to the Doppler frequency shift, so according to the Doppler frequency shift formula, if the Doppler frequency shift is known, then the movement speed corresponding to this frequency shift can be deduced.
V = Fd*c/[2*F0*cos(a)]
The original spectrogram depicts the signal strength (Y axis) as a function of the Doppler frequency shift (X axis). Due to the linear relationship between V and Fd, the spectrogram can be interpreted as the functional relationship between signal strength and blood cell movement speed.
Take the carotid artery Doppler spectrogram in the above figure as an example, from which we select the spectrogram (the power spectral density function curve of the signal) at the peak systolic (S) and end-diastolic (D) moments in a cardiac cycle. The results drawn by the curve are shown in the figure below, and the X-axis represents the flow rate. It can be seen from the figure that at the peak time of systole, the flow velocity is between 34~62cm/s, and the flow velocity at the end of diastole is between 0~18cm/s. Since the sampling gate only covers a part of the center of the blood vessel, there is a “empty window” phenomenon on the spectrum, that is, the intensity of the flow velocity range of 0~34cm/s displayed by the spectrum at time S is very low. As the sampling door increases, the “empty window” will decrease until it disappears (when the sampling door covers the entire vessel cavity), but as long as the sampling door always covers the center of the blood vessel, the upper edge of the flow velocity distribution is basically unchanged, that is, the highest flow velocity estimate Basically unchanged.
Generally, the estimation of the highest flow velocity has a numerical method based on a spectral curve function at a certain moment, and an image processing method based on a two-dimensional spectral image. The former is simple to calculate and is convenient for real-time estimation, so numerical methods are mostly used in actual systems. For ease of understanding, take the simplest threshold method as an example, that is, set a threshold that exceeds the noise intensity (as shown by the yellow line in the figure), and search for the first point that exceeds this threshold from the top of the spectrogram. In the figure, the first point exceeding the threshold at time S corresponds to a flow velocity of 62cm/s, and the corresponding point at time D that exceeds the threshold is 18cm/s. Therefore, the estimated maximum flow velocity at time S and D are 62cm/s and 18cm, respectively. /s. The selection of the threshold has a direct effect on the estimation of the highest flow rate. As the threshold increases, the estimated maximum flow rate decreases. In other words, the threshold is unchanged, but the Doppler gain is reduced, which will also cause the estimated maximum flow velocity to decrease. The actual system may estimate the highest flow rate of the original power spectral density function, so it will not be affected by the gain change.
Since it is generally fixed for the number of points in the height direction of the spectrogram, the larger the flow velocity range (PRF), the larger the velocity interval corresponding to each point, and the greater the flow velocity error of one point in the maximum flow velocity estimation. Therefore, when setting the PRF, try to make the spectrogram of arterial blood flow fill most of the image area, so as to minimize the maximum flow velocity estimation error.
Since the power spectral density function represents the distribution of the intensity of different flow velocity components, the average flow velocity of the blood flow covered by the sampling gate can be estimated by obtaining a weighted average.
The three commonly used parameters of S/D, PI and RI are all calculated based on the estimated maximum flow rate curve, and their definitions are as follows
S/D = V(Systole)/V(Diastole)
PI = [V(Systole)-V(Diastole)]/TAMAX
RI = [V(Systole)-V(Diastole)]/ V(Systole)
TAMAX is the highest flow rate curve intercepting a cardiac cycle and averaged, V (Diastole) may be Vmin (the minimum value of the highest flow rate curve in a cardiac cycle) or V (End-Diastole) (the highest flow rate in the end diastole). Preset is available in some systems.
When calculating the three parameters, we often don’t care about the Doppler correction angle a, because the numerator and denominator both contain a variable of 1/cos(a) when calculating these three parameters. The division operation just takes this variable eliminated.
In the evaluation of hemodialysis vascular access, what often mentioned are the three-phase high-impedance spectrum (preoperative or postoperative stenosis and blockage of the internal fistula) and the two-phase low-impedance spectrum (the mature and unobstructed internal fistula). If you need to use these three parameters in terms of representation, we can make a qualitative statement. The following figure shows the spectrum of arterial reactive hyperemia as an example. The first segment is the high-impedance spectrum, and the latter segment is the low-impedance spectrum. V (Systole) are equivalent, but the V (diastole) high-impedance spectrum is significantly lower than the low-impedance spectrum, so the S/D of the high-impedance spectrum is obviously larger. The high-impedance spectrum [V(Systole)-V( Diastole)] is also greater, so the RI is greater. The diastolic flow rate of the low-resistance spectrum decreases slowly, so the TAMAX of the low-resistance spectrum is obviously larger than that of the high-resistance spectrum. The [V(Systole)-V(Diastole)] of the low-resistance spectrum is smaller, so the PI of the low-resistance spectrum is also smaller.
The estimation of blood flow is an important indicator for the evaluation of the maturity and patency of internal fistula, and the estimation of blood flow generally cannot aovid the influence of correction angle, whether it is based on the highest flow rate curve or the average flow rate curve.
V ~ 1/cos(a)
There are two things here: on the one hand, the correction angle must be set accurately, that is, the line segment indicating the correction angle should be as parallel to the blood flow direction as possible (generally parallel to the vessel wall); on the other hand, by adjusting the deflection angle of the PW scan line The artificial inclination angle with the probe and the blood vessel makes the correction angle as small as possible. For most peripheral blood vessels parallel to the skin, the correction angle is expected to be close to 60 degrees. The minimum interval for manual adjustment of the correction angle of the ultrasound system is generally 1 degree. Assuming that the correction angle has been set accurately, let’s take a look at the different correction angles. When the error deviates by 1 degree, the flow rate measurement will bring much relative error:
Error = [V(a+1)-V(a)]/V(a) = cos(a)/cos(a+1)-1
It can be seen from the figure that 1/cos(a) increases non-linearly and rapidly as the correction angle increases, and the slope of the increase is greater the closer to 90 degrees. Considering that the error is only 1 degree, when the correction angle exceeds 70 degrees, the relative error exceeds 5%. Obviously, during the actual scanning, the actual correction angle error may exceed 1 degree due to the technique and the patient’s movement, and the relative error will be much larger. Therefore, if possible, try to make the correction angle smaller.
In summary, if conditions permit, by adjusting the probe tilt angle and PW scan line deflection, the correction angle is as small as possible to reduce the relative error of the average flow rate and flow measurement, and at the same time, a larger Doppler can be obtained. Frequency offset can also make it easier for the Doppler spectrum to fill most areas of the image, and minimize the estimation error of the maximum flow velocity, thereby obtaining more reliable S/D, RI, PI and other parameters.