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Copyright © 2015 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.
Sensorless Viscosity Measurement in a Magnetically-Levitated Rotary Blood Pump *Wataru Hijikata, †Jun Rao, †Shodai Abe, ‡§Setsuo Takatani, and *Tadahiko Shinshi *Precision and Intelligence Laboratory, Tokyo Institute of Technology; †Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama; ‡Division of Research and Development, MedTech Heart Inc.; and §Department of Cardiovascular Surgery, Nihon University School of Medicine, Tokyo, Japan
Abstract: Controlling the flow rate in an implantable rotary blood pump based on the physiological demand made by the body is important. Even though various methods to estimate the flow rate without using a flow meter have been proposed, no adequate method for measuring the blood viscosity, which is necessary for an accurate estimate of the flow rate, without using additional sensors or mechanisms in a noninvasive way, has yet been realized. We have developed a sensorless method for measuring viscosity in magnetically levitated rotary blood pumps, which requires no additional sensors or mechanisms. By applying vibrational excitation to the impeller using a magnetic bearing, we measured the viscosity of the
working fluid by measuring the phase difference between the current in the magnetic bearing and the displacement of the impeller. The measured viscosity showed a high correlation (R2 > 0.992) with respect to a reference viscosity. The mean absolute deviation of the measured viscosity was 0.12 mPa·s for several working fluids with viscosities ranging from 1.18 to 5.12 mPa·s. The proposed sensorless measurement method has the possibility of being utilized for estimating flow rate. Key Words: Sensorless viscosity measurement—Vibrational excitation—Phase difference —Magnetically levitated rotary blood pump—Flow rate estimation.
Rotary blood pumps (RBPs) have been used for both short-term and long-term circulation support, such as for cardiopulmonary bypass (CPB), bridge to decision, bridge to transplant, and destination therapy. In addition to developing RBP devices, sensorless technologies for measurements in RBPs, such as flow rate and pressure, are also an area of focus. Most implantable ventricular assist devices (VADs) avoid using flow meters and pressure transducers because of the cost, the complexity, the larger size, and the possible need for recalibration (1,2). However, it is desirable that the flow rate of VADs be measured and controlled to accommodate the physiological demands of the body (1). This is expected to be a more acute problem for future total artificial hearts (TAHs) using RBPs because of the
absence of a biological heart. Increasing the size of the system by adding a flow meter is also undesirable for portable extracorporeal RBPs. Furthermore, there is a need to measure the flow rate and the pressure in VADs for novel therapies that promote heart recovery, in which the flow rate of the VAD is controlled and the load to the biological heart deliberately increased (3). An alternative method to using flow meters, which is of great interest to many groups, is using sensorless technology to estimate the flow rate. Estimation of the flow rate ordinarily uses the motor current or motor power, as well as its rotational speed (1,2,4–7). The amplitudes of these signals are not only dependent on the flow rate, but also on the viscosity of the blood (4). In addition to the variations between individuals, the blood viscosity can change, even in the same patient, for example, due to transfusions, during which the hematocrit can decrease to less than 25% (8). Therefore, for the estimate of the flow rate to be of sufficient accuracy, calibration of the blood viscosity is required. However, an adequate method for measuring the blood viscosity without additional
doi:10.1111/aor.12440 Received June 2014; revised October 2014. Address correspondence and reprint requests to Dr. Wataru Hijikata, Precision and Intelligence Laboratory, Tokyo Institute of Technology, Mail box: R2-38, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan. E-mail: [email protected]
Artificial Organs 2015, 39(7):559–568
a
W. HIJIKATA ET AL.
Disposable pump head Displacement sensor Magnetic coupling disk
b
Z
X
Y
Outlet
Inlet
Housing
Fluid flow
Impeller Rotor
2
560
1
Electromagnet
Electromagnet
Magnetic coupling disk
1
185
Motor
φ50.6 Fluid clearance : 0.3 Fluid clearance : 0.3
FIG. 1. Extracorporeal MagLev centrifugal blood pump using a two-degree-of-freedom magnetic bearing. (a) Configuration and photograph; (b) cross-sectional view of the pump head.
sensors or mechanisms in a noninvasive way has yet to be developed. Hence, instead of viscosity, most groups (2,4–7) assume the use of a hematocrit, which requires invasive sampling of the blood, for flow rate estimation. Even during a CPB operation and intensive care, where ordinary sensors such as flow meters and pressure transducers are available, it is still desirable to periodically monitor the blood viscosity. Holsworth et al. (9) mentions the importance of monitoring blood viscosity during CPB using extracorporeal circulation, which involves intervention with regard to blood viscosity, that is, hemodilution. If the blood viscosity decreases due to hemodilution, an excessive increase in cerebral blood flow may possibly lead to an additional embolic load to the brain. Therefore, blood viscosity could provide useful information for improving management of perfusion in CPB patients (9). Tsukiya et al. (10) measured the blood viscosity from the motor current and rotational speed at a flow rate of zero by clamping the outlet cannula. The difficulty with this method, however, is that an additional clamping mechanism is required for the implantable VAD. Kitamura et al. (11) determined the viscosity by applying a random current to the motor so that the least squares error between the measured rotational speed and the estimated one obtained using dynamic models of the motor, the pump, and the cardiovascular system was minimized. One difficulty in using this method is that the flow rate of a native heart is required. Artif Organs, Vol. 39, No. 7, 2015
In this study, we propose a method for sensorless viscosity measurements using the control signals of a magnetically levitated (MagLev) RBP, without the need for additional sensors or mechanisms. In this technique, a small sinusoidal excitation force generated by the magnetic bearing is applied to the impeller. The blood viscosity is obtained from the phase difference between the sinusoidal current in the magnetic bearing and the displacement of the impeller. Although we used a MagLev centrifugal blood pump with a radial magnetic bearing (12,13), as shown in Fig. 1, the proposed method for measuring viscosity can be utilized with any MagLev RBP, such as an axial-flow pump or a pump with thrust magnetic bearings (14,15). Finally, the viscosity measurements were applied as compensation to the flow rate estimates, and the estimation accuracy was assessed by comparing the measurements with those made with an ultrasonic flow meter. MATERIALS AND METHODS Principle of sensorless viscosity measurement In the proposed method, a magnetic bearing is used for the sensorless viscosity measurement. As shown in Fig. 2, vibrational excitation with an angular frequency of ωexc is applied to the MagLev impeller by superimposing an additional sinusoidal current, i, to the electromagnets of the magnetic bearing, and the displacement response, x, of the impeller is measured. The viscosity, μ, of the working fluid is calculated using the following linear function:
VISCOSITY MEASUREMENT IN A MAGLEV RBP
Vibrational excitation: Xexc0·sin(wexct) Electromagnet of magnetic bearing
Fluid velocity synchronized with the excitation
Housing Y
dc
Impeller
Z
X
Fluid clearance region FIG. 2. Top view of centrifugal pump with magnetic bearing.
μ = k1φ + k0
( m0 + mf ) x + {c0 + cf ( n)} x + {kx 0 + kxf ( n)} x = ki i (2) where m0 is the mass of the impeller, c0 and kx0 are the damping coefficient and the negative stiffness of the magnetic bearing without rotation, respectively, and ki is the force-current factor. By replacing x and i in the time domain with X = X0·ejω and I in the frequency domain, the ratio of X to I is:
X ki = 2 2 I ( − mω + kx ) − j (cω )2
{( − mω 2 + kx ) − jcω}
m = m0 + mf
(4)
c = c0 + cf ( n)
(5)
kx = kx 0 + kxf ( n)
(6)
Because absolute value of kx0 is usually larger than kxf, the total stiffness, kx, is negative. The phase difference, ϕ, between the phase of the displacement, ϕx, and that of the current, ϕi, can be represented by the arctangent of the ratio of real part to the imaginary part in Eq. 3.
X −cω ⎞ − π, φ = φ x − φ i = ∠ ⎛ ⎞ = tan −1 ⎛⎜ ⎝ I⎠ ⎝ − mω 2 + kx ⎟⎠ π π − < tan −1 < (7) 2 2 −π in the second term on the right side is added because both −mω2 + kx and −cω are negative, and hence ϕ is between −π/2 and −π. Additionally, if |−mω2 + kx| is much larger than |−cω|, ϕ can be approximated as follows:
(1)
where k1 and k0 are constants and ϕ is the phase difference between the displacement, x, of the impeller and the additional current, i, of the magnetic bearing at an angular frequency of ωexc. The derivation of Eq. 1 is given in detail in the following. When the impeller levitates and rotates in the fluid, in any dynamic model of the impeller the effect of the fluid, such as additional mass, mf, additional damping, cf, and additional stiffness, kxf, has to be taken into consideration (16). kxf is well known as the stiffness of the hydrodynamic bearing. Note that cf and kxf vary with the rotational speed n of the impeller. The equation of motion of the MagLev impeller is:
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φ≈
−cω −π − mω 2 + kx
As the fluid clearance, dc, shown in Fig. 2, is sufficiently narrow in the case of MagLev RBPs (≤ several hundreds of μm), the flow velocity distribution synchronized with the excitation is expected to be similar to Couette flow in the fluid clearance region. Hence, the viscous shear stress, τ, can be written as:
⎛ ∂x ⎞ τ = μ⎜ ⎟ ⎝ ∂y ⎠
≈μ y = dc
x dc
(9)
where y is the distance from the housing wall to the impeller surface in the Y direction. Although blood behaves as a non-Newtonian fluid because of aggregation and deformation of the red blood cells, etc., it can be treated as a Newtonian fluid at shear rates of 100/s or more (17). Therefore, if the shear rate due to vibrational excitation is more than 100/s, the viscosity, μ, in Eq. 9 is independent of the shear rate. τ is presumed to be the dominant component in the damping force, cx :
(3)
where ω is the angular frequency, and m, c, and kx are the total mass, the total damping, and the total stiffness as shown in Eqs. 4–6, respectively.
(8)
cx ≈ Sτ ≈ μ
S x dc
(10)
where S is the projected area of the impeller on the X-Z plane in the fluid clearance region shown in Artif Organs, Vol. 39, No. 7, 2015
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FIG. 3. Signal flow of magnetic bearing system and sensorless viscosity measurement.
Fig. 2. From Eqs. 8 and 10, the relationship between μ and ϕ can be written as:
μ=
cdC dc − mω 2 + kx (φ + π) = ⋅ S S −ω
(11)
Therefore, the linear function Eq. 1 can be derived. Signal processing Figure 3 shows the signal flow of the magnetic bearing system and the proposed sensorless viscosity measurement. When the system measures the fluid viscosity, an excitation reference, xr_exc = Xexc0·sin(ωexct), is applied instead of adding the sinusoidal current directly to the electromagnet. The phases ϕx and ϕi at angular frequency ωexc are calculated in real time using Fourier transformations. In the synchronous phase process unit, the following equations are calculated:
a=
ω exc π
b=
ω exc π
∫
π ω exc − π ω exc
f0 ( t ) cos (ω exc t ) dt
(12)
f0 ( t ) sin (ω exc t ) dt
(13)
π ω exc
∫
− π ω exc
fωexc ( t ) = a ⋅ cos (ω exc t ) + b ⋅ sin (ω exc t )
(14)
a φωexc = ∠fωexc ( t ) = tan −1 ⎛ ⎞ ⎝ b⎠
(15)
Artif Organs, Vol. 39, No. 7, 2015
where a and b are the amplitudes of sine and cosine waves, respectively, f0(t) is the original signal, such as the measured current or displacement, fωexc(t) is the filtered signal synchronized with the angular frequency ωexc, and ϕωexc is the phase of fωexc(t). The phases ϕx and ϕi are each obtained from Eq. 15, and then the phase difference ϕ = ϕx − ϕi is calculated. A low-pass filter (LPF) with a cutoff frequency of 0.1 Hz is applied before calculating the viscosity, μmeas, to eliminate noise and the influence of pulsatile flow. The sensitivity of ϕ to μ is dependent on both the excitation amplitude Xexc0 and the excitation angular frequency ωexc. For the signal-to-noise ratio to be higher, Xexc0 should be larger. However, if Xexc0 is too large, the fluid clearance is reduced. With an impeller of 50 mm in diameter, hemolysis can dramatically increase if the fluid clearance is less than 100 μm (18). The MagLev RBP used in this study has a fluid clearance of 300 μm, and the vibrational amplitude of the impeller caused by rotation from 1400 to 3000 rpm is less than 30 μm (12). In this study, Xexc0 was chosen, such that the vibrational amplitude induced by the excitation would be 50 μm. Therefore, the total vibrational amplitude is less than 80 μm and the fluid clearance can be maintained at more than 200 μm, which is sufficiently greater than a fluid clearance of 100 μm. The sensitive excitation angular frequency ωexc is found by experimentally measuring the frequency characteristics of the phase difference using fluids with various viscosities.
VISCOSITY MEASUREMENT IN A MAGLEV RBP Experimental setup Devices and working fluid A MagLev centrifugal blood pump with a disposable pump head developed by our group, the configuration of which is shown in Fig. 1, was used for the experiment (12,13). The diameter of the impeller is 50.6 mm. The inner and outer lateral fluid clearances between the impeller and housing surface are both 0.3 mm, the axial fluid clearance between the impeller and housing surface at the bottom side is 1 mm, and that at the top side is 2 mm. Hence, the viscous shear stress generated on the lateral side of the impeller is dominant. The magnetic bearing actively controls the impeller motions in the radial X and Y directions. The motions in the axial and tilt directions are passively supported by the restoring force and restoring torque generated by the bias magnetic flux. During viscosity measurements, the excitation reference xr_exc is added in the actively controlled X direction. Signals for the magnetic bearing and the sensorless viscosity measurement are processed by a digital signal processor (DS1104, dSPACE GmbH, Paderborn, Germany). Even if we control the hematocrit, the viscosity of the blood can change by coagulation and aggregation, etc. The potential of the proposed method should be evaluated by eliminating the abovementioned uncertainties as much as possible. Therefore, instead of blood, we use a glycerol–water solution, whose viscosity is stable and shows good repeatability. Working fluids with five different viscosities ranging from 1.18 to 5.12 mPa s were made by mixing water, glycerol, and sodium chloride, as shown in Table 1. The viscosity of fluid No. 1 (1.18 mPa s) is the same as that of plasma at 37°C (19). The “apparent” viscosity of normal human blood at 37°C is about 4 to 5 mPa s at shear rates from 100 to 200/s (19). The viscosity of fluids No. 3 (4.02 mPa s) and No. 4 (5.12 mPa s) were chosen to simulate these values. In the case of hemodilution, the blood viscosity is decreased to between that of
TABLE 1. Properties of working fluid at 23.5°C Mass fraction wt%
No. 1 2 3 4 5
Water
Glycerol
Sodium chloride (NaCl)
88 67 54 50 59
0 29 45 50 39
12 4 1 0 2
Reference viscosity μref mPa·s
Density kg/m3
1.18 2.35 4.02 5.12 2.95
1.08 × 103 1.09 × 103 1.10 × 103 1.10 × 103 1.10 × 103
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plasma and that of normal blood. Therefore, to cover the range between 1.18 and 4.02 mPa s, fluid No. 2 (2.35 mPa s) was chosen. Sodium chloride is used for adjusting the density to that of 50wt% glycerol–water solution (No. 4 in Table 1). In this study, the density of blood is assumed to be constant. The static viscosity of each fluid, which is the product of the viscosity and the density, was measured by a vibrational viscometer (SV-10, A&D Co., Ltd., Tokyo, Japan, range: 0.3 to 10 000 mPa s, repeatability: 1%, accuracy: ± 3%). Then, the reference viscosity, μref, was obtained by dividing the measured static viscosity by the density. Because the viscosities of the working fluids are sensitive to temperature, this was controlled at 23.5 ± 0.4°C using a water bath during the experiments. Frequency characteristics of the impeller To experimentally determine the sensitive excitation angular frequency, ωexc, the transfer function of the ratio of the impeller displacement to the current in the magnetic bearing, X/I, was measured in working fluids No. 1 to No. 4. A frequency response analyzer (FRA5022, NF Co., Yokohama, Japan) was used for this measurement and the rotational speed of the impeller was fixed to 0 rpm. The sensitive excitation angular frequency ωexc, which was found from this experiment, was used in all the subsequent experiments. Sensorless viscosity measurement under continuous flow The parameters k1 and k0 in Eq. 1 were found, and then the measured viscosity, μmeas, obtained using the proposed sensorless measurement method, was evaluated under continuous flow. The MagLev RBP was connected to a mock circulatory loop. An ultrasonic flow meter (HT-320, Transonic System Inc., Ithaca, NY, USA, bandwidth: 10 Hz) and a screw cramp was located after the pump outlet. Two pressure transducers (KL76, Nagano Keiki Co., Tokyo, Japan) were used at the inlet and outlet. A reservoir was placed in a water bath to control the temperature of the working fluid. To determine k1 and k0 in Eq. 1, the relationship between the phase difference, ϕ, and the viscosity, μ, was measured at rotational speeds of 1500 to 3000 rpm in 500 rpm increments, which are the rotational speeds needed for this pump to provide adequate flow to a failing heart with an artificial lung (12). Because the proposed method for sensorless viscosity measurements is to be used to estimate the Artif Organs, Vol. 39, No. 7, 2015
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W. HIJIKATA ET AL. pressure transducers described above were used for the measurements. The mock circulatory loop was filled with fluid No. 4 because the phase difference with this fluid is the most sensitive to flow rate as mentioned below. For pulsatile flow conditions, the beat frequency of the pulsatile pump was set to 60 bpm, while for continuous flow conditions, this was set to 0 bpm. The rotational speed of the MagLev RBP was set to 2000 rpm for both conditions. In addition to this experiment, sensorless viscosity measurements were demonstrated under the same pulsatile flow conditions of 60 bpm. The circulatory loop was filled with working fluid No. 5, which was not used for determining k1 and k0. RESULTS
FIG. 4. Frequency characteristics of the ratio between the impeller displacement and the current, X/I.
flow rate, the viscosity should be obtained without measuring the flow rate. Hence, if a change in flow rate has a large affect on the phase difference, the accuracy of the measured viscosity will be poor. Therefore, the influence of the change in flow rate on the phase difference was also evaluated. In this measurement, the rotational speed of the MagLev RBP was fixed to 2000 rpm. Finally, the measured viscosity, μmeas, was compared with the reference viscosity, μref, using fluids No. 1 to No. 4. In this evaluation, the flow rate was set from 1 to 5 L/min in 2 L/min increments. The measurement was performed twice for each fluid and each flow rate. Sensorless viscosity measurement under pulsatile flow There is a possibility that the fluid force caused by pulsatile flow has an influence on the phase difference. Therefore, vibrational excitation with an angular frequency of ωexc was applied under both continuous and pulsatile flow, and the phase differences of each compared with one and other. The MagLev RBP was connected to a mock circulatory loop consisting of a pulsatile pump, an aorta simulator, a left atrium simulator, and a fluid resistance. The details of the mock circulatory loop are described in reference (20). The same ultrasonic flow meter and Artif Organs, Vol. 39, No. 7, 2015
Frequency characteristics of the impeller Figure 4 shows the measured frequency characteristics of the impeller displacement to current ratio, X/I. The phase difference, ϕ, varies greatly with viscosity at around 70 Hz, indicating that the sensitivity of ϕ to μ is high at this frequency. Hence, the excitation angular frequency, ωexc, was set to 440 rad/s (70 Hz) for the following measurements. Sensorless viscosity measurement under continuous flow Figure 5 shows the relationship between the phase difference, ϕ, and the reference viscosity, μref, at a flow rate of 3 L/min. k1 and k0 at each rotational speed were obtained by a least squares method. As given by Eq. 1, a linear dependency between ϕ and
FIG. 5. Relationship between the phase difference, ϕ, and the reference viscosity, μref, at 3 L/min.
VISCOSITY MEASUREMENT IN A MAGLEV RBP μref was observed, but the coefficient k1 and constant k0 were different for each rotational speed. The reason is that the damping, c, and stiffness, kx, are functions of the rotational speed as indicated by Eqs. 5 and 6. It is therefore necessary to compensate k1 and k0 with regard to the rotational speed, or change the rotational speed to the specific values at which k1 and k0 were measured, during the viscosity measurement. In this study, we conducted sensorless viscosity measurements at a rotational speed of 2000 rpm, which is close to a representative operating point at 5 L/min against a pressure of 100 mm Hg. k1 and k0 at 2000 rpm were found to be 0.360 mPa s/ degree and 64.4 mPa s, respectively. Figure 6 shows the relationship between the flow rate and the phase difference, ϕ, at 2000 rpm. From 1 to 5 L/min, ϕ varies by a maximum of 0.9 degree in fluid No. 4, which is equal to the viscosity measurement error of ± 0.16 mPa s. Figure 7 shows a comparison between the reference viscosity, μref, and the measured viscosity, μmeas. The high determination coefficient, R2 = 0.992, indicates a strong relationship between μref and μmeas. The mean absolute deviation, MAD, of this comparison is calculated from:
MAD =
∑
N
μ meas N − μ ref N all
(16)
where Nall = 24 is the number of times the measurements was performed. In this experiment, MAD was 0.12 mPa s in the range from 1.18 to 5.12 mPa s.
FIG. 6. Relationship between flow rate and phase difference, ϕ, at 2000 rpm.
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FIG. 7. Comparison between the measured viscosity, μmeas, by the proposed method and the reference viscosity, μref, at 2000 rpm.
Sensorless viscosity measurement under pulsatile flow Figure 8 shows the relationship between the average flow rate and the phase difference, ϕ, under both continuous and pulsatile flow. At an average flow rate of 1 L/min, the peak-to-peak amplitude of the pulsatile flow rate was 6 L/min, while at an average flow rate of 4.2 L/min, this was 3 L/min. Even under pulsatile flow, ϕ varied with the average flow rate, and there was little difference between continuous and pulsatile flow. The results of the viscosity measurements with fluid No. 5 are shown in Fig. 9. The excitation reference, xr_exc, was applied for between 10 and 40 s. The viscosity measurement settled 10 s after starting the excitation because an LPF with a cutoff frequency of 0.1 Hz was used in the signal process. The measured viscosity, μmeas, was 2.80 mPa s, which is in good agreement with the reference viscosity, μref, which
FIG. 8. Relationship between the phase difference, ϕ, and the average flow rate at 2000 rpm under continuous and pulsatile flow of fluid No. 4. Artif Organs, Vol. 39, No. 7, 2015
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W. HIJIKATA ET AL. rate was 0.31 L/min for continuous flow, and they achieved relatively high accuracy. One difficulty of using this method is that determining the parameters in the equation is complicated because it contains 19 coefficients. Moreover, invasive sampling of blood to compensate the viscosity is required. Wakisaka et al. (4) used a linear relationship between the flow rate and the ratio of the motor power to the square of the rotational speed. Although the accuracy was not clearly evaluated, the equation used in this method has only three coefficients, so calibration is easier than for other methods. More techniques for estimating flow rate are introduced in reference (1). In this study, the equation used for estimating the flow rate is based on Wakisaka et al. (4). To eliminate the influence of the copper loss in the motor, the ratio of the motor power to the square of the rotational speed, W/n2, is replaced by the ratio of the motor torque to the rotational speed, T/n. Moreover, the hematocrit, Ht, is replaced by the viscosity, μ:
Qest = k2
T + k3 μ + k4 n
(17)
DISCUSSION
where Qest is the estimated flow rate. k2 = 1.27 × 103 L rpm/(min Nm), k3 = −1.20 L/(min mPa·s), and k4 = −7.52 L/min were found from the reference flow rate, Qref, which was measured by the ultrasonic flow meter, and T/n with fluids No. 1 to No. 4 at flow rates of 1, 3, and 5 L/min at 2000 rpm. For convenience, T was measured by a torque meter (MD-503C, Ono Sokki Co., Ltd., Yokohama, Japan) placed between the magnetic coupling disk and the motor. Figure 10 shows comparisons between the reference flow rate measured with the ultrasonic flow meter, Qref, and the estimated flow rate, Qest, for
Improving the flow rate estimation utilizing sensorless viscosity measurements The applicability of the developed sensorless viscosity measurement method, which achieved a MAD of 0.12 mPa s in the range from 1.18 to 5.12 mPa s, was assessed by using it to estimate the flow rate. In previous studies, many different methods for estimating the flow rate have been proposed. Yu (21) used a dynamic model of the motor to estimate flow rate. Although they reported the accuracy of the estimation to be less than 0.5 L/min, they did not take the viscosity change into consideration. Granegger et al. (2) derived cubic equations with regard to the motor current and rotational speed to estimate the flow rate. The standard deviation of the difference between the estimated and reference flow
FIG. 10. Comparison between estimated and reference flow rate at 2000 rpm.
FIG. 9. Viscosity estimation of fluid No. 5 at 2000 rpm.
was 2.95 mPa s. At this point, the amplitudes of the impeller displacement and the current became 50 μm and 0.6 A, larger than those before applying xr_exc. The fluid clearance of 200 μm between the impeller and the housing wall is still maintained.
Artif Organs, Vol. 39, No. 7, 2015
VISCOSITY MEASUREMENT IN A MAGLEV RBP fluids No. 1 to No. 4 at 2000 rpm. For the clear symbols, the viscosity, μ, in Eq. 17 was the value measured by the proposed sensorless method. In contrast, μ was fixed to 3.17 mPa s for the black symbols, which is the average viscosity of fluids No. 1 to No. 4. By compensating for the viscosity, the standard deviation between Qref and Qest was improved from 1.83 to 0.36 L/min in the range from 1 to 5 L/min. Despite using a simple equation with only three coefficients, the accuracy of the estimated flow rate using the proposed method is comparable with that proposed by Granegger et al. (2). This result suggests that the proposed sensorless viscosity measurement method is sufficiently accurate for it to be applied to estimating the flow rate. Accuracy of sensorless viscosity measurement The difference between μmeas and μref in Fig. 7 is considered to be caused mainly by: (i) the variation in phase difference with flow rate; and (ii) the variation in fluid temperature. We consider the reason for (i), which led to the viscosity measurement error of ±0.16 mPa s mentioned above, to be the additional stiffness kfx, which is similar to the wedge effect in hydrodynamic bearings (22). The distribution of the flow velocity in the fluid clearance region is dependent not only on the rotational speed but also on the flow rate. The amplitude of the wedge effect therefore changes with flow rate, which leads to a change in phase difference. Moreover, the phase difference can vary in synchronization with the pulsatile flow, but owing to the LPF which has a cutoff frequency of 0.1 Hz, its influence could be eliminated as shown in Fig. 8. From a practical point of view, the influence of the flow rate is sufficiently small that the viscosity can be measured without any information required about the flow rate. As the fluid temperature was controlled at 23.5 ± 0.4°C, the variation of the fluid temperature causes a variation in viscosity of ± 0.05 mPa s in the case of fluid No. 4, for which the sensitivity to temperature of 0.12 mPa s/°C was the highest of the fluids tested. In this study, the error caused by (ii), the temperature control, was not negligible, in addition to that due to (i), the influence of the flow rate. Limitations and future work of this study Mixtures of water, glycerin, and sodium chloride were used for the working fluids. Because these solutions are Newtonian fluids, the influence of nonNewtonian characteristics was not considered. Moreover, even if the viscosity and density of these solutions are controlled at the desired values, the impeller dynamics can be different from those in
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blood. Therefore, further investigation using real blood is required to confirm whether a sufficiently accurate estimate can be obtained. As evaluation of the method was performed at 2000 rpm, the accuracy of the viscosity measurement is guaranteed only at this rotational speed. If the method is applied at different rotational speeds, additional evaluations at various rotational speeds are required. The amplitude Xexc0 and frequency ωexc of the excitation were 50 μm and 440 rad/s, respectively. In this case, the effective value of the excitation velocity vexc is
vexc =
X exc 0 ω exc 2
= 1.56 × 10 4 μm s
(18)
The fluid clearance was 300 μm. Hence, by dividing vexc by 300 μm, the shear rate due to the excitation obtained is 52/s. When the proposed method is applied to blood viscosity measurements in future work, the excitation amplitude Xexc0 will be more than 100 μm in order that the shear rate is greater than 100/s, thus avoiding non-Newtonian effects. Increasing Xexc0 is feasible, because the fluid clearance was maintained at more than 200 μm even during rotation and excitation as mentioned in the section “Sensorless viscosity measurement under pulsatile flow.” CONCLUSION A method for sensorless viscosity measurement in MagLev rotary blood pumps without any additional sensors or mechanisms has been developed. Using glycerol–sodium–water solutions, we achieved a mean absolute deviation of 0.12 mPa s in the range from 1.18 to 5.12 mPa s, which is sufficiently accurate to compensate the flow rate estimation. The influence of both continuous and pulsatile flow was sufficiently small that the viscosity could be obtained without the need to measure the pump flow rate. This advantage makes the flow rate estimation methods proposed by many groups feasible for clinical use. In future work, we plan to utilize the proposed method in blood to evaluate the influence of nonNewtonian characteristics. Acknowledgment: This research is partly supported by JSPS KAKENHI grant number 24360059. REFERENCES 1. Bertram CD. Measurement for implantable rotary blood pumps. Physiol Meas 2005;26:99–117. Artif Organs, Vol. 39, No. 7, 2015
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2. Granegger M, Moscato M, Casas F, Wieselthaler G, Schima H. Development of a pump flow estimator for rotary blood pumps to enhance monitoring of ventricular function. Artif Organs 2012;36:691–9. 3. Arakawa M, Nishimura T, Takewa Y, et al. Alternation of left ventricular load by a continuous-flow left ventricular assist device with a native heart load control system in a chronic heart failure model. J Thorac Cardiovasc Surg 2014;148:698– 704. 4. Wakisaka Y, Okuzono Y, Taenaka Y, et al. Noninvasive pump flow estimation of a centrifugal blood pump. Artif Organs 1997;21:651–4. 5. Tsukiya T, Taenaka Y, Nishikawa T, et al. Application of indirect flow rate measurement using motor driving signals to a centrifugal blood pump with an integrated motor. Artif Organs 2001;25:692–6. 6. AlOmari AH, Savkin AV, Karantonis DM, Lim E, Lovell NH. Non-invasive estimation of pulsatile flow and differential pressure in an implantable rotary blood pump for heart failure patients. Physiol Meas 2009;30:371–86. 7. Malagutti N, Karantonis DM, Cloherty SL, et al. Noninvasive average flow estimation for an implantable rotary blood pump: a new algorithm incorporating the role of blood viscosity. Artif Organs 2007;31:45–52. 8. Karkouti K, Beattie WS, Wijeysundera DN, et al. Hemodilution during cardiopulmonary bypass is an independent risk factor for acute renal failure in adult cardiac surgery. J Thorac Cardiovasc Surg 2005;129:391–400. 9. Holsworth RE, Shecterle LM, Cyr JA, Sloop GD. Importance of monitoring blood viscosity during cardiopulmonary bypass. Perfusion 2012;28:91–2. 10. Tsukiya T, Akamatsu T, Nishimura K, Yamada T, Nakazeki T. Use of motor current in flow rate measurement for the magnetically suspended centrifugal blood pump. Artif Organs 1997; 21:396–401. 11. Kitamura T, Matsushita Y, Tokuyama T, et al. Physical modelbased indirect measurements of blood pressure and flow using a centrifugal pump. Artif Organs 2000;24:589–93.
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12. Hijikata W, Shinshi T, Asama J, et al. A magnetically levitated centrifugal blood pump with a simple-structured disposable pump head. Artif Organs 2008;32:531–40. 13. Someya T, Kobayashi M, Waguri S, et al. Development of a disposable Mag-Lev centrifugal blood pump (MedTech Dispo) intended for one-month support in bridge-to-bridge applications: in vitro and initial in vivo evaluation. Artif Organs 2009;33:704–13. 14. Pagani FD. Continuous-flow rotary left ventricular assist devices with “3rd generation” design. Semin Thorac Cardiovasc Surg 2008;20:255–63. 15. Hoshi H, Shinshi T, Takatani S. Third-generation blood pumps with mechanical noncontact magnetic bearings. Artif Organs 2006;30:324–38. 16. Pai CN, Shinshi T, Shimokohbe A. Estimation of the radial force using a disturbance force observer for a magnetically levitated centrifugal blood pump. Proc Inst Mech Eng [H] 2010;224:1–12. 17. Chien S. Shear dependence of effective cell volume as a determinant of blood viscosity. Science 1970;168:977–9. 18. Hoshi H, Asama J, Hijikata W, et al. Hemolytic performance of a MagLev disposable rotary blood pump (MedTech Dispo): effects of MagLev gap clearance and surface roughness. Artif Organs 2006;30:949–54. 19. Baskurt OK, Meiselman HJ. Blood rheology and hemodynamics. Semin Thromb Hemost 2003;29:435–50. 20. Pai CN, Shinshi T, Shimokohbe A. Sensorless measurement of pulsatile flow rate using a disturbance force observer in a magnetically levitated centrifugal blood pump during ventricular assistance. Flow Meas Instrum 2010;21:33–9. 21. Yu YC. Minimally Invasive Flow Estimation for a Rotary Cardiac Assist Device. 5th IEEE Conference on Industrial Electronics and Applications 2010;1752–7. 22. Hori Y. Foundations of hydrodynamic lubrication. In: Shimada K, ed. Hydrodynamic Lubrication. Tokyo: Springer, 2006;9–22.
Copyright © 2015 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.
Sensorless Viscosity Measurement in a Magnetically-Levitated Rotary Blood Pump *Wataru Hijikata, †Jun Rao, †Shodai Abe, ‡§Setsuo Takatani, and *Tadahiko Shinshi *Precision and Intelligence Laboratory, Tokyo Institute of Technology; †Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama; ‡Division of Research and Development, MedTech Heart Inc.; and §Department of Cardiovascular Surgery, Nihon University School of Medicine, Tokyo, Japan
Abstract: Controlling the flow rate in an implantable rotary blood pump based on the physiological demand made by the body is important. Even though various methods to estimate the flow rate without using a flow meter have been proposed, no adequate method for measuring the blood viscosity, which is necessary for an accurate estimate of the flow rate, without using additional sensors or mechanisms in a noninvasive way, has yet been realized. We have developed a sensorless method for measuring viscosity in magnetically levitated rotary blood pumps, which requires no additional sensors or mechanisms. By applying vibrational excitation to the impeller using a magnetic bearing, we measured the viscosity of the
working fluid by measuring the phase difference between the current in the magnetic bearing and the displacement of the impeller. The measured viscosity showed a high correlation (R2 > 0.992) with respect to a reference viscosity. The mean absolute deviation of the measured viscosity was 0.12 mPa·s for several working fluids with viscosities ranging from 1.18 to 5.12 mPa·s. The proposed sensorless measurement method has the possibility of being utilized for estimating flow rate. Key Words: Sensorless viscosity measurement—Vibrational excitation—Phase difference —Magnetically levitated rotary blood pump—Flow rate estimation.
Rotary blood pumps (RBPs) have been used for both short-term and long-term circulation support, such as for cardiopulmonary bypass (CPB), bridge to decision, bridge to transplant, and destination therapy. In addition to developing RBP devices, sensorless technologies for measurements in RBPs, such as flow rate and pressure, are also an area of focus. Most implantable ventricular assist devices (VADs) avoid using flow meters and pressure transducers because of the cost, the complexity, the larger size, and the possible need for recalibration (1,2). However, it is desirable that the flow rate of VADs be measured and controlled to accommodate the physiological demands of the body (1). This is expected to be a more acute problem for future total artificial hearts (TAHs) using RBPs because of the
absence of a biological heart. Increasing the size of the system by adding a flow meter is also undesirable for portable extracorporeal RBPs. Furthermore, there is a need to measure the flow rate and the pressure in VADs for novel therapies that promote heart recovery, in which the flow rate of the VAD is controlled and the load to the biological heart deliberately increased (3). An alternative method to using flow meters, which is of great interest to many groups, is using sensorless technology to estimate the flow rate. Estimation of the flow rate ordinarily uses the motor current or motor power, as well as its rotational speed (1,2,4–7). The amplitudes of these signals are not only dependent on the flow rate, but also on the viscosity of the blood (4). In addition to the variations between individuals, the blood viscosity can change, even in the same patient, for example, due to transfusions, during which the hematocrit can decrease to less than 25% (8). Therefore, for the estimate of the flow rate to be of sufficient accuracy, calibration of the blood viscosity is required. However, an adequate method for measuring the blood viscosity without additional
doi:10.1111/aor.12440 Received June 2014; revised October 2014. Address correspondence and reprint requests to Dr. Wataru Hijikata, Precision and Intelligence Laboratory, Tokyo Institute of Technology, Mail box: R2-38, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan. E-mail: [email protected]
Artificial Organs 2015, 39(7):559–568
a
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Disposable pump head Displacement sensor Magnetic coupling disk
b
Z
X
Y
Outlet
Inlet
Housing
Fluid flow
Impeller Rotor
2
560
1
Electromagnet
Electromagnet
Magnetic coupling disk
1
185
Motor
φ50.6 Fluid clearance : 0.3 Fluid clearance : 0.3
FIG. 1. Extracorporeal MagLev centrifugal blood pump using a two-degree-of-freedom magnetic bearing. (a) Configuration and photograph; (b) cross-sectional view of the pump head.
sensors or mechanisms in a noninvasive way has yet to be developed. Hence, instead of viscosity, most groups (2,4–7) assume the use of a hematocrit, which requires invasive sampling of the blood, for flow rate estimation. Even during a CPB operation and intensive care, where ordinary sensors such as flow meters and pressure transducers are available, it is still desirable to periodically monitor the blood viscosity. Holsworth et al. (9) mentions the importance of monitoring blood viscosity during CPB using extracorporeal circulation, which involves intervention with regard to blood viscosity, that is, hemodilution. If the blood viscosity decreases due to hemodilution, an excessive increase in cerebral blood flow may possibly lead to an additional embolic load to the brain. Therefore, blood viscosity could provide useful information for improving management of perfusion in CPB patients (9). Tsukiya et al. (10) measured the blood viscosity from the motor current and rotational speed at a flow rate of zero by clamping the outlet cannula. The difficulty with this method, however, is that an additional clamping mechanism is required for the implantable VAD. Kitamura et al. (11) determined the viscosity by applying a random current to the motor so that the least squares error between the measured rotational speed and the estimated one obtained using dynamic models of the motor, the pump, and the cardiovascular system was minimized. One difficulty in using this method is that the flow rate of a native heart is required. Artif Organs, Vol. 39, No. 7, 2015
In this study, we propose a method for sensorless viscosity measurements using the control signals of a magnetically levitated (MagLev) RBP, without the need for additional sensors or mechanisms. In this technique, a small sinusoidal excitation force generated by the magnetic bearing is applied to the impeller. The blood viscosity is obtained from the phase difference between the sinusoidal current in the magnetic bearing and the displacement of the impeller. Although we used a MagLev centrifugal blood pump with a radial magnetic bearing (12,13), as shown in Fig. 1, the proposed method for measuring viscosity can be utilized with any MagLev RBP, such as an axial-flow pump or a pump with thrust magnetic bearings (14,15). Finally, the viscosity measurements were applied as compensation to the flow rate estimates, and the estimation accuracy was assessed by comparing the measurements with those made with an ultrasonic flow meter. MATERIALS AND METHODS Principle of sensorless viscosity measurement In the proposed method, a magnetic bearing is used for the sensorless viscosity measurement. As shown in Fig. 2, vibrational excitation with an angular frequency of ωexc is applied to the MagLev impeller by superimposing an additional sinusoidal current, i, to the electromagnets of the magnetic bearing, and the displacement response, x, of the impeller is measured. The viscosity, μ, of the working fluid is calculated using the following linear function:
VISCOSITY MEASUREMENT IN A MAGLEV RBP
Vibrational excitation: Xexc0·sin(wexct) Electromagnet of magnetic bearing
Fluid velocity synchronized with the excitation
Housing Y
dc
Impeller
Z
X
Fluid clearance region FIG. 2. Top view of centrifugal pump with magnetic bearing.
μ = k1φ + k0
( m0 + mf ) x + {c0 + cf ( n)} x + {kx 0 + kxf ( n)} x = ki i (2) where m0 is the mass of the impeller, c0 and kx0 are the damping coefficient and the negative stiffness of the magnetic bearing without rotation, respectively, and ki is the force-current factor. By replacing x and i in the time domain with X = X0·ejω and I in the frequency domain, the ratio of X to I is:
X ki = 2 2 I ( − mω + kx ) − j (cω )2
{( − mω 2 + kx ) − jcω}
m = m0 + mf
(4)
c = c0 + cf ( n)
(5)
kx = kx 0 + kxf ( n)
(6)
Because absolute value of kx0 is usually larger than kxf, the total stiffness, kx, is negative. The phase difference, ϕ, between the phase of the displacement, ϕx, and that of the current, ϕi, can be represented by the arctangent of the ratio of real part to the imaginary part in Eq. 3.
X −cω ⎞ − π, φ = φ x − φ i = ∠ ⎛ ⎞ = tan −1 ⎛⎜ ⎝ I⎠ ⎝ − mω 2 + kx ⎟⎠ π π − < tan −1 < (7) 2 2 −π in the second term on the right side is added because both −mω2 + kx and −cω are negative, and hence ϕ is between −π/2 and −π. Additionally, if |−mω2 + kx| is much larger than |−cω|, ϕ can be approximated as follows:
(1)
where k1 and k0 are constants and ϕ is the phase difference between the displacement, x, of the impeller and the additional current, i, of the magnetic bearing at an angular frequency of ωexc. The derivation of Eq. 1 is given in detail in the following. When the impeller levitates and rotates in the fluid, in any dynamic model of the impeller the effect of the fluid, such as additional mass, mf, additional damping, cf, and additional stiffness, kxf, has to be taken into consideration (16). kxf is well known as the stiffness of the hydrodynamic bearing. Note that cf and kxf vary with the rotational speed n of the impeller. The equation of motion of the MagLev impeller is:
561
φ≈
−cω −π − mω 2 + kx
As the fluid clearance, dc, shown in Fig. 2, is sufficiently narrow in the case of MagLev RBPs (≤ several hundreds of μm), the flow velocity distribution synchronized with the excitation is expected to be similar to Couette flow in the fluid clearance region. Hence, the viscous shear stress, τ, can be written as:
⎛ ∂x ⎞ τ = μ⎜ ⎟ ⎝ ∂y ⎠
≈μ y = dc
x dc
(9)
where y is the distance from the housing wall to the impeller surface in the Y direction. Although blood behaves as a non-Newtonian fluid because of aggregation and deformation of the red blood cells, etc., it can be treated as a Newtonian fluid at shear rates of 100/s or more (17). Therefore, if the shear rate due to vibrational excitation is more than 100/s, the viscosity, μ, in Eq. 9 is independent of the shear rate. τ is presumed to be the dominant component in the damping force, cx :
(3)
where ω is the angular frequency, and m, c, and kx are the total mass, the total damping, and the total stiffness as shown in Eqs. 4–6, respectively.
(8)
cx ≈ Sτ ≈ μ
S x dc
(10)
where S is the projected area of the impeller on the X-Z plane in the fluid clearance region shown in Artif Organs, Vol. 39, No. 7, 2015
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FIG. 3. Signal flow of magnetic bearing system and sensorless viscosity measurement.
Fig. 2. From Eqs. 8 and 10, the relationship between μ and ϕ can be written as:
μ=
cdC dc − mω 2 + kx (φ + π) = ⋅ S S −ω
(11)
Therefore, the linear function Eq. 1 can be derived. Signal processing Figure 3 shows the signal flow of the magnetic bearing system and the proposed sensorless viscosity measurement. When the system measures the fluid viscosity, an excitation reference, xr_exc = Xexc0·sin(ωexct), is applied instead of adding the sinusoidal current directly to the electromagnet. The phases ϕx and ϕi at angular frequency ωexc are calculated in real time using Fourier transformations. In the synchronous phase process unit, the following equations are calculated:
a=
ω exc π
b=
ω exc π
∫
π ω exc − π ω exc
f0 ( t ) cos (ω exc t ) dt
(12)
f0 ( t ) sin (ω exc t ) dt
(13)
π ω exc
∫
− π ω exc
fωexc ( t ) = a ⋅ cos (ω exc t ) + b ⋅ sin (ω exc t )
(14)
a φωexc = ∠fωexc ( t ) = tan −1 ⎛ ⎞ ⎝ b⎠
(15)
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where a and b are the amplitudes of sine and cosine waves, respectively, f0(t) is the original signal, such as the measured current or displacement, fωexc(t) is the filtered signal synchronized with the angular frequency ωexc, and ϕωexc is the phase of fωexc(t). The phases ϕx and ϕi are each obtained from Eq. 15, and then the phase difference ϕ = ϕx − ϕi is calculated. A low-pass filter (LPF) with a cutoff frequency of 0.1 Hz is applied before calculating the viscosity, μmeas, to eliminate noise and the influence of pulsatile flow. The sensitivity of ϕ to μ is dependent on both the excitation amplitude Xexc0 and the excitation angular frequency ωexc. For the signal-to-noise ratio to be higher, Xexc0 should be larger. However, if Xexc0 is too large, the fluid clearance is reduced. With an impeller of 50 mm in diameter, hemolysis can dramatically increase if the fluid clearance is less than 100 μm (18). The MagLev RBP used in this study has a fluid clearance of 300 μm, and the vibrational amplitude of the impeller caused by rotation from 1400 to 3000 rpm is less than 30 μm (12). In this study, Xexc0 was chosen, such that the vibrational amplitude induced by the excitation would be 50 μm. Therefore, the total vibrational amplitude is less than 80 μm and the fluid clearance can be maintained at more than 200 μm, which is sufficiently greater than a fluid clearance of 100 μm. The sensitive excitation angular frequency ωexc is found by experimentally measuring the frequency characteristics of the phase difference using fluids with various viscosities.
VISCOSITY MEASUREMENT IN A MAGLEV RBP Experimental setup Devices and working fluid A MagLev centrifugal blood pump with a disposable pump head developed by our group, the configuration of which is shown in Fig. 1, was used for the experiment (12,13). The diameter of the impeller is 50.6 mm. The inner and outer lateral fluid clearances between the impeller and housing surface are both 0.3 mm, the axial fluid clearance between the impeller and housing surface at the bottom side is 1 mm, and that at the top side is 2 mm. Hence, the viscous shear stress generated on the lateral side of the impeller is dominant. The magnetic bearing actively controls the impeller motions in the radial X and Y directions. The motions in the axial and tilt directions are passively supported by the restoring force and restoring torque generated by the bias magnetic flux. During viscosity measurements, the excitation reference xr_exc is added in the actively controlled X direction. Signals for the magnetic bearing and the sensorless viscosity measurement are processed by a digital signal processor (DS1104, dSPACE GmbH, Paderborn, Germany). Even if we control the hematocrit, the viscosity of the blood can change by coagulation and aggregation, etc. The potential of the proposed method should be evaluated by eliminating the abovementioned uncertainties as much as possible. Therefore, instead of blood, we use a glycerol–water solution, whose viscosity is stable and shows good repeatability. Working fluids with five different viscosities ranging from 1.18 to 5.12 mPa s were made by mixing water, glycerol, and sodium chloride, as shown in Table 1. The viscosity of fluid No. 1 (1.18 mPa s) is the same as that of plasma at 37°C (19). The “apparent” viscosity of normal human blood at 37°C is about 4 to 5 mPa s at shear rates from 100 to 200/s (19). The viscosity of fluids No. 3 (4.02 mPa s) and No. 4 (5.12 mPa s) were chosen to simulate these values. In the case of hemodilution, the blood viscosity is decreased to between that of
TABLE 1. Properties of working fluid at 23.5°C Mass fraction wt%
No. 1 2 3 4 5
Water
Glycerol
Sodium chloride (NaCl)
88 67 54 50 59
0 29 45 50 39
12 4 1 0 2
Reference viscosity μref mPa·s
Density kg/m3
1.18 2.35 4.02 5.12 2.95
1.08 × 103 1.09 × 103 1.10 × 103 1.10 × 103 1.10 × 103
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plasma and that of normal blood. Therefore, to cover the range between 1.18 and 4.02 mPa s, fluid No. 2 (2.35 mPa s) was chosen. Sodium chloride is used for adjusting the density to that of 50wt% glycerol–water solution (No. 4 in Table 1). In this study, the density of blood is assumed to be constant. The static viscosity of each fluid, which is the product of the viscosity and the density, was measured by a vibrational viscometer (SV-10, A&D Co., Ltd., Tokyo, Japan, range: 0.3 to 10 000 mPa s, repeatability: 1%, accuracy: ± 3%). Then, the reference viscosity, μref, was obtained by dividing the measured static viscosity by the density. Because the viscosities of the working fluids are sensitive to temperature, this was controlled at 23.5 ± 0.4°C using a water bath during the experiments. Frequency characteristics of the impeller To experimentally determine the sensitive excitation angular frequency, ωexc, the transfer function of the ratio of the impeller displacement to the current in the magnetic bearing, X/I, was measured in working fluids No. 1 to No. 4. A frequency response analyzer (FRA5022, NF Co., Yokohama, Japan) was used for this measurement and the rotational speed of the impeller was fixed to 0 rpm. The sensitive excitation angular frequency ωexc, which was found from this experiment, was used in all the subsequent experiments. Sensorless viscosity measurement under continuous flow The parameters k1 and k0 in Eq. 1 were found, and then the measured viscosity, μmeas, obtained using the proposed sensorless measurement method, was evaluated under continuous flow. The MagLev RBP was connected to a mock circulatory loop. An ultrasonic flow meter (HT-320, Transonic System Inc., Ithaca, NY, USA, bandwidth: 10 Hz) and a screw cramp was located after the pump outlet. Two pressure transducers (KL76, Nagano Keiki Co., Tokyo, Japan) were used at the inlet and outlet. A reservoir was placed in a water bath to control the temperature of the working fluid. To determine k1 and k0 in Eq. 1, the relationship between the phase difference, ϕ, and the viscosity, μ, was measured at rotational speeds of 1500 to 3000 rpm in 500 rpm increments, which are the rotational speeds needed for this pump to provide adequate flow to a failing heart with an artificial lung (12). Because the proposed method for sensorless viscosity measurements is to be used to estimate the Artif Organs, Vol. 39, No. 7, 2015
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W. HIJIKATA ET AL. pressure transducers described above were used for the measurements. The mock circulatory loop was filled with fluid No. 4 because the phase difference with this fluid is the most sensitive to flow rate as mentioned below. For pulsatile flow conditions, the beat frequency of the pulsatile pump was set to 60 bpm, while for continuous flow conditions, this was set to 0 bpm. The rotational speed of the MagLev RBP was set to 2000 rpm for both conditions. In addition to this experiment, sensorless viscosity measurements were demonstrated under the same pulsatile flow conditions of 60 bpm. The circulatory loop was filled with working fluid No. 5, which was not used for determining k1 and k0. RESULTS
FIG. 4. Frequency characteristics of the ratio between the impeller displacement and the current, X/I.
flow rate, the viscosity should be obtained without measuring the flow rate. Hence, if a change in flow rate has a large affect on the phase difference, the accuracy of the measured viscosity will be poor. Therefore, the influence of the change in flow rate on the phase difference was also evaluated. In this measurement, the rotational speed of the MagLev RBP was fixed to 2000 rpm. Finally, the measured viscosity, μmeas, was compared with the reference viscosity, μref, using fluids No. 1 to No. 4. In this evaluation, the flow rate was set from 1 to 5 L/min in 2 L/min increments. The measurement was performed twice for each fluid and each flow rate. Sensorless viscosity measurement under pulsatile flow There is a possibility that the fluid force caused by pulsatile flow has an influence on the phase difference. Therefore, vibrational excitation with an angular frequency of ωexc was applied under both continuous and pulsatile flow, and the phase differences of each compared with one and other. The MagLev RBP was connected to a mock circulatory loop consisting of a pulsatile pump, an aorta simulator, a left atrium simulator, and a fluid resistance. The details of the mock circulatory loop are described in reference (20). The same ultrasonic flow meter and Artif Organs, Vol. 39, No. 7, 2015
Frequency characteristics of the impeller Figure 4 shows the measured frequency characteristics of the impeller displacement to current ratio, X/I. The phase difference, ϕ, varies greatly with viscosity at around 70 Hz, indicating that the sensitivity of ϕ to μ is high at this frequency. Hence, the excitation angular frequency, ωexc, was set to 440 rad/s (70 Hz) for the following measurements. Sensorless viscosity measurement under continuous flow Figure 5 shows the relationship between the phase difference, ϕ, and the reference viscosity, μref, at a flow rate of 3 L/min. k1 and k0 at each rotational speed were obtained by a least squares method. As given by Eq. 1, a linear dependency between ϕ and
FIG. 5. Relationship between the phase difference, ϕ, and the reference viscosity, μref, at 3 L/min.
VISCOSITY MEASUREMENT IN A MAGLEV RBP μref was observed, but the coefficient k1 and constant k0 were different for each rotational speed. The reason is that the damping, c, and stiffness, kx, are functions of the rotational speed as indicated by Eqs. 5 and 6. It is therefore necessary to compensate k1 and k0 with regard to the rotational speed, or change the rotational speed to the specific values at which k1 and k0 were measured, during the viscosity measurement. In this study, we conducted sensorless viscosity measurements at a rotational speed of 2000 rpm, which is close to a representative operating point at 5 L/min against a pressure of 100 mm Hg. k1 and k0 at 2000 rpm were found to be 0.360 mPa s/ degree and 64.4 mPa s, respectively. Figure 6 shows the relationship between the flow rate and the phase difference, ϕ, at 2000 rpm. From 1 to 5 L/min, ϕ varies by a maximum of 0.9 degree in fluid No. 4, which is equal to the viscosity measurement error of ± 0.16 mPa s. Figure 7 shows a comparison between the reference viscosity, μref, and the measured viscosity, μmeas. The high determination coefficient, R2 = 0.992, indicates a strong relationship between μref and μmeas. The mean absolute deviation, MAD, of this comparison is calculated from:
MAD =
∑
N
μ meas N − μ ref N all
(16)
where Nall = 24 is the number of times the measurements was performed. In this experiment, MAD was 0.12 mPa s in the range from 1.18 to 5.12 mPa s.
FIG. 6. Relationship between flow rate and phase difference, ϕ, at 2000 rpm.
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FIG. 7. Comparison between the measured viscosity, μmeas, by the proposed method and the reference viscosity, μref, at 2000 rpm.
Sensorless viscosity measurement under pulsatile flow Figure 8 shows the relationship between the average flow rate and the phase difference, ϕ, under both continuous and pulsatile flow. At an average flow rate of 1 L/min, the peak-to-peak amplitude of the pulsatile flow rate was 6 L/min, while at an average flow rate of 4.2 L/min, this was 3 L/min. Even under pulsatile flow, ϕ varied with the average flow rate, and there was little difference between continuous and pulsatile flow. The results of the viscosity measurements with fluid No. 5 are shown in Fig. 9. The excitation reference, xr_exc, was applied for between 10 and 40 s. The viscosity measurement settled 10 s after starting the excitation because an LPF with a cutoff frequency of 0.1 Hz was used in the signal process. The measured viscosity, μmeas, was 2.80 mPa s, which is in good agreement with the reference viscosity, μref, which
FIG. 8. Relationship between the phase difference, ϕ, and the average flow rate at 2000 rpm under continuous and pulsatile flow of fluid No. 4. Artif Organs, Vol. 39, No. 7, 2015
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W. HIJIKATA ET AL. rate was 0.31 L/min for continuous flow, and they achieved relatively high accuracy. One difficulty of using this method is that determining the parameters in the equation is complicated because it contains 19 coefficients. Moreover, invasive sampling of blood to compensate the viscosity is required. Wakisaka et al. (4) used a linear relationship between the flow rate and the ratio of the motor power to the square of the rotational speed. Although the accuracy was not clearly evaluated, the equation used in this method has only three coefficients, so calibration is easier than for other methods. More techniques for estimating flow rate are introduced in reference (1). In this study, the equation used for estimating the flow rate is based on Wakisaka et al. (4). To eliminate the influence of the copper loss in the motor, the ratio of the motor power to the square of the rotational speed, W/n2, is replaced by the ratio of the motor torque to the rotational speed, T/n. Moreover, the hematocrit, Ht, is replaced by the viscosity, μ:
Qest = k2
T + k3 μ + k4 n
(17)
DISCUSSION
where Qest is the estimated flow rate. k2 = 1.27 × 103 L rpm/(min Nm), k3 = −1.20 L/(min mPa·s), and k4 = −7.52 L/min were found from the reference flow rate, Qref, which was measured by the ultrasonic flow meter, and T/n with fluids No. 1 to No. 4 at flow rates of 1, 3, and 5 L/min at 2000 rpm. For convenience, T was measured by a torque meter (MD-503C, Ono Sokki Co., Ltd., Yokohama, Japan) placed between the magnetic coupling disk and the motor. Figure 10 shows comparisons between the reference flow rate measured with the ultrasonic flow meter, Qref, and the estimated flow rate, Qest, for
Improving the flow rate estimation utilizing sensorless viscosity measurements The applicability of the developed sensorless viscosity measurement method, which achieved a MAD of 0.12 mPa s in the range from 1.18 to 5.12 mPa s, was assessed by using it to estimate the flow rate. In previous studies, many different methods for estimating the flow rate have been proposed. Yu (21) used a dynamic model of the motor to estimate flow rate. Although they reported the accuracy of the estimation to be less than 0.5 L/min, they did not take the viscosity change into consideration. Granegger et al. (2) derived cubic equations with regard to the motor current and rotational speed to estimate the flow rate. The standard deviation of the difference between the estimated and reference flow
FIG. 10. Comparison between estimated and reference flow rate at 2000 rpm.
FIG. 9. Viscosity estimation of fluid No. 5 at 2000 rpm.
was 2.95 mPa s. At this point, the amplitudes of the impeller displacement and the current became 50 μm and 0.6 A, larger than those before applying xr_exc. The fluid clearance of 200 μm between the impeller and the housing wall is still maintained.
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VISCOSITY MEASUREMENT IN A MAGLEV RBP fluids No. 1 to No. 4 at 2000 rpm. For the clear symbols, the viscosity, μ, in Eq. 17 was the value measured by the proposed sensorless method. In contrast, μ was fixed to 3.17 mPa s for the black symbols, which is the average viscosity of fluids No. 1 to No. 4. By compensating for the viscosity, the standard deviation between Qref and Qest was improved from 1.83 to 0.36 L/min in the range from 1 to 5 L/min. Despite using a simple equation with only three coefficients, the accuracy of the estimated flow rate using the proposed method is comparable with that proposed by Granegger et al. (2). This result suggests that the proposed sensorless viscosity measurement method is sufficiently accurate for it to be applied to estimating the flow rate. Accuracy of sensorless viscosity measurement The difference between μmeas and μref in Fig. 7 is considered to be caused mainly by: (i) the variation in phase difference with flow rate; and (ii) the variation in fluid temperature. We consider the reason for (i), which led to the viscosity measurement error of ±0.16 mPa s mentioned above, to be the additional stiffness kfx, which is similar to the wedge effect in hydrodynamic bearings (22). The distribution of the flow velocity in the fluid clearance region is dependent not only on the rotational speed but also on the flow rate. The amplitude of the wedge effect therefore changes with flow rate, which leads to a change in phase difference. Moreover, the phase difference can vary in synchronization with the pulsatile flow, but owing to the LPF which has a cutoff frequency of 0.1 Hz, its influence could be eliminated as shown in Fig. 8. From a practical point of view, the influence of the flow rate is sufficiently small that the viscosity can be measured without any information required about the flow rate. As the fluid temperature was controlled at 23.5 ± 0.4°C, the variation of the fluid temperature causes a variation in viscosity of ± 0.05 mPa s in the case of fluid No. 4, for which the sensitivity to temperature of 0.12 mPa s/°C was the highest of the fluids tested. In this study, the error caused by (ii), the temperature control, was not negligible, in addition to that due to (i), the influence of the flow rate. Limitations and future work of this study Mixtures of water, glycerin, and sodium chloride were used for the working fluids. Because these solutions are Newtonian fluids, the influence of nonNewtonian characteristics was not considered. Moreover, even if the viscosity and density of these solutions are controlled at the desired values, the impeller dynamics can be different from those in
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blood. Therefore, further investigation using real blood is required to confirm whether a sufficiently accurate estimate can be obtained. As evaluation of the method was performed at 2000 rpm, the accuracy of the viscosity measurement is guaranteed only at this rotational speed. If the method is applied at different rotational speeds, additional evaluations at various rotational speeds are required. The amplitude Xexc0 and frequency ωexc of the excitation were 50 μm and 440 rad/s, respectively. In this case, the effective value of the excitation velocity vexc is
vexc =
X exc 0 ω exc 2
= 1.56 × 10 4 μm s
(18)
The fluid clearance was 300 μm. Hence, by dividing vexc by 300 μm, the shear rate due to the excitation obtained is 52/s. When the proposed method is applied to blood viscosity measurements in future work, the excitation amplitude Xexc0 will be more than 100 μm in order that the shear rate is greater than 100/s, thus avoiding non-Newtonian effects. Increasing Xexc0 is feasible, because the fluid clearance was maintained at more than 200 μm even during rotation and excitation as mentioned in the section “Sensorless viscosity measurement under pulsatile flow.” CONCLUSION A method for sensorless viscosity measurement in MagLev rotary blood pumps without any additional sensors or mechanisms has been developed. Using glycerol–sodium–water solutions, we achieved a mean absolute deviation of 0.12 mPa s in the range from 1.18 to 5.12 mPa s, which is sufficiently accurate to compensate the flow rate estimation. The influence of both continuous and pulsatile flow was sufficiently small that the viscosity could be obtained without the need to measure the pump flow rate. This advantage makes the flow rate estimation methods proposed by many groups feasible for clinical use. In future work, we plan to utilize the proposed method in blood to evaluate the influence of nonNewtonian characteristics. Acknowledgment: This research is partly supported by JSPS KAKENHI grant number 24360059. REFERENCES 1. Bertram CD. Measurement for implantable rotary blood pumps. Physiol Meas 2005;26:99–117. Artif Organs, Vol. 39, No. 7, 2015
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