Simultaneous Control of Venous Reservoir Level and Arterial Flow Rate in Cardiopulmonary Bypass

doi:10.21203/rs.3.rs-1980291/v1

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Simultaneous Control of Venous Reservoir Level and Arterial Flow Rate in Cardiopulmonary Bypass

https://doi.org/10.21203/rs.3.rs-1980291/v1

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Performing a cardiopulmonary bypass (CPB) requires a well-trained perfusionist with skill and experience. In particular, operating the two occluders is difficult because it changes both the blood flow rate and reservoir level, and failure of the operation puts the patient’s life at risk. This study proposes an automatic control system with a two-degrees-of-freedom model matching controller nested in an I-PD feedback controller to simultaneously regulate the blood flow rate and the reservoir level. Experiments simulating CPB initiation and weaning were conducted using glycerin and bovine blood as perfusates. The results demonstrated that the arterial flow rate tracked the manually adjusted venous flow rate with a percentage error below 7.57%, and the reservoir level was maintained with an error below 4.89%. Then, experiments were conducted that simulated disturbances caused by venting/suction of blood from the surgical field and afterload fluctuation in the patient. The results showed that the control accuracies were not affected by afterload fluctuation; venting/suction disturbance worsened the accuracy of controlling the flow rate (3.26% error), while the reservoir level was maintained at 2.22% error. Thus, the robustness and control accuracies of the proposed system were demonstrated, and the system marks another step toward the automation of CPB.

The cardiopulmonary bypass (CPB) system is used to replace cardiac and pulmonary functions during cardiac surgery. It was first developed by Gibbon [1], and various improvements are being made to the devices installed in the system to ensure safety [2]–[5]. In the surgery, the perfusionists are responsible for a wide range of CPB operations, including blood flow rate control, reservoir level control, oxygen gas level concentration control, oxygen gas flow rate control, temperature control, cardioplegia fluid infusion, biometric monitoring, device information monitoring, and operation records. Among them, the regulation of blood flow and reservoir level are closely related, and it takes long-term training to control both of them at the same time [6], [7].

In the CPB circuit, a patient is connected to a blood pump and reservoir via vinyl tubing attached to the arterial and venous sides, with occluders on both the arterial and venous circuits. When the output of the blood pump is constant, the blood flow rate is controlled by opening and closing two occluders squeezing the venous and arterial tubes. The amount of blood flowing into and out of the reservoir is determined by the flow rate difference between the arterial and venous sides. Because the reservoir level corresponds to the volume of blood in the patient’s heart and lungs, an unstable reservoir level can lead to unintended blood pressure fluctuations in the patient, putting the patient’s life at risk. In addition, an extreme drop in the reservoir level can lead to air embolus and cause severe damage to the patient [8], [9]. Thus, occluder manipulation is a great mental burden for the perfusionist [10]. In recent years, it has been pointed out that automation of CPB operations is necessary to reduce the risk of medical accidents caused by human error [11].

Most studies aimed at automating blood flow rate operations have focused on CPB systems using roller pumps to facilitate control of the blood flow rate [12]–[14]. However, it has been pointed out that roller pumps have risks such as unintended increases in pressure in the arterial line and massive air embolus due to mishandling [15]. In addition, prolonged use of a roller pump can cause a risk of hemolysis [16]. Therefore, it is preferable to use a CPB system with a centrifugal pump. Several blood flow rate control systems have been developed for systems using centrifugal pumps [17], [18]; however, most systems were not designed to control the occluders but to maintain the target blood flow rate independent of the centrifugal pump speed. To solve this problem, a method was proposed to automatically control the occluder so that the arterial flow rate matches the manually-adjusted venous flow rate [14], [19]. However, these systems do not control the reservoir level, and thus, a small disturbance can cause fluctuations in the reservoir level, making it unfeasible for clinical application.

Therefore, in this paper, we propose a simultaneous automatic control system for the control of the arterial flow rate and the reservoir level, as shown in Fig. 1. The proposed system aimed to control the arterial occluder to match the arterial flow rate to the given venous flow rate and maintain the reservoir level. A two-degree-of-freedom model matching controller [20], [21] and an I-PD controller [22] were combined and nested to achieve accurate control and suppress the influence of inevitable disturbances caused by surgery. We examined the control accuracy of the proposed system by performing experiments simulating the initiation and weaning of CPB because the occluder operation becomes the most complex during these periods. In these experiments, an actual CPB circuit perfused with glycerin or bovine blood was used. The robustness of the system was then examined through experiments simulating disturbances caused by venting/suction and afterload fluctuations.

PROPOSED CPB SYSTEM

Figure 1 shows a general CPB system with the proposed system installed. A CPB system is composed of a hard-shell venous reservoir, a centrifugal pump, occluders to modulate blood flow rates, and electromagnetic flowmeters. The components are connected using polyvinyl chloride tubes, forming a closed circuit with the patient. The output of the centrifugal pump determines the maximum blood flow rate, and the flow rates in the arterial and venous lines are controlled using occluders.

The proposed system shown on the right side of Fig. 1 measures the venous flow rate and reservoir level and sends the control signal to the arterial occluder. The venous flow rate is measured using an electromagnetic flowmeter sampled by a microcontroller (Arduino Due) at a sampling frequency of f_flow and inputted to the measurement PC. Here, the venous and arterial flow rates are denoised using the N_low-order Butterworth low-pass filter with a cut off frequency of f_lowcut. The reservoir level is measured at a sampling rate f_level Hz by analyzing images captured by a web camera. Please refer to the Supplementary Material for the image analysis procedures. The controller PC implemented the proposed control system to determine the opening rate of the arterial occluder (green triangle in Fig. 1).

CONTROLLERS

Figure 2(a) shows the block diagram of the proposed system to control the opening rate of the arterial occluder ${O}_{cc}\left(s\right)$ that regulates the arterial flow rate $Q\left(s\right)$. The input and output relationship of this control target was described using the combination of a linear dynamic model and a nonlinear static model (hereafter referred to as the nonlinear controlled system). The linear dynamic model describes the dynamic characteristics for regulating the occluder, and The nonlinear static model generates the arterial flow rate $Q\left(t\right)$ from ${O}_{cc}^{{\prime }}\left(t\right)$ yielded by the linear dynamic model, as shown in the following equations:

$Q\left(t\right)={K}_{g}\left\{{O}_{cc}^{{\prime }}\left(t\right)\right\}$$=\frac{{\left(1+\frac{\varDelta {R}_{0}}{R}\right)Q}_{0}RA\left\{{exp}\left(K\cdot {O}_{cc}^{{\prime }}\left(t\right)\right)-1\right\}}{1+RA\left\{{exp}\left(K\cdot {O}_{cc}^{{\prime }}\left(t\right)\right)-1\right\}+\varDelta {R}_{0}A\left\{{exp}\left(K\cdot {O}_{cc}^{{\prime }}\left(t\right)\right)-1\right\} },$(1)

$${O}_{cc}^{{\prime }}\left(s\right)=\frac{{e}^{-Ls }}{1+Ts} {O}_{cc}\left(s\right),$$

where ${O}_{cc}\left(t\right)$ represents the opening rate of the occluder, R is the resistance of the entire CPB channel excluding that of the occluder channel, ${\Delta }{R}_{0}$ is the resistance of the occluder channel, ${Q}_{0}$ is the blood flow rate at 100% occlusion opening, and $A$ and $K$ are parameters that express the relationship between the ratio of the crushed tube diameter to the opening rate of the arterial occluder, L is the parameter of dead time, and $T$ is the first-order time constant. These parameters were determined by the nonlinear least square method using premeasured opening rates of the occluder and arterial flow rates.

Because the control target involves nonlinearity, a nonlinear feedforward (FF) controller was designed based on the nonlinear static model and the linear dynamic model included in the nonlinear controlled system as follows:

$${O}_{cc,m}\left(s\right)=\frac{\left(1+Ts\right)\left(1+Ls\right)}{{\left(1+{T}_{f}s\right)}^{2}}{Q}_{m}{\prime }\left(s\right) ,$$

${Q}_{m}^{{\prime }}\left(t\right)={K}_{g}^{-1}\left\{{Q}_{m}\left(t\right)\right\}$ $=\frac{1}{K}{ln}\left\{\frac{A{Q}_{m}\left(t\right)}{\left({Q}_{0}^{{\prime }}-{Q}_{m}\left(t\right)\right)R-\varDelta {R}_{0}{Q}_{m}\left(t\right)}+1\right\},$ (4)

where ${O}_{cc,m}\left(s\right)$ is the reference opening rate of the occluder and ${Q}_{m}\left(t\right)$ is the reference flow rate. Two first-order filters ($1+{T}_{f}s$) were introduced to generate a proper transfer function, and the dead time was approximated by a first-order delay $1/\left(1+Ls\right)$ to enable the pole placement method at the optimization phase. The reference trajectory ${Q}_{m}\left(s\right)$ inputted to the arterial flow rate control unit was generated using the following transfer function.

$${G}_{m}\left(s\right) = \frac{1}{{\left(1+\sigma s\right)}^{3}} ,$$

where ${G}_{m}\left(s\right)$ modeled a skilled perfusionist controlling the arterial occluder, and its behavior was specified using an arbitrary time constant $\sigma$.

To achieve automatic control of ${O}_{cc}\left(s\right)$, the proposed system was composed of an arterial flow rate control unit and a reservoir level control unit. The arterial flow rate control unit was nested in the reservoir level control unit to enable simultaneous modulation of reservoir level and arterial flow rates. Specifically, the reservoir level control unit modulated the opening rate of the arterial occluder, ${O}_{cc}\left(s\right)$, so that the reservoir level, ${Y}_{L}\left(s\right)$, matched the target reservoir level, ${R}_{L}\left(s\right)$. The arterial flow rate control unit modulated ${O}_{cc}\left(s\right)$ so that the arterial flow rate, $Q\left(s\right)$, tracked the reference flow rate, ${Q}_{m}\left(s\right)$. The arterial flow rate control unit is a two-degrees-of-freedom model matching controller consisting of the FF controller and feedback (FB) PID controller, ${C}_{e}\left(s\right)$, defined by the following transfer function:

$${C}_{e}\left(s\right)={K}_{P,e}+\frac{{K}_{I,e}}{s}+{K}_{D,e}s ,$$

where ${K}_{P,e},{K}_{I,e},{K}_{D,e}$ are the proportional, integral, and derivative gains of the arterial occluder control unit, respectively.

The reservoir level control unit employs an I-PD controller${ C}_{eL}\left(s\right)$ composed of an I controller ${C}_{eL,I}\left(s\right)$ and a PD controller ${C}_{eL,PD}\left(s\right)$ given by the following transfer functions:

$${C}_{eL,I}\left(s\right)=\frac{{K}_{I,L}}{s} ,$$

$${C}_{eL,PD}\left(s\right)=-{K}_{P,L}+{K}_{D,L}s ,$$

where ${K}_{P,L},{K}_{I,L},{K}_{D,L}$ are the proportional, integral, and derivative gains of the arterial occluder control unit, respectively. The output of the I-PD controller is then given by

$$Y\left(s\right)={C}_{eL,I}\left(s\right)\left\{{R}_{L}\left(s\right)-{Y}_{L}\left(s\right)\right\}+{C}_{eL,PD}\left(s\right){Y}_{L}\left(s\right)$$

where ${R}_{L}\left(s\right)$ is the target reservoir level, and ${Y}_{L}\left(s\right)$ is determined by integrating the difference between venous and arterial flow rates ($1/s$ element on the right side of Fig. 2(a)).

There are two types of disturbances caused by surgeries: the suction of blood from the surgical field $D\left(s\right)$ that increases the venous flow rate, and the fluctuation of the afterload ${D}_{y}\left(s\right)$, which is the resistance as the blood returns to the patient’s body that increases the reservoir level. It is theoretically provable by the final value theorem that the effect of disturbances such as suction flow rate $D\left(s\right)$ and afterload fluctuation ${D}_{y}\left(s\right)$ approaches zero over time (see Supplementary information A2 for the proof).

Simulation experiments were conducted to examine the efficacy of the proposed control system. This section explains the experimental system and experimental protocols.

Experimental System

Figure 2(b) illustrates the experimental system composed of the CPB circuit and the proposed system. The patient’s body was simulated using a softshell reservoir and a liquid tank in all experiments, and the other settings were configured in the same manner as a CPB system in clinical use. The CPB circuit was connected using polyvinyl chloride tubes. Electromagnetic flowmeters (FD-M5AT; Keyence Corp, Tokyo, Japan) were attached to the arterial line (3/8 inch tube) and the venous line (1/2 inch tube) to measure flow rates at a sampling frequency of f_flow = 100 Hz. A web camera (ELP-USBFHD06H-SFV; Ailipu Technology Co., Ltd, Guangdong, China) was attached to capture the venous reservoir image at f_level = 30 Hz. The parameters of the low pass filters to denoise the measured flow rate were N_low = 3 and f_lowcut = 5 Hz. The measured flow rates and reservoir images were then input into the proposed system, and signals were generated to control the arterial occluder (HAS-RH200; Senko Medical Instrument Mfg. Co., Ltd., Tokyo, Japan). A Hoffman clamp and a pressure gauge were attached to the arterial line to simulate afterload fluctuation. In addition, venting/suction was simulated by using a roller pump (MF-02; JMS Co., Ltd., Hiroshima, Japan) to transfer perfusate from the softshell reservoir (upper right of Fig. 2(b)) to the venous reservoir (HVR-4NFP; Senko Medical Instrument Mfg. Co., Ltd., Tokyo, Japan). Glycerin and bovine blood were used as perfusate. The glycerin solution was prepared by adding glycerin and red powdered paint (Dianix Red 200%; Mitsubishi Chemical Corp, Tokyo, Japan) to water. Viscosity was measured with an oscillating viscometer (SV-10; A&D Co., Ltd., Tokyo, Japan), and it was found to be 2.84 mPaཥs at 18.8°C. The bovine blood solution was prepared by mixing bovine red blood cell solution, the anticoagulant sodium citrate (Funakoshi Co., Ltd., Tokyo, Japan), and saline. The viscosity was 2.66 mPaཥs at 24.3 ℃, and the hematocrit was 25.0%.

Before proceeding to the experiments, the parameters included in the controllers must be determined. The parameters of the nonlinear static model (Eqs. (1) and (4)) were set based on our previous study [23]. In the linear dynamic model (Eqs. (2) and (3)), $T$ = 2.8 s, ${T}_{\text{f}}$ = 0.2 s, and $L$ = 0.8 s were set based on the premeasured dynamic characteristics. The time constant $\sigma =3.6$ s to generate a reference trajectory was chosen based on preliminary experiments. Finally, using this $\sigma$, the gain parameters of the PID and I-PD controllers were determined by the pole placement method [24] (see Supplementary Information A3).

Perfusion Process

The first experimental setting aimed to examine the accuracy of controlling the reservoir level and arterial flow rate. We performed simulation experiments under 6 configuration patterns of the proposed system: 3 configuration patterns of the arterial flow rate control unit employing either FF, FB, or both FF and FB controllers combined with 2 configuration patterns of the system, including or excluding the reservoir level control unit. The fault tolerance of the arterial flow rate control unit was tested by comparing the control accuracies yielded by its 3 configuration patterns because the configuration employing only the FF or FB controller can simulate the failure in either controller. The efficacy of the reservoir level control unit was verified by comparing the control accuracies of the proposed system with and without the reservoir level control unit. The system without the reservoir control unit was configured by removing ${C}_{eL}\left(s\right)$ and its associated inputs and outputs. Please refer to the Supplementary Material for the block diagram of the proposed system without the reservoir level control unit.

For the pre-experiment settings, the venous reservoir was filled with 5.0 L of glycerin solution or bovine blood, which was used as the perfusate. The potential for clinical application was tested by determining whether the characteristics of the perfusates affect the control accuracy. The maximum venous and arterial flow rates were each adjusted to 3.0 L/min using the Hoffman clamp and centrifugal pump with a rotational speed of 1700–2200 rpm. The target reservoir level was set to 0.45 L.

The experimental protocol was designed to simulate the operations of initiation and weaning. For initiation, the flow rate was increased from 0.0 L/min to 3.0 L/min in 100 s. Then, the flow rate was maintained at 3.0 L/min for 100 s. For weaning, the flow rate was reduced from 3.0 L/min to 1.0 L/min in 100 s, maintained at 1.0 L/min for 50 s, and finally perfusion was stopped by decreasing the flow rate instantaneously to 0 L/min. This protocol was repeated for 8 trials for each configuration pattern and each perfusate.

Disturbances

The second experimental condition was performed to examine the robustness against disturbances caused by surgery procedures. Experiments were performed using the system with and without the reservoir level control unit to reveal the efficacy of the reservoir level control unit.

The experimental protocol was designed to simulate disturbances caused by afterload fluctuation and venting/suction. Afterload fluctuation can easily occur during surgery due to hemodynamic changes in the patient, misalignment of the arterial cannulation, and bending of the blood circuit. This changes the relationship between the opening rate of the arterial occluder and the flow rate. Venting/suction is a surgical procedure in which blood from a bleeding surgical field is collected and returned to the venous line to restore the extracorporeal circulating blood volume. To simulate these disturbances, the CPB system was first stabilized at a perfusion flow rate of 1.5 L/min and a reservoir level of 0.45 L. Then, afterload fluctuation was simulated by adding a pressure drop of 150 mmHg before the liquid tank using the Hoffman clamp for 100 s, which resulted in a flow rate fluctuation of approximately 0.5 L/min. The disturbance of venting/suction was simulated by adding 0.35 L/min of perfusion flow directly to the venous reservoir for 100 s after stabilizing the CPB system. The simulation experiment of each disturbance was repeated for 5 trials for each configuration pattern.

Evaluation Criteria and Statistical Analysis

The efficacy of the proposed system was assessed by two aspects, which are the tracking accuracy of the arterial flow rate ${J}_{Q}$ and regulation accuracy of the reservoir level ${J}_{L}$, corresponding to the following two equations:

$${J}_{Q} =\frac{1}{N}{\sum }_{i=1}^{N}\left|{Q}_{m}\left(i\right)-Q\left(i\right)\right|,$$

$${J}_{L} =\frac{1}{N}{\sum }_{i=1}^{N}\left|{L}_{T}-L\left(i\right)\right|,$$

where ${J}_{Q}$ is the mean absolute error between the reference flow rate, ${Q}_{m}\left(i\right)$, and the measured arterial flow rate, $Q\left(i\right)$. Here, $i=1, 2, \cdots , N$ stands for the sampling number. ${J}_{L}$ is the mean absolute error between the target reservoir level and the measured reservoir level acquired using the web camera and video analysis. For all simulation experiments performed here, ${L}_{\text{T}}=0.45$ L.

In addition, we calculated the percentage errors to the target flow rate and reservoir level using the following equations:

$${J}_{Q\%} =\frac{1}{N}{\sum }_{i=1}^{N}\left|\frac{{Q}_{m}\left(i\right)-Q\left(i\right)}{{Q}_{m}\left(i\right)}\right|\times 100,$$

$${J}_{L\%} =\frac{1}{N}{\sum }_{i=1}^{N}\left|\frac{{L}_{T}-L\left(i\right)}{{L}_{T}}\right|\times 100,$$

In all experiments, the sampling interval was set to $\varDelta t$ = 0.01 s.The total measurement time was set to ${s}_{t}=$400 s for the perfusion process experiment and ${s}_{t}$ = 200 s for the disturbance experiment, where $N=$ ${s}_{t} /\varDelta t$. The values of evaluation functions were compared among different configuration patterns of the proposed system using multiple comparison tests with the Tukey method. The significance level was set at p < 0.05. Statistical analysis was performed using SPSS software version 22.0.

Figure 3 shows example results of the experiment simulating the perfusion process. The initiation of CPB started at 50 s, increasing the flow rate from 0.0 to 3.0 L/min in 100 s. Weaning started at 250 s, decreasing the flow rate to 0.0 L/min in 100 s. During these periods, the perfusionist only operated the venous occluder, and the arterial occluder was automatically controlled by the proposed system. In all 6 configuration patterns of the proposed system, the arterial flow rate tracked the venous flow rate, and their differences were not pronounced. In contrast, the reservoir level had large fluctuations when the reservoir level control unit was excluded, as shown in the bottom column, suggesting the importance of the reservoir level control unit.

Figure 4(a) compares the mean absolute errors of the flow rate ${J}_{\text{Q}}$, representing the tracking accuracy of the arterial flow rate to the venous flow rate with and without the reservoir level control unit. Each boxplot represents ${J}_{\text{Q}}$ obtained from 8 trials of the experiment simulating the perfusion process under each configuration. The figure indicates that the mean absolute errors were ${J}_{\text{Q}}<0.13$ L/min (Fig. 4(a), left), which corresponds to a percentage error ${J}_{\text{Q}\text{\%}}<5.84$% of the target flow rate. The comparison between the proposed system with and without the reservoir level control unit showed no significant difference in ${J}_{\text{Q}}$ (p $=$ 0.97). Therefore, the presence of the reservoir level control unit did not significantly affect the accuracy of the arterial flow rate control. In each graph of Fig. 4(a), the 3 boxplots represent the 3 configurations of the arterial flow rate control unit consisting of FF, FB, and both FF and FB controllers. In the system without the reservoir level control unit, ${J}_{\text{Q}}$ was significantly higher (p < 0.01) when employing only an FB controller (Fig. 4(a), left). This result suggests that the inclusion of the nonlinear FF controller could improve the tracking accuracy ${J}_{\text{Q}}$ in the system without a reservoir level control unit. However, there was no significant difference between the configurations in the proposed system.

Figure 4(b) shows the comparison of the mean absolute error ${J}_{\text{L}}$, representing the regulation ability of the reservoir level with and without the reservoir level control unit. The organization of the figure is the same as that in Fig. 4(a). The left side of Fig. 4(b) indicates that ${J}_{\text{L}}<0.12$ L (${J}_{\text{L}\text{\%}}=26.66$%) when the reservoir level control unit was excluded. The right of Fig. 4(b) demonstrates that ${J}_{\text{L}}<0.002$ L, which corresponds to a percentage error ${J}_{\text{L}\text{\%}}=4.89$% of the target reservoir level (0.45 L) when the reservoir level control unit was employed. The significant difference in ${J}_{\text{L}}$ between the proposed system with and without the reservoir level control unit indicates that the control unit effectively maintained the reservoir level. Comparisons between the configurations of the arterial flow rate control unit found that ${J}_{\text{L}}$ was significantly higher (p < 0.01) when employing only an FB controller for both the previous and proposed systems. This result indicates that the inclusion of a nonlinear FF controller in the arterial blood flow controller is also effective in maintaining reservoir levels.

Figure 5 shows the example results of the experiment using bovine blood with the reservoir level control unit. These examples show that arterial blood flow rate tracked venous blood flow rate and the reservoir level remained nearly constant, similar to when glycerin solution was used as the perfusate.

Figure 6 shows the evaluation function values obtained from the experiment with the reservoir level control unit using bovine blood as perfusate compared with the values obtained from the experiment using glycerin solution. In the case of bovine blood, the evaluation function values were ${J}_{Q}<0.15$ L/min (${J}_{\text{Q}\text{\%}}=7.57$%) and ${J}_{L}<0.014$ L (${J}_{\text{L}\text{\%}}=3.27$%) at worst when only the FB controller configured the arterial flow rate control unit. Including the nonlinear FF controller significantly improved the evaluation function values, as in the case of glycerin solution. A significant difference was not found between bovine blood and glycerin for both ${J}_{Q}$ (($p=0.839$) and ${J}_{L}$ ($p= 0.325$). These results indicate that the proposed system could control the blood flow rate within percentage errors of ${J}_{Q\%}=6.86$% of the target flow rate and ${J}_{L\%}=1.32$% of the target reservoir level. Changing the perfusate to bovine blood did not significantly affect the control accuracy.

The left and right sides of Fig. 7 show the experimental results simulating afterload fluctuation and venting/suction disturbance, respectively. As shown by the dashed red arrows, the disturbances were applied from approximately 50 s to 150 s. With afterload fluctuation disturbance, the arterial flow rate tracked the venous flow rate with mean absolute errors and percentage errors of ${J}_{Q}=0.06$ L/min (${J}_{Q\%}=4.97$%) for the proposed system and ${J}_{Q}=0.06$ L/min (${J}_{Q\%}=4.97$%) for the system without the reservoir level control unit. The reservoir level was maintained at the target level with mean absolute errors and percentage errors of ${J}_{L}=0.008$ L (${J}_{L\%}=1.78$%) and ${J}_{L}=0.006$ L (${J}_{L\%}=1.51$%) for the proposed system with and without the reservoir level control unit, respectively. These examples suggest that the arterial flow rate and the reservoir level could be accurately controlled using the proposed system with the reservoir level control unit even when afterload fluctuation disturbance was added.

With venting/suction disturbance, the arterial flow rate tracked the venous flow rate with a mean absolute error of ${J}_{Q}=$0.03 L/min (${J}_{Q\%}=2.87$%) without the reservoir level control unit, but the reservoir level deviated significantly from the target with ${J}_{L}=0.30$ L (${J}_{L\%}=67.16$%). In contrast, when the proposed system was used with the reservoir level control unit, the tracking accuracy of the arterial flow rate was ${J}_{Q}=$0.04 L/min (${J}_{Q\%}=3.26$%), and the reservoir level was maintained at the target level with ${J}_{L}=0.008$ L (${J}_{L\%}=1.88$%).

Figure 8 shows the evaluation function values yielded by the proposed system with and without the reservoir level control unit, where (a) and (b) show the disturbance experiment results of the afterload fluctuation and venting/suction, respectively. Figure 8(a) indicates that the proposed system could automatically control the arterial flow rate with a tracking accuracy of ${J}_{Q}<0.07$ L/min (${J}_{Q\%}=4.97$%) and maintain the reservoir level with ${J}_{L}<0.01$ L (${J}_{L\%}=2.22$%). In addition, there were no significant differences between the proposed system with and without the reservoir level control unit in both ${J}_{Q}$ (p $=$ 0.98) and ${J}_{L}$ (p $=$ 0.87). These results indicate that the systems with and without the reservoir level control unit could both absorb the effect of afterload fluctuation disturbance of 150 mmHg.

Figure 8(b) shows that the system without the reservoir level control unit could control the arterial flow rate with ${J}_{Q}<0.64$ L/min (${J}_{Q\%}=4.33$%) but with ${J}_{L}<0.49$ L (${J}_{L\%}=110.79$%). This result indicates that the venting/suction disturbance could cause large fluctuations in the reservoir level when the reservoir level is not controlled. In contrast, the proposed system could control the arterial flow rate with ${J}_{Q}<0.06$L/min (${J}_{Q\%}=3.26$%) and ${J}_{L}<0.008$ L (${J}_{L\%}=1.87$%). Compared to the system without the reservoir level control unit, ${J}_{Q}$ was not significantly different (p $=0.93$), but ${J}_{L}$ was drastically decreased (p < 0.001), indicating that the proposed system could maintain the reservoir level while controlling the arterial flow rate.

The aim of this study was to automate the control of arterial occluders in the CPB circuit to reduce the operational burden on perfusionists, and we proposed an automatic reservoir level and arterial flow rate control system with a nested structure. The proposed system was designed to accurately control arterial flow rate and reservoir levels and be robust to disturbances during surgery. Experiments were conducted to examine the control accuracies and robustness by simulating the perfusion process from CPB initiation to weaning and simulating disturbances of afterload fluctuations and venting/suction.

The experiment simulating the perfusion process using glycerin demonstrated control accuracies of the mean absolute errors of the flow rate ${J}_{\text{Q}}<0.13$ L/min (${J}_{\text{Q}\text{\%}}<5.84$%) (see Fig. 4(a)) and of the reservoir level ${J}_{\text{L}}<0.02$ L (${J}_{\text{L}\text{\%}}<4.89$%). When bovine blood was used as the perfusate, the control accuracies were ${J}_{Q}<0.15$ L/min (${J}_{\text{Q}\text{\%}}<7.57$%) and ${J}_{L}<0.014$ L (${J}_{\text{L}\text{\%}}<3.28$%). A qualified perfusionist is required to control the arterial flow rate and reservoir level within a percentage error of 10% [25], and the proposed system met the requirements in terms of control accuracy. In addition, a comparison of the accuracies between the perfusates indicated that the perfusate did not significantly affect the control accuracies (p > 0.33). This suggested the potential for clinical application of the proposed system.

We also compared the control accuracy among different configurations of the arterial flow rate control unit. In most cases, the poorest control accuracy was obtained when only the FB controller was employed, but it was still well below an error rate of 10% of the target flow rate and reservoir level. This indicates that a failure of the FF or FB controllers does not critically worsen the control accuracy, and thus the arterial flow rate control unit is fault-tolerant. This is another advantage of the proposed system that is important for clinical applications.

The experiment simulating afterload fluctuation disturbances demonstrated the control accuracies ${J}_{Q}<0.07$ L/min and ${J}_{L}<0.01$ L corresponding to ${J}_{Q\%}<4.97$% and ${J}_{L\%}<2.22$%, respectively. This result confirmed the robustness of the proposed system against afterload fluctuation. On the other hand, when the venting/suction disturbance was applied, the error of arterial flow rate was ${J}_{Q}<0.06$ L/min (${J}_{Q\%}=3.26$%), and the reservoir level was maintained at ${J}_{L}<0.008$ L (${J}_{L\%}=1.87$%). Therefore, the proposed system could control the reservoir level and arterial flow rate during venting/suction disturbance. Changes in the reservoir level directly affect the patient’s blood pressure and can be life-threatening due to microemboli caused by air induction. This fact highlights the importance of the reservoir level control unit. Furthermore, the robustness against disturbances of afterload fluctuation and venting/suction can be theoretically proven by the final value theorem so that the effect of the step disturbance input approaches zero over time. This theoretical analysis also supports the robustness of the proposed system against unavoidable disturbances in surgery.

Several studies have proposed systems that control arterial flow rate by tracking manually-regulated venous flow rate [14], [17], [18]. The control error of the most accurate system was 0.9% for a constant target flow rate and 6% for the flow rate modulated through CPB surgeries [18]. Our method could control the arterial flow rate with a percentage error of ${J}_{Q\%}=4.97$% of the target flow rate through simulated CPB processes, demonstrating that the accuracy was comparable to or better than the accuracy of the conventional systems. These previous studies pointed out the problem that afterload fluctuation can worsen the accuracy of the flow rate control [26]. This is because the conventional system controlled the arterial flow rate using only the nonlinear FF controller. In contrast, here, the proposed system was robust against afterload fluctuations with a high control accuracy because it employs a two-degree-of-freedom model matching control. More importantly, our results indicated that if the reservoir level control unit was not employed, the venting/suction disturbance caused a drastic increase in the reservoir level. Because conventional systems do not control reservoir levels, they can suffer from this problem. These facts highlight the advantages of the proposed system over conventional systems in preferentially controlling the reservoir level and suppressing the disturbance of afterload fluctuation and venting/suction.

With its robustness and high control accuracy, the proposed system would be beneficial to automate initiation and weaning operations, which are reported to be frequently performed incorrectly [27]. The proposed system is thus expected to reduce the operational burden on perfusionists and prevent accidents such as air embolus.

In this study, the maximum blood flow rate was limited to 3 L/min because the centrifugal pump was not controlled, and the rotational speed of the centrifugal pump was fixed at approximately 1800 rpm. Therefore, the centrifugal pump and occluder must be controlled in an interlocking manner to perfuse at a flow rate of 3 L/min or more. In addition, the venous flow rate also has to be automatically controlled to achieve fully automated CPB control. These issues will be addressed in future studies.

This paper presented a system to automatically control the arterial flow rate and reservoir level of the CPB system. Its control accuracy of arterial flow rate is comparable to or better than the conventional system with a perfusionist. Moreover, the proposed system is fault-tolerant and robust to the unavoidable disturbances during surgery. The characteristic of preferentially maintaining the reservoir level can protect the patient from acute blood pressure change. Therefore, it has a high potential for clinical application to prevent errors during operation and reduce the burden on the perfusionist, making another step forward to automate the operation of the CPB system.

Data availability

Te datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Acknowledgements

This research was supported by JSPS KAKENHI Grant Number JP 19K12851.

Author contributions statement

H.T. wrote the initial draft, and Z.S. and T.T. edited the manuscript. H.T. and T.T managed this study. H.T. and T.K. measured the data and analyzed the results. Z.S. contributed to data interpretation. T.K., S.O., S.M., and S.N. provided critical feedback and helped shape the research, analysis and manuscript. All authors reviewed the manuscript.

Competing interests

The authors declare no conflicts of interest associated with this manuscript.

Correspondence and requests for materials should be addressed to H.T. and T.T.

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No competing interests reported.

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Simultaneous Control of Venous Reservoir Level and Arterial Flow Rate in Cardiopulmonary Bypass

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