# A Non-Invasive Physiological Control System of a Rotary Blood Pump Based on Preload Sensitivity: Use of Frank–Starling-Like Mechanism

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Mock Circulation Loop (MCL)

_{lv}(t) is the ventricular compliance that changes according to left ventricular elasticity. State variables x

_{1}–x

_{6}represent the left ventricular pressure, left atrial pressure, arterial pressure, aortic pressure, aortic flow, and mitral valve flow, respectively, in the cardiovascular system, and x

_{7}represents the blood pump flow. Sets of state equations were derived from each of the circuits and combined into simultaneous ordinary differential equations, given as Equation (1), based on state variables. Solving Equation (1), the differential equations with MATLAB R2016a/SIMULINK (the MathWorks, Natick, MA) yields time series data of hemodynamic parameters. For details of parameters, variables, equations, and matrix, refer to reference [16,17].

#### 2.2. Control Strategy

#### 2.2.1. Estimate Average Pump Flow

_{p}(m) represents the pump flow calculated through state equations to the model developed by the authors in reference [17].

#### 2.2.2. Calculate the Desired Average Pump Flow

_{m}). A scaling factor (K) was introduced to provide a means of altering the sensitivity of the pump toward the changes in PLVED

_{m}, which made Equation (6) adaptive to various preload sensitivities of different patients [19]. The range of K values required for patients with different degrees of heart failure will be discussed and studied in the next chapter.

_{m}. If Emax is given, PLVED

_{m}is estimated through the fitting model (R

^{2}> 0.9310) in Equation (7).

_{t}) was determined according to the preload at t time (PLVEDm). According to Equation (8), the estimated average pump flow returned to CLn to obtain the intersection point OP

_{t+1,}which was the appropriate reference point for identifying the patient on the control baseline. The abscissa of OPt+1 was the reference average pump flow ($\overline{{\mathrm{Q}}_{\mathrm{est},\mathrm{t}+1}}$) required by the patient [20].

#### 2.2.3. Motor Speed Control

_{P}and K

_{I}were the proportional and integral gains, with the values 170 and 0.0001, respectively. The values were determined by using a critical proportioning method [17].

#### 2.3. Parameters Setting for Physiological States

_{S}represented the heart contraction, the heart rate, and the system circulation resistance of heart failure patients, respectively, and further details were referred to [17]. Table 2 describes the parameter settings of control systems at rest and motion. This paper simulated 30 cardiac cycles, out of which, the initial 15 cycles simulated the patient’s resting state during 15 s, 2.5 s simulated the state changing, while 16 to 30 cycles simulated the patient’s motion state in the next 7.5 s.

## 3. Results

_{n}tended to be flatter concerning smaller preload, resulting in a decrease in average pump flow. When K ≥ 1.7, severe oscillations were observed in $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}}}$. Thus, when the patient undergoes severe heart failure, this paper recommends the K value to be about 1.3. When the patient experiences moderate heart failure, as indicated in Figure 5b, K ≤ 0.5, and the data are over-adjusted. For 0.5 < K < 1.3, AOP, AOF, and $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}}}$ tend to stabilize. Similarly, $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}}}$ gradually decreases with the increase in the K value. For K ≥ 1.3, the system data oscillates. When the patient experiences moderate heart failure, the K value of around 1.0 is recommended in this article. When the patient undergoes mild heart failure, in Figure 5c, and 0.8 < K < 1.5, AOP, AOF, and $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}}}$ are relatively stable.

## 4. Discussion

_{t}in one cycle, the NAC-FSL control system proposed in this paper measured instantaneous preload instead of average preload. As a result, the system responded to the changes in the physiological state of the patient in time. Mahdi Mansouri et al. proposed a preload-based Frank–Starling system where they measured average preload to determine the patient’s working point and cost for at least two cycles and could not successfully respond to changes in the physiological state of the patient in time [18].

## 5. Conclusions

_{n}) that had a flat slope under high preload conditions. The NAC-FSL system could unload the left ventricle effectively and provide a greater pump flow and cardiac output with less error during the exercise state, as compared to the CSC system. Eventually, the K value in the NAC-FSL controller was optimized to meet the perfusion needs according to the hemodynamic parameters, which vary with different preload sensitivities (K values).

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Block diagram of the control system. CVS, reference cardiovascular system; LVAD, left ventricular assist device; ω, motor speed; $\overline{{\mathrm{Q}}_{\mathrm{est}}}$, estimated average pump flow; PLVED, left ventricular end-diastolic pressure; $\overline{{\mathrm{Q}}_{\mathrm{Pr}}}$, desired average pump flow; PI, proportional and integral controller; CLn, Control Line; S1, original state; S2 and S3, deviated states. Gray circles represent the position of operating points after a change in states. Black circles represent the positions of operating points upon arriving at the new steady-state located at the intersection between the control line and the new system line. The controller drives the changes in the operating points along the path indicated by the arrows along the new system line.

**Figure 3.**Pump flow regulator. OP

_{ND,t}, the original operating point; OP

_{t}, the unadjusted state point of the patient at time t; $\overline{{\mathrm{Q}}_{\mathrm{est},\mathrm{t}}}$, the pump flow of the patient at time t; OP

_{t+1}, the state point after the patient adjusts at t+1; $\overline{{\mathrm{Q}}_{\mathrm{est},\mathrm{t}+1}}$, the ideal pump flow after the patient adjusts at time t+1 (reference pump flow); θ

_{n}, the nth control angle of the operating angle of the baseline.

**Figure 4.**Effect of CSC control system and NAC-FSL control system on hemodynamic parameters from resting to exercise state. (

**a**) The measured and estimated mean pump flow in two states. $\overline{{\mathrm{Q}}_{\mathrm{P}1}}$ and $\overline{{\mathrm{Q}}_{\mathrm{P}2}}$ represent the measured mean pump flows of CSC and NAC-FSL, respectively. $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}1}}$ and $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}2}}$ represent the estimated mean pump flows of CSC and NAC-FSL, respectively. The error between the estimated mean pump flow and the measured mean pump flow was compared. (

**b**) The estimated power corresponding to the motor speed from resting to exercise. NAC-FSL

_{M}represents the mean pump power at a variable speed and CSC

_{M}represents the mean pump power at a fixed speed. (

**c**) Changes in the P-V loops of the two control systems.

**Figure 5.**Changes in hemodynamic parameters as K values change for different degrees of heart failure. (

**a**) Emax = 0.5, severe HF. (

**b**) Emax = 1.0, moderate HF. (

**c**) Emax = 1.5, mild HF. K: Scale factor. $\overline{{\mathrm{Q}}_{\mathrm{e}\mathrm{s}\mathrm{t}}}$: estimated average pump flow.

Parameters | Value | Physiological Meaning |
---|---|---|

f cell7 row 1 cell8 row 1 | 10.06 | constant |

g cell6 row 2 cell7 row 2 cell8 row 2 | 6.5-HCT × 3.25 × 10^{−2} | Linearly related values to HCT |

h cell6 row 3 cell7 row 3 cell8 row 3 | HCT × 4.67 × 10^{−3}–0.557 | Linearly related values to HCT |

i | 0.009-HCT × 2.90 × 10^{−4} | Linearly related values to HCT |

j | 0.0105 | constant |

k | 5.5 | constant |

ρ | 13,600 | reference liquid density (kg/m^{3}) |

g | 9.8 | gravity acceleration (m/s^{2}) |

η | 100% | efficiency of electrical power to hydraulic power |

β | 9.9025 × 10^{−7} | pump parameter (mmHg/rpm^{2}) |

Parameter | Rest State | Exercise State |
---|---|---|

Emax (mmHg/mL) | 1.0 | 1.0 |

HR (bpm) | 60 | 120 |

Rs (mmHg.s/mL) | 1.2 | 0.5 |

Emax | K | $\overline{{\mathbf{Q}}_{\mathbf{est}}}(\mathbf{L}/\mathbf{min})$ | $\overline{{\mathbf{Q}}_{\mathbf{P}}}(\mathbf{L}/\mathbf{min})$ | Error | Stability |
---|---|---|---|---|---|

0.5 | 1.0 | * | * | * | * |

1.2 | 5.0069 | 5.0591 | 1.68% | stable | |

1.3 | 4.9773 | 4.9058 | 1.44% | stable | |

1.5 | 4.7617 | 4.6595 | 2.15% | slight shock | |

1.7 | 4.3598 | 4.5163 | 3.59% | shock | |

1.0 | 0.5 | * | * | * | * |

0.8 | 5.1000 | 5.1933 | 1.87% | stable | |

1.0 | 4.9686 | 4.8988 | 1.2% | stable | |

1.3 | 4.7179 | 4.6247 | 1.4% | slight shock | |

1.5 | 4.3560 | 4.4967 | 3.23% | shock | |

1.5 | 0.4 | * | * | * | * |

0.8 | 4.9229 | 5.0477 | 2.24% | stable | |

1.0 | 4.7588 | 4.8539 | 1.99% | stable | |

1.3 | 4.3526 | 4.5904 | 5.46% | slight shock | |

1.5 | 4.0980 | 4.4797 | 9.31% | shock |

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**MDPI and ACS Style**

Wang, F.; Wang, S.; Li, Z.; He, C.; Xu, F.; Jing, T.
A Non-Invasive Physiological Control System of a Rotary Blood Pump Based on Preload Sensitivity: Use of Frank–Starling-Like Mechanism. *Micromachines* **2022**, *13*, 1981.
https://doi.org/10.3390/mi13111981

**AMA Style**

Wang F, Wang S, Li Z, He C, Xu F, Jing T.
A Non-Invasive Physiological Control System of a Rotary Blood Pump Based on Preload Sensitivity: Use of Frank–Starling-Like Mechanism. *Micromachines*. 2022; 13(11):1981.
https://doi.org/10.3390/mi13111981

**Chicago/Turabian Style**

Wang, Fangqun, Shaojun Wang, Zhijian Li, Chenyang He, Fan Xu, and Teng Jing.
2022. "A Non-Invasive Physiological Control System of a Rotary Blood Pump Based on Preload Sensitivity: Use of Frank–Starling-Like Mechanism" *Micromachines* 13, no. 11: 1981.
https://doi.org/10.3390/mi13111981