## 4 Discussion  
Implantable rotary blood pumps (IRBPs) are considered to be one of the most significant advancements in modern technology and have been used to improve the quality of life for heart failure (HF) patients. However, the implementation of control strategies for these devices is still under development. These devices need to manage the physiological requirements of the patient by continuous monitoring to meet the appropriate response by the IRBP. The broad aim of this work was to develop a sensorless physiological controller to adjust the pump flow in accordance with the demand of the body. Generally, the flow rate values in a human body for a healthy person range from 4.4 to 5.5 L/min. These values are significantly reduced for HF patients, with contents of 1.5 to 2 L/min. In this work, the pump flow rate variable was successfully used as a hemodynamic parameter to drive an IRBP. The results indicated that the fuzzy PI-type control system offered a robust method to maintain the CVS variables for patients with HF. As shown in Figures 6 and 7, the controller robustly tracked the desired reference flow within a minimal and clinically accepted value (0.25 L/min). As a result, the control system automatically adjusted the pump speed to prevent suction (>1.5 L/min) or overperfusion (<7.5 L/min). In both scenarios, the linear regression analysis between the estimated and actual flow was highly correlated and the slopes were close to unity. The results also showed that the mean absolute error between the estimated and actual flow converged to zero (Figures 6h and 7h). To accurately automate the pump speed and physiological perfusion for patients with HF, we assumed that the aortic valve was closed and that the total blood passed to the aorta through the IRBP. By employing these assumptions, our design method was able to maintain the stroke volume of patients with HF within a minimal range (\(\geq\)350 mL). In comparison, the simulation results showed that ventricular suction could occur at any time due to the stroke volume reaching 400 mL at a constant speed. However, these assumptions cannot be applied to all patients due to pulsatility and the useful amount of blood that passes through the aorta. Nonetheless, controlling the aortic valve function with a safe operating mode for an IRBP to maintain the physiological perfusion is still a preliminary issue [25]. For this reason, several researchers have developed physiological control methods based on aortic valves that might be assumed to be closed [21]. For instance, in 2019, [PERSON] et al. [26] proposed a novel control method for a full and a partial support to adjust the pump flow of IRBPs. The method was successfully implemented and evaluated based on a pump flow estimation and aortic valve state detection in a changing heart rate (HR) and contractility. Various control mechanisms have been developed and implemented based on multiple hemodynamic factors. These factors use intrinsic pump parameters based on the use of the linear functions of a CVS model. It might be challenging to use this approach when simulating patients. For example, a linear model may not be consistent across a group of patients. This may lead to simulation inaccuracy and an inconsistent quantization performance. Furthermore, the pump flow derived from intrinsic pump feedback signals as the total flow to humans may increase the estimation error [27]. However, in this study, the flow estimator model was stable and guaranteed the performance of the controller in providing significant tracking, as shown in Figures 6h and 7h. This work was designed based on an estimated pump flow parameter. The results in Table 4 illustrate that the CVS hemodynamic variables varied within acceptable clinical conditions. However, several researchers have used different variables for controlling IRBPs. These variables may include an afterload or aortic pressure, arterial pulsatility, suction detection, and he heart rate.