# Physiological Control Law for Rotary Blood Pumps with Full-State Feedback Method
## 2 Materials and Methods
### Control Strategy with a Pulsatile of Pump Flow  
In the cardiovascular system, pulsatile mechanical circulatory support has the benefit of generating physiological pressure and flow [23]. This can be useful for enhancing micro-circulation and preventing gastrointestinal circulation complications. However, the excessively large size and mechanical functioning of such systems are far beyond the advantages of pulsatile flow. These problems are solved by rotary pumps with more reliable devices [24]. The pulsatility index (PI) parameter was used as a control objective in this study. This index was validated to reflect the preload of the left ventricle. When the PI rises, the preload dose also rises, and vice versa [25]. Excessive PI declines can lead to ventricular collapse. The PI index is therefore a useful measure for sustaining the pump's reaction to changing the HF preload and afterload circumstances by providing the largest feasible suction-prevention flow rate [26]. This study has implemented a feedback control system for a newly proposed Starling controller that we consider clinically intuitive for the physician. The Starling-like controller emulates the Frank-Starling law of the heart, which adjusts the LVAD flow to the LV-filling pressure (or preload). Figure 2 illustrates the operation of the Starling-like controller. At any time, the operating point is located at the intersection of the target flow preload line (\(Ln\)) and the system flow-preload curve (C1 or C2), which is produced by changing the LVAD speed. Increasing the LVAD speed reduces the pulse flow rates and increases the pump's regular flow, whereas reducing the LVAD speed generates the reverse reaction. The flow curve of this scheme depends on circulatory circumstances (e.g., heart contractility, systemic vascular resistance, and total volume of circulation). For example, increasing the volume of the actual circulatory system changes the flow-preload curve to the right, from C2 to C1, as shown in Figure 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Unit** & **Healthy** & **Heart Failure** \\ \hline
**Left ventricle contractility (\(E_{\text{es,rp}}\))** & mm Hg/mL & 3.5443 & 0.7100 \\ \hline
**Right ventricle contractility (\(E_{\text{es,rp}}\))** & mm Hg/mL & 1.7235 & 0.5322 \\ \hline
**Systemic peripheral resistance (\(R_{\text{sa}}\))** & mm Hg\({}^{*}\)s/mL & 0.7411 & 1.1100 \\ \hline
**Total blood volume (\(V_{total}\))** & mL & 5300 & 5800 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cardiovascular system (CVS) model parameters used to simulate heart failure conditions. Figure 2: Control of the operating point with an acceptable range of pump flow and pulsatility of pump flow. Although a single gradient in relation is enough for adjusting the LV output (pumping flow) to the short-term changes in the right ventricular output, and therefore the LV preload (pumping flow pulsatility), migration to different gradients may compensate for LV contractility for long-term variations, and metabolic demands of the body. To modify the control gradient, a series of rules are implemented for the adjustment of the target flow preload line, based on the upper and lower limits for both the average pump flow and the pump flow pulsatility. As long as the operating point is within these limits (the current combination of the pump flow and pulsation), no slope changes are indicated. If the limits are exceeded for a certain period, suitable slope modifications are required. The Starling-like controller is also available in the literature [27] in more detail. Therefore, to generate and control the desired flow, we chose to regulate the operating point (red) located in the intersection between straight lines (such as L1 and L2) with curves (such as C1 and C2) within the bounded area, as shown in Figure 2. This area represents the acceptable range of movement to prevent suction and over perfusion.