## 7 Discussion and Future Work  
In this paper, we demonstrated a novel artificial pancreas system with a val valveless piezoelectric pump. Although the pump is mechanically simple, its design requires detailed analysis to ensure efficient operation. We optimized our design, based on high net flow rate and low power consumption objectives, by using numerical multi-physics simulations in COMSOL. Once satisfied, we derived a reduced-order mathematical model of the pump in MATLAB/Simulink for model-based closed-loop control of blood glucose level in T1 DM. In these simulations, the pump supplies insulin to three commonly used insulin-glucose models, namely, Ackerman, Bergman, and Sorensen. It must be noted that these models have parameters of different T1 DM patients. The input to the controllers is the difference between the target glucose level and measured blood glucose level of the patient. The reference value is given and the instantaneous value is the output of the insulin-glucose model. A standalone APS gets the instantaneous value from a sensor known as a continuous glucose monitor. Integrating a continuous glucose monitor model in our simulations is a part of future work. The produced prototype includes two closures and a piezoelectric actuator. A multi-jet fusion 3D printer successfully printed the closures with embedded inlet and outlet nozzles, which require high precision. The piezoelectric actuator is selected due to availability and it consists of a PZT disk attached to a thin brass substrate. Although the PZT is lead-based, and potentially toxic, it is not exposed to insulin in our design since the brass side faces the chamber. Lead-free piezoelectric materials, such as alkaline niobates or bismuth titanate [39], are interesting alternatives for future work. Another option is to use a separating layer, like a non-toxic coating or diaphragm, between the actuator and the chamber. Figure 14: Experimental and simulated electrical current (RMS) at different excitation frequencies. Figure 13: The experimental and simulated maximum displacement of the piezoelectric actuator at different excitation frequencies. The prototype pump does not include embedded electronics at this stage because it is experimented in a laboratory test setup. This enables us to test the pump with a range of inputs and to observe a multitude of outputs during development phase. A fully coupled simulation model of the APS is one of the major contributions of this work. Hence, the experiments serve as a basis and validation for the development of the simulation model as well as the pump. The main drawback of the existing test setup is the lack of an accurate flow sensor. Because of this, instead of measuring the net flow rate we measured the maximum displacement of the actuator and compared with the simulations to find that the values are within 10% of each other at the experimented frequencies. This discrepancy can be extended to net flow rate, but supporting this with experimental proof is our first priority in future work. In the literature, there are several studies [13; 30] that investigate the dynamics of valveless piezoelectric pumps. Our contribution here is that we coupled the piezoelectric pump dynamics with three types of well-known glucose-insulin models. Furthermore, we applied PID and optimal controllers on the blood glucose level control problem. For blood glucose level control with an APS, it is crucial to show that the proposed pump can deliver insulin with the flow rates required by the blood glucose controller. The [PERSON]'s and [PERSON]'s glucose-insulin models are relatively simple so that they are used for the design of optimal and PID controllers, respectively. The comprehensive Sorensen model is used for performance assessment in model-based simulations. Because of its complexity, the Sorensen model requires more computational power and time. This issue must be considered when electing an embedded controller for a standalone APS.