# Evaluation of Different Control Algorithms for Carbon Dioxide Removal with Membrane Oxygenators
## 4 Conclusions  
This work presents a comparison between PI, NMPC, and deep RL control algorithms for blood CO\({}_{2}\) partial pressure reference tracking for membrane oxygenators in simulation. While PI and RL require less computational power when deployed, the NMPC was found to be the most suitable overall, in terms of accuracy, speed, and patient comfort. However, hardware limitations could restrict the use of an NMPC controller. Figure 4: Results of the RL controller training for \(n=1\), 5, and 10. The agents with \(n=1\) and 10 showed diverging behavior. Furthermore, a compartmental dynamical model of a membrane oxygenator was presented, which fixed and simplified the already existing model, without a loss of information for the carbon dioxide removal setting. Additionally, it was shown that the blood flow rate was suitable to be a manipulated variable in the carbon dioxide removal setting of membrane oxygenators. All three types of controllers used both the sweep and the blood flow rate to achieve reference tracking and disturbance rejection. The oxygenator model that was used for the assessment of the performance of the different control algorithms has several limitations. Firstly, it is assumed that the compartments are perfectly mixed, i.e., are homogenous. This means that the concentration polarization layer effect at the membrane surface is not considered, which can negatively affect the gas flux through the membrane. However, this simplification is necessary because solving for the spatial concentrations is very computationally expensive and is not suitable for the presented application. Furthermore, most of the parameters of the model are temperature-dependent, while in the presented model, the values for 37 \({}^{\circ}\)C are used. This issue can be fixed by including the temperature as an additional disturbance acting on the model and modeling the temperature dependence of the variables. Finally, changing the blood flow rate also changed the pressure inside the catheter, which could lead to potential harm to the patient. However, because our catheter allows the blood to flow also around it in the vena cava and the drainage and return sites are close to each other, changing the blood flow rate should not induce high pressure changes in the circulation system of the patient. Recirculation, which is usually an undesired phenomenon because it lowers the efficiency of the system to exchange gases, helps in this case to keep blood pressure within physiological conditions. Further investigations should be carried out to test this hypothesis. In the previous work, we presented an accurate estimator for the most important hydrodynamic parameters of the blood--flow rate, pressure difference, and viscosity [37]. Together with the control of the gases, the most important vital parameters--hemodynamics and gas exchange--were covered. In future work, they have to be integrated into one control system and their performance investigated and validated in in silico, in vitro, and then, finally, in vivo settings. Membrane oxygenators are medical devices, thus patient safety is one of the main concerns. Any automatic control scheme has to show proof of robustness and stability before it can be applied to any human patient. Additionally, safety control mechanisms can be implemented to supplement the control of hemodynamics and blood gases. A venous-venous membrane oxygenator can benefit from a pressure detection system that can be used for suction prevention and thrombus detection. Moreover, the blood flow rate control can be extended to pulsatile control to mimic better physiological conditions. Conceptualization, M.E., B.L., P.E. and C.J. ; methodology, M.E. ; software, M.E. ; validation, M.E., B.L., P.E. and C.J. ; formal analysis, M.E. ; investigation, M.E. ; resources, M.G. and M.H. ; writing--original draft preparation, M.E. ; writing--review and editing, M.E., B.L., P.E., C.J. and M.G. ; visualization, M.E; supervision, M.G. ; project administration, M.G. ; funding acquisition, M.G. and M.H.