Control of Circumferential Wall Stress and Luminal Shear Stress Within Intact Vascular Segments Perfused Ex Vivo

Proportional, integral, and derivative (PID) controllers have proven to be robust in controlling many applications, and remain the most widely used control system architecture. The purpose of this work was to use this architecture for designing and tuning two PID controllers. The first was used to control the physiologic arterial circumferential wall stress (CWS) and the second to control the physiologic arterial shear stress (SS) imposed on intact vascular segments that were implanted into an ex vivo vascular perfusion system (EVPS). In order to most accurately control the stresses imposed onto vascular segments perfused ex vivo, analytical models were derived to calculate the CWS and SS. The mid-vein-wall CWS was calculated using the classical Lamé solution for thick-walled cylinders in combination with the intraluminal pressure and outer diameter measurements. Similarly, the SS was calculated using the Hagen–Poiseuille equation in combination with the flow rate and outer diameter measurements. Performance of each controller was assessed by calculating the root mean square of the error (RMSE) between the desired and measured process variables. The performance experiments were repeated ten times $(N=10)$ and an average RMSE was reported for each controller. RMSE standard deviations were calculated to demonstrate the reproducibility of the results. Sterile methods were utilized for making blood gas and temperature measurements in order to maintain physiologic levels within the EVPS. Physiologic blood gases (pH, $pO2$⁠, and $pCO2$⁠) and temperature within the EVPS were very stable and controlled manually. Blood gas and temperature levels were recorded hourly for several $(N=9)$$24h$ perfusion experiments. RMSE values for CWS control $(0.427±0.027KPa)$ indicated that the system was able to generate a physiologic CWS wave form within 0.5% error of the peak desired CWS over each cardiac cycle. RMSE values for SS control $(0.005±0.0007dynes∕cm2)$ indicated that the system was able to generate a physiologic SS wave form within 0.3% error of the peak desired SS over each cardiac cycle. Physiologic pH, $pO2$⁠, $pCO2$⁠, and temperature levels were precisely maintained within the EVPS. The built-in capabilities and overall performance of the EVPS described in this study provide us with a novel tool for measuring molecular responses of intact vascular segments exposed to precisely simulated arterial biomechanical conditions.