Automated Hemodynamic Regulation with Model Predictive Control Brian Aufderheide, Ramesh R. Rao and B. Wayne Bequette Isermann Department of Chemical Engineering Rensselaer Polytechnic Institute Troy NY 12180-3590 Abstract-A multiple model adaptive predictive controller is designed to regulate mean arterial pressure and cardiac output in critical care subjects using inotropic and vasoactive drugs. The algorithm uses a multiple model adaptive approach in a model predictive control framework to account for inter- and intra-patient variability and explicitly handle drug rate constraints. The controller is evaluated on canines that were pharmacologically altered to exhibit symptoms of hypertension and depressed cardiac output. I. INTRODUCTION Critical care physicians maintain certain patient state variables within acceptable operating ranges by infusing several drugs and/or intravenous fluids. Constant monitoring and manual regulation of the physiological variables can be tedious. Hence, it is desirable to have an automated system to perform such tasks. Reference [1] provides a comprehensive review of research in control of drug infusion. Model predictive controllers (MPC) are a class of controllers that employ an identifiable model to predict the future behavior of the system over an extended prediction horizon [2]. A cost function (based on setpoint tracking error over a prediction horizon of P steps) is minimized by adjusting a set of future manipulated variable moves (M steps), subject to constraints on the manipulated inputs and controlled outputs. Optimal closed-loop feedback is achieved by implementing only the first control move and repeating the complete sequence of steps at subsequent sample times in a receding horizon fashion. An important issue in the design of drug infusion systems is the need to impose bounds on dosages and infusion rates to avoid overdosing or drug toxicity. For example, sodium nitroprusside (SNP) used in reducing hypertension should be infused less than 10 μ g kg -1 min -1 . Alternatively, the physician may want to specify an operating range of the mean arterial pressure instead of a specific setpoint. While most control strategies handle such constraints in an ad hoc manner, the primary advantage to MPC is its ability to handle constraints explicitly. Its optimization- based framework allows computation of the optimal infusion rates subject to input and output constraints. However, this approach relies on the availability and accuracy of the prediction models and requires on-line adaptation to account for patient variability. In multiple model adaptive control (MMAC), the basic idea is to use a bank of models to capture the possible input-output response behavior. The control parallel is to use a bank of controllers, to achieve a desired closed-loop performance from a wide variety of possible patients; controller k is designed based on model k from the model bank.. Using a Bayesian approach, the probability of each model representing the patient response is computed and the resultant control action is the probability-weighted average of control moves of each controller. The model probabilities get altered as the drug sensitivities change in inter/intra patient variations. The primary advantage to this approach is that no a priori model identification is necessary during initial stages of drug administration. The controller is initialized with a predefined, usually equal, probability and adapted using subsequent measurements. In this work we present a novel approach combining the MPC and MMAC strategies for regulation of hemodynamic variables in canines. A probability-weighted average of output predictions from a bank of models is used in a MPC framework to calculate drug infusion rates for regulation of mean arterial pressure and cardiac output. This approach has the combined advantage of model adaptation according to patient variations and the ability to handle explicit input and output constraint specifications often desired by the critical physicians. II. SYSTEM DESCRIPTION The overall control objective is to maintain two hemodynamic variables, mean arterial pressure (MAP) and cardiac output (CO), at desired setpoints by automated infusion of inotropic and vasoactive drugs. SNP is administered for arterial vasodilation. Dopamine (DPM) is used as an inotrope to enhance cardiac performance; Phenylephrine (PNP) is used for arterial vaso-constriction. The model bank constitutes of ten linear first order + dead-time or second order models with different gains and time constant values corresponding to each drug and its hemodynamic response. The parameters are chosen to bound nominal drug responses. The controller was initially evaluated and tuned in closed loop simulations using a elaborate non-linear canine circulatory model ([3], [4]) as the “patient” before moving to the experimental phase. III. EXPERIMENTAL SETUP The controller was evaluated on three mongrel dogs under IACUC approved protocol. Following induction of a surgical plane of anesthesia, the animal was intubated and mechanically ventilated (Siemens-Elena 900C Servo-Ventilator) with isoflurane or halothane anesthesia. An arterial line was placed in the femoral artery to provide continuous arterial pressure tracings on a Mennen Horizon monitor. A Swan-Ganz catheter (Baxter Edwards Swan Ganz Intellicath CCO/VIP Thermodilition), connected to a Baxter Vigilance monitor, was introduced in the pulmonary arterial tree to provide continuous cardiac output measurement. Control calculations were performed on a Dell Pentium II PC running a custom built Windows based GUI. The pressure and flow measurements were received from the monitors through RS-232 ports. The control loop was closed with rotary infusion pumps (Critikon Simplicity 2100A) modified to accept digital inputs via a digital output card. IV. RESULTS The responses to the drugs administered varied greatly depending on the anesthetic used as well as which canine received them. Isoflurane lowers systemic vascular resistance yet the contractility of the heart and the baroreceptor reflex remain relatively strong. With