Rotary Heart Assist Devices

The left ventricular assist device (LVAD) is a mechanical device implanted in patients with congestive heart failure to assist the heart in pumping blood through the circulatory system. The latest generation of this device is comprised of a rotary pump which is generally much smaller, lighter, and quieter than the first-generation conventional pulsatile-type pump. The rotary pump is controlled by varying the rotor (or impeller) speed to adjust the amount of blood flow through the LVAD. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician to meet the patientʼs blood needs. However, an important challenge facing the increased use of these devices is the desire to allow the patient to return home. The development of an appropriate feedback controller that is capable of automatically adjusting the pump speed is therefore a crucial step in meeting this challenge. In addition to being able to adapt to changes in the patientʼs daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of excessive pumping. This dangerous phenomenon, known as suction, may cause collapse of the ventricle and damage to the heart muscle. In order to be able to develop such a controller based on modern control theory an appropriate mathematical model of a combined cardiovascular system and LVAD must first be developed. In this chapter, we develop such a model. The model is dynamic, time-varying, and consists of six coupled nonlinear differential equations. The time variation occurs over four consecutive intervals representing the contraction, ejection, relaxation, and filling phases of the left ventricle. The LVAD in the model along with its inlet and outlet cannulae are represented by a nonlinear differential equation which relates the pump rotational speed and pump flow to the pressure difference across the pump. Suction is accounted for by adding a nonlinear resistance in the LVAD model when the pressure in the left ventricle drops below a specified threshold. Using this model we discuss some of the challenges faced in the development of: (1) an appropriate feedback controller for the LVAD, and (2) an effective algorithm for detection of suction in the left ventricle.

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