A Dynamical State Space Representation and Performance Analysis of a Feedback Controlled Rotary Left Ventricular Assist Device

Abstract

The Left Ventricular Assist Device (LVAD) is a mechanical device that can assist an ailing natural heart in performing its functions. The latest generation of such devices is a rotary-type pump which is generally much smaller, lighter, and quieter than the conventional pulsatile-type pump. The rotary-type pumps are controlled by varying the rotor (impeller) speed. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician. However, an important challenge facing the increased use of these LVADs, is the desire to allow the patient to return home. The development of an appropriate patient adaptive feedback speed controller for the pump is therefore crucial to meet this challenge. In addition to being able to adapt to changes in the patient’s daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of suction. In this paper we will discuss the theoretical and practical issues associated with the development of such a controller. As a flrst step, we will present a state-space mathematical model, based on a nonlinear equivalent circuit flow model, which represents the interaction of the pump with the left ventricle of the heart. The associated state space model is a 5-dimensional vector of time varying nonlinear difierential equations. The time variation occurs over 4 consecutive intervals representing the contraction, ejection, relaxation, and fllling phases of the left ventricle. The pump in the model is represented by a nonlinear equation which relates the pump rotational speed and the pump flow to the pressure difierence across the pump. Using this model, we will discuss a gradient based feedback controller which increases the pump speed to meet the patient requirements up to the point where suction may occur. At that point the controller will maintain a constant pump speed keeping the gradient of the minimum pump flow at zero. Simulation results using the model equipped with the feedback controller are presented for two cases representing two levels of patient activities. Performance of the controller for noisy measurements of pump blood flow is also investigated. Our results show that such a feedback controller performs very well and is fairly robust against measurements noise.