Mathematical modeling of ventricular suction induced by a rotary ventricular assist device

Abstract

Ventricular suction (VS) is an event caused by operating a rotary ventricular assist device (VAD) at a high speed in a patient with low blood volume in the left ventricle (LV). VS occurs when the blood flow out of the ventricle exceeds the flow into the ventricle, causing the ventricle to collapse. Because of this, it is risky to use a VAD on a long-term basis without changing the speed as the demand of a human body changes dramatically over time. As a result, a controller that can automatically adjust pump speed based on a patient's physiological needs with the capability of suction detection and avoidance would be important for developing a rotary VAD for long-term use. Computer modeling of the cardiovascular system has been used extensively for controller design and testing. To test the capability of a VAD controller to respond to VS, a mathematical model that can simulate VS must be integrated with a cardiovascular system model. In this paper, a nonlinear resistance as a function of the LV pressure, the absolute value of the LV pressure derivative, and the pump inlet pressure was identified to model VS. This was done by fitting a curve to data sets from animal experiments with the HeartMate II VAD. The model fit the data well with an average root-mean-squared (RMS) error of 10.93%. The model was validated against 23 different animal data sets with a mean RMS error of 29.98%. An existing suction model was tested with the same validation data sets and yielded a mean RMS error of 67.41%. The newly developed model showed a significant improvement from the existing model. It will be integrated with a cardiovascular model for future development of a suction detector and physiologic controller for a VAD.

Real-time Projected Gradient-based Nonlinear Model Predictive Control with an Application to Anesthesia Control

“…The definition of Γ is given in (5) and the detailed derivation of Theorem 3 is given in the upcoming section. Theorem 3 allows to conclude the following Corollary: Corollary 1: Under Assumptions 4-5, ∀x ∈ Γ the system (1) under Algorithm 1 is asymptotically stable.…”

“…However, medical control poses various challenges such as 1) nonlinearities from physiological models, 2) model uncertainty due to inter-and intra-patient variability, and 3) strict safety specifications [3]. In this paper we specifically focus on the class of automated drug infusion problems which have received considerable attention in recent times as they can be modelled well [4] and cover relevant applications such as control of: Blood pressure [5], hemoglobin [6], haemodialysis [7], anesthesia [8], and others [9].…”

Developments in control systems for rotary left ventricular assist devices for heart failure patients: a review

“…The response of the developed control system together with the suction detection algorithm was robust, stable and safe when tested under a wide range of in vitro mock circulatory loop and clinical studies. To obtain a mathematical model of ventricular suction, Yu and Porter (2006) have identified a nonlinear resistance as a function of the LV pressure, the absolute value of the LV pressure derivative and the pump inlet pressure. In 2008, Mason et al have investigated the clinical performance of seven expertly selected time domain indices of suction based on the observed positive spike induced in the RBP impeller speed waveform (Mason et al 2008).…”