Performance Analysis of aFeedback-Controlled Rotary LVAD

Dr: Tohidkhah

Presented By: M. Babakmehr

LVAD is a battery-operated, mechanical pump-type device that's surgically implanted

Introduction

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Goal of LVAD: providing the patient with as close to a normal lifestyle as possible until a donor heart becomes available or, in some cases, until the patient’s heart recovers.

What Is The Problem?What Is The Problem?

An important challenge facing the increased use of these LVADs is the desire to allow the patient to return home.

An appropriate feedback controller for the pump speed

Ability to prevent the suction (which may cause collapse of the ventricle.)

Why Controller?

Wide variation of the patient’s SVR:

varying levels of physical activity

emotional changes

Control Approaches

feedback control approach using the heart rate to control the pump speed.

suction problem

using oxygen saturation of the blood for feedback control purpose requires implanted transducers limitations in respond to sudden changes in the patient’s blood demand.

New approach: use of pump flow as a feedback signal for controlling the pump speed

LV MODEL

•A fifth-order lumped parameter circuit model which can reproduce the left ventricle hemodynamics of the heart. (assumption: RV and pulmonary circulation are healthy)

Table of parameters:

LV MODEL

Preload & Pulmonary Circulations

Mitral Valve Aortic Valve

Aortic Compliance

Afterload

Compliance C(t) is the reciprocal of the ventricle’s elastance E(t).

The elastance describes the relationship between the ventricle’s pressure and volume:

Elastance Function Of The LV

E(t) = 1/C(t) & Cardiac Cycle=60/HR)

“double hill” function:

Three! Different Modes Of Operation Of The LV

every mode operation within the cardiac cycle is modeled by a different circuit, and hence a different set of DEs.appropriately modeling : by appropriately modeling the diodes as nonlinear elements, it is possible to write only one set of differential equations, which describes the behavior of the entire model for all three modes. write only one set of DEs.

Deriving The State Equations

The table of state variables

The solution is oscillatory in nature due to the cyclic nature of the terms C’(t)/ C(t) and 1/C(t)

MODEL VALIDATION #1

•Diastolic Pressure•Systolic Pressure

Simulation waveforms of the hemodynamics for an adult with heart rate of 75 bpm

Gyton’s textbook

MODEL VALIDATION #2

Is it a linear relationship between End-Systolic Pressure and LV Volume? (i.e. linear ESPVR)

vary the preload and afterload conditions, while keeping the left ventricle parameters (Emax, Emin, V0) constant.

Changing afterload Conditions By Selecting Different SVRs While Keeping EDV ConstantChanging Preload Conditions By Changing The Mitral Valve Resistance RM

MODEL VALIDATION #3

comparing the hemodynamic waveforms obtained from the model to those of a human patient.

SW model = 10492 mmHg.ml

SWMeasured=10690 mmHg.ml

Error=4.4%

CARDIOVASCULAR-LVAD MODEL

x6(t): blood flow through the pump

Ri & Ro: inlet and outlet resistances of pump cannulae.

Li & Lo: inlet and outlet inertances of pump cannulae

Rk: NLTV-pressure-dependent resistor (suction)

threshold pressure

Pressure difference across the pump:

Cardiovascular And LVAD Model (Forced System)

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Control Variable:

Development Of Feedback Controller

Speed of rotation : The only available mechanism to control a rotary LVAD is to increase or decrease the speed of rotation of the pump in order to meet certain goals

typically related to the well being of the patient

A major challenge for over 15 years:Providing required cardiac output

Suction does not occur

Our method in control:

A full state feedback Controller may be developed if the hemodynamic variables can be continuously measured in real-time. However, current implantable sensor technology to achieve this goal does not exist. The pump flow state variable , on the other hand, is the only state variable that

can be measured in real time

In this study the pump speed is increased linearly until

suction is reached while observing the pump flow signal. This

data shows that the onset of suction is characterized by several phenomena which include:

1- sudden large drop in the slope of the envelope of the minimum pump flow signal

2- Sudden change in the signature of the pump flow signal

Pump Flow signal measured in an animal in-vivo Study using WorldHeart LVAD

Envelope Of The Minimum Pump Flow Signal

changing from a positive value to a large negative value

Examining The Behavior Of x6(t) In Our Model

similar characteristics as the in-vivo animal data

feedback controller

Controller functions:

The controller consists of three basic functions . The first, labeled “Extract Minimum” will track the minimum value of the pump flow signal within each cardiac cycle.

The second, labeled “Calculate Slope,” will estimate the slope of the envelope of minimum values.

The third function, labeled “Speed Update” provides a mechanism for adjusting the pump speed based on the calculated slope until the maximum of the minimum pump flow signal is reached

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Simulation Results

To be able to assess the performance of our controller we need to determine the suction speed as a function of RS

RS= level of activity of the patient

RS level of activity

RS level of activity

able to increase and maintain the pump speed to a level below the suction speed

Performance Analysis: Simulation #1 RS=cte

Performance Analysis: Simulation #2 RS=Var

able to increase and maintain the pump speed to a level below the suction speed

Performance Analysis: Simulation #3 RS=cte , SNR = 29.40 (dB)

able to increase and maintain the pump speed to a level below the suction speed

Performance Analysis: Simulation #3RS=var , SNR = 5.48 (dB)

the pump speed was getting in and out of suction frequently (while the controller performed very well by keeping the pump speed below the suction speed for a high SNR)

Refrences

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

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY.(2009)

Performance Prediction of a Percutaneous Ventricular Assist System Using Nonlinear Circuit Analysis Techniques

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, FEBRUARY 2008

Modeling, analysis, and validation of a pneumatically driven left ventricle for use in mock circulatory systems

Medical Engineering & Physics 29 (2007) 829–839

Any Questions?

Contact information:

mbmce.2008@gmail.com

Thank You For Your Attention