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

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

Three! Different Modes Of Operation Of The LV

Deriving The State Equations

The table of state variables

MODEL VALIDATION #1 Diastolic Pressure Systolic Pressure

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 (E max, E min, V 0 ) constant. Changing afterload Conditions By Selecting Different SVRs While Keeping EDV Constant Changing Preload Conditions By Changing The Mitral Valve Resistance R M

MODEL VALIDATION #3 comparing the hemodynamic waveforms obtained from the model to those of a human patient. SW model = mmHg.ml SW Measured =10690 mmHg.ml SW model = mmHg.ml SW Measured =10690 mmHg.ml Error=4.4%

CARDIOVASCULAR-LVAD MODEL x 6 (t): blood flow through the pump R i & R o : inlet and outlet resistances of pump cannulae. L i & L o : inlet and outlet inertances of pump cannulae R k : NLTV-pressure-dependent resistor (suction) threshold pressure Pressure difference across the pump:

Cardiovascular And LVAD Model (Forced System) ? 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

Examining The Behavior Of x 6 (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.

Simulation Results To be able to assess the performance of our controller we need to determine the suction speed as a function of R S RS= level of activity of the patient RSRS level of activity RSRS

able to increase and maintain the pump speed to a level below the suction speed Performance Analysis: Simulation #1 R S =cte

Performance Analysis: Simulation #2 R S =Var able to increase and maintain the pump speed to a level below the suction speed

Performance Analysis: Simulation #3 R S =cte, SNR = (dB) able to increase and maintain the pump speed to a level below the suction speed

Performance Analysis: Simulation #3 R S =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)

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

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