Transcript Biomedical Engineering Faculty Biological System Modeling seminar

Biomedical Engineering Faculty
Biological System Modeling seminar
Modeling of Ventricular Assist
Devices(VADs)
Instructor:
Dr. towhidkhah
Presented by:
Ehsan Rouhani
Spiring
2008
Introduction
Heart disease is the leading cause of death in the united
states.The traditional soluation to end stage congestive
heart failure(is one diseas that the heart muscle is too
weak to provide enough perfusion for the body) is heart
transplantion.some patients are eligible for a transplant
beacause of age or health reasons.Therefore mechanical
circulatory assist devices,called artificial heart
pumps(AHPs) have been introduced to save some lives of
end-stage CHF patients since the 1960s.
Artificial Hearts
It pumps blood continously yhrough the circulatory system.
- Total Artificial Hearts(TAHs)
The Institute of Medicine(in the US) estimates that 10,000 to
20,000 people per year will be condidates for the TAHs.
- Left Ventricular Assist Devices(LVADs)
A left ventricular assist device(LVAD) is a battery operated,
mechanical pump type device that is surgically implanted.
This device is sometimes called a “bridge to transplant” .
Advantages
Less costly
Uneligible for heart transplants
Recovery of the failed ventricle
LVADs
- Arroe LionHeart LVAD(Pulsatile pumps):
Since the 1960s. It pumps blood in a cycle of pump/relax,
just like the heart does.
The pulsatile pump up to 10 litrs of blood per minute.
- Rotary pumps:
These pumps are currently under development.
Some studies have showed this type of pumps
demonstrating as excellent hemolytic performance over
some rotary pump with contact bearing.
Total artificial Heart
Left Ventricular Assist Device
Percutaneous Ventricular Assist Device
Nimbus pump(LVAD)
The pump Model
• The rotary pump is a mechanical device driven by a motor
• The electrical power is converted to mechanical power
J
Mechanical
Part
d  (t )
 T i  T e  B  (t ) T p
dt
B
Damping coefficient
Te
Motor torque
TP
Load torque exerted on the pump
J
Inertia load of the rotor
T P  a0  a1Q 
3
2
d 3
J
 K b  B   Q  (a0  a1 2 )
dt
2
Electrical Part
di (t )
v(t )  L
 Ri (t )  K b (t )
dt
 (t )
Rotating speed
Kb
EMF constant
Pump effieiency
Th  HQ
H is pressure difference between the outlet and the inlet of the pump
Q is flow rate
   (N s )
1/ 2
NQ
Ns 
3/ 4
H
• specific speed , a none-dimensional is used to describe the characteristic of the
pump in the design range
• the design objective is to achive the maximal efficiency at a specific speed
Patient status in LVAD application
I . if the left ventricle has no contractility ,Th becomes a
constant,the speed and current of LVAD will become
constant evetually
II . if the left ventricle has contractility , Th fluctuates ,
speed , current will be under the influence of this term
 Because of difficulties of solving these equations for H
and Q directly,some researches turn to estimating H
and Q with functions of current and speed
experiment
d 3
J
 K b  B   Q  (a0  a1 2 )
dt
2
J  0.916e  16
B  0.66e  6
H   0Q p  1
dQ p
  2 2
dt
 0  0.296, 1  0.027,  2  0.0000933
a0  0.738e  12
a1  0.198e  10
Pump characteristic equation
R i =R o =0.0677mmHg/(ml/s)
Li  Lo  0.0127mmHg /(ml / s 2 )
H  0Q p  1
dQ p
dt
  2 2
0  0.1707, 1  0.02177,  2  0.0000903
0  0.296, 1  0.027,  2  0.0000933
Modeling of suction
0
Rk  
3.5 x1  3.5Pth
Pth  1mmHg
if x1  Pth
otherwise
Another pump model
The motor inductance and the pump moment of inertia J are small,the
motor equation is simplified as :
P
 P 
  2  2   1 2   0


 
PQR
linearization
V 
 K e  
Q  1P   2V
 K t
Q
2
Mock human circulatory loop
A mock human circulatory loop was set up an in vitro test rig for a َ
different versions of prototype LVADs, as shown in figure . This test
rig can simulate different normal or pathologic states and activities of
a cardiovascular system. A small pump MY2 was used in the place
od an LVAD in the testing
Percutaneous Ventricular Assist Devices
(PVADs)
Introduction

is a device that bypasses blood from left atrium to femoral
artery through a blood pump

A percutaneous left heart assist system , including a
transseptal cannula, a blood pump, and a femoral arterial
cannula

Selecting an appropriate size of arterial cannula to maximize
the blood flow rate

Determining the system performance based on the selection
of arterial cannula

The computer model could also be a tool for cardiologist to
choose appropriate size of arterial cannula for patients
Electrical analog of the model
since the purpose of this model is to predict the average flow,the
transient response in the system negligible
Nonlinear function of fluid flow
P  f (Q )
f
f
(Q  Q )
*
P  f (Q ) 
(Q  Q ) 
Q Q Q *
Q 2 Q Q *
2
2
* 2
*
P  P  f (Q * ), Q  Q  Q *
P  R 0 Q  R1Q 2
R  R 0  R I . Q
PI  R I 0 .Q  R II . Q .Q
Determined by Least square fit to exprimental data
I. Single arterial cannula
Q1  Q

The switch is open
Pp  PI  PO  MAP  LAP
B  B  4AC
A . Q .Q  B .Q  C  0  Q 
2A
2
II. Dual arterial cannula with the same sizes
Q
Q1  Q 2 
2

The switch is closed
PO  PO 1  PO 2
PO  PO 1  PO 2
 RO 10 
 RO 11 
PO  RO 10 .Q1  RO 11. Q1 .Q1  
 .Q  
 . Q .Q
 2 
 2 
III. Dual arterial cannula with the different sizes
RO 20

RO10
PO  RO 10 .Q1  RO 11. Q1 .Q1  RO 20 .Q 2  RO 21. Q 2 .Q 2
2

 RO 10   PO  
1  RO 10
Q  (1  ) 
 
 


  2RO 11
2
R
R
O 11 
O 11 




  

  
PO  Q 
R

R
.
Q
 O 10 
 O 11 


1


1






  
  

R

 O 10 
 RO 11.Q
  1 
  1
2
R EQ
Experiment(test loop)
• Generating data to identify the model parameters
• Providing data to validate the accuracy of the model in predicting total
bypass flow by changing pump speed
Model parameter identification
n
EI 
2
[
Q
(
k
)

Q
(
k
)]
 measured
estimate
k 1
n
2
Q
(
k
)
 measured
k 1
*100%
Conclusion
• sensorless method for evaluate hemodynamic variable of
pump
• PVAD : A simple nonlinear circuit model
• Model can predict the bypass flow rate through the system
• Adavantage : cardiac catheterization laboratory within a
short period of time with a major open-heart surgery
Refrences
[1] S Chen,J R Boston and J F Antaki ”An Investigation of the Pump Operating
Characteristics as a Novel Control Index for LVAD Control”International
Journal of Control,Automation,and Systems,vol. 3,no. 1,March 2005
[2] Yi Wu,Paul E.Allaire and Gang Tao ”Modeling , Estimation and control of
Human circulatory system with a Left Ventricular Assist Devices”IEEE
TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY,vol.15.No 4
July 2007.
[3] S.H.Chen,BAROREFLEX-BASED PHYSIOLOGICAL CONTROL OF A
LEFT VENTRICULAR ASSIST DEVICE,PHD thesis,Pittsburgh,2006
[4] Y.C.Yu,M.A.Simaan,N.V.Zorn and S.Mushi ”Model-based Prediction of a
Percutaneous Ventricular Assist Device Performance”IEEE
Conference,portland 2005
[5] S Choi,J R Boston,D Thomas and J F Antaki ”Modeling and Identification of
an Axial Flow Blood Pump”Proceeding of the American Control Conference
1997 .
Thanks for your attention!
Any Questions?