DEVELOPMENT AND IDENTIFICATION
OF A CLOSED-LOOP MODEL
OF THE CARDIOVASCULAR SYSTEM
INCLUDING THE ATRIA
A. PIRONET*, J. A. REVIE**, S. PAEME*,
P. C. DAUBY*, J. G. CHASE**, T. DESAIVE*
* CARDIOVASCULAR RESEARCH CENTER, UNIVERSITY OF LIEGE, LIEGE, BELGIUM** DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF CANTERBURY, CHRISTCHURCH, NEW ZEALAND
8TH IFAC SYMPOSIUM ON BIOLOGICAL AND MEDICAL SYSTEMS
• Initial CVS model
• Introduction of the atria
• Parameter identification
• Results
CONTENTS
1
Aorta& Right ventricle Pulmonary artery Pulmonary& vein& Vena cava Le1& ventricle&
Flow resistance
Valve
METHODS
2
ORIGINAL CVS MODEL
P
1
P
2
R
Q
P
1
– P
2
R
Q =
P
1– P
2R
Q =
if P
1> P
20
otherwise
Valve:
P
1
P
2
R
Q
No valve:
METHODS
2
ORIGINAL CVS MODEL
1
P
=
E(t)
V
Other chambers:
Cardiac chambers:
Le1&
ventricle& ventricle&Right&
P
=
E
V
Pulmonary&
vein& Aorta&
Pulmonary&
artery& Vena&cava&
METHODS
2
ORIGINAL CVS MODEL
Continuity equation:
V
Q
out
Q
in
V = Q
.
in
- Q
out
METHODS
2
ORIGINAL CVS MODEL
1
Pulmonary artery Pulmonary
vein atrium Left
Right
ventricle atrium Right Vena cava Aorta Left
ventricle
Flow resistance
Valve
+ 1 Active chamber + 1 Resistance + 1 Active chamber + 1 Resistance
METHODS
2
INTRODUCTION OF THE ATRIA
Left atrial pressure
(mmHg)
METHODS
2
INTRODUCTION OF THE ATRIA
2
16
12
8
12
8
6
10
Left atrial volume (mmHg)One heartbeat
Filling
a
v
Left atrium
P(V,
t)
=
P
a
e(t) + E
V
(1 – e(t))
Atrial
volume pressure Atrial
METHODS
2
INTRODUCTION OF THE ATRIA
Left atrium
P(V,
t)
=
P
a
e(t) + E
V
(1 – e(t))
Atrial
volume pressure Atrial Active component
e(t) 1
METHODS
2
INTRODUCTION OF THE ATRIA
Left atrium
P(V,
t)
=
P
a
e(t) + E
V
(1 – e(t))
Atrial
volume pressure Atrial Passive component
e(t) 0
METHODS
2
INTRODUCTION OF THE ATRIA
Left atrium
P(V,
t)
=
P
a
e(t) + E
V
(1 – e(t))
Atrial
volume pressure Atrial Driver function
e(t) in [0, 1]
METHODS
2
INTRODUCTION OF THE ATRIA
Left atrium
P(V,
t)
=
P
a
e(t) + E
V
(1 – e(t))
METHODS
2
INTRODUCTION OF THE ATRIA
2
Pa A-wave peak pressure Maximum diastolic ventricular pressure Offset (atrio-ventricular pressure gradient)Left atrium
P(V,
t)
=
P
a
e(t)
+ E
V
(1 –
e(t)
)
Driver function e(t) in [0, 1]METHODS
2
INTRODUCTION OF THE ATRIA
2
Time of atrial contraction Time of maximum diastolic ventricular pressureLeft atrium
P(V,
t)
=
P
a
e(t)
+
E
V
(1 –
e(t)
)
Driver function e(t) in [0, 1]METHODS
2
INTRODUCTION OF THE ATRIA
2
Width of driver
function Width of driver function Fixed Atrial passive
Model simulation Reference measurement
XX
METHODS
2
PARAMETER IDENTIFICATION
3
Initial parameter value Model simulation Reference measurement New parameter value
XX
METHODS
2
PARAMETER IDENTIFICATION
3
Pulmonary artery
Left atrium
Right
ventricle atrium Right
Aorta Left ventricle Fixed pulmonary vein pressure Fixed vena cava pressure
P
vc
P
pu
METHODS
2
PARAMETER IDENTIFICATION
3
Identification of the
systemic model Identification of the pulmonary model
Identification of ventricular elastances Computation of ventricular interaction
METHODS
2
PARAMETER IDENTIFICATION: STEP 1
Dataset 1 Dataset 2 Dataset N
…
Average valve resistancesMETHODS
2
PARAMETER IDENTIFICATION: STEP 2
Identification of the
systemic model Identification of the pulmonary model
Identification of ventricular elastances Computation of ventricular interaction Fixed valve resistances
METHODS
2
PARAMETER IDENTIFICATION: STEP 3
Pulmonary artery
Left atrium
Right
ventricle atrium Right
Aorta Left ventricle Fixed pulmonary vein pressure Fixed vena cava pressure
P
vc
P
pu
METHODS
2
PARAMETER IDENTIFICATION: STEP 4
Pulmonary artery Pulmonary vein Left atrium Right
ventricle atrium Right Vena cava Aorta Left
ventricle
METHODS
2
PARAMETER IDENTIFICATION: STEP 4
METHODS
2
• Pig with induced pulmonary
embolism
• Measurements: ventricular
pressures and volumes, aortic and
pulmonary artery pressure
• Taken every 30 minutes, providing
10 data sets for identification
PORCINE EXPERIMENTS AND DATA
METHODS
2
• Pig with induced pulmonary
embolism
• Measurements: ventricular
pressures and volumes, aortic and
pulmonary artery pressure
• Taken every 30 minutes, providing
10 data sets for identification
PORCINE EXPERIMENTS AND DATA
METHODS
2
• Pig with induced pulmonary
embolism
• Measurements: ventricular
pressures and volumes, aortic and
pulmonary artery pressure
• Taken every 30 minutes, providing
10 data sets for identification
PORCINE EXPERIMENTS AND DATA
Time
0.47
0.97
RESULTS
3
PULMONARY RESISTANCE (PRU)
8.05
RESULTS
3
Time
3.67
3.35
1.11
Le1&atrium& atrium&Right&
