Efficient Implementation of a Non-linear CardioVascular System Model for Real-Time Therapy
Assistance in Critical Care
THE 12th INTERNATIONAL CONFERENCE ON BIOMEDICAL
ENGINEERING
C. E. Hann1, J. G. Chase1, G. M. Shaw2,
1Department
2
of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand
Department of Intensive Care Medicine, Christchurch Hospital, Christchurch, New Zealand
Introduction
• Cardiovascular disturbances difficult to diagnose
• Masked by reflex response
• Disease scenarios, clinical history, quick diagnosis
 experience, intuition
• Physiological, identifiable, validated computer model
• FE methods
• PV methods, specific CVS function
• Minimal cardiac model – primary parameters
• Model drug treatment
 fast forward simulations, set up the maths right
 standard PC, palm pilot
Single Chamber
V  Q1  Q2
P1  P2  Q1 R1

Q1 
L1
P2  P3  Q2 R2

Q2 
L2
P2  e(t ) Ees (V  Vd )  (1  e(t )) P0 (e (V V0 )  1),
e(t )  e 80( t 0.375)
2
Full Model
•
Event solver, computationally heavy, many combinations
Heaviside formulation
V  H (Q1 )Q1  H (Q2 )Q2
P  P  Q1R1
Q1  H ( H ( P1  P2 )  H (Q1 )  0.5) 1 2
L1
P  P  Q2 R2
Q 2  H ( H ( P2  P3 )  H (Q2 )  0.5) 2 3
L2
Filling:
H ( K (t ))  0, K (t )  0
 1, K (t )  0
Q1  0, Q2  0, P2  P1  P3  Q 2  0
P2  P2  P1, Q1  0,
P2  P1 , Q1  0
Contraction:
Q1 valve doesn’t shut
Q1 valve shuts inertia
P1  P2  P3 , Q1  0, Q2  0
P2  P2  P3, Q2 valve opens open on pressure
• Ejection and relaxation, similar
Simpler Heaviside formulation
P1  P2  Q1R1
P2  P3  Q2 R2



V  H (Q1 )Q1  H (Q2 )Q2 , Q1 
, Q2 
L1
L2
Q2
2000
Q2
1500
1000
1000
-1000
flow (ml s )
500
-1
-1
flow (ml s )
0
-2000
-3000
-4000
0
-500
-5000
-1000
-6000
0
0.5
1
1.5
0.1
time (s)
Q2 (t )  Q2 (t1 )e ( R2 / L2 )(t t1 ) 
L2  R2
0.15
0.2
0.25
0.3
time (s)
0.35
0.4
1 t ( R2 / L2 )(t  )
( P2 ( )  P3 )d
t1 e
L2
 small transient
0.45
0.5
Ventricular Interaction
e(t ) Ees,spt (Vspt  Vd ,spt )  (1  e(t )) P0,spt ( e
spt (Vspt V0 , spt )
 e(t ) Ees,lvf (Vlv  Vspt )  (1  e(t )) P0,lvf ( e
lvf (Vlv V0, spt )
 e(t ) Ees,rvf (Vrv  Vspt )  (1  e(t )) P0,rvf ( e
•
•
 1)
 1)
rvf (Vrv V0, spt )
 1)
Has no direct solution
Solve for Vspt every time step  very slow
e
sptVspt
 asptVspt  bspt , e
lvf Vspt
 alvf Vlvf  blvf , e
rvf Vspt
 arvf Vrvf  brvf
12
10
8
approximation
6
e
4
sptVspt
0.1
0.1
2
Vspt,old
0
0
0.2
0.4
0.6
Vspt (ml)
0.8
1
Results
•
•
Simulate healthy human
Output
Value
Cardiac output
5.3 L/min
Max Plv
119.2 mmHg
Max Prv
26.2 mmHg
Pressure in aorta
116.6/79.1 mmHg
Pressure in pulmonary artery
25.7/7.8 mmHg
Computational times
Method
CPU
time (s)
Event solver
101.9
Speed
increase
First Heaviside
70.0
1.5
Simpler Heaviside
26.3
3.9
4.3
23.7
Simpler Heaviside +
analytical Vspt formula
Results
•
New method versus first Heaviside
(20 heart beats)
•
New method 19 beats + first Heaviside
1 beat versus first Heaviside 20 heart beats
Results
• Comparing the accuracy of the new method
Disease state
Total & error
Mean
S.D.
Healthy
0.14
0.21
Mitral stenosis
0.20
0.28
Aortic stenosis
0.15
0.22
Pulmonary embolism
0.18
0.31
Septic shock
0.09
0.15
Conclusions
• New method 24 times faster
• No loss in accuracy
• Clinically, simulate large number of treatments
• Future work – non-linear D.E’s  piecewise linear D.E’s
 piecewise analytical solutions
 standard PC or palm pilot, real time
• Human trials planned
Questions ???
Dr Geoff Chase
Dr Geoff Shaw
AIC2, Kate, Carmen and Nick
Dr Bram Smith