FAST IDENTIFICATION OF A MINIMAL CARDIAC MODEL
C. E. Hann1, J. G. Chase1 G. M. Shaw2, B. W. Smith3
1
Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.
2
Department of Intensive Care Medicine, Christchurch Hospital, Christchurch, New Zealand.
3
Centre for Model-based Medical Decision Support, Aalborg University, Aalborg, Denmark.
INTRODUCTION: A minimal cardiac model [1] has been developed to enable identification of
abnormal cardio-vascular system (CVS) dynamics. A fast and accurate integral-based parameter
identification method is presented for clinical application of this research.
METHODS: For a single elastic chamber with inertia and constant upstream and downstream
pressures P1 and P3 the differential equations are defined [1]:
P  P3  Q2 R2
P  P2  Q1 R1 
V  Q1  Q2 , Q 1  1
, Q2  2
L1
L2
(1)
where Q1 and Q2 are the flows in and out, L1 and L2 are inertances of the blood, R1 and R2 are resistances
and the pressure in the chamber is defined:
P2  e(t ) Ees (V  Vd )  (1  e(t ))P0 (e  (V V0 )  1), e(t )  e 80(t 0.375)
2
(2)
where Ees is elastance, Vd is volume at zero pressure and P0 ,  and V0 define gradient, curvature and volume
at zero pressure of the EDPVR curve [1]. Assuming that e(t), V(t), Vd, V0, P0,  , Q1 and Q2 are given or
measured as in Figure 1, Equation (1) can be reformulated in terms of integrals giving 30 linear equations
in 5 patient specific unknowns Ees, R1, R2, L1, and L2.
RESULTS: The results of the integration based identification are provided in Table 1.
Outflow
Inflow
Fig. 1:Discretised curves analogous to
measured data.
Parameter
True value
Optimised
value
Percentage error
E es
3.5555  108
3.5555  108
0.02
R1
R2
L1
L2
83000
81128
2.26
81000
81768
0.95
430000
430876
0.20
480000
479868
0.03
Table 1. Optimised parameter values
DISCUSSION & CONCLUSIONS: The integral based optimization successfully identified the patient
specific parameters for the single chamber model to within 2.5%, which is well within clinically effective
requirements, and can be readily extended to the full model. Clinically, this approach means medical staff
will be able to obtain rapid patient specific data to assist in diagnosis, and can trial and test different
therapies on the identified model in clinical real time (3-5 minutes). Overall, such an approach would add
significant clinical value in therapy selection, particularly in the use of volume therapy.
REFERENCES:
1
Smith, B W, Chase, J G, Shaw, G M, Nokes, R and Wake, G C (2004). "Minimal Haemodynamic
System Model Including Ventricular Interaction and Valve Dynamics," Medical Eng and Physics, Vol
26(2), pp. 131-139.