Poster Gnb I Cong Naz Bioing 2008 Conf Effects Of Intraventricular Pathologies Described By A Lumped Parameter Computer Model

Primo Congresso Nazionale di Bioingegneria Pisa 3-5 luglio 2008

EFFECTS OF INTRAVENTRICULAR PATHOLOGIES DESCRIBED BY A LUMPED PARAMETER COMPUTER MODEL Fragomeni G. A, Colacino FM A, Piedimonte F. B, Danieli G. C, Arabia M. C A

Magna Graecia University (Catanzaro), B University of Rome “Tor Vergata” (Rome) , C Calabria University (Rende)

INTRODUCTION & AIM Various manifestations of mechanical dysfunction in the ischemic myocardium, as a result of coronary arterial blood flow reduction, have been observed in many studies. Ventricles affected by ischemia (IS) causing regional dyssynchrony (RD) and reduced contractility are characterized by wall portions’ non uniform electrical and/or mechanical behavior. Among intraventricular pathologies, RD alone causes contraction delay in different ventricular regions, while IS causes a decrease of their contractility. A worsening of the ventricular end-systolic pressure-volume relationship (ESPVR) is observed in vivo in both the cases. The aim of the present work is the investigation and the analysis of these pathologies in humans by computer simulation. A computer model of a left ventricle (LV) divided in two regions has been developed. They are likely to have variable sizes and different working conditions: one of them works physiologically, the other can be affected by ischemia, dyssynchrony, or both (RD+IS). Results have been validated by literature data [1-3]. The information given by this computer model can be used: • to infer the worsened global end-systolic pressure-volume relationship (ESPVR), as observed in presence of IS, RD, or both; • to better understand the behaviour of a pathological left ventricle, and of its relationship with preload and afterload; • for diagnostic purposes.

a

METHODS In order to investigate how a ventricle affected by RD and/or reduced contractility modifies its flow rate, pressure and volume curves, a computer model of the LV has been developed which allows different working conditions to different ventricular portions. LV is represented by a non linear time-varying elastance (NTVE) model [4, 5] (Eq. 1). It allows relating instantaneous blood pressure and volume inside the ventricle during the whole cardiac cycle.

dV t  (Eq. 1) P(t )  P0   V (t ), t   R dt where t = time, V(t) = instantaneous blood volume inside the ventricle, P(t) = instantaneous blood pressure inside the ventricle, R = Inner Resistance. The instantaneous value of the elastance is given by the slope of the time-varying curve ϕ[V(t),t] at time t and volume V(t). Similar relations, but different parameters, are used to represent the atrium (see [5] for details). The LV has been connected to an open loop vascular circuit. The venous circuit is represented by the Guyton’s model [6], while the output of the ventricle is loaded by a 5-component Noordergraaf model of the arterial systemic circuit. Both LV’s valves are represented by a direct and an inverse resistance in series connection with an inductor. The divided LV has been represented by two NTVE models [5] and its total ventricular contractility has been split up. Pressure has been always assumed equal in each ventricular portion. The total volume V(t) has been divided in two portions V1(t) and V2(t), and all the model parameters have been divided accordingly. The LV model of each portion can be written as follows: dV1 t  Eq.2; Pt   P0  1 V1 t , t   R1 dt dV2 t  Eq.3. Pt   P0   2 V2 t , t   R2 dt

Parameters Symbol

Cases

Units



Description

Physio LV

RD

IS

RD+IS

0,76

0,53

0,62

0,43

Efficiency

dp/dtmax

mmHg/s

1609,01

2355,06

971,40

2666,32

Maximum value of dp/dt

PAo-ave

mmHg

99,51

86,64

83,53

96,25

Average aortic pressure (mmHg)

PAt-ave

mmHg

6,50

5,81

6,53

5,97

Average left atrial pressure (mmHg)

QA-ave

l/min

5,51

4,11

4,38

3,33

Average flow rate in Aorta (l/min)

rmax

cm

3.03

3.32

3.28

3.42

End diastolic radius

SV

cm3

71,59

58,69

57,72

51,50

Stroke Volume

VAED

cm3

59,22

45,70

59,33

59,01

Maximum left atrial volume (cm3)

VAES

cm3

27,62

15,61

32,96

21,64

Minimum left atrial volume (cm3)

Vmean

cm3

79,41

116,16

109,34

142,05

LV’s mean volume

VVED

cm3

115,20

145,50

138,20

167,80

Left end-diastolic Volume (cm3)

VVES

cm3

43,61

86,81

80,48

116,30

Left end-systolic Volume (cm3)

wmin

cm

1.25

1.22

1.16

1.06

s

mmHg

94,39

109,20

106,21

124,70

tIC

s

0.11

0.13

0.15

0.10

End diastolic wall thickness Systolic ventricular wall stress Duration of the isometric contraction

Table 1 – Simulation results

b

RESULTS AND DISCUSSION All the simulations carried out with the model described above allow to get information about the behaviour of a ventricle affected by IS and/or RD (see Table 1). Particularly, the presence of this kind of pathologies modifies pressure and flow rate curves, causing a variation in systolic and diastolic times. An increase of mean ventricular volume can be observed. Therefore, under the hypothesis of constant wall volume, there is a ventricular wall stress increase due to wall’s thickness reduction. In relation to the physiological conditions, pathological cases show changes also from an energetic point of view: PV loops shift rightward, mean ventricular volume increases, stroke volume decreases, and the ventricular efficiency worsens as a consequence. Figure 1 shows a physiological LV PV loop compared with PV loops in presence of RD (a), IS (b), RD+IS (c). The depressed ventricular function caused by regional IS and RD may be manifest as a reduction in the slope of the ESPVR, a parallel rightward shift of the ESPVR, or both [1]. As a consequence, the LV PV loops shift rightward. This computer model can be translated into the clinical practice for diagnosis of intraventricular myocardial dysfunction. It is possible to get information like the percentage of ischemic myocardium or conduction delay and the global corresponding contractility of the LV, thus allowing the optimization of the therapeutic phase in order to improve its impact on peripheral perfusion and haemodynamics.

c

REFERENCES

[1].Sunagawa, K., et al. Circ Res, 1983. 52(2): p. 170-8. [2].Arts, T., et al. Biophys J, 1991. 59(1): p. 93-102. [3].Suga, H. Physiol. Rev., 1990. 70: p. 247-277.

[4].Burkhoff, D., et al. Am J Physiol Heart Circ Physiol, 2005. 289(2): p. H501-12. Figure 1 – PV loop for the three pathological cases: RD (a), IS (b), and RD+IS (c).

[5].Colacino, F.M., et al. Asaio J, 2007. 53(3): p. 263-77. [6].Guyton, A.C., et al., Circulatory Physiology: Cardiac Output and its Regulation. II ed. 1973: W.B. Saunders.