A ventricular-arterial transfer function to evaluate systemic and pulmonary ventricular-arterial interaction

Introduction: the heart is a pulsatile hydraulic pump that generates a flow signal with a relevant amount of frequency components. Objective: to evaluate the interaction between the ventricle (pump) and the arterial system (hydraulic load). Material and metods: The right and left ventricular pressure (Prv and Plv) and the aortic and pulmonary pressures (P Ao and Ppu) were registered (Konisberg) in 6 sheeps. The biventricular volume was calculated with sonomicrometry, based on the ellipsoidal subtraction model. Two transfer functions in the frequency domain between arterial and ventricular pressure were used. The systemic one (Hs=PAo/Plv), relating the Pao to the Plv, and the pulmonary (Hp=Ppu/Prv), relating Ppu with Prv. The slope of the end-systolic pressure volume relation (Ees ) was used to evaluate the ventricular contractility. An adaptive model (ARMA 3x3) was used to calculate the transfer functions Hs and Hp. The filtering selectivity was characterized by the descending slope H (1-10) within the band of interest (1-10 Hz) using an asymptotic Bode diagram. The Ees of left and right ventricles (Ees LV and Ees RV) were estimated from the linear regression coefficient of the pressure-volume values derived from the pre -load maneuver (occlusion of the inferior cava vessel). Results: the results are shown on the following table (M±SD): Discussion: the attenuation within the dynamic range is 5 times greater in aorta, what makes the systemic circuit more selective, respect pulmonary circuit. The contractility relationship is accordingly related supported by the fact that also dE/dt max is 5 times higher (p<0.05) in the left ventricle. Conclusion: since a more contractile ventricle generates higher frequency components the system coupling reacts enhancing his cushioning ability. INTRODUCTION The heart and the arterial system interact in order to provide adequate flow and pressure (P) to peripheral tissues. Whereas the ventricle generates a pulsate flow, the arterial system is responsible for two main issues [1] : a) distribution (conducting function); b) filtering or cushioning, supplying constant flow to the tissues (buffering function). In order to describe the arterial system as a hydraulic load, the wall mechanical response should be evaluated. Large arteries mechanical response might be described with a viscoelastic model [2] . The elastic (E) and viscous (η) module can be calculated from a pressure-diameter (P-D) loop to asses a simple model of two parallel elements [3] . In the first-order model response, the E/η time constant might be adopted to describe the diameter response to a steep P [4] . Both the systemic and the pulmonary circuits are based on a pump (the ventricle) and a hydraulic load (the arterial system), each of which generates and receives the same blood volume respectively. Nevertheless, these circuits exhibit distinctive characteristics regarding their P values, effective length [5] , arterial diameter (D) and compliance, myocardial contractility, cardiac cycle phases [6] and peripheral resistance, among others. This makes it impossible to extrapolate the characteristics of the ventricular-arterial interaction (VAI) from one circuit to the other, making their simultaneous dynamic characterization essential for a proper comparison. Interactions between the ventricle and the arterial system, has been previously analyzed by many others [710]. Two different approaches have been used. The first method involves pressure-volume loops and static ventricle-arterial elastances [11 -15]. The second, concerning impedance concepts, showed to be more solid theoretically but less practical and accurate [16,17]. This work deals with VAI in both circuits simultaneously, in steady state. A 3x3 ARMA adaptive model fits the output arterial pressure (AP) and input ventricular pressure (VP) signals in time domain. In addition, a linear function, relating AP to VP is calculated in the frequency domain. Two transfer functions are obtained. The systemic (Hs = APAo/VPL), relating the aortic AP to the left VP, and the pulmonary (Hp = AP Pu/VPR), relating the pulmonary AP to the right VP. OBJECTIVE The aims are: 1) to provide a simple and original approach in the VAI study through AP to VP transfer functions in the frequency domain, both in the systemic and pulmonary circuits, simultaneously; 2) to use these transfer functions to quantify the hydraulic filtering capacity of each one of the circuits; 3) to contrast the systemic and pulmonary VAI with the arterial wall mechanical response related to the hydraulic load. MATERIAL AND METHOD Six adult sheep were anesthetized and ventilated. The heart was exposed by a thoracotomy, and 4 P transducers (Konigsberg) were positioned in the left and right ventricles, aorta (AO) and in pulmonary artery (PU). The arterial D was measured by ultrasonic piezoelectric crystals (3 MHz) implanted in each artery, and connected to a sonomicrometer (Triton Technology). At the end of each experiment, the animal was sacrificed, conformed to international norms (NIH Pub N °86-23, revised 1985). The P signals (VPL, VPR, APAo, APPu ) and arterial diameters (DAo,D Pu) were simultaneously monitored and recorded in real time. A Kelvin-Voigt model was adopted to characterize the arterial wall. Accordingly, total P developed by the wall to resist stretching can be separated into an elastic and a viscous P component [2] . As viscous P is proportional to the first derivative of the D, the elastic P component can be obtained as: where h is the wall viscous modulus. To separate the purely elastic wall properties, the viscous term must be subtracted from the total AP, finding the optimal value through the hysteresis loop disappearance criteria [2] . The resulting purely elastic behaviour was used to calculate the elastic modulus (E) [2] . To analyze the temporal response of the wall the following P -D equation, using (1) and E, is proposed, where the η/E time constant would characterize the temporal exponential D response to a steep P increase: An adaptive model (ARMA 3x3) was employed to obtain the systemic (Hs) and pulmonary (Hp) transfer functions (Figure 1). Ten consecutives stable P cycles were selected for each adaptation in the time domain. Using the 7 fitted coefficients (a0-3,b1-3), Hs and Hp frequency domain functions were calculated and approximated through an asymptotic Bode diagram. The filtering selectivity was characterized by the descending slope, within the band of interest (1-10Hz). In addition, the transference values in zero frequency [Hs (0) and Hp (0)] were calculated. Mean squared error was calculated for each adaptation to quantify the model-system adjustment. Statistical results are expressed as mean values±SD. A paired t-student test with a p<0.05 significance level was adopted. The normalized mean squared error (MSE) between the AP and the (1)