A novel nonlinear afterload for ex vivo heart evaluation: Porcine experimental results

FIGURE 1. Circuit analogy of the parallel 4‐element Windkessel model with signals: Driving current (aortic flow) u c , corresponding voltage (aortic pressure) y c , and parameters: Peripheral resistance, R p ; arterial compliance, C; characteristic aortic impedance, R c ; and perfusate inertance, L.

FIGURE 2. Ex vivo setup, with the afterload (A). Roller pump R1 delivers perfusate to the preload (P) at the left atrium (LA). At the preload, the perfusate goes through a vortex to lower its linear momentum to limit forced atrial filling. A compliant reservoir sits above the vortex, allowing a column of perfusate to accumulate, resulting in atrial preload pressure. Ports D, above the compliant reservoir and the highest point of the afterload, provide de‐airing driven by small roller pumps. The heart pumps the perfusate from the left ventricle (LV) through the aorta (AO) and the afterload and back to the reservoir. The perfusate in the reservoir is circulated by roller pump R2 through an oxygenator (O2) that also provides heat exchange via a heater‐cooler unit (H). An additional roller pump (not pictured) is used to provide Langendorff perfusion when the cardioplegic heart is first placed in the system.

FIGURE 3. The ex vivo working heart model, with the afterload (A) pictured on the right attached to the aorta (AO), and preload (P) on the left attached to the left atrium (LA) and de‐airing (D). The heart is partially submerged in perfusate.

FIGURE 4. Schematic of the nonlinear adjustable afterload in diastole (left) and systole (right) adapted from Ref. [22]. Black arrows indicate the direction of fluid flow. Two pressures in the afterload are continuously controlled: The pressure in the diastolic‐limit chamber, and the pressure at which the systolic limit diaphragm valve opens. In diastole, air flows through a check valve from the diastolic‐limit chamber into the cuff. The air pressure in the cuff is exerted on the perfusate in the aorta, facilitating coronary perfusion. In systole, the contracting ventricle causes the perfusate pressure in the aorta to rise, compressing the air in the cuff, opening a perfusate lumen through the cuff, and closing the check valve. If the air pressure in the cuff exceeds the set point of the systolic‐limit diaphragm valve, air flows through the valve back into the diastolic‐limit chamber, maintaining the systolic pressure set point in the cuff and widening the lumen through the cuff.

FIGURE 5. Comparison of aortic pressure (AP), left ventricular pressure (LVP), left atrial pressure (LAP), and aortic flow in vivo and ex vivo, at rest and after a 20 μg adrenaline bolus. Measurements are from Heart 1 and representative of the group.

FIGURE 6. Aortic pressure (AP), aortic flow (AF), left atrial pressure (LAP), and heart rate (HR) in vivo (pink, circles) and ex vivo (measured values in green with triangle markers, interval between set afterload limits in blue) for each heart at rest. The pink and green bars show the total range and the markers show the mean of each value averaged over five cardiac cycles.

FIGURE 7. Aortic pressure (AP), aortic flow (AF), left atrial pressure (LAP), and heart rate (HR) in vivo (pink, circles) and ex vivo (measured values in green with triangle markers, interval between set afterload limits in blue) for each heart after a 20 μg adrenaline bolus. The pink and green bars show the total range and the markers show the mean of each value averaged over five cardiac cycles.

FIGURE 8. Instantaneous cardiac power of Heart 1, calculated as the pointwise in time product of left ventricular pressure and aortic flow, at rest and after a 20 μg adrenaline bolus, both in vivo and ex vivo.

FIGURE 9. Left ventricular pressure‐volume loop measurements over five cardiac cycles in Heart 1.

FIGURE 10. The feedback control structure used for the diastolic‐ and systolic‐limit pressures in the afterload, with cuff dynamics G and a hand‐tuned PID controller. In the diastolic case, the pressure of the diastolic‐limit chamber is controlled (setpoint r 1 and measurement y 1), with a roller pump forcing air into the chamber at flow rate u. In the systolic case, a roller pump generates air flow rate u to pressurize the membrane of a diaphragm valve; the pressure in the cuff must exceed the set pressure of the diaphragm valve (setpoint r 1 and measurement y 1) to escape from the cuff back into the diastolic‐limit chamber. Disturbance d represents the offset between the measured diastolic or systolic aortic pressure and the corresponding afterload pressure. An outer loop (gray) may be added to compensate for d using aortic pressure feedback, with diastolic or systolic‐limit set point r 2 and corresponding aortic measurement y 2.