In addition, the pump inertance was modeled to account for pressure changes related to acceleration and deceleration of pump flow and was adjusted in the model to generate normal clinical values of the pump pulsatility index.
Mitral Valve Model
The pressure-flow relationship across the mitral valve was modeled as Bernoulli’s resistance (pressure difference proportional to flow squared) with inertial term to account for pressure changes related to acceleration and deceleration of flow (Equation 2), according to Sun et al.5 Viscous resistance is small in this case and was therefore ignored in the model.
AMV is the effective orifice area of the mitral valve in cm2, ρ is blood density in kg/cm3, QMV is the flow across the mitral valve in ml/s, and LMV is the length of the mitral valve in cm. The term QMVQMV is used instead of QMV 2 so that Equation 2 applies to both antegrade and retrograde flow. dQMV/dt is the first derivative of QMV. The constant 1.333 is the required for unit conversion to mm Hg. For the antegrade flow, the AMV was set to 4 cm2. For the retrograde flow through the mitral valve (regurgitation), the AMV was set to the value of effective regurgitant orifice (ERO). ERO was set to three different values to simulate mild, moderate, and severe MR as defined by the echocardiographic criteria7 (Table 2). In simulations with a competent mitral valve, the flow was only antegrade and ERO was zero.
Influences of four different grades of MR (Table 2), three stages of LV failure (Table 3), and eight levels of LVAD support (no support, levels from 8,000 to 10,000 RPM) on regurgitant volume, left atrial pressure, pulmonary artery pressure, and pump flow were studied. Pressure-volume area (PVA) of the right ventricle as a measure of right ventricular myocardial oxygen consumption was also analyzed.8
An open loop configuration of the model was used in all simulations, with the cardiovascular system disconnected at the level of systemic veins. A constant flow of 5 L/min (83.3 ml/s), simulating venous return, was applied to the distal end of systemic veins, whereas a constant pressure of 0 mm Hg was applied to the proximal end of systemic veins (Figure 2). Peripheral resistance was held constant at 1 mm Hg·s/ml and heart rate at 80 bpm. As a result, after 200 s of each simulation run, when the steady state was reached, the cardiac output was 5 L/min and the mean arterial pressure was 83 mm Hg, regardless of the stage of MR, LV dysfunction, or the level of LVAD support, enabling comparisons among different combinations of MR, LV failure, and LVAD support.
At constant ERO, increasing LVAD RPM to 9,200 slowly decreased the regurgitant volume. At RPM higher than 9,200, when the aortic valve stopped opening and all cardiac output was through the LVAD, the regurgitant volume decreased rapidly (Figure 3). For ERO of 0.6 cm2, the regurgitant volume was 62.2 ml without LVAD support and 52.3 ml with 9,200 RPM LVAD support, which corresponds to only 16% reduction in the regurgitant volume. At higher RPM, the systolic pressure of the LV decreased below the aortic pressure and also generated significantly lower regurgitant volumes. For ERO of 0.6 cm2, the regurgitant volume was 21.1 ml with 10,000 RPM LVAD support, which corresponds to 66% reduction in the regurgitant volume.
Left Atrial Pressure and Pulmonary Artery Pressure
Without LVAD support, the mean left atrial pressure was significantly higher in severe LV dysfunction and severe MR (ERO 0.6 cm2); however, even at very low LVAD RPM, the pressure dropped and the difference between different grades of MR and LV dysfunction decreased. Increasing the LVAD RPM further decreased the mean left atrial pressure, and at 10,000 RPM, there were no differences between different grades of LV dysfunction and only 1 mm Hg difference between severe MR and no MR (Figure 4). The changes in mean pulmonary artery pressure were identical to the changes in mean left atrial pressure because the flow through the pulmonary circulation and the pulmonary vascular resistance were constant in all simulation runs.
Pressure-Volume Area of the Right Ventricle
The PVA of the right ventricle was proportionate to the pressure in the pulmonary artery. Without LVAD support, the PVA was significantly higher in severe LV dysfunction and severe MR (ERO 0.6 cm2); however, even at very low LVAD RPM, PVA dropped and the differences between different grades of MR and LV dysfunction decreased (Figure 5). In the unsupported LV, the PVA was 0.25 Ws without MR and 0.39 Ws with severe MR. Therefore, severe MR increased myocardial oxygen consumption of the right ventricle by 52%. With LVAD support at 9,200 to 9,600 RPM, the PVA decreased to <0.20 Ws (<PVA without MR and LVAD support) and severe MR increased PVA by only 11% to 16%.
With constant ERO, heart rate, and length of the systole, the main determinant of the regurgitant volume is the systolic pressure difference between the LV and the left atrium. At lower LVAD RPM, the volume of the LV is large enough to generate pressure that is higher than the aortic pressure and opens the aortic valve. This pressure also generates a significant regurgitant volume. At higher LVAD RPM, the volume of the LV decreases further and the ventricle cannot generate pressure higher than the aortic pressure. Lower systolic pressure in the LV results in decrease in the regurgitant volume.
Clinically, the severity of MR is defined by echocardiographic criteria.7 The two most important quantitative criteria are regurgitant volume in ml per beat and ERO area in cm2. In patients with MR, regurgitant volume and ERO usually correspond well, so that the patients with severe MR have ERO ≥0.4 cm2 and regurgitant volume ≥60 ml per beat. Although ERO is the measure of the defect on the closed mitral valve, the regurgitant volume is the measure of the volume overload of the LV that causes an increase in the left atrial pressure. As the model has shown, this matching of ERO and regurgitant may be different in patients with LVAD where, despite constant ERO, regurgitant volume decreased with LVAD support. In addition, the left atrial and the pulmonary artery pressures were low, despite significant regurgitant volume while on LVAD support.
The short-term and long-term outcomes in patients with HM II support of the LV depend on the function of the right ventricle, and efforts to preserve the right ventricular function are therefore crucial in the management of these patients. In patients with HM II and MR, the pump speed setting that is least detrimental for the right ventricle should be chosen. Increasing HM II RPM leads to a reduction in regurgitant volume, which may somewhat decrease the right ventricular afterload; however, the cardiac output increases and the LV volume is reduced. This may lead to an increased right ventricular workload due to a higher flow and shift of the interventricular septum and abolish opening of the aortic valve, which may lead to thrombosis of the aortic root. A better option is to have the pump RPM at a lower setting that maintains adequate LV volume, which results in opening of the aortic valve, a lesser reduction in right ventricular contractility due to septal ventricular interaction, and a slightly lower cardiac output. The regurgitant volume of the mitral valve is larger at lower RPM; however, as the model has shown, the increase in the right ventricular afterload is minimal.
Limitations of the Model
The heart model does not include any mechanical interaction between the two ventricles (such as septal or pericardial), only the series ventricular interaction. High LVAD support may decrease the right ventricular function by rightward shift of the ventricular septum directly decreasing the right ventricular contractility,9 whereas the decrease in total intrapericardial volume and intrapericardial pressure may promote right ventricular filling and increase the right ventricular output.3
In the model, the ERO of the mitral valve was constant at different levels of LVAD support although it is known that particularly in functional MR, common with a failing LV, the ERO decreases with decreased size of the unloaded LV.10,11 Thus, the model probably underestimates the decrease in MR with LVAD support at least in patients with functional MR.
The computer model has shown that the regurgitant volume of the mitral valve falls significantly only after the systolic pressure in the LV decreases, which occurs at higher LVAD RPM when there is no ejection through the aortic valve. However, at low LVAD RPM and ejection through the aortic valve, the pressures in the left atrium and the pulmonary artery decrease significantly, despite a small decrease in regurgitant volume. We conclude that LVAD support decreases MR and that regurgitant volume has a smaller impact on the right ventricular afterload when compared with a heart without LVAD support. Furthermore, the decrease in ERO after unloading the LV in functional MR, common in advanced heart failure, decreases regurgitant volume.
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Keywords:Copyright © 2013 by the American Society for Artificial Internal Organs
left ventricular assist device; mitral regurgitation; right ventricular failure