AoV, Left Ventricle, and Aorta

The AoV, left ventricle, and aorta were modeled as previously described. A detailed description and corresponding mathematical implementation can be found in the Supplemental Methods . Briefly, the AoV consists of a narrow orifice whose area varies over time and whose proximal and distal structures are the left ventricle and the aorta, respectively ( Figure 1 A). The flow across the AoV in our model is derived by assuming unsteady, incompressible, and nonviscous plug flow traveling from the left ventricle into the aorta through the AoV. The effective opening orifice area of the AoV is 5 cm ² . In AR, the AoV does not close completely, giving rise to backward flow. Hence, in our implementation, effective ROA is 0 cm ² in the healthy situation, whereas a nonzero ROA allows regurgitant flow (AR) to occur.

The left ventricle is modeled as a cavity surrounded by the LV free wall and septal wall. According to Laplace’s law, LV pressure is determined by LV volume and wall tension, which depends on active and passive stress in the myofibers. Diastolic LV stiffness is varied by modifying the passive stress component, as explained in more detail in the Supplemental Methods . Normal diastolic LV stiffness is evident at an LV volume of 132 mL and an LV pressure of 15 mm Hg at mitral valve closure.

The aorta is treated as a compliant large blood vessel, whose distal structure is the peripheral vascular circulation modeled as a systemic vascular resistance. Hemodynamics in the aorta are governed by a pressure–cross-sectional area relationship arising from stress and strain in the vessel walls. This relationship depends on the exponent k as described in the Supplemental Methods , which represents the nonlinearity in the stiffness of the aortic wall. When aortic stiffness is normal ( k = 8), the corresponding systemic arterial compliance is 1.51 mL · mm Hg ⁻¹ , as shown in Supplemental Figure S3 .

Simulation Protocols

Our reference simulation, representing the healthy situation, corresponded to both normal LV and aortic stiffness and no AR (ROA = 0 cm ² ). From this reference simulation with normal levels of stiffness, increases in ROA to 0.05, 0.25, and 0.6 cm ² were simulated, representing mild, moderate, and severe AR, respectively, following current clinical guidelines. For all four ROAs, simulations were performed with high LV stiffness, with high aortic stiffness, and with high LV and aortic stiffness ( Figure 1 B). Simulations of AR with high LV or aortic stiffness represent patients with AR with coexisting clinical conditions that increase vascular or ventricular stiffness, summarized in Table 1 . Global LV stiffness was increased up to 125% above normal LV stiffness, resulting in LV pressure and volume at mitral valve closure of 19 mm Hg and 131 mL, respectively, with normal aortic stiffness. Aortic stiffness was increased by increasing k from 8 to 15, resulting in a systemic arterial compliance of 0.82 mL · mm Hg ⁻¹ , with normal LV stiffness, as shown in Supplemental Figure S3 . In total, 192 simulations were performed ( Figure 1 B). All other model parameters were kept constant in all simulations. Simulations were performed at a heart rate of 71 beats/min and with cardiac output (CO) and mean arterial pressure maintained at 5 L/min and 91 mm Hg, respectively, to represent homeostatic pressure-flow regulation through adaptation of systemic vascular resistance and circulating blood volume.

Indices of AR Severity

Four indices that are commonly used in echocardiographic assessment of AR severity in patients were calculated for all simulations: ROA, regurgitant volume (RVol), regurgitant fraction (RF), and pressure half-time (PHT). RVol was the total blood volume flowing backward across the AoV during diastole, in milliliters per beat ( Figure 2 A). RF was the ratio of RVol over stroke volume (SV), expressed as a percentage ( Figure 2 A). SV was defined as the total forward volume ejected by the left ventricle during one cardiac cycle. The effective SV was defined as the blood volume reaching the peripheral circulation during one cardiac cycle (i.e., SV − RVol). CO was defined as heart rate times effective SV. PHT was computed as the time for the maximal flow velocity of the AoV, v _max , to decay to v _PHT , whose value is v _max /√2, as defined by Samstad et al. ( Figure 2 B, Supplemental Methods ). AoV flow velocity was calculated as AoV blood flow divided by the area of the AoV. Table 2 summarizes the cutoff values of ROA, RVol, RF, and PHT used in current clinical guidelines to grade AR severity as mild, moderate, or severe. Mean left atrial pressure (mLAP) was also calculated directly from the left atrial pressure traces simulated by the model.

ROA and LV Stiffness Determine the Diastolic Pressure-Volume Working Range

When LV and aortic stiffness were normal, increasing the ROA led to higher LV end-diastolic volume and pressure, shifting the pressure-volume loop rightward and upward ( Figure 3 A). Diastolic LV pressure and volume followed the same nonlinear relationship for all ROAs, and ROA determined the working range within this relationship. In contrast, increasing LV stiffness with the same (moderate) ROA led to a steeper diastolic LV pressure-volume relationship ( Figure 3 B).

LV pressure-volume loops with increasing ROA and LV stiffness. (A) LV pressure-volume loops showing the effect of increasing ROA with normal LV and aortic stiffness. Increasing ROA led to right and upward shifting of the loops, resulting in higher end-diastolic LV volume and pressure. Diastolic LV pressure and volume followed the same nonlinear relationship for all ROAs, whereas the working range within this relationship was determined by the actual ROA value. (B) LV pressure-volume loops showing the effect of increasing LV stiffness with normal aortic stiffness and moderate ROA. Increasing LV stiffness led to steeper and upward shifting of the diastolic LV pressure-volume relationships, leading to higher diastolic LV pressure.

Increasing ROA Resulted in Shorter PHT and Larger RF

In the simulations with normal LV and aortic stiffness, diastolic regurgitant flow velocity patterns were qualitatively similar to flow velocity recordings from patients with AR in their shape and steepness ( Figure 4 , top and middle rows ). Increasing ROA in the simulations caused a faster decay in diastolic regurgitant flow velocity across the AoV, giving shorter PHT values ( Figure 4 , middle row ). RVol also rose relative to SV with increasing ROA, leading to progressive rises in RF values ( Figure 4 , bottom row ). Thus, increasing ROA resulted in shorter PHT and larger RF and RVol in the simulations, for all stiffness values.

Flow velocity and blood flow across the AoV with increasing ROA. Simulated flow velocity ( middle row ) and blood flow ( bottom row ) across the AoV from mild, moderate, and severe ROA with normal LV and aortic stiffness. For comparison, example continuous-wave spectral Doppler recordings from three patients with AR are shown. The first patient was an asymptomatic 72-year-old woman with a history of hypertension, nonspecific thickening of the AoV, and mild AR. The second patient was a 65-year-old woman with a calcified AoV, moderate aortic stenosis, and moderate AR. She had dyspnea on exertion but no clinical heart failure. The third patient was a 42-year-old man with a bicuspid AoV who developed Staphylococcus aureus endocarditis of the AoV with leaflet perforation, giving rise to severe AR. He developed acute heart failure and required urgent surgical AoV replacement. The methods from the guidelines of the American Society of Echocardiography were used to determine ROA, RF, and PHT from the patient data. The simulated diastolic flow velocity patterns were qualitatively similar in shape and steepness compared with the patient data in the top row . The severity graded by the PHT and RF values when increasing ROA are consistent with the one graded by the ROA value.

High Stiffness Caused a Faster Decay in Diastolic Regurgitant Flow Velocity

The effects of aortic and/or LV stiffness on diastolic regurgitant flow velocity across the AoV are shown for the simulations with moderate ROA in Figure 5 ( top row ). Increasing aortic stiffness resulted in a faster decay in diastolic regurgitant flow velocity across the AoV and, hence, shorter PHT values. The same effect was observed with increasing LV stiffness, although the shortening in PHT was less pronounced compared with the simulations with increased aortic stiffness. Increasing both LV and aortic stiffness resulted in the shortest PHT compared with the other simulations at the same ROA. Similar effects were observed in the simulations with mild and severe ROA ( Table 3 ). We do not have measures of LV or aortic stiffness in our human examples ( Figure 4 ). Importantly, our simulations of increasing LV and/or aortic stiffness led to changes in PHT that may overestimate AR severity ( Table 3 and Supplemental Table S2 ). This finding can be appreciated by comparing the diastolic regurgitant flow velocity in the moderate ROA simulation with increased LV and aortic stiffness ( Figure 5 , top right ) with the recording from the patient with severe AR ( Figure 4 , top right ).

Flow velocity and blood flow across the AoV with increasing LV and aortic stiffness. The simulated flow velocity ( top row ) and blood flow ( bottom row ) signals with moderate ROA (ROA = 0.25 cm ² ) provided the PHT and RF values, respectively. From left to right , the displayed signals are with normal LV and aortic stiffness, the highest LV stiffness, the highest aortic stiffness, and the highest LV and aortic stiffness. The signals with normal LV and aortic stiffness are displayed for comparison ( white line ). High LV and/or aortic stiffness led to faster decay in the diastolic flow velocity, resulting in lower PHT, and to lower regurgitant blood volume, resulting in lower RF.

The changes in diastolic regurgitant flow velocity across the AoV induced by variations of aortic and/or LV stiffness can be explained by the related changes in the transvalvular pressure gradient. At a given ROA, increasing aortic stiffness resulted in increased aortic pulse pressure and a faster drop in diastolic aortic pressure compared with normal aortic stiffness. Increasing LV stiffness caused a larger rise in diastolic LV pressure compared with normal LV stiffness. Hence, the diastolic decay in the transvalvular pressure gradient and in the regurgitant flow velocity became steeper in both cases. Examples of LV and aortic pressure tracings with 0 and 0.25 cm ² ROA are provided in Supplemental Figure S4 .

High Stiffness Led to Decline in Regurgitant Blood Flow

Simulations demonstrating the effect of LV and aortic stiffness on RF and RVol at moderate ROA are shown in Figure 5 ( bottom row ). Increasing aortic stiffness caused decreases in both the RF and RVol indices compared with normal levels of stiffness at the same ROA. Increasing LV stiffness also showed decreases in RF and RVol indices. In addition, increasing both LV and aortic stiffness resulted in the largest drop in RF and in RVol compared with normal levels of stiffness at the same ROA. Similar effects on regurgitant blood flow (RF and RVol) were observed when increasing LV and aortic stiffness in the simulations with mild or severe ROA ( Table 3 ).

ROA Determined Stiffness Dependency of PHT and RF

The top row of Figure 6 shows that PHT became less dependent on LV and aortic stiffness with increasing ROA (note the loss of color gradient from mild to severe ROA). In contrast, RF became more dependent on levels of stiffness with increasing ROA (note the gain of color gradient from mild to severe ROA).

PHT and RF maps for mild, moderate, and severe ROA with increasing LV and aortic stiffness. The PHT maps ( top row ) and the RF maps ( bottom row ) show the PHT and RF values, respectively, obtained in the simulations for mild, moderate, and severe ROA (ROA = 0.05, 0.25, and 0.6 cm ² in the left , middle , and right columns , respectively). The effect of LV and/or aortic stiffness on PHT and RF is identified by the inconsistent distribution in colors for each ROA. PHT takes values from mild (600 msec, yellow ) to severe (75 msec, red ) and RF from mild (10%, yellow ) to severe (60%, red ). RF and PHT values are displayed for a gradual increase in LV stiffness (y axis) and in aortic stiffness (x axis), and at each bottom left corner the values correspond to simulations with normal LV and aortic stiffness.

Inconsistency of AR Severity Scores

Figure 7 shows how AR severity scores vary depending on whether ROA, RF, or PHT is used to assess AR severity. The ROA, RF, and PHT severity scores are plotted against one another for four cases: normal stiffness, the highest LV stiffness, the highest aortic stiffness, and the combination of highest LV and aortic stiffness. At normal stiffness, the shortening in PHT and the rise in RF with increasing ROA resulted in consistent AR severity grades between these indices. Although increasing LV stiffness led to shorter PHT and lower RF compared with normal levels of stiffness, the resulting severity scores remained consistent with each other. However, increasing aortic stiffness or increasing both LV and aortic stiffness led to inconsistent scores, with lower RF indicating lower severity and shorter PHT indicating overestimation of AR severity.

High LV and/or aortic stiffness lead to inconsistent scores when grading AR severity by ROA, RF, and PHT. Mismatch in colors indicates inconsistency between severity scores graded by PHT, RF, and ROA. RF is plotted against the corresponding PHT with normal LV and aortic stiffness, the highest LV stiffness, the highest aortic stiffness, and the highest LV and aortic stiffness for mild, moderate, and severe ROA (ROA = 0.05, 0.25, and 0.6 cm ² in rounds , triangles , and diamonds , respectively). Both axes contain cutoff values for PHT and RF used to grade AR as mild, moderate, and severe.

Relation between mLAP and AR Severity Indices

Increasing ROA caused a rise in mLAP ( Figure 8 A). In addition, rises in mLAP were related to larger RF and shorter PHT ( Figures 8 B and 8C). Whereas in our simulations it is possible to determine mLAP from these changes in ROA, RF, and PHT with normal tissue properties ( Figure 8 , empty circles ), this determination could no longer be performed when tissue properties varied ( Figure 8 , all points ). Changes in LV and aortic stiffness caused mLAP to vary by up to 10 mm Hg, despite similar AR severity as measured by ROA, RF, or PHT ( Figures 8 A–8C). The biggest variability in mLAP was induced by increases in LV stiffness, whereas aortic stiffness had a smaller effect on mLAP.

Relation between mLAP as a proxy for pulmonary congestion and hemodynamic indices with increasing LV and aortic stiffness. mLAP is plotted against (A) ROA, (B) RF, and (C) PHT for all simulations. Marker shape indicates LV stiffness. Marker fill indicates aortic stiffness. Increasing ROA leads to higher mLAP. Larger RF and shorter PHT were accompanied by higher mLAP. The effect of LV stiffness induced significant variability in mLAP given similar ROA, RF, and PHT values. Changing aortic stiffness caused less variability in mLAP.

ROA and LV Stiffness Determine the Diastolic Pressure-Volume Working Range

When LV and aortic stiffness were normal, increasing the ROA led to higher LV end-diastolic volume and pressure, shifting the pressure-volume loop rightward and upward ( Figure 3 A). Diastolic LV pressure and volume followed the same nonlinear relationship for all ROAs, and ROA determined the working range within this relationship. In contrast, increasing LV stiffness with the same (moderate) ROA led to a steeper diastolic LV pressure-volume relationship ( Figure 3 B).

LV pressure-volume loops with increasing ROA and LV stiffness. (A) LV pressure-volume loops showing the effect of increasing ROA with normal LV and aortic stiffness. Increasing ROA led to right and upward shifting of the loops, resulting in higher end-diastolic LV volume and pressure. Diastolic LV pressure and volume followed the same nonlinear relationship for all ROAs, whereas the working range within this relationship was determined by the actual ROA value. (B) LV pressure-volume loops showing the effect of increasing LV stiffness with normal aortic stiffness and moderate ROA. Increasing LV stiffness led to steeper and upward shifting of the diastolic LV pressure-volume relationships, leading to higher diastolic LV pressure.

Increasing ROA Resulted in Shorter PHT and Larger RF

In the simulations with normal LV and aortic stiffness, diastolic regurgitant flow velocity patterns were qualitatively similar to flow velocity recordings from patients with AR in their shape and steepness ( Figure 4 , top and middle rows ). Increasing ROA in the simulations caused a faster decay in diastolic regurgitant flow velocity across the AoV, giving shorter PHT values ( Figure 4 , middle row ). RVol also rose relative to SV with increasing ROA, leading to progressive rises in RF values ( Figure 4 , bottom row ). Thus, increasing ROA resulted in shorter PHT and larger RF and RVol in the simulations, for all stiffness values.

Flow velocity and blood flow across the AoV with increasing ROA. Simulated flow velocity ( middle row ) and blood flow ( bottom row ) across the AoV from mild, moderate, and severe ROA with normal LV and aortic stiffness. For comparison, example continuous-wave spectral Doppler recordings from three patients with AR are shown. The first patient was an asymptomatic 72-year-old woman with a history of hypertension, nonspecific thickening of the AoV, and mild AR. The second patient was a 65-year-old woman with a calcified AoV, moderate aortic stenosis, and moderate AR. She had dyspnea on exertion but no clinical heart failure. The third patient was a 42-year-old man with a bicuspid AoV who developed Staphylococcus aureus endocarditis of the AoV with leaflet perforation, giving rise to severe AR. He developed acute heart failure and required urgent surgical AoV replacement. The methods from the guidelines of the American Society of Echocardiography were used to determine ROA, RF, and PHT from the patient data. The simulated diastolic flow velocity patterns were qualitatively similar in shape and steepness compared with the patient data in the top row . The severity graded by the PHT and RF values when increasing ROA are consistent with the one graded by the ROA value.

High Stiffness Caused a Faster Decay in Diastolic Regurgitant Flow Velocity

The effects of aortic and/or LV stiffness on diastolic regurgitant flow velocity across the AoV are shown for the simulations with moderate ROA in Figure 5 ( top row ). Increasing aortic stiffness resulted in a faster decay in diastolic regurgitant flow velocity across the AoV and, hence, shorter PHT values. The same effect was observed with increasing LV stiffness, although the shortening in PHT was less pronounced compared with the simulations with increased aortic stiffness. Increasing both LV and aortic stiffness resulted in the shortest PHT compared with the other simulations at the same ROA. Similar effects were observed in the simulations with mild and severe ROA ( Table 3 ). We do not have measures of LV or aortic stiffness in our human examples ( Figure 4 ). Importantly, our simulations of increasing LV and/or aortic stiffness led to changes in PHT that may overestimate AR severity ( Table 3 and Supplemental Table S2 ). This finding can be appreciated by comparing the diastolic regurgitant flow velocity in the moderate ROA simulation with increased LV and aortic stiffness ( Figure 5 , top right ) with the recording from the patient with severe AR ( Figure 4 , top right ).

Flow velocity and blood flow across the AoV with increasing LV and aortic stiffness. The simulated flow velocity ( top row ) and blood flow ( bottom row ) signals with moderate ROA (ROA = 0.25 cm ² ) provided the PHT and RF values, respectively. From left to right , the displayed signals are with normal LV and aortic stiffness, the highest LV stiffness, the highest aortic stiffness, and the highest LV and aortic stiffness. The signals with normal LV and aortic stiffness are displayed for comparison ( white line ). High LV and/or aortic stiffness led to faster decay in the diastolic flow velocity, resulting in lower PHT, and to lower regurgitant blood volume, resulting in lower RF.

The changes in diastolic regurgitant flow velocity across the AoV induced by variations of aortic and/or LV stiffness can be explained by the related changes in the transvalvular pressure gradient. At a given ROA, increasing aortic stiffness resulted in increased aortic pulse pressure and a faster drop in diastolic aortic pressure compared with normal aortic stiffness. Increasing LV stiffness caused a larger rise in diastolic LV pressure compared with normal LV stiffness. Hence, the diastolic decay in the transvalvular pressure gradient and in the regurgitant flow velocity became steeper in both cases. Examples of LV and aortic pressure tracings with 0 and 0.25 cm ² ROA are provided in Supplemental Figure S4 .

High Stiffness Led to Decline in Regurgitant Blood Flow

Simulations demonstrating the effect of LV and aortic stiffness on RF and RVol at moderate ROA are shown in Figure 5 ( bottom row ). Increasing aortic stiffness caused decreases in both the RF and RVol indices compared with normal levels of stiffness at the same ROA. Increasing LV stiffness also showed decreases in RF and RVol indices. In addition, increasing both LV and aortic stiffness resulted in the largest drop in RF and in RVol compared with normal levels of stiffness at the same ROA. Similar effects on regurgitant blood flow (RF and RVol) were observed when increasing LV and aortic stiffness in the simulations with mild or severe ROA ( Table 3 ).

ROA Determined Stiffness Dependency of PHT and RF

The top row of Figure 6 shows that PHT became less dependent on LV and aortic stiffness with increasing ROA (note the loss of color gradient from mild to severe ROA). In contrast, RF became more dependent on levels of stiffness with increasing ROA (note the gain of color gradient from mild to severe ROA).

PHT and RF maps for mild, moderate, and severe ROA with increasing LV and aortic stiffness. The PHT maps ( top row ) and the RF maps ( bottom row ) show the PHT and RF values, respectively, obtained in the simulations for mild, moderate, and severe ROA (ROA = 0.05, 0.25, and 0.6 cm ² in the left , middle , and right columns , respectively). The effect of LV and/or aortic stiffness on PHT and RF is identified by the inconsistent distribution in colors for each ROA. PHT takes values from mild (600 msec, yellow ) to severe (75 msec, red ) and RF from mild (10%, yellow ) to severe (60%, red ). RF and PHT values are displayed for a gradual increase in LV stiffness (y axis) and in aortic stiffness (x axis), and at each bottom left corner the values correspond to simulations with normal LV and aortic stiffness.

Inconsistency of AR Severity Scores

Figure 7 shows how AR severity scores vary depending on whether ROA, RF, or PHT is used to assess AR severity. The ROA, RF, and PHT severity scores are plotted against one another for four cases: normal stiffness, the highest LV stiffness, the highest aortic stiffness, and the combination of highest LV and aortic stiffness. At normal stiffness, the shortening in PHT and the rise in RF with increasing ROA resulted in consistent AR severity grades between these indices. Although increasing LV stiffness led to shorter PHT and lower RF compared with normal levels of stiffness, the resulting severity scores remained consistent with each other. However, increasing aortic stiffness or increasing both LV and aortic stiffness led to inconsistent scores, with lower RF indicating lower severity and shorter PHT indicating overestimation of AR severity.

High LV and/or aortic stiffness lead to inconsistent scores when grading AR severity by ROA, RF, and PHT. Mismatch in colors indicates inconsistency between severity scores graded by PHT, RF, and ROA. RF is plotted against the corresponding PHT with normal LV and aortic stiffness, the highest LV stiffness, the highest aortic stiffness, and the highest LV and aortic stiffness for mild, moderate, and severe ROA (ROA = 0.05, 0.25, and 0.6 cm ² in rounds , triangles , and diamonds , respectively). Both axes contain cutoff values for PHT and RF used to grade AR as mild, moderate, and severe.

Relation between mLAP and AR Severity Indices

Increasing ROA caused a rise in mLAP ( Figure 8 A). In addition, rises in mLAP were related to larger RF and shorter PHT ( Figures 8 B and 8C). Whereas in our simulations it is possible to determine mLAP from these changes in ROA, RF, and PHT with normal tissue properties ( Figure 8 , empty circles ), this determination could no longer be performed when tissue properties varied ( Figure 8 , all points ). Changes in LV and aortic stiffness caused mLAP to vary by up to 10 mm Hg, despite similar AR severity as measured by ROA, RF, or PHT ( Figures 8 A–8C). The biggest variability in mLAP was induced by increases in LV stiffness, whereas aortic stiffness had a smaller effect on mLAP.

Relation between mLAP as a proxy for pulmonary congestion and hemodynamic indices with increasing LV and aortic stiffness. mLAP is plotted against (A) ROA, (B) RF, and (C) PHT for all simulations. Marker shape indicates LV stiffness. Marker fill indicates aortic stiffness. Increasing ROA leads to higher mLAP. Larger RF and shorter PHT were accompanied by higher mLAP. The effect of LV stiffness induced significant variability in mLAP given similar ROA, RF, and PHT values. Changing aortic stiffness caused less variability in mLAP.

LV and Aortic Stiffness Modulate Diastolic Regurgitant Flow Velocity

The study simulations demonstrated that high ventricular stiffness leads to larger increases in diastolic LV pressure. In addition, high aortic stiffness leads to larger decline in diastolic aortic pressure. Consequently, a faster balance between diastolic LV and aortic pressures occurs when cardiac and/or aortic wall stiffness is high. This faster balance in diastolic pressures implies a faster decay in diastolic regurgitant flow velocity across the AoV and that less blood volume travels backward into the left ventricle ( Figure 5 ). Hence, regurgitant blood flow velocity decreases faster with increasing LV and/or aortic stiffness.

PHT Overestimates AR Severity in the Presence of Increased LV and/or Aortic Stiffness

The AR severity scores provided by RF and PHT were consistent with the corresponding score provided by ROA when LV and aortic stiffness were normal ( Figures 4 and 7 ). In contrast, increased ventricular and/or aortic stiffness caused a shorter PHT because of a faster decay in diastolic regurgitant flow velocity. Increased ventricular and/or aortic stiffness also caused lower RVol and RF because of lower regurgitant blood volume ( Table 3 and Figure 7 ). Therefore, increasing stiffness led to, on one hand, shorter PHT indicating higher AR severity and, on the other hand, lower RVol and RF indicating lower AR severity. Hence, inconsistencies in grading AR severity and overestimation of AR severity by PHT arise from the influence of ventricular and aortic tissue properties.

In clinical practice, PHT is often used to corroborate AR severity as assessed by other parameters. Previous studies have demonstrated the high dependence of PHT on cardiovascular properties. The latter may explain why PHT has been removed from the most current American guidelines, although it remains in the European guidelines. As PHT mirrors the steepness of regurgitant blood flow velocity and the diastolic transvalvular pressure gradient, it provides information about diastolic LV and aortic pressures and regurgitant blood volume. Importantly, because PHT overestimates AR severity when LV and/or aortic stiffness is increased, PHT may aid in assessing LV diastolic function when AR coexists with comorbidities affecting tissue stiffness.

Variations in mLAP Despite Similar AR Severity Scores

Whereas AR severity indices such as ROA, RF, and PHT are more sensitive to changes in aortic stiffness ( Figures 5–7 ), mLAP is more influenced by variations in LV stiffness ( Figure 8 ). Therefore, simulations with similar AR severity scores could have marked differences in mLAP caused by variations in tissue properties. Consequently, the risk for pulmonary congestion in patients with similar AR severity may be greater when comorbidities affecting LV and aortic stiffness are present ( Table 1 ).

Implications in Acute AR

AR can occur acutely in cases such as aggressive endocarditis, aortic dissection, blunt chest trauma, and after transcatheter AoV replacement because of procedural or anatomic causes. The sudden imposition of regurgitant flow causes acute volume loading of the same nonremodeled LV tissue; that is, the tissue’s working range shifts to higher volumes on the same diastolic pressure-volume relationship. In patients with acute severe AR, the clinical consequences are a rise in LV diastolic pressure and consequently left atrial pressure, leading to a risk for pulmonary congestion and life-threatening pulmonary edema. Our results suggest that patients with acute severe AR coexisting with pathologies increasing ventricular and/or aortic stiffness have a higher risk for developing pulmonary edema not reflected by the AR severity ( Figure 8 ).

Implications in Chronic AR

Common causes of long-standing development of AR include bicuspid AoV or calcific AoV disease. Chronic AR results in a gradual deterioration of AoV closure, leading to progressive LV enlargement through myocardial remodeling. Compensatory LV enlargement permits a large LV end-diastolic volume without a significant rise in LV filling pressure, and hence a much larger regurgitant volume can occur than in the acute situation. Chronic AR can eventually lead to impaired LV function and heart failure as the remodeling process becomes decompensated. Hence, in patients with chronic severe AR, the clinical consequences are volume overload and potential risk for decompensated LV remodeling. The variations in LV stiffness simulated in our study can also be interpreted as LV remodeling response in patients with chronic AR, although we did not simulate concomitant LV dilatation. Our results indicate that rises in mLAP, indicating raised LV filling pressure, in patients with adversely remodeled and thereby stiffened left ventricles can occur without changes in AR severity scores.

Implications for Assessment of LV Diastolic Function in AR

In both acute and chronic AR, accurate quantification of the valve lesion and hemodynamic consequences is crucial for determining whether and when to intervene surgically. LV filling pressure and diastolic dysfunction should be noninvasively assessed following the updated American Society of Echocardiography and European Association of Cardiovascular Imaging recommendations. Our results reinforce the importance of assessing diastolic function in patients with AR because coexisting pathologies altering LV and aortic tissue properties may exacerbate pulmonary congestion in a manner not reflected by AR severity scores. Increased mLAP and LV diastolic pressure occur as hemodynamic consequences in AR, whereas LV tissue properties vary when AR coexists with comorbidities. Care should therefore be taken to distinguish tissue dysfunction from the altered hemodynamics arising from AR. Data on the accuracy of determining LV filling pressures in the presence of chronic severe AR are limited. Therefore, further research is needed to provide indices that better reflect LV and aortic stiffness in acute or chronic AR and thereby improve assessment of both AR severity and its hemodynamic consequences. Indices such as mitral E-wave velocities to assess LV diastolic compliance, aortic pulse-wave velocity to assess aortic stiffness, and other markers concerning myocardial tissue viability, such as peak systolic strain rate and peak early diastolic strain rate, are likely to be influenced by AR, thereby not being helpful for tissue properties assessment in presence of AR. Therefore, new indices incorporating the stiffness of the left ventricle and aorta during AR may be required to perform a more accurate and integrative assessment of the true hemodynamic and clinical status of a patient with AR.

Study Limitations

The CircAdapt model simulates blood flow across the AoV. Hence, all the RF and RVol values in our study were derived directly from the simulations. In the clinic, the proximal isovelocity surface area or flow convergence method is generally used to approximate RF and RVol. Moreover, PHT is derived from the diastolic regurgitant jet as imaged by continuous-wave Doppler, whereas we computed PHT directly from the blood flow velocity across the AoV. Although we assumed plug flow across the AoV, blood flow can become turbulent in severe AR, especially when accompanied by aortic stenosis. With turbulent flow, the mechanical energy is partly lost by means of irregular motion. Consequently, diastolic LV pressure will not rise as high as with plug flow, so our simulations might overestimate the steepness of the diastolic transvalvular pressure gradient. To allow comparison between the simulations, hemodynamics were simulated assuming that a mean arterial pressure of 91 mm Hg and a CO of 5 L/min were sustainable through homeostatic regulation. Hence, increases in LV preload and systolic aortic pressure may be exaggerated in our simulations with AR. In acute AR, the decline in CO is partly compensated by higher heart rate and stronger ventricular contraction. We acknowledge that including few patient examples was a limitation and that a future larger comparative study of patients with AR would be of interest.