Single‐Beat Estimation of Right Ventricular Contractility and Its Coupling to Pulmonary Arterial Load in Patients With Pulmonary Hypertension

Figure 1. Single‐beat estimation of the end‐systolic pressure‐volume relationship (ESPVR). A, Multiple‐beat ESPVR (black curve). The end‐systolic points for a series of loops were determined as those with maximal stress/strain ratio (open black circles) and were fitted against the equation for the ESPVR (P=A×In(VV0)×In(1+Vwallv)) using a nonlinear least‐square method, with the use of an iterative method to determine the zero‐stress volume, V0(MB). B, Single‐beat ESPVR (red curve) was estimated by fitting points between the peak systolic pressure and the end‐systolic points (red open points) on the signal‐averaged baseline loop against the equation, P=A×In(VV0)×In(1+Vwallv) (equation (2) in the main text) using the nonlinear least‐squares method. The end‐systolic point (ie, the last point used for the curve fitting; black closed point) in this figure has been determined uniformly using an algorithm on the basis of an iterative method, as described in detail in Figure S5. The red closed point represents the zero‐stress volume of the single‐beat ESPVR (V0[SB]).

Figure 2. Outline of the single‐beat estimation of the preload recruitable stroke work relationship. A, A novel physiologic feature that links the end‐systolic mean ejection pressure (Pm)‐volume relationship (EMPVR) and the preload recruitable stroke work (PRSW) relationship. The squares represent the rectangular‐transformed pressure‐volume (PV) loops that have the same area (ie, stroke work [SW]) and width (ie, stroke volume [SV]) as the original PV loops. The trajectory of the left‐upper corners of the squares was denoted as the EMPVR. The bottoms of the squares were aligned at the volume axis; hence, the height of the square represents the absolute value of the Pm (SW/SV). The units for volume‐axis and the slope of the PRSW relationship (Vsw and Msw) are mL and mm Hg, respectively. When the point (Vsw, Msw) is plotted as a blue point on the PV plane, this point is on the EMPVR curve, as demonstrated mathematically in the main text. B, Schematic flow chart of an example of single‐beat estimation of Msw. The Pm of the baseline single beat (Pm_sb=37 mm Hg) was calculated as the SW of the baseline single beat (SWsb=2620 mL×mm Hg) divided by the SV of the baseline single beat (=70 mL). The…

Figure 3. A novel ventriculoarterial coupling framework on the basis of the end‐systolic mean ejection pressure (Pm)‐volume relationship (EMPVR). If the preload recruitable stroke work relationship can be assumed to be linear, Ees′, the slope of the red segment between the end‐systolic point of the baseline square (Ves, Pm) and the point (volume‐axis intercept of the preload recruitable stroke work [PRSW] relationship [Vsw], slope of the PRSW relationship [Msw]) is equal to MswSV, as shown in equation (9) in the text. Moreover, the effective arterial elastance for the rectangular pressure‐volume loop (Ea′=PmSV, black slope) represents the vascular impedance that accounts for both steady and pulsatile afterload, as shown in Data S2. The pump performance of the ventricle can be determined by Ees′/Ea′ in a similar way to Ees/Ea. Furthermore, Ees′/Ea′ can be simply formulated as Msw/Pm, as shown in equation (11) in the text. SV indicates stroke volume.

Figure 4. Single‐ and multiple‐beat end‐systolic pressure‐volume relationship (ESPVR). Scatterplots comparing zero‐stress volumes of single‐ vs multiple‐beat ESPVRs (V0[SB] and V0[MB], respectively).

Figure 5. Estimated and measured preload recruitable stroke work slope, Msw. A, Scatterplots comparing the estimated preload recruitable stroke work (PRSW) slope (Msw[SB]) on the basis of the single‐beat method using measured right ventricular wall volume to the multiple‐beat PRSW slope (Msw[MB]). B, Similar analysis using the assumed right ventricular (RV) end‐diastolic wall/chamber volume ratio. C, Bland‐Altman plots for Msw(SB) on the basis of the single‐beat method using measured RV wall volume. D, Bland‐Altman plots for Msw(SB) using the assumed RV end‐diastolic wall/chamber volume ratio.

Figure 6. Single‐beat estimation of a novel index of right ventricular–pulmonary arterial coupling. A, Scatterplots comparing single‐ and multiple‐beat slope of the preload recruitable stroke work (PRSW) relationship (Msw)/mean ejection pressure (Pm), calculated using measured right ventricular (RV) wall volume. A stronger correlation was observed in those with greater RV systolic pressure (median of 44 mm Hg or greater; closed red points). B, Similar analysis using the assumed RV end‐diastolic wall/chamber volume ratio. Msw(MB) indicates the multiple‐beat PRSW slope; and Msw(SB), the estimated PRSW slope from a single beat.