Thirty two datasets (mean age 61, 22 men) were selected from the Cardiovascular Biophysics Laboratory database.²⁰ Subjects underwent elective cardiac catheterization to determine presence of suspected coronary artery disease at the request of their referring physicians. All participants provided informed consent prior to the procedure using a protocol approved by the Washington University Human Research Protection Office (HRPO).

Sixteen datasets of subjects in NSR, were selected so they were aged matched with the 16 subjects of the chronic AF group (average duration 7.3±4.1 years). All were in AF during data acquisition. Selection criteria for the NSR group were: no active ischemia, normal valvular function, normal LV ejection fraction (LVEF50%), no history of myocardial infarction, peripheral vascular disease, or bundle branch block, and clear diastatic intervals following E-waves. Selection criteria for the AF group were similar, with the exception that four of the 16 AF subjects had LVEF somewhat < 50%. Among the 16 NSR datasets, 9 had normal LV end-diastolic pressure (LVEDP<14 mmHg), 3 had 15 mmHg < LVEDP < 20 mmHg and 4 had elevated LVEDP (>21 mmHg). The distribution of LVEDPs in the 15 AF group datasets were: 3 with LVEDP<14, 9 with 15<LVEDP<20 mmHg and 4 with LVEDP>21. A total of 650 cardiac cycles (20 beats/subject) of simultaneous echocardiographic-high fidelity hemodynamic (conductance catheter) data were analyzed. The clinical descriptors of the 32 subjects and their hemodynamic and echocardiographic indices are shown in Table 1 and 2.

The high fidelity, simultaneous echocardiographic transmitral flow and pressure-volume (P-V) data recording method has been previously described.^17,20-²⁴ Briefly, immediately prior to arterial access a complete 2-D echo-Doppler study in a supine position using a Philips (Andover, MA.) iE33 system is performed according to American Society of Echocardiography (ASE) criteria.²⁵ After arterial access and placement of a 64-cm, 6-Fr sheath (Arrow, Reading, PA), a 6-Fr micromanometer conductance catheter (SPC-560, SPC-562, or SSD-1034, Millar Instruments, Houston, TX) was directed across the aortic valve under fluoroscopic control. Pressure and volume signals were processed through clinical amplifier systems (Quinton Diagnostics, General Electric, CD Leycom) and recorded by a custom personal computer via a standard interface (Sigma-5). Simultaneous transmitral Doppler images were obtained²⁵ using a clinical imaging system (Philips iE33, Andover, MA). Following data acquisition, end-systolic and end-diastolic volumes (ESV, EDV) were determined by calibrated quantitative ventriculography.

For each subject, approximately 1-2 minutes of continuous transmitral flow data were recorded in the pulsed-wave Doppler mode. Echocardiographic data acquisition is performed in accordance with published ASE²⁶ guidelines. In accordance with convention, the apical 4-chamber view was used for Doppler E-wave recording with the sample volume located at the leaflet tips. An average of 20 beats per subject were analyzed (650 cardiac cycles total for the 32 subjects).

Doppler transmitral E-wave contours were analyzed using the conventional triangle shape approximation,^27,28 yielding peak E-wave velocity (E_peak), acceleration time (AT), deceleration time (DT), velocity-time integral (E-VTI), E/E’.

Each E-wave was also analyzed via the Parametrized Diastolic Filling (PDF) formalism (see Appendix 1) to yield, mathematically unique PDF parameters for each E-wave (stiffness parameter (k), chamber viscoelasticity/relaxation parameter (c), load parameter (x_o)).^23,29,30

Stiffness (DT_s) and relaxation (DT_r) components of DT were computed via the fractionation method employed previously¹⁹ (see Appendix 2) such that DT=DT_s+DT_r. By determining DT_s and DT_r of each E-wave, the total DT can be expressed as the fraction due to stiffness (S=DT_s/DT) and the fraction of DT due to relaxation (R=DT_r/DT) for each E-wave analyzed.

Hemodynamics were determined from the high-fidelity Millar LV P-V data from each beat. The quantitative ventriculography was used to determine end-systolic and end-diastolic volumes which defined the limits of volume tracing of conductance catheter has been previously detailed.^23,24,31,32 After calibration of conductance volume, LV pressure and volume at diastasis were measured beat-by-beat using a custom MATLAB program. End-diastasis points were defined by ECG P wave onset.^24,31-³³ As previously^24,32 for each subject, diastatic P-V data points generated by load varying cardiac cycles were fit via linear regression, to provide diastatic chamber stiffness as the slope (K) of D-PVR.

The classes of prescribed medications among the 16 subjects of the AF group were as follows: 14 on anticoagulants/antithrombotics, 9 on beta blockers, 7 on lipid lowering agents, 7 on ACE inhibitor or ARB, 6 on calcium channel blockers, 6 on diuretics, and 5 on digoxin.

For each subject, parameters were averaged for the beats selected. Comparisons of diastatic stiffness, AT, DT, E_dur, PDF parameters, and other parameters between NSR and AF groups were carried out by Student’s t-test using MS-Excel (Microsoft, Redmond, WA).

LV (passive) chamber stiffness measured as the slope of the D-PVR is significantly higher in the AF group than that in the NSR group (0.18±0.08 mmHg/ml vs. 0.11±0.05 mmHg/ml, p<0.01). In contrast to NSR, (where diastatic pressure and volume is different than end-diastolic pressure and volume at end atrial systole), in AF, diastatic pressure and volume is the same as end-diastolic pressure and volume since there is no atrial contraction in AF. In AF diastatic pressure and volume are similar to the diastatic pressure and volume in NSR (18 ± 4 mmHg for AF vs. 17 ± 5 mmHg for NSR, p=0.48 and 167 ± 55 ml for AF vs. 159 ± 12 ml for NSR, p=0.59).

Figure 1 shows that E-wave DT and E-wave duration (E_dur) are significantly shorter in the AF group than NSR group (DT: 153 ± 22 msec vs. 192 ± 19 msec, p<0.001, E_dur: 236 ± 26 msec vs. 281 ± 27 msec, p<0.001). E-wave acceleration time (AT) is not significantly different between the two groups (84 ± 8 msec vs. 89 ± 11 msec, p=0.13).

Figure 1. AT, DT, and Edur determined by approximating E-wave shape as a triangle in NSR group (16 subjects) and AF group (16 subjects). Significant differences between DT and Edur are denoted by asterisk (*). (DT: p<0.001, Edur: p<0.001) between groups. See Table 2 and text for details.

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Results from PDF analysis show (Figure 2) that PDF stiffness parameter (k) in AF group is higher (stiffer) than NSR group (274 ± 70 1/sec² vs. 191 ± 41 1/sec², p<0.001). PDF parameters c, x_o are not significantly different between AF and NSR groups (c: 15.7±3.0 1/sec vs. 16.3±3.5 1/sec, p=0.65 and x_o: 10.2±2.5 cm vs. 10.1±2.9 cm, p=0.93).

Figure 2. PDF parameters (k, c, and xo) in NSR group (16 subjects) and AF group (16 subjects). Significant (p<0.001) differences between groups for k are denoted by asterisk (*) indicating that AF chambers at diastasis are stiffer than NSR chambers at diastasis. See text for details.

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Figure 3 shows the stiffness and relaxation components in both groups and their contribution to DT. The relaxation (DT_r) component of DT in AF is shorter than in NSR (DT_r AF=30±12 vs. DT_r NSR=50±10, p<0.001). The stiffness (DT_s) component of DT in AF, which is inversely related to chamber stiffness, is shorter than in NSR (DT_s AF=123±20 vs. DT_s NSR=142±14, p<0.005). The shorter DT_s in AF and the known inverse relation between DT_s and (diastatic) stiffness indicates that AF chambers are stiffer than NSR chambers. DT_s and diastatic stiffness derived from P-V data (K) were highly correlated in both NSR and AF groups (NSR: DT_s = -0.21 K + 0.16, R²=0.57, AF: DT_s = -0.19 K + 0.16, R²=0.56) (Figure 4). DT_r and time constant of isovolumic relaxation (τ) were highly correlated in both NSR and AF groups (NSR: DT_r = 1.30 τ - 0.03, R²=0.84, AF: DT_r = 1.11 τ - 0.03, R²=0.77) (Figure 5).

Figure 3. A) Comparison of stiffness (DTs), relaxation (DTr) components of total DT according to group. Asterisk (*) indicates DTs and DTr are both significantly shorter in AF than in NSR. B) Comparison of total DT between groups indicates significant difference (*). When DT is decomposed into its DTs, DTr components in NSR and AF groups, significant intergroup differences in components persist as shown in Panel A. See text for details.

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Figure 4. A) Least mean square determined linear fit of stiffness component of DT (DTs) vs. diastatic stiffness (K) in A) 16 NSR subjects, B) 16 AF subjects. See text for details.

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Figure 5. A) Least mean square determined linear fit of relaxation component of DT (DTr) vs. time constant of isovolumic relaxation (τ) in A) 16 NSR subjects, B) 16 AF subjects. See text for details.

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For the 16 NSR datasets 75% of total DT is due to stiffness and 25% is due to relaxation. For the 16 AF datasets 81% of DT is due to stiffness and 19% is due to relaxation (Figure 6). These differences are significant (p<0.005). If the four AF subjects with LVEF <50% are removed from the intergroup comparison, all of the conclusions remain unaltered.

Figure 6. Intergroup comparison of normalized DT showing percentage due to stiffness (S) and relaxation (R). A significantly larger percentage of total DT is due stiffness in the AF group. See text for details.

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Although multiple methods for LV chamber stiffness determination using echocardiography have been proposed,^16,23,34,35 one of the most important methods for characterizing passive chamber stiffness has been the end-diastolic pressure volume relation (EDPVR), defined by the locus of points inscribed by end-diastolic pressures and volumes at varying loads.¹¹ Considering the EDPVR in the setting of chronic AF raises a concern, however. Because there is no atrial contraction, end-diastole in (rate controlled) AF is the hemodynamic equivalent of diastasis. During diastasis the ventricle is in static equilibrium (for a brief period), atrial and ventricular pressures are equal and net transmitral flow is absent.³⁶ This equivalence between end-diastole and diastasis does not exist in NSR, and previous work³² has shown that in the same NSR heart, the D-PVR and EDPVR are physiologically distinct relations, with significantly different slopes and therefore different values for chamber stiffness. Hence, the D-PVR is the only physiologically justified invasive method available for chamber stiffness determination in AF. The use of D-PVR requires the determination of load-varying diastatic pressure and volume points.

In addition to invasive approaches, the stiffness of the LV chamber can also be estimated noninvasively. The PDF parameter k obtained from echocardiographic E-wave analysis is mathematically¹⁷ and experimentally related to the invasively measured chamber stiffness (ΔP/ΔV) during early rapid filling.²³ E-wave deceleration time (DT) has also been correlated with stiffness as proposed by Little et al..¹⁶ It was shown that an inverse square relationship exists between stiffness and E-wave DT.

Both the triangle based (DT) and PDF model based (k) non-invasive estimates of chamber stiffness showed significant difference between the AF and NSR groups, consistent with the invasive chamber stiffness findings between groups at diastasis.¹⁵ The significantly shorter DT in the AF group is not likely to be explained by the higher average HR of the AF group since it is known that in the presence of a diastatic interval, E-wave DT remains essentially unchanged when HR increases.³⁷

Average left ventricular (LV) chamber stiffness, ∆P/∆V, is an important diastolic function (DF) metric. An E-wave based determination of ∆P/∆V by Little et al predicted that deceleration time (DT) is related to stiffness according to ∆P/∆V = A/(DT)².¹⁶ This implies that if the DTs of two LVs are indistinguishable, their stiffness should be similarly indistinguishable. Shmuylovich et al.¹⁸ have shown that two subjects with indistinguishable E-wave determined DTs can have distinguishable catheterization-determined values of chamber stiffness, because of differences in relaxation, i.e. the viscoelastic parameter (PDF parameter c) in the two subjects. We found E-wave DT and its stiffness component are significantly (DT: p<0.001, DT_s: 0.005) shorter in the AF group (DT=153±22 msec, DT_s=123±20) than NSR group (DT=192±19 msec, DT_s=142±14). The shorter DT in AF group is primarily an effect of stiffness because the relaxation parameter c is similar in the two groups (p=0.65).

Because E-wave DT depends on both stiffness (k) and relaxation (c) we have previously proposed¹⁹ a method by which E-wave DT can be decomposed to stiffness (DT_s) and relaxation (DT_r) components. We have shown¹⁹ that DT_s was highly correlated (r=0.82) with (simultaneous) invasively determined (passive) diastatic chamber stiffness, and DT_r and the time-constant of IVR (τ) from simultaneous high fidelity pressure data and IVRT determined by echocardiography were highly correlated (r=0.94, r=0.89).

In the current study we analyzed simultaneous LV P-V and transmitral flow (echo) data and decomposed E-wave DT in to stiffness (DT_s) and relaxation (DT_r) components in NSR and AF groups. As expected diastatic stiffness and PDF stiffness parameter k were higher in AF group compared to NSR group and AF E-wave DT was shorter than in NSR. Figure 6 shows the fraction of DT accounted for by stiffness (S) in the AF group is significantly higher than in the NSR group (p<0.005), and the fraction of DT due to the relaxation (R) in the AF group is significantly lower than in the NSR group (p<0.005). Although the numerical value of the PDF relaxation parameter c is similar in NSR and AF, the fraction of the total DT due to relaxation (R = DT_r / DT (%)) is less in AF than in NSR because DT and DT_r in AF group is shorter (See Fig. 3) than in NSR. This is underscored by the difference in stiffness parameter k, being higher (stiffer) in AF vs NSR. This method is totally general. It fractionates total DT into its stiffness and relaxation components and thereby reflects actual chamber properties. As such, the method allows for longitudinal assessment and trending of beneficial vs. adverse effects of alternative treatment strategies on chamber properties of stiffness and relaxation in clinical settings where echocardiography is utilized.

Figure 7. Overview of DTs and DTr computation. A) A typical Doppler velocity profile. Note diastatic interval between E- and A-waves. B) AT and DT determination using triangle method. C) PDF model-predicted fit to E-wave (green) provides numerically unique PDF parameters c=21.8/s, k=248/s2, xo=11.2cm for each analyzed E-wave. D) Model predicted E-wave (red) having same xo, k values as original (green) E-wave but with PDF parameter c=0, assumes relaxation plays no role in determining waveform. The effect of relaxation (where c0) is to lengthen DT and decrease E-wave amplitude. Hence, green DT is longer and its amplitude is less than red waveform. The numerical difference between actual green (c0) DT minus red DT (c=0) equals DTr. DTs = DT – DTr. DT=0.206 s, DTr=0.077 s and DTs=0.129 s. See text for details.

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The conductance catheter method of volume determination has known limitations related to noise, saturation and calibration that we have previously acknowledged.^17,20-^24,32 In this study, the channels which provided physiologically consistent P-V loops were selected and averaged. However, since there was no significant volume signal drift during recording, any systematic offset related to calibration of the volume channels did not affect the result when the limits of conductance volume were calibrated via quantitative ventriculography.

The D-PVR is defined by a linear, least mean-squared error fit to the load varying locus of points at which diastasis is achieved. At elevated heart rates diastasis is usually eliminated. In this study datasets were selected such that for every analyzed cardiac cycle in AF or NSR a clear, diastatic interval was present after E-wave termination, prior to the onset of the next systole in AF, or prior to the onset of the Doppler A-wave in NSR.

Although the number of subjects (n=32) is modest, and may be viewed as a minor limitation regarding statistics, the total number of cardiac cycles analyzed (n=650) mitigates the sample size limitation to an acceptable degree.