Previous studies

In the LV, the flow rate is not only dependent on the instantaneous pressure but also on pressure and flow at previous time points (due to inertia and LV chamber properties). Flow impedances have been used in vascular biology to characterize vessel properties such as viscoelasticity and stiffness. Milnor 24 _{characterized ventricular afterload using aortic impedance. Murgo et al} 25

calculated aortic input impedance in humans and found that the pressure waveforms were correlated with input impedance. Aortic and pulmonary arterial impedance has been calculated in humans and experimental animals 26, 27 and it has been shown to be influenced by age, physiologic stimuli, disease and pharmacologic interventions 28- 30. More recently, Yano et al 31 showed that aortic wave reflection influenced LV relaxation and coronary flow.

Because pulsatile flow in an elastic vessel involves pulse wave propagation along the vessel and change in vessel cross sectional area, characteristic impedance is naturally resolved into directional components as in Eq. 7.4. Impedance depends on the local properties of the vessel and the blood. While input impedance (ZI) characterizes flow at the input to the vessel, ZL

  160  

ZL is not influenced by the impedance of the downstream vascular bed. Transverse impedance

(ZT) - the ratio of pressure to axial flow gradient, accounts for radial (transverse) displacement of

blood due to cross sectional area change in an elastic vessel in response to pulsatile pressure 10, thereby reflecting elastic properties (compliance) of the vessel wall 33.

Impedance as a LV DF metric was first proposed in 1999 34, 35. Subsequently, the input impedance concept was extended to LV filling by Wu et al 9. Characteristic and input impedance of the LV during early filling (E-wave) using simultaneous echocardiography and cardiac catheterization data (Eq. 7.1) was calculated. They found that E-waves manifesting the delayed relaxation pattern (prolonged DT > 220msec) showed increased phase differences between pressure and flow relative to normal, revealing a sub-optimal pressure-flow relationship. Subsequently, Wu and Kovács 36 investigated the relationship between increasing harmonics and E-wave deceleration time. In addition, De Mey et al 37 have proposed a method for the non- invasive estimation of ZL in LV using echocardiography and used it to analyze data from a

pulse/flow duplicator.

7.4.3 Trends in impedance values

We computed the 0th harmonic (resistance) and the first four harmonics for all 3 impedances for every analyzed beat in every subject (total beats analyzed = 578). We found that ZL was lower

than ZI, which was lower than ZT (ZL< ZI <<ZT, Fig 2) in every subject. Although, the 3

impedances have different dimensions ([P/Q] vs. [(P/cm)/Q] vs. [P/(Q/cm)]) comparing these quantities has value since they quantify the inertance and compliance aspects of the same physical phenomenon i.e. early diastolic filling (chamber recoil) and, therefore they are not independent as seen in Eq. 7.4. In the specific setting of early rapid filling, direct comparison of ZL and ZT is facilitated by taking into account the effective cross-sectional (approx. 10 cm2) area

of the chamber. When considered in that light, the units of ZL and ŽT   are the same and ŽT  

dominates ZL by a factor of 34. Moreover, directional features of LV filling have been studied

previously using other imaging modalities 23, 38. These studies have also shown that longitudinal volume accommodation is the dominant mode of LV filling.

The trend in harmonic variation of ZL and ZT amplitudes showed that in both the

directions the impedance amplitude was lowest in the first harmonic and then increased with higher harmonics (Table 7.3). This was similar to the trends seen in ZI, which was also lowest at

the 1st harmonic and then increased steadily with higher harmonics in all the subjects. The input resistance (0th harmonic) should be viewed as the resistance of the process if it were nonpulsatile. In both the directions, the resistance was higher in value than the 1st harmonic. Earlier work by Wu et al 9 noted a similar trend in ZI. In addition, De Mey et al 37 calculated ZL and found that ZL

was lowest in the 1st harmonic and increased subsequently. Our results agree with these previous

studies. The trend in ZL shows that for a given pressure gradient (dP/dz) in the LV, the flow rate

(Q) decreases with increase in harmonics. In the transverse direction, our results indicate that the pressure required to generate a given axial flow gradient (dQ/dz), is higher in higher harmonics.

0th 1st 2nd 3rd 4th p-value

ZI (mm Hg. s/cm3) 16±7 3±2 5±3 6±4 7±5 p<0.001

ZL (mm Hg. s/cm4) 1.3±0.9 0.7±0.4 0.9±0.6 1.1±0.8 1.4±0.9 0.022

ZT (mm Hg. s/cm2) 4623±7313 238±316 426±567 545±582 584±683 p<0.001

ŽT (mm Hg. s/cm4) 462±731 22±31 40±56 51±58 55±68 p<0.001

Table 7.3: Impedance values. The average value of input (ZI), longitudinal (ZL) and transverse

impedance (ZT and ZT`) for the 0th – 4th harmonics for all 17 subjects and standard deviations.

The last column shows p-value for inter harmonic comparison of each type of impedance via single tailed ANOVA. See text for details.

  162  

Power was calculated as the product of pressure and flow rate amplitude for each harmonic. It was highest at the 0th harmonic (resistive component) and decreased with higher harmonics (Fig 7.3) indicating that the maximum filling power is generated when the pressure and flow rate have no phase difference. By definition, the 0th component has no phase difference between P and Q. The phase difference between P and Q manifests with the first harmonic (1.4 rad) and partly explains the observed reduction of oscillatory power at higher harmonics. In addition, the amplitude of P and Q both were highest in the 0th harmonic and decreased with higher harmonics.This trend is in concordance with findings of Wu et al 9.