# Kinematic Modeling Based Decomposition of Transmitral Flow (Doppler E-Wave) Deceleration Time into Stiffness and Relaxation Components

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## Abstract

The mechanical suction-pump feature of the left ventricle aspirates atrial blood and generates a rapid rise and fall in transmitral flow (Doppler E-wave). Initially, E-wave deceleration time (DT), a routine index of clinical diastolic function, was thought to be determined only by chamber stiffness. Kinematic modeling of filling, in analogy to damped oscillatory motion [Parametrized Diastolic Filling (PDF) formalism], has been extensively validated and accurately predicts clinically observed E-wave contours while, revealing that DT is actually an algebraic function of both stiffness (PDF parameter *k*) and relaxation (PDF parameter *c*). We hypothesize that kinematic modeling based E-wave analysis accurately predicts the stiffness (DT_{s}) and relaxation (DT_{r}) components of DT such that DT = DT_{s} + DT_{r}. For validation, pressure–volume (*P*–*V*) and E-wave data from 12 control (DT < 220 ms) and 12 delayed-relaxation (DT > 220 ms) subjects, 738 beats total, were analyzed. For each E-wave, DT_{s} and DT_{r} was compared to simultaneous, gold-standard, high fidelity (Millar catheter) determined, chamber stiffness (*K* = Δ*P*/Δ*V*) and chamber relaxation (time-constant of isovolumic relaxation—*τ*), respectively. For the group linear regression yielded DT_{s} = *α* *K* + *β* (*R* = 0.82) with *α* = −0.38 and *β* = 0.20, and DT_{r} = *m* *τ* + b (*R* = 0.94) with *m* = 2.88 and *b* = −0.12. We conclude that PDF-based E-wave analysis provides the DT_{s} and DT_{r} components of DT with simultaneous chamber stiffness (*K*) and relaxation (*τ*) respectively, as primary determinants. This kinematic modeling based method of E-wave analysis is immediately translatable clinically and can assess the effects of pathology and pharmacotherapy as causal determinants of DT.

## Keywords

LV stiffness LV relaxation Diastolic function PDF formalism E-wave deceleration time## Nomenclature

- AT
E-wave acceleration time (ms)

- DF
Diastolic function

- DR
Delayed relaxation

- DT
E-wave deceleration time (ms)

- DT
_{r} Relaxation component of DT (ms)

- DT
_{s} Stiffness component of DT (ms)

*E*_{dur}E-wave duration

- IVR
Isovolumic relaxation

- IVRT
Isovolumic relaxation time (ms)

*K*Diastatic stiffness (mmHg/mL)

- LV
Left ventricle/ventricular

- LVEDV
Left ventricular end diastolic volume (mL)

- LVEF
Left ventricular ejection fraction

- LVEDP
Left ventricular end diastolic pressure (mmHg)

- NR
Normal relaxation

Parametrized Diastolic Filling

*P*–*V*Pressure–volume

*τ*Time constant of isovolumic relaxation (ms)

## Notes

### Acknowledgments

This work was supported in part by the Alan A. and Edith L Wolff Charitable Trust, St. Louis, and the Barnes-Jewish Hospital Foundation. Sina Mossahebi was supported in part by a teaching assistantship from the Physics Department, Washington University College of Arts and Sciences. We thank sonographer Peggy Brown for expert echocardiographic data acquisition, and the staff of Barnes Jewish Hospital Cardiovascular Procedure Center’s Cardiac Catheterization Laboratory for their assistance.

### Conflict of interest

The authors have no conflicts of interest to disclose with the reported study.

### Human Subjects

Prior to data acquisition, subjects provided signed, institutional review board (IRB) approved informed consent for participation in accordance with Washington University Human Research Protection Office (HRPO) criteria.

### Animal Studies

This work did not include any animal studies.

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