# Kinematic Modeling-based Left Ventricular Diastatic (Passive) Chamber Stiffness Determination with *In-Vivo* Validation

## Abstract

The slope of the diastatic pressure–volume relationship (D-PVR) defines passive left ventricular (LV) stiffness \( \mathcal{K}.\) Although \( \mathcal{K} \) is a relative measure, cardiac catheterization, which is an absolute measurement method, is used to obtain the former. Echocardiography, including transmitral flow velocity (Doppler E-wave) analysis, is the preferred quantitative diastolic function (DF) assessment method. However, E-wave analysis can provide only relative, rather than absolute pressure information. We hypothesized that physiologic mechanism-based modeling of E-waves allows derivation of the D-PVR_{E-wave} whose slope, \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \), provides E-wave-derived diastatic, passive chamber stiffness. Our kinematic model of filling and Bernoulli’s equation were used to derive expressions for diastatic pressure and volume on a beat-by-beat basis, thereby generating D-PVR_{E-wave}, and \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \). For validation, simultaneous (conductance catheter) *P*–*V* and echocardiographic E-wave data from 30 subjects (444 total cardiac cycles) having normal LV ejection fraction (LVEF) were analyzed. For each subject (15 beats average) model-predicted \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \) was compared to experimentally measured \( \mathcal{K}_{\text{CATH}} \) * via* linear regression yielding as follows: \( \mathcal{K}_{{\text{E-}}{\text{wave}}} = \alpha {\mathcal{K}}_{\text{CATH}} + b\;(R^{2} = 0.92), \) where, α = 0.995 and *b* = 0.02. We conclude that echocardiographically determined diastatic passive chamber stiffness, \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \), provides an excellent estimate of simultaneous, gold standard (*P*–*V*)-defined diastatic stiffness, \( \mathcal{K}_{\text{CATH}} \). Hence, in chambers at diastasis, passive LV stiffness can be accurately determined by means of suitable analysis of Doppler E-waves (transmitral flow).

### Keywords

Diastolic function Kinematic modeling Left ventricle Diastatic stiffness Echocardiography Hemodynamics## Notes

### Acknowledgments

This study was supported in part by the Alan A. and Edith L. Wolff Charitable Trust, St. Louis, and the Barnes-Jewish Hospital Foundation, St. Louis. The authors thank sonographer Peggy Brown for expert echocardiographic data acquisition, and the staff of the BJH Cardiovascular Procedure Center’s Cardiac Catheterization Laboratory for their assistance.

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