# 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.

## References

- 1.Bauman, L., C. S. Chung, M. Karamanoglu, and S. J. Kovács. The peak atrioventricular pressure gradient to transmitral flow relation: kinematic model prediction with in vivo validation.
*J. Am. Soc. Echocardiogr.*17:839–844, 2004.CrossRefGoogle Scholar - 2.Boskovski, M., L. Shmuylovich, and S. J. Kovács. Transmitral flow velocity-contour variation after premature ventricular contractions: a novel test of the load-independent index of diastolic filling.
*Ultrasound Med. Biol.*34(12):1901–1908, 2008.CrossRefGoogle Scholar - 3.Chung, C. S., D. M. Ajo, and S. J. Kovács. Isovolumic pressure-to-early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization echocardiography.
*J. Appl. Physiol.*100:528–534, 2006.CrossRefGoogle Scholar - 4.Chung, C. S., M. Karamanoglu, and S. J. Kovács. Duration of diastole and its phases as a function of heart rate during spine bicycle exercise.
*Am. J. Physiol. Heart Circ. Physiol.*287:H2003–H2008, 2004.CrossRefGoogle Scholar - 5.Chung, C. S., and S. J. Kovács. Physical determination of left ventricular isovolumic pressure decline: model prediction with in vivo validation.
*Am. J. Physiol.*294:H1589–H1596, 2008.Google Scholar - 6.Courtois, M., S. J. Kovács, and P. A. Ludbrook. Transmitral pressure–flow velocity relation. Importance of regional pressure gradients in the left ventricle during diastole.
*Circulation*78:661–671, 1988.CrossRefGoogle Scholar - 7.Dent, C. L., A. W. Bowman, M. J. Scott, J. S. Allen, J. B. Lisauskas, M. Janif, S. A. Wickline, and S. J. Kovács. Echocardiographic characterization of fundamental mechanisms of abnormal diastolic filling in diabetic rats with a parameterized diastolic filling formalism.
*J. Am. Soc. Echocardiogr.*14(12):1166–1172, 2001.CrossRefGoogle Scholar - 8.Eucker, S. A., J. B. Lisuaskas, J. Singh, and S. J. Kovács. Phase plane analysis of left ventricular hemodynamics.
*J. Appl. Physiol.*90:2238–2244, 2001.Google Scholar - 9.Feigenbaum, H. Echocardiography. Baltimore, MD: Williams & Wilkins, p. 677, 1993.Google Scholar
- 10.Flachskampf, F. A., A. E. Weyman, J. L. Guerrero, and J. D. Thomas. Calculation of atrioventricular compliance from the mitral flow profile: analytic and in vitro study.
*J. Am. Coll. Cardiol.*19:998–1004, 1992.CrossRefGoogle Scholar - 11.Garcia, M. J., M. S. Firstenberg, N. L. Greenberg, N. Smedira, L. Rodriguez, D. Prior, and J. D. Thomas. Estimation of left ventricular operating stiffness from Doppler early filling deceleration time in humans.
*Am. J. Physiol. Heart Circ. Physiol.*280:H554–H561, 2001.Google Scholar - 12.Garcia, M. J., J. D. Thomas, and A. L. Klein. New Doppler echocardiographic applications for the study of diastolic function.
*J. Am. Coll. Cardiol.*32:865–875, 1998.CrossRefGoogle Scholar - 13.Hall, A. F., and S. J. Kovács. Automated method for characterization of diastolic transmitral Doppler velocity contours: early rapid filling.
*Ultrasound Med. Biol.*20:107–116, 1994.CrossRefGoogle Scholar - 14.Ishida, Y., J. Meisner, K. Tsujioka, J. Gallo, C. Yoran, R. Frater, and E. Yellin. Left ventricular filling dynamics: influence of left ventricular relaxation and left atrial pressure.
*Circulation*74:187–196, 1986.CrossRefGoogle Scholar - 15.Kass, D. A., J. G. F. Bronzwaer, and W. J. Paulus. What mechanism underline diastolic dysfunction in heart failure?
*Circ. Res.*94:1533–1542, 2004.CrossRefGoogle Scholar - 16.Kovács, S. J., B. Barzilai, and J. E. Pérez. Evaluation of diastolic function with Doppler echocardiography: the PDF formalism.
*Am. J. Physiol.*87:H178–H187, 1987.Google Scholar - 17.Kovács, S. J., M. D. McQueen, and C. S. Peskin. Modeling cardiac fluid dynamics and diastolic function.
*Philos. Trans. R. Soc. A*359:1299–1314, 2001.CrossRefMATHGoogle Scholar - 18.Kovács, S. J., J. S. Meisner, and E. L. Yellin. Modeling of diastole.
*Cardiol. Clin.*18:459–487, 2000.CrossRefGoogle Scholar - 19.Kovács, S. J., R. Setser, and A. F. Hall. Left ventricular chamber stiffness from model-based image processing of transmitral Doppler E-waves.
*Coron. Artery Dis.*8:179–187, 1997.CrossRefGoogle Scholar - 20.Lee, D. S., P. Gona, R. S. Vasan, M. G. Larson, E. J. Benjamin, T. J. Wang, J. V. Tu, and D. Levy. Relation of disease pathogenesis and risk factors to heart failure with preserved or reduced ejection fraction: insights from the Framingham heart study of the national heart, lung, and blood institute.
*Circulation*119:3070–3077, 2009.CrossRefGoogle Scholar - 21.Lisauskas, J. B., J. Singh, A. W. Bowman, and S. J. Kovács. Chamber properties from transmitral flow: prediction of average and passive left ventricular diastolic stiffness.
*J. Appl. Physiol.*91:154–162, 2001.Google Scholar - 22.Lisauskas, J. B., J. Singh, M. Courtois, and S. J. Kovács. The relation of the peak Doppler E-wave to peak mitral annulus velocity ratio to diastolic function.
*Ultrasound Med. Biol.*27:499–507, 2001.CrossRefGoogle Scholar - 23.Little, W. C., M. Ohno, D. W. Kitzman, J. D. Thomas, and C. P. Cheng. Determination of left ventricular chamber stiffness from the time for deceleration of early left ventricular filling.
*Circulation*92:1933–1939, 1995.CrossRefGoogle Scholar - 24.Maeder, M. T., and D. M. Kaye. Heart failure with normal left ventricular ejection fraction.
*J. Am. Coll. Cardiol.*53:905–918, 2009.CrossRefGoogle Scholar - 25.Marino, P., W. C. Little, A. Rossi, E. Barbieri, M. Anselmi, G. Destro, A. Prioli, L. Lanzoni, and P. Zardini. Can left ventricular diastolic stiffness be measured noninvasively?
*J. Am. Soc. Echocardiogr.*15:935–943, 2002.CrossRefGoogle Scholar - 26.Miki, S., T. Murakami, T. Iwase, T. Tomita, Y. Nakamura, and C. Kawai. Doppler echocardiographic transmitral peak early velocity does not directly reflect hemodynamic changes in humans.
*J. Am. Coll. Cardiol.*17:1507–1516, 1991.CrossRefGoogle Scholar - 27.Mossahebi, S., and S. J. Kovács. Kinematic modeling-based left ventricular diastatic (passive) chamber stiffness determination with in-vivo validation.
*Ann. BME.*40(5):987–995, 2012.Google Scholar - 28.Mossahebi, S., L. Shmuylovich, and S. J. Kovács. The thermodynamics of diastole: kinematic modeling based derivation of the P–V loop to transmitral flow energy relation, with in vivo validation.
*Am. J. Physiol. Heart Circ. Physiol.*300:H514–H521, 2011.CrossRefGoogle Scholar - 29.Murakami, T., O. Hess, J. Gage, J. Grimm, and H. Krayenbuehl. Diastolic filling dynamics in patients with aortic stenosis.
*Circulation*73:1162–1174, 1986.CrossRefGoogle Scholar - 30.Nagueh, S. F., C. P. Appleton, T. C. Gillebert, P. N. Marino, J. K. Oh, O. A. Smiseth, A. D. Waggoner, F. A. Flachskampf, P. A. Pellikka, and A. Evangelista. Recommendations for the evaluation of left ventricular diastolic function by echocardiography.
*J. Am. Soc. Echocardiogr.*22(2):107–133, 2009.CrossRefGoogle Scholar - 31.Nikolic, S. D., E. L. Yellin, K. Tamura, H. Vetter, T. Tamura, J. S. Meisner, and R. W. Frater. Passive properties of canine left ventricle: diastolic stiffness and restoring forces.
*Circ. Res.*62:1210–1222, 1988.CrossRefGoogle Scholar - 32.Oh, J. K., C. P. Appleton, L. K. Hatle, R. A. Nishimura, J. B. Seward, and J. Tajik. The noninvasive assessment of left ventricular diastolic function with two-dimensional and Doppler echocardiography.
*J. Am. Soc. Echocardiogr.*10:246–270, 1997.CrossRefGoogle Scholar - 33.Ohte, N., S. Nakano, Y. Mizutani, T. Samoto, and T. Fujinami. Relation of mitral valve motion to left ventricular end-diastolic pressure assessed by M-mode echocardiography.
*J Cardiogr.*16(1):115–120, 1986.Google Scholar - 34.Oki, T., T. Tabata, Y. Mishiro, H. Yamada, M. Abe, Y. Onose, T. Wakatsuki, A. Iuchi, and S. Ito. Pulsed tissue Doppler imaging of left ventricular systolic and diastolic wall motion velocities to evaluate differences between long and short axes in healthy subjects.
*J. Am. Soc. Echocardiogr.*12:308–313, 1999.CrossRefGoogle Scholar - 35.Omens, J., and Y. C. Fung. Residual strain in rat left ventricle.
*Circ. Res.*66:37–45, 1990.CrossRefGoogle Scholar - 36.Owan, T. E., D. O. Hodge, R. M. Herges, S. J. Jacobsen, V. L. Roger, and M. M. Redfield. Trends in prevalence and outcome of heart failure with preserved ejection fraction.
*N. Engl. J. Med.*355:251–259, 2006.CrossRefGoogle Scholar - 37.Riordan, M. M., C. S. Chung, and S. J. Kovács. Diabetes and diastolic function: stiffness and relaxation from transmitral Flow.
*Ultrasound Med. Biol.*31:1589–1596, 2005.CrossRefGoogle Scholar - 38.Shmuylovich, L., and S. J. Kovács. E-wave deceleration time may not provide an accurate determination of left ventricular chamber stiffness if left ventricular relaxation/viscoelasticity is unknown.
*Am. J. Physiol. Heart Circ. Physiol.*292:H2712–H2720, 2007.CrossRefGoogle Scholar - 39.Templeton, G. H., and L. R. Nardizzi. Elastic and viscous stiffness of the canine left ventricle.
*J. Appl. Physiol.*36:123–127, 1974.Google Scholar - 40.Thomas, J. D., C. Y. P. Choong, F. A. Flachskampf, and A. E. Weyman. Analysis of the early transmitral Doppler velocity curve: effect of primary physiologic changes and compensatory preload adjustment.
*J. Am. Coll. Cardiol.*16:644–655, 1990.CrossRefGoogle Scholar - 41.Thomas, J. D., F. A. Flachskampf, C. Chen, J. L. Guerrero, M. H. Picard, R. A. Levine, and A. E. Weyman. Isovolumic relaxation time varies predictably with its time constant and aortic and left atrial pressure: implications for the noninvasive evaluation of ventricular relaxation.
*Am. Heart J.*124:1305–1313, 1992.CrossRefGoogle Scholar - 42.Thomas, J. D., J. B. Newell, C. Y. P. Choong, and A. E. Weyman. Physical and physiological determinants of transmitral velocity: numerical analysis.
*Am. J. Physiol. Heart Circ. Physiol.*260(23):H1718–H1730, 1991.Google Scholar - 43.Weiss, J. L., J. W. Frederiksen, and M. L. Weisfeldt. Hemodynamic determinants of the time-course of fall in canine left ventricular pressure.
*J. Clin. Investig.*58(3):751–760, 1976.CrossRefGoogle Scholar - 44.Zhang, W., C. S. Chung, L. Shmuylovich, and S. J. Kovács. Viewpoint: is left ventricular volume during diastasis the real equilibrium volume and, what is its relationship to diastolic suction?
*J. Appl. Physiol.*105:1012–1014, 2008.CrossRefGoogle Scholar - 45.Zhang, W., and S. J. Kovács. The diastatic pressure–volume relationship is not the same as the end-diastolic pressure–volume relationship.
*Am. J. Physiol. Heart Circ. Physiol.*294(6):H2750–H2760, 2008.CrossRefGoogle Scholar - 46.Zhang, W., L. Shmuylovich, and S. J. Kovács. The E-wave delayed relaxation pattern to LV pressure contour relation: model-based prediction with in vivo validation.
*Ultrasound Med. Biol.*36:497–511, 2010.CrossRefGoogle Scholar - 47.Zile, M. R., C. F. Baicu, and W. H. Gaasch. Diastolic heart failure—abnormalities in active relaxation and passive stiffness of the left ventricle.
*N. Engl. J. Med.*350:1953–1959, 2004.CrossRefGoogle Scholar - 48.Zile, M. R., and D. L. Brutsaert. New concepts in diastolic dysfunction and diastolic heart failure: part I.
*Circulation*105:1387–1393, 2002.CrossRefGoogle Scholar