TY - JOUR

T1 - Evaluation of diastolic function with Doppler echocardiography

T2 - The PDF formalism

AU - Kovacs, S. J.

AU - Barzilai, B.

AU - Perez, J. E.

PY - 1987

Y1 - 1987

N2 - A new parameterized diastolic filling (PDF) formalism for evaluation of holodiastolic (left and right) ventricular function via Doppler echocardiography is presented. It is motivated by the empiric observation that during diastole the heart behaves as a suction pump whose dynamics, in certain respects, are those of a damped harmonic oscillator. An expression for elastic recoil (suction) initiated ventricular diastolic fluid inflow velocity v(t) is obtained by differentiation from the solution x(t) of the linear differential equation that describes the motion of a forced, damped harmonic oscillator. It is solved for 'over-damped' motion, for zero initial velocity and initial displacement = x0 cm. An explict forcing term F(t) = F0sin(ωt) is included to account for late diastolic (atrial) filling. The quantitative parameters of the model include inertia (mass; m), viscosity (damping constant; c), source of stored energy for suction (spring constant; k), and its initital displacement x0, the amplitude and frequency of the (atrial) forcing term F0,ω. The mathematical behavior of the solution v(t) and its dependence on the parameters, x0, c, and k, which characterize the contour of the Doppler velocity profile (DVP), is discussed. When clinical examples of normal and abnormal transmitral DVPs are compared with v(t) calculated using the harmonic oscillator model, excellent agreement |DVP - v(t)|v(t) ~ 0.05 is obtained throughout diastole. Thus the model allows accurate qualitative and quantitative characterization of global ventricular diastolic behavior by noninvasive means in a variety of normal and abnormal stiffness-compliance states. In addition, it may serve as a prototype for a class of mathematical models that can encompass the essential dynamic elements of ventricular diastolic function that couple to flow and further enhance the role of the heart as a suction pump.

AB - A new parameterized diastolic filling (PDF) formalism for evaluation of holodiastolic (left and right) ventricular function via Doppler echocardiography is presented. It is motivated by the empiric observation that during diastole the heart behaves as a suction pump whose dynamics, in certain respects, are those of a damped harmonic oscillator. An expression for elastic recoil (suction) initiated ventricular diastolic fluid inflow velocity v(t) is obtained by differentiation from the solution x(t) of the linear differential equation that describes the motion of a forced, damped harmonic oscillator. It is solved for 'over-damped' motion, for zero initial velocity and initial displacement = x0 cm. An explict forcing term F(t) = F0sin(ωt) is included to account for late diastolic (atrial) filling. The quantitative parameters of the model include inertia (mass; m), viscosity (damping constant; c), source of stored energy for suction (spring constant; k), and its initital displacement x0, the amplitude and frequency of the (atrial) forcing term F0,ω. The mathematical behavior of the solution v(t) and its dependence on the parameters, x0, c, and k, which characterize the contour of the Doppler velocity profile (DVP), is discussed. When clinical examples of normal and abnormal transmitral DVPs are compared with v(t) calculated using the harmonic oscillator model, excellent agreement |DVP - v(t)|v(t) ~ 0.05 is obtained throughout diastole. Thus the model allows accurate qualitative and quantitative characterization of global ventricular diastolic behavior by noninvasive means in a variety of normal and abnormal stiffness-compliance states. In addition, it may serve as a prototype for a class of mathematical models that can encompass the essential dynamic elements of ventricular diastolic function that couple to flow and further enhance the role of the heart as a suction pump.

UR - http://www.scopus.com/inward/record.url?scp=0023197635&partnerID=8YFLogxK

U2 - 10.1152/ajpheart.1987.252.1.h178

DO - 10.1152/ajpheart.1987.252.1.h178

M3 - Article

C2 - 3812709

AN - SCOPUS:0023197635

VL - 252

SP - H178-H187

JO - American Journal of Physiology - Heart and Circulatory Physiology

JF - American Journal of Physiology - Heart and Circulatory Physiology

SN - 0363-6135

IS - 1 (21/1)

ER -