Page 10 - CBAC Newsletter 2015

represent different levels of technological innovation, for filling-related energy losses (10). The spring constant
much remains to be learned in relation to how to k primarily determines the width of the E-wave. A high
interpret the recorded data. In our kinematics-based spring constant (stiff spring) will generate a tall narrow
approach we advocate the use of physical models and E-wave as seen in the ‘constrictive-restrictive’ pattern.
mathematical techniques in order to extract The resistance/damping parameter is mainly
relevant information from all modes of imaging and responsible for the deceleration portion of the E-wave
thereby more fully understand the rules that govern how and is directly responsible for the inflection point
the heart works when it fills. (change in curvature from ‘cup-down’ to ‘cup-up’)
seen in the deceleration portion. A high value for the
Echocardiography and The Parametrized Diastolic resistance/damping parameter in general gives rise
Function (PDF) Formalism to the ‘delayed relaxation’ pattern on the E-wave. Ac-
cordingly, the resistance/damping parameter c can be
In routine practice, the curvature of the E-wave is interpreted as a relaxation parameter.
ignored when the E-wave is approximated as a triangle.
By considering the kinematic analog of the role of the The PDF model parameters (χ ,c, k) for each E-wave can
o
heart as a suction pump, we have gained deeper be obtained through the steps detailed in Figure 2 and
understanding into the physiologic determinants of made explicit in (31). Briefly, after the E-wave is selected,
E-wave curvature, thereby making the triangular the maximum velocity envelope is identified and is fit
approximation unnecessary. numerically by the solution to the PDF equation, yielding
the three, best-fit PDF parameters (χ ,c, k) and a
o
Ventricular filling can be modeled in analogy to the measure of goodness-of-fit.
motion of a recoiling spring (a mechanical oscillator) that
has an inertial load and is moving against a resistance With a mathematically accurate model-based
(9). The model is called the Parametrized Diastolic approximation to the E-wave, subtle details of curvature
Function (PDF) formalism. To be specific, this formalism that are absent in the triangular shape approach are
(kinematic model) stems from Newton’s Laws of motion made explicit and are seen to be useful. The analysis of
and characterizes the E-wave in terms of a driving force E-waves via this model has shown that diabetes
(the atrioventricular pressure gradient), a increases the resistance/relaxation parameter c of early
damping/viscous force that resists transmitral flow rapid filling in both rats (4) and humans (15). Important-
(cross bridge uncoupling or relaxation rate), and an ly, these two studies showed that for hearts with normal
inertial load due to tissue and blood. LVEF, in contrast to the relaxation/viscosity parameter
c, conventional E-wave indexes such as E peak or DT were
Using this conceptual framework as a model one can unable to differentiate between normal and diabetic
solve the associated differential equation (of motion); subjects. A further manifestation of the
mitral flow velocity can be mathematically predicted as resistance/relaxation property of the ventricle is that all
the solution to the equation of motion. In other words ventricles fill to a volume that is less than the maximum
–all ventricles are mechanical suction pumps and fill by (lossless) ideal filling volume. An index which
obeying the same law of motion. The parameters that characterizes this efficiency of filling, the kinematic filling
specify the motion, however, vary from heart to heart. efficiency index (KFEI) has been shown to be lower in
As a simple analogy consider the trajectory of a stone normal LVEF diabetics compared to normal controls (26).
thrown in the air. The arced path the stone follows Furthermore, the resistance/relaxation parameter c has
varies from throw to throw, and depends on the initial been shown to be linearly related to relaxation charac-
velocity and angle of launch – while the laws of inertia terized by τ, the (invasively determined) time-constant of
and gravity that determine the stone’s actual trajectory isovolumic relaxation (3).
remain the same for each throw.
Differentiating between pseudonormal and normal
Each transmitral E-wave can be uniquely determined by E-wave patterns
three parameters, the initial displacement of the spring
χ , which is linearly related to the area under the E-wave Pseudonormal (PN) Doppler E-wave filling patterns
o
contour, its velocity-time integral VTI (the volumetric indicate diastolic dysfunction but are indistinguishable
preload) (10), the stiffness parameter k, which is linearly from the normal filling (NL) pattern using the triangle
related to chamber stiffness (dP/dV) (8) and a approximation for E-wave shape. To differentiate PN
resistance/damping parameter or chamber from NL, maneuvers to alter load or to additionally
viscoelasticity/relaxation index c (g/s) which accounts measure peak E’ are required. E-wave deceleration time

4 | CBAC Center Heartbeat