2Pa5-8
Numerical Estimation of the Intraventricular Pressure Gradients
Based on Echo-Dynamography and Bernoulli's Principle
Echo-Dynamography 法とベルヌーイ定理に基づく
心室内圧力勾配の推定法
Shiho furudate1†, Takuro Ishii1,2, Naoya Kanno1, Yasuyuki Shiraishi3, Yoshifumi Saijo1,(1Grad.School Biomed. Eng., Tohoku Univ.; 2Frontier Research Institute for Interdisciplinary Sciences,Tohoku Univ. 3Institute of Development, Aging and Cancer, Tohoku Univ.)
古舘志歩 1†, 菅野尚哉 1, 石井琢郎 1,2, 白石泰之 3，西條芳文 1(1 東北大院・医工, 2 東北大 学際科学フロンティア研究所, 3 東北大 加齢医学研究所）

1. IntroductionIntraventricular pressure gradients (IVPG) are
how much pressure changes between the apex andthe base of the left ventricle (LV), and is related to
cardiac function1). The diastolic IVPG was reported
to reflect the efficiency of blood filling, while theejection IVPG was suggested to be related to
myocardial contractility2,3). Such IVPG assessments,
however, could only be obtained by measuring
pressure at multiple points in the LV with invasive
catheterization of pressure sensors.
Recently,colorDoppler
M-modeechocardiography has been proposed as a new
method for noninvasively estimating IVPG1). Thismethod assumed that the Doppler M-mode cursor
approximates the streamlines, but the straight lines
and streamlines unlikely match throughout thecardiac cycle. In addition, the IVPG value wasestimated with limited information as the color MDoppler method could only measure the velocity
component parallel to the ultrasound beam. As asolution, an ultrasound vector flow imaging methodthat can visualize two-dimensional velocity field in
the LV, so called Echo-Dynamography (EDG)
method4), may be used to estimate streamlines ofblood flow in the LV more accurately.
In this study, we hypothesized that consistentestimation of the IVPG is possible by combing theEDG method and a pressure gradient estimation
method using streamlines5). The feasibility of theIVPG estimation using those methods was evaluatedusing a custom-made volume-driven LV phantom.
2. Method
In this study, we first obtained time-resolved
flow vector fields in the LV using the EDG method.
From the obtained blood flow vectors, a streamline
was generated, and the pressure difference along thestreamline was estimated by substituting the velocity
gradient along the streamline into the Bernoulli
equation. The EDG and the pressure gradientshiho.furudate.t7@dc.tohoku.ac.jp

estimation methods are respectively described inSections 2.1 and 2.2.
2.1 Echo-Dynamography (EDG) method
EDG method4) can estimate the velocity
component that is perpendicular to the radial
component obtained by color Doppler and hence, it
can visualize flow vector filed in the LV. First, theflow is divided into two streams with different
properties. Next, the direction perpendicular to theultrasonic beam is obtained by applying varioushydrodynamic laws to each of the two flows.
Finally, the two-dimensional velocity vector isobtained by summing the velocity along beam
direction and perpendicular velocity.
2.2 Pressure estimation using the blood velocity
gradient
3D flow is governed by the Navier-Stokes
equations for incompressible fluids. Rewriting theNavier-Stokes equations into a scalar equation
following a streamline, omitting the terms of thegravity and viscosity, yields the following:
𝜕𝑣𝑠𝜕𝑣𝑠
𝑑𝑝𝑠 = −𝜌 [𝑑𝑠 + 𝑣𝑠𝑑𝑠 ](1)
𝜕𝑡𝜕𝑠where 𝑑𝑝𝑠 is the individual pressure gradient, and𝜌 is the density of blood, and 𝑑𝑠 is an element ofdistance along the streamline that runs in thedirection 𝑠, and 𝑣𝑠 is the scalar product of a fluid’s
velocity field 𝑣⃗(𝑟⃗, 𝑡) = (𝑣𝑥 (𝑡), 𝑣𝑦 (𝑡), 𝑣𝑧 (𝑡)) and thevector that lies tangent to the streamline 𝑑𝑠 .
Integrating the individual pressure gradient 𝑑𝑝𝑠
along a streamline, from the 𝑙1 to 𝑙2 , yields theunsteady Bernoulli equation:
22𝑙2𝑣𝑠,𝑙2− 𝑣𝑠,𝑙1
𝜕𝑣𝑠∆𝑃(𝑡) = −𝜌 [+ ∫𝑑𝑠 ] (2)2𝑙1 𝜕𝑡
In this study, we used the EDG method that provides
a two-dimensional vector velocity field 𝑣⃗(𝑟⃗, 𝑡) =(𝑣𝑥 (𝑡), 𝑣𝑦 (𝑡)). Thus, we assumed that 𝑣𝑧 (𝑡)inthis proposed method.

Using the LV phantom, the pressure change ina streamline could be evaluated from the velocity
vector obtained by the EDG method. It is necessary
to verify the accuracy of the proposed method bycomparing it with other blood pressure
measurements.
4. Conclusion

2.3 Experimental setup and data acquisition
To confirm the feasibility of the proposed
method, an experiment was carried out using acustom-made volume-driven LV phantom. The LVchamber (shown as the deep blue triangle in Fig.1)
made of conical silicon rubber was assembled in theouter chamber, which was filled with water andconnected to a piston pump. As the piston moved,
the volume of the water in the outer chamberchanged and the LV chamber was deformedaccordingly. The piston pump was set to resemble aheart rate of 60 bpm and a stroke volume of about 60
ml. As the blood mimicking liquid, inside of LV
chamber was filled with an aqueous solution of 10
wt% glycerin and 0.1 wt% ultrasound scatterer(Godd Ball, Suzukiyushi Industrial Corp.).
A color Doppler movie was recorded in acommercial Ultrasound scanner (Xario1 , Canon
Medical Systems, Tochigi, Japan). The central
frequency was 3. MHz, and the frame rate was 14fps. The acquired color Doppler images were
processed offline using MATLAB.

In this study, we evaluated the feasibility of theEDG and streamline pressure estimation methods
using the LV phantom. The experiment indicated thatthe proposed method would estimate pressurechanges accurately and be useful for deriving IVPGindexes noninvasively.
References
1. N.L. Greenberg et al.: Am J Physiol 280 (2 1)
H25 7–H2515
2. K. Steine et al.: Circulation 99 (1999) 2 482 54
3. R. Yotti et al.: JACC 43 (2 4) 1654-1662
4. S. Ohtsuki et al.: Journal of Visualization 9(2 6) 69-82
5. J.B. Olsen et al.: IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 65 (2 18) 7 9-719

[cm]
2Apex
Relative pressure mmHg

Fig. 1 The experimental system

468

Diastolic and systolic color Doppler images
were acquired to estimate the pressure differencealong the streamline using the LV phantom.
Fig. 2 (a) shows the diastolic vector velocity
by the EDG method and streamline. The yellow
arrows represent velocity vectors, and the green line
represents streamline. Fig. 2 (b) shows pressurechanges in a streamline in the diastolic and thestarting point of the streamline, which is set tommHg, is the LV inflow area. The pressure
difference between the apex and the inlet (IVPG)
was approximately - .38 mmHg.
Fig. 3 (a) shows the systole vector velocity by
the EDG method and streamline. The yellow arrows
represent velocity vectors, and the green line
represents streamline. Fig. 3 (b) shows pressurechanges in a streamline in the systole and the starting
point of the streamline, which is set to mmHg, isthe apex in the LV. The pressure difference between
the outlet and the apex (IVPG) was approximately-3. mmHg.

10Inlet-4

Outlet2[cm]0-2- .2- .3- .4

1 2 3 4 5 6 7Distance from the start point [cm]
cm(a)

(b)

Fig. 2 (a) Diastolic vector velocity and streamline(b) Pressure changes in a streamline in the diastolic[cm]Apex
4

Relative pressure mmHg

3. Result and Discussions

- .1

6
8
10

Inlet
-2

Outlet0(a)2[cm]-1-2-3-4

1 2 3 4 5 6 7Distance from the start point [cm]cm(b)Fig. 3 (a) Systole vector velocity and streamline(b) Pressure changes in a streamline in the systole