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Ultrasonics 44 (2006) e179–e183 www.elsevier.com/locate/ultras

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O. Basset a, G. Courbebaisse b, P. Delachartre b, P. Tortoli c, C. Cachard a

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S. Balocco

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3D dynamical ultrasonic model of pulsating vessel walls

CREATIS, Universite´ Claude Bernard Lyon 1, CNRS UMR 5515, INSERM U630, Lyon, France b CREATIS, INSA Lyon, CNRS UMR 5515 INSERM U630, Lyon, France c Microelectronic Systems Design Laboratory, Universita` di Firenze, Italy

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Available online 30 June 2006

Abstract

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The aim of this work is to introduce a novel 3-D model of pulsating vessels, through which the dynamic acoustic response of arterial regions can be predicted. Blood ﬂow is numerically simulated by considering the ﬂuid-dynamic displacements of the scatterers (erythrocytes), while a mechanical model calculates the wall displacement due to ﬂuid pressure. The acoustic characteristics of each region are simulated through the FIELD software. Two numerical phantoms of a carotid artery surrounded by elastic tissue have been developed to illustrate the model. One of them includes a plaque involving a 50% stenosis. B-mode and M-mode images are produced and segmented to obtain the wall displacement proﬁle. A cylindrical holed phantom made of cryogel mimicking material has been constructed for the model validation. In pulsatile ﬂow conditions, ﬂuid and wall displacements have been measured by Doppler ultrasound methods and quantitatively compared to simulated M-mode images, showing a fairly good agreement. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Ultrasound; 3-D arterial model; Arterial mechanics; Wall displacement measurement

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1. Introduction

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A signiﬁcant portion of recent ultrasound research has been dedicated to studies concerning signals originated from regions of the cardio-vascular system aﬀected by atherosclerosis. Atherosclerosis is a disease characterized by hardening and thickening of the arterial walls due to the formation of plaques. As the disease progresses, the arterial elasticity properties change and the plaque formation reduce the arterial lumen area creating irregular blood ﬂow patterns [1]. The arterial wall displacement obtained from the segmentation of B-mode sequences or directly from M-mode images can be helpful for diagnostic purposes.

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Corresponding author. Address: CREATIS, Universite´ Claude Bernard Lyon 1, CNRS UMR 5515, INSERM U630, Lyon, France. E-mail address: [email protected] (S. Balocco). 0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.045

A 3D ultrasonic model has recently been introduced and shown suitable for simulating the dynamic ﬂow in pathological vessels [2]. The model enables the representation of various vessel structures, including bifurcations, with associated pathologies such as local arterial wall thickening, aneurysms, stenosis and atherosclerotic plaques. The model has been conceived as a candidate to supply reference phantoms to evaluate, compare and validate morphological (B-Mode), and hemodynamic (Doppler) measurements. In this paper, the model is completed with the capability of simulating also the arterial wall elasticity and M-mode images showing the dynamic wall displacement are provided. A validation of this capability is performed by comparing simulated data with an ‘‘in vitro’’ experiment. Section 2 describes the geometrical model and the ﬂuid dynamics, as well as the mechanical and acoustic analysis performed by the model. Section 3 reports the experimental setup and the experimental work made to validate the pulsating model.

S. Balocco et al. / Ultrasonics 44 (2006) e179–e183

vortex and recirculating zones are present. Research [4–6] performed on the biological aspect of this phenomenon had led to the hypothesis that the ﬂow disturbances play a major inﬂuence in the localization of the disease. Fundamental to the analysis of ﬂuid ﬂow is the Reynolds number, which represents the ratio between inertial and viscous forces. Reynolds numbers less than 2000 usually indicate a laminar ﬂow, whereas numbers above 2500 indicate turbulent ﬂow. In our model, the nonlinear eﬀects of turbulence have also been considered. The Navier–Stokes nonlinear equation describes the movement in incompressible ﬂuids through:

2. Method

2.2. Flow analysis

ov T rgðrv þ ðrvÞ Þ þ qðvrÞv þ rp ¼ F ot

ð1Þ

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where v is the velocity vector of an inﬁnitesimal mass element at a point in 3D space, p is the scalar pressure at the same point, q is the mass density at the point, l is the kinematic viscosity of the medium, and F is a vector associated to the external forces. Blood pressure and velocity map have been obtained by a ﬁnite element analysis of the 3D meshed geometry using Femlab software [7]. A cyclic pulsating blood velocity proﬁle is integrated as realistic heart pulsation. The laminar inﬂow condition is issue from the experimental validation as shown in Section 4. 2.3. Mechanical analysis The hydrostatic pressure on the wall boundaries is deduced solving Navier–Stokes equation inside the tube. The pressure calculated in each external node of the tube is then used as stress normal force applied to the surrounding tissues. A ﬂuid-structure interaction problem is solved and a mechanical anisotropic elastic model, based on the Hook law (Eq. (2)) is applied to the nodes representing the tissue.

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The plaque deposition due to atherosclerosis usually occurs in sharp curvatures, especially where standing

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The topology of the vascular structure is generated by means of a complex-shaped object within the family of right generalized cylinder (RGC) described by Azencot [3]. A continuous deformation of a planar curve (contour) along the object’s axis describes its 3D surface. This RGC state formalism gives access to morphological parameters such as curvature and torsion of the axis, area of cross-sections, and volume of a cylinder segment. Two such RGC sharing the same axis geometry are used for modeling the geometry of a vessel wall. The multi-layer model enables the user to control the Intima-Media thickness in each point of the vessel to simulate atherosclerotic diseases. In this work, two straight phantoms have been built (Figs. 1 and 2). Each phantom is 100 mm long and composed by a 3 layer structure: blood (6 mm diameter) in the central area, vessel wall (1 mm thickness) between the two RGC and surrounding tissues (10 mm) in the external area. One of them includes a plaque involving a 50% stenosis (Fig. 2).

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2.1. Geometrical model

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Fig. 1. Geometry of the 3 layer phantom simulating a healthy vessel.

Fig. 2. Geometry of the 3 layer phantom simulating a stenosed vessel.

Fig. 3. Finite element simulation of the stenosed cylinder. The grayscale represents the speed of the ﬂuid, whereas the arrows symbolize the wall displacement.

S. Balocco et al. / Ultrasonics 44 (2006) e179–e183

E¼

F =S oh=h

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ð2Þ

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where E is the Young modulus, F the applied force, S the surface, h the total displacement. The ﬁnite element solver is thus able to determine the value of the vector displacement. Fig. 3 shows the result of the ﬁnite element analysis on the stenosed tube (Fig. 2).

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Fig. 5. Simulated M-mode image of the straight tube during a pulsating cycle.

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FIELD software [8] has been used to obtain ultrasound radio-frequency echo-signals. An independent acoustic characterization of each region in terms of number of scatterers (Table 1), distribution and acoustic reﬂection amplitude, has also been performed. The virtual ultrasound probe can be arbitrarily located at diﬀerent regions of the phantom to perform B-Mode, M-Mode, intravascular, Color Pulsed Doppler imaging. In this work, virtual echo signal received by a 5 MHz central frequency probe, and sampled at 100 MHz frequency, have been generated. The linear probe consists in a transducer with 192-elements, of which 64 are simultaneously active. The element height is 5 mm, the width is 0.3 mm and the kerf is 0.05 mm. The displacements obtained from the ﬁnite element analysis are used to calculate for each timestep the new scatterer position. A sequence of 63 Bmode frames covering a heart cycle has been generated for both the straight and the stenosed vessel. Fig. 4 shows images taken from the B-mode sequences for the healthy and the stenosed vessel, respectively. Fig. 5 reports an M-mode image of the pulsating straight tube phantom.

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2.4. Acoustic analysis

Backscattering value

Wall Blood Tissue

500 5 100

Number of scatterers per resolution cell 10 10 10

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Table 1 Acoustic characteristics of the 3 layer model used in the FIELD software

Fig. 6. Displacement values (of upper and lower wall), obtained from segmentation of the M mode image shown in Fig 5.

In order to retrieve the vessel wall pulsation proﬁles, segmentation by thresholding of the ultrasound M-mode image (Fig. 5) was made. The resulting displacement are plotted in Fig. 6. 3. Results 3.1. Experimental setup In order to reproduce the dynamic behavior of a human artery and to simulate the tissue resistance to the vessel dilatation, a cylindrical holed phantom made of cryogel tissue mimicking material, 100 mm long with 6 mm and 36 mm, respectively, for inner and outer diameter was integrated in a hydraulic circuit. A latex tube 0.3 mm thin was inserted inside the cylinder to assure the watertight of the hydraulic system. The eﬀect of the latex tube on the mechanical behavior of the phantom is assumed negligible. 3.2. Input and output parameters

Fig. 4. Simulated B-mode images of the healthy (left) and the stenosed (right) vessel.

The ﬂuid velocity proﬁle in the tube center (Fig. 7) and wall displacements (Fig. 8) have been simultaneously measured by Doppler ultrasound methods [9]. The maximal

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Fig. 7. Fluid velocity in the center of the vessel measured through Doppler ultrasound analysis.

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Fig. 9. Comparison of the displacement values obtained by ﬁnite element simulation, segmentation of simulated M-mode images and experimental measurement values.

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Table 2 Comparison of the displacement measurements

jD2 D1j [m] jD3 D1j [m]

Max

Mean

Std

4.05e-004 1.20e-003

5.78e-005 1.94e-004

1.75e-004 4.4e-004

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The analysis shown in Fig. 9 and Table 2 illustrates the good matching between the ﬁnite element simulation and the wall proﬁles obtained from the ultrasound simulation. The errors of the second measurement are probably caused by a non accurate segmentation of the arterial wall, caused by the presence of speckle noise on the ultrasound image. The third shape (D3), even though presents the same amplitude, does not match perfectly with the reference one. A more complex mechanical model, including viscoelastic nonlinear equation could be introduced to better reproduce an ‘‘in vivo’’ behavior.

Fig. 8. Wall displacement of the inner wall of the tube measured by Doppler ultrasound analysis.

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velocity measured in the center of the vessel was 0.7 m/s as shown in Fig. 7. The Young modulus of the surrounding tissue was afterwards measured on a mechanical traction machine (E = 1634 Pa). The ﬂuid velocity proﬁle and the Young modulus were used as input parameters in the model, while the wall displacement was compared to the simulation results to evaluate the discrepancies. 3.3. Wall displacement comparison

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In order to evaluate the accuracy of the model, ﬁnite element displacements, M-mode wall displacement measured by segmentation of simulated US images and experimental displacement data measured by Doppler are qualitatively compared in Fig. 9. The arterial wall displacement corresponding to three measurements are also quantitatively compared in Table 2. Let D1 be the vector of the displacement values simulated by FEMLAB on a pulsating cycle, D2 the vector of the displacement measured on M-mode simulated images and D3 the measured wall displacement on the ‘‘in vitro’’ phantom.

4. Conclusion and discussion This paper has presented a 3D model capable of reproducing the physical and the acoustic behavior of vessels. Such a tool includes a dynamic wall pulsating model, based on structural mechanic elastic properties of biological human tissues. A ﬂuid-structure analysis based on physical equations is performed and the arterial wall displacement could be calculated and reproduced in ultrasound images. A more realistic wall displacement behavior could be obtained using a visco-elastic mechanical model instead of the Hook law. The model can be of interest for the development and validation of various ultrasonic signal and image processing applications such as data segmentation, tissue characterization, elastography measurement, contrast agent evaluation or innovative Doppler techniques and 3D acoustic imaging. The experimental phantom used in the experiments has a low Young modulus, leading to displacements larger than

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those expected for carotid arteries. However, since the main purpose of this work was the model validation, the absolute displacement value is not particularly important.

[4] A. Scotti, U. Piomelli, Numerical simulation of pulsating turbulent channel ﬂow, Phys. Fluids 13 (5) (2001). [5] H.F. Younis, A.G. Isasi, C. I. Chung, R.C. Chan, R.D. Kamm, Three dimensional ﬁnite element analysis of the atherosclerotic human carotid bifurcation based on in vivo magentic resonance images, in: Bioengineering Conference ASME, 2001. [6] J. Ryval, A.G. Straatman, D.A. Steinman, Low Reynolds number modeling of pulsatile ﬂow in a moderately constricted geometry, in: 11th annual conference of the CFD society of Canada, Vancouver, 2003. [7] COMSOL A, FEMLAB reference manual, 2004. [8] J.A. Jensen, Estimation of Blood Velocities Using Ultrasound, A Signal Processing Approach, Cambridge University Press, New York, 1996. [9] G. Bambi, T. Morganti, S. Ricci, E. Boni, F. Guidi, C. Palombo, P. Tortoli, A novel ultrasound instrument for investigation of arterial mechanics, Ultrasonics 42 (2004) 731–737.

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