Embed Size (px)
Citation preview
RADIOSS
1, 2Kim H. Parker
3 1
1.
2.
3. Department of Bioengineering, Imperial College, London
1.
[1, 2, 3]
Fig. 1
[4]
Fig. 2, 3[5, 6]
[7]
Fig. 4[8]
Figure 1. Comparison of the PWV obtained from the computation and those obtained from the modified
Moens-Korteweg equation. The dotted line indicates the line of equality between the two parameters.
Figure 2. Wall displacement waveforms of the 60% stenosed artery with a stenosed length Ls of 100 mm.
Figure 3. Wall displacement waveforms of the 50 mm aneurysmal artery with an aneurysmal length La of
100 mm.
(a) (b)
Figure 4. Radial and longitudinal displacement waveforms of a human carotid artery.
2.
2-1.
ri 10 mm h 2 mm
L L = 1000 mm
= 100ri Es
0.5 MPa 1000 kg/m3
0.45 μ 4.0 10-3
Pa s
Z-X Y
Fig. 5 1 476 224
5 mm
147987 141400
Figure 5. Schematic views of the artery model, and one-fourth of the cross sections of the symmetrical
model used in this study. The bold line in the cross section represents the border of the fluid and solid
regions. The number of elements in one cross section; 476 for the fluid, 224 for the solid.
2-2.
RADIOSS ver.
4.6 RADIOSS ALE
f u jf( )
t+
f uif u j
f( )xi
=p
x j
+ μ2u j
f
xi xi (1)
f
t+
f uif( )
xi= 0 (2)
fui
fp μ
fp c
f=
0
f+p
c 2 (3)
0f
1000 kg/m3
ij
x jV
dV =s ui
s
tVdV (4)
ij = Cijkl kl (5)
ij Cauchy Cijkl kl
2-3.
(6)
(7) (8)
uif= ui
s (6)
p
t= f c
unf
t+ c
p p( )2lc
(7)
uis= 0 (8)
f s
n c p
1.0 10-3
~ 1.0 10-2
mm 0.1% ~ 1%
Re 1000
10 ms
Re 4000 Fig. 6
Figure 6. Boundary condition at the inlet. A steady flow was imposed before a single pulse as the basic
flow. The time taken to establish the basic flow was around 10 s.
3.
x = 0 uy Ic
Dl Us
Fig. 7
Us
2
Ic 1 Us
uy
Us
0.1 m/s 2
2 t = 75 ms y = 450 mm Ic
Dl
1.0 Pa 0.5 Pa
t = 0 ms
Us
0.5 Pa
(a) t = 0 ms (b) t = 15 ms
(c) t = 30 ms (d) t = 45 ms
(e) t = 60 ms (f) t = 75 ms
Fig._7_Wave propagation and WSS distribution in the uniform artery model. Top shows color-coded
distribution of the longitudinal velocity uy at the plane x = 0. The scale in the radial direction is multiplied
by 4 for clarity. Middle shows the circumferential increment Ic (red solid), longitudinal displacement Dl
(blue solid), and the longitudinal wall velocity Us (green dotted). Bottom shows the WSS t (black bold)
during the pulse propagation.
4.
1.0 Pa
0.5 Pa t = 0 ms
2 Us
Us
Dl
Us
Ic uy
Us
Us
2
t = 75 ms
Figure 7
0.5 Pa
0.5 Pa
2
1.0 Pa
t = 75 ms y = 450 mm
2
1000 mm 200 mm
RADIOSS ver. 4.6
[1] Caro CG, Fitzgerald JM, and Schroter RC. Atheroma and arterial wall shear:
observation, correlation and proposal of a shear dependent mass transfer mechanism for
atherogenesis. Proceedings of the Royal Society, London 177: 109-159, 1971.
[2] Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, and Glagov S.
Carotid bifurcation atherosclerosis: quantitative correlation of plaque localization with
flow velocity profiles and wall shear stress. Circulation Research 53: 502-514, 1983.
[3] Malek AM, Alper AL, and Izumo S. Hemodynamic shear stress and its role in
atherosclerosis. JAMA: Journal of the American Medical Association 282: 2035-2042,
1999.
[4] Fukui T, Imai Y, Tsubota K, Ishikawa T, Wada S, Yamaguchi T, and Parker KH. A
fluid-solid interactions study of the pulse wave velocity in uniform arteries.
Biomechanics at Micro- and Nanoscale Levels Vol. III, Computational Biomechanics,
World Scientific, 146-156, 2007.
[5] Giller CA, Giller AM, Batjer HH, and Kopitnik TA. An unusual transcranial Doppler
waveform associated with vessel distortion in giant intracranial aneurysms.
Neurosurgery 34: 1068-1071, 1994.
[6] Weber T, Auer j, O’Rourke MF, Kvas E, Lassnig E, Berent R, and Eber B. Arterial
stiffness, wave reflection, and the risk of coronary artery disease. Circulation 109:
184-189, 2004.
[7] Fukui T, Parker KH, Tsubota K, Wada S, and Yamaguchi T. Differentiation of
stenosed and aneurysmal arteries by pulse wave propagation analysis based on a
fluid-solid interaction computational method. Technology and Health Care 15: 79-90,
2007.
[8]
pp. 51, 2008.
