3D harmonic and transient dynamic vascular elastography Rheology
of biological soft tissues Time-varying viscoelasticity of a mimicking deep vein thrombi
Patents, first publications and scientific
communications of the group
3D harmonic and transient dynamic vascular
elastography The
harmonic case
An
original application of dynamic elastography to venous and arterial
pathologies was developed. The aim was to model analytically and to study,
theoretically and experimentally, shear-wave scattering by a venous clot,
modeled by a cylindrical soft inclusion, surrounded by an infinite soft
medium. Using
a modal decomposition technique, a 3D analytical model was developed to
simulate the scattering of a harmonic plane shear wave by a cylindrical
inclusion for an arbitrary incident angle. The superposition principle of
harmonic solutions (stationary displacement fields) served to obtain the 3D
scattered field for an arbitrary incident transient plane shear wave. One can
note that this model can be coupled with magnetic resonance elastography or
sonoelastography techniques. The
transient case
In the
examples given here, from a mechanical point of view, the heterogeneity and surrounding
materials modeled a deep venous thrombosis. Both media were assumed to be
homogeneous, isotropic and linear viscoelastic materials made of agar-gelatin
mixture with viscoelasticity mean values equal to m = (14600 + 0.7iw) Pa for the surrounding
medium and It
is important to point out that the presence of oscillations in the
heterogeneity observed in the horizontal planes and along the vertical
direction are directly related to the inclusion constitutive material
viscoelasticity. Indeed, on one hand oscillation wavelengths are a function
of elasticity, and on the other hand their amplitudes depend on both
elasticity and viscosity. Another scattered wave characteristic is its
spatial distribution in a given horizontal plane, i.e. the shear wave slowing
down after crossing the inclusion, the orientation of diffraction lobes in
the surrounding medium, the 2D shape of oscillations into the inclusion, the
wave diffraction angle into the inclusion with respect to its axis, etc. All
these behaviors are related to the internal and external viscoelastic
properties, but also to the contrast between them. Consequently, one could
exploit this rich information to characterize mechanical properties of
heterogeneous media.
The incident plane shear wave is now
considered to be parallel to the cylinder axis, propagating along the x-axis
and polarized along the y-axis. Both media are assumed to be homogeneous,
linear, viscoelastic and incompressible. Taking into account the geometrical
and mechanical conditions of the problem, one can assume a plane strain
mechanical state which reduce the acoustical problem to a two dimensional
one. Consequently, displacement field in both inclusion and surrounding
medium is contained in the x-y plane. This configuration corresponds to a
particular case of the general 3D configuration.
The
figure above shows the typical experimental and theoretical propagation of a 200
Hz harmonic shear wave interacting with a cylindrical inclusion (diameter
equal to 8.0 mm) filled with coagulated blood. The motion source positioned
on the left side generated a plane shear wave that traveled form left to
right. After the shear wave diffraction by the inclusion, a distortion and a
deceleration appeared due to viscoelastic differences between the clot, m = (943 +0.35iw) Pa, and surrounding medium, m = (14600 +0.7iw) Pa,. Pattern distributions
observed into the inclusion clearly depicted shorter wavelengths than in the
agar-gelatin surrounding medium. These behaviors can be exploited in an
inverse problem to characterize the viscoelastic properties of both inclusion
(heterogeneity) and surrounding media. Rheology of biological soft tissues The coagulated blood example Deep
venous thrombosis (DVT) is a vascular pathology annually diagnosed in 67 per
10000 individuals for the general population. This pathology is characterized
by the formation of a blood clot or thrombi in lower limb veins and can lead
to pulmonary embolism. Screening of deep vein thrombus formation and its
spatio-temporal mechanical evolution are of importance for determining an
appropriate therapy. Most imaging methods proposed so far suffer from two
important drawbacks: the viscoelasticity reconstruction is biaised, and the
elasticity is assessed only when the blood clot is formed. This section
presents the validation a Voigt viscoelastic model to simulate the
rheological behavior of blood clots.
To validate the assumption of the Voigt’s
model as a simple and realistic viscoelastic representation of blood clots,
we represent the frequency dependence (50-190 Hz) of a plane shear wave
velocity (vs) and attenuation (a) 3 hours after
adding CaCl2 to blood (to force coagulation) at a hematocrit of
40%. The plane shear wave was propagating into a homogeneous and parallelepipedal volume of
coagulated blood. Voigt’s and
Maxwell’s models fitted on experimental data are plotted on the same
figure. The Voigt’s model (m = 943 Pa, h = 0.35 Pa.s) correctly predicted the blood clot
mechanical behavior. Indeed, both models fitted well the velocity (around
0.92 m/s) but only the Voigt’s model was appropriate for the
description of viscous effects on attenuation.
The study of plane shear wave propagation into a
homogeneous blood sample also permit to assess the viscoelasticity evolution
during clotting. The shear wave velocity and attenuation during the formation
of a blood clot were studied from 50 min (liquid to solid transition) to more
than 3 hours following the addition of CaCl2 (see figure above).
From these results, we calculated the elasticity (m) and viscosity (h) corresponding to Voigt’s model. It is shown that when the
medium became solid (after the clotting time), the 1D dynamic elastography
permits to follow the clot mechanical evolution: the shear wave velocity
increases (from 0.76 m/s to 1.01 m/s) and the attenuation decreases (from
95 Np/m to 54 Np/m). Retrieved elasticity and viscosity showed an
evolution in two phases: blood clot hardening (m and h increasing) during approximately 50 min followed by a mechanical
structure stabilization when the viscoelastic parameters reach a plateau (m @ 1100 Pa, h @ 0.3 Pa.s).
Time-varying viscoelasticity of a mimicking deep vein thrombi Inverse problem Staging mechanical properties of deep vein
thrombi (elasticity and viscosity) can be of importance for therapy planning
because the compactness of a blood clot impacts the efficiency of
thrombolysis drugs. Dynamic
Vascular Elastography (DVE) can serve to evaluate these mechanical
properties. In the current example, it consists to retrieve viscoelastic
parameters of 8-mm diameter blood clot cylindrical inclusions, embedded in an
agar-gelatin material, from the diffraction characteristics of a harmonic
shear wave.
The
technique firstly implies the generation of a harmonic plane shear wave (with
a frequency of 200 Hz) in the heterogeneous medium and the tracking of this
wave with an ultra-fast ultrasound scanner (frame rate > 3000 Hz). Using
the 2D dimensional model presented above, an inverse problem was formulated
as a least-square minimization between simulations and experimental results
of viscoelasticity. Dynamic
Vascular Elastography proved to have sufficient sensitivity to follow the
time-varying blood coagulation process and to differentiate mechanical
properties of blood samples with different hematocrits.
One
can observe that the lower the hematocrit, the harder and more viscous was
the blood clot. We also showed that the clotting time was affected by the
hematocrit. The results given by the Dynamic
Vascular Elastography method are promising to quantify the time-varying
mechanical properties of a small blood inclusion during coagulation. This
approach may be applicable in vivo.
Dynamic
Macro-Elastography Sonix
RP ultrasonic scanner (Ultrasonix Medical Corporation, Dynamic
Micro-Elastography VisualSonics
scanner Vevo 770 (VisualSonics Inc.,
A. Hadj Henni, C. Schmitt and G. Cloutier, “Shear
wave induced resonance for dynamic elastography and material characterization”,
United States Provisional Patent L80004902US, July 30, 2008. A. Hadj Henni, C. Schmitt and G. Cloutier, “3D transient and
harmonic shear-wave scattering by a soft cylinder for dynamic vascular
elastography”, J. Acoust. Soc. Am. (October 2008) (in press). A. Hadj Henni, C. Schmitt and G. Cloutier, “Shear
Wave Induced Resonance: a new excitation mode for dynamic elastography
imaging”, IEEE Ultrasonics Symposium, 2-5 November 2008, C. Schmitt, A. Hadj Henni and G. Cloutier, “Dynamic Micro-Elastography (DME) applied to
viscoelastic characterization of mimicking carotid arteries”,
IEEE Ultrasonics Symposium, 2-5 November 2008, C. Schmitt, A. Hadj Henni and G. Cloutier, “Viscoelastic characterization of soft
tissues by dynamic micro-elastography (DME) in the frequency range of 300 Hz
-1500 Hz”, IEEE Ultrasonics Symposium, 2-5 November 2008,
Beijing, China. A.
Hadj Henni, C. Schmitt and G. Cloutier, “Analytical modeling of plane
shear wave diffraction by a radially layered cylinder for dynamic vascular
elastography”, IEEE Ultrasonics Symposium, 28-31 October 2007, New
York, USA. C.
Schmitt, A. Hadj Henni and G. Cloutier, “Characterization of
time-varying mechanical viscoelastic parameters of mimicking deep vein
thrombi with 2D dynamic elastography”, IEEE Ultrasonics Symposium,
28-31 October 2007, E.
Montagnon, A. Hadj Henni, C. Schmitt and G. Cloutier, “Shear-wave
induced resonance elastography (SWIRE) of elliptical mechanical
heterogeneities”, International Conference on the Ultrasonic
Measurement and Imaging of Tissue Elasticity, 27-30 October 2008, Austin,
USA. A. Hadj Henni, C. Schmitt and G. Cloutier, “3D Analytical modeling of transient and harmonic plane
shear wave diffraction by a soft cylinder for dynamic vascular elastography ”, International Conference on the Ultrasonic
Measurement and Imaging of Tissue Elasticity, 2-5 November 2007, Santa Fe,
USA.
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