The application of a fractal model to the scattering of ultrasound in biological media

Javanaud, C.

doi:10.1121/1.398228

Cited by 32 publications

(14 citation statements)

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“…The flow field is generated in the upper compartment between the stationary plate and an upper rotating altuglas plane disk driven by a stepper motor. In the lower compartment filled with water to ensure good ultrasonic coupling, a transmitter-receiver circular 46 The European Physical Journal E transducer (Vermon, France) (incident beam diameter d ≈ 5 mm) is driven by a pulse function generator which sends electrical sinusoidal pulses at a frequency of 8 MHz (resonant frequency of the transducer) and a repetition rate of 200 Hz. The piezoelectric non focused transducer connected to the altuglass plate by an acoustic window emits short ultrasonic bursts (pulsewidth δt = 0.4 µs) in the direction perpendicular to the plane-plane flow device.…”

Section: Rheo-acoustical Methodsmentioning

confidence: 99%

“…In the fractal scattering regime, the scattered power from a collection of large structures (kR 1) becomes sensitive to the fractal dimension of clusters and equation (13) predicts a frequency dependence scaling as ν 4−D . For most of biological media with a long ranged structure such as liver, the frequency dependence of the ultrasound scattered power indeed obeys the power law χ a ≈ ν f with f ≈ 2 [45,46] which indicates a fractal dimension D = 4 − f ≈ 2.…”

Section: Shear Break-up Of Hardened Red Cell Aggregatesmentioning

confidence: 99%

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Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Snabre

Haider²,

Boynard³

2000

The European Physical Journal E - Soft Matter

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Shear break-up of reversible fractal clusters is investigated by ultrasound and multiple light scattering in the low shear regime. We consider a dense suspension of Rayleigh scatterers (particles or clusters) with acoustic properties close to those of the surrounding liquid so that the attenuation of the ultrasonic coherent field is weak and multiple scattering is negligible. The concept of variance in local particle volume fraction is used to derive an original expression of the ultrasound scattering cross-section per unit volume for Rayleigh fractal clusters. On the basis of a scaling law for the shear break-up of aggregates, then we derive the shear stress dependence of the ultrasound scattered intensity from a suspension of reversible fractal clusters. In a second part, we present rheo-acoustical experiments to study the shear breakup of hardened red cell aggregates in plane-plane flow geometry and we examine both the self consistent field approximation and the scaling laws used in microrheological models. We further compare the ability of acoustical backscattering and optical reflectometry techniques to estimate the critical disaggregation shear stress and the particle surface adhesive energy. Finally, the microrheological model from Snabre and Mills [5] based on a fractal approach is shown to describe the non Newtonian behavior of a dense distribution of hardened red cell aggregates. PACS. 42.25.Fx Diffraction and scattering -43.35.+d Ultrasonics, quantum acoustics, and physical effects of sound -43.80.+p Bioacoustics Nomenclature ν frequency (Hz), λ wavelength (m), a particle radius (m), R cluster radius (m), R maximum size of filling space subclusters at rest (m), δz axial resolution of the transducer (m), h gap width between rotating plates (m), z distance between the transducer and the insonified region (m), V particle volume (m 3 ), V a cluster volume (m 3 ), Ω volume of an elemental voxel (m 3 ), n particle number per unit volume (m −3 ), n a cluster number per unit volume (m −3 ), k, s incident and scattered wave number (m −1 ), q scattering wave number (q = s − k) (m −1 ), B cross-sectional area of the ultrasound beam (m 2 ), A c contact area between two particles (m 2 ), A particle area (m 2 ), a e-mail: snabre@imp-odeillo.fr b UPR 8521 du CNRS c phase velocity of the ultrasound wave (m/s), δtpulsewidth (s), ω particle number in a voxel, N particle number in a cluster, N b number of subunits of size 1/q in a cluster, D fractal dimension of a cluster, φ particle volume fraction, φ a cluster volume fraction, φ * maximum packing volume fraction, φ g gelation or percolation threshold, m critical exponent for cluster breakup, γ shear rate (s −1 ), τ shear stress (N/m 2 ), τ c critical disaggregation shear stress (N/m 2 ), τ * critical shear stress for cluster breakup (N/m 2 ), τ o yield stress (N/m 2 ), µ, µ a shear viscosity of the suspension (Ns/m 2 ), µ o shear viscosity of the suspending fluid (Ns/m 2 ), µ r relative shear viscosity of the suspension (µ r = µ a /µ o ), σ, σ α differential scattering...

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Section: Rheo-acoustical Methodsmentioning

confidence: 99%

Section: Shear Break-up Of Hardened Red Cell Aggregatesmentioning

confidence: 99%

Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Snabre

Haider²,

Boynard³

2000

The European Physical Journal E - Soft Matter

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“…Usually, the branching of vessels over several generations has been quantified using the box counting method to determine the fractal dimension. The geometry of the liver circulation in health and disease has also been characterized using fractal analysis [ 6 , 16 , 26 , 55 ]. Here, Fourier analysis is more suitable to undertake to quantify the topography of the sinusoids because they do not undergo repeated branching to successively smaller vessels, but rather are a reticular branching network of vessels of a similar size [ 16 ].…”

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confidence: 99%

Effects of Old Age on Vascular Complexity and Dispersion of the Hepatic Sinusoidal Network

et al. 2008

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Objectives-In old age, there are marked changes in both the structure of the liver sinusoidal endothelial cell and liver perfusion. The objective of this study was to determine whether there are also aging changes in the microvascular architecture and vascular dispersion of the liver that might influence liver function.Methods-Vascular corrosion casts and light micrographs of young (4 mths) and old (24 mths) rat livers were compared. Fractal and Fourier analyses, and microcomputed tomography were used. Vascular dispersion was determined from the dispersion number for sucrose and 100 nm microspheres in impulse response experiments.Results-Age did not affect sinusoidal dimensions, sinusoidal density or dispersion number. There were changes in the geometry and complexity of the sinusoidal network as determined by Fractal dimension and degree of anisotropy.Conclusions-There are small age-related changes in the architecture of the liver sinusoidal network, which may influence hepatic function and reflect broader aging changes in the microcirculation. However sinusoidal dimensions and hepatic vascular dispersion are not markedly influenced by old age.

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“…The blood vessels supplying it are arranged as a fractal tree (43), its cellular network has fractal properties (44), and the perfusion of blood at the terminal branches is heterogeneous (45). Both transient and steady state reactions occurring within such spaces can exhibit anomalous behaviour.…”

Section: Discussionmentioning

confidence: 99%

Fractal Michaelis-Menten Kinetics Under Steady State Conditions: Application to Mibefradil

Marsh

Tuszyński

2006

Pharm Res

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The application of a fractal model to the scattering of ultrasound in biological media

Cited by 32 publications

References 0 publications

Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Effects of Old Age on Vascular Complexity and Dispersion of the Hepatic Sinusoidal Network

Fractal Michaelis-Menten Kinetics Under Steady State Conditions: Application to Mibefradil

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