Anomalous diffusion of water in biological tissues

Köpf, Manfred; Corinth, C.; Haferkamp, O; Nonnenmacher, T. F.

doi:10.1016/s0006-3495(96)79865-x

Cited by 90 publications

(75 citation statements)

References 22 publications

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“…The molecular motion is assumed independent of the preceding waiting time but dependent on the velocity at the starting point. Generally, as α decreases from the Galilei-invariant Gaussian at α = 1 to the Galilei-variant forms there is an increase in a long displacement tail which is in agreement with the effects on the propagators for the heterogeneous gels observed in this study and has been previously observed for heterogeneous porous media [54,55].…”

Section: Hydrodynamic Dispersion In Porous Mediasupporting

confidence: 92%

Erratum to: Hydrodynamic dispersion in $ \beta$ -lactoglobulin gels measured by PGSE NMR

et al. 2011

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Abstract. The displacement scale dependent molecular dynamics of solvent water molecules flowing through β-lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different pH conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

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Section: Hydrodynamic Dispersion In Porous Mediasupporting

confidence: 92%

Erratum to: Hydrodynamic dispersion in $ \beta$ -lactoglobulin gels measured by PGSE NMR

et al. 2011

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“…It is a common practice to put a Wishart distribution (see definition below) prior, on the concentration matrix in multivariate analysis. Moreover, in the case of a Wishart distribution, a closed form expression for the Laplace transform exists and leads to a Rigaut-type asymptotic fractal law [16] which has been observed in many biological systems [8] (see explanation below).…”

Section: The Mixture Of Wisharts Model and Denoising Kernelmentioning

confidence: 96%

“…The Wishart distribution γ p, Σ is known to have the closed-form Laplace transform: (8) where (ϴ + Σ −1 ) ∈ n . Let f in Eq.…”

Section: Definition 1 [10] For σ ∈ N and For P Inmentioning

confidence: 99%

Feature Preserving Image Smoothing Using a Continuous Mixture of Tensors

Subakan

Jian

Vemuri

et al. 2007

2007 IEEE 11th International Conference on Computer Vision

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Many computer vision and image processing tasks require the preservation of local discontinuities, terminations and bifurcations. Denoising with feature preservation is a challenging task and in this paper, we present a novel technique for preserving complex oriented structures such as junctions and corners present in images. This is achieved in a two stage process namely, (1) All image data are pre-processed to extract local orientation information using a steerable Gabor filter bank. The orientation distribution at each lattice point is then represented by a continuous mixture of Gaussians. The continuous mixture representation can be cast as the Laplace transform of the mixing density over the space of positive definite (covariance) matrices. This mixing density is assumed to be a parameterized distribution, namely, a mixture of Wisharts whose Laplace transform is evaluated in a closed form expression called the Rigaut type function, a scalar-valued function of the parameters of the Wishart distribution. Computation of the weights in the mixture Wisharts is formulated as a sparse deconvolution problem. (2) The feature preserving denoising is then achieved via iterative convolution of the given image data with the Rigaut type function. We present experimental results on noisy data, real 2D images and 3D MRI data acquired from plant roots depicting bifurcating roots. Superior performance of our technique is depicted via comparison to the state-of-the-art anisotropic diffusion filter.

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“…Indeed the time evolution of the concentration and velocity profile predicted by Fick or Darcy is described by exponential-type solution and, several deviations from experimental results have been found in scientific literature regarding fluid flows in biological tissues [4,5] usually referred to long-tails of the diffusion processes as well as through biological membranes [6,7]. The difference among Fick prediction and experimental results have been captured, recently, considering particle transport at nanometric scale by means of molecular dynamics simulations [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%