scispace - formally typeset
Search or ask a question
Proceedings ArticleDOI

4J-3 A New Rheological Model Based on Fractional Derivatives for Biological Tissues

01 Oct 2006-pp 1033-1036
TL;DR: A new rheological model relying on fractional derivatives closer to the viscoelastic properties of in vivo data is introduced and seems to emphasize the necessity to take into account the solid-liquid duality of tissues in the rheology model choice for elastography reconstructions.
Abstract: The intuitive use of viscoelastic properties is routinely done by physicians via the palpation. However, such an examination relies on the physician experience and is not quantitative nor reproducible. Thus, elastography has been developed to complement the palpation by reliable and reproducible measurements. The principle of elastography is to image elastic waves propagation in a medium. To evaluate the shear moduli, Helmholtz transforms are applied to the displacement images. Then the waves movie is interpreted using a rheological model. For instance, the Voigt model explains the observed frequency dependence of the measured shear wave speed. It has been shown to be a reliable model for mimicking tissue phantoms such as gelatin based phantoms. However, we show here that neither this model nor the Maxwell model are applicable to biological tissues using in vivo data (breast) and ex vivo data (liver). Although these simple models are widely used in the elastography community, they have been substituted by more relevant models in the micro-rheology community in order to reveal the solid-liquid duality of tissues. Based on these experimental observations, we introduce a new rheological model relying on fractional derivatives closer to the viscoelastic properties of in vivo data. Indeed, we observed that the dynamic modulus (Gd) and the loss modulus (Gl) have the same frequency behavior: a non-integer frequency power law smaller than 1. This frequency behavior is contradictory with the use of the Voigt model or any kind of simple arrangements of dash pots and springs. In order to explain this frequency behavior the concept of spring pot was introduced. Moreover, we observed that the ratio Gl /Gd is constant and not linked to the non-integer power observed, not predicted by the spring pot model. Thus we build a network of spring pots where the basic element is responsible of the frequency power and the network is responsible of the ratio Gl/Gd . The experiments were conducted on fresh liver samples and phantoms between 50 Hz and 100 Hz. The frequency behavior was analyzed by plotting the real and imaginary parts of the complex shear modulus using MR-elastography as well as 3D ultrasound based elastography. By applying the fractional derivatives model to these data sets, we observed that the frequency power law in the liver was equal to 0.75 (a liquid-like behavior), while the ratio parameter of the network was equal to 0.15 (a solid-like behavior). The dispersion curves of Gd and Gl obtained through this model correlates much better with the experimental observations. The model parameters values seem to emphasize the necessity to take into account the solid-liquid duality of tissues in the rheological model choice for elastography reconstructions
Citations
More filters
Journal ArticleDOI
TL;DR: A model of elastic behavior that is based on the flow of viscous fluids through the extensive network of tissue microchannels in response to applied stress is developed and appears to predict the stress-relaxation behavior and the dispersive shear wave behavior of bovine liver specimens and other soft tissues and phantoms.
Abstract: A number of advances, including imaging of tissue displacements, have increased our ability to make measurements of tissue elastic properties of animal and human tissues. Accordingly, the question is increasingly asked, 'should our data be fit to a viscoelastic model, and if so which one?' In this paper we focus solely on soft tissues in a functional (non-pathological) state, and develop a model of elastic behavior that is based on the flow of viscous fluids through the extensive network of tissue microchannels in response to applied stress. This behavior can be captured in a 2-parameter model, and the model appears to predict the stress-relaxation behavior and the dispersive shear wave behavior of bovine liver specimens and other soft tissues and phantoms. The relationship of the microchannel flow model to more traditional models is also examined.

49 citations


Cites methods from "4J-3 A New Rheological Model Based ..."

  • ...…order integrals and derivatives, and the Kelvin-Voigt Fractional Derivative (KVFD) model has been applied to a number of experimental results from different tissues (Caputo 1967, Bagley and Torvik 1983, Suki et al 1994, Taylor et al 2001, Kiss et al 2004, Robert et al 2006, Zhang et al 2007)....

    [...]

Journal ArticleDOI
TL;DR: Advances in MRE technique, including 3D MRE, automated liver elasticity calculation, improvements in shear wave delivery and patient experience, are promising to provide a faster and more reliable MRE of liver.
Abstract: Non-invasive evaluation of liver fibrosis has evolved over the last couple of decades. Currently, elastography techniques are the most widely used non-invasive methods for clinical evaluation of chronic liver disease (CLD). MR elastography (MRE) of the liver has been used in the clinical practice for nearly a decade and continues to be widely accepted for detection and staging of liver fibrosis. With MRE, one can directly visualize propagating shear waves through the liver and an inversion algorithm in the scanner automatically converts the shear wave properties into an elastogram (stiffness map) on which liver stiffness can be calculated. The commonly used MRE method, two-dimensional gradient recalled echo (2D-GRE) sequence has produced excellent results in the evaluation of liver fibrosis in CLD from various etiologies and newer clinical indications continue to emerge. Advances in MRE technique, including 3D MRE, automated liver elasticity calculation, improvements in shear wave delivery and patient experience, are promising to provide a faster and more reliable MRE of liver. Innovations, including evaluation of mechanical parameters, such as loss modulus, displacement, and volumetric strain, are promising for comprehensive evaluation of CLD as well as understanding pathophysiology, and in differentiating various etiologies of CLD. In this review, the current status of the MRE of liver in CLD are outlined and followed by a brief description of advanced techniques and innovations in MRE of liver.

42 citations

Journal ArticleDOI
TL;DR: This commentary compares MR and ultrasound elastography methods and their utility in clinical practice and indicates that MRElastography has a higher diagnostic performance and fewer technical failures than ultrasound-based elastographic techniques in assessing hepatic fibrosis.
Abstract: Liver stiffness is now a well-established noninvasive biomarker for assessing fibrosis in chronic liver disease. MRI-based and ultrasound-based dynamic elastography techniques have been introduced for assessment of liver stiffness and useful in clinical staging of hepatic fibrosis. Several different elastography techniques are now available with each method having inherent strengths and limitations. The published literature generally indicates that MR elastography has a higher diagnostic performance and fewer technical failures than ultrasound-based elastography techniques in assessing hepatic fibrosis. There is also significant potential to further develop elastography techniques to implement multiparametric methods that have promise for distinguishing between processes such as inflammation, fibrosis, venous congestion, and portal hypertension that can result in increased liver stiffness. In this commentary, we compare MR and ultrasound elastography methods and their utility in clinical practice.

31 citations

Journal ArticleDOI
TL;DR: It is shown that in some cases the maximum time constant of the microchannel flow model could be altered in a way that has major impact on the observed tissue response, which could explain why an inflamed region is palpated as a harder bump compared to surrounding normal tissue.
Abstract: Recent advances have enabled a new wave of biomechanics measurements, and have renewed interest in selecting appropriate rheological models for soft tissues such as the liver, thyroid, and prostate. The microchannel flow model was recently introduced to describe the linear response of tissue to stimuli such as stress relaxation or shear wave propagation. This model postulates a power law relaxation spectrum that results from a branching distribution of vessels and channels in normal soft tissue such as liver. In this work, the derivation is extended to determine the explicit link between the distribution of vessels and the relaxation spectrum. In addition, liver tissue is modified by temperature or salinity, and the resulting changes in tissue responses (by factors of 1.5 or greater) are reasonably predicted from the microchannel flow model, simply by considering the changes in fluid flow through the modified samples. The 2 and 4 parameter versions of the model are considered, and it is shown that in some cases the maximum time constant (corresponding to the minimum vessel diameters), could be altered in a way that has major impact on the observed tissue response. This could explain why an inflamed region is palpated as a harder bump compared to surrounding normal tissue.

28 citations


Cites background from "4J-3 A New Rheological Model Based ..."

  • ...…1981a), the power law and fractional derivative models (Caputo 1967, Bagley and Torvik 1983, Suki et al 1994, Taylor et al 2001, Kiss et al 2004, Robert et al 2006, Zhang et al 2007, Holm et al 2013, Holm and Nasholm 2014), poroelastic models (Biot 1941, 1962, Mow et al 1980, 1984, Mak 1986,…...

    [...]

Journal ArticleDOI
TL;DR: A pilot study measuring in vivo mechanical-property characteristics of rodent mammary tumors using an ultrasonic shear-wave imaging technique to relate soft-tissue mechanical behavior to biological characteristics of tumor structures, specifically the collagenous ECM protein content.

27 citations


Cites background from "4J-3 A New Rheological Model Based ..."

  • ...The Kelvin–Voigt (K-V) model is the current default, but recent studies suggested a role for other models.(10,11) More complex rheological models often require a larger number of tissue parameters to fully represent tissue dispersion curves in vivo....

    [...]

References
More filters
Journal ArticleDOI
TL;DR: Initial results of several phantom and excised animal tissue experiments are reported which demonstrate the ability of this technique to quantitatively image strain and elastic modulus distributions with good resolution, sensitivity and with diminished speckle.

3,636 citations


"4J-3 A New Rheological Model Based ..." refers background in this paper

  • ...Elastography relies on the link between the shear waves propagation and the viscoelastic properties of the probed medium [3]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors established a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to visco-elasticity.
Abstract: This article establishes a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to viscoelasticity. The molecular theory addresses the viscoelastic properties of polymer solids with no crosslinking. It is shown that the results of these molecular theories are equivalent to constitutive relationships written in terms of the fractional calculus. Such relationships, developed previously from an empirical base, have been shown to be useful tools for engineering analyses. The establishment of a theoretical basis for these new constitutive relationships enhances their value, as they may now be used with increased confidence.

1,633 citations


"4J-3 A New Rheological Model Based ..." refers background in this paper

  • ...Although the frequency behavior of Gd and Gl is predicted by the fractional derivative models, the observed ratio is still not predicted by the spring pot model [6] which is the simplest fractional derivative model....

    [...]

  • ...If the data were modelized by a spring pot [6], the ratio Gl/Gl would not be frequency dependant, i....

    [...]

Journal ArticleDOI
TL;DR: Elastography has the potential to be useful in the evaluation of areas of shadowing on the sonogram and also may be helpful in the distinction of benign from malignant masses.
Abstract: PURPOSE: To determine the appearance of various breast lesions on elastograms and to explore the potential of elastography in the diagnosis of breast lesions. MATERIALS AND METHODS: A total of 46 breast lesions were examined with elastography. Patients underwent biopsy or aspiration of all lesions, revealing 15 fibroadenomas, 12 carcinomas, six fibrocystic nodules, and 13 other lesions. The elastogram was generated from radio-frequency data collected with use of a 5-MHz linear-array transducer. The elastogram and corresponding sonogram were evaluated by a single observer for lesion visualization, relative brightness, and margin definition and regularity. The sizes of the lesions at each imaging examination and at biopsy were recorded and compared. RESULTS: Softer tissues such as fat appear as bright areas on elastograms. Firm tissues, including parenchyma, cancers, and other masses, appear darker. The cancers were statistically significantly darker than fibroadenomas (P < .005) and substantially larger on...

980 citations


"4J-3 A New Rheological Model Based ..." refers background in this paper

  • ...During this exam, the physician is detecting stiffer region in the breast which can be linked to tumors (benign or malignant) or cyst [1]....

    [...]

Journal ArticleDOI
TL;DR: Results indicated that the elasticity imaging of the liver may provide significant clinical values if the elastic modulus can be accurately measured, and that severity of fibrosis had a good correlation with stiffness of the Liver.
Abstract: Viral hepatitis causes fibrosis in the liver and may change mechanical properties of the liver. To evaluate the impact of fibrosis on elastic properties of human liver and to investigate potential benefits of ultrasonic elasticity imaging, 19 fresh human liver samples and 1 hepatic tumor (focal nodular hyperplasia) sample obtained during operations were studied. Simple 1-D estimates based on the cyclic compression-relaxation method were performed. Elastic modulus values were derived from the predetermined strain (controlled by a step motor system) and the stress values (measured by an electronic balance). Each specimen subsequently received histologic examination and a grade of liver fibrosis was scored from 0 to 5. Results show that the elastic modulus values were on the order of several hundreds to thousands of Pascals. The elastic modulus generally increased with the fibrosis grade, although some discrepancies existed at the middle grades of fibrosis (scores 1 to 3). The correlation between the fibrosis score and the elastic modulus was significant (p < 0.01) based on the statistical analysis using the Pearson correlation method. In addition, the relation between the elastic modulus and the fibrosis grade generally exhibited a quadratic trend. It was concluded that severity of fibrosis had a good correlation with stiffness of the liver. Results also indicated that the elasticity imaging of the liver may provide significant clinical values if the elastic modulus can be accurately measured. (E-mail: paichi@cc.ee.ntu.edu.tw)

423 citations

Journal ArticleDOI
TL;DR: It is shown that quantitative viscosity mapping is still possible if one uses an appropriate inverse problem that fully takes into account diffraction in solids.
Abstract: Two main questions are at the center of this paper. The first one concerns the choice of a rheological model in the frequency range of transient elastography, sonoelasticity or NMR elastography for soft solids (20-1000 Hz). Transient elastography experiments based on plane shear waves that propagate in an Agar-gelatin phantom or in bovine muscles enable one to quantify their viscoelastic properties. The comparison of these experimental results to the prediction of the two simplest rheological models indicate clearly that Voigt's model is the better. The second question studied in the paper deals with the feasibility of quantitative viscosity mapping using inverse problem algorithm. In the ideal situation where plane shear waves propagate in a sample, a simple inverse problem based on the Helmholtz equation correctly retrieves both elasticity and viscosity. In a more realistic situation with nonplane shear waves, this simple approach fails. Nevertheless, it is shown that quantitative viscosity mapping is still possible if one uses an appropriate inverse problem that fully takes into account diffraction in solids.

371 citations

Related Papers (5)