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Samp MA, Iovanac NC, Nolte AJ. Sodium Alginate Toughening of Gelatin Hydrogels. ACS Biomater Sci Eng 2017; 3:3176-3182. [DOI: 10.1021/acsbiomaterials.7b00321] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael A. Samp
- Department of Chemical Engineering, Rose-Hulman Institute of Technology, 5500 Wabash Avenue, Terre
Haute, Indiana 47803, United States
| | - Nicolae C. Iovanac
- Department of Chemical Engineering, Rose-Hulman Institute of Technology, 5500 Wabash Avenue, Terre
Haute, Indiana 47803, United States
| | - Adam J. Nolte
- Department of Chemical Engineering, Rose-Hulman Institute of Technology, 5500 Wabash Avenue, Terre
Haute, Indiana 47803, United States
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2
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Zhang HM, Wang Y, Fatemi M, Insana MF. Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters. MEASUREMENT SCIENCE & TECHNOLOGY 2017; 28:035703. [PMID: 28239236 PMCID: PMC5319561 DOI: 10.1088/1361-6501/aa5531] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques - ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material's fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, EA . The slope of EA versus η is determined by α and the applied indentation ramp time Tr. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η - EA relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties.
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Affiliation(s)
- Hong Mei Zhang
- Key Laboratory of Biomedical Information Engineering, Ministry of Education, School of Life Science and Technology, Xi'an JiaoTong University, Xianning West Road No.28, Xi'an, Shaanxi, 710049, P. R. China; Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA
| | - Yue Wang
- Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA
| | - Mostafa Fatemi
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, USA
| | - Michael F Insana
- Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA
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3
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Abstract
Viscoelasticity Imaging (VEI) has been proposed to measure relaxation time constants for characterization of in vivo breast lesions. In this technique, an external compression force on the tissue being imaged is maintained for a fixed period of time to induce strain creep. A sequence of ultrasound echo signals is then utilized to generate time-resolved strain measurements. Relaxation time constants can be obtained by fitting local time-resolved strain measurements to a viscoelastic tissue model (e.g., a modified Kevin-Voigt model). In this study, our primary objective is to quantitatively evaluate the contrast transfer efficiency (CTE) of VEI, which contains useful information regarding image interpretations. Using an open-source simulator for virtual breast quasi-static elastography (VBQE), we conducted a case study of contrast transfer efficiency of VEI. In multiple three-dimensional (3D) numerical breast phantoms containing various degrees of heterogeneity, finite element (FE) simulations in conjunction with quasi-linear viscoelastic constitutive tissue models were performed to mimic data acquisition of VEI under freehand scanning. Our results suggested that there were losses in CTE, and the losses could be as high as -18 dB. FE results also qualitatively corroborated clinical observations, for example, artifacts around tissue interfaces.
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Affiliation(s)
- David Rosen
- 1 Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
| | - Yu Wang
- 1 Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
| | - Jingfeng Jiang
- 1 Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
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4
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Galaz BA, Acevedo RH. Optimization of a Pixel-to-Pixel Curve-Fitting Method for Poroelastography Imaging. ULTRASOUND IN MEDICINE & BIOLOGY 2017; 43:309-322. [PMID: 27765386 DOI: 10.1016/j.ultrasmedbio.2016.09.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2016] [Revised: 08/31/2016] [Accepted: 09/06/2016] [Indexed: 06/06/2023]
Abstract
Ultrasound poroelastography is an imaging modality used to characterize the temporal behavior of soft tissue that can be modeled as a solid permeated by interconnected pores filled with liquid (poroelastic medium). It could be useful in the stage classification of lymphedema. Generally, time-constant models are applied to strain images, and precision of the fitting process, computational cost and versatility in response to changes in tissues properties are crucial aspects of clinical applications. In the work described here, we performed creep experiments on poroelastic phantoms and used rheologic models to visualize the changes in viscoelastic response associated with fluid mobility. We used the Levenberg-Marquardt algorithm as a fitting tool and performed parametric studies to improve its performance. On the basis of these studies, we proposed an optimization schema for the pixel-to-pixel curve-fitting process. We determined that the bimodal Kelvin-Voigt model describes efficiently the temporal evolution of the strain images in heterogeneous phantoms.
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5
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Altahhan KN, Wang Y, Sobh N, Insana MF. Indentation Measurements to Validate Dynamic Elasticity Imaging Methods. ULTRASONIC IMAGING 2016; 38:332-345. [PMID: 26376923 DOI: 10.1177/0161734615605046] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We describe macro-indentation techniques for estimating the elastic modulus of soft hydrogels. Our study describes (a) conditions under which quasi-static indentation can validate dynamic shear-wave imaging estimates and (b) how each of these techniques uniquely biases modulus estimates as they couple to the sample geometry. Harmonic shear waves between 25 and 400 Hz were imaged using ultrasonic Doppler and optical coherence tomography methods to estimate shear dispersion. From the shear-wave speed of sound, average elastic moduli of homogeneous samples were estimated. These results are compared directly with macroscopic indentation measurements measured two ways. One set of measurements applied Hertzian theory to the loading phase of the force-displacement curves using samples treated to minimize surface adhesion forces. A second set of measurements applied Johnson-Kendall-Roberts theory to the unloading phase of the force-displacement curve when surface adhesions were significant. All measurements were made using gelatin hydrogel samples of different sizes and concentrations. Agreement within 5% among elastic modulus estimates was achieved for a range of experimental conditions. Consequently, a simple quasi-static indentation measurement using a common gel can provide elastic modulus measurements that help validate dynamic shear-wave imaging estimates.
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Affiliation(s)
- Khaldoon N Altahhan
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Yue Wang
- Department of Bioengineering, Beckman Institute of Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Nahil Sobh
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Michael F Insana
- Department of Bioengineering, Beckman Institute of Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA
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6
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Urban MW, Nenadic IZ, Qiang B, Bernal M, Chen S, Greenleaf JF. Characterization of material properties of soft solid thin layers with acoustic radiation force and wave propagation. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 138:2499-2507. [PMID: 26520332 PMCID: PMC4627930 DOI: 10.1121/1.4932170] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2015] [Revised: 08/26/2015] [Accepted: 09/21/2015] [Indexed: 06/05/2023]
Abstract
Evaluation of tissue engineering constructs is performed by a series of different tests. In many cases it is important to match the mechanical properties of these constructs to those of native tissues. However, many mechanical testing methods are destructive in nature which increases cost for evaluation because of the need for additional samples reserved for these assessments. A wave propagation method is proposed for characterizing the shear elasticity of thin layers bounded by a rigid substrate and fluid-loading, similar to the configuration for many tissue engineering applications. An analytic wave propagation model was derived for this configuration and compared against finite element model simulations and numerical solutions from the software package Disperse. The results from the different models found very good agreement. Experiments were performed in tissue-mimicking gelatin phantoms with thicknesses of 1 and 4 mm and found that the wave propagation method could resolve the shear modulus with very good accuracy, no more than 4.10% error. This method could be used in tissue engineering applications to monitor tissue engineering construct maturation with a nondestructive wave propagation method to evaluate the shear modulus of a material.
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Affiliation(s)
- Matthew W Urban
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55902, USA
| | - Ivan Z Nenadic
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55902, USA
| | - Bo Qiang
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55902, USA
| | - Miguel Bernal
- Cardiovascular Dynamics Research Group, Universidad Pontificia Bolivariana, Medellin, Colombia
| | - Shigao Chen
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55902, USA
| | - James F Greenleaf
- Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55902, USA
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7
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Manickam K, Machireddy RR, Seshadri S. Characterization of biomechanical properties of agar based tissue mimicking phantoms for ultrasound stiffness imaging techniques. J Mech Behav Biomed Mater 2014; 35:132-43. [PMID: 24769915 DOI: 10.1016/j.jmbbm.2014.03.017] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2013] [Revised: 03/22/2014] [Accepted: 03/25/2014] [Indexed: 11/24/2022]
Abstract
Pathological changes of the body have been observed to change the mechanical properties of soft tissue types which can be imaged by ultrasound elastography. Though initial clinical results using ultrasound elastography in detection of tumors are promising, quantification of signal to noise ratio, resolution and strain image patterns are the best achieved under a controlled study using phantoms with similar biomechanical properties of normal and abnormal tissues. The purpose of this work is to characterize the biomechanical properties of agar based tissue mimicking phantoms by varying the agar concentration from 1.7 to 6.6% by weight and identify the optimum property to be used in classification of cancerous tissues. We performed quasi-static uniaxial compression test under a strain rate of 0.5mm/min up to 15% strain and measured Young's modulus of phantom samples which are from 50kPa to 450kPa. Phantoms show nonlinear stress-strain characteristics at finite strain which were characterized using hyperelastic parameters by fitting Neo-Hookean, Mooney Rivlin, Ogden and Veronda Westmann models. We also investigated viscoelastic parameters of the samples by conducting oscillatory shear rheometry at various precompression levels (2-5%). Loss modulus values are always less than storage modulus which represents the behavior of soft tissues. The increase in agar concentration increases the shear modulus of the samples as well as decreases the linear viscoelastic region. The results suggest that dynamic shear modul are more promising than linear and nonlinear elastic modul in differentiation of various classes of abnormal tissues.
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Affiliation(s)
- Kavitha Manickam
- Biomedical Engineering Group, Department of Applied Mechanics, IIT Madras, Chennai 600 036, India.
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8
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Abstract
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
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Affiliation(s)
- M M Doyley
- University of Rochester, Department of Electrical and Computer Engineering, Hopeman Engineering Building 413, Box 270126, Rochester, NY 14627, USA.
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9
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Abstract
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
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Affiliation(s)
- M M Doyley
- University of Rochester, Department of Electrical and Computer Engineering, Hopeman Engineering Building 413, Box 270126, Rochester, NY 14627, USA.
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10
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Sun C, Standish B, Yang VXD. Optical coherence elastography: current status and future applications. JOURNAL OF BIOMEDICAL OPTICS 2011; 16:043001. [PMID: 21529067 DOI: 10.1117/1.3560294] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Optical coherence tomography (OCT) has several advantages over other imaging modalities, such as angiography and ultrasound, due to its inherently high in vivo resolution, which allows for the identification of morphological tissue structures. Optical coherence elastography (OCE) benefits from the superior spatial resolution of OCT and has promising applications, including cancer diagnosis and the detailed characterization of arterial wall biomechanics, both of which are based on the elastic properties of the tissue under investigation. We present OCE principles based on techniques associated with static and dynamic tissue excitation, and their corresponding elastogram image-reconstruction algorithms are reviewed. OCE techniques, including the development of intravascular- or catheter-based OCE, are in their early stages of development but show great promise for surgical oncology or intravascular cardiology applications.
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Affiliation(s)
- Cuiru Sun
- Department of Electrical and Computer Engineering, Biophotonics and Bioengineering Laboratory, Ryerson University, Toronto, Ontario M5B 2K3, Canada
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11
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Perreard IM, Pattison AJ, Doyley M, McGarry MDJ, Barani Z, Van Houten EE, Weaver JB, Paulsen KD. Effects of frequency- and direction-dependent elastic materials on linearly elastic MRE image reconstructions. Phys Med Biol 2010; 55:6801-15. [PMID: 21030746 DOI: 10.1088/0031-9155/55/22/013] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
The mechanical model commonly used in magnetic resonance elastography (MRE) is linear elasticity. However, soft tissue may exhibit frequency- and direction-dependent (FDD) shear moduli in response to an induced excitation causing a purely linear elastic model to provide an inaccurate image reconstruction of its mechanical properties. The goal of this study was to characterize the effects of reconstructing FDD data using a linear elastic inversion (LEI) algorithm. Linear and FDD phantoms were manufactured and LEI images were obtained from time-harmonic MRE acquisitions with variations in frequency and driving signal amplitude. LEI responses to artificially imposed uniform phase shifts in the displacement data from both purely linear elastic and FDD phantoms were also evaluated. Of the variety of FDD phantoms considered, LEI appeared to tolerate viscoelastic data-model mismatch better than deviations caused by poroelastic and anisotropic mechanical properties in terms of visual image contrast. However, the estimated shear modulus values were substantially incorrect relative to independent mechanical measurements even in the successful viscoelastic cases and the variations in mean values with changes in experimental conditions associated with uniform phase shifts, driving signal frequency and amplitude were unpredictable. Overall, use of LEI to reconstruct data acquired in phantoms with FDD material properties provided biased results under the best conditions and significant artifacts in the worst cases. These findings suggest that the success with which LEI is applied to MRE data in tissue will depend on the underlying mechanical characteristics of the tissues and/or organs systems of clinical interest.
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Affiliation(s)
- I M Perreard
- Department of Radiology, Dartmouth-Hitchcock Medical Center, One Medical Center Drive, Lebanon, NH 03756, USA
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12
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Crecea V, Oldenburg AL, Liang X, Ralston TS, Boppart SA. Magnetomotive nanoparticle transducers for optical rheology of viscoelastic materials. OPTICS EXPRESS 2009; 17:23114-22. [PMID: 20052238 PMCID: PMC2883324 DOI: 10.1364/oe.17.023114] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
The availability of a real-time non-destructive modality to interrogate the mechanical properties of viscoelastic materials would facilitate many new investigations. We introduce a new optical method for measuring elastic properties of samples which employs magnetite nanoparticles as perturbative agents. Magnetic nanoparticles distributed in silicone-based samples are displaced upon probing with a small external magnetic field gradient and depth-resolved optical coherence phase shifts allow for the tracking of scatterers in the sample with nanometer-scale sensitivity. The scatterers undergo underdamped oscillations when the magnetic field is applied step-wise, allowing for the measurement of the natural frequencies of oscillation of the samples. Validation of the measurements is accomplished using a commercial indentation apparatus to determine the elastic moduli of the samples. This real-time non-destructive technique constitutes a novel way of probing the natural frequencies of viscoelastic materials in which magnetic nanoparticles can be introduced.
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Affiliation(s)
- Vasilica Crecea
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801, USA
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA
| | - Amy L. Oldenburg
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1406 W. Green St., Urbana, IL 61801, USA
| | - Xing Liang
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1406 W. Green St., Urbana, IL 61801, USA
| | - Tyler S. Ralston
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1406 W. Green St., Urbana, IL 61801, USA
| | - Stephen A. Boppart
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1406 W. Green St., Urbana, IL 61801, USA
- Department of Bioengineering, University of Illinois at Urbana-Champaign, 1304 West Springfield Avenue, Urbana, IL 61801, USA
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13
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Kalyanam S, Yapp RD, Insana MF. Poro-Viscoelastic Behavior of Gelatin Hydrogels Under Compression-Implications for Bioelasticity Imaging. J Biomech Eng 2009; 131:081005. [DOI: 10.1115/1.3127250] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Ultrasonic elasticity imaging enables visualization of soft tissue deformation for medical diagnosis. Our aim is to understand the role of flow-dependent and flow-independent viscoelastic mechanisms in the response of biphasic polymeric media, including biological tissues and hydrogels, to low-frequency forces. Combining the results of confined and unconfined compression experiments on gelatin hydrogels with finite element analysis (FEA) simulations of the experiments, we explore the role of polymer structure, loading, and boundary conditions in generating contrast for viscoelastic features. Feature estimation is based on comparisons between the biphasic poro-elastic and biphasic poro-viscoelastic (BPVE) material models, where the latter adds the viscoelastic response of the solid polymer matrix. The approach is to develop a consistent FEA material model (BPVE) from confined compression-stress relaxation measurements to extract the strain dependent hydraulic permeability variation and cone-plate rheometer measurements to obtain the flow-independent viscoelastic constants for the solid-matrix phase. The model is then applied to simulate the unconfined compression experiment to explore the mechanics of hydropolymers under conditions of quasi-static elasticity imaging. The spatiotemporal distributions of fluid and solid-matrix behavior within the hydrogel are studied to propose explanations for strain patterns that arise during the elasticity imaging of heterogeneous media.
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Affiliation(s)
- Sureshkumar Kalyanam
- Beckman Institute for Advanced Science & Technology, Department of Bioengineering, University of Illinois at Urbana-Champaign Urbana, IL 61801
| | - Rebecca D. Yapp
- Beckman Institute for Advanced Science & Technology, Department of Bioengineering, University of Illinois at Urbana-Champaign Urbana, IL 61801
| | - Michael F. Insana
- Beckman Institute for Advanced Science & Technology, Department of Bioengineering, University of Illinois at Urbana-Champaign Urbana, IL 61801
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14
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Orescanin M, Toohey KS, Insana MF. Material properties from acoustic radiation force step response. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 125:2928-36. [PMID: 19425636 PMCID: PMC2736740 DOI: 10.1121/1.3106129] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
An ultrasonic technique for estimating viscoelastic properties of hydrogels, including engineered biological tissues, is being developed. An acoustic radiation force is applied to deform the gel locally while Doppler pulses track the induced movement. The system efficiently couples radiation force to the medium through an embedded scattering sphere. A single-element, spherically-focused, circular piston element transmits a continuous-wave burst to suddenly apply and remove a radiation force to the sphere. Simultaneously, a linear array and spectral Doppler technique are applied to track the position of the sphere over time. The complex shear modulus of the gel was estimated by applying a harmonic oscillator model to measurements of time-varying sphere displacement. Assuming that the stress-strain response of the surrounding gel is linear, this model yields an impulse response function for the gel system that may be used to estimate material properties for other load functions. The method is designed to explore the force-frequency landscape of cell-matrix viscoelasticity. Reported measurements of the shear modulus of gelatin gels at two concentrations are in close agreement with independent rheometer measurements of the same gels. Accurate modulus measurements require that the rate of Doppler-pulse transmission be matched to a priori estimates of gel properties.
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Affiliation(s)
- Marko Orescanin
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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15
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Coussot C, Kalyanam S, Yapp R, Insana MF. Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2009; 56:715-726. [PMID: 19406700 PMCID: PMC2704493 DOI: 10.1109/tuffc.2009.1094] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The viscoelastic response of hydropolymers, which include glandular breast tissues, may be accurately characterized for some applications with as few as 3 rheological parameters by applying the Kelvin-Voigt fractional derivative (KVFD) modeling approach. We describe a technique for ultrasonic imaging of KVFD parameters in media undergoing unconfined, quasi-static, uniaxial compression. We analyze the KVFD parameter values in simulated and experimental echo data acquired from phantoms and show that the KVFD parameters may concisely characterize the viscoelastic properties of hydropolymers. We then interpret the KVFD parameter values for normal and cancerous breast tissues and hypothesize that this modeling approach may ultimately be applied to tumor differentiation.
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Affiliation(s)
- Cecile Coussot
- Department of Bioengineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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16
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Abstract
Understanding contrast mechanisms and identifying discriminating features is at the heart of diagnostic imaging development. This paper focuses on how pH influences the viscoelastic properties of biopolymers to better understand the effects of extracellular pH on breast tumour elasticity imaging. Extracellular pH is known to decrease as much as 1 pH unit in breast tumours, thus creating a dangerous environment that increases cellular mutation rates and therapeutic resistance. We used a gelatin hydrogel phantom to isolate the effects of pH on a polymer network with similarities to the extracellular matrix in breast stroma. Using compressive unconfined creep and stress relaxation measurements, we systematically measured the viscoelastic features sensitive to pH by way of time-domain models and complex modulus analysis. These results are used to determine the sensitivity of quasi-static ultrasonic elasticity imaging to pH. We found a strong elastic response of the polymer network to pH, such that the matrix stiffness decreases as pH was reduced; however, the viscous response of the medium to pH was negligible. While physiological features of breast stroma such as proteoglycans and vascular networks are not included in our hydrogel model, observations in this study provide insight into viscoelastic features specific to pH changes in the collagenous stromal network. These observations suggest that the large contrast common in breast tumours with desmoplasia may be reduced under acidic conditions, and that viscoelastic features are unlikely to improve discriminability.
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Affiliation(s)
- R D Yapp
- Department of Bioengineering, University of Illinois, Urbana-Champaign, IL 61801, USA.
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17
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Abstract
In vivo measurements of the viscoelastic properties of breast tissue are described. Ultrasonic echo frames were recorded from volunteers at 5 fps while applying a uniaxial compressive force (1-20 N) within a 1 s ramp time and holding the force constant for up to 200 s. A time series of strain images was formed from the echo data, spatially averaged viscous creep curves were computed, and viscoelastic strain parameters were estimated by fitting creep curves to a second-order Voigt model. The useful strain bandwidth from this quasi-static ramp stimulus was 10(-2) < or = omega < or = 10(0) rad/s (0.0016-0.16 Hz). The stress-strain curves for normal glandular tissues are linear when the surface force applied is between 2 and 5 N. In this range, the creep response was characteristic of biphasic viscoelastic polymers, settling to a constant strain (arrheodictic) after 100 s. The average model-based retardance time constants for the viscoelastic response were 3.2 +/- 0.8 and 42.0 +/- 28 s. Also, the viscoelastic strain amplitude was approximately equal to that of the elastic strain. Above 5 N of applied force, however, the response of glandular tissue became increasingly nonlinear and rheodictic, i.e., tissue creep never reached a plateau. Contrasting in vivo breast measurements with those in gelatin hydrogels, preliminary ideas regarding the mechanisms for viscoelastic contrast are emerging.
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Affiliation(s)
- Mallika Sridhar
- Department of Biomedical Engineering, University of California, One Shields Avenue, Davis, California 95616, USA
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18
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Righetti R, Righetti M, Ophir J, Krouskop TA. The feasibility of estimating and imaging the mechanical behavior of poroelastic materials using axial strain elastography. Phys Med Biol 2007; 52:3241-59. [PMID: 17505100 DOI: 10.1088/0031-9155/52/11/020] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In this paper, we have investigated the feasibility of imaging the mechanical behavior of poroelastic materials using axial strain elastography. Cylindrical samples obtained from poroelastic materials having different elastic and permeability properties were subjected to a constant compression force (a classical creep experiment), during which poroelastographic data were acquired. For comparison, we also tested a few gelatin phantoms and non-homogeneous poroelastic phantoms constructed by combining different poroelastic materials. From the acquired data, we generated time-dependent sequences of axial strain elastograms and effective Poisson's ratio elastograms, which were then used for generating axial strain and effective Poisson's ratio time-constant elastograms. Thereafter, the various poroelastographic images were analyzed to evaluate the presence of statistically significant differences among the two types of poroelastic samples and for image quality analysis. The results of this study demonstrate that it is technically feasible to use axial strain elastography to distinguish among homogeneous poroelastic materials characterized by different elastic and permeability properties. They also show that the use of axial strain elastography instead of effective Poisson's ratio elastography results in objectively higher quality poroelastograms of the temporal behavior of the poroelastic materials under loading. However, the use of effective Poisson's ratio elastography may in any case be required to verify that the temporal changes occurring in the axial strains of the homogeneous poroelastic samples are also accompanied by temporal changes of the effective Poisson's ratios and are therefore due to poroelastic behavior.
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Affiliation(s)
- Raffaella Righetti
- Ultrasonics Laboratory, Department of Radiology, The University of Texas Medical School, 6431 Fannin St., Houston, TX 77030, USA
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Abstract
Techniques are being developed to image viscoelastic features of soft tissues from time-varying strain. A compress-hold-release stress stimulus commonly used in creep-recovery measurements is applied to samples to form images of elastic strain and strain retardance times. While the intended application is diagnostic breast imaging, results in gelatin hydrogels are presented to demonstrate the techniques. The spatiotemporal behaviour of gelatin is described by linear viscoelastic theory formulated for polymeric solids. Measured creep responses of polymers are frequently modelled as sums of exponentials whose time constants describe the delay or retardation of the full strain response. We found the spectrum of retardation times tau to be continuous and bimodal, where the amplitude at each tau represents the relative number of molecular bonds with a given strength and conformation. Such spectra indicate that the molecular weight of the polymer fibres between bonding points is large. Imaging parameters are found by summarizing these complex spectral distributions at each location in the medium with a second-order Voigt rheological model. This simplification reduces the dimensionality of the data for selecting imaging parameters while preserving essential information on how the creeping deformation describes fluid flow and collagen matrix restructuring in the medium. The focus of this paper is on imaging parameter estimation from ultrasonic echo data, and how jitter from hand-held force applicators used for clinical applications propagate through the imaging chain to generate image noise.
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Affiliation(s)
- M Sridhar
- Department of Biomedical Engineering, University of California, Davis, CA 95616, USA
| | - J Liu
- Department of Bioengineering, University of Illinois, Urbana-Champaign, IL 61801, USA, E-mail:
| | - M F Insana
- Department of Biomedical Engineering, University of California, Davis, CA 95616, USA
- Department of Bioengineering, University of Illinois, Urbana-Champaign, IL 61801, USA, E-mail:
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