## 2Key Lab for Health Informatics of the Chinese Academy of Sciences,

### Citations

550 |
Finite Element Procedures in Engineering Analysis
- Bathe
- 1982
(Show Context)
Citation Context ...s adopted to describe the mechanical behaviour of the tissue in quasi-static elastography for the computational simplicity, and the relationship of the stress σ and the strain obeys the Hooke’s law =-=[25]-=-: σ = S (1) where S is the strain-stress matrix. Let u(x, y) and v(x, y) be the displacement along the x- and y-axis of a point, the infinitesimal strain tensor of the point is: = ⎡ ⎢⎢⎢⎢⎢⎢⎣ ∂u ∂x ∂... |

65 |
Ponnekanti H, Yazdi Y, Li X. Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason Imaging
- Ophir, Cespedes
- 1991
(Show Context)
Citation Context ...d through the Kalman filter in the minimum mean square error (MMSE) sense. Introduction A tumour or a suspicious pathological growth is normally much stiffer than the background of normal soft tissue =-=[1]-=-. So when a mechanical compression or vibration is applied, the tumour deforms less than the surrounding tissue, i.e. the strain in the tumour is less than the surrounding tissue. Hence a strain image... |

51 |
Random field finite elements
- Liu, Belytschko, et al.
- 1986
(Show Context)
Citation Context ... various nature. It is thus necessary to develop a strategy, the stochastic finite element method (SFEM), which has been used widely for structural dynamic analysis in probability analysis frameworks =-=[28,29]-=-. In SFEM, structural material properties are described by random fields, possibly with known prior statistics. In our implementation, a Delaunay triangulated finite element mesh is constructed at the... |

36 | Dense non-rigid motion estimation in sequences of 3D images using differential constraints,
- Benayoum, Nastar, et al.
- 1995
(Show Context)
Citation Context ...ochastic finite elementmethod In the past decades, the deterministic finite element method has been able to provide an effective and convenient platform for bio-mechanical studies in the past decades =-=[26,27]-=-. However, it does not have the capability to process the uncertainties of material properties, and kinematic observations, i.e. measurements of the displacement. Especially the ultrasound imaging-der... |

19 |
Freehand ultrasound elastography of breast lesions: clinical results. Ultrasound Med Biol 2001
- KM, Krüger, et al.
(Show Context)
Citation Context ...ntation. For example, as one of incompressible materials, the Poisson’s ratio of tissue can be set close to 0.5. The state space representation of Equation (4) becomes ẋ(t) = Acx(t) + BcW (t) + n(t) =-=(8)-=- where n(t) is the process noise and it is white noise (E[n(t)] = 0; E[n(t)n(s)′] = Qn(t)δts, where Qn is the process noise covariance). The system matrices Ac, Bc and input forces W (t) are: Ac = [ 0... |

16 |
A constrained modulus reconstruction technique for breast cancer assessment
- Samani, Bishop, et al.
(Show Context)
Citation Context ... Bc = [ 0 0 0 −M−1 ] W (t) = [ 0 R(t) ] An associated measurement equation, which describes the observations y(t) provided by the ultrasonic RF data, can be expressed in the form: y(t) = Hx(t) + e(t) =-=(9)-=- where e(t) is the measurement noise and it is white noise (E[e(t)]= 0;E[e(t)e(s)′]= Re(t)δts, and Re is the measurement noise covariance), independent of n(t). H is the measurement matrix which shoul... |

16 |
Control Theory
- Glad, Ljung
- 2000
(Show Context)
Citation Context ...rement vector y(t). In order to run the dynamic equation (Equation (4)) in computer, it should be transformed into a discrete state-space equation, typically seen in control and estimation literature =-=[30,31]-=-. We discretize Equation (8) and (9) over a constant time interval T. Since the interval T is always a known constant, we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), ... |

14 |
The feasibility of elastographic visualization of HIFU-induced thermal lesions in soft tissues,” Ultrasound Med
- Kallel, Stafford, et al.
- 1999
(Show Context)
Citation Context ...asurement noise. In order to evaluate the performance quantitatively, we define the following two factors, the lateral displacement relative error (DRE) and contrast-to-noise ratio (CNR): DRE = ē d̄ =-=(14)-=- CNR = √ 2(s̄b − s̄t)2 σ 2b + σ 2t (15) where ē is the average nodal displacement error, d̄ is the average nodal displacement value, s̄t and s̄b are the spatial strain average of the target and backg... |

14 |
Elastography: imaging the elastic properties of soft tissues with ultrasound
- Ophir, Alam, et al.
- 2002
(Show Context)
Citation Context ...romRF signals using different approaches [18]. Numerous techniques have been proposed to solve the reconstruction problem of strain images for quasi-static ultrasound elastography in the last decades =-=[19]-=-, but the estimation of strain images in ultrasound elastography still remains as a challenging researching topic at present because of its ill-posed nature [20]. The general procedure of quasi-static... |

12 |
tochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters
- Shi
- 2003
(Show Context)
Citation Context ...rement vector y(t). In order to run the dynamic equation (Equation (4)) in computer, it should be transformed into a discrete state-space equation, typically seen in control and estimation literature =-=[30,31]-=-. We discretize Equation (8) and (9) over a constant time interval T. Since the interval T is always a known constant, we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), ... |

11 |
An Inverse Problem Solution for Measuring the Elastic Modulus of Intact Ex Vivo Breast Tissue Tumours,” Phys.
- Samani, Plewes
- 2007
(Show Context)
Citation Context ...se. In addition, errors will be introduced when the tissue incompressibility assumption is invalid. The recovery of strain and elasticity of tissue from the sparse displacement is one inverse problem =-=[2,23,24]-=-, therefore, it is necessary to develop a robust framework with a more meaningful bio-mechanical constraint to recover a full displacement field from the ultrasonic measurements. The rest of this pape... |

9 |
A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements
- Sumi, Nakayama
- 1998
(Show Context)
Citation Context ...se. In addition, errors will be introduced when the tissue incompressibility assumption is invalid. The recovery of strain and elasticity of tissue from the sparse displacement is one inverse problem =-=[2,23,24]-=-, therefore, it is necessary to develop a robust framework with a more meaningful bio-mechanical constraint to recover a full displacement field from the ultrasonic measurements. The rest of this pape... |

7 |
Elastographic characterization of HIFU-induced lesions in canine livers. Ultrasound Med Biol
- Righetti, Kallel, et al.
- 1999
(Show Context)
Citation Context ...he performance quantitatively, we define the following two factors, the lateral displacement relative error (DRE) and contrast-to-noise ratio (CNR): DRE = ē d̄ (14) CNR = √ 2(s̄b − s̄t)2 σ 2b + σ 2t =-=(15)-=- where ē is the average nodal displacement error, d̄ is the average nodal displacement value, s̄t and s̄b are the spatial strain average of the target and background, σ 2t and σ 2b are the spatial st... |

6 |
Tanter M , Fink M . Supersonic shear imaging: a new technique for soft tissue elasticity mapping
- Bercoff
(Show Context)
Citation Context ... able to remotely generate mechanical vibration sources radiating low-frequency, shear waves inside tissues, and then reconstruct the viscoelastic properties of tissue from the propagated shear waves =-=[17]-=-. Among different forms of ultrasound elastography, quasi-static ultrasound elastography is one popular technique because of its simplicity: two sets of radio-frequency (RF) echo frames are first coll... |

5 |
Samani A, Sciarretta J: Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography. Phys Med Biol 2000
- Plewes, Bishop
(Show Context)
Citation Context ... ⎡ ⎢⎢⎢⎢⎢⎢⎣ ∂u ∂x ∂v ∂y ∂u ∂y + ∂v ∂x ⎤ ⎥⎥⎥⎥⎥⎥⎦ (2) Under the plane strain condition [25], strain-stress matrix S can be derived as: S = E (1 + ν)(1 − 2ν) ⎡ ⎢⎢⎢⎣ 1 − ν ν 0 ν 1 − ν 0 0 0 1 − 2ν2 ⎤ ⎥⎥⎥⎦ =-=(3)-=- S is a material-dependent matrix, E stands for the Young’s modulus, and ν stands for the Poisson’s ratio. Here, the Young’s modulus E and the Poisson’s ratio ν are two materialspecific parameters. Th... |

5 |
Finet G, Delachartre P, Vray D: Axial strain imaging of intravascular data: results on polyvinyl alcohol cryogel phantoms and carotid artery. Ultrasound Med Biol 2001
- Brusseau, Fromageau
(Show Context)
Citation Context .... We discretize Equation (8) and (9) over a constant time interval T. Since the interval T is always a known constant, we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), =-=(10)-=- where A = eAcT , (11) B = A−1c (eAcT − I)Bc (12) The associated measurement equation can be: y(k) = Dx(k) + e(k) (13) where y(k) is the measurement vector contained the displacement extracted from ul... |

4 |
time tissue elasticity imaging using the combined autocorrelation method
- Shiina, Nitta, et al.
(Show Context)
Citation Context ...deformation caused by external compressions, and then the displacement field, strain field and even the distribution of tissular elasticity are reconstructed fromRF signals using different approaches =-=[18]-=-. Numerous techniques have been proposed to solve the reconstruction problem of strain images for quasi-static ultrasound elastography in the last decades [19], but the estimation of strain images in ... |

3 |
Rouviere O, Gelet A: Visualisation of HIFU lesions using elastography of the human prostate in vivo: preliminary results
- Souchon
(Show Context)
Citation Context ...a state-space representation of the continuous-time linear stochastic system. First the kinematic vector x(k) and the material parameter vector θ are defined as: x(t) = [ U(t) U̇(t) ] (6) θ = [ E ν ] =-=(7)-=- where the kinematic vector x(t) is consisted of displacement U(t) and velocity U̇(t) information, and the material parameter vector θ is consisted of Young’s modulus E and Lu et al. BioMedical Engine... |

3 |
Mastik F, de Korte C: Advancing intravascular ultrasonic palpation toward clinical applications. UltrasoundMed Biol 2001b
- Doyley
(Show Context)
Citation Context ... we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), (10) where A = eAcT , (11) B = A−1c (eAcT − I)Bc (12) The associated measurement equation can be: y(k) = Dx(k) + e(k) =-=(13)-=- where y(k) is the measurement vector contained the displacement extracted from ultrasound RF data. In most quasi-static elastography, only theaxial component of displacement vector is extracted. Ther... |

3 |
Boctor E, Choti M, Hager G: Real-time regularized ultrasound elastography
- Rivaz
(Show Context)
Citation Context ...olution in the axial direction is much higher than that in the lateral direction in ultrasound imaging, that is why the estimation of the axial component of the motion has received the most attention =-=[1,21]-=-. Recently, quite a few approaches have been proposed to recover the lateral and shear strain fields (i.e. reconstruct the strain tensor), Poisson’s ratio and Young’s modulus [21], but their performan... |

3 |
Ying K, Bai J: Elasticity reconstruction for ultrasound elastography using a radial compression: an inverse approach
- Luo
(Show Context)
Citation Context ...se. In addition, errors will be introduced when the tissue incompressibility assumption is invalid. The recovery of strain and elasticity of tissue from the sparse displacement is one inverse problem =-=[2,23,24]-=-, therefore, it is necessary to develop a robust framework with a more meaningful bio-mechanical constraint to recover a full displacement field from the ultrasonic measurements. The rest of this pape... |

3 |
The stochastic finite element method. Comput Struct
- Contreras
- 1980
(Show Context)
Citation Context ... various nature. It is thus necessary to develop a strategy, the stochastic finite element method (SFEM), which has been used widely for structural dynamic analysis in probability analysis frameworks =-=[28,29]-=-. In SFEM, structural material properties are described by random fields, possibly with known prior statistics. In our implementation, a Delaunay triangulated finite element mesh is constructed at the... |

2 |
Mariappan Y, Hubmayr RD, Manduca A, Ansell K, Ehman RL. Calculation of shear stiffness in noise dominated magnetic resonance elastography data based on principal frequency estimation. Phys Med Biol 56: 4291–4309
- KP, Lake
- 2011
(Show Context)
Citation Context ...g that the material parameters E (Young’s modulus) and ν (Poisson’s ratio) are temporally constant but varying spatially, we can have the following dynamic governing equation [25]: MÜ + CU̇ + KU = R =-=(4)-=- where U is the displacement vector, and R is the load vector. Mass matrix M here is a known function of the material density and is temporally and spatially constant. Stiffness matrix K is a function... |

2 |
A new approach to elastography usingmutual information and finite elements
- Miga
(Show Context)
Citation Context ... = b be known from the imaging data at selected sampling nodes of the boundary, then the additional constraining equation μUb = μb is enforced on the system dynamics through MÜ+ CU̇+ KU+ μUb = R+ μb =-=(5)-=- where weighting coefficient μ depends on the confidence of each displacement, with large μ values (1 × 104 in this study) indicating highly trustworthy data points and small μ values for others. In t... |

2 |
der Steen A, Woutman H, Bom N: Characterization of plaque components with intravascular ultrasound elastography in human femoral and coronary arteries in vitro. Circulation 2000
- Korte, Pasterkamp, et al.
(Show Context)
Citation Context ...on (8) and (9) over a constant time interval T. Since the interval T is always a known constant, we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), (10) where A = eAcT , =-=(11)-=- B = A−1c (eAcT − I)Bc (12) The associated measurement equation can be: y(k) = Dx(k) + e(k) (13) where y(k) is the measurement vector contained the displacement extracted from ultrasound RF data. In m... |

2 |
Carlier S, Mastik F:Morphological andmechanical information of coronary arteries obtained with intravascular elastography. Feasibility study in vivo
- Korte
(Show Context)
Citation Context ...ant time interval T. Since the interval T is always a known constant, we can replace kT with k in following equations x(k + 1) = Ax(k) + Bw(k) + n(k), (10) where A = eAcT , (11) B = A−1c (eAcT − I)Bc =-=(12)-=- The associated measurement equation can be: y(k) = Dx(k) + e(k) (13) where y(k) is the measurement vector contained the displacement extracted from ultrasound RF data. In most quasi-static elastograp... |

2 | Techavipoo U, Liu W: Elastographicmeasurement of the area and volume of thermal lesions resulting from radiofrequency ablation: pathologic correlation - Varghese |

2 |
Z: Comparative elvaluation of strain-based andmodel-based modulus elastography. Ultrasound Med Biol 2005
- Doyley, Srinivasan, et al.
(Show Context)
Citation Context ...sound elastography in the last decades [19], but the estimation of strain images in ultrasound elastography still remains as a challenging researching topic at present because of its ill-posed nature =-=[20]-=-. The general procedure of quasi-static elastography is first to recover internal tissue displacements from two ultrasound radio-frequency (RF) frames before and after tissue deformation due to a quas... |

2 |
An experimental method for evaluating constitutive models of myocardium in in vivo hearts
- LL, MJ, et al.
- 1994
(Show Context)
Citation Context ...ochastic finite elementmethod In the past decades, the deterministic finite element method has been able to provide an effective and convenient platform for bio-mechanical studies in the past decades =-=[26,27]-=-. However, it does not have the capability to process the uncertainties of material properties, and kinematic observations, i.e. measurements of the displacement. Especially the ultrasound imaging-der... |

1 |
Ophir J: Elastography of breast leisons: initial clinical results. Radiology
- Garra, Cespedes
- 1997
(Show Context)
Citation Context ...ransformed into a state-space representation of the continuous-time linear stochastic system. First the kinematic vector x(k) and the material parameter vector θ are defined as: x(t) = [ U(t) U̇(t) ] =-=(6)-=- θ = [ E ν ] (7) where the kinematic vector x(t) is consisted of displacement U(t) and velocity U̇(t) information, and the material parameter vector θ is consisted of Young’s modulus E and Lu et al. B... |

1 | Raghavan K, Yagle A, Skovoroda A, O’Donnell M: Lateral displacement estimation using tissue incompressibility - Lubinski, Emelianov - 1996 |

1 |
HF: A strain-based ultrasound elastography using phase shift with prior estimates andmeshfree shape function
- JW, HY, et al.
(Show Context)
Citation Context ...ne Elasticity QA Phantom (Model 049, CIRS Inc. USA) using a PC-based Ultrasonix RP ultrasound machine (UltrasonixMedical Corporation, Burnaby, BC, Canada). One phase-shift method with prior estimates =-=[32]-=- is used to estimate the axial displacements from the RF signals, and the full displacement field is recovered from the axial displacement measurements. And then all the strain images are displayed in... |