Forward and inverse problems in elasticity imaging of soft tissues

Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

“…The complexity of the heart physiology -and of the related models -is such that this biophysical personalization procedure cannot be simply performed "manually", such as by directly extracting the required quantities from the available measurements, hence some automated estimation procedures are much needed in this endeavor [40,2,18]. Moreover, as some biophysical parameters are strongly correlated with the functional state of the organ, the automatic estimation of these parameters can be envisioned as a diagnosis tool.…”

Maximum-likelihood approach to strain imaging using ultrasound

“…It has been shown 50,51 that if the dimensions of the support function are large compared to those of the correlation area in r j plus the translation τ a , then the cross power spectral density is (11) If G r 0 r 0 (u) and G r 1 r 1 (u) are the autospectral densities, then the complex coherence and magnitude squared coherence (MSC) functions are, respectively, (12) where 0≤|γ r 0 r 1 (u)| 2 ≤1. 52 Finally, the Fourier transform of a single realization of a scalar random function whose vector coordinates undergo a linear transformation and translation is given by (13) Related results are derived in Appendix A and in Ref.…”

A limitation in the use of spatially stationary strain variance estimation in the regularization of shear modulus reconstruction

“…For shear modulus reconstruction, various reconstruction methods have also been developed [1][2][3][4][5][6] in addition to magnetic resonance (MR)-based techniques [7,8]. The reconstruction methods fall into two approaches, i.e., direct [1][2][3][4]7,8] and iterative [5,6] inversion approaches.…”

“…Accordingly, many researchers including ourselves have been developing strain-or displacement-measurement-based shear modulus reconstruction methods [1][2][3][4][5][6][7][8] and using various ultrasonic (US) strain/displacement measurement methods, e.g., the Doppler method and autocorrelation method [9,10], the cross-correlation method [11][12][13], the sum-squared difference (SSD) method [14], our developed multidimensional cross-spectrum phase gradient method (MCSPGM), i.e., 3-dimensional (3D) or 2D CSPGM [15][16][17], the multidimensional autocorrelaion method (MAM) [18,19] and the multidimensional Doppler method (MDM) [18,19].…”

“…The reconstruction methods fall into two approaches, i.e., direct [1][2][3][4]7,8] and iterative [5,6] inversion approaches. In the iterative inversion approach, a generated displacement field is estimated using an estimate of the shear modulus distribution, and the difference between the measured and estimated displacement fields is minimized by iteratively updating the estimated shear modulus distribution.…”