Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Possible depth-resolved reconstruction of shear moduli in the cornea following collagen crosslinking (CXL) with optical coherence tomography and elastography

Corneal collagen crosslinking (CXL) is commonly used to prevent or treat keratoconus. Although changes in corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic optical coherence elastography (OCE) by tracking mechanical wave propagation, depth dependent changes are still unclear if the cornea is not crosslinked through the whole depth. Here, phase-decorrelation measurements on optical coherence tomography (OCT) structural images are combined with acoustic micro-tapping (A$\mu$T) OCE to explore possible reconstruction of depth-dependent stiffness within crosslinked corneas in an ex vivo human cornea sample. Experimental OCT images are analyzed to define the penetration depth of CXL into the cornea. In a representative ex vivo human cornea sample, crosslinking depth varied from $\sim 100\mu m$ in the periphery to $\sim 150\mu m$ in the cornea center and exhibited a sharp in-depth transition between crosslinked and untreated areas. This information was used in an analytical two-layer guided wave propagation model to quantify the stiffness of the treated layer. We also discuss how the elastic moduli of partially CXL-treated cornea layers reflect the effective engineering stiffness of the entire cornea to properly quantify corneal deformation.Comment: Submitted to Biomedical Optics Express on June 13th 2023, Manuscript ID: 497970 - Under Review. Manuscript, 10 pages / 6 figures / 2 tables. Supplementary, 7 pages / 4 figure

Possible depth-resolved reconstruction of shear moduli in the cornea following collagen crosslinking (CXL) with optical coherence tomography and elastography

Collagen crosslinking of the cornea (CXL) is commonly employed to prevent or treat keratoconus. Although the change of corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic Optical Coherence Elastography (OCE) by tracking mechanical wave propagation, the depth dependence of this change is still unclear if the cornea is not crosslinked through the whole depth. Here we propose to combine phase-decorrelation measurement applied to OCT structural images and acoustic micro-tapping (A$\mu$T) OCE to explore possible depth reconstruction of stiffness within crosslinked corneas in an ex vivo human cornea sample. The analysis of experimental OCT images is used to define the penetration depth of CXL into the cornea, which varies from $\sim$100$\mu m$ in the periphery to $\sim$150$\mu m$ in the central area and exhibits a sharp transition between areas. This information was used in a two-layer analytical model to quantify the stiffness of the treated layer. We also discuss how the elastic moduli of partially CXL-treated cornea layers reconstructed from OCE measurements reflect the effective mechanical stiffness of the entire cornea to properly quantify surgical outcome.Comment: Main: 10 Pages, 6 Figures Supplemental: 12 Pages, 3 Figure

Inverse material identification in coupled acoustic-structure interaction using a modified error in constitutive equation functional

International audienceThis work focuses on the identification of heterogeneous linear elastic moduli in the context of frequency-domain, coupled acoustic-structure interaction (ASI), using either solid displacement or fluid pressure measurement data. The approach postulates the inverse problem as an optimization problem where the solution is obtained by minimizing a modified error in constitutive equation (MECE) functional. The latter measures the discrepancy in the constitutive equations that connect kinematically admissible strains and dynamically admissible stresses, while incorporating the measurement data as additional quadratic error terms. We demonstrate two strategies for selecting the MECE weighting coefficient to produce regularized solutions to the ill-posed identification problem: 1) the discrepancy principle of Morozov, and 2) an error-balance approach that selects the weight parameter as the minimizer of another functional involving the ECE and the data misfit. Numerical results demonstrate that the proposed methodology can successfully recover elastic parameters in 2D and 3D ASI systems from response measurements taken in either the solid or fluid subdomains. Furthermore, both regularization strategies are shown to produce accurate reconstructions when the measurement data is polluted with noise. The discrepancy principle is shown to produce nearly optimal solutions, while the error-balance approach, although not optimal, remains effective and does not need a priori information on the noise level

Numerical Techniques for the Noninvasive Assessment of Material Properties and Stresses in Soft Biomaterials

The noninvasive measurement of finite displacements and strains in biomaterials by magnetic resonance imaging (MRI) may be shown to enable mathematical estimates of stress distributions and material properties within structures of the body such as articular cartilage or the intervertebral disc. Such methods will allow for non-contact and patient-specific modeling in a manner not currently possible with traditional mechanical testing or finite element techniques. Therefore, the objective of this thesis was to develop computational methods incorporating imaging-based measures of deformation, composition, and local microstructure to permit nondestructive analysis of a range of complex biomechanical systems. Finite strain-based models were developed and applied towards the analysis of several biomaterial systems of increasing material complexity. First, a model for the analysis of a homogeneous, single material system was created and applied to juvenile porcine cartilage for both linear and nonlinear material assumptions under plane stress conditions. Through this study, the viability of estimating stresses within a homogeneous material system solely from MRI-based displacement and strain measures could be established. The model was then expanded to encompass single-plane, multi-region structures and applied towards the analysis of regional stresses within a rabbit intervertebral disc degeneration model. This model incorporated imaging-based methods to estimate heterogeneous properties within the disc structure based upon local biochemical composition, and showed that the degeneration state of a tissue system could effectively be visualized through the use of finite strain-based modeling. A multi-constituent mixture-based material model was next implemented in the analysis of agarose gel constructs. Material parameter estimates from this model were found to agree with those determined by an unconfined compression validation model, establishing physical relevance of noninvasive parameter estimates produced by the models. Finally, the mixture-based material model was applied towards an in situ analysis of the human intervertebral disc

QUANTITATIVE ELASTICITY IMAGING AND SOFT TISSUE CHARACTERIZATION USING TAGGED MAGNETIC RESONANCE IMAGING

Ph.DDOCTOR OF PHILOSOPH

Level Set Methods for MRE Image Processing and Analysis

Ph.DDOCTOR OF PHILOSOPH

Développement et évaluation des paramètres quantitatifs de l’IRM de la prostate

The purpose of this thesis is to develop and evaluate the quantitative methods of multiparametric MRI of prostate in discriminating Gleason score (GS) ≥7 cancers. We suppose that the quantitative parameter of MRI could help standardizer the diagnostic, reduce the inter-lecture and/ or inter-institution variation in diagnostic of prostate cancer. This thesis is divided into three chapters. The firs chapter, entilted « Quantitative T2 MRI of prostate » is a retrospective study on a database of prostate cancer patients before radical prostatectomy. The second chapter, entilted « Multi-parametric Quantitative MRI of prostate » is also a retrospective study before radical prostatectomy. The third chapter, entitled « MR elastography of prostate by transperineal approach », is an experimental study. Our first study shows that T2 value is robust between machines of different constructors. T2 value is significant predictor, but of weak performance, of aggressively cancer of prostate at 3T. Our second study shows that the combination of ADC_10th percentile with Time-to-peak (TTP) improved the diagnosis performance, and this model is also robust between two machines of different constructors. Our third study shows the initial results on elasticity of the prostate. These results show that MRI elastography of prostate at high excitation frequency (>100 Hz) by trans-perineale approach was feasible. The elastography may, in the future, be integrated in quantitative multi-parametric MRI to improve the diagnosis performanceL'objectif de cette thèse est de développer et d'évaluer des paramètres quantitatifs de l'IRM de la prostate en discriminant les cancers de score de Gleason (GS) ≥7. Nous supposons que les paramètres quantitatifs de l'IRM pourraient aider à standardiser le diagnostic, et à diminuer la variation inter-lecteur et/ou inter-institution du diagnostic du cancer de la prostate. Cette thèse est divisée en trois chapitres. Le premier chapitre, intitulé « IRM T2 quantitatif de la prostate », est une étude rétrospective sur une base de données des patients avant prostatectomie radicale. Le deuxième chapitre, intitulé « IRM multiparamétrique quantitative de la prostate », est aussi une étude rétrospective avant prostatectomie radicale. Le troisième chapitre, intitulé « Élastographie IRM de la prostate par voie trans-périnéale» est une étude expérimentale. Notre première étude montre que le T2 est robuste sur les machines de constructeurs différents. Le T2 est un prédicteur significatif, mais de faible performance, d'agressivité du cancer de la prostate à 3T. Notre deuxième étude montre que la combinaison du 10ème centile de l'ADC avec le Time-topeak (TTP) améliore la performance du diagnostic, et ce modèle est lui aussi robuste entre des machines de constructeurs différents. Notre troisième étude montre les résultats préliminaires sur l'élasticité de la prostate. Ces résultats montrent que l'élastographie IRM de la prostate en haute fréquence d'excitation (>100 Hz) par voie trans-périnéale est faisable. L'élastographie pourrait à l'avenir être intégrée à l'IRM multiparamétrique quantitative pour améliorer la performance de diagnosti