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

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed

Evaluation of cerebral cortex viscoelastic property estimation with nonlinear inversion magnetic resonance elastography

Objective. Magnetic resonance elastography (MRE) of the brain has shown promise as a sensitive neuroimaging biomarker for neurodegenerative disorders; however, the accuracy of performing MRE of the cerebral cortex warrants investigation due to the unique challenges of studying thinner and more complex geometries. Approach. A series of realistic, whole-brain simulation experiments are performed to examine the accuracy of MRE to measure the viscoelasticity (shear stiffness, μ, and damping ratio, ξ) of cortical structures predominantly effected in aging and neurodegeneration. Variations to MRE spatial resolution and the regularization of a nonlinear inversion (NLI) approach are examined. Main results. Higher-resolution MRE displacement data (1.25 mm isotropic resolution) and NLI with a low soft prior regularization weighting provided minimal measurement error compared to other studied protocols. With the optimized protocol, an average error in μ and ξ was 3% and 11%, respectively, when compared with the known ground truth. Mid-line structures, as opposed to those on the cortical surface, generally display greater error. Varying model boundary conditions and reducing the thickness of the cortex by up to 0.67 mm (which is a realistic portrayal of neurodegenerative pathology) results in no loss in reconstruction accuracy. Significance. These experiments establish quantitative guidelines for the accuracy expected of in vivo MRE of the cortex, with the proposed method providing valid MRE measures for future investigations into cortical viscoelasticity and relationships with health, cognition, and behavior

Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

Changes in biomechanical properties of biological soft tissues are often associated with physiological dysfunctions. Since biological soft tissues are hydrated, viscoelasticity is likely suitable to represent its solid-like behavior using elasticity and fluid-like behavior using viscosity. Shear wave elastography is a non-invasive imaging technology invented for clinical applications that has shown promise to characterize various tissue viscoelasticity. It is based on measuring and analyzing velocities and attenuations of propagated shear waves. In this review, principles and technical developments of shear wave elastography for viscoelasticity characterization from organ to cellular levels are presented, and different imaging modalities used to track shear wave propagation are described. At a macroscopic scale, techniques for inducing shear waves using an external mechanical vibration, an acoustic radiation pressure or a Lorentz force are reviewed along with imaging approaches proposed to track shear wave propagation, namely ultrasound, magnetic resonance, optical, and photoacoustic means. Then, approaches for theoretical modeling and tracking of shear waves are detailed. Following it, some examples of applications to characterize the viscoelasticity of various organs are given. At a microscopic scale, a novel cellular shear wave elastography method using an external vibration and optical microscopy is illustrated. Finally, current limitations and future directions in shear wave elastography are presented

Early characterisation of neurodegeneration with high-resolution magnetic resonance elastography

This thesis contributes to recent interest within medical imaging regarding the development and clinical application of magnetic resonance elastography (MRE) to the human brain. MRE is a non-invasive phase-contrast MRI technique for measurement of brain mechanical properties in vivo, shown to reflect the composition and organisation of the complex tissue microstructure. MRE is a promising imaging biomarker for the early characterisation of neurodegeneration due to its exquisite sensitivity to variation among healthy and pathological tissue. Neurodegenerative diseases are debilitating conditions of the human nervous system for which there is currently no cure. Novel biomarkers are required to improve early detection, differential diagnosis and monitoring of disease progression, and could also ultimately improve our understanding of the pathophysiological mechanisms underlying degenerative processes. This thesis begins with a theoretical background of brain MRE and a description of the experimental considerations. A systematic review of the literature is then performed to summarise brain MRE quantitative measurements in healthy participants and to determine the success of MRE to characterise neurological disorders. This review further identified the most promising acquisition and analysis methods within the field. As such, subsequent visits to three brain MRE research centres, within the USA and Germany, enabled the acquisition of exemplar phantom and brain data to assist in discussions to refine an experimental protocol for installation at the Edinburgh Imaging Facility, QMRI (EIF-QMRI). Through collaborations with world-leading brain MRE centres, two high-resolution - yet fundamentally different - MRE pipelines were installed at the EIF-QMRI. Several optimisations were implemented to improve MRE image quality, while the clinical utility of MRE was enhanced by the novel development of a Graphical User Interface (GUI) for the optimised and automatic MRE-toanatomical coregistration and generation of MRE derived output measures. The first experimental study was performed in 6 young and 6 older healthy adults to compare the results from the two MRE pipelines to investigate test-retest agreement of the whole brain and a brain structure of interest: the hippocampal formation. The MRE protocol shown to possess superior reproducibility was subsequently applied in a second experimental study of 12 young and 12 older cognitively healthy adults. Results include finding that the MRE imaging procedure is very well tolerated across the recruited population. Novel findings include significantly softer brains in older adults both across the global cerebrum and in the majority of subcortical grey matter structures including the pallidum, putamen, caudate, and thalamus. Changes in tissue stiffness likely reflect an alteration to the strength in the composition of the tissue network. All MRE effects persist after correcting for brain structure volume suggesting changes in volume alone were not reflective of the detected MRE age differences. Interestingly, no age-related differences to tissue stiffness were found for the amygdala or hippocampus. As for brain viscosity, no group differences were detected for either the brain globally or subcortical structures, suggesting a preservation of the organisation of the tissue network in older age. The third experiment performed in this thesis finds a direct structure-function relationship in older adults between hippocampal viscosity and episodic memory as measured with verbal-paired recall. The source of this association was located to the left hippocampus, thus complementing previous literature suggesting unilateral hippocampal specialisation. Additionally, a more significant relationship was found between left hippocampal viscosity and memory after a new procedure was developed to remove voxels containing cerebrospinal fluid from the MRE analysis. Collectively, these results support the transition of brain MRE into a clinically useful neuroimaging modality that could, in particular, be used in the early characterisation of memory specific disorders such as amnestic Mild Cognitive Impairment and Alzheimer’s disease

Magnetic resonance elastography (MRE) of the human brain: technique, findings and clinical applications

Neurological disorders are one of the most important public health concerns in developed countries. Established brain imaging techniques such as magnetic resonance imaging (MRI) and x-ray computerised tomography (CT) have been essential in the identification and diagnosis of a wide range of disorders, although usually are insufficient in sensitivity for detecting subtle pathological alterations to the brain prior to the onset of clinical symptoms—at a time when prognosis for treatment is more favourable. The mechanical properties of biological tissue provide information related to the strength and integrity of the cellular microstructure. In recent years, mechanical properties of the brain have been visualised and measured non-invasively with magnetic resonance elastography (MRE), a particularly sensitive medical imaging technique that may increase the potential for early diagnosis. This review begins with an introduction to the various methods used for the acquisition and analysis of MRE data. A systematic literature search is then conducted to identify studies that have specifically utilised MRE to investigate the human brain. Through the conversion of MRE-derived measurements to shear stiffness (kPa) and, where possible, the loss tangent (rad), a summary of results for global brain tissue and grey and white matter across studies is provided for healthy participants, as potential baseline values to be used in future clinical investigations. In addition, the extent to which MRE has revealed significant alterations to the brain in patients with neurological disorders is assessed and discussed in terms of known pathophysiology. The review concludes by predicting the trends for future MRE research and applications in neuroscience

Novel applications, model, and methods in magnetic resonance elastography

Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique that maps and quantifies the mechanical properties of soft tissue related to the propagation and attenuation of shear waves. There is considerable interest in whether MRE can bring new insight into pathologies. Brain in particular has been of utmost interest in the recent years. Brain tumors, Alzheimer's disease, and Multiple Sclerosis have all been subjects of MRE studies. This thesis addresses four aspects of MRE, ranging from novel applications in brain MRE, to physiological interpretation of measured mechanical properties, to improvements in MRE technology. First, we present longitudinal measurements of the mechanical properties of glioblastoma tumorigenesis and progression in a mouse model. Second, we present a new finding from our group regarding a localized change in mechanical properties of neural tissue when functionally stimulated. Third, we address contradictory results in the literature regarding the effects of vascular pressure on shear wave speed in soft tissues. To reconcile these observations, a mathematical model based on poro-hyperelasticity is used. Finally, we consider a part of MRE that requires inferring mechanical properties from MR measurements of vibration patterns in tissue. We present improvements to MRE reconstruction methods by developing and using an advanced variational formulation of the forward problem for shear wave propagation

On an inverse problem from magnetic resonance elastic imaging

The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Frechet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton-Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Frechet differentiability of the appropriate nonlinear operator, which we justify