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

A Mathematical Model for Two Solutes Transport in a Poroelastic Material and Its Applications

Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially different sizes dissolved in fluid and are transported through pores of different sizes. The stress tensor, the main force leading to the material deformation, is taken not only in the standard linear form but also with an additional nonlinear part. The model is constructed in 1D space and consists of six nonlinear equations. It is shown that the governing equations are integrable in stationary case, therefore all steady-state solutions are constructed. The obtained solutions are used in an example for healthy and tumour tissue, in particular, tissue displacements are calculated and compared for parameters taken from experimental data in cases of the linear and nonlinear stress tensors. Since the governing equations are non-integrable in non-stationary case, the Lie symmetry analysis is used in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with non-trivial Lie symmetries are identified. As a result, multi-parameter families of exact solutions are constructed including those in terms of special functions(hypergeometric and Bessel functions). A possible application of the solutions obtained is demonstrated.Comment: 6 figure

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