It is well known in medicine that changes in tissue elasticity may be related to pathological phenomena such as cancer and other disease. Physicians routinely use palpation as means of inspecting the thyroid, prostate, and breast, where a palpably hard mass can often indicate the presence of a malignant lesion. Magnetic Resonance Elastography (MRE) has emerged as a relatively new elasticity imaging technique which can be used to spatially map and measure displacement patterns resulting from harmonic shear-wave propagation in soft tissue. Displacement fields are then used in reconstructing the tissue’s elastic property distributions. The feasibility of using MRE as a noninvasive means of characterizing the mechanical properties of silicone phantom mimicking human breast, was investigated though experiments involving MRE acquisitions of four phantoms. To achieve sufficient excitation of the phantom tissue, an acoustic actuator was developed. The results of these studies have shown the MRE acquisition to be successful in capturing sufficient data for elastic parameter reconstruction. Another different type of actuator has been developed and tested in the laboratory. The results show the potential for future use of this actuator in MRE experiments.

A three-dimensional, incompressible, Rayleigh damped magnetic resonance elastography (MRE) material property reconstruction algorithm capable of reconstructing the spatial distribution of both the real and imaginary parts of the shear modulus, density and bulk modulus from full-field MR-detected harmonic motion data was developed. The algorithm uses a subzone-based implementation of motion error minimization techniques, using 27 hexahedral finite elements, and is written in FORTRAN to run on high performance distributed computing systems. The theory behind the methods used is presented in a form that is directly applicable to the code's structure, to serve as a reference for future research building on this algorithm. Globally defined Rayleigh damping parameter reconstructions using simulated data showed that it is possible to reconstruct the correct combination of Rayleigh parameters under noise levels comparable to MR measurements. The elastic wave equation is used to demonstrate that use of a one parameter damping model to fit a Rayleigh damped material can lead to artefacts in the reconstructed damping parameter images, a prediction that is verified using simulated reconstructions. Initial results using MR-detected motion data from both gelatine phantoms and in-vivo cases produced good reconstructions of real shear modulus, as well as showing promise for successful imaging of damping properties. An initial investigation into an alternative elemental basis function approach to supporting the material property distribution produced some promising results, as well as highlighting some significant issues with large variations across the elements.

Attenuation and damping in elastography are naturally of great interest as the presence of these effects in biological tissue goes without question and therefore must be addressed if quantitative assessment of tissue elastic properties is to be achieved. Additionally, given the change in the tissue structure present in the diseases that elastographic imaging seeks to detect and diagnose, there is every reason to expect that the resulting lesions will also exhibit a change in their attenuation behaviour, indicating diagnostic value to any description of the damping property distribution elastographic methods are able to provide. This thesis will present the unique contribution of the development of several Elastographic models for MR based reconstructions of soft tissue. A method for the reconstruction of both Viscoelastic and Rayleigh damping based damped elastic properties has been developed for use with MR detected time-harmonic motion data and has been shown to lead to reasonable results in both homogeneous and heterogeneous phantoms of varying material types. A poro-elastic modelling is thought to provide a more accurate description of tissue structure by accounting for, in part, the complex interactions between the solid and fluid phases present in vivo. The foundation for a poro-elastic material behaviour will be explored and presented to support the premise. A meaningful mapping of the orthotropic shear moduli distributions in three directions has demonstrated enough evidence that the orthotropic MRE can be a feasible technique to determine orthotropic elasticity parameters of a biological tissue, noninvasively. The orthotropic achievements throughout this project can be useful for future clinical cancer diagnostics by augmenting the information obtained from the orthotropic MRE reconstructions between normal tissue and tumours.

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) Is capable of non-invasively quantifying the mechanical properties of skeletal muscles in vivo. This information can be clinically useful to understand the effects of pathologies on the mechanical properties of muscle and to quantify the effects of treatment. Advances in inversion algorithms quantify muscle anisotropy in two-dimensional (2D) and three-dimensional (3D) imaging. Databases of the shear stiffness of skeletal muscle have been presented in the relaxed and contracted states in the upper extremity (biceps brachii, flexor digitorum profundus, and upper trapezius), distal leg muscles (tibialis anterior, medial gastrocnemius, lateral gastrocnemius, and trapezius), and proximal leg muscles (vastus lateralis, vastus medialis, and sartorius). MRE measurements have successfully validated a mathematical model of skeletal muscle behavior in the biceps brachii, correlated to electromyographic data in the distal leg muscles and quantified the effects of pathologies on the distal and proximal leg muscles. Future research efforts should be directed toward improving one-dimensional (1D) and 3D MRE data acquisition and image processing, tracking the effects of treatment on pathologic muscle and correlating the shear stiffness with clinical measurements.

Magnetic Resonance Elastography (MRE) is an emerging medical imaging modality that allows quantification of the mechanical properties of biological tissues in vivo. MRE typically involves time-harmonic tissue excitation followed by the displacement measurements within the tissue obtained by phase-contrast Magnetic Resonance Imaging (MRI) techniques. MRE is believed to have great potential in the detection of wide variety of pathologies, diseases and cancer formations, especially tumors. This thesis concentrates on a thorough assessment and full rheological evaluation of the Rayleigh damping (RD) material model applied to MRE. The feasibility of the RD model to accurately reconstruct viscoelastic and damping properties was assessed. The goal is to obtain accurate quantitative estimates of the mechanical properties for the in vivo healthy brain via the subzone optimization based nonlinear image reconstruction algorithm. The RD model allows reconstruction of not only stiffness distribution of the tissue, but also energy attenuation mechanisms proportionally related to both elastic and inertial effects. The latter allows calculation of the concomitant damping properties of the material. The initial hypothesis behind this research is that accurate reconstruction of the Rayleigh damping parameters may bring additional diagnostic potential with regards to differentiation of various tissue types and more accurate characterisation of certain pathological diseases based on different energy absorbing mechanisms. Therefore, the RD model offers reconstruction of three additional material properties that might be of clinical diagnostic merit and can enhance characterisation of cancer tumors within the brain. A pneumatic-based actuator was specifically developed for in vivo human brain MRE experiments. Performance of the actuator was investigated and the results showed that the actuator produces average displacement in the range of 300 µmicrons and is well suited for generation of shear waves if applied to the human head. Unique features of the the actuator are patient comfort and safety, MRI compatibility, flexible design and good displacement characteristics. In this research, a 3D finite element (FE) subzone-based non-linear reconstruction algorithm using the RD material model has been applied and rigorously assessed to investigate the performance of elastographic based reconstruction to accurately recover mechanical properties and a concomitant damping behaviour of the material. A number of experiments were performed on a variety of homogenous and heterogeneous tissue-simulating damping phantoms comprising a set of materials that mimic range of mechanical properties expected in the brain. The result showed consistent effect of a poor reconstruction accuracy of the RD parameters which suggested the nonidentifiable nature of the RD model. A structural model identifiability analysis further supported the nonidentifiabilty of the RD parameters at a single frequency. Therefore, two approaches were developed to overcome the fundamental identifiability issue. The first one involved application of multiple frequencies over a broad range. The second one was based on parametrisation techniques, where one of the damping parameters was globally defined throughout the reconstruction domain allowing reconstruction of the two remaining parameters. Based on the findings of this research, multi-frequency (MF) elastography was performed on the tissue-simulating phantoms to investigate improvement of the elastographic reconstruction accuracy. Dispersion characteristics of the materials as well as RD changes across different frequencies in various materials were also studied. Simultaneous multi-frequency inversion was undertaken where two models were evaluated: a zero-order model and a power-law model. Furthermore, parametric-based RD reconstruction was carried out to evaluate enhancement of accurate identification of the reconstructed parameters. The results showed that parametric-based RD reconstruction, compared to MF-based RD results, allowed better material characterisation on the reconstructed shear modulus image. Also, significant improvement in material differentiation on the remaining damping parameter image was also observed if the fixed damping parameter was adjusted appropriately. In application to in vivo brain imaging, six repetitive MRE examinations of the in vivo healthy brain demonstrated promising ability of the RD MRE to resolve local variations in mechanical properties of different brain tissue types. Preliminary results to date show that reconstructed real shear modulus and overall damping levels correlate well with the brain anatomical features. Quantified shear stiffness estimates for white and gray matter were found to be 3 kPa and 2.1 kPa, respectively. Due to the non-identifiability of the model at a single frequency, reconstructed RD based parameters limit any physical meaning. Therefore, MF-based and parametric-based cerebral RD elastography was also performed.

Abdominal aortic aneurysm (AAA) is a form of cardiovascular disease whereby a change in the material properties of the vessel wall results in a localised dilation of the abdominal aorta. The primary risk of AAAs is rupture with mortality rates close to 90%. Whilst surgical intervention can be performed to repair AAAs, such procedures are considered high risk. As a result, surgery is only performed upon AAAs that are considered likely to rupture. The current method of prediction is the diameter criterion, with surgical intervention performed if the diameter of the AAA exceeds 5.5cm. Research has demonstrated that this is a weak method of predicting rupture and as such other methodologies are sought. One promising method is patient specific modelling (PSM) which involves the reconstruction of individual patient AAA geometries from imaging datasets, and finite element analysis (FEA) to calculate the stresses acting on the AAA wall, with the peak stress typically used as the predictor. A weakness of this methodology is the lack of patient specific material property values defined in the simulation. A potential technique to address this limitation is magnetic resonance elastography (MRE), an MR-based technique which utilises a phase-contrast sequence to characterise displacements caused by shear waves induced into the tissue by an external mechanical driver. An inversion algorithm is used to calculate local material property values of the tissue from these displacements. The aim of this thesis was to investigate the capability of utilising MRE to obtain material property measurements from AAAs that could be incorporated into PSM. To achieve this an FE method of modelling MRE was developed. The influence of modelling parameters upon the material property measurements made using the direct inversion (DI) algorithm was investigated, with element type and boundary conditions shown to have an effect. The modelling technique was then utilised to demonstrate the influence that the size of an insert had upon shear modulus measurements of that insert using DI in both 2- and 3-dimensions, and the multi-frequency dual elasto-visco algorithm (MDEV), an extension of DI combining information from multiple frequencies. Meanwhile a comparison of the modelling technique against an MRE scan of a phantom showed that whilst measurements made from the two techniques were different at low frequencies, they became similar as the frequency increased. This suggested that such differences were attributable to increased noise in the scanned data. FEA of MRE performed on idealised AAA geometries demonstrated that AAA size, shear viscosity of the thrombus and shear modulus of the AAA wall all influenced the accuracy of MRE measurements in the thrombus. Meanwhile MRE scanning of a small cohort of AAA patients had been undertaken and phase images investigated for signs of wave propagation to investigate the capabilities of the current MRE setup. Phase images were dominated by noise and there was no wave propagation visualised in any of the AAAs. This thesis demonstrates that the current MRE setup is not capable of achieving accurate measurements of material properties of AAA for PSM. Visualisation of wave propagation in AAAs is technically demanding and requires further development. A more fundamental concern however is the size dependence of the inversion algorithm used and the inability to consistently make accurate measurements from AAA geometries.

Atherosclerosis is the root cause of a wide range of cardiovascular diseases. Although it is a global arterial disease, some of the most severe consequences, heart attack and stroke, are caused by ischemia due to local plaque rupture. The risk of rupture is related to the mechanical properties of the plaque. Magnetic resonance elastography (MRE) images tissue elasticity by inverting, externally excited, harmonic wave displacement into a stiffness map, known as an elastogram. The aim of this thesis is to computationally and experimentally investigate the application of MRE to image the mechanical properties of atherosclerotic plaques. The cardiac cycle, lumen boundary, size and inhomogeneous nature of atherosclerotic plaques pose additional complications compared to more well-established MRE applications. Computational modelling allowed these complications to be assessed in a controlled and simplified environment, prior to experimental studies. Computational simulation of MRE was proposed by combining steady state shear waves, yielded by finite element analysis, with the 2D Helmholtz inversion algorithm. The accuracy and robustness of this technique was ascertained through models of homogeneous tissue. A computational sensitivity study was conducted through idealised atherosclerotic plaques, incorporating the effects of disease variables and mechanical, imaging and inversion parameters on the wave images and elastograms. Subject to parameter optimisation, a change in local plaque shear modulus with composition was established. Amongst other variables, an increase of the lipid pool volume in 10mm3 increments was shown to decrease the predicted shear modulus for stenosis sizes between 50% and 80%. The limitations of the Helmholtz inversion algorithm were demonstrated. A series of arterial phantoms containing plaques of various size and stiffness were developed to test the experimental feasibility of the technique. The lumen was identifiable in the wave images and elastograms. However the experimental wave propagation, noise and resolution left the vessel wall and plaque unresolvable. A computational replica of the phantoms yielded clearer wave images and elastograms, indicating that changes to the experimental procedure could lead to more successful results. The comparison also highlighted certain areas for improvement in the computational work. Imaging protocol for in vivo MRE through the peripheral arteries of healthy volunteers and peripheral artery disease patients was developed. The presence of physiological motion and low signal to noise ratios made the vessel anatomy unidentifiable. The application of MRE to atherosclerotic plaques through simulations, arterial phantoms, healthy volunteers and patients has shown that although there is the potential to identify a change in shear modulus with composition, the addition of realistic experimental complications are severely limiting to the technique. The gradual addition of complications throughout the thesis has allowed their impact to be assessed and in turn has highlighted areas for future research.

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Mechanical properties of muscle tissue are linked to its function. Magnetic Resonance Elastography (MRE) has the capability toquantitively measure these mechanical properties of soft tissue in-vivo. However, most MRE methods assume tissue isotropy during MRE reconstruction which is not an appropriate assumption for muscle tissue. To obtain tissue mechanical properties with higher accuracy, muscle anisotropy must be considered during MRE reconstruction. Therefore, the aim of this thesis was to implement an anisotropic MRE reconstruction. The anisotropic MRE reconstruction used solves three independent viscoelastic parameters (G||, G⊥, E||), that is based on a transverse isotropic (TI) inversion. The reconstruction was validated in a phantom study by comparison with an isotropic reconstruction, and in-vivo on gastrocnemius (ankle plantar flexor) and tibialis anterior (ankledorsi flexor) of one human subject. Also, a TI phantom was created to be included in the phantom study along with a commercial isotropic phantom. However, due to poor image quality, the TI phantom was excluded from further validation. Results from the isotropic phantom did not agree with the assumption of equal shear modulus in different planes of the isotropic medium. In-vivo study showed that the anisotropic reconstruction yielded mean moduli values in the range of what the literature suggests. The unequal shear modulus and young's modulus G||≠G⊥≠E|| of anisotropy in TI material was observed, indicating that the reconstruction method was able to identify the anisotropy ofmuscle tissue. However, further analysis including more human subjects are needed to conclude the reliability of the reconstruction method. / Muskelvävnadens mekaniska egenskaper är kopplade till dess funktion. Magnetresonans-Elastografi (MRE) har förmågan att kvantitativt mätadessa mekaniska egenskaper i mjukvävnad in-vivo. De flesta MRE metoder antar dock att vävnaden är isotropisk under MRE rekonstruktionen, vilket inte är ett lämpligt antagande för muskelvävnad. För att med högre noggrannhet estimera mekaniska egenskaper i vävnad måste muskel anisotropi tas i hänsyn under MRE rekonstruktionen. Därav var syftet i denna uppsats att implementera en anisotropisk MRE rekonstruktion. Den implementerade anisotropa MRE rekonstruktionenlöser tre oberoende viskoelastiska parametrar (G||, G⊥, E||), som ärbaserad på en transversell isotropisk (TI) inversion. Rekonstruktionen validerades i en fantomstudie genom jämförelse med en isotropisk rekonstruktion samt in-vivo på gastrocnemius (ankel plantarflexion) och tibialis anterior (ankel dorsalflexion) hos en människa. Dessutom skapades en TI-fantom för att inkluderas i fantomstudien tillsammansmed en kommersiell isotropisk fantom. På grund av dålig bildkvalitet uteslöts TI-fantomen från ytterligare validering. Resultat från den isotropa fantomen överensstämde inte med antagandet om lika skjuvmodul i olika plan av det isotropa mediet. In vivo-studien visade att den anisotropa rekonstruktionen gav medelvärden för modulerna inom intervallet av vad litteraturen antyder. Olikheten av skjuvmodulen och elasticitetsmodulen för anisotropi i TI-material G||≠G⊥≠E|| observerades vilket är en indikation att rekonstruktionsmetoden kunde identifiera muskelvävnadens anisotropi. Det krävs dock ytterligare analys inklusive fler mänskliga försökspersoner för att dra slutsatsen ifall rekonstruktionsmetoden är tillförlitlig