Orthogonal invariant sets of the diffusion tensor and the development of a curvilinear set suitable for low-anisotropy tissues.

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional anisotropy and the diffusion mode. The alternative invariant set possesses a different structure to the other known invariant sets; the second and third members of the curvilinear set measure the degree of orthotropy and oblateness/prolateness, respectively. The proposed advantage of these invariants is that they may work well in situations of low diffusion anisotropy and isotropy, as is often observed in tissues such as cartilage. We also explore the other orthogonal invariant sets in terms of their geometry in relation to eigenvalue space; a cylindrical set, a spherical set (including fractional anisotropy and the mode), and a log-Euclidean set. These three sets have a common structure. The first invariant measures the magnitude of the diffusion, the second and third invariants capture aspects of the anisotropy; the magnitude of the anisotropy and the shape of the diffusion ellipsoid (the manner in which the anisotropy is realised). We also show a simple method to prove the orthogonality of the invariants within a set

A nuclear magnetic resonance study of water in aggrecan solutions

Aggrecan, a highly-charged macromolecule found in articular cartilage, was investigated in aqueous salt solutions with proton Nuclear Magnetic Resonance. The longitudinal and transverse relaxation rates were determined at two different field strengths, 9.4 T and 0.5 T, for a range of temperatures and aggrecan concentrations. The diffusion coefficients of the water molecules were also measured as a function of temperature and aggrecan concentration, using a pulsed field gradient technique at 9.4 T. Assuming an Arrhenius relationship, the activation energies for the various relaxation processes and the translational motion of the water molecules were determined from temperature dependencies as a function of aggrecan concentration in the range 0 – 5.3 % w/w. The longitudinal relaxation rate and inverse diffusion coefficient were approximately equally dependent on concentration and only increased by ≤ 20% from that of the salt solution. The transverse relaxation rate at high field demonstrated greatest concentration dependence, changing by an order of magnitude across the concentration range examined. We attribute this primarily to chemical exchange. Activation energies appeared to be approximately independent of aggrecan concentration, except for that of the low-field transverse relaxation rate, which decreased with concentration

Activation Energy Mapping in Articular Cartilage

Magnetic resonance imaging of articular cartilage has, in the past, had a primary focus on clinical, qualitative imaging or quantitative mapping purely using relaxation times (e.g. T1 and T2) and the development of phenomenological models to link these to physical properties, such as GAG content. Recent work in the field has looked at more advanced imaging methods, such as dGEMRIC, gagCEST and diffusion tensor imaging in order to attempt to develop a more direct link to physical and biochemical properties of the cartilage. This link is important to further understand the structure and function of cartilage, and here we investigate a novel method to probe the physical and biochemical properties of cartilage tissue. We present a novel method for visualising cartilage using magnetic resonance imaging techniques, which have been developed for probing the structure, mobility and hydration of soft-matter systems. This approach has been used to determine the dynamic activation energy (EA) of water within articular cartilage. Two related imaging methods have been explored: firstly quantitative mapping of the T1-relaxation time over a range of temperatures and secondly, quantitative mapping of the apparent diffusion coefficient over a range of temperatures. These are complementary techniques that probe the local tissue environment by extracting the rotational activation energy of the water within articular cartilage from the T1-relaxation time mapping, and the translational activation energy from the apparent diffusion coefficient mapping. These methods have been shown to provide different information from within the articular cartilage tissue to that seen with other imaging techniques. These quantitative maps can provide a link to biochemical contents or physical properties of articular cartilage tissue and can be interpreted in terms of the known structure and properties of cartilage from other methods

Quantifying T2 relaxation time changes within lesions defined by apparent diffusion coefficient in grey and white matter in acute stroke patients

The apparent diffusion coefficient (ADC) of cerebral water, as measured by diffusion MRI, rapidly decreases in ischaemia, highlighting a lesion in acute stroke patients. The MRI T 2 relaxation time changes in ischaemic brain such that T 2 in ADC lesions may be informative of the extent of tissue damage, potentially aiding in stratification for treatment. We have developed a novel user-unbiased method of determining the changes in T 2 in ADC lesions as a function of clinical symptom duration based on voxel-wise referencing to a contralateral brain volume. The spherical reference method calculates the most probable pre-ischaemic T 2 on a voxel-wise basis, making use of features of the contralateral hemisphere presumed to be largely unaffected. We studied whether T 2 changes in the two main cerebral tissue types, i.e. in grey matter (GM) and white matter (WM), would differ in stroke. Thirty-eight acute stroke patients were accrued within 9and#8201;h of symptom onset and scanned at 3 T for 3D T 1-weighted, multi b-value diffusion and multi-echo spin echo MRI for tissue type segmentation, quantitative ADC and absolute T 2 images, respectively. T 2 changes measured by the spherical reference method were 1.94and#8201;and#8201;and#177;and#8201;and#8201;0.61, 1.50and#8201;and#8201;and#177;and#8201;and#8201;0.52 and 1.40and#8201;and#8201;and#177;and#8201;and#8201;0.54and#8201;ms h-1 in the whole, GM, and WM lesions, respectively. Thus, T 2 time courses were comparable between GM and WM independent of brain tissue type involved. We demonstrate that T 2 changes in ADC-delineated lesions can be quantified in the clinical setting in a user unbiased manner and that T 2 change correlated with symptom onset time, opening the possibility of using the approach as a tool to assess severity of tissue damage in the clinical setting.</p

Determining T2 relaxation time and stroke onset relationship in ischaemic stroke within apparent diffusion coefficient-defined lesions. A user-independent method for quantifying the impact of stroke in the human brain

Background and objective:In hyperacute ischaemic stroke, T2 of cerebral water increases with time. Quantifying this change may be informative of the extent of tissue damage and onset time. Our objective was to develop a user-unbiased method to measure the effect of cerebral ischaemia on T2 to study stroke onset time-dependency in human acute stroke lesions. Methods:Six rats were subjected to permanent middle cerebral occlusion to induce focal ischaemia, and a consecutive cohort of acute stroke patients (n=38) were recruited within 9 hours from symptom onset. T1-weighted structural, T2 relaxometry, and diffusion MRI for apparent diffusion coefficient (ADC) were acquired. Ischaemic lesions were defined as regions of lowered ADC. The median T2 difference (ΔT2) between lesion and contralateral non-ischaemic control region was determined by the newly-developed spherical reference method, and data compared to that obtained by the mirror reference method. Linear regressions and receiver operating characteristics (ROC) were compared between the two methods. Results:ΔT2 increases linearly in rat brain ischaemia by 1.9 ± 0.8 ms/h during the first 6 hours, as determined by the spherical reference method. In patients, ΔT2 linearly increases by 1.6 ± 1.4 and 1.9 ± 0.9 ms/h in the lesion, as determined by the mirror reference and spherical reference method, respectively. ROC analyses produced areas under the curve of 0.83 and 0.71 for the spherical and mirror reference methods, respectively. Conclusions:Data from the spherical reference method showed that the median T2 increase in the ischaemic lesion is correlated with stroke onset time in a rat as well as in a human patient cohort, opening the possibility of using the approach as a timing tool in clinics.</p