Tissue characterization using invariants of higher order tensors

The aim of this project is to make available a range of new measures with greater sensitivity and specificity to the nature of tissue structure and pathology in the human brain.

The means to achieve this is magnetic resonance imaging (MRI) together with new mathematical results from the theory of tensors.Diffusion MRI (dMRI) measures diffusion using pulsed field gradients during the imaging process.

We will investigate a recent type of dMRI modality, called multidimensional dMRI (mdMRI), that employs more complicated – and also more general – waveforms.

The measurements then produce estimated tensors with new “fingerprints” which are “hidden” in the tensor components.

These fingerprints have to be formed (Aim 1) and given a clinical relevance (Aim 2).In Aim 1, we will develop a new framework to describe higher order tensor invariants (fingerprints) for mdMRI.

Our preliminary results show these are well suited for describing, in a rotationally invariant manner, anisotropic tissue properties.

Thus they are potentially powerful mdMRI biomarkers for characterising tissue microstructure.In Aim 2, we will apply the developed framework in Aim 1 to analyse human mdMRI data.

We will explore healthy brain tissue and compare the "fingerprints" our new invariants will have on both grey and white matter.The clinical importance lies in the fact that these new measures may help grading of tumors as well as early detection of disorders like schizophrenia and multiple sclerosis.