A spatiotemporal theory for MRI T2 relaxation time and apparent diffusion coefficient in the brain during acute ischaemia: Application and validation in a rat acute stroke model

Abstract

The objective of this study is to present a mathematical model which can describe the spatiotemporal progression of cerebral ischaemia and predict magnetic resonance observables including the apparent diffusion coefficient (ADC) of water and transverse relaxation time T2. This is motivated by the sensitivity of the ADC to the location of cerebral ischaemia and T2 to its time-course, and that it has thus far proven challenging to relate observations of changes in these MR parameters to stroke timing, which is of considerable importance in making treatment choices in clinics. Our mathematical model, called the cytotoxic oedema/dissociation (CED) model, is based on the transit of water from the extra- to the intra-cellular environment (cytotoxic oedema) and concomitant degradation of supramacromolecular and macromolecular structures (such as microtubules and the cytoskeleton). It explains experimental observations of ADC and T2, as well as identifying the rate of spread of effects of ischaemia through a tissue as a dominant system parameter. The model brings the direct extraction of the timing of ischaemic stroke from quantitative MRI closer to reality, as well as providing insight on ischaemia pathology by imaging in general. We anticipate that this may improve patient access to thrombolytic treatment as a future application.