The influence of spherical pores within the white matter on Diffusion-Weighted MRI signals : a numerical study using Monte-Carlo simulations

Disabilities, diseases or disorders caused by brain damage are quite vast, ranging from simply aging to mental illnesses such as schizophrenia as well as stroke, multiple sclerosis, autism or Alzheimer’s disease. These diseases and disorders affect children, women or men worldwide without any discrimination, at any stage of their life. Therefore, any tool that might help in the early detection of those abnormalities or any of their characteristic features is eagerly welcome. Interestingly, in the past few decades, a new and non-invasive imaging method, diffusion-weighted magnetic resonance imaging (DW-MRI), also known as diffusion-weighted imaging (DWI), has emerged for assessing the microstructure of the brain (e.g. the orientation of the axons or their radius). This approach is based on the diffusion of water molecules within tissues. Researchers have started to investigate this method as injuries alter the diffusion in a characteristic manner due to the fact that diffusion of water molecule is sensitive to the underlying tissue microstructure . Additionally, links were established between diseases and microstructural abnormalities, for example, damage affecting small-diameter axons were linked to cognitive impairment, whereas damage caused by a large-diameter were related to physical disabilities. Subsequently, MRI methods were numerously developed and used to assess brain characteristics. For example multi-compartmental tissue models, in which fascicles of axons are modelled by infinitely long cylinders and glial cells by spherical pores, were used to evalute which model is best suited for clinical. Additional researchers used multi-compartmental models to find the optimal PGSE sequence settings, to validate a phantom that mimic tumour cellular structure, or to investigate the diffusion in compartment models based on animal diseases. Consequently, this Master’s Thesis aims to provide additional insight into the theory of DW-MRI, especially in the development of multi-compartmental tissue models, by validating biophysically the use of an apparent lower intrinsic diffusivity. Altough lowering this value allows to artificially incorporate additional (restriction) phenomena that are not simulated. For instance, the apparent diffusion coefficient is influenced by membrane permeability, cellular volume fraction, extracellular or intracellular diffusion. To do so, theoretical notions of DW-MRI are first developed in chapter 1, together with a quick overview of existing multi-compartmental models. Then in chapter 2, reference is made on the synthetic generation method of the DWI signals developed along with the proposed acquisition sequences needed to simulate those signals. In this chapter, the microstructure environments are also thoroughly detailed along with their configuration settings. Afterwards, in chapter 3, emphasis is put on the determination of the simulation parameters that are necessary to synthetically generate the DWI signals. Additionally, a comparative study of the simulated signal is provided. This study investigate two different sets of configuration parameters of our multi-compartment environments while considering two physical representations for the pores. The latter is considered as glial cells, when filled with water molecules, and as macromolecules in quasi solid-state or cellular debris, when empty. Finally, by considering different values for the diffusivity, microstructure parameters that justify the use of an effective diffusivity are highlighted.