A multi-scale sub-voxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data

Abstract

We propose a new mathematical model to infer capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed-dimension flow and transport model for brain tissue perfusion on a sub-voxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal-time curves that can be compared to clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall conductivity is a good indicator for characterizing activity of lesions, even if other patient-specific model parameters are not well-known.\n\nAuthor summaryThe use of advanced brain imaging techniques has supported in-vivo research targeted to the integrity of the blood-brain barrier. We propose a new type of post-processing for raw image data using contrast agent perfusion simulations on the data-poor capillary scale. Combining modern simulation techniques with the clinical image data allows us to determine patient-specific and pathologically relevant parameters such as the capillary wall conductivity. The presented simulation model is a step towards the quantification of contrast agent leakage in the brain, which is typical for acute multiple sclerosis lesions, but also occurs with other diseases affecting the blood-brain-barrier, such as cerebral gliomas.