A multiscale subvoxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data

Abstract

We propose a new mathematical model to learn 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 subvoxel 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 with 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.

Quantitative Characterization of Tumoural Leakage Phenomena Using Dynamic Susceptibility Contrast Perfusion Imaging 

“…Hence, a homogeneous distribution of the leaked interstitial GBCA is likely to exhibit T1 dominant signal behaviour, while a compartmentalised/heterogeneous distribution, favours T2* effects. [20] The positive-negative dichotomy to the interpretation of K2 values that we underscore among PCNSL, GBM, and Mets borrows from the work of Liu et al [11] 2…”

“…GBCA induced T1 relaxivity changes are microscale effects, that stem from T1 shortening of protons adjacent to the GBCA molecule. In contrast, T2* relaxivity changes result from superposition of mesoscale field perturbations induced by susceptibility gradients across tissue compartment interfaces [20]. Hence, a homogeneous distribution of the leaked interstitial GBCA is likely to exhibit T1 dominant signal behaviour, while a compartmentalised/heterogeneous distribution, favours T2* effects.…”

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

“…In this section, we identify four major areas of research at the tissue scale (shown in Figure 4 ) and discuss the modeling strategy or strategies applied to these areas. Broadly, these areas include: (1) representing the evolving geometry of the tumor’s vascular network (panel a in Figure 4 ) [ 29 , 82 , 87 , 88 , 119 , 120 , 121 , 122 , 123 ], (2) estimating the associated blood flow and vascular transport of substances (panel b in Figure 3 ) [ 81 , 88 , 122 , 123 , 124 , 125 , 126 , 127 ], (3) describing the mechanisms underlying the complex interplay between tumor growth and vasculature dynamics (panel c in Figure 4 ) [ 32 , 81 , 87 , 88 , 121 , 123 , 128 , 129 ], and (4) determining the effect of cytotoxic, targeted, and anti-angiogenic therapies on the tumor-associated vascular network as well as the tumor itself (panel d in Figure 4 ) [ 28 , 85 , 86 , 124 ].…”

“…The modeling of vascular flow usually includes a description of flow in the blood vessels, along with its coupling with flow in the tissue through a mass flux at the capillary walls or at the terminal ends of larger vessels. Similar to the cell-scale models reviewed in Section 3 , these phenomena can be modeled by discrete [ 33 , 87 , 88 , 122 , 123 , 126 , 130 , 131 , 132 ], continuous [ 128 , 129 , 133 , 134 ], or hybrid [ 127 , 135 , 136 ] approaches. In discrete vascular models both the pre-existing and the angiogenic vasculature are frequently approximated by a 1D network of connected straight cylinders with the flow in each cylinder simulated using the 1D Poiseuille law [ 33 , 87 , 88 , 122 , 123 , 126 , 130 , 131 , 132 ].…”

“…Similar to the cell-scale models reviewed in Section 3 , these phenomena can be modeled by discrete [ 33 , 87 , 88 , 122 , 123 , 126 , 130 , 131 , 132 ], continuous [ 128 , 129 , 133 , 134 ], or hybrid [ 127 , 135 , 136 ] approaches. In discrete vascular models both the pre-existing and the angiogenic vasculature are frequently approximated by a 1D network of connected straight cylinders with the flow in each cylinder simulated using the 1D Poiseuille law [ 33 , 87 , 88 , 122 , 123 , 126 , 130 , 131 , 132 ]. In continuous vascular flow models the vasculature is described with a spatially averaged, continuous variable (e.g., vasculature density or vascular volume fraction), and the transport of the substance of interest (e.g., drug or nutrient) through the interstitial space is described with a reaction-diffusion-advection model [ 128 , 129 , 133 , 134 ] describing the delivery, diffusion, and the transport of that substance due to bulk fluid flow.…”