A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications.
SUMMARYUsing a sequential time-marching approach, we describe and implement effective solution strategies for the equations governing immiscible displacement in a porous medium. By combining adaptive grid refinement with an operator-splitting technique based on the modified method of characteristics, the saturation equation is treated in a consistent and accurate way. For the pressure equation we construct accurate piecewise linear velocity components from a piecewise linear pressure approximation.
Contrast enhanced dynamic MRI data is important for classifying anomalies in tissue and blood circulation, e.g. tumors, stokes, kidney failure. The resulting sequence of images providing spatial-temporal representation of contrast agent concentration must be given meaningful clinical interpretation. Current processing typically relies on localized strategies, where the images are analyzed voxel by voxel. The consensus seems to be that taking direct advantage of the global structure of the images potentially will allow for more accurate and robust interpretations.Based on a workflow that has been extensively studied within both petroleum and ground water research, the current paper combines explicit porous media flow modelling and state of the art data assimilation. Starting from a multi-compartment global flow model, we explore MRI interpretation via synthetic cases where model generated images are used as input to a parameter identification algorithm based on ensemble based data assimilation like the ensemble Kalman filter (EnKF).From reasonable assumptions, the procedure demonstrates ability to identify relevant model parameters for two synthetic cases.This study indicates that flow based assimilation of MRI data is viable and that it might provide valuable supplementing insight compared to state of the art. Regularizations are made on a firm statistical basis, eliminating the need for ad hoc parameters, and leading to estimates that are rigorous in terms of error thresholds. A priori knowledge can easily be incorporated in the procedure. The flow model allows explicit representation of basic material properties, and adds regularization to the procedure by enforcing globally consistent flow fields.
This paper presents an approach for rate allocation for individual wells by combining a transient well flow model and the ensemble Kalman filter. Specifically, we aim to utilize available high frequency measurements of pressure and temperature, focussing particularly on the early time period after changing influx conditions. The transition between two steady state flow periods implies natural excitation of the well flow, and during this phase an individual sensor experiences a golden age compared to the single value associated with a steady state. Thus, by taking proper advantage of the transient periods, it is reasonable to believe that important insight into the subsequent steady state conditions can be obtained.We explore a couple case studies, indicating the feasibility of our approach and then draw some preliminary conclusions from our investigations.
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