Geir Nævdal

The measurement of perfusion and filtration of blood in biological tissue give rise to important clinical parameters used in diagnosis, follow-up, and therapy. In this paper, we address techniques for perfusion analysis using processed contrast agent concentration data from dynamic MRI acquisitions. A new methodology for analysis is evaluated and verified using synthetic data generated on a tissue geometry.

The measurement of perfusion and filtration of blood in biological tissue give rise to important clinical parameters used in diagnosis, follow-up, and therapy. In this paper we address techniques for perfusion analysis using processed contrast agent concentration data from dynamic MRI acquisitions. New methodology for analysis is evaluated and verified using synthetic data generated on a tissue geometry. Author summary: Accurate knowledge of tissue perfusion is crucial for proper diagnostics and treatment of several medical disorders. Traditional methods based on medical imaging are fast, but usually lack precision and robustness. In this paper, we address methodology to develop better diagnosis and treatment strategies for malignant tumors and stroke where blood perfusion may be altered. In our work, mathematical models for estimating perfusion are calibrated using magnetic resonance imaging (MRI) data, and more accurate representations of tissue parameters are provided. This methodology is a step towards minimal invasive and individually tailored diagnosis and treatment. We demonstrate the methodology with a twin-experiment using models of different complexity for generating data and estimating the tissue parameters. Both models are based on a mathematical description of how fluids flows in a porous medium, where the data-generating model uses higher resolution and a network representation of blood vessels than the estimating model. The calibration of unknown tissue parameters is done using a statistical framework, and the choice of methodology is motivated by applications from sub-surface reservoir characterization.

In this document we present a workflow for ensemble-based 4D seismic history matching. Ensemble-based history matching has become standard for production data, but 4D seismic data poses a number of additional challenges. One issue is that the amount of data is considerably larger, but another, probably more complicating factor is that for utilizing the seismic data, either the seismic data must be inverted to properties that is included in the reservoir simulation model, or a seismic response must be modeled, given the current estimate of the reservoir properties. This leads to a number of choices on how to utilize the information of the 4D seismic data. We will discuss this, as well as point to approaches for handling large amounts of data in ensemble-based history matching. The developed approach has been applied on the Norne field and is currently being evaluated at the Ekofisk field. This document is primarily addressed to reservoir engineers and researchers that are working on history matching 4D seismic data, but it might also be of interest to those working with 4D seismic data from a geophysical perspective. After all, 4D seismic history matching should be viewed as an interdisciplinary subject. Although, our focus has been on ensemble-based history matching, some of the choices that have to be made in utilizing 4D seismic data is independent of the actual method used for history matching.

Uncertainty quantification in the context of seismic imaging is important for interpreting inverted subsurface models and updating reservoir models. The limited illumination, noisy data, and poor initial models in the seismic full-waveform inversion (FWI) lead to inversion uncertainties. This is particularly true for anisotropic elastic FWI, which suffers from extra parameter trade-off challenges. We have addressed the uncertainty quantification of the anisotropic elastic FWI problem in the framework of Bayesian inference. In particular, we estimate the uncertainties of the subsurface elastic parameters in Bayesian anisotropic elastic FWI by combining the iterated extended Kalman filter with an explicit representation of the sensitivity matrix with Green’s functions. The sensitivity matrix is based on the integral equation approach, which is also within the context of the nonlinear inverse scattering theory. We determine the results of numerical tests with examples for anisotropic elastic media. They show that the adopted Bayesian inversion method can provide reasonable reconstructed results for the elastic coefficients of the stiffness tensor and the framework is suitable for accessing the uncertainties.

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. An accurate simulation of blood-flow in the human brain can be used for improved diagnostics and assignment of personalized treatment regimes. However, current algorithms are limited to simulation of blood flow within tumours only, and in terms of parameter estimation, traditional compartment models have limited accuracy due to lack of spatial connectivity within the models. As a remedy, we propose a data-driven computational fluid dynamics model where the geometric domains for simulation are defined from state-of-the art MR acquisitions enabling a segmentation of large arteries and veins. In the capillary tissue we apply a two-compartment porous media model, where the perfusion is pressure-driven and is defined as the transition of blood from arterial to venous side. In addition, we propose a model for dealing with the intermediate scale problem where the vessels are undetectable and the flow does not adhere to requirements of porous media flow. For this scale, we propose a support function distributing the fluid in a nearby region around the vessel terminals. Combining these elements, we have developed a novel full human brain blood-flow simulator.

Summary: Ensemble-based history-matching methods have received much attention in reservoir engineering. In real applications, small ensembles are often used in reservoir simulations to reduce the computational costs. A small ensemble size may lead to ensemble collapse, a phenomenon in which the spread of the ensemble of history-matched reservoir models becomes artificially small. Ensemble collapse is not desired for an ensemble-based history-matching method because it not only deteriorates the capacity in uncertainty quantification, but also forces the ensemble-based method to later stop updating reservoir models. In practice, distance-based localization is thus introduced to tackle ensemble collapse. Distance-based localization works well in many problems. However, one prerequisite in using distance-based localization is that the observations have associated physical locations. In certain circumstances with complex observations, this may not be true, and it thus becomes challenging to apply distance-based localization. In this work, we propose a correlation-based adaptive localization scheme that does not rely on the physical locations of the observations. Instead, we use the spatial distributions of the correlations between model variables and the corresponding simulated observations. In the course of history matching, we update model variables by only using the observations that have relatively high correlations with them, while excluding those that have relatively low correlations. This is equivalent to introducing a data-selection procedure to the history-matching algorithm. As a result, the threshold values for data selection play an essential role in the proposed adaptive localization scheme, and we develop both ideal and practical approaches to the choices of the threshold values. We demonstrate the efficacy of the proposed localization scheme using seismic history-matching problems—one 2D and one 3D—in which ensemble collapse is severe in the presence of large amounts of observational data, but distance-based localization may not be applicable because of the lack of physical locations of the seismic data in use. In contrast, correlation-based localization works well to prevent ensemble collapse and also renders good history-matching results. We also note some practical conveniences of the proposed localization scheme, including the applicability to nonlocal observations, the relative simplicity in implementation, the transferability of the same codes among different (either 2D or 3D) case studies, and the adaptivity to different types of observations and petrophysical parameters.

In this work, we propose an ensemble based petrophysical parameter inversion framework to estimate static and dynamic reservoir/petrophysical parameters such as saturation, pressure and porosity fields using seismic data. The method uses reservoir-engineering data for the static and dynamic parameters as prior information. Here, we use acoustic impedance data (I_p) as seismic data, apply multilevel discrete wavelet transforms (DWT) to the measurements, and estimate noise level of resulting wavelet coefficients. We then select the wavelet coefficients above a certain threshold value, and perform petrophysical inversion using an iterative ensemble smoother. We apply the proposed framework to the 3D Norne field reservoir model. The numerical results indicate that the proposed framework can integrate the reservoir-engineering data as prior knowledge with seismic data, while achieving reasonably good estimates of both static and dynamic reservoir variables. Presentation Date: Tuesday, September 26, 2017 Start Time: 10:35 AM Location: 330A Presentation Type: ORAL