Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors

<p>Abstract</p> <p>Background</p> <p>Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.</p> <p>Results</p> <p>We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.</p> <p>Conclusions</p> <p>The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.</p> <p>Reviewers</p> <p>This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).</p

Comparison between Local Ensemble Transform Kalman Filter and PSAS in the NASA finite volume GCM: perfect model experiments

This paper explores the potential of Local Ensemble Transform Kalman Filter (LETKF) by comparing the performance of LETKF with an operational 3D-Var assimilation system, Physical-Space Statistical Analysis System (PSAS), under a perfect model scenario. The comparison is carried out on the finite volume Global Circulation Model (fvGCM) with 72 grid points zonally, 46 grid points meridionally and 55 vertical levels. With only forty ensemble members, LETKF obtains an analysis and forecasts with lower RMS errors than those from PSAS. The performance of LETKF is further improved, especially over the oceans, by assimilating simulated temperature observations from rawinsondes and conventional surface pressure observations instead of geopotential heights. An initial decrease of the forecast errors in the NH observed in PSAS but not in LETKF suggests that the PSAS analysis is less balanced. The observed advantage of LETKF over PSAS is due to the ability of the forty-member ensemble from LETKF to capture flow-dependent errors and thus create a good estimate of the true background uncertainty. Furthermore, localization makes LETKF highly parallel and efficient, requiring only 5 minutes per analysis in a cluster of 20 PCs with forty ensemble members.Comment: 50 pages, 11 figure

Final Report on Characterizing the Dynamics of Spatio-Temporal Data

One principal goal of the grant was to model and analyze the dynamics of spatially extended chaotic systems. One of the principal tools used in the analysis was KLTOOL, a computer package developed by the principal investigators for Karhunen-Loeve analysis. The package was used to analyze video data from a laboratory experiment on cellular flames. A second goal of the project was to analyze complex time series whose underlying dynamics may be low dimensionally chaotic. Particular emphasis was placed on systems of possible relevance to energy production and distribution. The work attempted to characterize low-dimensional aspects of the dynamics of a fluidized bed, in particular, a transition from periodic to irregular behavior. Finally, collaborators worked on aspects of targeting in chaotic dynamical systems. This work showed that it is possible to switch a moderately high-dimensional chaotic process rapidly between prespecified periodic saddle orbits embedding within the attractor. Additional work extended previously-developed algorithms for the highly accurate computation of stable manifolds of periodic saddle orbits, which is essential to the successful application of targeting algorithms

The Prediction of Chaotic Time Series: a Variation on the Method of Analogues

This paper describes a procedure for making short term predictions by examining trajectories on a reconstructed attractor that correspond to a dynamical feature of interest, namely, the trajectories near a spiral saddle fixed point in the attractor. Reasonable predictions can be made from short time series records and very good predictions from longer records using local linear approximations of the dynamics, if the dimension of the attractor is not too large. Two methods are described. The first uses nearest-neighbor comparisons similar to E. N. Lorenz&apos; &quot;method of analogues.&quot; The second method uses a collection of closely matched trajectories to compute a basis of singular vectors. The observations can be projected onto a subset of the new basis with little loss of information. In the new coordinates, good predictions can be made by finding the slope of a certain least squares line through the origin. 1 Introduction Our strategy in the analysis of chaotic time series data has been to..