Minisymposia Abstracts

Speaker: Chiara Dalla Man
University of Padova, Padova, Italy
Title: Estimating Meal Glucose Rate of Appearance in Type 1 Diabetes
Abstract: Meal is one of the major disturbances, which precludes to reach good glycemic control in type 1 diabetes. Understanding how Meal Glucose Rate of Appearance (Rameal) changes due to meal composition and other factors could be of great help in the design of glucose predictors, advisory systems or closed-loop control algorithms. Estimating the Rameal is a typical inverse problem, since one wants to reconstruct the input of the system from noisy and sparse measurements of the output, i.e. plasma glucose samples.

To solve this problem regularized deconvolution can be used. The main advantage of this technique is that it is model-independent, i.e. one has not to assume a particular shape for the unknown curve. However, it also requires that glucose kinetics is completely known. Unfortunately, this is never the case, and glucose kinetics must be derived from multiple tracer experiments. This is obviously a big limitation, since most of the clinical centers are not equipped for tracer employment.

Another option is to resort to a model-based approach. In this case, the main advantage is that glucose tracers are not needed. On the other hand, important assumptions have to be made on Rameal profile. Therefore, the model must be validated against model independent method.

Once validated, the model-based approach can be applied to experimental data to estimate Rameal from non-tracer experiments in type 1 diabetic subjects.

Speaker: Valeriya Naumova
Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences
Title: Extrapolation in Variable RKHSs with Application to the Blood Glucose Reading
Abstract: In this talk we present a new scheme of a kernel adaptive regularization algorithm, where the kernel and the regularization parameter are adaptively chosen within regularization procedure. The construction of such fully adaptive regularization algorithm is motivated by the problem of reading the blood glucose concentration of diabetic patients. We describe how proposed scheme can be used for this purpose and report the results of numerical experiments with real clinical data. It is joint research with Sergei Pereverzyev (RICAM) and Sivananthan Sampath (RICAM).

Speaker: Nathan Gibson
Oregon State University
Title: Time-domain Electromagnetic Interrogation of Biological Materials
Abstract: We consider wide bandwidth electromagnetic pulse interrogation problems for the determination of dielectric response parameters in complex dispersive materials such as biological tissue. We couple Maxwell's equations with an auxiliary ODE modeling dielectric polarization. A problem of particular interest is to identify parameters in a standard polarization model (e.g., Debye) using time-domain electric field data. A larger class of materials (e.g., anomalously dispersive media) can be represented by assuming distributions of parameters (e.g., relaxation times). We present results for an inverse problem for the relaxation time distribution based on a least squares cost functional and utilizing generalized Polynomial Chaos in the forward problem. It is joint research with Megan Armentrout, Oregon State University.

Speaker: Ryan A. Hass Oregon State University
Title: Comet Tail Artifacts in 2D Computed Tomography
Abstract: Computed tomography inversion formulas that are dependent on π-lines are investigated.  For each point in the support of the function, the domain of integration in the inversion formula varies with respect to source position.  We hypothesize that this property is the cause of the so-called comet tail artifact found in the numerical reconstructions.  We develop theory to describe the location of the artifact in fan-beam for many types of π-lines.

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