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
(Ra_{meal}) changes due to meal composition and other factors could be of great help in
the design of glucose predictors, advisory systems or closedloop control algorithms.
Estimating the Ra_{meal} 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 modelindependent, 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 modelbased 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 Ra_{meal} profile. Therefore, the model must be validated against model independent method. Once validated, the modelbased approach can be applied to experimental data to estimate Ra_{meal} from nontracer 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:  Timedomain 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
timedomain 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 πlines 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 socalled comet tail artifact found in the numerical reconstructions. We develop theory to describe the location of the artifact in fanbeam for many types of πlines.

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