Physics of Radiology

On optimal control of partial differential equations

We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts. We also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part. By using a suitable time semi-implicit discretization, our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes. It is asymptotic preserving in the following sense: when the mean free path of the particles is small, our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model. A uniform stability property is proved for the simple telegraph model. Various boundary conditions are studied. Our method is validated in one-dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes.

/pdf/a-new-asymptotic-preserving-scheme-based-on-micro-macro-21eiwbu6ff.pdf

A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

This study analyzes and solves a patient transportation problem arising in large hospitals. The aim is to provide an efficient and timely transport service to patients between several locations in a hospital campus. Transportation requests arrive in a dynamic fashion and the solution methodology must therefore be capable of quickly inserting new requests in the current vehicle routes. Contrary to standard dial-a-ride problems, the problem under study includes several complicating constraints which are specific to a hospital context. The study provides a detailed description of the problem and proposes a two-phase heuristic procedure capable of handling its many features. In the first phase a simple insertion scheme is used to generate a feasible solution, which is improved in the second phase with a tabu search algorithm. The heuristic procedure was extensively tested on real data provided by a German hospital. Results show that the algorithm is capable of handling the dynamic aspect of the problem and of providing high-quality solutions. In particular, it succeeded in reducing waiting times for patients while using fewer vehicles.

https://kluedo.ub.uni-kl.de/files/1957/bericht104.pdf

Dynamic transportation of patients in hospitals

https://kluedo.ub.uni-kl.de/files/2274/bericht_195.pdf

Thermodynamic consistent transport theory of Li-ion batteries

For the numerical simulation of 3D radiative heat transfer in glasses and glass melts, practically applicable mathematical methods are needed for optimal handling of problems using workstation-class computers. Since the exact solution would require supercomputer capabilities, approximate solutions with a high degree of accuracy are given. An improved diffusion approximation is presented. In contrast to the classical Rosseland approximation this method makes use of the geometry and the nongrey character for the absorption of glass. The improved 3D diffusion approximation studied in this paper has the advantage to be both efficient and sufficiently accurate.

https://kluedo.ub.uni-kl.de/files/743/itwm_4.pdf

Three-dimensional radiative heat transfer in glass cooling processes

Hypothesis: Cochlear fluid pharmacokinetics can be better represented by three-dimensional (3D) finite-element simulations of drug dispersal. Background: Local dr

/pdf/cochlear-pharmacokinetics-with-local-inner-ear-drug-delivery-46xzp5jsrk.pdf

Cochlear Pharmacokinetics with Local Inner Ear Drug Delivery Using a Three-Dimensional Finite-Element Computer Model

We present a model for dose calculation in photon radiotherapy based on deterministic transport equations. The model consists of two coupled equations, one for photon and one for electron transport and an equation for the absorbed dose. No assumptions are made with respect to the geometry or the homogeneity of the irradiated medium, so irradiation of any heterogenous medium can be simulated. To get a mathematically simpler model, approximations to the exact equations are presented which keep the essential physical contents of the exact equations, but which can be solved with less numerical effort. The results of dose calculations for simple examples are presented and discussed.

Deterministic model for dose calculation in photon radiotherapy.

In this paper domain decomposition methods for radiative transfer problems including conductive heat transfer are treated. The paper focuses on semi-transparent materials, like glass, and the associated conditions at the interface between the materials. Using asymptotic analysis we derive conditions for the coupling of the radiative transfer equations and a diffusion approximation. Several test cases are treated and a problem appearing in glass manufacturing processes is computed. The results clearly show the advantages of a domain decomposition approach. Accuracy equivalent to the solution of the global radiative transfer solution is achieved, whereas computation time is strongly reduced.

https://kluedo.ub.uni-kl.de/files/746/itwm_6.pdf

Boundary layers and domain decomposition for radiative heat transfer and diffusion equations: applications to glass manufacturing process

Temperature distributions within semi-transparent materials like glass strongly determine their behavior. It is fundamental to take radiation into account to determine exact temperature distributions. The Rosseland Approximation for radiation is usually an appropriate method, but is only valid with an optically thick glass. In the present paper, we propose an improved approximation that is both efficient and sufficiently accurate even for the semi-transparent region. This new radiation model is used to determine the temperature along the flat glass thickness during tempering. The impact of temperature evaluation on residual stresses is discussed.

Norbert Siedow

Papers

Three-dimensional radiative heat transfer in glass cooling processes

Cochlear Pharmacokinetics with Local Inner Ear Drug Delivery Using a Three-Dimensional Finite-Element Computer Model

Deterministic model for dose calculation in photon radiotherapy.

Boundary layers and domain decomposition for radiative heat transfer and diffusion equations: applications to glass manufacturing process

Application of a New Method for Radiative Heat Transfer to Flat Glass Tempering