# Startseite der Technischen Universität Dresden

##### ESSIM 2012

 ESSIM 2012 The Summer School — COURSES

## Mathematical models and simulation of the human cardiovascular system.

Notification: Februar 10, 2012 by Dr. A. Noack

Teacher:  Alexandra Moura (Technical University of Lisbon, Portugal)

The use of mathematical models and numerical simulations to study blood flow in the circulatory system and related pathologies is an active interdisciplinary field of research. It constitutes an inexpensive and non invasive tool, providing information difficult to obtain in vivo and easily allowing the analysis of different scenarios, for instance in surgery planning. Due to the complexity of the human cardiovascular system, the use of computational models and simulation to study blood circulation in healthy and pathological situations is a challenge to mathematicians and engineers. Nevertheless, the enormous advances in this field in the last decade make it nowadays a reliable tool which is increasingly used in clinical applications, such as the placement of stents in arteries with atherosclerotic plaques, or the understanding of aneurysm growth and rupture.

In this course some of the fundamental aspects of mathematical modeling and numerical analysis and simulation of blood flow in the human cardiovascular system will be introduced and described. The main challenges, such as the use o patient-specific geometrical models and accounting for the global circulation in local simulations, will be addressed.

Course Script

## An Introduction to Algorithmic Differentiation.

Notification: March 12, 2012 by Dr. A. Noack

Teacher:  Kshitij Kulshreshtha (Universität Paderborn, Germany)

Many applications like nonlinear optimisation and the solution of systems of nonlinear equations or the simulation of complex systems require the computation of derivatives.
In most applications not only the standard gradients and jacobian matrices are required but also directional derivatives and higher order derivatives.

Most often the functions that are to be differentiated are provided in the form of computer programs. Algorithmic Differentiation is a way to provide the required derivatives efficiently and accurately. In this course we shall derive methods of computing directional derivatives in forward mode, adjoints in reverse mode, and higher order derivatives (hessain matrices) in a mix of forward and reverse mode on the basis of the chain rule of differentiation. We shall also examine the complexity of these calculations and discuss various implementation issues and strategies.

Course Script
Exercises   Exercises
Exam with Solutions

## Environmental Modelling (Airborne Pollution studies).

Notification: April 10, 2012 by Dr. A. Noack

Teacher:  Christopher Coles (University of Strathclyde, Glasgow, UK)

Increased Environmental, Health and Safety issues connected to airbourne particulates eminating from industrial plants have resulted in a requirement for a greater knowledge of the pollutant concentration. This course will examine a number of mathematical models and associated solution techniques in order to estimate the likely ground-level particulate concentrations under various conditions.

## Introduction to Mathematical Biology.

Notification: April 24, 2012 by Dr. A. Noack

Teacher:  Osvaldo Chara, Lutz Brusch (Technische Universität Dresden, Germany)

The life sciences are rapidly turning from qualitative into quantitative sciences. Integration of the increasing amount of biological data in a systematic way requires development and application of mathematical models.
The goal of Mathematical Biology is to gain a mechanistic understanding of biological problems through the analysis of appropriate mathematical models. During the course mathematical models (especially ordinary and partial differential equations, and cellular automata) are introduced and applied to biological key problems from developmental biology and tissue morphogenesis.

Script Monday   Script Tuesday   Script Wednesday   Script Thursday

updated August 2012

##### Contact

Chair:
Prof. Dr. Stefan Siegmund
ECMI-coordinator
of Technische Universität Dresden

Contact Person
Dr. Antje Noack
Technische Universität Dresden
Dep. of Mathematics
Institute of Algebra
Phone: +49 351 463-32149
Fax: +49 351 463-34235
antje.noack@tu-dresden.de

Mail to:
TU Dresden
Institute of Algebra
01062 Dresden
Germany

Bulk mail to:
TU Dresden
Helmholtzstraße 10
01069 Dresden
Germany