Felix Breitenecker

Modeling arterial and left ventricular coupling for non-invasive measurements

Abstract The aim of the presented work has been the development of an algorithm for a non-invasive, portable, easy-to-use, and affordable device for measuring systemic cardiovascular parameters such as cardiac output and peripheral resistance. The data acquisition is based on a common oscillometric measurement using an occlusive blood pressure cuff, and no additional calibration is necessary. The novel algorithm introduced here combines several simulation techniques like neural networks or differential equations, which will be explained briefly. The determination of the hemodynamical parameters is based on the idea that the ejection work of the left ventricle is subject to an optimization principle. This kind of model needs no additional external calibration and opens therefore good perspectives for non-expert use in cardiovascular risk stratification and hypertension therapy optimization. To verify the approach we present some clinical results and a relevant discussion on it, followed by a view of future work.

Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata – A comparative study

Abstract The Kermack–McKendrick susceptible-infected-recovered (SIR) model describes the dynamics of epidemics in a cumulative way. This contribution compares different approaches for introducing spatial patterns into these dynamics. The applied techniques cover lattice gas cellular automata (LGCA), stochastic cellular automata (SCA) and partial differential equations (PDE). Even though these methods involve distinct types of spatial interaction, it can be shown, that consistent qualitative and quantitative model behaviour can be obtained by means of parameter adaptions and slight technical modifications. These modifications are motivated by stochastic analysis of distributed interaction (PDE, SCA) and diffusion dynamics (LGCA) as well as prevailing physical analogies. The law of large numbers permits to approximate stochastic contacts by distributed interaction. Diffusion of particles can be approximated through empiric adjustment of a Gaussian diffusion distribution.

Interdisciplinary Strategies for Simulation-Based Optimization of Energy Efficiency in Production Facilities

This paper presents an approach for interdisciplinary optimization of energy efficiency in production plants. Domain-specific areas of action are discussed as well as the integration into a dynamic co-simulation that helps predicting the impact and financial benefit of selected energy saving measures by comparing and quantifying different scenarios. This should help giving incentives and creating impulses for strategic investment decisions. In a comprehensive methodological approach, optimization potential of both the production process itself as well as the production infrastructure is combined. The technical implementation involves several simulation environments and a framework for synchronization and data exchange in terms of co-simulation. The paper concludes with a discussion of some exemplary simulation results.

Love emotions between Laura and Petrarca —an approach by mathematics and system dynamics

Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair. F. J. Jones - a scientist for literary - recognised in these changes between love and despair an oscillating behaviour - from 1328 to 1350 -, which he called Petrarchs emotional cycle. The mathematician S .Rinaldi investigated this cycle and established a mathematical model based on ordinary differential equation: two coupled nonlinear ODEs, reflecting Lauras and Petrarchs emotion for each other, drive an inspiration variable, which coincides with Petrarch s emotional cycle. These ODEs were starting point for the investigations in two directions: mapping the mathematical model to a suitable modelling concept, and trying to extend the model for love dynamics in modern times (F Breitenecker et al). This contribution introduces and investigates a modelling approach for love dynamics and inspiration by means of System Dynamics, as well as for Lauras and Petrarchs emotions as well as for a modern couple in love. In principal, emotions and inspiration emerge from a source, and are fading into a sink. But the controlling parameters for increase and decrease of emotion create a broad variety of emotional behaviour and of degree of inspiration, because of the nonlinearities. Experiments with an implementation of this model approach and selected simulations provide interesting case studies for different kind of love dynamics - attraction, rejection and neglect, - stable equilibriums and chaotic cycles.

Blood glucose response to stress hormone exposure in healthy man and insulin dependent diabetic patients: prediction by computer modeling

To establish a qualitative and quantitative model of blood glucose response to stress hormone exposure, healthy subjects (HS) on and off somatostatin (250 mu gf/h) and insulin-dependent diabetic patients were infused with either epinephrine, glucagon, cortisol, growth hormone, or a cocktail of these hormones, raising plasma stress hormones to values seen in severe diabetic ketoacidosis. The developed input/output model consists of two submodels interconnected in series plus two additional submodels for correction of gains describing both sensitivity of tissue response and utilization as well as provision of glucose. It was shown and confirmed experimentally that blood glucose response to stress hormones was essentially nonlinear. Furthermore, the mathematical models for healthy subjects and for insulin-dependent diabetic patients proved to be of the same structure, differing only in the values of some typical parameters.<<ETX>>

Simulation of influenza epidemics with a hybrid model - combining cellular automata and agent based features

To understand and predict epidemic patterns ODEs and PDEs have been used since the beginning of the last century. But these approaches have a quite relevant shortcoming. Trying to model a multiply heterogeneous population (e.g. with individual characteristics, varying population densities) increases complexity beyond limits. To bring individual effects into epidemic models a new approach is necessary. Agent-based (AB) models as well as cellular automata (CA) represent tools which allow incorporating such influences. In this paper we shall present a hybrid model that combines the flexibility of an AB-framework with the computational efficiency of CAs. We will also look at the potential benefit of such a structure by taking a look at first (academic) results.

Development of Simulation Software - from Simple ODE Modelling to Structural Dynamic Systems

This contribution presents development and trends of simulation software, from the simple structures for ‘static’ explicit ODE models to modelling of structural dynamic systems with DAEs. Simulation emerged in the 1960’ in order to be able to analyse nonlinear dynamic system and to synthesize nonlinear control systems. Since that time simulation as problem solving tool has been developed towards the third pillar of science (beneath theory and experiment), and simultaneously simulation software has been developed further on. The paper first follows roots in the CSSL standard for simulation languages, from simple ODE modelling structures to discrete elements in ODE modelling, using the classical state space approach. Next, the extensions from explicit state space description to implicit model descriptions and their consequences for numerical algorithms and for structure of simulators are discussed, like DAE solvers and implicit model translation. Besides DAE modelling, state event description and state event handling has become a key feature for simulators – sketched by a state event classification and options for implementation. In the following, the last major steps of the development are presented: a-causal physical modelling, the new Modelica standard for ODE and DAE modelling, state chart and structural dynamic systems. Physical modelling and Modelica is outlined by examples, and for structural dynamic systems a new approach by means of internal and external events is presented – together comfortable state chart descriptions based on UML-RT. The last section reviews state-of-the-art simulators for availability of extended and structural features necessary for these last developments: DAE modelling, acausal physical modelling, state events, Modelica modelling, state chart modelling, structural decomposition for structural dynamic systems, and related features. At the end, a table summarises and compares the availability of structural approaches and features. CSSL STRUCTURE IN CONTINUOUS SIMULATION Simulation supported various developments in engineering and other areas, and simulation groups and societies were founded. One main effort of such groups was to standardise digital simulation programs and to work with a new basis: not any longer simulating the analog computer, but a self-standing structure for simulation systems. There were some unsuccessful attempts, but in 1968, the CSSL Standard became the milestone in the development: it unified the concepts and language structures of the available simulation programs, it defined a structure for the model, and it describes minimal features for a runtime environment. The CSSL standard suggests structures and features for a model frame and for an experimental frame. This distinction is based on Zeigler’s concept of a strict separation of these two frames. Model frame and experimental frame are the user interfaces for the heart of the simulation system, for the simulator kernel or simulation engine. A translator maps the model description of the model frame into state space notation, which is used by the simulation engine solving the system governing ODEs. This basic structure of a simulator is illustrated in Figure 1; an extended structure with service of discrete elements is given in Figure 3. In principle, in CSSL’s model frame, a system can be described in three different ways, as an interconnection of blocks, by mathematical expressions, and by conventional programming constructs as in FORTRAN or C. Mathematical basis is for the simulation engine is the state space description 0 0 ) ( ), , ), ( ), ( ( ) ( x t x p t t u t x f t x r r r r r r & r = = , which is used by the ODE solvers of the simulation engine. Any kind of textual model formulation, of graphical blocks or structured mathematical description or host languages constructs must be transformed to an internal state equation of the structure given above, so that the vector of derivatives ) , , , ( p t u x f r r r r can be calculated for a certain time instant ) , ), ( ), ( ( p t t u t x f f i i i i i r r r r r = . This vector of derivates is fed into an ODE solver in order to calculate a state update ) , . ( 1 h f x x i i i r r r Φ = + , h stepsize (all controlled by the simulation engine). Proceedings 22nd European Conference on Modelling and Simulation ©ECMS Loucas S. Louca, Yiorgos Chrysanthou, Zuzana Oplatkova, Khalid Al-Begain (Editors) ISBN: 978-0-9553018-5-8 / ISBN: 978-0-9553018-6-5 (CD) Essential is CSSL’s concept of SECTIONs or REGIONs, giving a certain structure to the model description. First, CSSL defines a set of operators like INTEG, which formulates parts of the state space description for the system governing ODEs. Other memory operators like DELAY for time delays, TABLE functions for generating (technical) tables, and transfer functions complete dynamic modelling parts. The dynamic model description builds up the DYNAMIC or DERIVATIVE section of the model description. Mapping the model description onto state space description, requires automatic sorting of the equations (blocks) to proper order of the calculation – an essential feature of the translator. Sometimes together with the state space equations we also meet parameter equations, parameter dependent initial values, and calculations with the terminal values (e.g. for cost functions in an optimisation). In principle, all this calculations could be done in the dynamic model description, but then they are calculated at each evaluation of the derivative vector of the ODE solver – although they have to be calculated only once. As example, we consider the model description for a pendulum. The well-known equations (length l, mass m, and damping coefficient d) and initial values, parameter and static relations and dependencies are given by ) ( 180 ) ( , , , 2 , 0 , , sin ) (

Optimierung in kontinuierlichen Simulatiossprachen: Aspekte bei Modellen technischer Systeme

Der vorliegende Beitrag beschaftigt sich mit den Moglichkeiten zur Optimierung in kontinuierlichen Simulationssprachen, indem zunachst Optimierung in Compiler- und interpKeter- orientierten Simulationssprachen gegenubergestellt wird. Als weiterer Aspekt werden Rechenzeit und State-event- Handling betrachtet, die zum Vergleich von digitaler und hybrider Simulation fuhren. Vie angefuhrten Aspekte werden an drei technischen Simulationen untersucht: zeitoptimale Steuerung einer Verladebrucke, Optimierung einer Zug fahrt bezuglich Fahrstrategie und Trassenfuhrung, Optimierung in einem hydroenergetischen System.

Introducing MATLAB into basic mathematic lectures using a custom e-learning system

To counter the decreasing interest and understanding in the basic mathematic lectures in geodesy, it was decided to supplement these lectures with MATLAB. Due to licence issues, the MATLAB Web server was used, changing the lecture to a blended learning course. A special interface for the Web server was created for a better separation of content and Web server, and the system has proven satisfactory.

Implementation der Optimierungsumgebung GOMA in ACSL

Der vorliegende Beitrag beschaftigt sich mit der Integration von Optimierungsmoglichkeiten in Simulationssprachen. Nach einer kurzen Ubersicht wird eine Implementierungsmoglichkeit von Optimierungs-algorithmen in Simulationssprachen vom CSSL-Typ angegeben. Dabei wird im wesentlichen das von der Simulationssprache erzeugte „Simulations-Hauptprogramm“ erweitert. In der Folge wird der Optimierungs-Preprozessor „GOMA“ vorgestellt, der automatisch fur ein ACSL-Modell diese Programmerweiterungen generiert; im besonderen wird auf die komplexe und unter Umstanden mehrdeutige Wertubergabe zwischen Simulations- und Optimierungsprogramm eingegangen.