Spatiotemporal Modeling and Simulation

Introduction to spatiotemporal modeling and simulation of biological systems

This course teaches modeling techniques for spatially resolved systems. You will learn to account for the geometry of a system and for transport in space. After repetition of the basics from mathematics and physics, you will model processes such as diffusion and flow, and simulate them in the computer.


Contents

dimensionality analysis, causality diagrams, vector fields, particle methods, governing equations for diffusion and flow, hybrid particle-mesh methods for computer simulations, student project: simulation of a biological system.


Time/Place

Lecture: Tuesdays, 13:00-14:30, CSBD Auditorium (Pfotenhauerstr. 108) / FIRST LECTURE: APR 4
Exercises: TO BE AGREED / FIRST TUTORIAL: APR


Teachers

Lecture: Prof. Ivo F. Sbalzarini
Exercises: Dr. Vojtech Kaiser


Learning goals
  • Analysis of the dynamic behavior of biological or physical systems with spatial structure

  • Formulation of a model of the system behavior

  • Computer simulation of the model using numerical methods

Special remarks

We focus on biological systems. The taught methods and concepts are, however, applicable in a much broader sense.


Lecture language: ENGLISH


Please find below the lecture syllabus, the slides, the self-check questions, and the exercises:
  • Lecture 1 - Administration and Introduction
  • Lecture 2 - Dimensional Analysis
  • Lecture 3 - Modeling Dynamics: Reservoirs and Flows
  • Lecture 4 - Recap on Vector Analysis
  • Lecture 5 - Conservation Laws and Control Volume Methods
  • Lecture 6 - Particle Methods
  • Lecture 7 - Diffusion
  • Lecture 8 - Reaction-Diffusion
  • Lecture 9 - Advection-Diffusion
  • Lecture 10 - Flow
  • Lecture 11 - PDEs
Script

Full lecture notes will be provided to the students of the course.


Project

The student project will aim at implementing the Quorum Sensing model proposed by J. Müller et al. as described here.