Teaching plan for the course unit



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General information


Course unit name: Biological Systems Modelling

Course unit code: 363750

Academic year: 2021-2022

Coordinator: Agustin Gutierrez Galvez

Department: Department of Electronic and Biomedical Engineering

Credits: 6

Single program: S



Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Problem-solving class

Face-to-face and online




-  Laboratory session




Supervised project


Independent learning




Competences to be gained during study



To be able to analyse and summarize (Instrumental).


To be able to work in a team or a multidisciplinary group (Personal).


To be able to work in a multilingual environment and communicate and transmit knowledge, procedures, results, abilities and skills (oral and written) in a native and a foreign language (Instrumental).


To know about and apply engineering concepts to the study of biological processes and the functions of the human organism. To gain knowledge of the atomic, molecular, cellular and organic levels of the physical mechanisms and phenomena that have an impact on health and disease.

Learning objectives


Referring to knowledge

— Understand the pervasive nature of models and its crucial role in mediating our comprehension of the real world.


— Understand the concept of model, its types, uses and constraints.


— Be able to follow the classical approach to build a working model of a biological system.


— Build Forrester diagrams to capture the hypothesis of a biological model.


— Choose an adequate procedure to estimate the parameters of a biological model.


— Determine the evolution of the dynamical system before solving differential equations.


— Ensure the proper capacity for generalisation of our model using validation methods.


— Classify equilibrium points in terms of their stability.


— Determine the equilibrium points of a dynamical system and linearise them.


— Draw the layout of the trajectories of the system according to the stability of the equilibrium points.


— Determine if a system shows chaotic behaviour through Lyapunov exponents.


— Understand the role of chaos and fractals in biological systems.


— Build Forrester diagrams to capture the hypothesis of a biological model.


Referring to abilities, skills

— Use programming languages to integrate dynamic models based on differential equations.


— Analyse a dynamical model without having to integrate its equations.


— Determine the chaotic nature of a dynamical system.


— Build qualitative and quantitative models of biological systems.



Teaching blocks


1. Introduction to biological modelling

Systems, models and modelling

Uses of scientific models

Example: hemodynamic system

Classification of models

Constraints of model structures

2. Building biological models

Qualitative and quantitative model formulation

Parameter estimation

Model validation

Examples: respiratory and population models

3. Dynamic systems

State-space models

Stationary solutions

Stability and linearisation

Disturbances in dynamic models

Example: disease models

4. Chaotic systems


Autonomous and non-autonomous dynamic systems

Stationary state and limit sets

Poincare maps

Lyapunov exponents

Attractor and fractal dimensions

Example: Nervous system – Fitzhugh-Nagumo model



Teaching methods and general organization


This course is taught in English.

The methodology includes classroom activities and laboratory sessions to convey the required contents. Classroom activities provide the theoretical background of the course, presented through the use of slides and the blackboard. More information is delivered through slides, including the support of images, graphs and figures. On the other hand, the blackboard is more adequate to present mathematical expressions and proofs and allows students to better assimilate them through the elaboration of their notes. Additionally, in classroom activities guided problems are solved. In this course, laboratory sessions are of particular importance since they allow students to solve the biological models numerically. In this way, they experiment with complex models and reinforce the theoretical concepts explained in the classroom. Distance-learning activities include problem-solving exercises and lab reports. A distribution of the time devoted to each of these activities is shown at the beginning of this course plan.

Depending on the situation of restrictive access to classrooms due to the current health situation, face-to-face activities will be adapted. For theory sessions, students will be split nto two groups if inter-personal distance so requires and replaced by online lectures if face-to-face sessions are not allowed. The same applies to computer laboratory sessions, that will be carried out at home with online assistance.



Official assessment of learning outcomes


• Laboratory practice: 30%.

• Problem-solving exercises: 5%.

• Small project: 15%.

• Examinations: 50%.



Examination-based assessment

Single examination composed of questions and problems



Single examination composed of questions and problems



Reading and study resources

Consulteu la disponibilitat a CERCABIB


Modelling biological systems : principles and applications.  James W. Haefner. New York : Springer,  2005

Modelling of dynamic systems. L. Lung, T. Glad. Prentice-Hall, 1994

Dynamics of Biological Systems. Michael Small. CRC Press. Taylor and Francis, 2012

Chaos: An introduction to dynamical systems. Kathleen T. Alligood , Tim D. Sauer,  James A. Yorke. Springer-Verlag, New York, 1996.