Department of Information Technology

Mathematical modelling of the human smooth pursuit mechanism

The extraocular system has been studied for hundreds of years and several mathematical models have been proposed. Apart from being mathematical curiosities, the models have also helped to achieve a better understanding of the underlying system. Further, they may have numerous applications in medicine. They could be translated into model-based tools for quantification of medical conditions such as Parkinson's disease, Multiple sclerosis, schizophrenia, Huntington's chorea, brain concussion, etc. where eye movement impairment is a common symptom. Modern eye tracking techniques have significantly simplified estimation and validation of eye models.


Mobile eye-tracking station based on tablet computer Microsoft Surface Pro and Eye Tribe eye tracker

A model of the eye must consist of a biomechanical part and a controller part. The biomechanical part attempts to describe the dynamics of the eye plant and how it reacts to neural stimulation. The controller part must describe how the eye responds to visual stimuli. It simulates the interaction of the brain with the extraocular system.

Once a model structure has been established, unknown parameters must be determined by means of system identification. Currently, we are investigating how linear nonlinear black-box models with application to the quantification of symptoms in Parkinson's Disease. We work in close collaboration with the group of Dag Nyholm at Akademiska Sjukhuset in Uppsala, Department of Neurology.

  • Graduated PhD student: Daniel Jansson


  • Smooth pursuit eye test is formulated as a nonlinear system identification problem
  • Dynamical visual stimuli design problem is solved by optimization
  • The utility of second-order Volterra models in modeling of smooth pursuit in health and disease is demonstrated


PhD thesis

Licentiate theses

Journal Papers

  • D. Jansson, O. Rosén, A. Medvedev "Parametric and non-parametric analysis of eye-tracking data by anomaly detection", IEEE Transactions on Control Systems Technology, V.23(4), July 2015, pp.1578 - 1586.

Book Chapters

  • D. Jansson, A. Medvedev, H. Axelson and D. Nyholm, "Stochastic Anomaly Detection in Eye-Tracking Data for Quantification of Motor Symptoms in Parkinson´s Disease", in Adv Exp Med Biol. 2015;823:63-82 Springer.

Conference Papers

  • V. Bro, A. Medvedev, "Nonlinear Dynamics of the Human Smooth Pursuit System in Health and Disease: Model Structure and Parameter Estimation", 56th IEEE Conference on Decision and Control, Melbourne, Australia, 2017.
  • V. Bro, A. Medvedev, "Constrained SPICE in Volterra-Laguerre Modeling of Human Smooth Pursuit", 2017 IEEE Conference on Control Technology and Applications, Kohala Coast, Hawaii.
  • D. Jansson, A. Medvedev, "Capturing Age-Related Alternations in the Human Smooth Pursuit Mechanism by Volterra Models", American Control Conference, Boston, MA, 2016.
  • D. Jansson, A. Medvedev "System Identification of Wiener Systems via Volterra-Laguerre Models: Application to Human Smooth Pursuit Analysis", European Control Conference, Linz, Austria, July, 2015
  • D. Jansson, A. Medvedev "Identification of Polynomial Wiener Systems via Volterra-Laguerre Series with Model Mismatch", 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, Saint Petersburg, Russia, June, 2015
  • D. Jansson and A. Medvedev, "Volterra Modeling of the Smooth Pursuit System with Application to Motor Symptoms Quantification in Parkinson's Disease", European Control Conference, Strasbourg, France, June 24-27, 2014.
  • D. Jansson, A. Medvedev, H. Axelson and D. Nyholm, "Stochastic anomaly detection in eye-tracking data for quantification of motor symptoms in Parkinson's disease", International Symposium on Computational Models in Life Sciences, Sydney, Australia, 2013, Best Student Paper Prize.
  • D. Jansson, A. Medvedev, "Parametric and Non-Parametric Stochastic Anomaly Detection in Analysis of Eye-Tracking Data", 52nd IEEE Conference on Decision and Control, Firenze, Italy, December, 2013.
  • D. Jansson, P. Grenholm, H. Axelson, D. Nyholm and A. Medvedev, "Parametric and non-parametric system identification of oculomotor system with application to the analysis of smooth pursuit eye movements in Parkinson´s disease", Neuroinformatics 2013, Stockholm, Sweden, 27 Aug - 29 Aug, 2013.
  • D. Jansson, O. Rosen, A. Medvedev, "Non-parametric analysis of eye-tracking data by anomaly detection", European Control Conference, Zurich, Switzerland, July 17-19, 2013
  • D. Jansson and A. Medvedev, "Visual Stimulus Design in Parameter Estimation of the Human Smooth Pursuit System from Eye-Tracking Data", 2013 American Control Conference, Washington DC, June 17-19.
  • D. Jansson and A. Medvedev, "Dynamic Smooth Pursuit Gain Estimation from Eye Tracking Data", 50th IEEE Conference on Decision and Control , Orlando, FL, December, 2011.
  • D. Jansson, A. Medvedev, H. W. Axelson, P. Stoica, "Mathematical Modeling and Grey-Box Identification of the Human Smooth Pursuit Mechanism", 2010 IEEE Multi-conference on Systems and Control, Yokohama Japan.
Updated  2020-05-11 11:04:09 by Alexander Medvedev.