Ordinary differential equation-based modeling of cells in human cartilage

Ordinary differential equation (ODE)-based “ionic” or “membrane” modeling of excitable, living cells is an established formalism in computational physiology permitting insight into their function. In this project, a recent model of the electrophysiology of a non-excitable cell, the chondrocyte (which maintains and sustains cartilage) – will be supported and explored.

Mammalian articular joints are essential for locomotion, postural stability, proprioception and motor learning. This results in requirements for a wide range of dynamic motion coupled with remarkable stability, supported at the tissue and cellular levels.
The cell physiology-oriented focus of this project is the articular chondrocyte, which plays a key role in extracellular matrix (ECM) synthesis and degradation in all vertebrates. The presence of mature healthy chondrocytes, and a full functional repertoire for these cells are essential for normal articular joint motion. Some of the important classes of transducer elements at the level of individual chondrocytes are ion channels, exchangers or pumps that are expressed in the cells’ surface membranes.
Within the last decade, a number of different ion selective channels and exchangers have been identified and shown to play essential roles in chondrocyte physiology. Chondrocytes may generate action potential-like signals, are metabolically active, and are capable of responses to commonly-used drugs for treating hypertension. This essential physiological regulation is possible because these cells set and maintain a stable resting membrane potential as part of their electrophysiological regulation, which can be modeled via a classic Hodkin-Huxley formalism using a nonlinear system of ordinary differential equations (ODEs)..
The mathematical modeling that forms the basis of this project represents a continuation of two published studies modeling chondrocyte electrophysiology, with an emphasis on understanding the basis for the resting potential and its physiological implications for cartilage function.
Theoretical studies of this type are essential components of ongoing efforts to address important gaps in the background knowledge of the chondrocyte, including identification of early disease markers in chondrocytes, and perhaps most importantly, understanding of and drug development for osteoarthritis.


The goal of this Master’s thesis project is to work with a previously published mathematical model of the chondrocyte. Specifically, the project entails:
1\. Porting and redeveloping legacy code (in Matlab) for the chondrocyte model to an updated language and formatting (e.g. python)
2\. Testing said model for functionality, including benchmarking with respect to previously published figures and data
3\. Employing the new implementation of the chondrocyte model in experiments designed to probe model stability and parameter uncertainty, using a “population of models” approach as based on recent work in another cell type
4\. Incorporating new experimental data into the new model implementation via reparameterizations to e.g. test the effects of drugs in silico

Learning outcome

The Master’s student will
• Gain experience working with legacy/non-expert/research code, efficient reimplementation, and meeting downstream user needs
• Gain understanding of basic physiology, electrophysiology and modeling of both excitable and non-excitable tissues and cells
• Gain understanding of and experience with ODE ionic models and related formalisms
• Learn core physiological and medical concepts, enabling translational work i.e. in the medical device, pharma, or other bioengineering industries


The Master’s student will ideally have:
• Completed a bachelor’s degree in informatics or a related discipline
• Have facility with coding in python for research applications
• Have some exposure to and interest in biology, human physiology and/or disease processes
• Willingness to have >50% of supervision remotely
• Self-motivation and an ability to meet deadlines in a timely fashion


  • Molly Maleckar
  • Hermenegild Arevalo
  • Ali Mobasheri, University of Oulu

Collaboration partners

  • Ali Mobasheri, University of Oulu
  • Wayne Giles, University of Calgary



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