Model and discretization error estimates for real-time simulation

Development of model and discretization error estimates for the real time simulation of soft tissues

Position: Post-doctorant

Location: Strasbourg

Research topic: Medical Simulation

Projet: Mimesis

Scientifique Responsable: Stéphane Cotin



Work Environment

The position will take place in Strasbourg, within the MIMESIS team from Inria, the French National Institute for computer science and applied mathematics. Research at Inria is organised in project teams which bring together researchers with complementary skills to focus on specific scientific projects. With this open, agile model, Inria is able to explore original approaches with its partners in industry and academia and provide an efficient response to the multidisciplinary and application challenges of the digital transformation.  The scientific objectives of the MIMESIS team are related to the development of new approaches supporting advanced simulations in the context of simulation for training, planning and per-operative guidance. The underlying objectives include patient-specific biophysical modeling, dedicated numerical techniques for real-time computation, data assimilation, dynamic topological representations, and image-driven simulation. This last topic is a transversal research theme and raises several open problems, ranging from non-rigid registration to augmented reality. The MIMESIS team works in close relationship with our start-up InSimo and IHU Strasbourg, a new institute developing clinical technologies at the intersection of the fields of laparoscopy, interventional flexible endoscopy and interventional radiology. We also have a important number of international partners. More information, on our website


“Everything should be made as simple as possible, but not simpler”

This quote describes succinctly the main constraint in the development of real time simulations of soft tissues, model complexity and overly refined meshes should be sacrificed in order to maximize the frame rate. Indeed, real-time computation is a major requirement for simulations in the context of both training and assistance in the operating room [2]. Yet, providing solutions for accurate, patient-specific biomechanical modeling is essential. One of the main research interests of the MIMESIS team is to propose numerical methods and dedicated models to meet real-time constraints (for instance, the use of Euler Bernoulli beam theory over 3D elasticity [1]). Despite these models are most of the time validated experimentally in static cases [3], there is a need to provide feedback to the surgeons allowing for the estimation of the error and the reliability of the models during the simulation.


In this position, the candidate will develop error estimates for two types of errors. First, we will investigate the discretization error which assesses the validity of the mesh. Second, we will study the model error which characterizes the validity of the surrogate/simplified models used in the simulation [4]. In this context surrogate models mean, for instance, the use of beam theory instead of 3D elasticity or the use homogenised models instead of the real multiphase materials. Besides the development of such estimates, the candidate will  also develop error indicators and strategies for adaptivity. The error indicators will enable us to identify of the regions that contribute most to the error whilst the adaptive strategies will enable us to apply corrective measures when required, i.e. mesh refinement for high discretization error or reintroduction of a more complex description for high model error. As a result, this will allow us to keep the accuracy under control while at the same time limiting the computational cost. This idea has already been tested and a first journal article on the topic of error-controlled refinement is under revision. As done for this preliminary work, the different developments will be implemented in the open source framework SOFA (

Qualifications for Applicants

  • Master of science in applied mathematics and/or computer science is required.
  • Strong academic record with a weighted average grade of master’s or equivalent education with a grade of B or higher.
  • Good to excellent expertise in C++
  • Special interests for and competence within medical technology, medical imaging, development of technology for improved image guided patient diagnostics and therapy, practical experience with research methods, and R&D work  
  • We emphasize collaborative skills, initiative, ability to accomplish tasks, practical skills, and ability to create and establish new projects in collaboration with colleagues
  • Knowledge of error estimation and real-time simulations would be a plus

Selected References

  1. Igor Peterlík, Christian Duriez, Stéphane Cotin. Modeling and real-time simulation of a vascularized liver tissue. International Conference on Medical Image Computing and Computer-Assisted Intervention.
  2. François Faure, Christian Duriez, Hervé Delingette, Jérémie Allard, Benjamin Gilles, Stéphanie Marchesseau, Hugo Talbot, Hadrien Courtecuisse, Guillaume Bousquet, Igor Peterlik, Stéphane Cotin. Sofa: A multi-model framework for interactive physical simulation. Soft Tissue Biomechanical Modeling for Computer Assisted Surgery
  3. Stéphanie Marchesseau , Tobias Heimann , Simon Chatelin , Rémy Willinger , and Hervé Delingette. Multiplicative Jacobian Energy Decomposition Method for Fast Porous Visco-Hyperelastic Soft Tissue Model. International Conference on Medical Image Computing and Computer-Assisted Intervention.
  4. Daniel Paladim, José Moitinho de Almeida, Stéphane Bordas and Pierre Kerfriden. Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales. In International Journal of Numerical Methods for Engineering, 2016
  5. Daniel Paladim, Pierre Kerfriden, José Moitinho de Almeida, Mathilde Chevreuil, and Stéphane Bordas. Advances in error estimation for homogenisation. In 13th US National Congress on Computational Mechanics, 2015.