Image-guided real-time simulation using stochastic filtering

Scientific Context

Interventional Radiology is a branch of minimally invasive surgery, which uses image-guided procedures to treat and diagnose diseases. Low dose X-ray imaging (called fluoroscopy) provides the surgeon with real-time feedback to follow and control the motion of the organs and the surgical tools. These are rather long-lasting procedures and, due to the use of ionizing radiations, they present some associated risks potentially inducing cancers. Conventionally a fluoroscopic procedure requires from 15 to 30 frames per second (fps). In order to reduce both operator and patient exposure to radiation, low rate fluoroscopy at 7.5 fps can be performed, but this entails a loss of useful medical information and a lack of reactivity from the system. In order to preserve the display frame rate, while further reducing the acquisition frame rate, fluoroscopic images could be dropped and replaced by simulated images. But even if computer-based simulation has made tremendous progress over the recent years, reaching a high level realism for training purpose, simulated images still deviate rapidly from real images acquired online [1].

A current major scientific challenge aims at correcting such deviations to provide a short-term prediction of the behaviour of the environment through simulation. A promising research path investigates ways to continuously feed the simulation with real online data: such data are tainted by various sources of uncertainties so that a compromise must be found for the simulated scene to be both mechanically compliant and close to the real data. Bayesian filters offer an appropriate theoretical framework to this approach. Uncertainties, either on the model parameters or stemming from noise on the data, for example, can be propagated to maintain a probabilistic description of the mechanical state of the model. The most probable state, with regard to the data, can then be chosen for display. Kalman filter is the most widely known filter, but it is too simple to properly handle complex phenomena such as collisions and friction or manage multiple path hypotheses (e.g. at bifurcations during endovascular navigation) that can strongly affect the probability density function of the mechanical state. More sophisticated filters, such as particle filters [2], must be used but they are computationally expensive [3].

The objective of this thesis is to develop a methodology to provide a short-term prediction of the endovascular tool position during interventional radiology procedures. The scientific challenge behind this thesis is to estimate the parameters of the model, to predict the evolution of the process, using information extracted from previous images. A real-time image-based simulation will be developed, to perform fluoroscopy procedures while maintaining the same number of fps, in order to preserve image quality, but with a consequent reduction of absorbed dose since a part of the video stream will be just simulated.

Mission

This thesis will investigate two filtering frameworks: particle filters and polynomial chaos expansions. The former have been successfully used to solve tracking problems in computer vision based on rather simple behavior models [2]. The latter have been designed to perform stochastic analyses on complex numerical models [4,5]. Both have in common to require acquiring multiple samples of the state for each acquired image, each sample corresponding to an instance of the simulation. This prevents us from using them in a real-time context.

Three main objectives will be pursued in this thesis:

  • Study both frameworks and argue on their adequacy with our specific mechanical simulation context.
  • Investigate ways to reduce the number of required samples, following recent work that exploits the description of the state with independent components in the case of particle filters [6] and compressed sensing techniques in the case of polynomial chaos expansion [7].
  • Propose a preliminary extra-low-dose fluoroscopy imaging system based on intermediary simulated images for use in interventional neuroradiology procedures [8].

Skills and profile

Required qualification: Master (in applied mathematics or computer science).

We are looking for a highly motivated student with very strong inclination for interdisciplinary research. Candidates must have a solid math background (system theory, probability, stochastic processes), and a good knowledge of medical imaging techniques. The ideal application includes expertise in C/C++ and python or Matlab.

Additional Infos

Starting date: between Oct. 1st 2015 and Jan. 1st 2016.

Salary: 1 958 euros gross monthly (about 1 580 euros net) during the first and the second years. 2 059 euros the last year (about 1 661 euros net). Medical insurance is included.

Bibliography

[1] Towards interactive planning of coil embolization in brain aneurysms. J. Dequidt, C. Duriez, S. Cotin et al. In MICCAI 2009, LNCS no 5761, pp. 377-385. Springer (2009). Available at http://hal.inria.fr/inria-00430867

[2] CONDENSATION – Conditional Density Propagation for Visual Tracking, M. Isard, A. Blake. International Journal of Computer Vision 29(1):5-28 (1998)

[3] Particle filtering and moving horizon estimation. J.B. Rawlings and B. R. Bakshi. Computers and Chemical Engineering 30:1529-1541 (2006).

[4] Polynomial chaos expansion for an efficient uncertainty and sensitivity analysis of complex numerical models. E. Bastug, A. Menafoglio and T. Okhulkova. In ESREL 2013. Available at http://www.laneas.com/publication/polynomial-chaos-expansion-efficient-uncertainty-and-sensitivity-analysis-complex

[5] Stochastic finite element methods and reliability: A state-of-the art report. B. Sudret and A. Der Kiureghian.
Dept. ot Civil and Environmental Engineering, Univ. of California, Berkeley. Technical Report no UCB/SEMM-2000/08 (2000). Available at http://citeseerx.ist.psu.edu/showciting?cid=3884272

[6] Sub-sample swapping for Sequential Monte Carlo approximation of high-dimensional densities. S. Dubuisson, C. Gonzales, and X. N Guyen. International Journal on Approximate Reasoning, 54(7):934-953 (2014).

[7] Compressed sampling of polynomial chaos expansion: Convergence analysis and sampling strategies. J; Hampton and A. Doostan. Journal of Computational Physics, 280:363–386 (2015)

[8] New approaches to catheter navigation for interventional radiology simulation Stéphane Cotin, Christian Duriez, Julien Lenoir, Paul Neumann and Steven Dawson. Proceedings of the MICCAI Conference, Springer LNCS Vol 3749, pp 534-542, 2005.

Contacts

Stéphane Cotin

Research Director