Analysis of uncertainty and variability in finite element computational models for biomedical engineering: characterization and propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering

Characterization of mismatch between behavioral stimuli and FRMI data using the Kalman filter

The advance of blood oxygen level dependent function magnetic resonance imaging, (BOLD fMRI), allows researchers to non-invasively investigate the functioning human brain. The BOLD fMRI response to brief stimuli is called the hemodynamic response function (HRF), which can vary across brain regions and across subjects. Models of the HRF are used to increase sensitivity of statistical maps; however, they often don\u27t account for spatial and temporal variance. Physiological effects, such as learning, fatigue or habituation, introduce mismatch between statistical models and the data. Methods that use minimal a priori information and track time varying signals are able to show the processing of information over time and thereby elucidate such effects. The method of Kalman filtering was employed to characterize mismatches occurring between statistical models and BOLD data. The Kalman filter operates on data point by point. This contrasts regression techniques, that use blocks of data to find a single estimate. Functional MRI data was collected from ten subjects at Columbia University while they engaged in three visual experiments and four olfactory experiments. The Kalman filter was used to distinguish between the fMRI response to a 2 second and a 12 second visual stimulus. The results from this analysis showed the extracted responses from the two stimuli significantly differed. The same analysis was also used to distinguish between primary and secondary olfactory cortices. These brain regions have shown differential temporal responses to odorants. The extracted responses were not significantly different. Extracted responses from one stimulus (visual or olfactory) were used to test if this subject specific information would predict the next experimental session, better than standard a priori models of the data. The results of this analysis showed this not to be the case. The extracted response over time to the odorant stimuli were tractable with the Kalman filter, and shown to decay as predicted from the literature. This temporal change was hypothesized to decrease predictability from one session to the next, causing the null result. To alleviate this, models were tested for their predictability across hemisphere, within session. The results showed that inclusion of subject specific information improved this fit over other a priori models. The implications of this analysis are the ability to extract temporally varying fMRI responses over an experiment without knowledge of the expected response to a stimuli. Results of such analyzes offer a look into how the brain responds and processes stimuli over the course of an experiment. This contrasts method that offer summary, or average, results from an experiment

Generalized Image Models and Their Application as Statistical Models of Images

International audienceA generalized image model (GIM) is presented. Images are represented as sets of 4-dimensional sites combining position and intensity information, as well as their associated uncertainty and joint variation. This model seamlessly allows for the representation of both images and statistical models, as well as other representations such as landmarks or meshes. A GIM-based registration method aimed at the construction and application of statistical models of images is proposed. A procedure based on the iterative closest point (ICP) algorithm is modified to deal with features other than position and to integrate statistical information. Furthermore, we modify the ICP framework by using a Kalman filter to efficiently compute the transformation. The initialization and update of the statistical model are also described

Generalized Image Models and Their Application as Statistical Models of Images

PMID: 15450229International audienceno abstrac

Abstract Generalized image models and their application as statistical models of images

A generalized image model (GIM) is presented. Images are represented as sets of four-dimensional (4D) sites combining position and intensity information, as well as their associated uncertainty and joint variation. This model seamlessly allows for the representation of both images and statistical models (such as those used for classification of normal/abnormal anatomy and for interpatient registration), as well as other representations such as landmarks or meshes. A GIM-based registration method aimed at the construction and application of statistical models of images is proposed. A procedure based on the iterative closest point (ICP) algorithm is modified to deal with features other than position and to integrate statistical information. Furthermore, we modify the ICP framework by using a Kalman filter to efficiently compute the transformation. The initialization and update of the statistical model are also described. Preliminary results show the feasibility of the approach and its potentialities. Ó 2004 Elsevier B.V. All rights reserved