Bayesian calibration of predictive computational models of arterial growth
14:00 - 15:00
Sebastian Kehl (MPA)
New Seminar Room, E 0.11
Abstract: Measurement data used in the calibration of complex nonlinear computational models for the prediction of growth of abdominal aortic aneurysms (AAAs) - expanding balloon-like pathological dilations of the abdominal aorta, the prediction of which poses a formidable challenge in the clinical practice - is commonly available as sequence of clinical image data (MRT/CT/US). This data represents the Euclidian space in which the model is embedded as a submanifold. The necessary observation operator from the space of images to the model space is not straightforward and prone to the incorporation of systematic errors which will affect the predictive quality of the model. To avoid these errors, the formalism of surface currents is applied to provide a systematic description of surfaces representing a natural description of the computational model. The formalism of surface currents furthermore provides a convenient formulation of surfaces as random variables and thus allows for a seamless integration into a Bayesian formulation. However, this comes at an increased computational cost which adds to the complexity of the calibration problem induced by the cost for the involved model evaluations and the high stochastic dimension of the parameter spaces. To this end, a dimensionality reduction approach is introduced that accounts for a priori information given in terms of functions with bounded variation. This approach allows for the solution of the calibration problem via the application of advanced sampling techniques such as Sequential Monte Carlo.