title: Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability.
abstract: Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).
authors.affiliation: Inria Paris & Sorbonne Universités UPMC Paris 6, Laboratoire Jacques-Louis Lions, Paris, France.
authors.forename: Sanjay
authors.identifier: 0000-0002-2081-308X
authors.initials: S
authors.lastname: Pant
authors.affiliation: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering 'Giulio Natta', Politecnico di Milano, Milan, Italy.
authors.forename: Chiara
authors.initials: C
authors.lastname: Corsini
authors.affiliation: Cardiac Unit, UCL Institute of Cardiovascular Science, and Great Ormond Street Hospital for Children, London, UK.
authors.forename: Catriona
authors.initials: C
authors.lastname: Baker
authors.affiliation: Cardiac Unit, UCL Institute of Cardiovascular Science, and Great Ormond Street Hospital for Children, London, UK.
authors.forename: Tain-Yen
authors.initials: TY
authors.lastname: Hsia
authors.affiliation: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering 'Giulio Natta', Politecnico di Milano, Milan, Italy.
authors.forename: Giancarlo
authors.initials: G
authors.lastname: Pennati
authors.affiliation: Inria Paris & Sorbonne Universités UPMC Paris 6, Laboratoire Jacques-Louis Lions, Paris, France irene.vignon-clementel@inria.fr.
authors.forename: Irene E
authors.initials: IE
authors.lastname: Vignon-Clementel
mesh_terms: D006339:Heart Rate / Q000502:physiology*; D006439:Hemodynamics / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular
keywords: data assimilation; haemodynamics; heart rate; parameter estimation; single-ventricle physiology; unscented Kalman filter