Data assimilation and modelling of patient-specific single-ventricle physiology with and without valve regurgitation

Abstract

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

“…Similarly, the single-ventricle volume variation was measured via MRI between 10 ml and 29 ml, whereas that reproduced by the model is between 10.7 ml and 24.5 ml [17]. Measurements such as venrticular pressure which are not employed for parameter estimation also show a good agreement with the model output [17].…”

“…where l a0 , l am , l af and l ae describe the dependence of sarcomere length l on active stress [17], t a is the time elapsed since contraction activation, t max is the activation duration of the chamber in one cardiac cycle, v 0 is the initial sarcomere shortening velocity, T a0 is the maximum active sarcomere stress and c v is a shape parameter. The passive stress is given by…”

“…Similar to [17] c v ¼ 0 is assumed and gðt a Þ is parametrized by three parameters: t a SA , the activation duration of the heart chambers, namely the single atrium; t a SV , the activation duration of the single ventricle; and t 1 , the overlap between the end of atrium activation and the beginning of ventricle activation (figure 2).…”

“…By contrast, in a closed-loop setting the asynchronization between the measurements cannot be automatically accounted for. Preliminary tests suggested that parameter estimation on individual open-loop segments of figure 1 may not result in as good a reproduction of all the measurements when substituted in the closed-loop model (also see [44] where in an open-loop configuration the heart parameters estimated for patient A are considerably different from those estimated in a closed-loop setting in [17]). Thus, in what follows, estimation is performed directly on the closed-loop model.…”

“…Both patients correspond to stage I surgery for the hypoplastic left/right heart syndrome, a form of single-ventricle physiology. The parameter estimation results for these two patients are presented in [17] and the reader is referred to this study for the choice of model, time evolution of parameter estimates with the UKF method, validation of the parameter estimates and the clinical significance of the results. Here, the method to set up the UKF and the results of parameter variances, neither of which is included in [17], are presented.…”