A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands.

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

Computational electrophysiology of the coronary sinus branches based on electro-anatomical mapping for the prediction of the latest activated region.

This work dealt with the assessment of a computational tool to estimate the electrical activation in the left ventricle focusing on the latest electrically activated segment (LEAS) in patients with left bundle branch block and possible myocardial fibrosis. We considered the Eikonal-diffusion equation and to recover the electrical activation maps in the myocardium. The model was calibrated by using activation times acquired in the coronary sinus (CS) branches or in the CS solely with an electroanatomic mapping system (EAMS) during cardiac resynchronization therapy (CRT). We applied our computational tool to ten patients founding an excellent accordance with EAMS measures; in particular, the error for LEAS location was less than 4 mm. We also calibrated our model using only information in the CS, still obtaining an excellent agreement with the measured LEAS. The proposed tool was able to accurately reproduce the electrical activation maps and in particular LEAS location in the CS branches, with an almost real-time computational effort, regardless of the presence of myocardial fibrosis, even when information only at CS was used to calibrate the model. This could be useful in the clinical practice since LEAS is often used as a target site for the left lead placement during CRT. Overall picture of the computational pipeline for the estimation of LEAS.

Trends in biomedical engineering: focus on Patient Specific Modeling and Life Support Systems.

Over the last twenty years major advancements have taken place in the design of medical devices and personalized therapies. They have paralleled the impressive evolution of three-dimensional, non invasive, medical imaging techniques and have been continuously fuelled by increasing computing power and the emergence of novel and sophisticated software tools. This paper aims to showcase a number of major contributions to the advancements of modeling of surgical and interventional procedures and to the design of life support systems. The selected examples will span from pediatric cardiac surgery procedures to valve and ventricle repair techniques, from stent design and endovascular procedures to life support systems and innovative ventilation techniques.

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval.

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and stochastic basis functions, both of which evolve over time. A key to our proof is to find a suitable equivalent formulation of the original problem. The so-called Dual Dynamically Orthogonal formulation turns out to be convenient. Based on this formulation, the DLR approximation is recast to an abstract Cauchy problem in a suitable linear space, for which existence and uniqueness of the solution in the maximal interval are established.

A hybrid collocation-perturbation approach for PDEs with random domains.

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a Quantity of Interest (QoI) is an important problem. The random domain is split into large and small variations contributions. The large variations are approximated by applying a sparse grid stochastic collocation method. The small variations are approximated with a stochastic collocation-perturbation method and added as a correction term to the large variation sparse grid component. Convergence rates for the variance of the QoI are derived and compared to those obtained in numerical experiments. Our approach significantly reduces the dimensionality of the stochastic problem making it suitable for large dimensional problems. The computational cost of the correction term increases at most quadratically with respect to the number of dimensions of the small variations. Moreover, for the case that the small and large variations are independent the cost increases linearly.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology.

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations.

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation.

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient-specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models.