Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

Improving Efficiency of Data Assimilation Procedure for a Biomechanical Heart Model by Representing Surfaces as Currents

“…In this work, we adopt a hybrid approach made [1,6] of the combination of a simple nudging operator on the large state space -namely P x = γ1 -which is in charge of reducing the initial state error ζ x and the model error ω -that we couple with Reduced-order Unscented Kalman Filtering (RoUKF) in charge of the remaining parameter uncertainty ζ θ in oder to define (P xθ ,P θ ). Therefore in our approach as in all other choices of data assimilation strategies we have to give a definition of the observation operator H, the observation space Z and its norm · Z .…”

“…We rely on the model extensively described in [1,12] built under the general principle of dynamics in Lagrangian formulation. The state variables are the displacement y of the solid from a reference configuration, its velocity v and the internal mechanical variables e c , k c , τ c describing the strains, active stiffnesses and stresses in the sarcomeres.…”

“…For the same reason the internal pressures in the cavities are prescribed as a function of time, typically obtained from measurements or from another model. On this mechanical heart model, we expect to retrieve some contractility parameters that are relevant to represent infarcted tissues -as already done in other data assimilation investigations such as [1] -in order to illustrate the interest of the introduction of the current formalism for the data processing.…”

“…Data assimilation methods are widely accepted [1,3,7,8,12,15,16] as an essential tool in heart modeling in order to personalize from various sources of measurements -in particular image-data -not only the specific heart geometry of a patient but also the biomechanical parameters describing a particular physiological state -healthy or pathological. A large variety of data assimilation methodologies have already been used in conjunction with various biomechanical models of the heart.…”

Current-Based 4D Shape Analysis for the Mechanical Personalization of Heart Models

“…cine-MR images). Several approaches to the problem of cardiac model personalization have been suggested in the recent years, often formulating the inverse problem via the framework of variational data assimilation [6] or that of optimal filtering theory [14][13] [3]. The output of these methods is dependent on the set of parameters used to initialize the algorithm; for this reason calibration procedures are introduced as a preprocessing stage, such as the one developed in [16].…”