Page 69 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 1 Multi-scale models of the heart for patient-specific simulations 39

valve, in which the opening angle is determined dynamically by
matching an interface condition. In the approach presented here,
the dynamics is handled by a reduced degree of freedom system,
namely the pressure-driven 0D valve system already presented in
section 1.4.1. This dynamic system then maps its opening phase
to the pre-computed matching kinematic frame, which is used to
impose no-slip boundary conditions on the surrounding fluid. In
Chapter 2 we provide more details about this approach.

1.5 Current approaches to parameter
estimation

As computational models mature and numerical solvers be-
come more efficient, scientists started to investigate how these
models could be applied for clinical problems [5,6,8,9,47]. Sev-
eral personalization approaches have been proposed, from en-
tirely manual to automatic image-based methods. For instance,
a common arterial Windkessel (WK) model personalization tech-
nique can be found in [185,186]. However, personalizing electro-
mechanical models is a more challenging endeavor due to the sig-
nificantly higher computational cost of the forward simulations
and the larger number of free parameters to estimate. Several cat-
egories of methods can be identified in the literature, including
gradient-based and gradient-free inverse optimization methods,
data assimilation methods, methods based on machine learning
(ML), and stochastic approaches. The following sections provide a
brief overview of each of these strategies. One specific implemen-
tation is detailed in Section 2.5.

1.5.1 Inverse optimization
The standard approach to estimate tissue parameters from
data is based on optimization, as in [6,18] for instance. The
idea is to design a cost function that calculates the distance be-
tween computed parameters and their clinical measurements,
and minimize that cost function by tuning the free parameters
of the model. A common choice is to use gradient-free meth-
ods [187], as the cost functions and their derivatives with respect
to model parameters can be complex to derive analytically. For
instance, in [188], the authors proposed a gradient-free optimiza-
tion method to estimate patient-specific biomechanical contrac-
tility from myocardial velocity. Mathematical representation of
heart shape and motion was also exploited in [189] to evaluate
the goodness of fit between the biomechanical simulation and