Page 54 - Artificial Intelligence for Computational Modeling of the Heart

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

The Rice model [123] is commonly used in recent simulation stud-
ies. It has been further augmented with metabolic and energetic
considerations [124]. This type of models captures most of the
known cellular and molecular mechanisms involved in myofila-
ment function, from the CICR mechanisms to troponin function
and ion binding to force generation. These models can comprise
more than 40 ordinary differential equations that need to be in-
tegrated. Scaling up these models at the organ level is therefore
challenging and computationally demanding (40+ equations per
mesh node), although not impossible [123,125], provided they are
coupled with an electrophysiology model that can calculate di-
rectly the intra-cellular Ca 2+ concentration. Nonetheless, the very
large number of free parameters (40+) and their direct link to ionic
and molecular properties make these models difficult, if not im-
possible, to personalize from standard of care clinical data.

Phenomenological models
The idea behind phenomenological models is to provide an
integrated description of the biological mechanisms from the my-
ofilaments to the organ [103,126]. The transition from one spatio-
temporal scale to another is achieved mathematically, using mean
field theory for instance [103], ultimately resulting in a set of sim-
plified equations that are controlled by fewer parameters (usually
four to five parameters). Sermesant et al. [45] proposed a simpli-
fied version of these models, with analytical integration for model-
based image analysis. A multi-scale model that also considers en-
ergy exchange during the heart beat was then proposed in [103],
to ensure the balance between oxygen supply and energy con-
sumption. Details of a phenomenological model used for patient-
specific simulations are given in section 2.3.2.

Lumped models
Lumped models are analytical models of the fiber contraction
that do not consider spatial variability – therefore not requiring
3D meshes to be solved. They focus on an averaged myocyte re-
sponse, with a small number of bulk response laws characteriz-
ing the contraction [127]. These models can be solved very effi-
ciently but they cannot capture regional abnormalities of the my-
ocardium in patients, like scars or localized fibrosis for instance.
As the research community focuses more on patient-specific sim-
ulations, lumped models regained interest for their computa-
tional efficiency. In particular, hyper-reduced models have been
developed as surrogates of more complex 3D models, in order to
achieve fast model personalization [128,129].