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CHA PTE R

Towards the Real-Time Modeling of the Heart

,†
R.R. Rama* , S. Skatulla* ,†
*Center for Research in Computational and Applied Mechanics, UCT, Cape Town, South Africa
†
Department of Civil Engineering, Computational Continuum Mechanics Research Group, UCT, Cape Town, South Africa

8.1 INTRODUCTION

Computational cardiac mechanics have seen a significant amount of research activity during the last decade in an
effort to support and supplement clinical and experimental work. In order to simulate the pumping heart, one needs
to describe the nonlinear elastic material behavior of the heart muscle tissue [1, 2], the electrophysiology pacing the
contraction of the heart muscle [3], the active contraction effect to eject blood into the lungs and systemic circulatory
system [2], and the coupling of the blood circulatory system to the heart in terms of varying blood pressure and flow
resistance [4] using mathematical and computational models. As a result, those models have become increasingly
realistic to the extent that patient-specific heart simulations can provide for qualitative and quantitative predictions
of the heart’s function in health, injury, and disease leading to advances in diagnostic and therapeutic procedures
(see e.g., Baillargeon et al. [5]).However,inthose mathematical models stated, complex coupled nonlinear partial
and ordinary differential equations are employed and need to be solved using iterative schemes. These computa-
tional calculations are extremely time consuming [6]. In Refs. [7–10], it has been found that the required computa-
tional resources can vary from 16 to as much as 200 processors for calculation times ranging between 1 and 50 h for
only one single heartbeat. Practical medical and research application of heart modeling would usually involve a mul-
titude of simulations for time periods significantly longer than one single heartbeat to study variations in physio-
logical conditions with respect to hemodynamical loads, disease progression, therapeutical measures or medication,
etc. This, however, cannot yet be achieved by conventional means of computer modeling. For this reason, the appli-
cation of such models has been very limited in the medical practice, as they would be usually required to be run on
common desktop or laptop machines.
Current advances in computing power do not yet allow for a speed-up in these types of numerical computa-
tions. Hence, in the literature, many researchers have explored alternative ways. One popular approach consists of
the use of a mass-spring model [11, 12]. As elaborated, for example, in Meier et al. [12], a mass-spring model
defines a geometrical mesh in terms of discrete mass points that are interconnected by springs. With the help
of the Newtonian law of motion and a time discretization scheme, the deformation of the mesh can be solved
for when subjected to external forces. This method is considered simple and computationally efficient [13], and
has led to a wide range of applications. For example, Nedel and Thalmann [14] simulated the brachialis muscle
of the upper arm. Liu et al. [15] studied a nonbiomechanics related example, namely the hanging of cloth. Using the
mass-spring approach, they achieved a calculation frequency ranging from 0.2 to 185 Hz, but with relatively large
errors. In Ref. [16], Luboz et al. modeled the deployment of a stent in the femoral artery using an inflated balloon.
Their simulations were carried out at a frequency range of 26–53 Hz. Even though high computational speed was
achieved using the mass-spring method, Nealen et al. [13] reported that the models had low accuracy, and accord-
ing to Meier et al. [12], unrealistic behavior, such as delays in deformation propagation and unphysical oscillations.
Another common approach for more realistic real-time simulation is through the use of the linear finite element
method (FEM) [17, 18]. Thelatterdoesnot requireanupdateofthestiffnessmatrixtosolveforthemechanical
fields such as displacement, stress, and strain. Some examples of its application in the literature are as follows:
Cotin et al. [11]proposedan “enhanced linear elastic FEM model” in order to account for the nonlinear behavior

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