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Morgan et al. Vessel Plus 2020;4:6 I http://dx.doi.org/10.20517/2574-1209.2019.32 Page 9 of 14

patterns of cardiac structure, which can then be related to function and correlated with clinical outcomes.
This has been previously used on the RV to identify differences in patients with pulmonary hypertension
(PH) compared to normal controls, demonstrating that patients with PH have increased RV eccentricity
[59]
(a rounder shape), with bulging of the apex and the tricuspid annulus . Increased RV size and sphericity
have also been associated with the known cardiovascular risk factors of hypertension, diabetes, obesity,
[60]
and smoking . In congenital heart disease, for patients with single-ventricle pathology, changes in
[58]
ventricular shape have been clinically correlated to symptom severity . As data accrue for different RV
and TV pathologies, shape analysis will allow creation of non-invasive predictive tools of disease severity
and outcomes.

Finite element modeling
Finite element (FE) modeling is a tool that allows the calculation of the stress-strain behavior of complex
materials by breaking them down into small pieces, or elements. This tool has been applied for the last
three decades to increase understanding of cardiac mechanics in diverse ways, including modeling the LV
and mitral valve and simulating mitral ring annuloplasty, mitral leaflet resection, and percutaneous mitral
clip application [19-22,61] . Modeling of the TV has lagged behind models of the left heart; the RV and TV are
more complex in shape and behavior than the LV and mitral valve; their anatomy is more variable between
patients and between time points in the same patient; the right and left heart are interdependent, with
RV behavior altered by LV pressure and by the function of the interventricular septum; and, to model the
right heart, some measures of right-sided cavity pressures are required, which typically involve invasive
procedures such as cardiac catheterization. Furthermore, extant computational models ignore the complex
interaction between the TV and RV, and as yet, no patient-specific models of the RV + TV, or the LV + RV
+ TV, have been created. Development of such models will allow direct comparison of different repairs
for a specific patient to determine the ideal repair type, accounting for the effect of such repairs on the
ventricles and valve as a unit.

Modeling the RV + LV
To create an FE model of the myocardium, the 3D geometry of the ventricles is first captured with
cardiac imaging, using echo, computed tomography (CT), or cardiac MRI. These images are “contoured”,
outlining the endocardium and epicardium, to create a virtual mesh of the LV, RV, or both. The stress-
strain relationships, or material property laws, of regions of the myocardium are then specified. Multiple
formulations of these material property laws exist; our lab employs the version developed by Drs.
[62]
McCulloch and Guccione (CMISS/Continuity) . These laws are based directly on the 3D fiber angle
distributions of the myocardium [Figure 4], are commonly used, and have been validated experimentally
under multiple conditions [63,64] . Biventricular models of rat, swine, and canine hearts have been created
with this technique to demonstrate increased myocardial stress in heart failure and pressure overload [65-67] .
In addition, of more direct clinical relevance, human, patient-specific biventricular models have been
[68]
created to accurately predict the effect of cardiac resynchronization therapy . To date, these models have
not examined the ventricles in patients with TR, and they have not incorporated the TV.

Modeling the isolated TV
To create patient-specific models of the TV, high-resolution images are required to describe its complex
valvular geometry. Initial studies focused on excised cadaver valves, which are stationary and easy
[69]
to structurally define . In living patients, 3D echocardiography images of the TV can be contoured
in individual slices at a particular point in the cardiac cycle, to obtain a mesh of the overall valvular
structure. Material properties are then applied as described above for the myocardium; these properties
have been obtained experimentally from excised leaflet tissue, using predominantly biaxial stretching
[70]
to determine stress-strain relationships . Using these techniques, the first computational model of the
[69]
TV, based on excised human cadaver tissue, was created in 2010 . Initial patient-specific models of the