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Prescott et al. Vessel Plus 2019;3:13 I http://dx.doi.org/10.20517/2574-1209.2018.70 Page 5 of 10

Figure 3. Radial stress-strain response of human hypertrophic obstructive cardiomyopathy anterior and posterior leaflet samples,
experimental data vs. model simulation

Table 1. Reduced polynomial material parameters used to define the mechanical behaviour of the mitral valve tissue
Leaflet C 10 C 20 C 30 C 40 C 50 D 1 D 2 D 3 D 4 D 5
Anterior 0.00964 -0.106 0.788 -2.364 2.514 0.001 0 0 0 0
Posterior 0.00110 0.00152 -0.00389 0.00222 0.00079 0.001 0 0 0 0

For the anterior leaflet, the model parameters were obtained by fitting the constitutive equation to
[17]
experimental radial stress-strain data of HOCM anterior valve tissue provided in the literature . It should
be noted that the anterior and posterior leaflets exhibit different mechanical behaviour, with the posterior
leaflet having higher extensibility (i.e., lower stiffness). Due to a lack of stress-strain data for the HOCM
[17]
posterior leaflet, a shift, based on the difference measured for healthy anterior and posterior leaflets ,
has been applied to the stress-strain data for HOCM anterior leaflet in order to capture the increased
extensibility of a posterior leaflet. The shifted stress-strain data were then used to calibrate the model
parameters for the HOCM posterior leaflet. The resulting curve fit and model parameters can be seen in
Figure 3 and Table 1, respectively, and were obtained by conducting single-element simulation using the
described material model. The compressibility (D) parameters were fixed based on the assumption of MV
[18]
tissue being “nearly incompressible” , whilst the C values were refined iteratively to obtain the closest fit.
3
A density of 10.4 g/cm was assigned to all MV tissue. This value is ten times higher than the actual value to
[13]
account for the inertial effects of blood flow .
As aforementioned, the mechanical behaviour of the chordae tendineae was described using a simplified
spring stiffness approach. The value of 1.6 N/mm was estimated according to chordae properties given in
[12]
the literature . The use of built-in SPRINGA elements from the Abaqus library is ideal for simulating the
response of the chordae tendineae, as this element is able to transmit axial load through a line of action and
[19]
this line of action is able to rotate when subjected to large-displacement analysis , which is characteristic of
the simulations within this study.

RESULTS
Continuum mechanics can be used to describe the deformation of structures through the use of a nine-
component stress tensor. However, individually, these values can be difficult to interpret and use in a
practical sense. Therefore, more informative stress values can be obtained through the use of mathematical
operations, derived from the original nine-component tensor. In this study, the results were provided with