1. are called the chordae tendineae. Studies on the

1. Introduction


The mitral valve
(MV) separates the left atrium (LA) from the left ventricle (LV) and controls
the blood flow from the LA into the LV. It is a complex cardiac structure
composed of the valve annulus, the valve leaflets (anterior and posterior), the
chordae tendineae and the papillary muscles (PMs) (Fig. 1).
Each leaflet of the valve can be divided into 3 segments: lateral, middle and
medial, as proposed by Carpentier (Carpentier
1983), thus allowing precise description of the location of the valve
dysfunction. Both leaflets are anchored to the PMs by cord-like tendons which
are called the chordae tendineae. Studies on the chordae tendineae have distinguished
different types of the chordae by their location of insertion into the leaflets:
(a) marginal chordae are inserted into the free margin of the leaflets; (b)
basal chordae are found near the annular attachment; and (c) strut chordae attach
PMs to the central parts of the leaflets (Lam
1970; Kunzelman 1990).

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!

order now

the diastole, the MV opens as a result of increased pressure in the LA as it
fills with blood. The blood then flows to the LV. The chordae tendineae are
relaxed during the diastole because the MV is opened. The diastole ends with
atrial contraction and the leaflets close thus preventing the backflow of the
blood into the LA. Since the pressure in the LA becomes much lower than in the
LV, the leaflets attempt to evert to the lower pressure region. The chordae
tendineae prevent this eversion, called prolapse, by becoming tense and holding
the leaflets in closed position.

prolapse is a condition in which the MV does not close smoothly but instead one
or both leaflets bulge upward into the LA. This is occasionally due to the
rupture of the chordae tendineae that support the MV (Shah 2010). In some cases, the prolapsed MV lets a small amount of
blood flow backwards from the LV into the LA. This disorder is called mitral
regurgitation (MR). If
mild, MR may not cause problems, however, severe MR can lead to a
life-threatening emergency including pulmonary congestion and heart failure.
The severity of MR generally depends on the number and location of the ruptured
chordae. A single ruptured chorda may lead to mild MR which requires no
treatment, while the multiple chordae ruptured simultaneously can cause severe
MR (Gabbay 2010). The rupture of the
marginal chordae almost always leads to severe MR, while the ruptured basal
chordae are usually not critical (Dal-Bianco

The underlying causes of chordae tendineae
rupture include subacute endocarditis, rheumatic heart disease, myxomatous
degeneration and other heart and valvular diseases (Gabbay 2010). Mechanical properties of diseased chordae are
significantly different from those of normal chordae (Barber 2001), therefore the rupture occurs when the strain forces
exceed the stretching threshold of the diseased chordae (Gabbay 2010).

MR caused by
chordae tendineae rupture is typically corrected by the chordae replacement
with expanded polytetrafluoroethylene (ePTFE), also known as Gore-Tex, sutures (Ibrahim 2014). These sutures appear to
be a good material for the synthetic chordae replacement because of their
biomechanical properties, similar to those of the natural chordae (Salvador 2008).

A variety of surgical techniques for the chordae
replacement are available (Ibrahim 2012).
The most common technique for replacing the ruptured chordae with the
neochordae is called the loop technique. This technique uses a set of premade
ePTFE suture loops which are anchored to the PM and then used to re-suspend the
prolapsing segment of the leaflet (Seeburger
2010). The disadvantage of this technique is that during the surgery the
heart is stopped and the cardiopulmonary bypass pump takes over the work of the
heart and the lungs. Another disadvantage is that the required length of
neochordae is obtained by a process of trial and error, therefore the heart may
have to be stopped and restarted few times during the surgery (Ibrahim 2012).

Recently, a new
technique of neochordae implantation was introduced. NeoChord DS1000 device (Fig. 2) enables off-pump (also called “beating-heart”)
transapical implantation of neochordae. The device is passed into the beating
heart through a small incision and advanced through the MV into the LA under
echocardiographic guidance. A grasping mechanism with a semi-dull needle on the
tip of the device is used to anchor the neochordae to the prolapsing segment of
the leaflet. The neochordae are then secured under proper tension to the LV
apex (Merk 2014).

transapical implantation of neochordae shows promising clinical results (Lancellotti 2016; Colli 2017), it
requires additional experience and further studies. Some aspects of this
technique, such as exact positioning of the neochordae to the prolapsing
segment or the length adjustment of the neochordae to eliminate prolapse while
preventing additional restriction of the leaflet, can only be assumed at this
moment (Seeburger 2012). Therefore,
the use of a numerical simulation approach to clarify these aspects should be

simulation of the MV structure based on the patient-specific data has proven to
be useful to evaluate the effects of the MV surgical repair techniques (Choi 2014; Rim 2015; Morgan 2016a). However,
only a few studies on the numerical simulation of the MV repair with neochordae
implantation were published (Rim 2014;
Sturla 2014; Sturla 2015a; Morgan 2016b). Moreover, none of them has
addressed the problem of the transapical MV repair.

Therefore, the
purpose of this study is to evaluate the transapical MV repair using numerical
simulation approach and to determine the effect of the length adjustment of the
neochordae on the function of the prolapsing MV.


2. Materials and Methods


2.1. Data acquisition


has become routinely used in the diagnosis, management and follow-up of
patients with any heart disease. Transthoracic echocardiography (TTE) is the
most common type of echocardiography for the assessment of morphology and
geometry of the MV, which provides accurate quantification of valvular
dysfunction (Zeng 2014). During TTE,
the ultrasonic transducer is placed on the chest of the subject to get various
real-time views of the heart.

The data of the
movement of the non-prolapsing MV at the heart rate of 66 bpm,
characterized by a 22 Hz time frequency, was obtained during TEE at Leiden
University Medical Center (The Netherlands) using Vivid e95 (GE
Healthcare) ultrasound machine. The acquired data set was stored as a
volumetric medical image (VolDICOM) and exported for further processing.


2.2. Image processing


reconstruction of the MV geometry was performed using the custom platform
developed in MATLAB (Mathworks) by Biomechanics Research Group of Politecnico
di Milano (Italy) (Sturla 2015b).
The procedure consisted of the following steps: (1) positioning of the coordinate
reference system into the VolDICOM; (2) generation of the radial planes; (3) manual
tracing of the positions of the MV and the PMs; and (4) reconstruction of the 3D
MV geometry. Afterwards, the input file for the analysis in Abaqus/Explicit
(Dassault Systèmes) was prepared.

XYZ coordinate system was positioned into the acquired VolDICOM so that Z axis would
connect the LV apex and the MV centroid, while X and Y axes would be
perpendicular to the MV annular plane, thus creating two long-axis (ZX and ZY)
and one short-axis (XY) planes. By rotating a long-axis plane by 10 degrees
along Z axis, 18 radial planes were generated.

end-diastole (ED) was chosen as the initial state for the analysis, since at
this point in time the MV can be assumed as approximately unloaded (Sturla 2015b). The positions of the MV
annulus and free margin were manually identified on every radial plane during the
ED. For each leaflet, the identified points were interpolated with cubic spline
of 32 points, uniformly distributed along the length of the leaflet. By fitting
the 4th order Fourier approximation function to these points, a 3D point cloud
was generated, consisting of 32 levels running from the annulus to the free
margin, each with 200 points, uniformly distributed along the circumference of
the MV.

created points were connected into a mesh of 3-node shell elements (type S3R in
Abaqus). Regionally varying thickness was assigned to the leaflets, as
suggested by Kunzelman et al. (Kunzelman 2007), with an average value
of 1.32 mm for the anterior leaflet and 1.26 mm for the posterior one.

addition, the points of the PM tips were manually traced during the ED. A
branched network of the chordae tendineae of three orders, i.e. marginal, basal
and strut, was created, connecting the PM tips and the valve leaflets. The number
of the chordae and their insertion points on the leaflets were determined in
accordance to ex vivo study by Lam et al. (Lam 1970) and indications by clinicians (Stevanella 2011). The marginal, basal and strut chordae were
modeled as truss elements (type T3D2 in Abaqus) with constant cross-sectional
area values of 0.40, 0.79 and 1.15 mm2 respectively.


2.3. Mechanical properties


tissue of the MV leaflets is composed of collagen, elastin and muscle fibers. Such
tissue demonstrates higher stiffness along the collagen fiber direction
compared with the cross-fiber one. Since collagen fibers are oriented along the
longitudinal direction (i.e. parallel to the annulus) of the leaflets, the
mechanical response in this direction is stiffer than in the transversal one
(i.e. perpendicular to the annulus). Therefore, the mechanical behavior of the
MV leaflets was assumed non-linear and anisotropic, and described through a constitutive
model, proposed by Lee et al. (Lee 2014):



where ? is a
strain energy density function, I1
and I4 are the invariants
of the right Cauchy-Green strain tensor, ?
is a constitutive parameter governing the level of material anisotropy, and ci are the remaining
constitutive parameters. All the constitutive parameters where identified by stress-strain
curve fitting to planar biaxial mechanical test data, reported by May-Newman
and Yin (May-Newman 1998).

mechanical behavior of the chordae tendineae was assumed non-linear and
isotropic. It was described as hyperelastic strain energy functions available
in Abaqus material library: (1) 2nd order polynomial model for marginal and
strut chordae; and (2) 5th order Ogden model for the basal chordae. The
corresponding constitutive parameters were defined by fitting uniaxial test
data, reported by Kunzelman et al. (Kunzelman 1990).

tips were modeled as nodes without physical properties.


2.4. Boundary conditions


order to incorporate patient-specific kinematic boundary conditions, the motion
of the MV annulus was manually traced for the time frame between the ED and the
peak systole (PS) as described previously. Annular contraction was modeled by
applying nodal displacements to the points of the annulus identified at ED. The
same procedure was performed to model the movement of the PMs – the motion of
the PM tips was manually traced during the same time frame, and the nodal
displacements to the points identified at the ED were applied.

time-dependent physiologic transvalvular pressure curve with values increasing from
0 mmHg during the ED up to 119 mmHg during the PS was applied on the
ventricular surface of the leaflets.

was modeled for the atrial side of the MV leaflets, using a general contact algorithm
available in Abaqus, with scale penalty method and the friction coefficient of
0.05 between the leaflets.


2.5. Neochordae implantation


most common segment involved in the MV prolapse is the middle segment of the
posterior leaflet (P2) (Suzuki 2012).
In order to simulate prolapse of the MV, marginal and basal chordae inserted
into the P2 segment were ruptured.

position of the LV apex was manually traced during the time frame between the
ED and the PS, and the apex movement was modeled by applying nodal displacement
to the apex position identified at the ED. Virtual transapical repair of the MV
was then performed, connecting the prolapsing segment of the leaflet and the LV
apex with the neochordae.

general, implantation of more than two neochordae is desired to balance a load
per suture and to provide structural support as needed. Early clinical results
show that three to six ePTFE CV-4 type sutures with a diameter of 0.307 mm
are usually implanted, and the
implantation of four neochordae is the most common case (Rucinskas 2014, Colli 2016). Therefore, virtual transapical repair
using four neochordae, evenly distributed along the free margin of the P2
segment, was planned. In order to evaluate the effect of the length of
the neochordae on post-repair MV function, a total of four virtual repairs
using sutures of different length were performed. In the first case four neochordae
were added between the LV apex and the P2 segment without changing their lengths,
while in the next three cases the lengths of the sutures were increased by 5%,
10% and 15% respectively. The neochordae were modeled as
nonlinear truss elements (type T3D2 in Abaqus) and their mechanical behavior
was described using 2nd order polynomial model. The constitutive parameters
were defined by fitting uniaxial test data, reported by Dang et al. (Dang 1990).

time-dependent boundary conditions were applied and the function of the MV before
and after virtual repairs for the time frame between the ED and the PS was
simulated in Abaqus/Explicit.


3. Results


post-repair MV functions were compared with the functions of the MV prior to
virtual repair and evaluated in terms of several aspects:

(1) coaptation
area of the leaflets, i.e., the area of each MV leaflet in contact with the opposite

(2) coaptation
length, as the length of the leaflet apposition measured on septal-lateral diameter
of the MV;

(3) tenting
height, defined as the distance from the coaptation point to the annular plane measured
on septal-lateral diameter of the MV;

(4) stress distribution
across the leaflets;

(5) chordal tension.

All virtual
repair procedures eliminated prolapse and considerably increased the coaptation
area. The smallest increase of this area by 84.2% was obtained after the
implantation of the longest neochordae (?L = 15%),
while the largest increase by 140.7% was acquired in virtual repair using the
neochordae with ?L = 5%.

As the MV prior
to virtual repair was prolapsing, the leaflets on septal-lateral diameter was
not in a contact, so there were no actual coaptation length. Therefore, all
virtual repair procedures restored different level of the coaptation length,
ranging from 3.9 mm (neochordae with ?L = 0)
to 7 mm (neochordae with ?L = 10%).