Flow can be described as laminar,
vortical,
or turbulent.
Although laminar flow,
which can occur in straight blood vessels,
is characterized by parallel stream lines,
vortical and turbulent flows are dominated by swirling motion of the fluid at different scales.
In the 15th century,
Leonardo da Vinci pictured vortices in the sinuses above the aortic valve.
Until today,
vortices in the human circulation remain a challenging aspect of fluid dynamics.
Modern phase-contrast magnetic resonance imaging (MRI) has shown that vortical flow is a common finding in the human heart,
as well as in the great arteries.
Vortices are created when the boundary layer of a fluid detaches from a sharp edge.
In the left ventricle laminar mitral inflow is converted into a vortex formation at the tips of the mitral valve leaflets.
This vortex formation maintains the momentum of the blood and allows smooth redirection of blood flow toward the outflow tract during systole with minimal generation of turbulence,
thus avoiding large losses of kinetic energy .
The malfunction of the cardiac pump,
in particular of the left ventricle,
represents a primary cause of death in the modern society.
Until few years ago the clinical studies were focussed to the pumping phase,
i.e.,
the left ventricle contraction known as systole,
whose pathologies represent a reduction in the heart’s ability to pump the oxygenated blood in the circulation.
It is now well known that a systolic pathology represents only the terminal stage of a generalised cardiac dysfunction whose initial minor symptoms can be recognised during the diastolic phase,
i.e.,
the ventricle filling with the blood that enters from the left atrium through the mitral valve,
therefore the early clinical diagnosis pays particular attention to the features of the diastolic filling.
Diagnoses are commonly performed by mean of non-invasive techniques (magnetic resonance,
Echo-Doppler) which give an advanced but still incomplete picture of the fluid dynamics during the left ventricle filling ,
the typical diagnostic indicators have not a clear interpretation in terms of the corresponding mechanics and are thus difficult to be verified or quantified.
An accurate modelling of the flow,
and flow–wall interactions,
inside the left ventricle is therefore necessary to improve the interpretation of the clinical observations on the basis of the physical phenomena.
In this work we consider an idealised model left ventricle under healthy conditions (Ranjbar S.
et al.
(2013) recently developed the first novel left ventricular myocardial model mathematically based on echocardiography,
by MATLAB software in normal subjects,
which dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could be created by adding together the sequential steps of the multiple fragmented sectors of that fiber.
The left ventricular myocardial modeling of the heart shows that in normal cases myocardial fibers initiate from the posterior-basal region of the heart,
continues through the left ventricular free wall,
reaches the septum,
loops around the apex,
ascends,
and ends at the superior-anterior edge of left ventricle) with achievability of the assessment of the mitral valve leaflets by mathematical equations of inelasticity,
these assumptions consider the phenomena related to the three-dimensional geometry and to the valve movement at the beginning of the filling process; however this complex geometry is often used as a basic substitute for the many possible biological shapes and is here adopted in order to define the reference phenomena,
and to not reduce the number of some parameters.
Therefore,
results should be read in a theoretical perspective as a basis for the more complex flow that may be encountered under realistic conditions.
The system of equations written in primitive variables is solved numerically by a finite difference approach in boundary-fitted moving coordinates,
allowing a next extension to three-dimensional flow.
An accurate description of the vortex dynamics occurring in the idealised ventricle is presented,
dependencies from the inlet orifice opening are systematically sought; comparisons with existing numerical and experimental findings are reported and interpretative schemes in terms of routine clinical observation are given.
This presentation is organized as follows: We present methods for flow simulations based on the motion of the LV boundary.
And we focus on ultrasound imaging and review current options for analysis of boundary conditions and blood flow tracking inside LV,
with particular attention to the emerging echo-data.
And the methods for combining the flow field obtained from computational fluid dynamics and experimental measurements are discussed.