Keywords:
Cardiac, Computer applications, Molecular imaging, Echocardiography, Echocardiography (transoesophageal), Image manipulation / Reconstruction, Acceptance testing, Biopsy, Ablation procedures, Blood, Image verification, Pathology
Authors:
M. Karvandi, S. Ranjbar; Tehran/IR
Conclusion
Previous investigations have strongly used searching points by image-processing machinery method,
but our study demonstrates regional and global of the myocardial function by introducing a mathematical fibered model of it,
which is rendered by a piece of software.
This method is also very robust,
reproducible,
and user friendly.
Its clinical values remain to be established,
however.
As another application of the method described in this presentation,
we can model the motion of blood in the ventricles.
This initiation is for normal and diseased hearts.
The model can be used for instructional purposes and diagnosis of heart ailments.
The standard way to model the motion of blood inside the LV would be to treat the LV as an elastic membrane obeying Newton’s laws of motion with forces calculated in part from the elasticity of the membrane and in part by evaluating the fluid stress tensor on the surface of the membrane.
Then the fluid equations would have to be supplemented by the constraint that the velocity of the fluid on either side of the membrane must agree with the instantaneously known velocity of the elastic membrane itself.
There is a difficulty with this standard approach to the problem.
Challenge is the practice of evaluating the fluid stress tensor on either side of the boundary.
This seems difficult (or at least messy) to do numerically,
unless the computational grid is aligned with the boundary.
On the other hand,
in a moving boundary problem,
it is both expensive and complicated to re-compute the grid at every time step in order to achieve alignment.
This means that the sum of the elastic force and the fluid force on any part of the boundary has to be zero.
Once we know this,
it becomes unnecessary to evaluate the fluid stress tensor at the boundary at all! We can find the force of any part of the boundary on the fluid by evaluating the elastic force on that part of the boundary.
Note the use of Newton’s third law: the force of boundary on fluid is minus the force of fluid on boundary.
All we need is a method for transferring the elastic force from the boundary to the fluid.
On a Cartesian grid,
this may be done by spreading each element of the boundary force out over nearby grid points.
The fundamental quantity that describes the motion of the fluid is represented by the vorticity defined as the tendency of fluid elements to spin; more precisely,
vorticity can be related to rotation of fluid elements and the formation of circulatory areas.
Quantitative parameters of the intra-ventricular vortex were also extracted on the basis of the vorticity (curl v= 0,
rotational blood flow is happened).
This approach can be used for instructional purposes and diagnosis of heart ailments.
In this presentation,
we were able to define how to reconstruct the LV myocardium mathematically,
by MATLAB software,
in normal tissues.
These data potentially allow the implementation of an image-based approach for patient-specific modeling of LV.