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
Purpose
As stated by Jacques Hadmard in 'science and hypothesis',
mathematical creation and mathematical intelligence are not without connection with creation in general and with general intelligence.
A great proportion of prominent mathematicians have been creators in other fields.
One of the greatest,
Gauss,
carried out important and classical experiments on magnetism; and Newton's fundamental discoveries in optics are well known.
And Leibniz influenced by their mathematical abilities on philosophical ones.
The research perspectives I propose here,
are motivated by my background and previous research,
and are supposed to indicate my general directions in forthcoming research.
Following Poincare,
each research subject is formed by an attempt to link two fields in sciences,
in order to contribute to at least one of the two.
In this proposal,
always the medical imaging part is the part which takes the benefit.
Currently,
an echocardiogram presents the left ventricle (LV) based on images obtained from ultrasound methods.
Utilizing mathematical equations,
specific echocardiographic data may provide more detailed,
valuable and practical information for physicians.
In a great many problems the microscopic structure of matter can be disregarded and a biological body replaced by a continuous mathematical model whose geometrical points are identified with material points of the body. The learning of such models is in the province of the mechanics of continuous media,
which covers a vast range of problems in elasticity,
hemodynamics,
aerodynamics,
plasticity,
and electrodynamics.
When the relative position of points in a continuous biological body is altered,
we say that the body is strained.
The change in the relative position of a point is a deformation,
and the study of deformations is the region of the analysis of strain.
In this presentstionr,
the left ventricular myocardium is taken as a biological elastic body and modeled by mathematical/imaging techniques.