Preface.- 1. Studying the deformation of left ventricular myocardium based on different techniques regarding to the echocardiography.- 2. Left ventricular modeling as a polygon.- 3. Considering the torsion calculation of left ventricular muscle by Speckle Tracking in echocardiography.- 4. Motion analysis of left ventricular inner-wall.- 5. Generalized strain components of the left ventricular myocardium.- 6. Mathematical techniques to assess left ventricular myocardial forces based on echocardiography.- 7. Left ventricular fiber arrangements and orientations.- 8. Left ventricular myocardial force vectors- Mathematical work lab.- 9. Laganjian mechanic of the left ventricle.- 10. Dynamic features creating (which cause) the blood direction inside the left ventricle.- 11. A novel quantitative indicator of the left ventricular contraction based on volume changes of the left ventricular myocardial segments.- 12. Different Mathematical Techniques to Measure Left Ventricular 2D Deformations: Strain Imaging.- 13. Bernoulli Equation in the Mitral Valve of Heart.- 14. Discovery and the development of the mathematical solution for patient-specific human heart modelling based on echocardiographic imaging.