A novel mathematical fluid dynamic of left ventricular dilated cardiomyopathy Poster No.:

450

Congress:

ESCR 2014

Type:

Scientific Poster

Authors:

M. Karvandi, S. A. Hassantash, S. Ranjbar; Tehran/IR

Keywords:

Cardiac, MR physics, Molecular imaging, Echocardiography, Echocardiography (transoesophageal), MR, Computer Applications-3D, Comparative studies, Computer ApplicationsDetection, diagnosis, Blood, Image verification, Pathology

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Purpose Modifications in diastolic function occur in a broad range of cardiovascular diseases and there is an increasing evidence that abnormalities in left ventricular function may contribute significantly to the symptomatology. The flow inside the left ventricle duringthe diastole is here investigated by numerical solution of the Navier-Stokes equations under the axisymmetric assumption. The equation are written in a body-fitted, movingprolate spheroid, system of coordinates and solved usinga fractional step method. The system is forced by a given volume time-law derived from clinical data, and varying the twodegrees-of-freedom ventricle geometry on the basis of a simple model. The solution under healthy conditions is analysed in terms of vorticity dynamics, showing that the flow field is characterised by the presence of a vortex wake; it is attached to the mitral valve duringthe acceleratingphase of the E-wave, and it detaches and translate towards the ventricle apex afterwards. The flow evolution is discussed, results are also reported as an M-mode representation of colour-coded Doppler velocity maps. So demonstration of blood flow direction inside cardiac chambers can provide valuable information in normal subjects and pathologic cardiac processes. In this project we have attempted to define blood flow pattern in left ventricular dilated cardiomyopathy. Ranjbar S. et al. (2013) recently developed the first novel left ventricular myocardial model mathematically based on echocardiography, by MATLAB software and LSDYNA 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 superioranterior edge of left ventricle. In the presence of the left ventricular dilation, papillary muscles away from each other and the left ventrile is like a sphere (Figure 1,2,3 and 4) Images for this section:

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Fig. 1: Normal left ventricular chamber in MATLAB software

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Fig. 2: Lower figure shows that papillary muscles are in a normal position.Upper figure presents an abnormal variation between papillary muscles position.

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Fig. 3: Left ventricular dilation in LSDYNA software

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Fig. 4: Left ventricular dilation (at the left side). Normal left ventricular chamber (at the right side)

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Methods and Materials The study was conducted on 20 patients (figure 5 to 11) whom their LV models were already determined, based on their echocardiograpic data. This information along with blood flow parameters including: local interacted force with the myocardial segments, velocity vectors (local radial, local longitudinal and local circumferential), local relative strength of blood with the 16 myocardial segments (radial, longitudinal and circumferential) and curvature index were defined and used as input into algorithm to solve the partial deferential Navier- Stocks equations. For all calculations average mean ± standard deviation was used. Images for this section:

Fig. 5: A left ventricular dilated case at early diastolic phase.

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Fig. 6: A left ventricular dilated case at early systolic phase.

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Fig. 7: Analyzing the same left ventricular dilated patient by using of the velocity vector imaging method to extract motion and deformation data.

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Fig. 8: Endocardial vector point velocity at the same case.

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Fig. 9: Endo long velocity at the same case.

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Fig. 10: Endo long strain at the same case.

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Fig. 11: Endo long strain rate at the same case.

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Results In patients with Dilated Cardiomyopathy (DCM), the vortex was located at the center of the LV throughout diastole and systole and did not redirect flow in a coherent, sequential fashion as in normal subjects. In normal subjects, the average vortex was compact, elliptically shaped, and was located apically. This vortex was persistent during diastole and directs vectors towards the LVOT. In patients with DCM, a spherical, centrally located vortex was observed with incoherent direction of LV flow (Figures 12 to 19) Images for this section:

Fig. 12: a left ventricular dilation at early diastolic phase

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Fig. 13: The same left ventricular dilated case at the end of diastolic phase.

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Fig. 14: The flow vortices inside the same left ventricular dilated at early diastolic phase.

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Fig. 15: The flow vortices inside the same left ventricular dilated case at diastasis phase. it shows a decreasing at vorticity in slow filling phase.

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Fig. 16: The irrotational flow vortices inside the same left ventricular dilated at atrial contraction time.

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Fig. 17: The rotational flow vortices inside the same left ventricular dilated at isovolumic contraction time

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Fig. 18: The irrotational flow direction into the LVOT at the same left ventricular dilated in ejection time.

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Conclusion In the presence of ventricle dilatation the mitral jet extends farther inside the ventricle, propagation velocity decreases, and the fluid stagnates longer at the apex. And blood flow pattern is followed in three distinct branches where two of them are helically back forwarded to the left atrium (mitral regurgitation) and third branch goes to aorta (Figures 20 to 25). (In compared with the normal fluid dynamic in LV) For the first time we have innovated a novel software that shows complete blood flow path inside the LV. Detailed information can be obtained about heart function by interfacing the related software within the echocardiograph machine. This innovation also opens doors to much more research in the heart chambers in normal and diseased hearts. Images for this section:

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Fig. 19: Two regurgitant branch flow inside the left ventricular dilated case.

Fig. 20: Velocity vectors of blood flow inside the left ventricular dilated case.

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Fig. 21: Velocity vectors of blood flow inside the left ventricular dilated case.

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Fig. 22: Velocity vectors of blood flow inside the left ventricular dilated case.

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Fig. 23: Velocity vectors of blood flow inside the left ventricular dilated case.

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Fig. 24: Velocity vectors of blood flow inside the left ventricular dilated case.

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Fig. 25: Velocity vectors of blood flow inside the left ventricular dilated case.

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References 1- Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash, Mahnoosh Foroughi. Brief communication: Mathematical concepts of mechanisms of left ventricular myocardium. International Journal of Medical Imaging, 2014; 2(2): 19-23. 2- Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash. Mechanical mitral valve modeling: Advancing the field through emerging science. International Journal of Medical Imaging, 2014; 2(2): 24-28. 3- Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash . An essential calculated power formula as a new index to study myocardial function of heart. International Journal of Clinical Medicine Research, 2014; 1(1):5-10.

4- Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash. Dynamic features creating (which cause) the blood direction inside the left ventricle. International Journal of Medical Imaging, 2014; 2(2): 14-18. 5- Mersedeh Karvandi, Saeed Ranjbar, Mehrdad Shahshahani, Arash Rastegar, Seyed Ahmad Hassantash, Mahnoosh Foroughi, Fariba Ranjbar. A research proposal in mathematical modeling applied to heart and mathematical concepts of mechanisms of heart. American Journal of Science and Technology, 2014; 1(1): 30-35.

US patents: 1- Saeed Ranjbar, Mersedeh Karvandi. System and method for modeling left ventricle of heart. US Patent Number: 8,414,490. 2- Saeed Ranjbar, Mersedeh Karvandi. Solution Navier-stocks equations of the blood as a non-Newtonian fluid in the left ventricle. NOTICE OF ALLOWANCE in January 27, 2014.US Publication number: US-2011-016646467-A1

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