Background: The ability to measure and quantify myocardial motion and deformation provides a useful tool to\r\nassist in the diagnosis, prognosis and management of heart disease. The recent development of magnetic\r\nresonance imaging methods, such as harmonic phase analysis of tagging and displacement encoding with\r\nstimulated echoes (DENSE), make detailed non-invasive 3D kinematic analyses of human myocardium possible in\r\nthe clinic and for research purposes. A robust analysis method is required, however.\r\nMethods: We propose to estimate strain using a polynomial function which produces local models of the\r\ndisplacement field obtained with DENSE. Given a specific polynomial order, the model is obtained as the least\r\nsquares fit of the acquired displacement field. These local models are subsequently used to produce estimates of\r\nthe full strain tensor.\r\nResults: The proposed method is evaluated on a numerical phantom as well as in vivo on a healthy human heart.\r\nThe evaluation showed that the proposed method produced accurate results and showed low sensitivity to noise\r\nin the numerical phantom. The method was also demonstrated in vivo by assessment of the full strain tensor and\r\nto resolve transmural strain variations.\r\nConclusions: Strain estimation within a 3D myocardial volume based on polynomial functions yields accurate and\r\nrobust results when validated on an analytical model. The polynomial field is capable of resolving the measured\r\nmaterial positions from the in vivo data, and the obtained in vivo strains values agree with previously reported\r\nmyocardial strains in normal human hearts.
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