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Myocardial strains from 3D displacement encoded magnetic resonance imaging

Katarina Kindberg12, Henrik Haraldsson123*, Andreas Sigfridsson23, Jan Engvall3, Neil B Ingels45, Tino Ebbers1236 and Matts Karlsson12

Author affiliations

1 Department of Management and Engineering, Linköping University, SE-581 83 Linköping, Sweden

2 Center for Medical Image Science and Visualization (CMIV), Linköping University, SE-581 85 Linköping, Sweden

3 Department of Medical and Health Sciences, Linköping University, SE-581 85 Linköping, Sweden

4 Department of Cardiothoracic Surgery, School of Medicine, Stanford University, Stanford, CA 94305, USA

5 Research Institute of the Palo Alto Medical Foundation, Palo Alto, CA 94305, USA

6 Department of Science and Technology, Linköping University, SE-581 83 Linköping, Sweden

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Citation and License

BMC Medical Imaging 2012, 12:9  doi:10.1186/1471-2342-12-9

Published: 25 April 2012



The ability to measure and quantify myocardial motion and deformation provides a useful tool to assist in the diagnosis, prognosis and management of heart disease. The recent development of magnetic resonance imaging methods, such as harmonic phase analysis of tagging and displacement encoding with stimulated echoes (DENSE), make detailed non-invasive 3D kinematic analyses of human myocardium possible in the clinic and for research purposes. A robust analysis method is required, however.


We propose to estimate strain using a polynomial function which produces local models of the displacement field obtained with DENSE. Given a specific polynomial order, the model is obtained as the least squares fit of the acquired displacement field. These local models are subsequently used to produce estimates of the full strain tensor.


The proposed method is evaluated on a numerical phantom as well as in vivo on a healthy human heart. The evaluation showed that the proposed method produced accurate results and showed low sensitivity to noise in the numerical phantom. The method was also demonstrated in vivo by assessment of the full strain tensor and to resolve transmural strain variations.


Strain estimation within a 3D myocardial volume based on polynomial functions yields accurate and robust results when validated on an analytical model. The polynomial field is capable of resolving the measured material positions from the in vivo data, and the obtained in vivo strains values agree with previously reported myocardial strains in normal human hearts.