Abstract
This study presents a novel method for building parametric representations of myocardial microstructure of the left ventricle from multi-directional diffusion weighted magnetic resonance images (DWI). The direction of maximal diffusion is directly estimated from the DWI signal intensities using finite element field fitting. This framework avoids the need to compute diffusion tensors, which introduces errors due to least squares fitting that are generally neglected when building microstructural models of the heart from DWI. Nodal parameters describing cardiac myocyte orientations throughout a finite element model of the left ventricle were fitted to a series of raw diffusion signals using non-linear least squares optimisation to determine the direction of maximum diffusion. An ex vivo DWI data set from a Wystar-Kyoto rat was processed using the proposed method. The fitted myocyte orientations were compared against conventional diffusion tensor/eigenvector analysis and the degree of correlation was measured using a normalised dot product (nDP). Good agreement (nDP = 0.979) between the new method and the traditional tensor analysis approach was observed for regions of high fractional anisotropy (FA). In regions of low FA, the errors were much more variable, but the proposed method maintains a smoothly varying myocyte angle distribution as is generally used in tissue and organ scale heart models.
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Notes
- 1.
The fitted diffusion tensor was projected back onto the original set of j gradient directions to get a set of estimated signal strengths (\(S_{e(j)}\)). The estimated signal strengths, the measured signal strengths (\(S_{m(j)}\)), and the mean of the measured signal strengths (\(\bar{S}_m\)) were then used to calculate the coefficient of determination:
$$\begin{aligned} R^2=1- \frac{\sum _j(S_{m(j)}-S_{e(j)})^2}{\sum _j(S_{m(j)}-\bar{S}_{m})^2}. \end{aligned}$$(1).
- 2.
The MathWorks, Inc., Natick, Massachusetts, United States.
- 3.
\(\gamma \) represents the gyromagnetic ratio of protons, \(\delta \) and G the duration and magnitude of application of the motion probing gradient along direction g \(_{(j)}\), \(D_{(j)}\) the apparent diffusivity in the same direction, and \(\varDelta \) the time difference between the centres of a pair of gradient pulses.
- 4.
least squares quasi Newton function, OPT++ optimisation library, http://software.sandia.gov/opt++.
- 5.
OpenCMISS-Cmgui application, www.opencmiss.org.
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Freytag, B. et al. (2016). Parameterisation of Multi-directional Diffusion Weighted Magnetic Resonance Images of the Heart. In: Camara, O., Mansi, T., Pop, M., Rhode, K., Sermesant, M., Young, A. (eds) Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges. STACOM 2015. Lecture Notes in Computer Science(), vol 9534. Springer, Cham. https://doi.org/10.1007/978-3-319-28712-6_7
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