Robust assessment of the transmural extent of myocardial infarction in late gadolinium-enhanced MRI studies using appropriate angular and circumferential subdivision of the myocardium

Abstract

A computer-assisted method is proposed to estimate transmural extent of myocardial infarction. In 40 patients with chronic myocardial infarction and 3 control subjects, late gadolinium enhancement images were acquired with magnetic resonance imaging. Segmental infarct transmural extent was visually assessed by two experts on a 5-point scale. A fuzzy c-means algorithm was applied on both the cavity and myocardium to estimate an enhancement index for 12 sub-regions of each segment. A threshold was defined on a training database (n=29) to establish the transmurality extent of each sub-segment and was applied to the validation database (n=14). Inter-observer reproducibility reached an absolute agreement (Aa) of 85% and a kappa value (κ) of 0.83 when considering the whole training database; Aa decreased to 62% and κ to 0.68 when excluding homogeneous segments. On the validation database, segments were subdivided into three angular sub-segments. Then, inter-observer visual reproducibility reached Aa of 93% and κ of 0.92. Moreover, the absolute comparison of each expert with the computer-assisted method yielded Aa higher than 88% and κ higher than 0.86. The computer-assisted method quantifies infarct transmurality without defining remote and infarcted regions, and the transmural extent is accurately characterized when dividing each segment into three angular sub-segments.

Appendix

The fuzzy c-means algorithm was used to classify image pixels by computing their measure of membership for a specified class; in this application, two classes are considered, the first class contains enhanced pixels and is called C _{E ,} the second class characterizes non-enhanced pixels and is called C _NE .

The image pixels are characterized by their grey levels. Therefore, the membership function of each pixel p for the two classes C _E and C _NE , which are respectively called $u_p^{C_E }$ and $u_p^{C_{NE} }$ (0 ≤$u_p^{C_E }$≤1, 0 ≤$u_p^{C_{NE} }$≤1) which indicates the similarity between each pixel and the centroid of each class is defined by:

$$u_p^{C_E } = \left[ {\left( {\frac{{\left\| {I_p - I_{C_E } } \right\|}}{{{\text{ }}\left\| {I_p - I_{C_{NE} } } \right\|{\text{ }}}}} \right)^{\frac{1}{{q - 1}}} + 1} \right]^{ - 1} \;and\;u_p^{C_{NE} } = \left[ {\left( {\frac{{\left\| {I_p - I_{C_{NE} } } \right\|}}{{{\text{ }}\left\| {I_p - I_{C_E } } \right\|{\text{ }}}}} \right)^{\frac{1}{{q - 1}}} + 1} \right]^{ - 1} $$

where I _p is the grey level intensity within the pixel p, $I_{C_E }$ and $I_{C_{NE} }$are respectively the intensity of the C _E and C _NE centroids, and q is the amount of the classification fuzziness (q = 2, here).

To estimate the centroids and the corresponding membership functions, the global cost function O _fcmean defined below is minimized:

$$O_{fcmean} = \sum\limits_{p \in IM} {\left\{ {\left[ {u_p^{C_E } } \right]^q \cdot \left\| {I_p - I_{C_E } } \right\| + \left[ {u_p^{C_{NE} } } \right]^q \cdot \left\| {I_p - I_{C_{NE} } } \right\|} \right\}} ,$$

where IM is the region that includes both the myocardium and the cavity.

The fuzzy c-means algorithm was applied for each slice level independently because of possible large grey level variations from one slice to another, and the maps of membership for the class C _E , $u_p^{C_E }$, were stored.Using this configuration, the centroid of the class C _E is a grey level inside the cavity, thus insuring that pixels with higher intensity, i.e., infarct pixels had a high membership for the class C _E and that all pixels with low intensity, i.e., normal myocardium pixels, have a low membership for this class C _E. The classification in three classes for normal myocardium, cavity and infarct was not judged relevant for two reasons: firstly, the class of infarcted pixels did not always exist; secondly, even if it existed, the sometimes low contrast between cavity and infarct did not enable a more efficient estimation of the infarct compared with the two-class estimation.