Volume quantification by fuzzy logic modelling in freehand ultrasound imaging

Many algorithms exist for 3D reconstruction of data from freehand 2D ultrasound slices. These methods are based on interpolation techniques to fill the voxels from the pixels. For quantification purposes, segmentation is involved to delineate the structure of interest. However, speckle and partial volume effect errors can affect quantification.

This study aimed to assess the effect of the combination of a fuzzy model and 3D reconstruction algorithms of freehand ultrasound images on these errors.

We introduced a fuzzification step to correct the initial segmentation, by weighting the pixels by a distribution function, taking into account the local gray levels, the orientation of the local gradient, and the local contrast-to-noise ratio. We then used two of the most wide-spread reconstruction algorithms (pixel nearest neighbour (PNN) and voxel nearest neighbour (VNN)) to interpolate and create the volume of the structure. Finally, defuzzification was used to estimate the optimal volume.

B-scans were acquired using 5 MHz and 8 MHz ultrasound probes on ultrasound tissue-mimicking phantoms. Quantitative evaluation of the reconstructed structures was done by comparing the method output to the real volumes. Comparison was also done with classical PNN and VNN algorithms.

With the fuzzy model quantification errors were less than 4.3%, whereas with classical algorithms, errors were larger (10.3% using PNN, 17.2% using VNN). Furthermore, for very small structures (0.5 cm(3)), errors reached 24.3% using the classical VNN algorithm, while they were about 9.6% with the fuzzy VNN model.

These experiments prove that the fuzzy model allows volumes to be determined with better accuracy and reproducibility, especially for small structures (<3 cm(3)).