A novel method for volume determination using MR image sequences

Joe P. Windham, Allan M. Haggar, David O. Hearshen, Joseph R. Roebuck, and David A. Reimann

In Book of Abstracts, volume 2, page 1081, Society of Magnetic Resonance in Medicine, Seventh Annual Meeting, San Francisco, California, 22-26 August 1988.

The ability to isolate a feature of interest and to account for partial volume effects is significant in tissue volume calculations. A linear filter (Eigenimage Filtering) which has excellent segmentation characteristics and produces an image in which partial volume effects are accounted for has been developed (1). This technique, produces a single composite image (Eigenimage) depicting a particular feature of interest while suppressing one or more undesired features from a MR image sequence generated using different pulse sequences. The eigenimage with the feature of interest segmented and adjacent features supressed, and having partial volume information pertaining to the desired feature, can be used to make accurate tissue volume estimates.

The method requires the determination of the appropriate weighting components to be used in the linear filter based upon the criterion that the desired feature is to be enhanced while the interfering feature(s) is suppressed. The technique requires the identification of signature vectors for the desired and undesired features and generates a vector (eigenvector) whose arguments are the weighting factors for the linear filter. A mathematical description of the technique is given in reference 1.

If it is assumed that the magnetic resonance signal from a voxel containing more than one material is given by the volume weighted summation of the individual signals from the different materials, then the gray level of the corresponding pixel is the summation of the volume weighted gray levels of the different materials that would be obtained for voxels containing pure samples of the different materials. This is a reasonable assumption since the signal from a voxel is directly portional to the net magnetization; the net magnetization is the sum of all of the individual magnetic moments provided that the frequency bandwidth across the voxel is larger than the chemical shift of the different materials in the voxel.

With this assumption, the partial volume of the desired material in the ij-th voxel, vdij, is given by:

vdij = (Sij/e.d)V

where d is the signature vector of the desired material and e is the eigenvector used in the linear filter. Sij is the gray level of the ij-th pixel corresponding to the ij-th voxel and V is the voxel volume. The total volume of the desired material is determined by summing over all voxel volumes. Since the interfering features are suppressed in the eigenimage, that is their projection into the eigenimage is zero, they do not contribute to the volume calculation.

To test the accuracy and reproducibility of this teshnique a series of phantom studies were performed. The phantoms used consisted of an embedding base material with one or more caities containing a different material than the base material. A multiple echo series of contiguous slices through the phantom that encompassed the cavity was obtained. An eigenimage using a particular cavity as the desired feature and other cavities and the embedding base material as undesired features was produced for each slice. The volume of the cavity in each slice was determined and the total volume was found by summation over all slice volumes.

The accuracy of the technique was determined by comparing the calculated volume with the true volume as measured by water displacement. The reproducibility of the technique was measured by comparing repeated experiments with the same phantom. The technique was also compared with the threshold pixel counting technique.

The accuracy of the technique was found to be better than 3% on phantom studies with a standard deviation of better than 1% in repeated measurements. A comparison of the eigenimage technique with the pixel counting technique is shown in Figure 1. The ratio of the calculated volume to the measured true volume, Vc/Vm, is plotted versus thq percent threshold for the two techniques. The percent threshold is with respect to the gray level of the projection of the desired process into the eigenimage.

Results from the phantom studies appear highly accurate and reproducible. The technique may be useful for in-vivo diagnosis and as a monitor of volume charges due to the progression of disease or therapy.

1. Joe P. Windham, Mahmoud A. Abd-Allah, David A. Reimann, Jerry W. Froelich, and Allan M. Haggar. Eigenimage filtering in MR imaging. Journal of Computer Assisted Tomography, 12:1-9, 1988.

Supported in part by NIH Grant Number 1RO1 CA 46124-01.

Copyright © 1988, David A. Reimann. All rights reserved.