Figure 1.
Vibrating, simply supported Kirchoff plate subjected to a uniform, instantaneously-applied, face loading.
(A) Theoretical vibrational modes of a two-dimensional vibrating plate (2×1 units). Contours indicate the relative displacement out-of-plane (red positive; blue negative). (B) The first nine principal components of vibration; four of the nine differ from the “input” vibration modes used to generate the displacement field. (C) The input modes can be reconstructed from the linear combinations of the estimated principal components.
Figure 2.
Method applied to rotating viscoelastic gelatin cylinder.
(A) MR images of the gel phantom cylinder (top) were rotated to remove rigid body motion (bottom) prior to analysis. (B) The procedure resulted in a prediction of the time course of the cylinder's angular motion using the outer boundary. (C) More than 80% of the total variance is explained by the first four principal components. (D) Quiver plots for each principal component (PC), from left to right, are shown for the gel cylinder. Plots are scaled differently to highlight detail, so magnitude is not equivalent between principal components. Corresponding deformed mesh grids for the first four principal components are scaled by their eigenvalues.
Figure 3.
Method indicating degeneracy of principal components.
(A) Modal coefficients of principal components 2 and 3 overlaid to show their similar frequency. (B) Linear combinations of principal components 2 and 3 (the difference, left, and sum, right) yield intuitive radial patterns.
Figure 4.
Method applied to the human brain.
(A) Rigid body motion of the skull was removed prior to principal component analysis. (B) First four principal components account for approximately 75% of data set variance. (C) Quiver plot of first 4 principal components (top) associated with the mechanical response of the brain to a rotational deceleration (shown from left to right). Plots are scaled independently to highlight detail within each of the principal components. Deformed mesh grids for the first four principal components (bottom), scaled in proportion to their eigenvalues. (D) Modal coefficients show no evidence of degeneracy indicated by unique temporal variation. (E) PC1 overlaid on a scout image to emphasize anatomical correlation. (F) PC2 overlaid on a scout image.
Figure 5.
Comparison of multiple results.
A subject comparison of 3 subjects in two planes 2 cm apart.