Incorporating uncertainty in the determined seed orientation. The bold vector represents the nominal fitted orientation of the seed which defines the z-axis in the TG-43 coordinate system. The coordinates of a dose point in this frame are (r,θ,φ). The error in the seed orientation relative to the nominal orientation is described by inclination α and azimuth β. The separation angle γ is the angle between the seed and the measurement point.
Phantom validation of the fitting procedure. Strands were embedded into grooves based on (a) cubic and (b) quadratic functions, which were etched into sheets of solid water. The phantom was imaged and the seeds segmented and fit using the spline algorithm. For both cases, the RMS error was <0.3, the maximum absolute error was 0.5 mm, and the maximum error in the curve tangent (seed orientation) was 2°.
The sensitivity simulation-derived probability density of the seed inclination error α for four different levels of applied noise in (a) central and (b) terminal seeds. Noise levels (see Table I) are in increasing order of magnitude.
The sensitivity simulation-derived probability density of the seed azimuth error β for four different levels of applied noise in (a) central and (b) terminal seeds. Noise levels (see Table I) are in increasing order of magnitude.
The probability densities of the fitted seed inclination (in deg−1) plotted for measurement points every 10° of inclination for (a) central seeds and (b) terminal seeds. Multiple densities are overlaid on a single plot for compactness; each is centered at the measurement inclination (θ) and falls to zero on either side. The dependence of these plots on the azimuth φ of the measurement point can be seen when comparing the densities of points at and using the probability density of the fitted seed azimuth derived from sensitivity-simulations. Making the assumption that P(β) is uniform splits the difference in the extremes and eliminates the dependence of the measurement azimuth [in the seed (TG-43) frame].
Probability density (in deg−1) of the (a) inclination and (b) azimuth for stranded seeds in the CT coordinate system. Histogram bars are the raw counts in bins of 5°, and solid curves represent the orientation probability density P SO. The probability density assumed by the 1D formalism is shown for comparison. (c) In this image, P SO is projected onto the unit sphere using bright intensity to highlight regions of high density. The grid interval is 10°, and the directions of the CT axes are labeled (A—anterior, P—posterior, R—right, L—left, I—inferior, S—superior). Most seeds exhibit an approximately 20° pitch from the coronal plane toward the anterior of the patient.
(a) Volumes with an absolute difference between 1D and 2D-weighted dose distributions of greater than 7.2 Gy (5% of prescription) (left) and 14.4 Gy (10% of prescription) (right). (b) 1D (left) and 2D (right) prescription isodose surfaces for one patient. The 1D formalism tends to overestimate dose margins at the superior and inferior aspects, and underestimate dose margins at the lateral boundaries and in the medial regions.
Noise level parameters, expressed as the standard deviations in each CT axis for zero-mean Gaussian noise.
Errors in sensitivity analysis. A test-set of five reconstructed strands had simulated noise applied and the effects on the computed position and orientation of their seeds were studied. Fitted error in seed position and polar orientation (α) are reported for each noise level. Values are means, plus/minus one standard deviation for the orientations. Maximum values are displayed in parentheses.
Cohort means and patient-controlled differences in selected dose metrics, comparing the 1D and 2D-weighted dose-calculations methods. Listed p-values are for t-tests of the respective mean paired difference from zero.
Article metrics loading...
Full text loading...