^{1}, Martin J. Murphy

^{1}, Dorin A. Todor

^{1}, Elisabeth Weiss

^{1}and Jeffrey F. Williamson

^{1,a)}

### Abstract

**Purpose:**

To experimentally validate a new algorithm for reconstructing the 3D positions of implanted brachytherapy seeds from postoperatively acquired 2D conebeam-CT (CBCT) projection images.

**Methods:**

The iterative forward projection matching (IFPM) algorithm finds the 3D seed geometry that minimizes the sum of the squared intensity differences between computed projections of an initial estimate of the seed configuration and radiographic projections of the implant. In-house machined phantoms, containing arrays of 12 and 72 seeds, respectively, are used to validate this method. Also, four postimplant patients are scanned using an ACUITY digital simulator. Three to ten x-ray images are selected from the CBCT projection set and processed to create binary seed-only images. To quantify IFPM accuracy, the reconstructed seed positions are forward projected and overlaid on the measured seed images to find the nearest-neighbor distance between measured and computed seed positions for each image pair. Also, the estimated 3D seed coordinates are compared to known seed positions in the phantom and clinically obtained VariSeed planning coordinates for the patient data.

**Results:**

For the phantom study, seed localization error is. For all four patient cases, the mean registration error is better than 1 mm while compared against the measured seed projections. IFPM converges in 20–28 iterations, with a computation time of about 1.9–2.8 min/iteration on a 1 GHz processor.

**Conclusions:**

The IFPM algorithm avoids the need to match corresponding seeds in each projection as required by standard back-projection methods. The authors’ results demonstrate accuracy in reconstructing the 3D positions of brachytherapy seeds from the measured 2D projections. This algorithm also successfully localizes overlapping clustered and highly migrated seeds in the implant.

This work was supported in part by grants from Varian Medical Systems and the National Institutes of Health (Grant No. P01 CA 116602). The authors gratefully acknowledge Virginia Gilbert of Virginia Commonwealth University (VCU) for her continuous support in collecting patient data. The authors would like to thank Tom Becker for his contributions to phantom construction. The authors thank James Ververs of VCU for editing the manuscript.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. IFPM algorithm

II.B. Image acquisition details and autosegmentation of the seeds

II.C. Algorithm details

II.C.1. Initial seed configuration estimates and computed projection images

II.C.2. Similarity measure and gradient search

II.C.3. Two-step adaptive Gaussian blurring

II.D. Algorithm validation

II.D.1. Brachytherapy phantom design

II.D.2. Patient data acquisition

II.D.3. Assessment of seed registration/reconstruction error

III. RESULTS

III.A. Validation test with phantoms

III.B. Patient study

IV. DISCUSSION

V. CONCLUSIONS

### Key Topics

- Medical imaging
- 131.0
- Image sensors
- 33.0
- Medical image reconstruction
- 30.0
- Brachytherapy
- 18.0
- Cone beam computed tomography
- 15.0

## Figures

The perspective projection geometry for the imaging system. The 3D seed configuration is in the world coordinate system, which is defined by three translational and three rotational coordinates relative to the CBCT isocenter. The image receptor plane is defined by the imaging viewpoint angles , where and denote the constant values between the source to isocenter and detector to isocenter distances, respectively. The imaging axis rotates by angle around the x axis. The pixel index denotes the projected seed in the 2D imaging plane .

The perspective projection geometry for the imaging system. The 3D seed configuration is in the world coordinate system, which is defined by three translational and three rotational coordinates relative to the CBCT isocenter. The image receptor plane is defined by the imaging viewpoint angles , where and denote the constant values between the source to isocenter and detector to isocenter distances, respectively. The imaging axis rotates by angle around the x axis. The pixel index denotes the projected seed in the 2D imaging plane .

(a) The ACUITY imaging system in the brachytherapy imaging suite and a phantom setup. (b) Schematic of the geometrical configuration of a precision-machined phantom containing 72 dummy seeds arranged as four nine-seed slabs alternating with three 12-seed slabs in a rectangular grid. This phantom was used to test the IFPM seed localization accuracy. The centers of the seeds were coplanar and perpendicular to the plane of the slabs.

(a) The ACUITY imaging system in the brachytherapy imaging suite and a phantom setup. (b) Schematic of the geometrical configuration of a precision-machined phantom containing 72 dummy seeds arranged as four nine-seed slabs alternating with three 12-seed slabs in a rectangular grid. This phantom was used to test the IFPM seed localization accuracy. The centers of the seeds were coplanar and perpendicular to the plane of the slabs.

An example case of the image postprocessing of the projection images obtained from the Varian 4030CB digital simulator. (a) Raw projection image, (b) filtered image, (c) seed-only image, and (d) blurred image using the IFPM algorithm for patient III (81 implanted Theragenics model 200 seeds).

An example case of the image postprocessing of the projection images obtained from the Varian 4030CB digital simulator. (a) Raw projection image, (b) filtered image, (c) seed-only image, and (d) blurred image using the IFPM algorithm for patient III (81 implanted Theragenics model 200 seeds).

The convergence rate of the IFPM algorithm for the two example cases: 12-seed and 72-seed phantom data sets.

The convergence rate of the IFPM algorithm for the two example cases: 12-seed and 72-seed phantom data sets.

Histograms of the seed positional error for the 12-seed and 72-seed phantom study.

Histograms of the seed positional error for the 12-seed and 72-seed phantom study.

An illustration of the iterative sequence morphing of the convergence process. (a) Initial estimate of the seed configuration, (b) computed images after first step of convergence, (c) computed images after second step of convergence, and (d) the measured images at different gantry angle for patient III. Despite large differences between the preplanned seed geometry (based on a TRUS volume study acquired about a week before the implant) and that observed 4 weeks after the implant, IFPM was able to accurately reproduce the desired seed configuration.

An illustration of the iterative sequence morphing of the convergence process. (a) Initial estimate of the seed configuration, (b) computed images after first step of convergence, (c) computed images after second step of convergence, and (d) the measured images at different gantry angle for patient III. Despite large differences between the preplanned seed geometry (based on a TRUS volume study acquired about a week before the implant) and that observed 4 weeks after the implant, IFPM was able to accurately reproduce the desired seed configuration.

The similarity metric convergence for the two-step IFPM algorithm for the four patient cases. The arrow in the button of the figure indicates the transition from larger to smaller Gaussian spread for patient III. The one-dimensional image-intensity profiles in the inset illustrate the capture ranges of the two-step filtering operations.

The similarity metric convergence for the two-step IFPM algorithm for the four patient cases. The arrow in the button of the figure indicates the transition from larger to smaller Gaussian spread for patient III. The one-dimensional image-intensity profiles in the inset illustrate the capture ranges of the two-step filtering operations.

Superposition of measured seed images (white seeds) with automatically detected seed positions (black markers) projected on the detector planes. (a) 0° gantry angle, (b) −20° gantry angle, and (c) gantry angle for patient III. While many seeds coincided exactly, a few still exhibit significant discrepancies.

Superposition of measured seed images (white seeds) with automatically detected seed positions (black markers) projected on the detector planes. (a) 0° gantry angle, (b) −20° gantry angle, and (c) gantry angle for patient III. While many seeds coincided exactly, a few still exhibit significant discrepancies.

Seed registration error calculated from the nearest-neighbor distance between measured and computed seed position on each detector plane for patient III. The RMS error was found to be (0°), , and (−20°) gantry angles, respectively.

Seed registration error calculated from the nearest-neighbor distance between measured and computed seed position on each detector plane for patient III. The RMS error was found to be (0°), , and (−20°) gantry angles, respectively.

Seed-by-seed vector difference between IFPM coordinates and those obtained from the VariSeed planning system for patient III data sets.

Seed-by-seed vector difference between IFPM coordinates and those obtained from the VariSeed planning system for patient III data sets.

Overlay of the measured seed images (white seeds) with automatically detected seed positions (black markers) projected on the detector planes for patient IV, who presents with incomplete data: 60 seeds are thought to be implanted but only 59 seeds are found on the week four postimplant dosimetry study. Gantry angle 0° is shown in (a), −20° is shown in (b), and is shown in part (c). The circle in part (b) indicates the extra seed found by IFPM at convergence. The IFPM algorithm converged accurately, recreating the identified 59 seed positions, including overlapping clustered and highly migrated seeds.

Overlay of the measured seed images (white seeds) with automatically detected seed positions (black markers) projected on the detector planes for patient IV, who presents with incomplete data: 60 seeds are thought to be implanted but only 59 seeds are found on the week four postimplant dosimetry study. Gantry angle 0° is shown in (a), −20° is shown in (b), and is shown in part (c). The circle in part (b) indicates the extra seed found by IFPM at convergence. The IFPM algorithm converged accurately, recreating the identified 59 seed positions, including overlapping clustered and highly migrated seeds.

## Tables

Summary of the comparisons of the seed positions deduced by the IFPM algorithm and by the VariSeed planning system for all example case patients. The mean value, standard deviation (sd) in each of the three directions, and overall 3D RMS error is reported. The seed registration error in the 2D image plane in terms of RMS value. The sd and the maximum displacement of the seed is also presented.

Summary of the comparisons of the seed positions deduced by the IFPM algorithm and by the VariSeed planning system for all example case patients. The mean value, standard deviation (sd) in each of the three directions, and overall 3D RMS error is reported. The seed registration error in the 2D image plane in terms of RMS value. The sd and the maximum displacement of the seed is also presented.

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