Generating amorphous target margins in radiation therapy to promote maximal target coverage with minimal target size
Introduction
Modern radiation therapy requires high geometric accuracy in treatment planning and delivery. Motion and positional uncertainties can compromise the desired dose distribution and must be addressed to deliver adequate dose to the treatment target and to minimize the risk of normal tissue toxicities. The most widely used technique for considering positional uncertainties is to add safety margins around the target. The standard sets of margins are those described by the International Commission on Radiation Units and Measurements (ICRU) [1], [2], [3]. The reports from the ICRU present the gross tumor volume (GTV) consisting of observable disease, along with expansions of the GTV: the clinical target volume (CTV) to account for subclinical disease, the internal target volume (ITV) to account for anatomic motion, and the planning target volume (PTV) to account for setup error and limited machine precision. The underlying principle is that by designing a treatment plan to deliver the desired dose to the PTV, the CTV will receive adequate dose regardless of the effects of positional uncertainties.
When implementing safety margins to address uncertainties, the challenge is determining the appropriate margin magnitude; too small and target coverage is compromised, too large and the PTV will include excessive amounts of normal tissue, increasing the risk of toxicity. Margin magnitude has been a major theme during the development of image-guided radiation therapy. Numerous reports have presented the observed motion of various tumor sites using a large number of imaging techniques [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. In addition, several formulas have been created to calculate the necessary margins based on estimates of positional uncertainties [22], [23], [24]. A well-known approach is that presented by van Herk et al., which determines the theoretical CTV-to-PTV margin required to provide a minimum CTV dose of 95% of the prescription for 90% of patients [23].
While margins are ubiquitous in radiation therapy, their implementation typically remains limited to either isotropic or anisotropic morphological dilations along three orthogonal anatomic axes [5], [10], [15], [16], [18], [25]. Some have refined the precision of anisotropic margins through registration of selective anatomic regions-of-interest when estimating setup uncertainties [16], [19], [21], [26], [27]. Others have made efforts to provide more local estimates of motion on the voxel or sector level [28], [29], [30], [31]. Local estimates are subsequently averaged to create expansions in a few directions, likely to correspond with the functionality of current treatment planning systems. However, simple expansions in a few directions cannot account for spatial complexities in target shape or motion. As a result, any given margin will be suboptimal, compromising CTV coverage and/or normal tissue sparing.
Other efforts at local margins are rooted in statistical descriptions of target coverage. This can be achieved by thresholding a probabilistic description of the CTV [22], [27], [32], or by iterative evaluation of the margins based on dosimetric target coverage [33]. While these techniques provide the advantage of a statistical evaluation of coverage to the target as a whole, they do not preclude generating a margin that results in under-dosing a particular region of the target. Some prior work was focused on a voxelized measurement of target coverage. However, this retrospective analysis only considered margin expansions in 6 directions and its ability to generalize the observed margins to other patients may be limited [34].
The purpose of the work presented here was to describe and evaluate two alternative margin-generating algorithms. These algorithms are heuristic approaches that, unlike the above-described approaches to margins, are designed to be highly flexible, prospective methods for generating PTVs that ensure adequate target coverage. They automatically consider local characteristics of the shape of the target and an unrestricted model of target motion. The resulting PTVs provide the desired amount of coverage on a voxel level with a more minimal size. To illustrate the application and efficacy of these approaches, PTVs were generated for two example CTVs and a previously treated lung cancer patient. The PTVs were compared with, and consistently outperformed, probabilistic threshold-based margins and conventional (an)isotropic margins.
Section snippets
Amorphous PTV margin algorithms
Presented here are two algorithms used to generate amorphous PTV margins. The PTVs are amorphous in that their boundary is highly flexible to accommodate local effects of the CTV shape and motion. The two amorphous margin algorithms are denoted as the mixed-PDF and independent-PDF algorithms. Both are based on a user-defined model of CTV motion. The CTV motion model is comprised of a probability density function (PDF) for each CTV voxel that represents the relative likelihood that the voxel
Results
PTV margins were generated for the two example CTVs at various levels of desired target coverage using the four techniques described above (mixed-PDF, independent-PDF, threshold, and (an)isotropic margin techniques). The performance of these margin techniques is presented for CTV1 and CTV2 in Fig. 3. For all margin techniques, the minimum coverage provided to a CTV voxel increased with the size of the PTV, though this effect diminished with increasing PTV size. Also, for a given level of
Discussion
This work describes the mixed-PDF and independent-PDF amorphous margin-generating algorithms and demonstrates that the performance of these heuristic approaches was consistently better than margins created by thresholding the CTV probability distribution or by an (an)isotropic expansion of the CTV. For a given level of minimum CTV voxel coverage, the mixed-PDF margin achieved the coverage with the smallest PTV, followed by the independent-PDF margin, the threshold margin, and the (an)isotropic
Conclusion
Presented are heuristic PTV margin-generating algorithms that 1) are automatic with the inclusion of a model of motion and/or uncertainty, 2) are generalizable to motion/uncertainty models of all forms, including those describing non-rigid tissue deformation, 3) result in amorphous margins determined by local features of the CTV and of the motion/uncertainty model, and 4) ensure a minimum level of coverage to each CTV voxel with a PTV consistently smaller than those created using conventional
Conflict of interests
I have no real or perceived conflicts of interest to disclose.
Acknowledgments
I would like to thank Mich Price, Ph.D., Manuel Morales, Ph.D., and George Ding, Ph.D. for insightful comments regarding the preparation of this manuscript.
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