Dose optimization with first-order total-variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT)

Abstract

Purpose: A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem.

Methods: The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases.

Results: Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, first-order TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT.

Conclusions: The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse planning problem requiring large memory space. The new treatment scheme is shown to outperform conventional IMRT in terms of dose conformity to both the targetand the critical structures, while maintaining high delivery efficiency.

FIG. 1.

(a)–(c) Three axial slices showing all structures on CT images in the HN case. Target volumes, which are quite complex in shape, are surrounded by critical structures such as brainstem, cord, mandible, and oral cavity.

FIG. 2.

Planning results in the prostate case. (a), (c), (e) The variations of CN, CN1; and CN2, (b), (d), (f) iso-dose distributions with 80 segments for 7, 15, and 30 beams. CN and visualized dose conformity to the PTV tend to increase as the number of beams increases. Also, the dose distribution with 30 beams is better nearby the femoral heads and normal tissues than that with 7 beams.

FIG. 3.

Planning results in the HN case. (a), (c), (e) The variations of CN, CN1, and CN2, (b), (d), (f) iso-dose distributions with 75 segments for 7, 15, and 30 beams. Improvement in dose conformity to the PTV becomes more remarkable than the prostate case.

FIG. 4.

(a) DVHs of the resultant plans with 7, 15, and 30 beams in the prostate case and (b) the magnified views, where the solid(-), the dashed-dotted(-•), and the dashed lines(–) correspond to 7, 15, and 30 beams, respectively. The DVHs were acquired with 80 segments for all plans. The dose conformity to the critical structures, especially left/right femoral heads, is noticeably enhanced with DASSIM-RT (15 and 30 beams) over IMRT (7 beams).

FIG. 5.

(a) DVHs of the resultant plans with 7, 15, and 30 beams in the HN case, and (b) the magnified views, where the solid(-), the dashed-dotted(-•), and the dashed lines(–) correspond to 7, 15, and 30 beams, respectively. The DVHs were acquired with 75 segments for all plans. The dose conformity to the critical structures, such as brainstem and spinal cord, is improved with the greater number of beams.

FIG. 6.

Conformation number as a function of (a) the number of beam segments and (b) the modulation index for the IMRT plan (7 beams) and the DASSIM-RT plans (15 and 30 beams) in the HN case. DASSIM-RT is able to achieve higher dose conformity with less intensity modulation and similar or even less number of segments.

FIG. 7.

Conformation number as a function of (a) the number of beam segments and (b) the modulation index for the IMRT plan (7 beams) and the DASSIM-RT plans (15 and 30 beams) in the HN case. The improvement in the PTV dose conformity is more noticeable in the HN case than the prostate case mainly due to more complicated PTV structure.

FIG. 8.

Optimized fluence maps for the three prostate plans (gantry angle 280° for 7 beam, and gantry angle 288° for 15 and 30 beams) before passing through the leaf-sequencing algorithm. As the beam angular sampling increases, the resultant fluence maps become simple and tend to be piecewise constant.

FIG. 9.

Optimized fluence maps acquired by the three HN plans (gantry angle 120°) before passing through the leaf-sequencing algorithm.

FIG. 10.

Comparisons of the plans from the proposed methods (solid lines) and the QP-based approaches with TV form (dotted lines) in (a), (c) DVHs, and (b), (d) iso-dose distribution for the prostate and HN cases.