Analysis of a novel X-ray lens for converging beam radiotherapy

Abstract

We describe the development and analysis of a new teletherapy modality that, through a novel approach to targeted radiation delivery, has the potential to provide greater conformality than conventional photon-based treatments. The proposed system uses an X-ray lens to reflect photons from a conventional X-ray tube toward a focal spot. The resulting dose distributions have a highly localized peak dose, with lower doses in the converging radiation cone. Physical principles governing the design of this system are presented, along with a series of measurements analyzing various characteristics of the converging beam. The beam was designed to be nearly monoenergetic (~ 59 keV), with an energy bandwidth of approximately 10 keV allowing for treatment energies lower than conventional therapies. The focal spot was measured to be approximately 2.5 cm long and 4 mm wide. Mounting the proposed X-ray delivery system on a robotic arm would allow sub-millimeter accuracy in focal spot positioning, resulting in highly conformal dose distribution via the optimal placement of individual focal spots within the target volume. Aspects of this novel radiation beam are discussed considering their possible clinical application as a treatment approach that takes maximum advantage of the unique properties afforded by converging X-ray beam therapy.

Figure 1

(a) Representative relative depth dose distributions for a diverging 6 MV photon beam, 60 keV orthovoltage beam, and 60 keV converging beam focused to a depth of 8 cm. (b) Conceptual illustration of the CRnR system, in which an X-ray lens converts a diverging beam into a converging beam, producing a localized dose peak within a target.

Figure 2

(a) Illustration of diffraction by a perfect crystal in Bragg reflection and Laue transmission geometries with interplanar distance d for Bragg angle ${\mathrm{\theta }}_{\text{B}}$. (b) Depiction of a mosaic crystal with thickness T₀ composed of individual crystallite blocks with thickness t₀, each of which varies in angle $\mathrm{\Delta }\mathrm{\theta }$ around the mean Bragg reflecting plane, which has an angle $\mathrm{\delta }$ relative to the crystal surface. The incident beam, with an incident angle $\mathrm{\theta }$ with respect to the mean Bragg plane, illustrates non-symmetric reflection geometry, in which the incident beam angle relative to crystal surface $\mathrm{\phi }$ and exit beam angle ${\mathrm{\phi }}^{\prime }$ are not equal owing to the non-coplanar nature of the mean Bragg reflecting plane with the crystal surface.

Figure 3

(a) CRnR lens concept. (b) Isometric view of the first-generation prototype CRnR X-ray lens. (c) Cut view with labels for each of the rings displaying the tile positions. (d) Beams-eye-view of the lens. Not shown is a lead block in the central aperture for preventing direct pass-through X-rays.

Figure 4

(a) Illustration of transverse and longitudinal film positions relative to the converging CRnR beam. (b) Transverse EBT-QA film measurements in air at positions above and below the focal spot. Positive numbers denote transverse positions upstream of the focal spot, whereas negative numbers denote transverse positions downstream of the focal spot. (c) Transverse EBT-QA film measurements in water. (d) Longitudinal EBT-QA film measurement in air. (e) Longitudinal EBT-QA film measurement in water.

Figure 5

Relative isodose curves normalized to the peak dose for focused 60-kV X-rays. (a) Focal spot set to 5 cm depth in water. Long-dashed line represents the longitudinal profile line while the short-dashed line represents the transverse profile line. (b) Focal spot set to 7 cm depth in water. (c) Focal spot set to 10 cm depth in water. (d) Focal spot set to 14 cm depth in water.

Figure 6

(a) Longitudinal focal spot beam size as defined by the central axis plot full width half maximum (FWHM). (b) Transverse focal spot beam size as defined by the FWHM perpendicular to the central axis at the focal spot maximum.

Figure 7

(a) Photon spread-out peaks (PSOPs) designed from 3 focal spots at depths of 2–5 cm in water. (b) Longitudinal surface dose map of the shallow PSOP. (c) PSOP designed from 5 focal spots at depths of 4–8 cm in water. (d) Longitudinal surface dose map of the deep PSOP.

Figure 8

Energy spectrum of the Bragg-diffracted converging beam in air at the focal spot location.

Figure 9

Early concept art showing the robotically mounted CRnR radiation platform with covers where the delivery head houses the X-ray and lens.