Dose gradient curve: A new tool for evaluating dose gradient

<div><p>Purpose</p><p>Stereotactic radiotherapy, which delivers an ablative high radiation dose to a target volume for maximum local tumor control, requires a rapid dose fall-off outside the target volume to prevent extensive damage to nearby normal tissue. Currently, there is no tool to comprehensively evaluate the dose gradient near the target volume. We propose the dose gradient curve (DGC) as a new tool to evaluate the quality of a treatment plan with respect to the dose fall-off characteristics.</p><p>Methods</p><p>The average distance between two isodose surfaces was represented by the dose gradient index (DGI) estimated by a simple equation using the volume and surface area of isodose levels. The surface area was calculated by mesh generation and surface triangulation. The DGC was defined as a plot of the DGI of each dose interval as a function of the dose. Two types of DGCs, <i>differential</i> and <i>cumulative</i>, were generated. The performance of the DGC was evaluated using stereotactic radiosurgery plans for virtual targets.</p><p>Results</p><p>Over the range of dose distributions, the dose gradient of each dose interval was well-characterized by the DGC in an easily understandable graph format. Significant changes in the DGC were observed reflecting the differences in planning situations and various prescription doses.</p><p>Conclusions</p><p>The DGC is a rational method for visualizing the dose gradient as the average distance between two isodose surfaces; the shorter the distance, the steeper the dose gradient. By combining the DGC with the dose-volume histogram (DVH) in a single plot, the DGC can be utilized to evaluate not only the dose gradient but also the target coverage in routine clinical practice.</p></div

Dose gradient curve: A new tool for evaluating dose gradient - Fig 1

<p>(A) Two-dimensional dose distribution displayed using isodose lines on an axial CT-slice. (B) Three-dimensional illustration of two isodose surfaces. Double-headed arrows indicate the distances between two isodose surfaces. The volume and surface area of isodose levels were used to estimate the average distance between two isodose surfaces. <i>V</i> and <i>S</i> represent the volume and surface area of an isodose level, and the subscripts <i>L</i> and <i>H</i> represent the lower and higher doses.</p

The cylindrical sector-like Volume-of-Interest (VOI), with its axis passing through the planning isocenter.

<p>Using the VOI, the DGC would provide the information about the dose gradient in a particular direction.</p

Geometric objects for verification of the dose gradient index (DGI) calculation.

<p>(A) A sphere and its uniform expansion with a spacing <i>d</i>, (B) a cube and its uniform expansion with a spacing <i>d</i>, (C) an irregular shaped structure, and (D) a multi-layer structure at regular intervals (1 mm), produced by uniform expansion of the structure described in (C).</p

Dose gradient index (DGI) of the multi-layer structure generated by uniform expansion of an irregularly shaped structure at 1-mm regular intervals.

<p>Dose gradient index (DGI) of the multi-layer structure generated by uniform expansion of an irregularly shaped structure at 1-mm regular intervals.</p

The dose gradient curve.

<p>(A) The <i>differential</i> dose gradient curve (dDGC) generated by data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0196664#pone.0196664.t002" target="_blank">Table 2</a>. The dDGC is a plot in which each point represents the average distance between each isodose interval (the <i>differential</i> dose gradient index; dDGI); the shorter the distance, the steeper the dose gradient. (B) The corresponding <i>cumulative</i> dose gradient curve (cDGC) is a plot of the <i>cumulative</i> dose gradient index (cDGI) generated by summing the DGI values from the prescription dose (100% isodose) to each dose. Each point of the cDGC indicates the average distance from the prescription isodose surface to the corresponding isodose level.</p

Schematic representation of the basic concept of the dose gradient curves (DGC).

<p>(A) The differential DGC and (B) the cumulative DGC.</p

Plot options for the dose gradient curve (DGC).

<p>Plot options for the dose gradient curve (DGC).</p