Reducing the tracking drift of an uncontoured tumor for a portal-image-based dynamically adapted conformal radiotherapy treatment

Abstract

Accurate tracking of organ motion during treatment is needed to improve the efficacy of radiation therapy. This work investigates the feasibility of tracking an uncontoured target using the motion detected within a moving treatment aperture. Tracking was achieved with a weighted optical flow algorithm, and three different techniques for updating the reference image were evaluated. The accuracy and susceptibility of each approach to the accumulation of position errors were verified using a 3D-printed tumor (mounted on an actuator) and a virtual treatment aperture. Tumor motion up to 15.8 mm (peak-to-peak) taken from the breathing patterns of seven lung cancer patients was acquired using an amorphous silicon portal imager at ~ 7.5 frames/s. The first approach (INI) used the initial image detected, as a fixed reference, to determine the target motion for each new incoming image, and performed the best with the smallest errors. This method was also the most robust against the accumulation of position errors. Mean absolute errors of 0.16, 0.32, and 0.38 mm were obtained for the three methods, respectively. Although the errors are comparable to other tracking methods, the proposed method does not require prior knowledge of the tumor shape and does not need a tumor template or contour for tracking.

Appendix

1.1 Using mathematical induction to formulate the equations for the position of aperture and targets

In the first method (INI), direct registration with an initial reference frame was performed for every image (Fig. 1). The optical flow algorithm was applied to determine the interframe displacements between all images with the initial image. Following the method of induction, the initial position of the aperture Pos_aperture(1) and target Pos_target(1) are given in Eqs. (14) and (15). This assumes that the target was positioned at the isocenter verified by the setup procedure. Without prior motion information, the position of the aperture in the second image Pos_aperture(2) is given by Eq. (16):

Initial conditions:

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(1)=0 $$

(14)

$$ {\mathrm{Pos}}_{\mathrm{target}}(1)=0 $$

(15)

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(2)=0 $$

(16)

Applying tracking between the first and second image provides the displacement of the target given by the optical flow vector OF_DIR(1):

Subsequent motion tracking:

$$ {\mathrm{Pos}}_{\mathrm{target}}(2)={\mathrm{Pos}}_{\mathrm{aperture}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(1)={\mathrm{OF}}_{\mathrm{INI}}(1) $$

(17)

where OF_INI(1) = OF(IM(1), IM(2)) is the weighted average value of the optical flow vectors obtained between IM(1) and IM(2).

To maintain tracking of the object, the aperture position Pos_aperture(3) in the subsequent image IM(3) was updated following the object motion OF_INI(1). The position of the target in that aperture would then be given, respectively, by:

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(3)={\mathrm{Pos}}_{\mathrm{aperture}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(1)={\mathrm{Pos}}_{\mathrm{aperture}}(1)+{\mathrm{OF}}_{\mathrm{ini}}(1) $$

(18)

$$ {\mathrm{Pos}}_{\mathrm{target}}(3)={\mathrm{Pos}}_{\mathrm{aperture}}(3)+{\mathrm{OF}}_{\mathrm{INI}}(2)=\left[{\mathrm{Pos}}_{\mathrm{aperture}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(1)\right]+{\mathrm{OF}}_{\mathrm{INI}}(2)=\left[{\mathrm{Pos}}_{\mathrm{aperture}}(1)+{\mathrm{OF}}_{\mathrm{INI}}(1)\right]+{\mathrm{OF}}_{\mathrm{INI}}(2) $$

(19)

where Pos_aperture(1) and Pos_aperture(2) are defined in Eqs. (14) and (16), respectively. Similarly, the position of the aperture in the fourth image frame Pos_aperture(4) was obtained by updating its position from image IM(3) with the computed motion given by OF_INI(2) and the target positon determined by OF_INI(3):

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(4)={\mathrm{Pos}}_{\mathrm{aperture}}(3)+{\mathrm{OF}}_{\mathrm{INI}}(2)=\left[{\mathrm{Pos}}_{\mathrm{aperture}}(1)+{\mathrm{OF}}_{\mathrm{INI}}(1)\right]+{\mathrm{OF}}_{\mathrm{INI}}(2) $$

(20)

$$ {\mathrm{Pos}}_{\mathrm{target}}(4)={\mathrm{Pos}}_{\mathrm{aperture}}(4)+{\mathrm{OF}}_{\mathrm{INI}}(3)=\left[{\mathrm{Pos}}_{\mathrm{aperture}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(1)\right]+{\mathrm{OF}}_{\mathrm{INI}}(3)={\mathrm{Pos}}_{\mathrm{aperture}}(1)+{\mathrm{OF}}_{\mathrm{INI}}(1)+{\mathrm{OF}}_{\mathrm{INI}}(2)+{\mathrm{OF}}_{\mathrm{INI}}(3) $$

(21)

For the i^th image (i.e., IM(i)), the generalized representation of the position of the aperture and target can be written as:

For the i^th image:

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(i)={\mathrm{Pos}}_{\mathrm{aperture}}(1)+\sum \limits_i^n{\mathrm{OF}}_{\mathrm{INI}}\left(i-2\right);\kern1.75em i>3 $$

(22)

$$ {\mathrm{Pos}}_{\mathrm{target}}(i)={\mathrm{Pos}}_{\mathrm{aperture}}(1)+\sum \limits_i^n{\mathrm{OF}}_{\mathrm{INI}}\left(i-1\right);\kern2em i>2 $$

(23)

where OF_INI (i) = OF( IM(1), IM(i + 1) ) was obtained by computing the optical flow of image IM(i + 1) with the reference image IM(1). Letting Pos_aperture(1) = P₀:

$$ {\mathrm{Pos}}_{\mathrm{aperture}}(i)=\Big\{{\displaystyle \begin{array}{c}{P}_0\\ {}{P}_0+\sum \limits_i^n{\mathrm{OF}}_{\mathrm{INI}}\left(i-2\right);\end{array}}\kern0.5em {\displaystyle \begin{array}{c}i=1,2\\ {}i\ge 3\end{array}} $$

(24)

$$ {\mathrm{Pos}}_{\mathrm{target}}(i)={P}_0+\sum \limits_i^n{\mathrm{OF}}_{\mathrm{INI}}\left(i-1\right);\kern4.25em i\ge 2 $$

(25)

Following the motion detected using the INI method, the generalized expressions for the position of the aperture and the target at image IM(i) are provided by Eqs. (24) and (25), respectively, which are similar to Eqs. (1) and (2) shown in the main manuscript. A similar approach was used to formulate the expressions for the other two methods, i.e., SEQ and PERD methods.