Proof of concept of near real-time intra-fractional 3D monitoring of prostate position using a scheme based on the skeletonization of implanted marker images and recursive least squares approximation motion tracking

Abstract

Background:

The on-board imaging system using monoscopic X-ray technology struggles to detect motion along the beam direction. This study presents a method that combines skeletonization for marker recognition with a Recursive Least Squares Approximation (RLSA) algorithm to convert 2D motion data into a 3D representation.

Methods:

Fiducial markers were represented as 2D lines through masking and skeletonization of paired-planar images, allowing for the construction of a 3D motion model. An iterative closest point (ICP) algorithm determined the 6D transformation from online to planning images. The accuracy of 3D motion estimation was evaluated across various angular separations (10° –170°) for both large (10 mm, 3°) and small (3 mm) marker offsets. The RLSA algorithm was validated against different motion drift patterns.

Results:

The marker recognition process was robust against varying contrast noise ratios. Mean errors of various angle separation tests in the X and Y directions were within 0.3 mm for large offsets and 0.2 mm for small offsets across all angular separations. With The RLSA applied at 10-° intervals during a 360-° gantry rotation, mean errors in the beam direction for continuous drift and low, intermediate, and high-frequency excursions were (0.2 ± 0.3) mm, (0.2 ± 0.3) mm, (0.4 ± 0.5) mm, and (0.4 ± 0.5) mm, respectively, with a maximum error of 1.3 mm across all excursion conditions.

Conclusion:

The proposed method demonstrates significant potential in effectively converting 2D motion into 3D and enabling real-time 3D motion tracking during intrafraction radiation therapy.

1. Introduction

Gold markers in the prostate are used for precise localization during marker-guided radiation therapy (MGRT), which is essential for prostate stereotactic body radiation therapy (SBRT). Accurate positioning allows for reduced planning target volume (PTV) margins, better protection of surrounding organs, and higher doses to the prostate. Effective motion tracking of markers embedded within the prostate depends on precise marker identification and reliable 3D position estimation. Most 2D-image marker recognition studies in the literature use regional or pattern match, combined different matching criterion [1–4], depending on binary match or intensity match, which apply pixel edge templates or image intensity patches to a pre-selected region to segment or to correlate and match markers [5–12]. The presence of low contrast and high noise in the 2D images greatly affects the successful rate of accurate marker segmentation which correlates with accurate marker alignment [13,14]. Most modern linear accelerators are equipped with a kilovoltage (kV) x-ray tube and an onboard imaging system. The standard procedure for this imaging system involves capturing paired twodimensional images to assist in the registration process from 2D to 3D. However, this method is less effective for manual alignment with fiducial markers and lacks the ability to rotate along the common axis (longitudinal axis, roll direction) of the paired image panels. Hatipoglu and Mu implemented a template matching technique utilizing a modified Hidden Markov Model algorithm for fiducial identification, enabling 2D to 3D registration in six dimensions within a commercial system (CyberKnife; Accuray, Sunnyvale, CA) [11,12,15]. Nonetheless, this approach necessitates the installation of two oblique paired x-ray imaging systems, which may encounter x-ray occlusion from the treatment head. It has a frequency limit of 5 s for image capture but typically operates at 10–20 s during beam delivery [16].

The treatment duration for pre-treatment verification and intrafraction monitoring procedures in prostate SBRT is longer than conventional therapies, complicating treatment monitoring. The TrueBeam (Varian Medical Systems, Palo Alto, CA) features an on-board imager that tracks motion with kV images and allows for intervention via Auto Beam Hold software [17]. However, its reliance on a single 2D image limits its ability to achieve triangulated alignment and detect motion along the beam direction. The prostate exhibits various movement patterns during treatment, which may be transient, persistent, high frequency, or irregular excursion. The unpredictable movement of the prostate presents difficulties for motion tracking during radiation treatment when employing monoscopic x-ray projections. Research [18–20] has utilized target trajectories reconstructed from pre-treatment CBCT or mathematical inference models as prior-knowledge to assess the likelihood of target motion. This approach has enabled the estimation of target motion in three dimensions with a satisfactory level of accuracy. Further insights into real-time intrafraction monitoring in radiation therapy are available in a 2019 technical review [21].

Template matching involves aligning a reference pattern with a larger image through a sliding window technique to detect the pattern, whereas feature matching emphasizes the comparison of distinct features between images. This latter approach is less susceptible to changes in scale, rotation, or intensity conditions. The present study introduces a shape representation scheme aimed at identifying and aligning markers. A desired shape descriptor considers certain properties, e.g., uniqueness, completeness, invariant under geometrical transformation, sensitivity, and abstraction from detail [22]. The morphology of the gold marker used in MGRT is unique compared to the anatomy of human pelvis. Its medial axis is easily preserved using a skeletonization algorithm, e.g., grassfire, Euclidean distance transform, thinning, or combination of the three [22–25]. This study used 2D lines extracted from the medial axis of markers projected upon two orthogonal images to reconstruct 3D lines of markers. The 3D line model is invariant under linear geometrical transformation and can be used to compute the 6D motion information from 2D paired images. By utilizing projected 2D lines from the gantry angle perspective, this research presents a recursive least squares approximation to estimate 3D motion based on two consecutive intrabeam kV images. The study will also address the dependency of angle separation in x-ray images and the influence of motion drifting patterns on the accuracy of the approximation.

2. Methods

2.1. Marker recognition and localization: effect of contrast noise ratio

Gold markers with dimensions of 1 mm × 5 mm and 1.2 mm × 5 mm were used. The 1.2 mm × 5 mm gold marker is the standard marker used in our clinic for any intact prostate patient having either SBRT (800 cGy × 5) or moderate hypofractionation (270 cGy × 26). An automatic marker identification process (Fig. 1) was developed to extract the medial axis of the marker from planar images. The process utilized an enhanced Sobel filter to enhance the contrast between the marker and the surrounding image such that the marker shape and location can be masked by the Sobel filter. The mask was transformed to a Euclidean distance map for further removing spurious branches from the medial axis of the Skeleton. A thinning algorithm developed by Lee [26] was then applied to skeletonize the image such that a pure medial axis of the marker can be extracted. In-house software was built upon the OpenCV (open computer Vision) and Python platform. To evaluate the robustness of the marker recognition from the contrast noise ratio (CNR) of marker to the background, the same scheme was generated and tested using images produced using kV, 2.5 MV, and 6 MV beams all with three 1 mm × 5 mm markers sandwiched within 35 cm thickness of solid water phantom. The CNR of the marker to the surrounding material from each energy was evaluated. The marker lines in 2D (represented by the medial axis of the marker) extracted from images irradiated by different energy were compared.

Fig. 1.

A skeletonized scheme of extracting medial axis applied to image irradiated by 16X: Enhanced sobel filter->Euclidean distance transform->threshold the Euclidean transform->thinning the new mask.

2.2. 2D to 3D registration: 2D/3D registration before treatment

Using the 2D line extracted from kV orthogonal paired images, the 3D line model of the marker was reconstructed by identifying the corresponding points of the line from the common axis of the orthogonal images. The 3D model reconstructed by DRR images was utilized as the reference 3D marker position and the 3D model reconstructed by kV paired images was used as the real time 3D marker position with motion. A 3D iterative closest point (ICP) algorithm using nearest neighbor to locate the corresponding points between motion 3D line and reference 3D line followed by a 6D affine transformation was iteratively computed to calculate the translational and rotational movement from motion 3D points to reference 3D points.

2.3. 3D intrafraction monitoring

Motion evaluated from series of mono-kV images: 3D motion estimation.

2.3.1. Convert 2D ICP motion registration to 3D

After setup verification using orthogonal paired images, two 3D line models can be chosen to project onto any gantry angle direction. One corresponds to the reference 3D line model reconstructed from the DRR of the planning CT. The other is the 3D line model reconstructed from paired x-ray images with correction after applying couch shift. The 2D line pattern identified from kV image using the method in 2.1 can be registered to the 2D line projected from the 3D Line model using a 2D version ICP. The expected location (u, v) of the 2D line on the kV image can be predicted by:

$$u=SID(x\mathrm{c}\mathrm{o}\mathrm{s}(\theta )+ysin(\theta ))/(SAD-xsin(\theta )+y\mathrm{c}\mathrm{o}\mathrm{s}(\theta )),$$ (1)

$$v=SI{D}^{\mathrm{*}}\mathrm{z}/(SAD-\mathrm{x}sin(\theta )+\mathrm{y}\mathrm{c}\mathrm{o}\mathrm{s}(\theta )),$$ (2)

where θ is the gantry angle, SID is the source-to-imager distance, and SAD is the source-to-axis distance.

X is the couch lateral direction, y is the vertical direction, z is the longitudinal direction and is the same direction as the gantry rotation axis. Z is parallel to the v direction on the imager and independent of gantry angle θ.

2D ICP gives translational motion (Δμ,Δv) in the direction of panel coordinate μ and v (Δv is the same as Δz after applying a scaling factor), other two motion directions of patient coordinate Δx, Δy cannot be directly calculated from Δμ, however, it can be approximated analytically using linear approximation.

The imager rotates with the gantry. The imager coordinate (μ,ν) is a function of gantry angle θ and is differentiable at any gantry angle. The differential of the denominator of Eq. (2) can be ignored since SAD is much greater than ($-\mathrm{x}\mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\theta })+\mathrm{y}\mathrm{c}\mathrm{o}\mathrm{s}(\theta )$) such that

$$(SAD-x\mathit{sin}(\theta )+y\mathit{cos}(\theta ))/SID\approx SAD/SID=\mathit{scalefactor}=SF$$

and

$${\mu }^{\prime }=S{F}^{\mathrm{*}}\left[x^{\prime }cos(\theta )-xsin(\theta )+y^{\prime }\mathrm{s}\mathrm{i}\mathrm{n}(\theta )+y\mathit{cos}(\theta )\right]$$

When the marker is stationary such that Δx ≈ 0 and Δy ≈ 0, (x,y) can be derived from Δμ. It is approximated that the marker is stationary between two adjacent gantry angles θ₁ and θ₂, since the images are acquired quickly after one another:

$$\mathrm{\Delta }{\mu }_1=S{F}^{\mathrm{*}}\left[-xsin\left({\theta }_1\right)+ycos\left({\theta }_1\right)\right]$$ (3)

$$\mathrm{\Delta }{\mu }_2=S{F}^{\mathrm{*}}\left[-xsin\left({\theta }_2\right)+ycos\left({\theta }_2\right)\right]$$ (4)

(x,y) can be computed by solving Eqs. (3) and (4). With new (x,y), the offset of the markers Δx & Δy can be obtained by subtracting (x,y) from the ((${\mathrm{x}}_0,{\mathrm{y}}_0$) of the 3D line model points.

Fig. 2 demonstrates the workflow of using the marker identification on the paired images for the following 3d line model reconstruction (a) and 3d icp registration before treatment (b) and using 2d icp after (a) at each monoscopic X-ray image to estimate the 3D motion during treatment (B.1) using linear least squares fit to solve Eqs. (3) and (4).

Fig. 2.

Flowchart of the procedure of the proposed methods before treatment (A and B) and during treatment (A and B.1).

2.3.2. The angle separation dependency of deriving (Δx, Δy) from Δμ: (limit of angle separation between x-ray images for motion estimation)

Series of 2D x-ray images can be used to decompose the marker’s trajectory in 2D to 3D motion based on triangulation method. The analytical calculation accuracy of decomposing Δx & Δy from Δμ was validated against the gantry angle θ and the required delta gantry (Δθ, the angle separation between images) between ${\theta }_1\&{\theta }_2$ to derive (x,y) form Δμ. KV images were acquired every 10° during a full arc (181° to 179°) beam delivery using the Truebeam’s intrafraction motion review (IMR) triggered imaging feature, resulting in 36 images. A known marker offset from iso-center (($\mathrm{\Delta }{\mathrm{x}}^{\prime },\mathrm{\Delta }{\mathrm{y}}^{\prime },\mathrm{\Delta }{\mathrm{z}}^{\prime }$) was determined by CBCT and was used as standard for comparison. Using Eqs. (3) and (4) in 2.3.1, the (Δx,Δy,Δz) can be calculated from 2D (Δμ,Δv) information of the kV image at any two angle locations ${\theta }_1\&{\theta }_2$. Comparisons were made to validate the accuracy of (Δx,Δy,Δz) computed from any two consecutive gantry angles by varying Δθ from 10° to 170°. Two scenarios were developed to evaluate the minimum angle separation required for precise determination of marker position offset. Scenario A involves a significant position offset of 10 mm in translation and 3° in rotation, while Scenario B features a moderate offset of 3 mm in translation alone. This experiment was conducted using a prostate training phantom (Sun Nuclear, Inc, Melbourne, FL), which had three gold markers implanted in the tissue-equivalent prostate under ultrasound guidance. The offset scenarios A and B were validated through Cone Beam Computed Tomography (CBCT) using a Truebeam system equipped with a six degrees of freedom (6DoF) couch.

2.3.3. Motion tracking using recursive linear squares approximation (RLSA): mitigation of prostate excursion

Under stationary condition, Δμ₁ = Δμ₂. When there is a motion, Δμ is incremental, a recursive equation is expressed by (5),

$$\left\{\begin{array}{c}(x,y:\theta {)}_1=\left(x_0,y_0\right)\\ (x,y:\theta {)}_i=(x,y:\theta {)}_{i-1}+\mathrm{\Delta }\mu (x,y{)}_i\\ (x,y,\theta {)}_{i+1}=(x,y:\theta {)}_{i-1}+\mathrm{\Delta }\mu (x,y{)}_i+{\omega }_i(x,y)\mathrm{\Delta }\mu (x,y{)}_i\end{array}\right.$$ (5)

where $(x,y:\theta {)}_{i-1}$ can be obtained from step i-1 and substitute into (1), $(x,y:\theta {)}_i={\mu }_i$ and $(x,y:\theta {)}_{i+1}={\mu }_{i+1},{\omega }_i$ is the weight number multiplied to $\mathrm{\Delta }{\mu }_i$ to represent anotherincrementchangeati + 1.

The recursive relation at step i of Eq. (5) can be rewritten as (6):

$$\left\{\begin{array}{c}{\mu }_i=\left[x_{i-1}\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)+y_{i-1}\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)\right]+\left[-\mathrm{\Delta }\mu (x{)}_i\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)+\mathrm{\Delta }\mu (y{)}_i\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)\right]\\ {\mu }_{i+1}=\left[x_{i-1}\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)+y_{i-1}\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)\right]+\left[-\left(1+{\omega }_i\right)\mathrm{\Delta }\mu (x{)}_i\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)+\left(1+{\omega }_i\right)\mathrm{\Delta }\mu (y{)}_i\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)\right]\end{array}\right.$$ (6)

which can be expressed by (7),

$$\left(\genfrac{}{}{0pt}{}{{\mu }_i-\left[x_{i-1}\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)+y_{i-1}\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)\right]}{{\mu }_{i+1}-\left[x_{i-1}\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)+y_{i-1}\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)\right]}\right)=\left(\begin{array}{cc}-\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)& \mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)\\ -\left(1+{\omega }_i\right)\mathrm{s}\mathrm{i}\mathrm{n}\left({\theta }_i\right)& \left(1+{\omega }_i\right)\mathrm{c}\mathrm{o}\mathrm{s}\left({\theta }_i\right)\end{array}\right)\left(\genfrac{}{}{0pt}{}{\mathrm{\Delta }\mu (x{)}_i}{\mathrm{\Delta }\mu (y{)}_i}\right)$$ (7)

A Least Square Solution ($\mathrm{\Delta }\mathrm{\mu }(\mathrm{x}{)}_{\mathrm{i}},\mathrm{\Delta }\mathrm{\mu }(\mathrm{y}{)}_{\mathrm{i}}$) of w_i can be computed and the solution is added to position (x, y) at step i-1 to derive the position (x, y) at step i. Same recursive equations at step i + 1 can be computed with a solution derived from (7).

Various patterns of prostate excursion were simulated to evaluate the RLSA, including encompassing offset without drift, continuous drift, drift characterized by low or high frequency of excursion, and drift following a sinusoidal pattern.

3. Results

3.1. Marker recognition and the impact of CNR

The imaging parameters of each imaging combination were summarized in Table 1, in terms of energy (kV, 2.5X, 6X), panel size, and resolution of the image after the technique selection. The maximum signal-Sm (measured from the central profile) of the marker, the median signal the solid water-${\mathrm{S}}_{\mathrm{w}}$ (as background), and the standard deviation of the solid water- ${\mathrm{\sigma }}_{\mathrm{w}}$ (as noise) were recorded to calculate CNR (CNR $\equiv \left.\left({\mathrm{S}}_{\mathrm{m}}-{\mathrm{S}}_{\mathrm{w}}\right)/{\mathrm{\sigma }}_{\mathrm{w}}\right)$. KV had the best CNR of 15.4, CNR of 2.5X was median (10), and CNRs of 6X was the lowest (5). The location of each marker identified by each imaging technique is listed in the lower half of Table 1, in terms of the center of each of the three markers (Ctr_m), the centroid of the three markers, and the mean length (mean L.) of the three markers on the images. Using the marker recognition algorithm developed in this study, the location of the center of each marker and the centroid of the markers had a minimal difference on the order of one pixel (0.22–0.45 mm) among the images taken from different energies.

Table 1.

Summary of imaging parameters using in this study and the markers’ location identified.

	kV	2.5X-Hi	2.5X-Lo	6X-Hi	6X-Lo	16X-Hi	16X-Lo
panel size	39.6x29.8	43x43	43x43	43x43	43x43	43x43	43x43
pixel size	0.259	0.224	0.448	0.224	0.448	0.224	0.448
MU	101kV	1.5	1	3	1.5	3	1.5
CNR	15.4	8.5	10.0	5.3	4.3	7.0	5.3
Ctrm1	−6.9; −24.8	−6.8; −24.5	−6.8; −24.5	−6.7; −24.5	−7.2; −24.9	−6.5; −24.5	−6.7; −24.6
Ctrm2	15.5; −9.3	15.6; −9.1	15.5; −9.2	15.7; −9.2	15.2; −9.4	15.7; −9.4	15.7; −9.4
Ctrm3	−2.2; 15.2	−2.2; 15.4	−2.2; 15.4	−2; 15.0	−1.8; 15.8	−2; 15.6	−2; 15.5
Centroid	2.1; −6.3	2.1; −6.1	2.2; −6.1	2.5; −6,1	2.1; −6.1	2.4; −6.1	2.3; −6.2
mean L.	3.4	3.7	4	3.7	3.6	3.6	1.8

Unit: panel size: cm; pixel size, Ctr (X;Y), Centroid (X;Y), mean L.: mm.

3.2. The dependency of angle separation between x-ray images in 2D to 3D motion estimation

Fig. 3 displays the angle separation dependency of the accuracy (mean error) and precision (standard deviation) of motion estimate using a 2D monoscopic image compared to two known 3D motion scenarios (world coordinate): (a) X-1.6 mm, Y-9.8 mm, Z-4.5 mm, Yaw-2.2°, Pitch-3.3°, Roll-3.5°; (b) X-3 mm, Y-3 mm, Z-0 mm; Yaw-Pitch-Roll-0° . The (mean value) ± (standard deviation) of the Δv from 36 projected images (panel coordinate, which is the same as the Z world coordinate) were 4.3 ± 0.1 mm and 0.1 ± 0.1 mm in (a) & (b), respectively. The motion estimate using the approximation method in this study, with a minimum angle separation of 10° up to maximum angle separation of 160° (in a) −170° (in b), clockwise or counterclockwise, the mean error of both X & Y directions using approximated estimate were within 0.3 mm in (a) and 0.2 mm in (b). The STD of the error were within 0.3 mm between 20° to 120° angle separation. Of note, in case b, one of the three markers was invisible at the lateral images 40° (70°–110°, 250°–290°) such that only two markers were used for 2D ICP registration and the 3D motion estimate.

Fig. 3.

Polar plot of the accuracy (mean error) and precision (standard deviation-STD) of the motion estimated in X (a1 and b1) & Y (a2 and b2) (mm) from mono 2D projection (μ) versus gantry angle separation (°) in comparison to a known 3D motion. “Row a” & “row b” had known movements of (1.6 mm, 9.8 mm, 4.5 mm, 2.2°, 3.3°, 3.5°), and (3 mm, 3 mm, 0 mm, 0°, 0°, 0°), respectively.

3.3. Validation of RLSA in decomposing motion from different prostate excursion conditions

Fig. 4 demonstrates a comparison of RLSA calculated motion to ground truth motion at different drifting patterns: (i) stable portion of a (2 mm, 2 mm) displacement (lateral, vertical); (ii) continuous drift at vertical direction with a starting position displaced (0.5 mm, 0.5 mm); (iii-v) continuous drift with low to high frequency excursion at vertical direction; (vi) continuous drift with regular sine wave motion at vertical direction. The stationary condition was accurately estimated; the continuous drift, with wave or without wave and within a 4 mm drifted range, RLSA accurately estimated motion to within 0.3 mm STD; the continuous drift with low to high frequency excursion, within a 6 mm drifted range, the RLSA estimation accuracies were within 0.5 mm STD from low to intermediate frequency excursion and was 0.6 mm STD when it was high frequency excursion. The maximum estimated errors in the Y direction, which corresponds to the direction of greater prostate excursion, were recorded as 0.7 mm, 0.8 mm, 1.0 mm, and 1.3 mm for continuous drift, low, intermediate, and high frequency excursions, respectively. A subsequent experimental design aimed to decrease the magnitude of the Y direction excursion by 50 %. The findings are depicted in Fig. 5. Notably, the estimated errors remained comparable to those observed in the full excursion scenarios with maximum estimated errors in the Y direction of 0.5 mm, 1.3 mm, 1.3 mm, and 1.3 mm for continuous drift, low, intermediate, and high frequency excursions, respectively.

Fig. 4.

Scatter plots of simulation of motion tracking using RLSA. “•–” curve is the real motion at X (green color) and Y (red color); “x” curve is the RLSA calculated; the yellow “solid line“ is the 2d projection at μ direction calculation from real motion of (X,Y). Rx and Ry are mean ± STD of the residual error between calculation and real motion within gantry range of (91, 51). A 2 mm typical clinical threshold is displayed by the light blue shadow. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5.

Same Scatter plots of simulation of motion tracking using RLSA as in Fig. 5 with half of the excursion magnitude in the Y direction.

To illustrate the effectiveness of monoscopic x-ray imaging in monitoring prostate motion within a 2 mm threshold, the color shading within the motion range of (−2, 2) inFigs. 4 and 5 employs blue and orange to indicate overestimation and underestimation, respectively, without decomposing the X-Y motion. The figures utilize magenta and white to represent the overestimation and underestimation as determined by the RLSA method in comparison to the true motion. In the absence of 2D decomposition, there are 30 to 60° gantry angle spans where the imaging system may inaccurately estimate the motion alert by the 2 mm threshold, particularly around the anterior-posterior gantry angle direction. The RLSA method applied in this research significantly reduced the probability of erroneous motion estimates, confining the inaccuracy to within 10–20° gantry angle spans.

4. Discussion

Marker identification is essential in Image Guided Radiation Treatment (IGRT), where markers act as proxies for targets. By using skeletonization to extract the medial axis of symmetrical cylindrical markers, we can effectively capture their key features for 3D position reconstruction. Each marker consists of 8 to 15 continuous points, depending on its orientation within the prostate. This method converts a 2D paired-image match into a 3D point match, achieving sub-millimeter and sub-degree registration accuracy during pre-treatment verification with orthogonal paired images and allowing for the exclusion of missing points from one marker without significantly impacting overall accuracy during intrafraction monitoring. However, challenges arise with larger patients and lateral images, where the contrast-to-noise ratio (CNR) of the markers is reduced due to bone interference. While our study showed that reduced CNR at 6MV does not hinder marker detection compared to kV beams, some markers were occasionally indistinguishable in lateral images. Nonetheless, the absence of a single marker can still be reconstructed from 2D to 3D using this approach as two markers provide adequate spatial points to enable the matching of three-dimensional points.

Two measurements using IMR on a prostate phantom with known positional deviations were conducted. One measurement showed significant translational and rotational offsets, while the other had a minor translational offset. Both measurements indicated that 3D translational motion could be estimated accurately (standard deviation of 0.2 mm) by aligning projected 2D line images with calculated 2D lines from a 3D model, using a least squares solution with a 10-° angular separation. This separation allows for excellent temporal resolution in monitoring prostate motion, providing a sufficient sample size for applying the Recursive Least Squares Algorithm (RLSA) to decompose 2D motion into 3D motion. RLSA’s accuracy in estimating 3D motion is influenced by the drift pattern; it achieved high accuracy (error < 0.2 ± 0.3 mm) with continuous drift and low-frequency excursion but showed decreased precision and accuracy (mean error of 0.4 ± 0.5 mm, max error 1.3 mm) with intermediate and high frequency excursions. This represents a limitation of the proposed method. On a positive note, the application is designed for intervention during motion tracking. Significant underestimation or overestimation of motion due to high frequency excursion can be validated at 2–3 angular points. In practice, interventions can be structured to hold the beam only when two or three consecutive kV images detect motion errors exceeding the predetermined tolerance.

Prostate motion exhibits randomness over extended periods. The extent of this motion is influenced by airflow within the rectum and bowel movements. A clinical protocol for prostate treatment, which includes bowel preparation [27], is crucial for stabilizing the prostate during radiation therapy (RT). Numerous studies on prostate RT have indicated that prostate motion tends to drift continuously in both vertical and longitudinal axes, while remaining relatively stable in the lateral direction [28,29]. The likelihood of prostate motion exceeding 5 mm is infrequent, occurring in approximately 5 % of cases; however, intrafraction motion surpassing 3 mm can occur in more than 15 % of instances [30,31]. Using the MGRT technique for prostate patients, a three-dimensional line model, reconstructed from treatment plans or pre-treatment paired X-ray images, can be projected onto a two-dimensional kilovoltage (kV) panel in real time. This allows for the comparison of online images with three-dimensional motion tracking utilizing RLSA. In a typical stereotactic body radiation therapy (SBRT) plan employing volumetric modulated arc therapy (VMAT) with two arcs, the duration for each arc delivery ranges from 1 to 2 min, depending on whether a Flattening Filter Free (FFF) beam is utilized. Each 10-° arc motion takes approximately 1.5 to 3 s, while a 40-° arc motion requires about 5 to 10 s. At current minimum of 3 s between kV images using the IMR, an image trigger scheduled between 10 and 30° should facilitate the reconstruction of an accurate prostate trajectory with an image frame rate of every 3 to 10 s. Although the temporal resolution of triggering kV images as an intrafraction monitoring technique limits RLSA’s ability to detect rapid excursions in motion over short durations (less than 5 s), the slower motion of the prostate during treatment times of 2 to 5 min allows for the use of 2D projected images to estimate 3D motion effectively. The proposed MGRT monitoring scheme has been retrospectively evaluated offline to assess the feasibility of employing 2D kV images for online intervention in a small cohort of prostate SBRT patients, with 2D images triggered every 40° during the VMAT treatment with regular dose rate [32]. Further studies could be conducted to explore the feasibility and advantages of triggering 2D kV images every 10–20°, with and without using the FFF beam.

5. Conclusion

This study demonstrated that the medial axis of marker can be extracted to reconstruct 3D line model for 2D to 3D registration in 6D. The 3D model can be projected back to 2D imager in any gantry angle for motion monitoring and can be used to estimate the 3D motion using RLSA during treatment from two consecutive kV intrafraction triggered images with gantry angle separation as small as 10°. The technique proposed in the study achieves an automatic process with an accurate 6D alignment before treatment and a 3D motion monitoring during treatment. Implementation of the technique would improve the efficiency and accuracy in the treatment of prostate SBRT using gold marker as the surrogate of treatment target.

Table 2.

Summary of 2D to 3D registration accuracy in comparison to CBCT.

Translation	Vertical				Longitudinal				Lateral
	ALc	RLOc	ALm	RLOm	ALc	RLOc	ALm	RLOm	ALc	RLOc	ALm	RLOm
Correlation	.998	.998	.989	.989	1.00	1.00	.982	.991	1.00	1.00	.989	.991
Med. Diff	.1	.1	.1	−.1	−.1	−.3	.2	.3	−.2	−.1	.0	.0
Range	−.1/1	−.2/.9	−.4/.7	−.3/1.2	−.5/.5	−.5/.5	−.1/.7	.0/.7	−.8/.3	−.5/.5	−.1/.3	−.4/.3
Rotation	Yaw				Pitch				Roll
	ALc	RLOc	ALm	RLOm	ALc	RLOc	ALm	RLOm	ALc	RLOc	ALm	RLOm
Correlation	.986	.986	.889	.926	.998	.989	.975	.932	.970	.989	.541	.226
Med. Diff	.1	−.0	−.2	.2	.0	.0	−.1	−.1	.0	.0	1.5	1.4
Range	−.2/.4	−.2/.3	−2/1	−2/1	−.3/.2	−.1/.4	−1/1	−2/1	−.5/.8	−.6/.8	−5/5	−5/5

Unit in Med. Diff (median difference) & Range: Translation, mm; Rotation, °.