Medical Physics, Vol. 30, No. 2, pp. 103–110, February 2003
©2003 American Association of Physicists in Medicine. All rights reserved.
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Optimal marker placement in photogrammetry patient positioning system

Haisong Liu,a)Yan Yu, M. C. Schell, Walter G. O'Dell, Russell Ruo, and Paul Okunieff

Department of Radiation Oncology, University of Rochester, Rochester, New York 14642

Received: 24 May 2002; accepted: 6 November 2002; published: 10 January 2003

A photogrammetry-based patient positioning system has been used instead of the conventional laser alignment technique for patient set-up in external beam radiotherapy. It tracks skin affixed reflective markers with multiple infrared cameras. The three-dimensional (3D) positions of the markers provide reference information to determine the treatment plan isocenter location and hence provide the ability to position the lesion at the isocenter of the treatment linear accelerator. However, in current clinical practice for lung or liver lesion treatments, fiducial markers are usually randomly affixed onto the patients' chest and abdomen, so that the actual target registration error (TRE) of the internal lesions inside the body may be large, depending on the fiducial registration error (FRE). There exists an optimal marker configuration that can minimize the TRE. In this paper, we developed methods to design the patient-specific optimal configurations of the surface makers to minimize the TRE, given the patient's surface contour, the lesion position and the FRE. Floating genetic algorithm (GA) optimization was used to optimize the positions of the skin markers. The surface curve of the patient body was determined by an automatic segmentation algorithm from the planning CT. The method was evaluated using a body phantom implanted with a metal ball (a simulated target). By registering two CT scans using the surface markers and measuring the displacement of the target, the TRE was measured. The TRE was also measured by taking two orthogonal portal films after positioning the phantom using the photogrammetry based patient positioning system. A 50% reduction in TRE has been achieved by using the optimal configuration compared to the random configuration. This result demonstrates that the optimization of a fiducial configuration can result in improved tumor targeting ability. © 2003 American Association of Physicists in Medicine.


Contents

I. INTRODUCTION

Current 3D conformal radiotherapy and intensity modulated radiotherapy (IMRT) techniques can deliver radiation beams shaped tightly to the target volume. However, the patient set-up and organ motion-induced uncertainties can directly impair an optimal treatment plan, especially for extracranial tumors. Therefore, an accurate patient positioning and motion compensation system has great importance for the successful delivery of an optimal radiotherapy treatment.

Conventionally, patient positioning during treatment set-up is done by using laser alignment to skin marks. This technique has inherent difficulties including the operator-related laser misalignment and patient-related skin mark movement. This method is also highly subjective and prone to error, which is 2.0–2.5 mm for a perfectly immobilized phantom.1 Inadequate immobilization adds approximately 1–4 mm of error, depending on the site treated.1 Unimmobilized patients with thoracic lesions have been reported to show approximate 4 mm treatment-to-treatment variations and 6 mm simulation-to-treatment standard deviation in target position.2 A recent review stated that the standard deviation of the systematic and random setup errors of 3.5 mm can be considered as state of the art in routine clinical practice for lung cancer.3

Photogrammetry-based patient positioning systems have been developed in recent years aimed to improve the patient set-up accuracy. Skin affixed markers are tracked with multiple infrared charged-coupled device (CCD) cameras. The 3D positions of the markers are calculated by conventional photogrammetry methods and provide reference information to determine the treatment plan isocenter location. It can be used to actively position the target at the isocenter of the treatment linear accelerator. Several authors have described this system4,5,6 and reported high precision and accuracy when applied to a head phantom,4 or patients with head immobilization devices.5 Such a system has also been used to measure the accuracy of conventional laser centering techniques for patient repositioning.7,8

ExacTracTM is a commercially available photogrammetry-based patient positioning system developed by BrainLAB A.G. (Heimstetten, Germany), used for patients with body tumors. Several institutions have installed this system and evaluated its patient positioning ability. Soete et al.9 evaluated this system in 17 patients receiving conformal radiotherapy for prostate cancer. The standard deviation of measured setup errors along anteroposterior (AP), lateral and longitudinal axes are 2 mm, 1.6 mm, and 3.5 mm, respectively. Solberg et al.10 evaluated the system accuracy by a phantom study and found that the reproducibility of the phantom with rigidly attached markers is on the order of 1 mm when 3 mm thick axial CT slices are used to define marker and target positions. We have evaluated the ExacTrac system installed in our department with patients with lung or liver tumors.11,12 The mean position reproducibility was 3.5 mm for a representative patient with five isolated lung lesions. In that evaluation study, we also used a rigid body transform based target registration error (TRE) analysis13,14,15 to calculate the theoretical position errors of each target and compared them with the measured values, and obtained a reasonable agreement.

TRE is a function of the fiducial configuration, the number of fiducial markers, and the fiducial registration error (FRE). Our hypothesis is, therefore, that there exists an optimal fiducial configuration for a given patient anatomy and target location, which will minimize the TRE. However, in current clinical practice for lung or liver lesion treatments, fiducial markers are usually randomly placed onto the thorax region of the patient and the actual TRE of the lesion inside the body is not minimized. In this paper, we developed methods to design an optimal configuration of the surface makers to minimize the TRE. This work will help the photogrammetry patient positioning system improve the target positioning accuracy.

II. METHODS AND MATERIALS

A. TRE analysis (Refs. 13,14, 15)

In current clinical procedures, six to ten fiducial markers are randomly placed on the anterior and lateral aspects of the chest and abdomen. These body markers are retroreflective to infrared light and are radio-opaque CT-visible. A planning CT set is acquired and images are transferred to the Novalis planning system. From this, a treatment plan is made, targeting the internal tumor. The markers are identified and their 3D relative positions with regard to the isocenter are transferred to the ExacTrac system. Before each treatment session, the markers are placed back on the patient by adhesive film to marked spots on the skin. The ExacTrac system identifies the body markers with two infrared cameras and triangulates the marker 3D positions based on the known geometry and calibration of the system. The system then infers the location of the tumor relative to the isocenter of the machine from the marker positions. By re-positioning the patient so that the marker positions can have the best match with the planned positions, the tumor is assumed to be at the linac isocenter.

The system is essentially an intra-patient registration system. The process contains fiducial registration errors (FRE) as well as the inferred target registration error (TRE). FRE is a common measure of overall fiducial misalignment and can be calculated by taking the root-mean-square (RMS) distance between homologous fiducial markers after registration,

FRE<sub><i>i</i></sub> = <i>T</i>(<i>x</i><sub><i>i</i></sub>) – <i>y</i><sub><i>i</i></sub>,

where xi and yi are the corresponding fiducial points in spaces X and Y, respectively, belonging to marker i, and T denotes the transform.

TRE is simply the registration error calculated at the point of interest,

TRE = <i>T</i>(<i>x</i><sub><i>t</i></sub>) – <i>y</i><sub><i>t</i></sub>,

where t denotes the target. The predictable relationship between TRE and FRE incurred by point based rigid body registration is given by the equation from Fitzpatrick et al.:14

<TRE<sup>2</sup>> [approximate] ((<FRE<sup>2</sup>>)/(<i>N</i> – 2)) · (1+(1/3) [summation]<sub><i>k</i> = 1</sub><sup>3</sup> (<i>d</i><sub><i>k</i></sub><sup>2</sup>/<i>f</i><sub><i>k</i></sub><sup>2</sup>)),

where k increments over the three coordinate directions, dk is the distance of the target from the principal axis of k, and fk is the root-mean-square (RMS) distance of the fiducial markers from the principal axis of k. The < > is used to indicate the expected value. It can be seen from the above equation that isocontours of TRE are ellipsoidal and are centered at the center of the fiducial configuration.

B. GA optimization of the fiducial configuration

1. Brief description of the genetic algorithm (Refs. 16 and 17)

Genetic algorithm (GA) is inspired by Darwin's theory about evolution. It searches the solution space of a function through the use of simulated evolution, i.e., the survival of the fittest strategy. In general, the fittest individuals of any population tend to reproduce and survive to the next generation, thus improving successive generations. The solution to a problem solved by a genetic algorithm is evolved.

GA is started with a set of solutions (represented by chromosomes) called population. Solutions from one population are taken and used to form a new population. This is motivated by a hope, that the new population will be better than the old one. Solutions which are selected to form new solutions (offspring) are selected according to their fitness—the more suitable they are the more chances they have to reproduce.

This is repeated until some conditions (for example, a number of populations or improvement of the best solution) is satisfied. A more complete discussion of genetic algorithms can be found in the books by Holland16 and Goldberg.17 An outline of the basic GA is summarized below.

(1) Generate random population of n chromosomes (suitable solutions for the problem).

(2) Evaluate the fitness f(x) of each chromosome x in the population.

(3) Create a new population by repeating the following steps until the new population is complete.

   (3.1) Select two parent chromosomes from a population according to their fitness: the better fitness, the bigger chance to be selected (selection);

   (3.2) With a crossover probability cross over the parents to form a new offspring (crossover). If no crossover was performed, offspring is an exact copy of parents;

   (3.3) With a mutation probability mutate new offspring at each position in chromosome (mutation).

(4) Place new offspring in a new population.

(5) Use new generated population for a further run of algorithm.

(6) If the end condition is satisfied, stop, and return the best solution in current population.

(7) Go to step (2).

For machine-driven optimization, a number of robust, widely proven schemes are currently available, including GA and simulated annealing (SA). We have chosen GA as the optimization engine in this study because of its conceptual simplicity, the ease of programming entailed, and the small number of parameters to be defined. Also, in the long run, GA will probably be more efficient as parallel processor computers become a common commodity.

2. Optimization of the fiducial marker configuration in patient positioning system

In this paper, two procedures have been developed to obtain the optimal fiducial marker configuration in the photogrammetry patient positioning system.

(1) Automatic segmentation of the patient body surface curves is performed from the planning CT image set. This step is needed because the markers are placed on the patient so that the optimization searching space is constrained on the patient-specific body surface curve. The automatic segmentation is implemented by simple gray-scale thresholding because the gray-scale values of the background in CT images are less than the anatomy parts. For the CT images in which the intensity values of each pixel ranges from 0 to 4095, the threshold is set to 400 for the studies demonstrated in this paper. The segmentation algorithm first sets the searching range and scans the data matrix row-by-row or column-by-column and marks the first and last positions of the gray-scale values greater than the threshold. The pixels at these positions define the boundary points of the body surface. Experiments showed that this technique can produce accurate results for body surface segmentation.

(2) A Floating genetic algorithm (GA) is then used to optimize the positions of the surface markers. Given the preferred number of markers N, the algorithm searches in 2N float number space, representing the lateral (X) and superior–inferior (Z) coordinates of the markers. The anterior–posterior (Y) coordinates are determined by the surface curve of the patient body, which is pre-determined in step 1. The number of markers N and the searching depth along the anterior–posterior directions are user-defined options in the algorithm. Specific bounds are set to each X and Z value. The bounds can be set to the whole surface or different sub-areas for each marker. The initial population is a random set of marker positions within the bounds. The evaluation function is the TRE formula. If there are multiple lesions, the averaged TRE is used as the evaluation function. The GA algorithm terminates on a fixed number of generations or until a satisfactory TRE has been obtained. The algorithm was developed in Matlab software.

C. Verification of the optimal fiducial configuration

The advantage of the optimal fiducial configuration versus the random configuration was verified using a body phantom implanted with a spherical, metallic bead marker (simulated target). It was an anthropomorphic acrylic phantom with a pelvis, lumbar and thoracic spines imbedded. A 4.5 mm diameter steel marker was implanted approximately 2.3 cm deep from the surface at the left-upper chest area of the phantom. Two methods were used for the evaluation.

1. Evaluation by registering two CT image sets

First, two CT scans were taken on two consecutive days. The surface markers were removed from the phantom after the first scan and re-placed before the second scan according to ink "tattoos" drawn on the phantom. Then, the positions of the surface makers and the internal marker were identified in each CT image set, and the two image sets were registered using a fiducial point based rigid body registration method. Finally, the distance between the corresponding internal marker positions was measured to compute the TRE. The detailed steps are as follows.

(1) With the random fiducial configuration, obtain two CT scans;

(2) Identify the 3D marker positions and target position in each scan;

(3) Register these two CT scans by marker positions using point based rigid body registration, and compute the FRE and TRE;

(4) With the optimized fiducial configuration, obtain two CT scans; the surface markers were affixed onto the body phantom according to the optimal configuration with the help of lasers and the couch movement in the treatment room.

(5) Identify the 3D marker positions and target position in each scan;

(6) Register the two CT scans and compute the FRE and TRE;

(7) Compare results from (6) to those from (3).

The registration in step (3) is described as follows. In rigid-body registration, a rotation matrix R and a translation vector t are determined that minimize the FRE. The relationship between points in the initial, reference space x, and the subsequent test space y, is given by

<i>y</i> = <i>R</i><i>x</i> + <i>t</i>,

so that the FRE, as defined in Eq. (1), can be written as

FRE = sqrt((1/<i>N</i>) [summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup>|<i>R</i><i>x</i><sub><i>i</i></sub> + <i>t</i> – <i>y</i><sub><i>i</i></sub>|<sup>2</sup>).

A simple and reliable method was employed to determine R and t, as described by Fitzpatrick et al.13 and others. In brief, the method is as follows:

(1) Compute the weighted centroid of the fiducial configuration in each space:

<i>x</i>-bar  = [summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup><i>x</i><sub><i>i</i></sub>/[summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup>,   <i>y</i>-bar  = [summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup><i>y</i><sub><i>i</i></sub>/[summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup>.

(2) Compute the displacement from the centroid to each fiducial point in each space:

<i>x</i>-tilde<sub><i>i</i></sub> = <i>x</i><sub><i>i</i></sub> – <i>x</i>-bar,   <i>y</i>-tilde<sub><i>i</i></sub> = <i>y</i><sub><i>i</i></sub> – <i>y</i>-bar.

(3) Compute the weighted fiducial covariance matrix,

<i>H</i> = [summation]<sub><i>i</i> = 1</sub><sup><i>N</i></sup><i>w</i><sub><i>i</i></sub><sup>2</sup><i>x</i>-tilde<sub><i>i</i></sub><i>y</i>-tilde<sub><i>i</i></sub>.

(4) Perform the singular value decomposition of H:

<i>H</i> = <i>U</i> <i>Lambda</i> <i>V</i><sup>[prime]</sup>.

(5) Compute the rotation matrix:

<i>R</i> = <i>V</i>((1, 0, 0; 0, 1, 0; 0, 0, det(<i>V</i><i>U</i>)))<i>U</i><sup>[prime]</sup>.

(6) Compute the translation vector:

<i>t</i> = <i>y</i>-bar  – <i>R</i><i>x</i>-bar.

After obtaining R and t, FRE can be computed by Eq. (5), and TRE can be computed by

TRE = <i>R</i><i>x</i><sub><i>t</i></sub> + <i>t</i> – <i>y</i><sub><i>t</i></sub>.

2. Evaluation by measurement on portal films

The TRE values from the random and optimal configurations were also compared by measuring the distance from the implanted marker to the isocenter of the treatment machine on the portal films. The CT scans of the body phantom affixed with random markers was first transformed to Novalis planning system, and a dummy plan was made, targeting the internal marker. The relative positions, in three dimensions, of the surface markers were then transferred to the computer of the ExacTrac patient positioning system. The body phantom was then placed on the treatment couch, and the markers were detected by the pair of infrared cameras. By moving the phantom and the couch so that the marker positions matched with the planned positions, the internal marker was assumed to be at the isocenter. The matching procedure was performed by observing the error indication bars displayed on the monitor screen of the ExacTrac computer. AP and lateral portal films were taken, and the discrepancy of the internal marker to the center of the field was measured. The 3D difference in position was the actual TRE.

D. Evaluation of TRE improvement on real patient data

The verification of the optimal marker configuration described in Sec. II C was performed using a rigid phantom. Since the metallic bead marker was implanted in the left-upper lung, and the surface markers were all inferior to the simulated target in the random configuration, this arrangement may cause larger TRE than actual clinical cases. To fairly evaluate the improvement factor of the optimization technique, 2 other comparisons were performed by simulating on two real patient data. One patient had 5 separated lung tumors and 8 surface markers were used. The other one had a prostate tumor and 7 surface markers were used in treatment. We calculated the TRE values of the targets in treatment, and then used the optimization procedure to find optimal marker configurations, and then calculated the TRE values from the optimal configuration. Comparisons of the TRE values give a fair evaluation of the improvement of the optimization technique.

E. Simulation of the expected clinical FRE

Although both FRE and TRE for a particular testing case can be obtained by a CT registration method, an expected clinical FRE should be obtained in order to properly evaluate the improvement of <TRE> in the clinic.

A simulation of the expected clinical FRE has been performed in this paper. In clinical practice of the ExacTrac patient positioning system, three translation and three rotation error bars are displayed on the ExacTrac computer screen, and the radiation therapist observes the error bars and positions the treatment couch and patient to reduce these errors to within pre-determined tolerances. These error bar values are computed from the rigid-registration procedure as described in Sec. II C 1. FRE can be computed using these six values. In our treatment center, the tolerances of the three translation errors are 1.5 mm, and those of the rotation errors are 1 degree, and the maximum displacement of any marker along any axis is ±5 mm. The simulation procedure is described as follows: for N markers with given positions, 3N random numbers are created representing the displacements of each marker along each axis. These random numbers are of uniform distribution within ±5 mm. Then, a rigid registration is performed (follow the procedure in Sec. II C) to compute the rotation matrix and translation vector, since the rotation matrix can be written as

((cos(<i>E</i>)<sup>*</sup> cos(<i>A</i>), cos(<i>E</i>)<sup>*</sup> sin(<i>A</i>),  – sin(<i>E</i>);  – cos(<i>R</i>)<sup>*</sup> sin(<i>A</i>) + sin(<i>R</i>)<sup>*</sup> sin(<i>E</i>)<sup>*</sup> cos(<i>A</i>), cos(<i>R</i>)<sup>*</sup> cos(<i>A</i>) + sin(<i>R</i>)<sup>*</sup> sin(<i>E</i>)<sup>*</sup> sin(<i>A</i>), sin(<i>R</i>)<sup>*</sup> cos(<i>E</i>); sin(<i>R</i>)<sup>*</sup> sin(<i>A</i>) + cos(<i>R</i>)<sup>*</sup> sin(<i>E</i>)<sup>*</sup> cos(<i>A</i>),  – sin(<i>R</i>)<sup>*</sup> cos(<i>A</i>) + cos(<i>R</i>)<sup>*</sup> sin(<i>E</i>)<sup>*</sup> sin(<i>A</i>), cos(<i>R</i>)<sup>*</sup> cos(<i>E</i>))),

where R, E, and A represent rotation angles along each axis (Roll, Elevation, and Azimuth), respectively, the three rotation angles can be obtained. And the three translation errors are just the three component in the translation vector. If the six errors are all within the pre-defined values, then the FRE is computed and stored. By repeating this simulation a large amount of times, an FRE distribution can be obtained. The mean value of the FRE distribution can be considered as the expected clinical FRE.

F. Simulation of the TRE impact from the inaccuracies in marker placement

In clinical practice, since the markers need to be placed on the patient according to the optimal configuration by using lasers and digital table movement in the CT room, the small inaccuracies in marker placement will affect the optimal configuration. A simulation was performed to evaluate this problem. For N markers with given positions, 3N random numbers are created representing the displacements of each marker along each axis. These random numbers are of uniform distribution within ±5 mm, which is the estimation of the inaccuracies caused by the laser alignment and couch movement system. Then, the TRE value was computed using the optimal positions plus these random shifts. This procedure is repeated for a large amount of times so that a TRE distribution is obtained. The ratio of the amount of discrepancy to the optimal TRE value will reflect this impact.

III. RESULTS

A. Verification of the TRE estimation

The body phantom and eight randomly placed surface markers were used to verify the TRE formula. Figure 1 shows the configuration of the surface markers. The internal marker is located at the intersection of the two beams. Following the procedures described in Sec. II C.1, the FRE and TRE values were 1.11 and 1.02 mm, respectively. The estimated TRE from Eq. (3) was 0.99 mm; in good agreement with the measured value from the CT registration. This agreement shows that Eq. (3) is a reliable estimation of the TRE in rigid body transform.

Figure 1.

B. Evaluation of the optimal marker configuration by CT registration

The optimal configuration of 8 markers on the phantom was computed. The searching depth was set to the same as that of the random configuration. Figure 2 shows the optimal configuration of the surface markers on the phantom. The measured and estimated TRE values were 0.42 and 0.47 mm, respectively, based on the measured FRE of 1.0 mm. Since the FRE will be much larger in actual clinical practice than that in the CT registration method, the ratio of the <TRE> to the <FRE> was used to compare the different configurations. In this experiment, the ratio was 92% for the random configuration but only 42% for the optimal configuration.

Figure 2.

C. Evaluation of the optimal configuration by measurement on portal films

For the random configuration, the discrepancy from the internal marker to the isocenter was 1.25, 0.43, and 1.36 mm for AP, SI, and lateral views, respectively. The 3D displacement was 1.90 mm. For the optimal configuration, the displacements were 0.53, 0.59, and 0.20 mm for AP, SI, and lateral views, respectively. The 3D displacement was 0.82 mm; more than 50% less than that of the random configuration. Table I lists the comparison results between the optimal configuration and the random configuration by both evaluation methods. This comparison test demonstrates that the optimized configuration is superior to the random configuration in reducing the TRE.

D. Evaluation of TRE improvement on real patient data

Figure 3 compares the treatment marker configuration and the optimal marker configuration of the lung tumor case. Figure 4 compares those of the prostate tumor case. Table II gives the comparison of the TRE/FRE ratios from the actual marker configuration used in treatment and those from the optimal marker configuration. From this table, one can see that the TRE/FRE ratio was reduced 18% on average for the lung case, and 30% for the prostate case. For the lung case, the tumor 2 had the least improvement because it is much closer to the patient surface than the other 4 tumors. This observation follows Wang's study18 that the targeting error increases with an increase in target vector length. Since the target vector length of tumor 2 was much less than those of other tumors, it had the least improvement space.

Figure 3. Figure 4.

E. Simulation of the expected clinical FRE

The single simulation procedure was repeated for 300,000 times, and 11,065 random sets meet the error tolerance criteria, the FRE values show a normal distribution (as shown in Fig. 5), with a mean value of 4.46 mm and a standard deviation of 0.52 mm. The maximum and minimum values are 6.38 and 2.21 mm, respectively.

Figure 5.

F. Simulation of the TRE impact from the inaccuracies in marker placement

The single simulation procedure was repeated 10,000 times. The optimal configuration of the lung tumor case was used in this simulation. When the FRE is assumed to be 4.5 mm, the optimal TRE value is 2.18 mm, and the maximum TRE value of these disturbed configurations is 2.20 mm. The maximum discrepancy of the TRE value is within 1% of the optimal TRE value.

IV. DISCUSSION

In this paper, a floating GA optimization procedure was developed to obtain an optimal marker configuration used in the photogrammetry patient positioning system for external radiation beam treatment. The photogrammetry system has more accurate patient positioning ability than conventional laser alignment techniques. A commercially available system (ExacTrac, BrainLAB, AG) has been installed in our treatment center and used for setting up ~40 patients with body tumors since 2000. Many other groups have developed similar systems4,5,6 and the performances of these systems have been characterized.9,10 However, in current clinical practice, the surface markers are randomly placed on the patient. West15 and Wang18 investigated the relationship between the marker configurations and the alignment accuracy of the system, and provided some suggestions on how to place the markers to obtain better accuracy. However, they did not use an optimization procedure to find a best solution of the optimal marker positions, as we have performed in this paper, which has the potential to increase the target alignment accuracy of the photogrammetry system. The optimization results in this paper follow their suggestions, i.e., the targeting error increases with increase in target vector length, and decreases with an increase in marker separation. The advantage is that an optimal configuration could be automatically calculated based on this paper in comparison to a manual selection of points based on their suggestion.

The optimization method developed in this paper is based on a basic relationship between the TRE of an inner tumor and the configuration of the external markers [Eq. (3)] deducted by Fitzpatrick et al.13,14,15 Although this estimation is based on rigid body transform while the human body has elastic movement, we can still take advantage of it because the actual target localization error can be divided into two parts. One part is the systematic error (TRE) induced by the rigid body transformation, and the other is the random error induced by tumor movement, which can be measured by using bi-plane x-ray cameras.

The advantage of the optimal marker placement has been verified with a comparison study made on a body phantom. The TRE value of an implanted internal marker was measured by registering two CT scans. The TRE was reduced from 92% to 42% of the FRE, going from the random to the optimal configuration. The TRE values were also compared using normal clinical procedures to set up the phantom and taking portal films. It was reduced from 1.9 mm to 0.8 mm by measuring on the portal films. Another two comparisons using actual patient data have shown that the reduction of the TRE/FRE ratio could be about 20%–30% in real clinical practice. As shown in our simulation, the expected clinical FRE was 4.5±0.5 mm for patients with extracarnial lesions because of the respiration-induced marker movement. Therefore, the expected clinical TRE reduction will be about 1 mm.

Although the method of optimizing the marker configuration presented in this paper will improve the TRE, there will still be some limitations of implementing this method clinically using current available hardware. First of all, it will require an additional CT scan for each patient because the surface contour is obtained from the CT image sets. One CT scan is required to determine the patient surface contour, the target position and thus the optimal marker configuration, then a second scan is required with the markers in place. Another limitation is that the markers will need to be placed on the patient according to the optimal configuration. Currently, it may be performed by using lasers and digital couch movement in the CT room. The accuracy of transferring the ideal optimal configuration to the actual marker placement on the patient is limited by the hardware. Fortunately, the little amount of inaccuracies in the marker placement will not damage the improvement made by the optimization procedure, as shown in our simulation study.

ACKNOWLEDGMENTS

This work is financially supported by BrainLAB, AG under a research agreement with the University of Rochester, and American Cancer Society grant (RSG-02-155-01-CCE). The authors thank Dr. Fitzpatrick and Dr. Maurer for the helpful discussion with them and using the theoretical TRE analysis in their previous works. Thank the reviewers for their insightful and helpful comments and suggestions.

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FIGURES


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Fig. 1. Random configuration of the surface markers on the body phantom. First citation in article


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Fig. 2. Optimal configuration of the surface markers on the body phantom. First citation in article


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Fig. 3. Marker configurations of the lung tumor case; (a) and (b) marker configuration in the treatment; (c) and (d) optimal marker configuration; (a) and (c) are the rotated 3D view that can see both the markers and the lesions; (b) and (d) are the top view 2D projections; " * " represents the surface marker, and "+" represents the lesion. First citation in article


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Fig. 4. Marker configurations of the prostate tumor case; (a) 3D view of the marker configuration in the treatment; (b) 3D view of the optimal marker configuration; " * " represents the surface marker, and "+" represents the lesion. First citation in article


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Fig. 5. Simulated distribution of the expected clinical FRE. First citation in article

TABLES

Table I. A comparison of the results between random configuration and optimal configuration of a body phantom.
  Random
configuration
Optimal
configuration
Measured FRE by Eq. (5) 1.11  mm 1.00  mm
Measured TRE by Eq. (6) 1.02  mm 0.42  mm
Estimated <TRE > by Eq. (3) 0.99  mm 0.47  mm
TRE/FRE 0.92 0.42
Measured TRE by portal films 1.90  mm 0.82  mm
First citation in article

Table II. A comparison of the TRE/FRE ratios between treatment configuration and optimal configuration of two real cases.
  Treatment configuration Optimal configuration
Lung tumor case
1 0.71 0.49
2 0.53 0.46
3 0.70 0.50
4 0.68 0.47
5 0.67 0.50
Average 0.66 0.48
Prostate tumor case 0.78 0.48
First citation in article

FOOTNOTES

aAuthor to whom correspondence should be addressed. Telephone: (585) 273-2876; fax: (585) 275-1531; electronic mail: haisong_ liu@urmc.rochester.edu


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