Download Prediction of respiratory tumour motion for real-time image

INSTITUTE OF PHYSICS PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 49 (2004) 425–440
PII: S0031-9155(04)69607-2
Prediction of respiratory tumour motion for real-time
image-guided radiotherapy
Gregory C Sharp1, Steve B Jiang1, Shinichi Shimizu2 and Hiroki Shirato2
1 Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical
School, Boston, MA 02114, USA
2 Department of Radiation Medicine, Hokkaido University School of Medicine, Sapporo, Japan
E-mail: [email protected]
Received 26 September 2003
Published 16 January 2004
Online at stacks.iop.org/PMB/49/425 (DOI: 10.1088/0031-9155/49/3/006)
Abstract
Image guidance in radiotherapy and extracranial radiosurgery offers the
potential for precise radiation dose delivery to a moving tumour. Recent work
has demonstrated how to locate and track the position of a tumour in real-time
using diagnostic x-ray imaging to find implanted radio-opaque markers.
However, the delivery of a treatment plan through gating or beam
tracking requires adequate consideration of treatment system latencies,
including image acquisition, image processing, communication delays, control
system processing, inductance within the motor, mechanical damping, etc.
Furthermore, the imaging dose given over long radiosurgery procedures or
multiple radiotherapy fractions may not be insignificant, which means that we
must reduce the sampling rate of the imaging system. This study evaluates
various predictive models for reducing tumour localization errors when a realtime tumour-tracking system targets a moving tumour at a slow imaging rate
and with large system latencies. We consider 14 lung tumour cases where the
peak-to-peak motion is greater than 8 mm, and compare the localization error
using linear prediction, neural network prediction and Kalman filtering, against
a system which uses no prediction. To evaluate prediction accuracy for use
in beam tracking, we compute the root mean squared error between predicted
and actual 3D motion. We found that by using prediction, root mean squared
error is improved for all latencies and all imaging rates evaluated. To evaluate
prediction accuracy for use in gated treatment, we present a new metric that
compares a gating control signal based on predicted motion against the best
possible gating control signal. We found that using prediction improves gated
treatment accuracy for systems that have latencies of 200 ms or greater, and for
systems that have imaging rates of 10 Hz or slower.
0031-9155/04/030425+16$30.00 © 2004 IOP Publishing Ltd Printed in the UK
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1. Introduction
The goal of radiation therapy is to precisely deliver a lethal dose to the tumour while minimizing
the dose to surrounding healthy tissues and critical structures. Recent technical developments
such as intensity-modulated radiation therapy (IMRT) have advanced the capability of
delivering highly conformal radiation dose distributions to complex three-dimensional (3D)
static target volumes. However, internal organ motion and deformation during the treatment,
mainly caused by respiration, may greatly degrade the effectiveness and efficiency of IMRT
for the management of thoracic and abdominal lesions, especially when the treatment is
done in a hypo-fraction or single-fraction manner (Jacobs et al 1996, Engelsman et al 2001,
Langen and Jones 2001, Ozhasoglu and Murphy 2002).
To deliver the prescribed radiation dose to the entire volume of moving tumour while
avoiding high radiation to the adjacent healthy tissues, several techniques have been developed
or are under development. The simplest approach is to minimize the motion by breath holding,
either passively (Hanley et al 1999, Mah et al 2000, Rosenzweig et al 2000, Barnes et al
2001, Kim et al 2001, Sixel et al 2001) or actively (Wong et al 1999, Stromberg et al 2000).
Alternatively, a technology called respiratory gating can be used to reduce the tumour
motion during beam-on time by limiting radiation exposure to a portion of the breathing
cycle. Respiratory gating can be implemented using either an external respiratory signal
to infer the tumour position (Ohara et al 1989, Kubo and Hill 1996, Ramsey et al 1999a,
1999b, Kubo et al 2000, Minohara et al 2000, Vedam et al 2001, Keall et al 2002), or by
directly tracking implanted radio-opaque markers fluoroscopically (Shirato et al 1999, 2000a,
2000b, Shimizu et al 2000, 2001, Harada et al 2002). Arguably, a better way to treat a
moving target may be to follow the target dynamically with the radiation beam (beam
tracking). This was first implemented in a robotic radiosurgery system (Adler et al 1999,
Ozhasoglu et al 2000, Schweikard et al 2000, Murphy 2002, Murphy et al 2003). For linacbased radiotherapy, tumour motion can be compensated for using a dynamic multileaf
collimator (MLC) (Keall et al 2001, Neicu et al 2003).
For beam gating or beam tracking, the precise 3D location of a moving tumour should
be available in real-time, and can be obtained through real-time x-ray imaging of fiducial
markers during the treatment (Shirato et al 1999, 2000b, 2003, Shimizu et al 2001, Murphy
2002, Berbeco et al 2004). The x-ray images are generally taken at a constant frequency,
with each image providing the location of the tumour at a certain instant in time. After the
image is taken, but before the radiation beam can target the tumour at its new location, there
is always a system latency due to the time needed for image acquisition, image processing,
reaction times of the hardware (linac, MLC or Cyberknife), and so on (Litzenberg et al
2002). Let us assume images are taken at a period of t, the latency between imaging and
beam reaction is t and we have just taken an image at time t (see figure 1). Because
of the imaging rate and latency, decisions made for treatment between time t + t and
t + t + t are based on the tumour positions derived from the image at time t, preferably
using previous images too. When both the imaging period and system latency are small
enough, the tumour positions between t + t and t + t + t can be approximated using
its position at time t. However, this approximation can introduce significant localization
errors when system latency is not negligible, or when the x-ray imaging frequency is reduced
to limit imaging dose. Figure 2 shows the kind of errors that can be introduced by long
system latencies (left) and reduced imaging frequency (right). In these plots, the most
recent measurement is shown with a dashed line, and the true position is shown with a
solid line. Treatment based solely on the most recent measurement will consistently miss the
target.
Prediction of respiratory tumour motion
Image
Capture
427
Image
Capture
Image
Capture
Image
Capture
Imaging Rate (∆t)
Image processing,
Beam reaction, etc.
Image processing,
Beam reaction, etc.
Image processing,
Beam reaction, etc.
Image processing,
Beam reaction, etc.
System Latency (∆t')
Treatment
Treatment
time t
Treatment
time t+∆t'
Treatment
time
time t+∆t'+∆t
2
2
0
0
cranial-caudal motion (mm)
cranial-caudal motion (mm)
Figure 1. Because of limitations in imaging rate and system latency, the most recent image may
not accurately reflect the position of a tumour at the time of treatment. For a system with an
imaging period of t and a system latency of t , an image captured at time t (shown in grey)
must be used for treatment between time t + t and time t + t + t.
2
4
6
8
10
65
4
6
8
10
Measurements
System with latency
64
2
66
time (sec)
67
68
Measurements
System with low imaging rate
64
65
66
time (sec)
67
68
Figure 2. Effect of large system latency and slow imaging rate on tumour localization accuracy.
Left: a system with latency of 200 ms and imaging rate of 30 Hz. Right: a system with latency of
33 ms and imaging rate of 3 Hz.
Early studies using prediction of respiratory motion to overcome system latencies suggest
that improvements in targeting accuracies can be realized. Shirato et al (2000b) describe the
use of linear extrapolation to estimate the future position of a tumour, and have evaluated the
accuracy on phantom measurements. Murphy et al (2002) compare three methods, a tapped
delay line filter, a Kalman filter and a neural network, for predicting the future position of a
tumour using fluoroscopic simulation data and external markers. In this paper, we investigate
the performance of standard prediction algorithms to characterize the predictability of 3D
tumour motion for different imaging rates and system latencies. We investigate two kinds of
linear filters, two kinds of neural networks and a Kalman filter. Only stationary forms of these
predictors are considered. Prediction accuracy is evaluated for the lung tumour motion of 14
patients with peak-to-peak tumour motion greater than 8 mm, as measured during treatment
(Shirato et al 2000a, Seppenwoolde et al 2002). From our results, we hope to provide a useful
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estimate of the expected error in tumour localization during treatment for machines with
different latencies, and we hope to understand how to use prediction to reduce the fluoroscopic
frequency and imaging dose in a real-time image-guided radiotherapy system (Shirato et al
2000a, 2000b, Berbeco et al 2004).
2. Methods
In this section we describe the prediction methods that we have evaluated for predicting
the 3D marker position: linear prediction, artificial neural networks and the Kalman filter.
The methods for optimization of free parameters and the methods for evaluation of predictor
performance will also be described.
2.1. Prediction algorithms
2.1.1. Linear prediction. A linear predictor is a system which predicts the future output
signal as a linear function of a set of inputs. We consider linear predictors of the form
xt = a0 + a1 xt−1 + · · · + an xt−n
(1)
where xt is the 3D position of the tumour at time t. The position xt is therefore predicted as a
linear combination of the known previous positions xt−1 through xt−n .
From a set of training samples, the coefficients ak can be found by solving a linear
equation to minimize the mean squared error of predictions on a set of training examples.
However, determining the best number of histories to use is not a trivial question. We will
defer discussion of parameter optimization for section 2.2.
2.1.2. Linear extrapolation. As a special case of linear prediction, we also consider linear
extrapolation. Linear extrapolation uses the two most recent samples to find the signal velocity,
and predicts that the signal will maintain constant velocity. For a system where images are
sampled at a constant rate, we predict that
xt = 2xt−1 − xt−2 .
(2)
Because the constant velocity assumption is only valid for a short period of time, we have only
evaluated the linear extrapolation method for low latency systems.
2.1.3. Artificial neural networks. An artificial neural network (ANN) is a function
approximation technique modelled on the biological processing of brain neurons (Bishop
1995). Here we consider only predictors that are multilayer perceptrons, with two feedforward
stages. This means that there will be two computation stages performed sequentially. The first
stage computes a vector of intermediate values (called the hidden layer) from the recent history
of positions. The second stage computes the predicted positions from the hidden layer. Both
these stages compute a linear transformation, followed by a possibly nonlinear transformation
called the activation function.
In the first stage, the input layer is a history of the ni most recent 3D positions, but the
actual number of input values used is 3ni + 1. This is because in addition to the three 3D
coordinates of the marker for each history used, there is an additional input with a constant
value of 1. This additional input is called a bias unit, and it is used to bias the linear portion
of the computation. A sigmoid function is then used as the nonlinear activation function to
Prediction of respiratory tumour motion
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generate the nh values of the hidden layer. With input values denoted xi and hidden values
denoted yj , the equation for the first layer is given as
yj =
1
.
3ni +1
1 + exp − i=1 vij xi
(3)
In this stage, the free parameters to be optimized are the weights vij .
In the second layer of the neural network, predicted positions are computed from the
hidden layer. To predict no future 3D positions, we generate 3no output coordinate values;
nh + 1 intermediate values are used, including a bias node as before. The activation function
we use in the second stage is linear. Therefore, with hidden values denoted yj and output
values denoted zk , the equation for the second layer is given as
zk =
n
h +1
wj k yj .
(4)
i=1
In this stage, the free parameters to be optimized are the weights wj k .
2.1.4. Predicting slope with an ANN. As a special case of the ANN prediction we consider
a network which predicts not the future position of the marker, but the future velocity of the
marker. In other words, the ANN inputs are a history of positions, but the output is the velocity
to the next position. The future position is then predicted by extrapolating the current position
along the predicted velocity. In our experiments, this method will be referred to as ‘ANN
(slope)’. Because this method is also based on the constant velocity assumption, we only
evaluate the ANN (slope) method for low latency systems.
2.1.5. The Kalman filter. The Kalman filter is a method for estimation of the internal state
of a linear dynamic system (Kalman 1960). An excellent introduction is given by Welch and
Bishop (1995).
In using the Kalman filter to predict the 3D marker position, we assume that the marker
motion is generated by a linear dynamic system model with no dependence on a control input.
The equations for such a system are given by
xt = Axt−1 + w
(5)
zt = Bxt + v
(6)
where xt is the internal state of the system at time t, A is the state transition matrix which
describes how the state changes over time, w is normally distributed process noise with
covariance Q, zt is the observation at time t, B is the measurement matrix which describes
how the observation depends on internal state and v is normally distributed measurement noise
with covariance R. The measurement zt is the 3D position of the tumour as observed by the
x-ray imaging system.
The Kalman filter generates an optimal estimate for the state xt by combining the previous
estimate xt−1 , its covariance Pt−1 and the current measurement zt . As shown in figure 3, a
prediction of the internal state, denoted x̂t , is computed from the previous estimate of the state
xt−1 . From x̂t , we can predict the future value of the measurement using equation (6), and use
it for treatment. Later, when the actual measurement arrives, the internal state can be updated
to its optimal estimate xt .
Kalman filter estimation requires complete knowledge of the dynamic system.
Specifically, the transition matrix A, the measurement matrix B and the noise covariance
matrices Q and R must be known. In this study, we treat the state vector x as an abstract
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Previous
Estimated State
State Prediction
Predicted
State
Measurement
Prediction
Predicted
Tumour
Location
Treatment
Delivery
State Estimation
Measured
Tumour
Location
Imaging
System
Estimated
State
Figure 3. The Kalman filter generates an estimate of the current state of a linear dynamic system
from the previous estimated state and the measurement. Before the actual measurement arrives, a
predicted measurement ẑt can be computed from the predicted state and used for treatment.
unknown state of fixed dimension, and we treat the dynamic system matrices as unknowns
to be optimized. The matrices are optimized by estimating their maximum-likelihood values
using expectation maximization (EM) on a set of training samples (Digalakis et al 1993).
2.2. Parameter tuning
Each of the prediction methods described above, with the exception of linear extrapolation,
has a number of parameters that must be determined. We distinguish between two groups
of parameters, which we call configuration parameters and free parameters. The configuration
parameters are those which are generally considered to be design criteria, while the free
parameters are those generally solved by numeric optimization. For example, consider the
linear predictor. The number of previous histories to use is a design decision, but the weights
given to each history can be solved by linear regression. A list of the configuration parameters
and free parameters for each method is given in table 1.
Finding the best values for the configuration parameters is a question of model selection,
which is not an easy one. Various strategies have been developed to address this problem,
such as Akaike information criterion, minimum description length, cross-validation and
bootstrapping (e.g. Duda et al 2001). Solving for the best configuration parameters is beyond
the scope of this paper. Instead, we simply choose configuration parameters that minimize
error over the entire patient population, based on running multiple off-line simulations. Our
configuration parameter values are therefore tuned to perform well at a given latency and
imaging rate, but may not be well tuned for a given patient. Typical values used are between
two and five histories for the ANN and linear predictors, between five and ten hidden units for
the ANN and between three and five dimensions for the Kalman filter state vector.
Prediction of respiratory tumour motion
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Gather
training data
Compute
parameters
Warm-up
predictor
Treatment with
prediction
15 sec
2 sec
4 sec
As required
Figure 4. Training of free parameters is performed for each treatment fraction, and requires time
for gathering data, computing predictor parameters and warming up the predictor.
Table 1. Configuration parameters, free parameters and optimization methods used in this study.
Prediction
method
Configuration
parameters
Free
parameters
Optimization
method
Linear
Linear
extrapolation
ANN, ANN
(slope)
Kalman filter
Number of histories
None
a (equation (1))
None
Regression
None
Number of histories, number
of hidden units
Dimension of state
vector
vij , wj k
(equations (3), (4))
A, B, Q, R
(equations (5), (6))
Conjugate
gradient
Expectation
maximization
Once the configuration parameters are known, the free parameters are easily solved using
standard numerical optimization algorithms. To account for different breathing patterns in
different patients, we estimate these parameters on a fraction by fraction basis, according to
the fixed schedule described in figure 4. At the beginning of each fraction, we use the first
15 s (about four to five breaths) to gather training data which will be used to optimize the
free parameters. Next, we allocate exactly 2 s of computer processing time to perform the
optimization. The free parameters are fixed based on this computation, and are not updated
using subsequent data. Next, 4 s are allocated to ‘warm-up’ the predictors. The warming-up
period includes the time needed to gather the recent history of data points, or time to converge
to a stable state vector in the case of the Kalman filter. Finally, prediction accuracy is evaluated
by running the predictor on the remaining data.
2.3. Interpolation
Although the prediction methods described above can be used for prediction of an unevenly
sampled time series, we restrict our attention to uniform imaging rates. However, from a
uniform imaging rate we have no knowledge of the shape of the signal between samples.
Therefore, we implement a simple linear interpolation scheme to fill in the missing values
between predictions, as shown in figure 5. Depending upon the amount of latency and the
sampling rate, between one and three future marker positions will be predicted. The signal
is then interpolated between the most recent sample and these future positions to generate a
30 Hz prediction over the prediction interval.
2.4. Evaluating accuracy
We consider two metrics for evaluating the accuracy of the predictions: root mean squared
(rms) error and gating error. Root mean squared error is useful as a measure of accuracy for
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latency
interval
original 30 Hz
measurements
prediction
interval
prediction
interpolated
to 30 Hz
predicted future
3 Hz measurements
3 Hz measurements
Figure 5. Low frame rate predictions are interpolated up to full frame rate over a prediction
window by making multiple future predictions and interpolating between them.
6mm Gating
Window
True Signal
Predicted Signal
Ideal Gating Signal
Predicted Gating Control Signal
68
70
72
74
76
78
time (sec)
Figure 6. The gating error metric compares the ideal gating control signal against the gating
control signal determined by the predicted motion.
a treatment delivery method that tracks the tumour with the radiation beam (Ozhasoglu et al
2000, Keall et al 2001, Neicu et al 2003). To combine the error results for different patients,
we compute rms error for each patient separately, and average the results over all patients.
On the other hand, to provide a measure of accuracy for gated treatment (Shirato et al
1999, Shimizu et al 2000), we introduce the concept of gating error. Ideally, a gating system
should enable a gating control signal and begin treatment when the radio-opaque marker enters
a predetermined gating window, and disable the control signal when the marker leaves the
gating window. The gating error metric quantifies the error in the control of the gating signal.
It is computed by comparing a gating control signal based on the predicted motion against the
best possible gating control signal (see figure 6). For the experiments shown in this study, we
use a gating window which is a 6 mm diameter 3D cubic volume centred at the exhale position
of the setup (cf Shimizu et al 2001).
Two kinds of gating errors are possible: false negatives where the marker is in the window
but the prediction is out of the window, and false positives where the marker is out of the
window but the prediction is within of the window. From the false negatives, we can compute
the duty cycle of a treatment as a percentage of the maximum possible duty cycle. Let FN be
the number of false negatives, and let Ptot be the total number of time steps when the marker
was actually within the gating volume. Then, we have
Ptot − FN
.
(7)
duty cycle (% of max) =
Ptot
Prediction of respiratory tumour motion
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Table 2. Mean and standard deviation of breathing amplitude for the 14 lung tumour patients used
in this study.
Patient ID
Mean motion
amplitude
(mm)
Standard
deviation
(mm)
1
6
7
9
11
13
17
22.2
13.2
15.7
14.1
9.1
16.3
12.5
4.9
3.3
3.6
3.0
0.8
2.6
2.2
Patient ID
Mean motion
amplitude
(mm)
Standard
deviation
(mm)
18
26
30
31
34
38
40
11.6
11.9
27.5
14.3
14.7
13.8
31.6
1.5
1.3
5.3
1.7
3.3
1.7
2.3
Thus, the duty cycle describes the reduction in gated treatment efficiency due to prediction
errors.
From the false positives, we can compute the gating failure rate, which is the number
of incorrect beam-on predictions as a percentage of total beam-on predictions. Let FP be the
number of false positives, and let Ppred be the total number of time steps that the beam was
predicted to be within the gating window. Then, we have
gating failure rate =
FP
.
Ppred
(8)
Thus, the gating failure rate quantifies the incorrect beam-on time during gated treatment
due to prediction errors. Both duty cycle and gating failure rate should be considered when
comparing prediction methods.
3. Materials
We performed this study retrospectively using lung tumour movement data of patients treated
using the real-time tumour-tracking (RTRT) system at Hokkaido University (Shirato et al
1999, 2000b, Shimizu et al 2001, Seppenwoolde et al 2002). In this system, a 1.5 mm
diameter gold marker is inserted into or near the lung tumour mass through bronchofibrescopy
prior to treatment. The marker is imaged at a rate of 30 Hz using diagnostic fluoroscopy and
image processing computers to determine the three-dimensional coordinates of the marker
in real-time. Lung tumour motion data of 40 patients treated between 2001 and 2002 were
analysed, and the 14 patients with breathing amplitude greater than 8 mm were identified
and used to evaluate motion prediction accuracy. The average and standard deviation of the
breathing amplitudes of these 14 patients are shown in table 2. Evaluation of accuracy was
based on predictions made after the predictor was trained and warmed up, i.e. the fourth stage
of figure 4. The duration of the evaluation period varied between 48 and 342 s, with an average
evaluation period of 115 s.
A qualitative examination of the breathing patterns of the 14 patients shows that there
are significant differences between patients. An example of the breathing signals from four
different patients is shown in figure 7. Figure 7(a) shows a breathing pattern that is regular in
both period and amplitude. Regular breathing represents an ideal case for prediction, because
the motion pattern used for training continues during treatment. Figure 7(b) highlights the fact
that the raw tracking signal is often noisy. Two kinds of noise are present: an approximately
Gaussian noise of around 1–2 mm, and a spike noise of up to 10 mm. Figure 7(c) shows
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10
L-R
L-R
20
5
S-I
10
Motion (mm)
Motion (mm)
0
-5
-10
S-I
0
-10
A-P
A-P
-15
-20
-20
-30
80
100
Time (secs)
44
46
Time (secs)
(a)
(b)
120
140
160
38
180
40
42
48
50
52
15
20
L-R
10
L-R
10
S-I
0
S-I
Motion (mm)
Motion (mm)
5
0
-5
-20
-30
A-P
-10
-10
A-P
-40
-15
-50
-20
10
15
20
25
30
Time (secs)
(c)
35
40
45
80
90
100
110
Time (secs)
120
130
(d)
Figure 7. Examples of tumour motion and signal quality: (a) regular breathing; (b) noisy signal;
(c) breathing with cardiac motion; (d) drift in position and amplitude.
the motion pattern of a tumour that is influenced by both breathing and cardiac motion.
Figure 7(d) demonstrates a breathing pattern where both the exhale home position and the
amplitude drift over time.
Prediction of respiratory tumour motion
8
Extrapolation
Linear
ANN
ANN (slope)
Kalman filter
No prediction
7
RMS Error (mm)
435
6
5
4
3
2
1
0
Latency = 33 ms
30
8
1
Linear
ANN
Kalman filter
No prediction
7
RMS Error (mm)
10
3
Imaging Rate (Hz)
6
5
4
3
2
1
0
Latency = 200 ms
30
10
3
Imaging Rate (Hz)
1
12
RMS Error (mm)
10
8
6
4
Linear
ANN
Kalman filter
No prediction
2
0
30
Latency = 1 sec
10
3
Imaging Rate (Hz)
1
Figure 8. Root mean squared error of tumour position predictions as a function of imaging
frequency for (top) 33 ms latency, (middle) 200 ms latency and (bottom) 1 s latency.
4. Experimental results and discussion
Figure 8 shows the rms error averaged over all patients as a function of imaging rate for each
algorithm. Plots for three different latencies are shown: 33 ms (top), 200 ms (middle) and
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1 s (bottom). Results for linear extrapolation and ANN (slope) methods are computed only
for the case of 33 ms latency. We only consider this case for these two methods because both
methods are based on extrapolation of the motion velocity, which is only useful for a short
time.
It is seen that most forms of prediction have lower rms error compared to no prediction.
One notable exception is the case of linear extrapolation, which has a higher error at all
imaging rates. Prediction using linear extrapolation has been previously tested in phantom
experiments for the RTRT system at Hokkaido University (Shirato et al 2000b), but has not
been used for treatment because of our awareness about these potential errors.
The reason for the poor prediction accuracy of linear extrapolation is that the random
signal noise such as that shown in figure 7 makes it difficult to estimate the motion velocity
from two points. This noise occurs when the pattern matching software is employed on poor
contrast images such as those which occur when the marker is obscured by the bony skeleton.
In contrast to linear extrapolation, the other predictors use multiple history readings, and
therefore they can both smooth and predict the data.
We also note the relatively worse performance of the Kalman filter predictor when
compared with linear and ANN predictors. This may reflect the difficulty in estimating
the state transition matrix from such a small amount of data. Therefore, we expect that a handtuned Kalman filter will perform better than the Kalman filter derived from EM estimation.
In terms of accuracy, the best predictor allows us to achieve an rms error of 2 mm at
sampling rates as low as 3–4 Hz for the low latency (33 ms) case. A similar error rate is
possible at 30 Hz with 200 ms latency. However, with a 1 s latency we were not able to
achieve less than 5 mm rms error using the methods we investigated.
Figure 9 shows the gating error averaged over all patients as a function of imaging rate
for each algorithm. The plots on the left show the duty cycle achieved as a percentage
of the maximum duty cycle, while the plots on the right show the gating failure rate (see
section 3). Plots for the same three latencies are shown: 33 ms (top), 200 ms (middle) and 1 s
(bottom).
From the plots it is seen that at high frame rates and low latencies, gating failure rates are
worse when using prediction than when not using prediction. However, when using prediction
there is also a corresponding increase in duty cycle suggesting that actual performance may
be similar. This represents a trade-off between duty cycle and gating failure rates that
can be realized by adjusting the size of the gating window. At slower imaging rates, it is
seen that prediction improves the gating failure rate with a similar duty cycle. With longer
latencies, gating failure rates are still improved by using prediction, but the duty cycle becomes
considerably degraded, suggesting that prediction reliability may be insufficient.
One important consideration that we did not address within this study is the effect of the
non-stationary nature of breathing. Because we used only the first 15 s for training data, and
we did not update the predictor parameters online, it is likely that the prediction quality will
degrade over time as the breathing pattern changes. We expect this effect to be greater for
patients whose breathing patterns notably drift over time, and less for patients with regular
breathing. Prediction failures due to changes in breathing patterns can never be eliminated,
but they might be reduced by using the adaptive versions of these prediction algorithms.
5. Summary
In this paper we have presented a study on the use of prediction to compensate for system
latencies and reduced imaging rates in real-time image-guided radiation treatment. Five
prediction methods were compared for low latency systems, and three prediction methods
Prediction of respiratory tumour motion
437
14
Extrapolation
Linear
ANN
ANN (slope)
Kalman filter
No prediction
90
Gating Failure Rate (%)
Gating Duty Cycle (% of max)
12
80
70
60
Extrapolation
Linear
ANN
ANN (slope)
Kalman filter
No prediction
50
8
6
4
2
Latency = 33 ms
Latency = 33 ms
40
30
10
10
3
Imaging Rate (Hz)
0
1
30
10
3
Imaging Rate (Hz)
1
20
Linear
ANN
Kalman filter
No prediction
16
80
Gating Failure Rate (%)
Gating Duty Cycle (% of max)
90
70
60
Linear
ANN
Kalman filter
No prediction
50
12
8
4
Latency = 200 ms
Latency = 200 ms
0
30
10
3
Imaging Rate (Hz)
1
30
10
3
Imaging Rate (Hz)
1
40
Linear
ANN
Kalman filter
No prediction
Gating Failure Rate (%)
Gating Duty Cycle (% of max)
60
50
40
30
Linear
ANN
Kalman filter
No prediction
20
30
10
3
Imaging Rate (Hz)
30
20
10
Latency = 1 sec
1
Latency = 1 sec
0
30
10
3
Imaging Rate (Hz)
1
Figure 9. Gating error as a function of imaging frequency for (top) 33 ms latency, (middle) 200 ms
latency and (bottom) 1 s latency. These plots show (left) the percentage of the maximum possible
efficiency achieved, and (right) the percentage of time the beam would be enabled when the tumour
is outside the gating window.
were compared for high latency systems. Two different metrics were used to evaluate the
prediction methods: an rms error metric to compare the absolute accuracy of the prediction
and a gating error metric to compare the accuracy of gated treatment based on the predictions.
In all cases, we found that using prediction results in a lower rms error when compared
with not using prediction. This statement must be qualified, however, to exclude simple
438
G C Sharp et al
extrapolation (at all imaging rates) and ANN prediction (at high imaging rates). When
comparing gating error, we found that in most cases using prediction results in fewer cases
where the beam is mistakenly enabled. The exception to this statement is made when both the
latency is low (33 ms), and the imaging rate is high (10 Hz or faster). In these cases, there is
no clear improvement in gating error when using prediction.
The prediction methods used in this paper represent only simple, commonly used
algorithms and are not meant to be an exhaustive study. Additional improvements will
be made by incorporating data gathered from prior knowledge, physiological insight, online
parameter adaptation, outlier detection, optimizations targeted towards reducing gating error
and nonlinear filtering. In addition, we look forward to future developments that use
nonuniform imaging to selectively acquire images according to targeting uncertainty.
Acknowledgments
This work is partially supported by Varian Medical Systems Inc. and the Whitaker Foundation.
The authors thank Dr Ross Berbeco, Dr Toni Neicu, Dan Ruan and Dr David Castañón for
valuable discussions. Artificial neural network training was accomplished using the netlab
software package provided by Ian Nabney and Christopher Bishop (2003). EM fitting of
Kalman filter parameters was accomplished using the the Kalman filter software package
written by Kevin Murphy (2003).
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