Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 26

2.3.3.2 Hybrid Model with Adaptive Filter and Nonlinear Model

To compensate breathing tumor motion in the lung, an adaptive tumor-tracking
system (ATTS) was proposed by Ma et al. with an adaptive filter and a nonlinear
method [ 98 ]. Instead of only one signal, this adaptive system used two independent
signals to detect the lung tumor motion during irradiation: (1) direct signal, i.e.,
imaging of irradiated region using megavoltage imaging of the treatment beam
[ 99 ], and (2) indirect signal, i.e., optical marker with an infrared camera, as shown
in Fig. 2.14 [ 68 , 98 ]. The tumor position is directly visualized and located by the
acquired portal image (direct signal) using a tumor tracking algorithm without
internal fiducial markers [ 99 ]. Infrared camera signals (indirect signal) are used to
predict respiratory signals using the adaptive filter, and these respiratory signals
are correlated with the portal image to predict the tumor motion. A nonlinear
dynamic system is reconstructed by the system history based on the previous
measurement [ 98 ].
The adaptive filter continuously updated the coefficient parameters using least
mean square method to predict the respiratory motion, as follows:

y ð t Þ¼ B ð q Þ u ð t Þ; ð 2 : 15 Þ

where y(t) is prediction of the respiratory motion, B(q) is a linear model including
the delay operator q with B ðÞ¼ b 0 q 0 þ b 1 q 1 þþ b n 1 q n þ 1 , and u(t) is the
history information including the past n samples of the infrared camera. In addi-
tion, ATTS modeled the correlation between two signals using means of nonlinear
methods to determine the tumor position. That means dynamic nonlinear system
examines the current indirect signal in the past samples using x(and y)-coordinate
motion range (mm), maximum velocity of x(and y)-coordinate (mm/s), and mean
cycle period (s) and then the best-fitting direct signals were adapted to predict the
tumor motion [ 68 ]. Wilbert et al. showed that the maximum standard deviation
was 0.8 mm for x-coordinate and 1.0 mm for y-coordinate. However, there are
limits in velocity range between 8.5 mm/s (y(and z)-coordinate) and 9.5 mm/s
(x-coordinate), so that the amplitude acquired below these limits will not lead to
efficient prediction with such a linear model [ 68 ].

2.3.3.3 Interacting Multiple Model Filter

An interacting multiple model (IMM) filter can be used as a suboptimal hybrid
filter for respiratory motion prediction to combine different filter models with
improved control of filter divergence [ 72 , 81 , 83 ]. It makes the overall filter
recursive by modifying the initial state vector and covariance of each filter through
a probability weighted mixing of all the model states and probabilities, as shown in
Fig. 2.15 [ 81 , 83 ].
Figure 2.15 shows a recursive filter of IMM with a constant velocity (CV)
model and a constant acceleration (CA) model, where three steps—interaction,