Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 23

biological neuron process [ 75 ]. A neural network consists of input, hidden, and
output layers interconnected with directed weights (w), where we denote w ij as the
input-to-hidden layer weights at the hidden neuron j and w jk as the hidden-to-
output layer weights at the output neuron k, as shown in Fig. 2.12 [ 75 , 82 ].
In Fig. 2.12 , the input layer is a sequence history of breathing motions (n i )with
3D positions. In the hidden layer, the intermediate value (y j ) is calculated with the
history of breathing motions (3n i ) and bias unit using the nonlinear activation
function, as follows [ 75 ]:

1
1 þ exp P

y j ¼ ; ð 2 : 12 Þ

3n i þ 1

w ij x i

i ¼ 1

where we denote x i as input values, and y i as hidden values, respectively. The
additional input unit (bias) is used to bias the linear portion of the computation.
The practical prediction of respiratory motion is calculated with hidden values in
the output neuron (z k ), as follows:
z k ¼ X

n h

w jk y j ; ð 2 : 13 Þ

j ¼ 1

where output values z k denote predictions of breathing motions, and neural weights
(w ij and w jk ) in the network are generally resolved by numeric optimization. Sharp
et al. showed that the RMSE of NN predictor is less than 2 mm with low latency
(33 ms) [ 75 ]. But they only considered the form of stationary prediction.
For the adaptive filter training, Isaksson et al. used a feed-forward neural net-
work with two input neurons and one output neuron using the least mean square
scheme [ 93 ]. Here, the external markers were used as surrogates to predict the
tumor motion. This two-layer feed-forward neural network was used for predicting
irregular breathing pattern by Murphy et al. as well [ 57 , 79 , 82 ]. The network was
trained by a signal history from the beginning of the patient data record using
back-propagation algorithm, and kept updating the network weights with new test
data samples to adjust newly arrived breathing signals [ 57 , 79 ]. This adaptive filter
showed much better prediction error than stationary filter, e.g., RMSE of
0.5-0.7 mm for the most predictable cases and of 1.4-1.7 mm for the hardest cases
with 200 ms latency [ 57 ].

Table 2.3 Model-free prediction algorithms of respiratory motion

Methods Prediction error and evaluation metrics Features (system)

Adaptive filter [ 74 ] Less than 2 mm with 200 ms latency,

standard deviation

1D prediction (RPM)

Artificial neural networks
[ 75 ]

Around 2.5 mm with 200 ms latency,
RMSE

RMSE at 10 Hz (RTRT)

Adaptive neural network
[ 57 , 79 , 93 ]

1.4-1.7 mm with 200 ms latency,
normalized RMSE

30 Hz sample frequency
(CyberKnife)