Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 16

Raw data State models

1545

EOE EOE EOE EOE EOE

1544.5

1544

IN IN IN IN IN

X (1)

1543.5

EX EX EX EX EX

1543

X (0) 1542.5

1542

2.2806 2.2808 2.281 2.2812 2.2814 2.2816 2.2818

x 10 4

Time Stamp (sec)

Fig. 2.8 Finite state model with regular breathing cycles. The breathing motion patterns are
modeled with irregular (IRR), exhale (EX), end-to-exhale (EOE), and inhale (IN) breathing
states [ 78 ]. State transitions are initiated by the velocity of tumor motion with two vector points
X(t 0 ) and X(t 1 )

x pred ð t þ D Þ¼ x act ð t Þþ x SHL ð t þ D Þ x SHL ð t Þ ½ ; ð 2 : 3 Þ

where x SHL (t) is a fitted sinusoidal curve including SHL, given by x SHL ðÞ¼
A sin Bt þ ð Þ D with time sequences from t-SHL to t (t [ SHL, and A, B, C,
and D are the parameters of sinusoidal waveform model) [ 74 ].
Vedam et al. evaluated that the prediction error with 200 ms latency is less than
2 mm. This model also has a limitation with 1D prediction and the prediction
accuracy degrades with long latency [ 74 , 82 ].

2.3.1.4 Finite State Model

The breathing motion can be analyzed based on its natural understanding of
breathing states [ 78 ]. In finite state model (FSM), a regular respiratory motion is
subdivided into three states—exhale (EX), end-to-exhale (EOE), and inhale (IN),
as shown in Fig. 2.8 [ 78 , 82 ]. The other motions are categorized as irregular
breathing (IRR) except the above three states in this approach. Wu et al. repre-
sented the finite state automation for the transition from one state to another [ 78 ].
Line segments for finite states in Fig. 2.8 are determined by the velocity of tumor
motion and the average amplitude for two connected directed line segments. Let
X ðÞ¼ x 0 ; x 1 ; ... ; x f g as an n-dimensional vector point at time t. The length of a
directed line segment from X(t 0 )toX(t 1 ) is expressed as follows:

s

X

n

! jj ¼

ð x 1i x 0i Þ 2 jj X 0 X 1 : ð 2 : 4 Þ

i ¼ 1

The velocity of tumor motion is calculated with two vector points (X(t 0 ) and
X(t 1 )), as follows: