Liver and Chest/Abdomen Movement Analysis

The movements of liver, chest, and abdomen are measured through

electromagnetic sensors. The measured data are three-dimensional in the CC, AP, and

LR directions. This section shows the characteristics of the signals obtained from the

experiments. It also shows the type of the correlation model between the liver and the

chest/abdomen movement via a regression method.

„ Characteristics of Liver Movement

The liver motion is measured by the electromagnetic position tracking system in

the animal experiments. The trajectories have similar patterns and are almost periodic.

Figure 3.10 shows the liver motion signals of IVC, TRL, and TLL in the CC, AP, and

LR directions measured. The trajectories have frequencies around 0.35Hz with main

movements in the CC-direction, minor movements in the AP-direction, and the least

movements in the LR-direction. It shows that IVC has larger displacement than TRL

and TLL. Table 3.2 shows the average amplitude and standard deviation of the liver

movement for 6 pigs during 7 days. For IVC, the average amplitude in the CC-direction

is 11.68 mm, and the amplitudes range from 9.14 mm to 12.85 mm. In the AP-direction,

the average amplitude is 3.90 mm and the amplitudes are in the range from 2.66 mm to

5.27 mm. The smallest displacement is observed in the LR-direction, where the average 44

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amplitude is 1.39 mm, ranging from 1.03 mm to 1.93 mm. The movements of TRL and

TLL are similar to IVC, but their amplitudes are smaller than IVC. The average

amplitude of TRL is 7.12 mm in the CC-direction, 1.92 mm in the AP-direction, and

0.96 mm in the LR-direction. The average amplitude of TLL is 7.20 mm in the

CC-direction, 2.70 mm in the AP-direction, and 1.81 mm in the LR-direction.

Figure 3.10 Liver movement at IVC, TRL, and TLL. Main movement is in the CC-direction, and second main movement is in the AP-direction. Movement in the LR-direction is less than in the CC and AP directions. Movement at IVC is larger than at TRL and TLL.

Table 3.2 Average amplitude and standard deviation of liver motion in different days

for 6 pigs, and the breathing frequency of each pig.

Liver

location

Displacement

(mm)

Pig 1 Pig 2 Pig 3 Pig 4 Pig 5 Pig 6

IVC

CC 10.6/0.34 12.47/1.68 12.85/0.92 12.81/1.04 9.14/0.74ġ 12.20/0.79ġ

AP 2.66/0.51 4.34/0.49 3.27/0.55 5.27/0.83 3.09/0.16ġ 4.76/0.89ġ

LR 1.91/0.57 1.21/0.69 1.03/0.70 1.18/0.71 1.10/0.96ġ 1.93/1.49ġ

TRL

CC 5.16/0.24 6.28/1.08 9.41/0.68 8.11/1.20 5.71/0.27ġ 8.02/1.59ġ

AP 1.48/0.48 3.04/0.69 2.34/1.00 1.75/1.12 0.56/0.32ġ 2.36/0.42ġ

LR 0.75/0.40 1.74/0.26 0.44/0.06 1.34/0.58 0.72/0.55ġ 0.77/0.26ġ

TLL

CC 5.51/0.23 7.31/1.13 7.55/0.29 9.29/1.60 5.33/1.35ġ 8.21/1.00ġ

AP 3.42/0.85 4.20/0.40 1.06/0.22 2.98/0.38 3.07/0.77ġ 1.46/0.54ġ

LR 1.75/0.50 1.58/0.63 1.41/0.46 2.52/0.18 1.67/1.23ġ 1.91/0.49ġ

Frequency (Hz) 0.39/0.01 0.34/0.06 0.33/0.02 0.34/0.00 0.34/0.00 0.34/0.00

Average/SD

46

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„ Characteristics of External Surrogate Signals

The motion of chest/abdomen is considered to be the external surrogate for the

liver motion, which is measured at 12 locations by the electromagnetic tracking system.

Figure 3.11 shows the trajectories of surrogate C3 (on the left chest) and surrogate A2

(on the middle of upper abdomen). Both trajectories are of frequencies about 0.35Hz.

Surrogate C3 has small amplitude in all CC, AP, and LR-directions, which is about 1.79

mm. For surrogate A2, the main movement is in the AP-direction with average

amplitude 6.47 mm. The second largest movement is in the CC-direction with average

amplitude 2.23 mm. And the smallest movement is in the LR-direction with average

amplitude 0.78 mm.

Table 3.3 shows the average amplitudes measured from the different surrogate

locations for 6 pigs. Surrogate A2 has the largest amplitude than all the other surrogates.

The group of surrogates on the upper abdomen (A1 to A3) has the largest average

amplitude than the others. The group of the second largest average amplitude is on the

middle abdomen (A4 to A6). The surrogates on the lower abdomen (A7 to A9) have the

smallest average amplitude, possibly because they are farthest from the liver. For the

lower chest (C1 to C3), surrogate C2 has large movement in the AP-direction, and

surrogate C1 and C3 have smaller movement due to the limitation by ribs.

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Figure 3.11 Trajectories of the external respiratory surrogates at C3 and A2. Surrogate A2 has larger movement than C3 has. Main movement is in the AP-direction, and second main movement is in the CC-direction. Movement in the LR-direction is less than in the CC and AP directions.

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Table 3.3 Average amplitude and standard deviation of chest and abdominal motion

for 6 pigs in the AP-direction, and the breathing frequency of each pig.

Surrogate

location (mm)

Pig 1 Pig 2 Pig 3 Pig 4 Pig 5 Pig 6

C1 0.95/0.08 1.10/0.20 1.63/0.16 1.68/0.17 0.86/0.31 1.61/0.34

C2 2.97/0.18 3.93/0.55 3.56/0.18 4.50/0.44 3.06/0.12 3.58/0.49

C3 0.91/0.33 0.97/0.04 1.42/0.28 1.22/0.00 0.55/0.21 1.03/0.11

A1 4.35/0.57 5.38/1.10 5.42/0.38 5.64/0.50 2.66/0.28 5.11/0.82

A2 5.04/0.77 5.91/0.79 5.98/0.43 6.74/0.61 3.27/0.16 5.19/0.55

A3 2.54/0.68 4.75/0.61 4.96/0.52 5.09/0.61 2.67/0.22 4.37/0.71

A4 3.20/0.24 4.12/0.52 3.55/0.21 4.22/0.58 2.50/0.10 3.60/0.32

A5 3.30/0.34 4.10/0.73 4.01/0.26 4.81/0.63 3.04/0.15 3.87/0.56

A6 2.22/0.24 3.41/0.62 3.24/0.08 3.64/0.69 2.34/0.17 2.96/0.42

A7 2.49/0.17 2.73/0.34 2.21/0.45 2.30/0.71 1.78/0.12 2.57/0.68

A8 2.40/0.11 2.74/0.45 2.24/0.25 2.88/0.81 1.87/0.16 2.55/0.78

A9 2.45/0.27 2.61/0.28 2.34/0.27 3.04/0.86 1.82/0.07 2.63/0.37

Frequency (Hz) 0.39/0.01 0.34/0.06 0.33/0.02 0.34/0.00 0.34/0.00 0.34/0.00

Average/SD

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„ Liver-Abdomen Movement Correlation Development

Linear regression, a common statistical technique for relating a dependent variable

to an independent variable, helps finding a model fitting the correlation between the

liver motion and the chest/abdomen motion. This model assumes that the correlation

between the dependent variable y and the independent variable ݔ is linear. It takes the

form

ݕ = ܽݔ + ܿ (4)

Where ܽ and c are the coefficients of model. The coefficients can be calculated using

the least square method [79]. The chest/abdomen wall motion and the motion of liver

are measured and then analyzed. The result shows that they are highly correlated. Figure

3.12 (a) shows the linear correlation models between the abdomen motion in the

AP-direction and the liver movement of IVC in the CC, AP, and LR directions, and

Figure 3.12 (b) shows the distribution of the modeling error in each direction.

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(a) (b)

Figure 3.12 Results of correction modelling. (a) Correlation models (linear models) between the abdomen motion on the AP-axis and the liver movement of IVC on the CC, AP, and LR-axes. (b) The bar charts of the modeling errors in three axes.