18.1 Background
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Motion with an average amplitude of 12 mm in the lung for targets not attached to rigid structures
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13 mm superior-inferior motion of the spleen
18.2 Methods
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Three translations (in the x, y, z directions)
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Three rotations (about the x, y, z axes)
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Three directional scaling transformations (along the x, y, z axes)
18.2.1 Selecting a Sweeping Variable
x
n
| t/T |
---|---|
0 | 0.0000 |
1 | 0.1850 |
2 | 0.2265 |
3 | 0.2571 |
4 | 0.2830 |
5 | 0.3066 |
6 | 0.3292 |
7 | 0.3515 |
8 | 0.3747 |
9 | 0.4000 |
10 | 0.4308 |
11 | 0.5000 |
10 | 0.5692 |
9 | 0.6000 |
8 | 0.6253 |
7 | 0.6484 |
6 | 0.6708 |
5 | 0.6934 |
4 | 0.7170 |
3 | 0.7429 |
2 | 0.7735 |
1 | 0.8150 |
0 | 1.0000 |
18.2.2 Static CAD Model
18.2.3 Respiratory Cycle and CAD Tissues Affected by Respiration Motion
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Lungs
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Ribcage with 24 ribs (every rib is moved independently)
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Thoracic cage cartilage
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Sternum
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Pectoralis muscles (major/minor)
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Abdominal muscles
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Erector spinae muscles
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Heart (muscle)
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Liver
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Stomach
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Outer shell – average body
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Outer shell – skin
18.2.4 Required Accuracy: Total Body Mass
18.2.5 Algorithm
18.2.6 Polynomial Interpolation
Muscles | Polynomials of deformation factors (angles recorded in degrees) | ||
---|---|---|---|
Pectoralis minor (in local CS) |
Left
| Rot z | −7.149e − 5 ∗ t6 + 0.00252 ∗ t5 − 0.03393 ∗ t4 + 0.2181 ∗ t3 − 0.681 ∗ t2 +1.406 ∗ t + 0.005579 |
Move y | 0.0002042 ∗ t6 − 0.007194 ∗ t5 + 0.09695 ∗ t4 − 0.6231 ∗ t3 + 1.946 ∗ t2 −4.016 ∗ t − 0.01594 | ||
Scale y | 2.042e − 7 ∗ t6 − 7.194e − 6 ∗ t5 + 9.695e − 5 ∗ t4 − 0.0006 ∗ t3 + 0.001946 ∗ t2 −0.004 ∗ t + 0.999984 | ||
Right
| Rot z | 1.083e − 05 ∗ t6 + 8.348e − 05 ∗ t5 − 0.00957 ∗ t4 + 0.1344 ∗ t3 − 0.7021 ∗ t2 +1.774 ∗ t + 0.01398 | |
Move y | −3.095e − 5 ∗ t6 − 0.0002385 ∗ t5 + 0.02734 ∗ t4 − 0.3841 ∗ t3 + 2.006 ∗ t2 −5.067 ∗ t − 0.03994 | ||
Scale y | 3.09e − 8 ∗ t6 − 2.385e − 7 ∗ t5 + 2.73e − 5 ∗ t4 − 0.00038 ∗ t3 + 0.002 ∗ t2− 0.005067 ∗ t + 0.99996 | ||
Pectoralis major (in local CS) |
Left
| Move z | −0.00013 ∗ t6 + 0.004709 ∗ t5 − 0.0656 ∗ t4 + 0.4366 ∗ t3 − 1.388 ∗ t2 +2.397 ∗ t − 0.005142 |
Move y | −0.05 + 0.0002525 ∗ t6 − 0.00914 ∗ t5 + 0.1272 ∗ t4 − 0.8445 ∗ t3 + 2.673 ∗ t2 −4.721 ∗ t + 0.01132 | ||
Scale y | 2.6e − 7 ∗ t6 − 9.418e − 6 ∗ t5 + 0.0001312 ∗ t4 − 0.00087 ∗ t3 + 0.0028 ∗ t2 −0.0048 ∗ t + 1.00001028 | ||
Right
| Move z | −4.642e − 05 ∗ t6 + 0.001553 ∗ t5 − 0.02174 ∗ t4 + 0.1655 ∗ t3 − 0.6858 ∗ t2 +1.801 ∗ t + 0.02082 | |
Move y | 9.284e − 05 ∗ t6 − 0.003107 ∗ t5 + 0.04348 ∗ t4 − 0.331 ∗ t3 + 1.372 ∗ t2 −3.602 ∗ t − 0.04165 | ||
Scale y | 9.284e − 8 ∗ t6 − 3.107e − 6 ∗ t5 + 4.348e − 5 ∗ t4 − 0.00033 ∗ t3 + 0.00137 ∗ t2 −0.0036 ∗ t + 0.99995835 | ||
Erector Spinae (in local CS) |
Left
| Scale y | 8.987e − 06 ∗ t6 − 0.0003339 ∗ t5 + 0.004839 ∗ t4 − 0.03445 ∗ t3 + 0.1242 ∗ t2 −0.2474 ∗ t + 0.998756 |
Scale x | 4.493e − 06 ∗ t6 − 0.0001669 ∗ t5 + 0.00242 ∗ t4 − 0.01723 ∗ t3 + 0.06208 ∗ t2 −0.1237 ∗ t + 0.9993778 | ||
Move y | −1.123e − 05 ∗ t6 − 0.0004174 ∗ t5 + 0.006049 ∗ t4 − 0.04307 ∗ t3 + 0.1552 ∗ t2 −0.3093 ∗ t − 0.3093 | ||
Right
| Scale y | −0.02 ∗ t + 1 | |
Scale x | −0.02 ∗ t + 1 | ||
Move y | −0.05 ∗ t | ||
Abdominal (in global CS) | Move z | 0.09091 ∗ t ∗ 10−3 | |
Move y | −0.35 ∗ t ∗ 10−3 |
18.3 Results
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ANSYS Electronics Desktop software package
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CST Studio Suite software package
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MATLAB