Introduction
Materials and methods
Elasticity estimation
Preamble
Analytical derivation of elasticity
Numerical simulation of deformations
Estimating the \(\beta \) values by simulation in SOFA
Supine–prone and prone–supine simulation and matching in SOFA and Febio
Results
Validation of analytical stress calculation on geometric shapes
-
For cylinder, cubic and prism-like shapes that have a constant cross-sectional area (a and b), the numerically derived stress distribution matches the analytically derived one quite well. The \(\beta \) values derived by both methods are well comparable (deviation under 9%).
-
For shapes that do not have a constant cross-sectional area, but are substantially vertically supportive (c-h), the analytically calculated and SOFA-simulated \(\beta \) values are still comparable (deviation up to 18%) although the stress distribution is different.
-
For shapes in which the lower extremity is not vertically supported by the base, i.e., no vertical line of maximum height can be drawn that entirely lies within the model (i), both the analytically calculated \(\beta \) value and the stress distribution are inconsistent with simulations.
Geometric shape | Calculated \(\beta \) | Simulated \(\beta \) |
---|---|---|
a | 2375 | 2169 |
b | 2373 | 2229 |
c | 772 | 724 |
d | 1638 | 1581 |
e | 4500 | 4979 |
f | 213 | 205 |
g | 1932 | 2276 |
h | 3802 | 3797 |
i | 4942 | 26,499 |
Analytical derivation of elasticity of phantoms
Simulation of \(\beta \) in SOFA
Phantom |
\(\beta _\mathrm{s}\)
|
\(\beta _\mathrm{p}\)
|
\(\Delta H\)
|
E
|
---|---|---|---|---|
I | 1215 | 1298 | 3.28 | 7514 |
II | 1129 | 1269 | 4.73 | 4972 |
III | 1356 | 1444 | 3.58 | 7673 |
IV | 1420 | 1471 | 2.93 | 9677 |
Phantom |
\(\beta _\mathrm{s}\)
|
\(\beta _\mathrm{p}\)
|
\(\Delta H\)
|
E
|
---|---|---|---|---|
I |
\(1007 \pm 58\)
|
\(1134 \pm 38\)
| 3.28 |
\(6403 \pm 207\)
|
II |
\(947 \pm 41\)
|
\(1125 \pm 36\)
| 4.73 |
\(4297 \pm 113\)
|
III |
\(1131 \pm 48\)
|
\(1259 \pm 61\)
| 3.58 |
\(6549 \pm 213\)
|
IV |
\(1170 \pm 43\)
|
\(1383 \pm 34\)
| 2.93 |
\(8548 \pm 184\)
|
Numerical simulation by supine–prone and prone–supine matching in SOFA
Phantom |
\(E_\mathrm{sp}\)
|
\(E_\mathrm{ps}\)
| Mean E |
---|---|---|---|
I |
\(5047 \pm 374\)
|
\(6459 \pm 373\)
|
\(5688 \pm 272\)
|
II |
\(3395 \pm 189\)
|
\(4513 \pm 272\)
|
\(3895 \pm 159\)
|
III |
\(5381 \pm 376\)
|
\(6828 \pm 438\)
|
\(6040 \pm 288\)
|
IV |
\(6245 \pm 433\)
|
\(7445 \pm 322\)
|
\(6805 \pm 283\)
|
Phantom |
\(E_\mathrm{sp}\)
|
\(E_\mathrm{ps}\)
| Mean E |
---|---|---|---|
I |
\(5046 \pm 272\)
|
\(5252 \pm 307\)
|
\(5145 \pm 254\)
|
II |
\(4290 \pm 351\)
|
\(4298 \pm 273\)
|
\(4291 \pm 276\)
|
III |
\(5291.52 \pm 383\)
|
\(5639 \pm 456\)
|
\(5459 \pm 400\)
|
IV |
\(7916 \pm 1165\)
|
\(7564 \pm 957\)
|
\(7731 \pm 1016\)
|
Numerical simulation by supine–prone and prone–supine matching in FEBio
Comparison of different elasticity measurement methods
Phantom | Mean E |
---|---|
I |
\(6188 \pm 886\)
|
II |
\(4364 \pm 387\)
|
III |
\(6430 \pm 815\)
|
IV |
\(8190 \pm 1057\)
|