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The authors have no conflict of interest that could influence the work described in this manuscript.
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Appendices
1 2 3 4 5 6 7 8 9 10 11 12
-2 -1 0 1 2
Bp, Bd
Bp, Bd
Rib Number
Bp Bd
1 2 3 4 5 6 7 8 9 10 11 12
0.2 0.4 0.6 0.8
YPk, XPk (mm / Sx)
YPk, XPk
Rib Number
YPk XPk
1 2 3 4 5 6 7 8 9 10 11 12
Rib Number 0
50 100 150
φpia (deg)
φpia
1 2 3 4 5 6 7 8 9 10 11 12
Rib Number 0
50 100 150 200 250
Sx (mm)
Sx
Figure A1: The overall trends in in-plane model parameters across the adult population (N=20,627 ribs).
Boxes show the median and the 25thto 75thquantile ranges and whiskers extend to the±2.7σ range (99.7 % coverage).
Author Manuscript
Table A1: Average± standard deviation in fitted in-plane parameters and rib orientation parameters for all rib levels.
Sx XP k YP k φpia Bp Bd αP H αLS αBH
Rib N mm mm/Sx mm/Sx deg - - deg deg deg
1 1444 71.0 0.384 0.521 81.7 -0.43 1.81 58.2 36.2 11.6
±7.2 ±0.061 ±0.059 ±9.3 ±0.60 ±1.16 ±9.7 ±7.0 ±7.4
2 1665 110.9 0.318 0.621 111.8 -0.32 0.71 60.4 20.3 5.4
±9.6 ±0.048 ±0.054 ±8.6 ±0.23 ±0.55 ±9.6 ±4.6 ±6.9
3 1681 141.7 0.344 0.588 116.8 -0.51 0.36 61.1 20.7 5.4
±11.9 ±0.041 ±0.057 ±8.3 ±0.15 ±0.42 ±9.1 ±3.9 ±7.0
4 1661 166.8 0.322 0.527 115.4 -0.50 -0.05 60.3 22.9 6.9
±13.7 ±0.041 ±0.053 ±8.5 ±0.16 ±0.37 ±8.8 ±3.6 ±7.3
5 1650 184.8 0.312 0.480 113.9 -0.51 -0.37 59.2 24.6 8.2
±15.2 ±0.041 ±0.050 ±8.7 ±0.18 ±0.35 ±8.7 ±3.4 ±7.4
6 1659 197.3 0.297 0.439 112.0 -0.45 -0.51 57.6 28.0 10.7
±16.2 ±0.042 ±0.049 ±9.8 ±0.22 ±0.40 ±8.6 ±3.7 ±7.3
7 1714 208.8 0.284 0.391 109.3 -0.35 -0.17 55.9 33.9 14.6
±16.3 ±0.043 ±0.045 ±11.3 ±0.26 ±0.66 ±8.3 ±4.3 ±7.2
8 1780 209.1 0.297 0.364 104.8 -0.33 -0.22 53.7 39.9 16.6
±16.0 ±0.043 ±0.039 ±11.4 ±0.29 ±0.64 ±8.0 ±4.8 ±7.5
9 1863 199.0 0.346 0.356 97.4 -0.51 -0.09 53.0 46.5 14.0
±15.4 ±0.041 ±0.037 ±11.4 ±0.31 ±0.59 ±7.6 ±5.3 ±7.6
10 1905 183.7 0.372 0.329 90.0 -0.62 -0.09 51.4 56.1 11.2
±15.1 ±0.037 ±0.035 ±11.3 ±0.35 ±0.61 ±7.0 ±6.4 ±7.9
11 1850 154.2 0.388 0.275 82.7 -0.69 0.59 49.4 69.9 10.4
±17.4 ±0.036 ±0.036 ±12.9 ±0.56 ±1.37 ±5.9 ±7.6 ±9.0
12 1755 95.7 0.390 0.174 60.9 -1.29 1.37 53.3 94.0 14.6
±29.1 ±0.101 ±0.045 ±25.5 ±1.66 ±2.17 ±8.5 ±12.0 ±17.9
Figure A2: Individual parameter histograms (main diagonal) and inter-parameter correlation plots for the 6thribs. Histograms show parameter distributions in the population to be largely normal. While statistically significant for all pairs exceptBpvs.φpia andBpvsBd, inter-parameter correlations (Pearson’s R) are low for most parameter combinations, with the strongest between rib size (Sx) and aspect ratio (YP k).
Author Manuscript
Table A2: In-plane rib shape model with parameter coefficients predicted by demographics. Age (A) is in years, sex (S) is 0 for males and 1 for females, height (H) is in meters, weight (W) is in kilograms, along with the regression intercept (I). Subscript denotes scale factor. For example, WE-3 indicates weight in kg scaled by1 × 10−3. Coefficients significantly different from zero at thep < 0.01 level are shown in bold.
Sx XP k YP k
# I AE-3 SE-1 HE-1 WE-3 IE-3 AE-5 SE-3 HE-3 WE-5 IE-2 AE-5 SE-3 HE-3 WE-5
1 31 98 -24 190 40 415 -23 4 -17 8 62 -63 -9 -36 -7
2 56 129 -34 286 13 292 16 -3 26 -30 67 -83 0 2 -7
3 67 168 -39 403 -9 296 17 7 42 -42 63 -93 -1 -2 13
4 81 195 -61 469 -18 349 -6 4 -0 -31 57 -96 1 -8 24
5 88 237 -90 528 -15 398 -23 2 -39 -11 53 -104 7 -17 27
6 96 265 -102 562 -37 407 -48 -1 -54 8 49 -111 6 -20 37
7 106 283 -105 566 -33 437 -71 -4 -76 18 44 -109 2 -16 39
8 92 246 -106 651 -14 479 -74 -2 -94 20 45 -92 -5 -40 35
9 83 192 -104 648 14 481 -63 1 -70 18 41 -79 -4 -24 29
10 67 187 -93 628 55 467 -52 -8 -41 7 38 -70 -9 -14 11
11 38 168 -85 629 59 524 -48 -14 -62 -0 32 -57 -15 -10 5
12 8 35 -92 469 129 451 -48 -30 -30 33 10 -7 -5 42 15
φpia Bp Bd
# I AE-3 SE-1 HE-1 WE-3 IE-2 AE-4 SE-2 HE-2 WE-4 IE-2 AE-4 SE-2 HE-2 WE-4
1 83 71 10 -12 -34 -85 15 4 23 -8 165 92 -4 -28 22
2 118 62 30 -42 -40 -48 -5 6 9 -0 -5 38 -0 42 -18
3 114 71 32 -1 -27 -28 -17 0 -12 9 -22 10 6 37 -15
4 110 78 41 12 -23 -32 -18 -1 -12 13 50 -11 2 -22 -14
5 100 83 48 63 -36 -34 -19 -2 -6 4 23 -22 -1 -28 -3
6 98 76 59 73 -65 -23 -13 -2 -8 -2 12 -27 4 -27 -7
7 95 81 66 81 -79 -43 -3 -4 10 -7 -31 22 19 13 -34
8 84 69 50 135 -94 -67 -3 -5 26 -7 10 -4 16 1 -47
9 80 42 47 123 -91 -55 -12 -4 7 -1 65 -29 13 -19 -40
10 69 29 32 154 -100 -2 -18 -9 -37 19 32 2 -4 -19 -9
11 66 6 40 126 -84 -53 -29 -22 -14 38 207 81 31 -134 30
12 40 -52 -10 148 -5 -140 65 27 -7 -25 119 4 25 -22 50
αP H αLS αBH
# IE-1 AE-3 SE-2 HE-1 WE-3 I AE-3 SE-2 HE-1 WE-3 IE-1 AE-3 SE-1 HE-1 WE-3
1 756 96 -358 -236 235 32 -76 -26 95 -92 89 -18 -3 77 -113
2 757 103 -350 -238 263 15 -33 -124 69 -52 87 -7 -12 -1 -25
3 770 94 -350 -243 271 19 -33 -80 47 -47 62 -0 -2 13 -35
4 752 88 -354 -235 272 24 -28 -121 23 -40 93 12 1 6 -48
5 740 86 -357 -235 274 30 -24 -161 -3 -27 89 14 4 18 -54
6 702 87 -318 -227 280 35 -6 -209 -27 -15 107 30 4 25 -70
7 706 88 -266 -236 271 41 8 -205 -34 -6 90 47 1 63 -88
8 664 85 -175 -222 261 46 15 -203 -36 1 98 54 -9 85 -119
9 670 91 -128 -224 243 57 9 -166 -65 15 75 28 -23 103 -136
10 601 102 -78 -182 210 70 10 -126 -101 45 86 -18 -31 95 -133
11 544 77 -16 -132 164 83 25 -76 -103 40 65 -34 -48 107 -123
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0
Figure A3: Predicted in-plane rib shapes by age. Baseline demographic is the 5th percentile female with specific age represented by line color. Ribs become more elongated and increase in aspect ratio with age.
20 30 40 50 60 70 80 90
Figure A4: Expected values for rib arc length (L2d), inner angle at the distal end (φdia), and local curvature at posterior (κpost) and distal (κdist) locations, along with values from rebuilt ribs matching that demographic.
Regression models fitted to the values measured directly in the population are used to query for the expected values (with95 % confidence interval) for 5th percentile females of varying ages.