Linking clinical border morphology to cell-scale growth mechanisms in melanoma: a segmentation-to-simulation alignment study
Abstract
An irregular border is among the most informative visual cues for melanoma, yet the prevailing quantitative treatment of that irregularity, the box-counting fractal dimension, has rarely been connected to the cell-scale mechanism that produces it. We measured seven boundary descriptors on 1,581 lesions from the 2018 International Skin Imaging Collaboration archive segmented by an automatic thresholding route, retaining the expert ground-truth route as a sensitivity arm, and compared their medians across benign, in situ, and invasive grades. We then built a hybrid cellular automaton and swept four canonical cell-level mechanisms, scoring every simulated boundary with the same measurement code used on the patient images, before testing two mechanisms that lift the empty-neighbour division rule and aligning them to the observed malignant signature with a variance-based sensitivity analysis. The malignant signature is lobulation, not roughness: compactness rises from 1.351 to 1.810, solidity falls from 0.910 to 0.853, and convexity falls from 0.936 to 0.839 from benign to invasive lesions, with areas under the curve near 0.74, while the fractal dimension varies by only 0.024 across the three grades. All four canonical mechanisms, including loss of contact inhibition, converge on near-circular clusters at a distance of 1.147 to 1.166 from the malignant target. A long-range spatial heterogeneity in the growth rate, by contrast, reproduces the observed signature to a distance of 0.187, with the correlation length of the field, not its amplitude, the dominant parameter by total-effect index. A smooth, long-range growth-rate field is therefore sufficient to generate the lobular borders that characterise invasive melanoma, whereas the empty-neighbour assumption common to cellular automata is not. Because the winning field is imposed rather than emergent, the study resolves the alignment between border morphology and cell-scale mechanism while leaving open how such heterogeneity could arise from cell-autonomous dynamics.
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In-depth summary
Claude Opus 5.5 · xhigh effort · 7 Nov 2026 · from the full text of version 1 (30 Oct 2026) · CC BY 4.0
Across 1,581 ISIC 2018 lesions, melanoma borders differ from nevi mainly by coarse lobulation rather than fractal dimension; of six simulated mechanisms, only an imposed long-range growth-rate field reproduces this.
Image-based melanoma work scores or classifies border irregularity but does not explain which cell behaviour generates it, while cell-scale tumour models are mostly judged qualitatively or with metrics clinicians would not compute on patient images. Here one boundary-measurement pipeline, applied unchanged, scores both dermoscopic lesions and simulated tumours, so candidate growth rules can be ranked by how closely they reproduce the clinical border signature.
Key results
ShownIn automatically segmented lesions, malignancy tracks coarse lobulation (higher compactness, lower solidity and convexity), while the box-counting fractal dimension barely changes across grades and is the weakest of seven descriptors.
Medians benign vs invasive: compactness 1.351 vs 1.810 (in situ 1.800), solidity 0.910 vs 0.853, convexity 0.936 vs 0.839; invasive-vs-benign AUC 0.740, 0.739, 0.738, eta-squared 0.087, 0.088, 0.086. Fractal dimension 1.040 benign, 1.064 in situ, 1.048 invasive; AUC 0.625, eta-squared 0.024. · The malignant signature is lobulation, not…; A correction to the fractal-dimension narrative
ShownExpert polygon-traced ISIC masks reverse the sign of five of seven descriptors, which the authors attribute to tracing coarseness that scales with lesion size; the automatic-route signature holds in well-segmented and low-hair subsets.
Expert masks: 5 of 7 descriptors reversed (Holm-adjusted p 8.6e-05 to 1.4e-02; eta-squared 0.003 to 0.009); median straight-run vertex fraction 0.587, 24.7 percent of masks above 0.85. Automatic route, Dice at least 0.75 (1,232 paired lesions): all 7 significant (p 5.4e-06 to 9.8e-22). Least-hairy 40 percent: fractal-dimension effect size nearly doubles. · The signature survives the segmentation-route…; The segmentation-route lesson
ShownIn a hybrid cellular automaton, none of four standard candidate rules (weakened contact inhibition, an advantaged subclone, stronger migration, nutrient-driven fingering) escaped a near-circular cluster; the authors trace this to division requiring an empty adjacent site.
Best distances to the invasive-melanoma target in z-scored compactness/solidity/convexity space: 1.166 (contact inhibition, clonal heterogeneity), 1.153 (migration), 1.147 (nutrient fingering). Simulated compactness about 1.02 to 1.03, solidity near 0.98, convexity near 0.99 vs target 1.810, 0.853, 0.839. 60 runs (five levels, three seeds per mechanism). · Four canonical mechanisms fail to escape the…; The empty-neighbour assumption is the bottleneck; Cellular automaton model
SuggestedMultiplying division rates by a smooth, imposed long-range growth-rate field brings simulated borders close to the malignant signature. Letting surrounded cells push neighbours aside (mechanical displacement) does not.
Coarse sweep best distance 0.406 for spatial heterogeneity (compactness 1.485, solidity 0.886, convexity 0.902) vs 1.125 for mechanical displacement. Refined optimum (amplitude 0.58, correlation length 58 pixels): distance 0.187, with compactness 1.835 vs 1.810, solidity 0.873 vs 0.853, convexity 0.809 vs 0.839; reported as roughly sixfold better than the best canonical mechanism. · A long-range growth field aligns simulation to…; A long-range growth field aligns simulation to…; Mechanism alignment and sensitivity analysis
SuggestedThe field's correlation length dominates alignment by total-effect index, but mostly through interaction with amplitude (its first-order index is the smaller of the two); low distances form a band in the amplitude and correlation-length plane.
Saltelli estimator, 1,536 evaluations (base sample 256) over amplitude 0.1 to 1.0 and correlation length 24 to 284 pixels: correlation length first-order 0.113, total-effect 0.892; amplitude first-order 0.257, total-effect 0.406. One-at-a-time screening: maximum change in distance about 0.31 for each parameter. · A long-range growth field aligns simulation to…; A long-range growth field aligns simulation to…; Mechanism alignment and sensitivity analysis
Methods, data and reproducibility
Seven boundary shape descriptors, including box-counting fractal dimension, were computed on automatic Otsu and expert masks of ISIC 2018 dermoscopic lesions graded benign, in situ or invasive melanoma. The identical measurement code scored masks from an Anderson-style hybrid cellular automaton testing six growth mechanisms, ranked by z-scored distance to the invasive-melanoma median.
- ISIC 2018 Task 1-2 training archive (dermoscopic images, expert masks), diagnosis joined via ISIC Archive API diagnosis_3 field; 1,598 histopathologically confirmed · human (patient skin lesions) · n = 2,223 lesions (1,863 benign, 198 in situ, 162 invasive) · ISIC Archive collection 63
- Lesions passing quality control on the automatic Otsu segmentation route (primary analysis) · human (patient skin lesions) · n = 1,581 lesions (1,348 benign, 124 in situ, 109 invasive)
- Lesions passing quality control on the expert-mask route (sensitivity arm) · human (patient skin lesions) · n = 2,088 lesions (1,760 benign, 184 in situ, 144 invasive)
- Stratified sample used to choose automatic segmentation settings · human (patient skin lesions) · n = 90 lesions
- Well-segmented paired subset (Dice at least 0.75) for the segmentation-quality confound test · human (patient skin lesions) · n = 1,232 paired lesions
- Simulated tumours, canonical mechanism sweep on a 1,024-by-1,024 lattice grown to equivalent diameter 600 sites · n = 60 runs
- Simulated tumours, alignment and Saltelli sensitivity analysis on a 512-by-512 lattice grown to equivalent diameter 379 sites · n = 1,536 evaluations
- Methods & tools
- ISIC Archive API, Otsu thresholding (Lab luminance), DullRazor hair suppression, box-counting fractal dimension, hybrid cellular automaton (Anderson framework), Kruskal-Wallis test, Benjamini-Hochberg procedure, Holm correction, Jonckheere-Terpstra test, Dice coefficient, Bland-Altman analysis, Saltelli variance-based sensitivity estimator
- Data & accessions
- https://github.com/neobiosystem/melanoma_morphology_study
- Software & environment
- Configuration files fixing all statistical thresholds, random seeds and numeric constants are released with the code; software versions, containers or requirement files are not stated.
- Reproducibility gaps
- No compute requirements or software versions stated; raw images, masks and diagnoses must be obtained from ISIC and the ISIC Archive, for which no URL is printed.
Limitations (6)
- Simulations are 2D and model an expanding cell aggregate without the dermis below, so the fitted correlation length is an effective planar parameter, not a physically measured scale. · stated by the authors
- All lesions come from one archive (ISIC 2018) with archive-specific imaging and annotation habits, and grades are imbalanced (1,348 benign vs 109 invasive), which limits generality and the precision of invasive estimates; an independent cohort is needed. · stated by the authors
- Fractal dimension was estimated only by box-counting; other estimators such as capacity or correlation dimension might behave differently. · stated by the authors
- The winning growth-rate field is imposed, not emergent, so the model shows sufficiency but not how such heterogeneity could arise from cell-autonomous dynamics. · stated by the authors
- The 0.187 match comes from tuning amplitude and correlation length against the same three-descriptor target used for scoring, and the other four descriptors of the best simulated boundary are not reported, so no held-out check of the fit is shown. · noted in this summary
- Mechanical displacement, which directly lifts the empty-neighbour division rule, still gave a near-circular cluster (1.125), so that rule alone is not shown to be the bottleneck; canonical and alignment runs also used different lattice sizes (1,024 vs 512). · noted in this summary
Who should read:Read this if you derive shape features from segmented lesion images, or calibrate agent-based tumour growth models against clinical morphology and want an example of scoring both with identical code.
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