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Sander J. Leemans, Dirk Fahland, Wil M. Report: Business Process Intelligence Challenge Weber, D. Ferreira, J. De Weerdt. Mohammad Ehson Rangiha, Bill Karakostas. Alex Seret, Seppe K. Gani, M. Bouet, M. Schneider, F. Guerrouahane, S. Bouzouzou, L. Bouallouche-Medjkoune, D. Methods for Evaluating Process Model Search. Multi-dimensional Secure Service Orchestration. Using image analyses, microscopy and computed tomography CT on biological material, we show that African elephant skin channels are cracks that occur in the animal stratum corneum.

Our custom physics-based lattice model confirms that the combination of these three parameters is sufficient to cause mechanical bending stress to accumulate in between the skin elevations during the progressive thickening of the stratum corneum until cracks are formed.


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Previous research shows that these structures help the animal retain water and mud on its skin. In e , the narrow channels white dotted lines are no longer visible because they are confined to the extracted skin layer; note that the stratum corneum channels are confined in between papillae. The circled hair on both pictures serve as guides to the eye. Even though the pattern of papillae is present, narrow channels are not observed. Indeed, the mechanical removal of this skin layer results in a complete loss of the network of channels while it reveals a second underlying pattern composed of finger-like dermo-epidermal protrusions, hereafter referred as papillae , separated by lower-elevation troughs Fig.

These structures form an intricately shaped substrate for the stratum corneum.

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Note that the channels in the stratum corneum appear to follow troughs in the underlying network of papillae Fig. Although papillae are visible in Asian elephants Elephas maximus ; Fig. Next, we investigate the nature of these crevices. Our light and electron microscopic analyses reveal that each channel in the African elephant skin is a sharp discontinuity in the stratum corneum Fig. The keratin sheets of the latter display a clear alignment on both sides of the discontinuity, suggesting that, prior to the formation of the fissure, the stratum corneum was continuous in the trough, as observed in uncracked regions of the skin Fig.

All these observations are compatible with our initial hypothesis, namely that the channels visible on the skin of the African bush elephant are physical cracks of the stratum corneum. Stratum corneum morphology of cracked and uncracked samples. Moreover, the innermost sheets of the stratum corneum remain intact arrowheads , probably due to their higher hydration level. Dashed lines in b , c : boundary between the stratum corneum and the viable epidermis.

We then observe that African elephants exhibit orthokeratosis, i. Additional insight is provided by our histology results Fig. These characteristics orthokeratosis and lack of keratohyalin granules have been associated with a specific subtype of ichthyosis vulgaris 6 , a skin disorder that is known to affect desquamation and cause dry, scaly skin in humans 7 , 8.

Although of heuristic nature, this parallel hints at the possibility that cracks occur in the skin of elephants because of the growth of a desquamation-deficient highly keratinised and brittle stratum corneum on a pattern of papillae that effectively acts as an intricately curved substrate Fig.

The epidermis of African elephants exhibits orthokeratosis and lacks keratohyalin granules. Orthokeratosis is equally perceivable: the stratum corneum is thick but otherwise normal looking. Similar morphological features are often observed in human patients with ichthyosis vulgaris. The inset in Fig. Again, the absence of keratohyalin granules is clearly visible. The inset of c indicates that dark spots in the stratum corneum are not viable nuclei N but clusters of melanin granules M. Concretely, we suggest that crack formation results from the following chain of events.

Note that this configuration is likely permanent because the stratum corneum is composed of dead cells corneocytes that cannot rearrange topologically. As more keratinous sheets are added at the stratum basale , the outermost sheets of the stratum corneum are effectively pushed outwards. These effects intensify as the growth of the stratum corneum progresses.

In particular, one expects strong bending stresses to develop in the troughs.

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Note that deficient desquamation prevents the stratum corneum to shed before it attains critical strain levels that commit it to material failure. The occurrence of this sequence of events across the skin of the African elephant eventually leads to the formation of a network of cracks. The objective of our simulations is to analyse the mechanical response including fracture of the stratum corneum to the growth of additional underlying layers and to connect it with the distinctive cracking pattern present on the skin of the African elephant. We model the outermost part of the stratum corneum as a shell i.

These include its stretching and bending responses, its interaction with the underlying skin i. Contrary to finite-element approaches, our model handles the formation of discontinuities through a simple bond breaking mechanism, requires no geometry parametrisation and can easily be extended to include contact forces via, e. Importantly, all the parameters of the model can be approximately expressed in terms of physically measurable properties and quantities, i. While lattice methods have been extensively used in fields such as micromechanics 10 , elasticity and plasticity analyses 11 , fracture studies 12 , 13 , membrane physics 14 , 15 , 16 and others 17 , to the best of our knowledge this is the first time that they are applied to the study of shell structures.

More specifically, we describe in detail the lattice model in terms of energy contributions spring, volumetric, bending, substrate and contact energies , the relation between the model and physical parameters, convergence to the steady state through damped Newtonian dynamics, the bond breaking procedure, the treatment of contact forces, how the mesh geometry and regularity is generated and the development of stress distribution and crack localisation and orientation. Note that we do not implement skin abrasion in the numerical model as, while definitely present Supplementary Fig.

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The results of our simulations provide quantitative confirmation for the hypothesis that the outer stratum corneum , when pressured by the growth of additional sheets underneath, develops strong bending strains and stresses perpendicular to the direction of the troughs Fig.

This is followed by the propagation of cracks along the troughs and the formation of a cracking network that is essentially confined to the regions in between papillae Fig. Stratum corneum cracking by growth versus shrinkage. The visual aspect of the cracking pattern on the skin of the African elephant Fig. Using the same lattice model as above, we tested this hypothesis by simulating desiccation of the stratum corneum on the same underlying substrate papillary geometry Fig.

These computer simulations rejected the frustrated shrinkage hypothesis as they generated heterogeneous distributions of cracks that tend to propagate orthogonal to the direction of troughs Fig. Using an in-house developed tool see Methods and Supplementary Fig. Note that a qualitative understanding of this real and simulated crack junction wide angular dispersion can be obtained with the help of the simulated strain distribution Supplementary Fig.

The physical model captures qualitative and quantitative features of the cracked skin pattern. Propagating cracks tend to avoid the centre of trough junctions black dot in b because of the heterogeneous strain distribution at the intersection Supplementary Fig. The innermost uncracked sheets of stratum corneum are accounted for in the simulations see supplementary text. Finally, our numerical model recapitulates the rare occurrence of side cracks Fig. In all cases, we found the data from the real skin to be consistent with the proposed hypothesis of a cracking process generated by bending stress, although we can not rule out the possible existence of spatial anisotropy of the stratum corneum causing differences in its mechanical properties on papillae versus troughs that would confine the cracks to the troughs.

In addition to standard patterning mechanisms such as positional information and reaction—diffusion 26 , 27 , 28 , 29 , 30 , purely mechanical processes, such as folding 31 , 32 , can also generate self-organised patterns in biological systems. On the other hand, while physical cracking patterns are commonplace in non-living materials, they are far less ubiquitous in biological systems. Cracking has been proposed as a patterning mechanism in the development of tree bark fissures 33 , 34 , whereas the self-organised pattern of crocodile head scales has been suggested to form through an analogous process where skin bulges, generated by local cell proliferation, propagate in a tension field Here we show that the African elephant not only exhibits physiological and genuine physical cracking of its stratum corneum but that this process is also mechanistically distinct from the archetypal tensile cracking caused by frustrated shrinkage.

Indeed, the elaborate network of micrometre-width cracks on the African elephant skin is likely caused by local bending stress due to the growth of a highly keratinised skin on a pattern of millimetric skin elevations. Note that the process by which the papillae are patterned in the embryo is unknown. Further studies are also warranted to assess whether the lack of a cracking pattern on the skin of the Asian elephant is due to reduced orthokeratosis in comparison to the African elephant , preventing the stratum corneum either from drying sufficiently to break in a brittle fashion or from reaching large enough thickness to generate material failure bending stresses in the troughs.

Our results also suggest that a parallel exists between the physiological characteristics of the skin of African bush elephants and that of humans affected by ichthyosis vulgaris. However, this potential equivalence needs to be validated by detailed molecular cell biology comparisons, including the confirmation in African elephants of two key markers of ichthyosis vulgaris in humans 6 : the lack of keratohyalin granules in the lower stratum corneum and a substantial decrease in the expression of profilaggrin, a precursor of the protein filaggrin involved in the aggregation of keratin filaments.

Close-up photographs from a total of 16 specimens of African bush elephant Loxodonta Africana were acquired for image analysis and qualitative observations. To increase the resolution of the final result, several stacks were aligned and merged using a custom image registration script. Micro-CT imaging was used as a tool to produce meshes with a realistic geometry for the numerical simulations. The stratum corneum was mechanically removed prior to micro-CT scanning in order to obtain the geometry of the quasi-regular lattice of millimetric dermal elevations on which the stratum corneum grows.

Raw data were analysed and segmented using Amira 6. This regularised mesh output was then used in the numerical simulations.

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A number of numerical methods have been proposed to simulate shells 38 , 39 , 40 , These are almost universally based on some variation of the finite element method. To overcome these difficulties, we have developed a custom lattice spring model that takes into account the stretching and bending responses of the shell, the effects of a substrate with arbitrary geometry and the self-contact that can occur between different parts of the mesh. Data supporting the findings of this manuscript are available from the corresponding author upon reasonable request.

Large files with simulation 3D geometries are available from the corresponding author on reasonable request. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Wright, P. Do elephants need to sweat? Dunkin, R.

Climate influences thermal balance and water use in African and Asian elephants: physiology can predict drivers of elephant distribution. Spearman, R. The epidermis and its keratinisation in the African elephant. Lillywhite, H. Surface sculpturing and water-retention of elephant skin.

Feldhamer, G. Fleckman, P. Absence of the granular layer and keratohyalin define a morphologically distinct subset of individuals with ichthyosis vulgaris. Elias, P. Schmuth, M. Ichthyosis update: towards a function-driven model of pathogenesis of the disorders of cornification and the role of corneocyte proteins in these disorders. Levi, K. PhD thesis, Stanford Univ. Ostoja-Starzewski, M. Lattice models in micromechanics. Chen, H. A novel volume-compensated particle method for 2D elasticity and plasticity analysis. Solids Struct.

Leung, K. Pattern formation and selection in quasistatic fracture. Nishimoto, A. Numerical study of drying process and columnar fracture process in granule-water mixtures. E Stat. Soft Matter Phys. Kantor, Y. Crumpling transition in polymerized membranes. Seung, H. Defects in flexible membranes with crystalline order. A 38 , — Tallinen, T. The effect of plasticity in crumpling of thin sheets. Kot, M. Elastic moduli of simple mass spring models. Huxley, T. Muller, G. Starch columns: analog model for basalt columns. Geophys Res-Sol.

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