MPIKG Quantave shape analysis of intertesseral joints in tessellated calcified carlage of sharks and rays (elasmobranchs) Ronald Seidel 1 , Ahmed Hosny 2 , David Knötel 3 , Peter Fratzl 1 , Daniel Baum 3 , James Weaver 2 , Mason N. Dean 1 1 Max Planck Inst., Germany; 2 Wyss Inst., USA; 3 Zuse Inst., Germany Semi-automac ling recognion of tesserae networks Companion/Future studies Mesh-based quantave analysis of intertesseral joints Introducon: Sharks & rays have armored skeletons, comprised of uncalcified carlage covered by mineralised les (tesserae). The mechanical funcon of this skeletal tessellaon remains unclear. We used high-resoluon imaging and developed advanced 3D data processing tools to characterize how tesserae interact at ultrastructural levels, gaining insight into form-funcon relaonships of their complex joints and their roles in whole skeletal element performance. 1 mm 50 µm Dorsal photo Ventral microCT Tesserae Jaws Shark & ray tessellated carlage Acknowledgements: We thank Aravind Jayasankar & Jacob Naumann for providing images and colleagues at the MPI for fruiul discussion on these topics. A Human Froner Science Program Young Invesgator’s Grant (RGY0067) funded this work. Round sngray: Urobas halleri Characterizing ultrastructural features of tesserae and intertesseral joints A “best fit plane” bisects T1&2 joint space, allowing calculaon of intrusion, separaon and flatness of tesseral edges. Intertesseral fibrous zone ITF Intertesseral joint ITJ Intertesseral contact zone ICZ fb Tesserae Spokes Interspoke region Joint axis Heterogenous grey value distribuon (e.g. high values at edges, lower values in centers) Binary segmentaon separates tesserae from background Individual tesserae separated by applying a hierarchical watershed segmentaon to a 2D distance map Tesserae network graph representaon used to characterize 2D lings of the skeletal element’s surface Stascal informaon computed per tessera used to annotate an abstract graph representaon of the tesserae network i n i a l v o l u m e r e n d e r i n g f o r e g r o u n d s e g m e n t a o n n o v e l s e g m e n t a o n a l g o r i t h m g r a p h v i s u a l i s a o n & q u a n fi c a o n 2 D s u r f a c e l i n g Surfaces cut to isolate relevant region and to reduce verces and faces for faster computaon Joint region defined by a 30µm ROI enclosing opposing tesseral surfaces and the space between them Neighboring tesserae (T1&2) segmented and their surface geometries described by a triangle mesh T1&2 mesh regions in close proximity (≤2 µm) were idenfied as contact zones. Remaining T1&2 mesh regions within the 30µm ROI were idenfied as fibrous zones fr o m 3 D s e g m e n t a o n s u r f a c e p r o c e s s i n g d e fi n i n g j o i n t a r e a s S i z e o f te s s e r a e N u m b e r o f n e i g h b o r s S u r f a c e c u r v a t u r e Visualisaon of tesseral morphometrics allows comprehensive 3D analyses of the organisaon of tesseral networks to define underlying principles of form-funcon relaonships in the ling paern. SKELETAL ELEMENT & TESSERAE SHAPE ANALYSIS 0 500 1k 1.5k 2k 2.5k 3k 3 4 5 6 7 8 9 10 Number of neighbors Mean volume of tesserae [µm 3 ] 3 4 5 6 7 8 9 10 0 500 1000 1500 Number of neighbors Number of tesserae We developed custom modules for semi-automac ling-recognion using AmiraZIB Edion to segment individual les in microCT scans of tesseral mats and quanfy tesserae shape variaon across skeletal elements in 3D. TESSERAE SEGMENTATION PIPELINE We developed an advanced shape-analysis-algorithm in Python to quanfy tesserae interacon from microCT data by defining joint parameters, such as contact zones, joint flatness and interlocking. We present an exemplar data set; this technique will be applied to mulple joints in future work. TESSERAE JOINT CHARACTERISATION PIPELINE Intertesseral joints appear rather flat in 2D virtual vercal secons. 3D reconstrucons of the com- plex joint arrangment of fibrous aachment or contact zones. sp fb 2 µm fb T 100 µm 50 µm sp ifz ifz icz icz Backscaer & Environmental Scanning Electron Microscopy Polarized Light Microscopy TEM Preliminary analyses of a tesseral neighbor-pair illustrate that, although the joint surfaces of tesserae have convoluted topographies (~0.6 flatness) with comparavely large intrusions into the joint space (up to 27µm), they are dominated by fibrous aachment areas (~86%), with only small regions (~14%) of neighbor contact including scant areas (~4%) of apparent interlocking. This suggests that in tessellated carlage, unlike in other ‘led’ biological systems, interlocking plays lile role in mechanics and the limited abutment of tesserae at contact zones may offer adequate skeletal sffness in compression. These hypotheses will be tested via modeling work described in our ‘Companion/Future Studies’. FINDINGS Interlocking area 835.7 µm 2 = 4,15 % of ICZ Contact zone area Area of T1: 19514 µm 2 Area of T2: 20789 µm 2 Ø: 20151 µm 2 = 13,92 % of ITJ Fiber attachment area Area of T1: 120698 µm 2 Area of T2: 128586 µm 2 Ø: 124642 µm 2 = 86,1 % of ITJ Intertesseral joint area Area of T1: 140184 µm 2 Area of T2: 149346 µm 2 Ø: 144765 µm 2 Joint flatness Flatness of T1: 0.6 Flatness of T2: 0.57 Ø: 0.59 QUANTIFICATION OF TESSERAE INTERACTION Intrusion Ø intrusion: 7.2 µm Max. intrusion: 27 µm = 41 % of BFP Separaon Ø distance: 19.3 µm Max. distance: 64,1 µm = 23.3 % of BFP DOWNLOAD PUBLICATION DEFINING JOINT SYMMETRY VIA THE BEST FIT PLANE ‘BFP’ S y m m e t r y b e s t fi t p l a n e Red grid cells indicate intrusion (where the meshes breach the BFP), whereas blue grid cells indicate separaon. The rao of BFP and ITJ areas describes joint flatness, with values approaching 1.0 represenng flaer surfaces) 3D prints enable tesng of the degrees of freedom of intertesseral joints and... ...allow us to perform material tests with physical models of bio-inspired lings... ...the results of which can be verified by Finite Element Analyses of biomimicked tessellaons (Jayasankar et al. 2017, in press) Tesserae Perichondrium Unmineralized cartilage core Cross section of a skeletal element 25 µm icz ifz itj Vertical & planar section of tesserae SR-microCT fas = fiber aachment surface ics = intertesseral contact surface Tesserae abut against one another forming contact zones, or are linked via unmineralized fibrous zones. The collagenous joint fibers are firmly anchored in the mineralized matrix, forming flexible linkages. SR-microCT ics ics fas fas ics fas 20 µm Knötel et al. 2017, in prep. i n te r t e s s e r a l c o n t a c t z o n e i n t e r t e s s e r a l fi b r o u s z o n e