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Merkel cells and the individuality of friction ridge skin

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Agent-Based Model Introduction Biological Background Model Results Conclusions

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Introduction Main goal of the paper To model friction ridge skin (FRS) FRS once attracted much attention Patterns of heredity Diagnosing congenital diseases Most significant papers on FRS embryology are from the early 20 th century

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Introduction No consensus as to how the pattern is formed Ideaa complex interaction of: Mechanical stress Trophic factors Merkel cells

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Biological Background FRS is formed during the 10 th week Basal layer of epidermis becomes undulated, forming primary ridges Pattern appears: 1. Core & Nail Furrow 2. Proximal Phalangeal Crease 3. Fills in and reaches the deltas last

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Biological Background Volar pads determine overall pattern Large volar pads: whorls Medium volar pads: loops Small volar pads: arches They create compressive stress on the fingertips

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Biological Background Differential growth forces are responsible for the patterns The ridges follow the lines of smallest stress

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Merkel Cells Cells in the epidermis Slowly adapting mechano- sensors

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Merkel Cells Appear randomly in the volar skin at week 7 Multiply and cover the volar pads During the 10 th week, they organize along the primary ridges

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Ridge Formation – 3 Phases 1. Growth forces 2. Merkel cell rearrangement 3. Establishment of pattern

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Model

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Model: Movement of Cells

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Repulsion Force Aligned so that force at cell i from cell j points away from cell j

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Attraction Force - unit vector pointing in the direction of smallest compression in stress tensor field T - unit vector pointing in the direction of largest compression in stress tensor field T

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Attraction Force – cont. Where χ is a parameter between 0 to 1

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Meaning of χ χ = 0: attraction occurs along line of largest stress χ = 1: attraction occurs along line of smallest stress 0 < χ < 1: attraction between Merkel cells is generally toward each other, but biased along the lines of largest stress

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Values of Parameters

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General Cell Forces F a & F r 0 as r

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Simulation Concerns Initially, only repelling forces are present across the entire rectangular domain Attraction forces are incrementally added to the simulation. First in areas with large compression stress (core of whorls, the outer limits of the domain) and working out towards areas with decreasing degrees of stress Note: spring forces are added to the boundary to resist the movement of cells out of the domain.

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Simulation Concerns – cont. Number of cells in simulation: 10 5 Number of possible interactions: Rectangular domain is subdivided into rectangular boxes and interactions for cells in adjoining boxes are only used Slow moving cells – those in areas where the pattern is already established – are updated every 10 steps

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Tensor Field Either derived from simulation (see Kucken & Newell 2004, 2005) or from actual fingerprints The paper choose the latter Construct tensor field that will give the same ridge direction & choose magnitudes so that the formation occurs in the correct order Information about the direction of the ridges was extracted using the NBIS package from the NIST (see

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Results – Constant Tensor Field

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Results - Whorl

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Results A shift in initial Merkel cell placement changes minutiae placement

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Results A shift in a single Merkel cell results in different minutiae placement

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Small Displacements

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Results Too many bifurcations compared to ridge endingsusually a 1:2 ratio Too many minutiae surrounding deltas Occurrence of open fields (minutiae-less spots) is too frequent Minutiae combinations (double bifurcations) are too frequent

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Conclusions There are other models, why this one? Creates a pattern using Merkel cell alignment Fits well with old literature Builds on the theory that direction ridges are determined by stress fields, but the FRS arises from the Merkel cells

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Conclusions What makes fingerprints unique? Geometry of volar pads Timing of ridge initiation Buildup of compression stress The initial random configuration of Merkel cells

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