AGENT-BASED MODEL FOR FRICTION RIDGE

PATTERNS

Merkel cells and the individuality of friction ridge skin

Agent-Based Model

Introduction Biological Background Model Results Conclusions

Introduction

Main goal of the paperTo model friction ridge skin (FRS)

FRS once attracted much attentionPatterns of heredityDiagnosing congenital diseases

Most significant papers on FRS embryology are from the early 20th century

Introduction

No consensus as to how the pattern is formed

Idea—a complex interaction of:Mechanical stressTrophic factorsMerkel cells

Biological Background

FRS is formed during the 10th 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

Biological Background

Volar pads determine overall patternLarge volar pads: whorlsMedium volar pads: loopsSmall volar pads: arches

They create compressive stress on the fingertips

Biological Background Differential growth forces are responsible for the patterns

The ridges follow the lines of smallest stress

Merkel Cells

Cells in the epidermis

Slowly

adapting

mechano-

sensors

Merkel Cells

Appear randomly in the volar skin at week 7

Multiply and cover the volar pads

During the 10th week, they organize along the primary ridges

Ridge Formation – 3 Phases1. Growth forces

2. Merkel cell rearrangement

3. Establishment of pattern

Model Agent-based model where the Merkel Cells

are the agents Each agent is characterized by its position Begin with a random distribution of agents

on a rectangular domain On this domain, a tensor field represents

the stress distribution Merkel cells align with lines of smallest

stress

Model: Movement of Cells Two cells interacts with each other in two

ways: : repulsion force : attraction force

Movement of the Merkel cell at position

Where

Repulsion Force

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

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

Attraction Force – cont.

Where χ is a parameter

between 0 to 1

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

Values of Parameters

General Cell Forces

Fa & Fr → 0 as r →∞

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.

Simulation Concerns – cont. Number of cells in simulation: 105

Number of possible interactions: 1010

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

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 http://www.nist.gov/itl/iad/ig/nbis.cfm)

Results – Constant Tensor Field

Results – Constant Tensor Field

Results – Constant Tensor Field

Results – Constant Tensor Field

Results - Whorl

Results - Whorl

Results - Whorl

Results - Whorl

Results

A shift in initial Merkel cell placement changes minutiae placement

Results

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

Small Displacements

Results

Too many bifurcations compared to ridge endings—usually 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

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

Conclusions

What makes fingerprints unique?Geometry of volar padsTiming of ridge initiationBuildup of compression stressThe initial random configuration of

Merkel cells