Using Embryology to Simulate Fingerprints
Dr. Michael Kücken
ZIH, TU Dresden
Using Embryology to Simulate Fingerprints – p.1/21
About me
undergraduate degree in Maths (TU Dresden) and PhD in Applied Maths
(University of Arizona)
interested in developmental biology
PhD thesis on formation of fingerprints
now work on Hydra and coral morphogenesis
Using Embryology to Simulate Fingerprints – p.2/21
Aspects of fingerprints
ridge configurations such as whorls, loops and arches
Whorl
Loop
Arch
minutiae (defects) occurring in ridge patterns
end
island
fork
enclosure
short ridge
incipient ridge
Using Embryology to Simulate Fingerprints – p.3/21
Simulation of fingerprints
focus can be different
how do I produce a realisticly-looking fingerprint?
what mechanisms underly fingerprint formation?
simulations by Cappelli et. al.
directional map
ridge pattern simulation
noise and rendering
results impressive but still won’t fool most experts
Using Embryology to Simulate Fingerprints – p.4/21
Simulation of fingerprints
focus can be different
how do I produce a realisticly-looking fingerprint?
what mechanisms underly fingerprint formation?
simulations by Cappelli et. al.
directional map
ridge pattern simulation
noise and rendering
results impressive but still won’t fool most experts
Using Embryology to Simulate Fingerprints – p.5/21
Fingerprint Tree
continuum of possible patterns in a
coordinate system
What are the coordinates?
Using Embryology to Simulate Fingerprints – p.6/21
Embryology of Fingerprints
during the 10th week skin is composed of two main layers, the epidermis
(originating from the ectoderm) and the dermis (originating from the
mesenchyme)
the epidermis and the dermis of the fingertip during the 10th week:
upper layers
of the epidermis
basal layer
dermis
Using Embryology to Simulate Fingerprints – p.7/21
Embryology of Fingerprints
during the 10th week skin is composed of two main layers, the epidermis
(originating from the ectoderm) and the dermis (originating from the
mesenchyme)
the epidermis and the dermis of the fingertip during the 10th week:
upper layers
of the epidermis
basal layer
dermis
during the 11th week undulations in the basal appear (they are called
primary ridges) and become quickly prominent:
primary ridges
primary ridges encode the future surface pattern
Using Embryology to Simulate Fingerprints – p.7/21
Spread of epidermal ridges
ridges first appear in a small area on top of the fingertip, along the nail
furrow and a little later on the flexion crease
afterwards spread over the whole fingertip
finally triradii are filled in
Using Embryology to Simulate Fingerprints – p.8/21
The volar pads
volar pads are swellings of the palm of the embryo
on the fingertips volar pads arise around the 7th
week of pregnancy
regression of the pads starts at the 10th week
→ shape of the volar pads connected to pattern
type
Using Embryology to Simulate Fingerprints – p.9/21
Fingertip Geometry and Pattern Type
there is a relationship between pad geometry and pattern type
large curved pad → whorls
medium high, asymmetric pad → loops
flat pad → arches
symmetry of the pad determines the
type of loops
pads slanted to the right give rise to
loops opening up to the left and
vice versa
evidence from
human embryo studies
studies of fingerprints in malformed
digits
studies of monkey fingerprints (see
example)
Using Embryology to Simulate Fingerprints – p.10/21
Kristine Bonnevie
Kristine Bonnevie (1872-1941) became first female Norwegian professor in
1912
worked on cytology, genetics and embryology
from 1924 to 1934 series of articles on fingerprints
argued convincingly for a connection between pad shape and pattern type
Using Embryology to Simulate Fingerprints – p.11/21
curvature
Fingerprint Tree II
symmetry
Using Embryology to Simulate Fingerprints – p.12/21
Modeling Approach
many mechanisms for ridge formation have been suggested
ridges determined by pattern of innervating axons or capillaries
ridge pattern formed by fibroblast pattern in the dermis
evolutionary arguments
most convincing is the one suggested by Bonnevie (1927):
primary ridges form as a result of a buckling process
idea: stress in the basal layer is built up by differential growth until buckling
occurs
faster growth of the basal layer
basal layer
epidermis
dermis
buckling of the basal layer
compression of the basal layer
Using Embryology to Simulate Fingerprints – p.13/21
Equations
describe the buckling process by the well-known von Karman equations
equations for the elastic behavior of curved surfaces
first equation is a force balance equation, the second one a compatibility
equation
F,yy
F,xx
κwt + D∇ w +
+
− [F, w] + V ′ (w) = 0
Rx
Ry
w,yy
w,xx
1
1 4
∇ F−
−
+ [w, w] = 0
Eh
Rx
Ry
2
4
where
[F, w] = F,xx w,yy + F,yy w,xx − 2F,xy w,xy
w . . . out-of-plane displacement
F . . . Airy stress function
Using Embryology to Simulate Fingerprints – p.14/21
Equation Analysis
ridges form perpendicular to the greatest stress
hexagons are a stable solution for some parameters → actually found on
palms of some marsupials
big question: What is the stress distribution in the epidermis?
Using Embryology to Simulate Fingerprints – p.15/21
The Role of the Boundary
observations:
ridge lines parallel to nail furrow and
major flexion creases
ridge lines perpendicular to outline of
hand
conclusion: furrows and creases act as
obstacles to expansion
→ greatest stress forms perpendicular to
these obstacles
→ ridges form along furrows and creases
Using Embryology to Simulate Fingerprints – p.16/21
Curvature
Curved surfaces important design element in construction
curved surfaces can support perpendicular loads by tangential tension
Force
Using Embryology to Simulate Fingerprints – p.17/21
Curvature
Curved surfaces important design element in construction
curved surfaces can support perpendicular loads by tangential tension
Force
Primary ridges form perpendicular to the lines of largest stress.
The stress itself is determined by boundary forces and forces due to
geometry changes of the volar pads.
Using Embryology to Simulate Fingerprints – p.17/21
Finding the Stress in the Epidermis
impose forces on a fingertips shaped surface:
forces from the boundary
load forces on the center of the pad
simulations implemented by using finite elements
white lines represent lines of
smallest stress → direction of
the ridges
red/yellow regions: regions
with large stress → regions
where ridge formation take
place first (along nail furrow
and center of whorl)
blue: regions with large stress
→ regions where ridge formation take place last (triradii)
simulated pattern types and timing of ridge formation consistent to
observations
Using Embryology to Simulate Fingerprints – p.18/21
Finding the Buckling Pattern
use the obtained stress distribution as input into the von Karman equations
equations are integrated using a pseudospectral scheme
drive the system in the unstable regime and see what happens
Whorl
Loop
Arch
main pattern types reproduced
typical fingerprint defects reproduced, but not with the correct behavior
we have to look for more hints in embryology
Using Embryology to Simulate Fingerprints – p.19/21
Merkel cells
cells in the epidermis with contacts to nerve endings
origin and function is still controversial
Forces
Merkel cells form in a hexagonal pattern and are found later at the base of
the epidermal ridges
Merkel cells
epidermal ridges
fingerprints combination of mechanical forces (determining ridge direction)
and the location of the Merkel cells (determining minutiae)
Using Embryology to Simulate Fingerprints – p.20/21
Summary
curvature and symmetry of the volar pads determine pattern type
pattern itself arises by compression forces in the basal layer, crucial for this
process are
boundary effects
curvatures of the volar pads
original model does not offer adequate description of minutiae
Using Embryology to Simulate Fingerprints – p.21/21
Summary
curvature and symmetry of the volar pads determine pattern type
pattern itself arises by compression forces in the basal layer, crucial for this
process are
boundary effects
curvatures of the volar pads
original model does not offer adequate description of minutiae
understanding for the minutiae is likely to come through an interaction of
Merkel cells, the nervous system and growth forces
possible long-term goal: platform on which to
simulate fingerprints
explore issues of individuality
Using Embryology to Simulate Fingerprints – p.21/21