growing skin
serdar göktepe*, jonathan wong**, ellen kuhl**
*department of civil engineering, middle east technical university, ankara, turkey
**departments of mechanical engineering, bioengineering, and cardiothoracic surgery, stanford university
http://www.mursi.org
a computational model of skin growth
in reconstructive surgery
1
growing skin
serdar göktepe*, jonathan wong**, ellen kuhl**
*department of civil engineering, middle east technical university, ankara, turkey
**departments of mechanical engineering, bioengineering, and cardiothoracic surgery, stanford university
adrian buganza tepole
chris ploch
jonathan wong
arun gosain
ellen kuhl
growing skin
modeling skin
simulating skin
stretching skin
http://www.mursi.org
a computational model of skin growth
in reconstructive surgery
2
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growing skin
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skin expansion in forehead reconstruction
resurfacing of large congenital defects. the patient, a one-year old girl, presented with a giant congenital nevus.
three forehead and scalp expanders were implanted simultaneously for in situ forehead flap growth. the follow-up
photograph shows the girl at age three the initial defect was excised and resurfaced with expanded forehead and
scalp flaps.
growing skin
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skin expansion in forehead reconstruction
resurfacing of large congenital defects. the patient, a one-year boy, presented with a giant congenital nevus.
simultaneous forehead, cheek, and scalp expanders were implanted for in situ skin growth. this technique allows
to resurface large anatomical areas with skin of similar color, quality, and texture. the follow-up photograph shows
the boy at age three after forehead reconstruction.
growing skin
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tissue expanders in reconstructive surgery
typical applications are birth defect correction, scar revision in burn injuries, and breast reconstruction after tumor
removal. devices are available in different shapes and sizes, circular, square, rectangular, and crescent-shaped.
they consist of a silicone elastomer inflatable expander with a reinforced base for directional expansion, and a
remote silicone elastomer injection dome. mentor worldwide llc.
growing skin
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schematic sequence of tissue expansion
reference configuration
loaded configuration
grown configuration
unloaded configuration
at biological equilibrium, the skin is in a physiological state of resting tension. a tissue expander is implanted
subcutaneously between the skin and the hypodermis. when the expander is inflated, mechanical stretch induces
cell proliferation causing the skin to grow. growth restores the state of resting tension. expander deflation reveals
residual stresses in the skin layer.
growing skin
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langer‘s lines - orientation of collagen fibers
carl ritter von langer [1819-1887]
modeling skin
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collagen fibers - hierarchical microstructure
glycin
hydroxyprolin
prolin
amino acids
about 1000 amino acids
form collagen  chain
three  chains
form collagen triple helix
collagen fibrils
form collagen fiber
modeling skin
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wormlike chain model
kuhn [1936], [1938], porod [1949], kratky, porod [1949], treolar [1958], flory [1969], bustamante, smith, marko,
siggia [1994], marko, siggia [1995], rief [1997], holzapfel [2000], bischoff, arruda, grosh [2000], [2002], miehe,
göktepe, lulei [2004], kuhl, garikipati, arruda, grosh [2005], böl, reese [2008]
modeling skin
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nonlinear, anisotropic, locking
eight wormlike chains
unit cell bulk
eight-chain model
transversely isotropic eight chain model. individual chains are modeled as wormlike chains. eight chains are
assembled in a transversely isotropic unit cell. the energy of each unit cell consists of the bulk energy, the energy
of the eight individual chains, and their repulsive contributions.
modeling skin
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nonlinear, anisotropic, locking
nominal stress [N/cm2]
2.0
|| Langer’s lines
 Langer’s lines
1.6
1.2
0.8
0.4
0.0
1.00
1.25
1.50
1.75
2.00
stretch [-]
uniaxial tension test. transversely isotropic wormlike-chain based eight chain model. dots represent experiments
of rabbit skin tested parallel and perpendicular to langer's lines, lanir & fung [1974]. lines represent the
corresponding computational simulation. the model nicely captures the characteristic features of skin, including
the strong non-linearity, the anisotropy, and the locking stretches.
modeling skin
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kinematics of finite growth
illustration of covariant spatial metric g, deformation tensors C and Ce, stress tensors S, P, Pe and , and
mappings F = Fe · Fg and F-t = Fe-t · Fg-t between tangent spaces TB and cotangent spaces TB* in the material
configuration, the intermediate configuration, and the spatial configuration.
modeling skin
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stretch-induced area growth
deformation gradient
with
volume change
with
area change
with
growth tensor
lee [1969], rodriguez, hoger, mc culloch [1994], taber [1995], epstein, maugin [2000], lubarda, hoger [2002],
ambrosi, mollica [2002], himpel, kuhl, menzel, steinmann [2005], goriely, ben amar [2005], menzel [2005], kuhl,
maas, himpel, menzel [2007], garikipati [2009], goktepe, abilez, kuhl [2010]
modeling skin
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stretch-induced area growth
growth tensor
area growth
weighting function
growth criterion
himpel, kuhl, menzel, steinmann [2005], kuhl, maas, himpel, menzel [2007], goktepe, abilez, parker, kuhl [2010],
goktepe, abilez, kuhl [2010], schmid, pauli, paulus, kuhl [2011], buganza tepole, ploch, wong, gosain, kuhl [2011],
buganza tepole, gosain, kuhl [2011]
modeling skin
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relaxation & creep
area stretch [-]
5.0
4.0
area stretch [-]
u
u
5.0
u
F
F
constant total stretch
4.0
u
3.0
3.0
2.0
2.0
F
F
constant elastic stretch
1.0
1.0
0.00
0.24
0.48
0.72
0.96
normalized time [-]
0.00
0.24
0.48
0.72
0.96
normalized time [-]
temporal evolution of total area stretch, reversible elastic area stretch, and irreversible growth area stretch for
displacement- and force-controlled skin expansion. displacement control induces relaxation, a decrease in elastic
stretch, while the growth stretch increases at a constant total stretch. force control induces creep, a gradual
increase in growth stretch and total stretch at constant elastic stretch.
modeling skin
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algorithmic treatment
given
and
local newton iteration
check growth criterion
calculate growth function
calculate residual
calculate tangent
update growth multiplier
check converngence
calculate growth tensor
calculate elastic tensor
calculate elastic right cauchy green
calculate piola kirchhoff stress
calculate lagrangian moduli
simulating skin
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expander inflation & deflation
skin is modeled as a 0.2cm thin 1212cm2 square sheet, discretized with 32424=1728 trilinear brick elements,
with 42525=2500 nodes and 7500 degrees of freedom. the base surface area of all expanders is scaled to 148
elements corresponding to 37cm2. this area, shown in red, is gradually pressurized from below while the bottom
nodes of all remaining elements, shown in white, are fixed.
simulating skin
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fractional area gain & expander volume
expander volume [cm3]
fraction area gain [-]
300
1.6
250
1.2
200
150
0.8
100
0.4
50
0.0
0
0.00
0.24
0.48
0.72
0.96
normalized time [-]
0.00
0.24
0.48
0.72
0.96
normalized time [-]
tissue expander inflation. expanders are inflated gradually between t=0.00 and t=0.08 by linearly increasing the
pressure, which is then held constant from t=0.08 to t=1.00 to allow the skin to grow. under the same pressure, the
circular expander displays the largest fractional area gain and expander volume, followed by the square, the
rectangular, and the crescent-shaped expanders.
stretching skin
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fractional area gain & expander volume
expander volume [cm3]
fraction area gain [-]
300
1.6
250
1.2
200
150
0.8
100
0.4
50
0.0
0
0.00
0.24
0.48
0.72
0.96
normalized time [-]
0.00
0.24
0.48
0.72
0.96
normalized time [-]
tissue expander inflation. expanders are inflated gradually between t=0.00 and t=0.08 by linearly increasing the
pressure, which is then held constant from t=0.08 to t=1.00 to allow the skin to grow. under the same pressure, the
circular expander displays the largest area gain and expander volume, followed by the rectangular||, the square,
the crescent||, the crescent, and the rectangular expanders.
stretching skin
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quantitative expander classification
maximum
growth
[-]
initial
area
A0
[cm2]
absolute
area gain
A
[cm2]
fractional
area gain
A/A0
[-]
expander
volume
V
[cm3]
expander
pressure
p/E
[-]
residual
stress
/E
[-]
circular
2.36
37.00
58.74
1.59
257.45
0.002
0.42
square
2.35
37.00
50.63
1.37
186.77
0.002
0.41
rectangular
2.26
37.00
44.40
1.20
122.06
0.002
0.34
crescent
2.25
37.00
41.19
1.11
108.42
0.002
0.33
tissue expander inflation and deflation. maximum growth multiplier, absolute area gain, fractional area gain, and
expander volume under constant pressure loading at time t=50 and maximum principal residual stresses upon
unloading after a constant pressure growth until t=12 are are largest for the circular expander, followed by the
square, the rectangular, and the crescent shape expanders.
stretching skin
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area growth - isotropic skin model
1.00 1.35 1.70
2.05 2.40
tissue expander inflation. spatio-temporal evolution of area growth. under the same pressure applied to the same
base surface area, the circular expander induces the largest amount of growth followed by the square, the
rectangular, and the crescent-shaped expanders.
stretching skin
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area growth - anisotropic skin model
langer’s lines
1.00 1.35 1.70
2.05 2.40
tissue expander inflation. spatio-temporal evolution of area growth. the circular expander induces the largest
growth, followed by the square, the crescent-shaped, and the rectangular expanders. growth is smaller when the
expanders are placed orthogonal to the strong direction, orthogonal to langer's lines.
stretching skin
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area growth - anisotropic|| skin model
langer’s lines
1.00 1.35 1.70
2.05 2.40
tissue expander inflation. spatio-temporal evolution of area growth. the circular expander induces the largest
growth, followed by the rectangular, the square, and the crescent-shaped expanders. growth is larger when the
expanders are placed along material's strong direction, aligned with langer's lines.
stretching skin
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elastic stretch - isotropic skin model
0.90 0.95 1.00 1.05 1.10
tissue expander deflation. spatio-temporal evolution of elastic area stretch. as the expander pressure is gradually
removed, from left to right, the grown skin layer collapses. deviations from a flat surface after total unloading, right,
demonstrate the irreversibility of the growth process.
stretching skin
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residual stress - isotropic skin model
0.00 0.10 0.20 0.30 0.40
tissue expander deflation. spatio-temporal evolution of maximum principal stress. as the expander pressure is
gradually removed , from left to right, the grown skin layer collapses. remaining stresses at in the unloaded state,
right, are growth-induced residual stresses.
stretching skin
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growing skin
serdar göktepe*, jonathan wong**, ellen kuhl**
*department of civil engineering, middle east technical university, ankara, turkey
**departments of mechanical engineering, bioengineering, and cardiothoracic surgery, stanford university
http://www.mursi.org
a computational model of skin growth
in reconstructive surgery
27
growing skin
buganza tepole, ploch, wong, gosain, kuhl. growing
skin: a computational model for skin growth in
serdar göktepe*, jonathan wong**, ellen kuhl**
reconstructive* surgery, 2011; submitted.
department of civil engineering, middle east technical university, ankara, turkey
**
departments
of mechanical
engineering,
and cardiothoracic surgery, stanford university
buganza
tepole,
gosain, kuhl.
stretching bioengineering,
skin: the
physiological limit and beyond, 2011; submitted.
goktepe, abilez, kuhl. a generic approach towards
finite growth, j mech phys solids. 2010;58:1661-1680.
schmid, pauli, paulus, kuhl, itskov. how to utilise the
kinematic constraint of incompressibility for modelling
adaptation of soft tissues. comp meth biomech biomed
eng. 2011; doi:10.1080/1025 5842. 2010.548325.
ambrosi, ateshian, arruda, cowin, dumais, goriely,
holzapfel, humphrey, kemkemer, kuhl, olberding, taber,
garikipati. perspectives on biological growth and
remodeling. j mech phys solids. 2011;59:863-883.
http://biomechanics.stanford.edu/publications
http://www.mursi.org
a computational model of skin growth
in reconstructive surgery
28