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Prof. Cees W. J. Oomens
Eindhoven University of Technology, the Netherlands
“This book offers a fantastic approach to the non-invasive research of the skin. It
will be a valuable reference for not only students but also experts in skin research.”
Prof. Chil Hwan Oh
Korea University, South Korea
The accessibility of the skin in vivo has resulted in the development of noninvasive methods in the past 40 years that offer accurate measurements of skin
properties and structures from microscopic to macroscopic levels. However, the
mechanisms involved in these properties are still partly understood. Similar to
many other domains, including biomedical engineering, numerical modeling
has appeared as a complementary key actor for improving our knowledge of skin
physiology.
This book presents for the first time the contributions that focus on scientific
computing and numerical modeling to offer a deeper understanding of the
mechanisms involved in skin physiology. The book is structured around some skin
properties and functions, including optical and biomechanical properties and
skin barrier function and homeostasis, with—for each of them—several chapters
that describe either biological or physical models at different scales.

V421
ISBN 978-981-4463-84-3

Querleux

Bernard Querleux is senior research associate at the Worldwide
Advanced Research Center of L’Oreal Research & Innovation,
France. He obtained his doctorate in electronic engineering and
signal processing from the University of Grenoble, France, in
1987 and his habilitation in biophysics from Paris-Sud University,
France, in 1995. Since 2005, Dr. Querleux is serving as scientific
chairperson of the International Society for Biophysics and


Imaging of the Skin. Apart from being an expert in functional
brain imaging for the objective assessment of sensory perception,
his main research interests concern the development of new
non-invasive methods, including numerical modeling for skin
and hair characterization.

Computational Biophysics of the Skin

“This book presents an excellent overview of the state of the art in the computational
modeling of the skin, ranging from optical and biomechanical modeling to a
discussion on the skin barrier function and skin fluids. All chapters are written
by internationally well-known researchers in the field, each of them supplying a
comprehensive reference list for each chapter. It is an excellent read for anyone
starting in the field and also a very good source of information for experts.”

Computational
Biophysics of
the Skin

edited by

Bernard Querleux


Computational
Biophysics of
the Skin




1BO4UBOGPSE4FSJFTPO3FOFXBCMF&OFSHZ‰7PMVNF

Computational
Biophysics of
the Skin
editors

Preben Maegaard
Anna Krenz
Wolfgang Palz

edited by

Bernard Querleux

The Rise of Modern Wind Energy

Wind Power

for the World


CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20140625

International Standard Book Number-13: 978-981-4463-85-0 (eBook - PDF)
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To my wife, Sylvie
To my sons, Simon, Samuel, and Elie 


Look at the invisible skin to understand
the visible skin


—Inspired by The Picture of Dorian Gray,
Oscar Wilde, 1891
“The true mystery of the world is the visible,
not the invisible” 


Contents

Foreword
Preface

Part 1:  Skin Color
1. Multilayer Modeling of Skin Color and Translucency


Gladimir V. G. Baranoski, Tenn F. Chen, and Aravind Krishnaswamy












1.1 Introduction
1.2 Measurement of Skin Appearance

1.3 Light Transport Simulation Approaches
1.3.1 Deterministic Simulations
1.3.2 Stochastic Simulations
1.4 Practical Guidelines
1.4.1 BioSpec Model Overview
1.4.2 Predictability
1.4.3 Reproducibility
1.5 Future Prospects

2. Dermal Component–Based Optical Modeling of Skin
Translucency: Impact on Skin Color



Igor Meglinski, Alexander Doronin, Alexey N. Bashkatov,
Elina A. Genina, and Valery V. Tuchin





2.1 Introduction
2.2 Skin Color Calculator
2.2.1 Online Object-Oriented Graphics-Processing
Unit—Accelerated Monte Carlo Tool
2.2.2 Graphics-Processing Unit Acceleration of MC
2.2.3 Online Solution
2.3 Skin Spectra and Skin Color Simulation
2.3.1 Basics of MC







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viii


Contents














2.3.2 Skin Model and Skin Tissues Optical
Properties

2.4 Modeling Results

2.5 Simulation of Skin Tattoo: Toward Its Effective
Removal
2.5.1 Introductory Remarks

2.5.2 Skin Model and MC Simulation

2.5.3 Skin Immersion Optical Clearing and
Tattoo Modeling


2.5.4 Results of MC Modeling and Discussion

2.6 Summary

3. Mathematics and Biological Process of Skin Pigmentation



Josef Thingnes, Leiv Øyehaug, and Eivind Hovig








3.1 Background
3.1.1 The Tanning Response
3.1.2 Photobiology of the UV Radiation
3.1.3 Signal Transduction
3.1.4 Melanogenesis
3.1.5 Melanin is Delivered to Nearby Keratinocytes
through Dendrites
3.1.6 Further Distribution through Keratinocyte
Movement
3.2 Mathematical Modelling of Pigment Production
and Distribution
3.3 Mathematics of Tanning
3.3.1 Available Data

3.3.2 Results
3.3.2.1 Reproduction of empirical data
3.3.2.2 Dendricity
3.3.3 Discussion
3.3.4 Methods
3.3.4.1 UV intensity and signal substance
dynamics













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Contents











3.3.5 Melanin Production
3.3.5.1 Dynamics of dendrite length
3.3.5.2 Distribution of melanin as function
of dendritelength
3.3.5.3 Melanin dynamics within
keratinocytes
3.3.5.4 Estimates of parameter ranges
3.4 Conclusions

82
83
83

4. State-of-the-Art Constitutive Models of Skin Biomechanics

95

Part 2:  Skin Biomechanics

79
79

80




Georges Limbert









4.1 Introduction
96
4.2 Modeling Approaches for Skin Biomechanics
98
4.3 A Brief on Continuum Mechanics
100
4.3.1 Kinematics of a Continuum
100
4.3.2 Constitutive Equations
102
4.4 Nonlinear Elastic Models of Skin
103
4.4.1 Models Based on the Gasser–Ogden–Holzapfel
Anisotropic Hyperelastic Formulation
103
4.4.2 Models Based on the Weiss’s Transversely
Isotropic Hyperelastic Formulation
105
4.4.3 Models Based on the Bischoff–Arruda–Grosh’s
Formulation

106
4.4.4 Models Based on the Flynn–Rubin–Nielsen’s
Formulation
106
4.4.5 Model Based on the Limbert–Middleton/
Itskov–Aksel’s Formulation
107
4.4.6 Model Based on the Limbert’s Formulation 108
4.5 Nonlinear Viscoelastic Models of Skin
112
4.5.1 Quasi-Linear Viscoelasticity and Its
Derivatives
112
4.5.2 Explicitly Rate-Dependent Models
113
4.5.3 Internal Variables Based on Strain
Decomposition
114













ix




Contents









4.5.4 Internal Variables Based on Stress
Decomposition
4.6 Other Inelastic Models of Skin
4.6.1 Softening and Damage
4.6.2 Plasticity
4.6.3 Growth
4.7 A State-of-the-Art Application: Skin Wrinkles
4.8 Conclusion

5. Fiber-Matrix Models of the Dermis



Cormac Flynn











5.1 Introduction
5.2 Characteristics of the Dermis
5.2.1 Physical Components
5.2.2 Mechanical Properties
5.2.3 In vivo Tension
5.3 Computational Fiber-Matrix Dermis Models
5.3.1 Statistical Distribution Models
5.3.2 Structural Models with Phenomenological
Uncrimping Representations
5.3.3 Eight-Chain Non-Gaussian Network
Models
5.3.4 Discrete Fiber Icosahedral Structural
Models
5.4 Discussion





6. Cellular-Scale Mechanical Model of the Human
Stratum Corneum




Roberto Santoprete and Bernard Querleux








6.1 Introduction
6.2 Stratum Corneum: Structure and Biomechanics
6.2.1 Structure
6.2.2 SC Biomechanics at the Macroscopic Scale
6.2.3 SC Biomechanics at the Microscopic Scale
6.3 Stratum Corneum Numerical Model

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Contents










6.3.1
6.3.2
6.3.3
6.3.4

Structural Description
Mechanical Model
Estimation of Unknown Parameters
Relative Impact of the Three SC Major
Components
6.3.5 Simulation of Hydrated SC
6.4 Conclusion

174
176
178

7. Mathematical Models of Skin Permeability: Microscopic
Transport Models and Their Predictions

187

Part 3:  Skin Barrier



Gerald B. Kasting and Johannes M. Nitsche









7.1 Introduction
7.2 Review of Layer-Specific Properties and Models
7.2.1 Stratum Corneum
7.2.2 Viable Epidermis
7.2.3 Dermis
7.3 Analysis of Three Stratum Corneum Microscopic
Transport Models
7.3.1 Stratum Corneum Microstructure
7.3.2 Transport Properties and Predictions
7.3.2.1 MIT model
7.3.2.2 UB/UC model
7.3.2.3 CAU model
7.3.3 Targets for Future Research








8. Cellular Scale Modelling of the Skin Barrier




Arne Nägel, Michael Heisig, Dirk Feuchter, Martin Scherer,
and Gabriel Wittum




8.1 Introduction
8.2 Motivation for a Stratum Corneum Geometry
Model with Tetrakaidekahedra
8.3 Tetrakaidekahedron Model
8.3.1 Parameters of a Tetrakaidekahedron




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226

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xii

Contents



















8.3.2 Parameter for the Lipid Matrix
Tetrakaidekahedron
8.3.2.1 Thickness of the lipid layer
8.3.2.2 Base edge length
8.3.2.3 Diameter
8.4 Mathematical Model
8.4.1 Model Equations
8.4.2 Periodic Identification for a Finite Number
of Layers
8.4.3 Periodic Identification for an Infinite
Number of Layers
8.4.4 Homogenization for an Infinite Number
of Layers
8.5 Computational Results
8.5.1 Example of a Transient Simulation
8.5.2 Theoretical Results for Homogenized
Membranes
8.5.3 Application

9. Molecular Scale Modeling of Human Skin Permeation

228
228
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230
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231

231

233
234
234
235
236

243



Sophie Martel and Pierre-Alain Carrupt





9.1 Introduction
244
9.2 Skin Barrier
246
9.2.1 Stratum Corneum: Composition and
Organization
246

9.2.2 Skin Permeability Pathways
247
9.3 Experimental Methods for Human Skin Permeability
Prediction
248
9.3.1 Ex vivo Human or Animal Skin
Permeability
248
9.3.2 In vitro Models to Predict Skin Penetration 249
9.3.2.1 Reconstructed skin from
keratinocytes
249
9.3.2.2 Artificial membranes
252
9.3.2.3 Chromatographic-based
approaches
254











Contents














9.4 In silico Models to Predict Skin Penetration
9.4.1 Reliable Data for Skin Prediction Models
9.4.2 Models Based on Molecular Properties
9.4.2.1 Models based on lipophilicity and
molecular size
9.4.2.2 Models considering H bond
capacities
9.4.2.3 Considering solubility parameters
9.4.2.4 3D-QSARs
9.4.2.5 Others models (non-linear)
9.5 Conclusion

10. Accessing the Molecular Organization of the Stratum
Corneum Using High-Resolution Electron Microscopy
and Computer Simulation




Lars Norlén, Jamshed Anwar, and Ozan Öktem







10.1 Introduction
10.2 Skin Lipids
10.3 Molecular Structure Determination in situ
10.3.1 The Procedure
10.3.2 Cryo-Electron Microscopy of Vitreous
Sections
10.3.3 Modeling and Simulation of the Skin Lipid
Organization
10.3.4 Toward a Complete Molecular Model of the
Stratum Corneum
10.3.5 Tomography of Vitreous Sections
10.4 Molecular Organization of the Skin Lipids and
Its Significance
10.5 Introduction to Modeling of Data and Simulation
10.6 Introduction to Electron Tomography 3D
Reconstruction
10.6.1 The 3D Reconstruction Problem in the
Linear Setting
10.6.2 Concept of Ill-Posedness and
Regularization











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xiii


xiv

Contents
























10.6.3
10.6.4
10.6.5
10.6.6

Ill-Posedness in ET
Reconstruction Methods
Early Development
Established Methods
10.6.6.1 Analytic methods
10.6.6.2 Iterative methods
10.6.6.3 Comparing analytic and iterative
methods
10.6.7 Recent Developments
10.7 Introduction to Electron Microscopy
Simulation
10.7.1 Usages of Simulation in EM Imaging in
Life Sciences
10.7.2 Present State of EM Simulators in Life
Sciences
10.7.3 Phantom Generator
10.7.4 Simulation of Image Formation
10.8 Future Perspective
10.8.1 3D Reconstruction for ET

10.8.2 Regularization Functionals
10.8.3 Noise Model and Regularization Parameter
10.8.4 Simultaneous Reconstruction and
Image Processing
10.8.5 Statistical Regularization
10.8.6 EM Simulation

Part 4:  Skin Fluids and Components

11. Water Diffusion through Stratum Corneum


Bob Imhof  and Perry Xiao







11.1
11.2
11.3
11.4

Introduction
Assumptions and Approximations
Notation and Abbreviations
Components of the Model
11.4.1 Skin-Side Properties


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Contents




















11.4.2 Air-Side Properties

11.4.3 Boundary Properties

11.5 SC/Air Interaction


11.6 Calculations

11.6.1 Skin-Side Calculation
11.6.2 Air-Side Calculation

11.6.3 Combined Model Calculation

11.7 Results and Discussion

11.7.1 Normal Volar Forearm SC Barrier
Property

11.7.2 Normal Volar Forearm SC Surface
Hydration
11.7.3 Effect of Tape Stripping

11.8 Further Developments

11.9 Conclusions

12. Accurate Multiscale Skin Model Suitable for Determining
the Sensitivity and Specificity of Changes of Skin
Components

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349

353



Jürg Fröhlich, Sonja Huclova, Christian Beyer, and Daniel Erni



12.1 Introduction

354



12.3 Dielectric Properties of Constituents in
Human Skin


361














12.2 Brief Review on Skin Morphology and Composition
for Modeling
358
12.4 Features of the Dielectric Spectrum

12.5 Numerical and Semi-Analytical Modeling of Single
Biological Cells and Cell Suspensions
12.5.1 Modeling Effective Dielectric Properties
Using Mixing Formulas
12.5.1.1 Maxwell–Garnett

12.5.1.2 Hanai–Bruggeman

12.5.1.3 Landau–Lifshitz–Looyenga


12.5.2 Spectral Density Function Approach

362

364

364
364
365
365
366

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xvi

Contents















12.5.3 Three-Dimensional Modeling
366
12.5.4 Modeling of Tissue as a Composite
Material
368
12.6 Modeling Effective Dielectric Properties of
Materials Containing Diverse Types of
Biological Cells
369
12.6.1 Conclusions on Modeling Effective Dielectric
Properties of Materials Containing Diverse
Types of Biological Cells
373
12.7 Numerical and Semi-Analytical Modeling of
Multilayer Systems
374
12.8 Multiscale Approach
377
12.9 Sensitivity and Specificity Analysis
380
12.10Application to Human Skin
383
12.10.1A Preliminary Résumé on Appropriate
Models for Tissue Monitoring
386
12.11Conclusions
386


13. Model-Based Quantification of Skin Microcirculatory
Perfusion



Ingemar Fredriksson, Marcus Larsson, and Tomas Strömberg






13.1 Introduction
13.2 Model Description
13.3 Forward Calculation
13.3.1 Analytic Calculation of Single Shifted
Spectrum
13.3.2 Absorption Effects
13.3.3 Calculation of Doppler Power Spectrum
13.4 Inverse Problem
13.5 Accuracy and Sensitivity
13.6 In vivo Example
13.7 Discussion and Perspectives
13.7.1 Weaknesses and Strengths
13.7.2 Calibration











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Contents





13.7.3 Extensions
13.7.4 Clinical Impact

13.8 Conclusions

Part 5:  Skin Homeostasis

413
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415

14. Graphical Multi-Scale Modeling of Epidermal
Homeostasis with EPISIM

421



Thomas Sütterlin and Niels Grabe



14.1 Introduction





























14.2 Methods and Software Technologies

14.3 EPISIM Multi-Scale Modeling & Simulation
Platform

14.3.1 EPISIM Multi-Scale Model Architecture
14.3.2 EPISIM Modeller: The Graphical
Modeling System

14.3.3 EPISIM Simulator: The Multi-Agent–Based
Simulation Environment


14.4 Model of Human Epidermal Homeostasis

14.4.1 Cell-Center-Based Biomechanical Model
14.4.1.1 Optimal distance calculation
14.4.1.2 Cell migration based on
intercellular pressure,
cell–cell adhesion, and
basal membrane adhesion

14.4.2 Keratinocyte Cell Behavioral Model

14.4.2.1 Multi-scale cell cycle model

14.4.2.2 Multi-scale cell differentiation
model

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438

439

441

443

14.4.2.3 Transepidermal water flux and
diffusion model

444

14.4.3.1 Multi-scale cell cycle simulation

447

14.4.2.4 Mitosis model

14.4.3 Multi-Scale Epidermis Simulation Results

445

446

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Contents









14.4.3.2 Homeostatic epidermal in silico
tissue morphology
14.4.3.3 Transepidermal Ca2+ gradient
and barrier formation
14.4.3.4 Epidermal tissue kinetics
14.5 Discussion and Conclusion
14.6 Outlook

15. Heuristic Modelling Applied to Epidermal Homeostasis



François Iris, Manuel Gea, Paul-Henri Lampe,
and Bernard Querleux



15.1 Introduction




15.3 Problems Imposed by Enormous Variety of
Mechanisms to Be Considered



















15.2 Structural and Functional Characteristics of
the Epidermis
15.3.1 Considerations Addressing the DEJ

15.3.2 Considerations Addressing Keratinocyte
Stratification and Differentiation

15.3.3 Considerations Addressing Pigmentation

15.3.3.1 Genetic aspects

15.3.3.2 Biochemical and structural
aspects
15.3.3.3 Melanosome trafficking
and degradation

15.3.4 Signalling and Epidermal Homeostasis

448

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454
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462

463

466

467
469

472

474
475

478

480

15.3.5 The Role of Scaffold Proteins in Directing
Transduction Pathways and Modulating
Signalling Cross-Talks

486

15.4.1 Problem of Relevance Attached to
Available Data

490

15.4 Approaching Dermatological Problems through
Systems Biology Principles?
15.4.2 Changing the Analytical Paradigm

15.5 The Mechanisms Whereby OA1 Differentially
Affects Melanosome Biogenesis and Motility

489
492

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Contents











15.5.1 The Observed Facts

497

15.5.2 Event-Driven Data Integration and Negative
Selection of Working Hypotheses
499
15.5.2.1 The OA1-mediated mechanisms
in melanosome biogenesis

15.5.2.2 The OA1-mediated mechanisms
in melanosome motility

15.6 Conclusion

Index

499

503
505


525

xix



Foreword
We have learned much about skin. Starting in the 19th century,
the observations can truly be described as enlightenment.
Traditionally, this term is used for our basic knowledge in physics
and chemistry; however, it represents what occurred in skin
knowledge. The basics of anatomy, dissection, histology, cellular
anatomy, the cell, and the power of special stains propelled us to
what became possible in the 20th century.
The 20th century saw a rapid expansion, as the decades went
along, from a handful of laboratories to dozens of strong basic
and clinical science laboratories that took advantage of the start
of the 19th century knowledge. Special stains rapidly gained
prominence, followed by biochemistry, electron microscopy, and
eventually molecular biology.
By the end of the 20th century, the critical mass had been
reached that made this textbook possible.
The 21st century will see modeling become a main line part
of cutaneous science and many other areas of investigation.
In this textbook, Bernard Querleux has amassed a monumental
amount of information that had been widely dispersed and not
previously readily available to the passive and active scholar.
By dividing the book in broad sweeps, it becomes readily
absorbed. Scientists interested in color, mechanics, the inordinate

complexity of the many skin barriers, the numerous fluids, and
that all-encompassing area known as homeostasis will find welldisciplined packages that make for easy reading.
The limitation of this book’s scholar relates not to the power of
the computer or the programming but to the limitations of highquality biological observations that are currently available.
Whether at the subcellular, cellular, anatomic, functional
(physiology), pathologic, or pathology levels, the human brain,
programming, and the computer can do more than what is
available in terms of hard high-quality scientific observations.


xxii

Foreword

Much of this is in the realm of so-called big science obtaining
cooperative study groups to provide the data that is necessary to
predict with the power of the computer.
This volume will serve as the standard textbook for undergraduates, masters, and PhD students wishing to utilize the computer
and programs to understand the complexity of human cutaneous
biology.
It will likely be the source of dozens of masters and PhD theses
in the decades to come.
Because we are now at the critical mass and we have this
superb concise overview, we predict that the next decades will be
highly fruitful and will benefit many areas of science, in addition to
skin.



Howard I. Maibach, M.D.


The University of California School of Medicine
Department of Dermatology
San Francisco, California 94143-0989, USA
May 2014


Preface
For a long time, skin properties have been considered easy to
explore, as the skin is accessible to palpation and visual control.
If clinical exam remains the reference approach for individual
diagnosis, it has also shown its limits in reproducibility and
accuracy for quantifying skin properties, for instance, in clinical
studies aiming at characterizing chronological and photoaging,
skin specificity related to ethnic origins, and the evaluation of the
efficacy and safety of dermatological and cosmetic products.
Taking advantage of the accessibility of the skin in vivo, noninvasive methods were developed for about 40 years, which
nowadays offer accurate measurements of the skin color through
optical methods, firmness and elasticity measurements through
biomechanical devices, and even direct measurements of some skin
functions such as excretion, transepidermal water loss, perfusion,
and the barrier function. In vivo skin imaging has also appeared
in the past decades and gives us much information on the skin
structures from the microscopic to macroscopic levels.
However, we should admit that at the dawn of the 21st century,
the mechanisms involved in these properties are still partly
understood owing to the multidomain (biological, biochemical,
and biophysical domains) and multiscale dimension (cellular
and below to tissular and beyond) of the mechanisms. In many
domains, including biomedical engineering, numerical modeling

is nowadays recognized as a complementary key actor for
improving our knowledge.
This book presents for the first time the contributions that focus
on scientific computing and numerical modeling and simulations
to offer a deeper understanding of mechanisms involved in some
skin functions. The book is structured around some skin properties
and functions, with—for each of them—several chapters describing
either biological or physical models at different scales.
Part 1 is dedicated to skin optics. From skin color simulation
to the biology of skin pigmentation, these three chapters offer key
issues to modulate skin appearance.


xxiv

Preface

Part 2 deals with the biomechanical properties of the skin,
which are analyzed from the tissular scale toward the cellular
scale. These chapters bring new insights on the relative impact of
the main skin components on its non-linear biomechanical
properties.
One major function of the skin is to work as a protective barrier
against the penetration of external substances, allergens, and
microorganisms. Part 3 considers this function at different scales
and represents the state of the art in the understanding of skin
permeation.
Part 4 is focused on skin fluids, whose impact on the skin
physiology is very important but surprisingly have not been
studied much. Water behavior and state in the different skin layers

and a deeper description about skin microcirculation through
numerical simulation allow a better knowledge of some dynamic
properties of the skin physiology.
The last part of the book is more prospective and gathers two
chapters that introduce new modeling approaches based on the
“systems biology” approach. Aiming at integrating a large quantity
of data, the chapters discuss mathematical and non-mathematical
modeling of skin homeostasis.
I would like to thank all the authors for providing outstanding
contribution to this book and also for their support to this idea
that computational biophysics is a key approach to foster our
understanding of the physiology of organs such as the skin.
I am personally deeply grateful to Stanford Chong, from
Pan Stanford Publishing, who first suggested that I edit this
book and helped me broaden the covered topics. I don’t forget to
thank Sarabjeet Garcha and Arvind Kanswal from Pan Stanford
Publishing, not only for their great job concerning the publishing
but also for their permanent kindness to solve all the problems.
I hope this book will help all the readers, from master students
to confirmed researchers, coming from many disciplines such
as dermatology, cosmetic science, biology, chemistry, physics,
and computer science, in developing their own research of this
fascinating but complex organ, which is the human skin.

Bernard Querleux
May 2014


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