A Random Walk Model of Skin Permeation H' Frederick Frasch, Risk Anlaysis, Vol' 22, No' 2, 2002

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A Random Walk Model of Skin PermeationH.
Frederick Frasch, Risk Anlaysis, Vol. 22, No. 2,
2002

• Seminar talk by
• Mareike Moritz
• SS06

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Introduction

• Potential significance of dermal route!

• High patient compliance

• Chemical Industry airborne concentration
  regulations

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Background

• Random molecular motions ? passive diffusion

• Concentration gradient ?net mass transfer

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Background

• Steady-state rate of permanent transfer across
  homogeneous membrane

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Background

• Permeability coefficient ? in-vitro diffusion
  results

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Background

• Corneocytes filamentous keratins surrounded by
  a cornified envelope with covalently bound
  lipid surface

• lipid lamellae two closely apposed lipid
  bilayers (ceramides, fatty acids, cholesterol)

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Background

• Different chemical mobility in the two phases

• D depends on which phase the chemical is
  dissolved in!

• l depends on how lipophilic a chemical is

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Model-Overview

• Random walk ?several combinations for-
  Dcor/Dlip- Kcor_lip

• Several values for effective Diffusivity

• Calculate effective path length

• Closer look ? function ? non-linear regression ?
  parameter-fitting of random-walk-values

• Put together ?non-linear regression against
  Flynn-DB

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Model-Overview
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Diffusion Calculations

• Map membrane to coordinate system

• Locations uniquely determined by points (x,y)

• Particle placed randomly on upper
  membrane-surface

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Diffusion Calculations

• lateral (?x(n)) transverse (?y(n)) displacement

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Diffusion Calculations

• Displacement Calculation

• Random numbers between -1, 1 ?directions
  relative
  magnitudes

• Particle in corneocyte or lipid
  pahse??magnitude governed by Dcor/Dlip (Dlip
  constant)

• Varies with square root of D

• Max. displacement 1/2 to 1/4

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Diffusion Calculations

• New position within the same phase ?jump!

• Boundary between phases ? try to jump!

• Kcor_lip relates the steady-state chemical
  concentration in the corneocytes relative to
  the lipid phase

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Effective Diffusivity Effective Path Length
SC heterogeneous?different material in
different layer
Homogeneous membrane ? same material
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Effective Diffusivity Effective Path Length
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Effective Diffusivity
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Effective Path length

• Results ? mass accumulation vs. PC time data
  points

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Model Application

• Pugh et al. measured 45 chemicals

• Flynn data set human skin permeability
  coefficients

• Comparison random walk data experimental data

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Model Application
with alt0 to preserve analogy of lipids to
octanol
corneocytes to water
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Results

• Random walk simulations for mass penetration
  through SC with logKcor_lip0 Dcor/Dlip
  1.0/0.01

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Results ?effective diffusivity
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Results?effective path length

• Visual inspection ?strong dependence on
  logKcor_lip weak dependence on
  log(Dcor/Dlip)

• Values for the 3 parameters do not depend on the
  value for l0

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Results ?Steady state skin permeability
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Discussion? Advantages
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Discussion? Advantages

• Permits diffusion modelling within a
  morphologically realistic Stratum Corneum

• Applicable SC structures from any anatomical
  location from any species

• Useful extrapolation of skin permeability
  properties from animal to human

• Useful account for regional variability in
  human skin permeability

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Discussion

• homogeneous model mimics results from a
  heterogeneous membrane?

• Debate Penetration of chemicals only through
  intercellular (lipid) route? No transcellular
  routes?

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Discussion

• 84 of experimental variability for the
  permeability constant can be explained by the
  model

• R2 of steady-state-equation of Cleek and Bunge
  against Flynn-Database lt all values of table
  above

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Conclusion

• Ability to account for steady-state skin
  permeability

• Potential for prediction of non-steady-state
  diffusion

• Insight into mechanisms underlying chemical
  permeability through skin

• Predictive model where measurements are lacking

• Further Refinement is necessary!

• Doesnt favor lipid way as it is usual done!

• Reality 3-dimensional!

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References

• H. Frasch, A Random Walk Model of Skin
  Permeation, Risk Analysis. Vol.22, No.2, 2002
• A. Schätzlein, G. Cevec. Non-uniform cellular
  packing of the stratum corneum and
  permeability barrier function of intact skin a
  high-resolution confocal laser scanning
  microscopy study using highly deformable vesicles
  (Transfersomes). Br.J.Dermatol.138, 1996
• G.L. Flynn, Physicochemical determinants of skin
  absorption. In principles of route-to-route
  extrapolation for risk assessment, T.R. Garrity
  and C. J. Henry, Elsevier, 1990
• A. Einstein, The elementary theory of the
  Brownian motion. Zeit. Für Elektrochemie,
  1908. Reprinted in Investigations on the theory
  of the Brownian movement, A. Einstein. Dover
  Publications, 1956
• W.J. Pugh et al. Epidermal permeability-penetrant
  structure relationships 3. The effect of
  hydrogen bonding interactions and molecular size
  on diffusion across the stratum corneum,
  Int.J.Pharm. 138 1996

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The End....
Thank you for your attention!
Thanks to Jan Fuhrmann for excellent support!