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Understanding Formulation and Temperature Effects on Dermal Transport Kinetics by IVPT and Multiphysics Simulation



It is often unclear how complex topical product formulation factors influence the transport kinetics through skin tissue layers, because of multiple confounding attributes. Environmental factors such as temperature effect are also poorly understood. In vitro permeation testing (IVPT) is frequently used to evaluate drug absorption across skin, but the flux results from these studies are from a combination of mechanistic processes.


Two different commercially available formulations of oxybenzone-containing sunscreen cream and continuous spray were evaluated by IVPT in human skin. Temperature influence between typical skin surface temperature (32°C) and an elevated 37°C was also assessed. Furthermore, a multiphysics-based simulation model was developed and utilized to compute the flux of modeled formulations.


Drug transport kinetics differed significantly between the two drug products. Flux was greatly influenced by the environmental temperature. The multiphysical simulation results could reproduce the experimental observations. The computation further indicated that the drug diffusion coefficient plays a dominant role in drug transport kinetics, influenced by the water content which is also affected by temperature.


The in vitro testing and bottom-up simulation shed insight into the mechanism of dermal absorption kinetics from dissimilar topical products.

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c :

Drug concentration; initial value, c0

t :


ϕ :

Porosity; initial value, ϕ0

S :

Effective volumetric strain; initial value, S0

ε v :

Volumetric strain; initial value, εv0

σij :

Stress tensor of i and j directions

ε ij :

Strain tensor of i and j directions

p :

Interstitial fluid pressure; initial value, p0

K :

Bulk modulus of whole tissue

K s :

Bulk modulus of tissue solid mass

β :

Biot coefficient

v :

Poisson’s ratio of tissue

E :

Elasticity modulus of tissue

u i :

Tissue displacement along i direction

u i, j :

Tissue displacement gradient with respect to j direction

f i :

Net force along i direction

k :

Permeability of tissue; initial value, k0

μ :

Dynamic viscosity of interstitial fluid

ρ :

Interstitial fluid density

\(\overrightarrow{v}\) :

Interstitial fluid velocity

D eff :

Effective diffusion coefficient of drug

k g :

Mass transfer coefficient

MW :

Molecular weight

a :

Surface water activity

\({p}_{sat}^o\) :

Water saturated vapor pressure

RH :

Relative humidity

R :

Gas constant

δ :

Kronecker delta function

ω :

Thermal expansion coefficient

T :


T ref :

Initial temperature

E a :

Activation energy of diffusion


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Biospecimens were provided by the NCI funded Cooperative Human Tissue Network (CHTN). Other investigators may have received specimens from the same tissue specimens. The CHTN is comprised of six academic institutions who collect and distribute remnant human biospecimens from routine surgical and autopsy procedures to investigators for basic and applied science to advance biomedical research. The authors have no financial or proprietary interests in any material discussed in this article


Funding for this project was made possible, in part, by the University of Maryland Baltimore, School of Pharmacy Mass Spectrometry Center (Research Award SOP1841-IQB2014), the University of Maryland Baltimore, Institute for Clinical & Translational Research (ICTR) voucher program and the University of Maryland Baltimore Pharmaceutical Sciences Department Fellowship and Merit Awards.

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Correspondence to Tonglei Li or Audra L. Stinchcomb.

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Zambrana, P.N., Hou, P., Hammell, D.C. et al. Understanding Formulation and Temperature Effects on Dermal Transport Kinetics by IVPT and Multiphysics Simulation. Pharm Res 39, 893–905 (2022).

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  • computational fluid dynamics
  • diffusion
  • flux
  • in vitro permeation test
  • topical delivery