A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

The overall goal of this protocol is to determine the permeability and diffusion coefficients of 3D skin models in a small membrane insert system. These matters can help to answer key questions about 3D skin tissue engineering for pharmaceutical and cosmetic application in which the permeability and diffusion coefficient are essential quality factors. The main advantage of this technique is that it allows direct measurement of these coefficient within a small multi-well insert.

The small membrane insert system in the simulation can be further modified for the use in organ on the Ship devices and other applications that use membrane insert systems. To prepare an agarose gel, begin by applying 28.6 microliters of freshly prepared 80 degrees Celsius liquid agarose gel onto each membrane of a 96-well membrane inset system. After 10 minutes, the gel will have solidified and can ebe used for a permeability assay.

To prepare a collagen cell model, first mix 125 microliters of HBSS and one milliliter of collagen R solution on ice followed by neutralization with sodium hydroxide. Next add 125 microliters of primary fibroblasts suspended in complete medium to the mixture. And add 28.6 microliters of the resulting cell solution to each well of a new 96-well membrane inset system.

After 30 minutes in a cell culture incubator, add 75 microliters of complete medium to the gel's surface and 300 microliters of complete medium to the bottom of each well for an overnight incubation in the cell culture incubator. The next day, replace the medium with 75 microliters of human adult low-calcium, high-temperature keratinocytes to each collagen cell model and return the plate to the cell culture incubator for another three days. On the fourth day, aspirate the medium from the surface of the cell model and return the plate to the incubator for another seven days.

To perform a permeability assay, dispense 75 microliters of donor substance into either a small-well insert model system of interest and add 300 microliters of acceptor substance into the bottom of each well. Place the plate onto a shaker at 37 degrees Celsius, 95 percent humidity, and approximately 480 RPM for five hours, transferring the membrane insert system once hourly into an empty 96-well plate and measuring the diffused fluorescence within the bottom wells of the experimental plate on a plate reader. At the end of the permeability experiment, open the appropriate modeling software and start a new model.

Select Model Wizard and 3D model. Add Transport of Diluted Species and click study. Then select Time Dependent and click done.

Under Global Definitions, right-click to add parameters and enter the geometrical and physical parameters into the grid. Set up the geometry of the membrane insert system from the experiments, and right-click on Definitions to add two domain probes, selecting one probe as the acceptor domain and the other as the donor domain. Set both domains to average with an expression C and unit of mols per meter cubed.

And set the diffusion coefficient under transport properties one and transport of diluted species. Right-click on transport of diluted species to add a second transport properties two and select the second barrier in the domain selection. Under transport of diluted species, for initial values one, define the concentration as zero.

Right-click on transport of diluted species to add a second initial values two and select the donor as the third domain. Set the concentration as the initial concentration of the fluorescent donor substance. Right-click on transport of diluted species to add symmetry one and select all of the surfaces of the boundary selection that mirror the entire geometry.

Right-click on mesh to add two free tetrahedrals and set the second barrier as the domain. Right-click on free tetrahedral one to add the size of the pre-defined mesh to extra-fine. In the second free tetrahedral, set the acceptor and donor as domains and the pre-defined mesh to finer.

Then under study one, click compute to start the simulation. To fit the diffusion coefficient to the data generated by the diffusion simulation, open the add psychic menu and select mathematics. Locate optimization and sensitivity.

Select optimization and click add to component. Then right-click on definitions to add variables and manually enter the variables from table three. Next, under the component coupling menu, right-click on definitions, add average one followed by the manual addition of the acceptor as the operator name and select domain one.

Export the experimental data into a new text document. Use a semicolon to separate the data into columns and a line break to separate the data into rows. Right-click on optimization to add the global least squares objective and attach the text document to the experimental data.

Click global least squares objective to define the first column as time column one and the second column as value column one. In the expression of value column, enter the variable C.Right-click on optimization to add global control variables one. And declare D underscore search as a variable with an initial value of one, a lower bound of zero, and an upper bound of 1, 000.

Right-click on study one to add optimization. And select SNOPT as an optimization solver method. Set the optimality tolerance to one to the power of minus eight.

Then set the diffusion coefficient on the barrier to D.Set the simulation time under study setting from zero seconds to 22, 000 seconds with an interval of 100 seconds and click compute to begin the parameter optimization. Histological analysis of a collagen cell model reveals a slight staining of the fibroblasts within the central matrix. At the top of the collagen matrix, a layer containing many nuclei likely consisting of human adult low-calcium, high-temperature keratinocytes can be observed.

Using fluorescein sodium salt and fluorescein isothyocyanate dextran verify the impact of the molecular size of the diffusing substance reveals that for small molecular sizes, the simulation and the experimental data are in good agreement for both molecules. Larger molecular sizes, however, generate higher deviations in the curve progressions in simulations, demonstrating a delay in the beginning and a stronger rise in the later course of the graphs. Indeed, the permeation coefficient decreases as the molecular size increases with the simulated coefficients behaving similarly to the experimental permeability coefficients.

Of note, most models that use human adult low-calcium, high-temperature keratinocytes have lower permeation and diffusion coefficients compared to models without human adult low-calcium, high-temperature keratinocytes. The collagen sim model can be established in 11 to 12 days and the permeation measurement can be completed in six hours if it is performed properly. While performing the procedure, it's important to keep the boundary conditions like the temperature, the filling volume, the concentration of applied substance, the humidity, and the membrane process constant in order to reduce the variation of the permeation coefficient.

With the help of this module simulation, the experimental effort can be reduced and the long-time performance can be predicted. It can also be adapted to other permeation devices or organ ownership systems. This technique paves the way for researchers in the field of pharmaceutical and cosmetic applications as well as interact development in tissue engineering to explore the diffusion permeation processes in artificial tissues.