Name: a method for determination and simulation of permeability and diffusion in a 3d tissue model in a membrane insert system for multi-well plates
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This work was created with financial support from Deutsche Forschungsgemeinschaft (DFG) under grant No. PO413/12-1 and LA 1028/7-1.

<ol>
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Uwe Marx is the CEO and a shareholder and Gerd Lindner is a shareholder of TissUse GmbH, a company manufacturing and commercializing the MOC technology. Other authors declare no conflict of interests regarding the publication of this paper.

This study documents a method developed to quantify permeation through a tissue-construct engineered on a membrane. Permeation of substances with varying molecular sizes through agarose gel was first examined to test and validate the method and the corresponding simulation. It is well known that smaller molecules permeate faster through a matrix mesh (with the exception of the effect in gel filtration by permeability chromatography). Similar observations were made with size-exclusion experiments of substances through sclera26, human epidermal membrane27, human skin17, and rat skin28. An inverse correlation between permeability coefficients and the corresponding Stokes radius (the radius of a hard sphere that moves with the same diffusion rate as the molecules described, usually smaller than the effective radius of the molecule) has been shown26,28, and a similar relationship was observed in experiments with substances of different molecular sizes. By plotting the permeability coefficients over 1/Stokes radius, a linear correlation over the four groups with the smallest molecular size was found (R2 = 0.93) (Figure 6). This indicates that simulated permeability coefficients with the method suggested are in a realistic range.
The error of 46.15% in the experiments is slightly larger than reported for permeability experiments with the Franz diffusion cell system10. One possible explanation could be the size distribution of fluorescein-isothiocyanate-dextran, which is discussed later.
The method described has important advantages compared with methods using the Franz diffusion cell system. Firstly, the setup is more compact; the experiments are executed directly in a membrane insert system, which has the scale of a commercial well plate (&#8764; 13 cm x 8.5 cm). This enables multiple samples to be run simultaneously, whereas a separate Franz diffusion cell is needed for each sample. Secondly, the permeability of a skin model can be directly measured in the membrane insert, where the cultivation takes place. Using Franz diffusion cells, the samples have to be taken out and mounted on the system, which is more cumbersome for small samples and is also more time-consuming.
Permeation experiments with collagen cell matrices showed that this method can be applied successfully to cell-seeded systems. The model presented here was verified for skin models; however, the method can be applied to other types of organic cell cultures, e.g., kidney or liver.
In this study, a collagen-cell model was used in which the HaCaT cells completely covered the model surface (see Figure 5). This led to a reduction of permeability coefficient, demonstrating that the method is sensitive enough to distinguish the permeability coefficient between a collagen-cell model with and without a layer of HaCaT. Ideally, a skin model should build up a barrier, which approaches the epidermis of a real skin29, and it is therefore important to verify the quality (e.g., building of dermis, epidermis) of the skin model before actual use. The development of a skin model can be visualized with staining techniques and quantified from the detection of skin protein and collagen30,31,32. The permeability coefficient may also be an important factor for assessing the development of the skin model, but further experiments are required to confirm this. As previously mentioned, this method enables running multiple samples in parallel. It is also possible to take samples during the cultivation to measure permeability, and thereby observe the development of this parameter of the skin model.
It should be noted that permeability is measured through a gel/collagen-cell-model and a membrane simultaneously. The detected permeability coefficient is system-specific, whereby the results of different skin models can only be compared when using the same membrane insert. Furthermore, the skin model needs to cover the entire cultivation area in order to ensure that the test substance will permeate only through the model and not adjacent to it, which would induce errors in the permeability measured. Another aspect that should be considered in future experiments is the natural environment surrounding the skin. Normally, the temperature of the skin surface is lower in comparison to the inner region, which can influence permeation conditions.
In order to align lab experiments with computer simulations, a method which enables parameter optimization for applied simulation was presented. Simulations were found to coincide well with experimental data for substances with small molecular sizes. However, deviations between simulation and experimental data were observed for substances with larger molecular sizes. Large polysaccharide molecules can increase friction and slow down the diffusion process in a gel. This effect causes abnormal diffusion, which is a possible reason for the deviation between experimental and simulation values33,34. Another explanation might be the presence of smaller or larger particles in fluorescein-isothiocyanate-dextran. The manufacturer specifies the molecular weight of the substance as the mean size with a given range, which allows smaller and larger particles to be present. It is also unclear how dispersed these substances are, as the smaller particles permeate faster through the gel and the fluid channel. It is possible to extend the simulation to consider these diffusion and friction effects.
The permeability experiment and simulation were developed for use in a 2-OC. With the help of the simulation, this experimental method can be directly transferred to more sophisticated experimental setups. For example, the membrane insert system simulation can easily be transferred to the geometry of a 2-OC or to other systems with similar set-ups. This option of modulating the simulation can be used to support the design of future experiments. In addition, side effects such as evaporation, abnormal diffusion, and membrane effects can be integrated to enhance the simulation, thereby improving accuracy. The simulation program gives the opportunity to change or enhance the simulation equation, as well as to integrate other physical modules in order to investigate other aspects of skin model development. One example is the simulation of glucose consumption and lactate production in a collagen cell model.
A particularly interesting aspect in the testing of medical substances is how the substances are distributed in an organ-on-a-chip system. The simulation and permeability parameter my help to answer questions such as how fast a substance permeates into the system as well as which concentration will be available for other tissues in a multi-organ-chip. This method can support and enhance the development and testing of such organ-on-chip systems.

Organo-typical 3D cultures have become powerful tools for drug development and substance testing1. In this respect, human skin models are of special interest due to regulatory requirements, such as those in the cosmetics industry. They have subsequently led to the development of numerous 3D skin models, for use either on their own as single-organ cultures in multi-well plates, or in multi-organ-chips in combination with additional organ models, e.g., the liver2.
With respect to cultivation of a skin equivalent, the air-liquid interface (ALI) is an essential element for proper epidermal differentiation3. Cell culture inserts composed of a vessel with a liquid-permeable membrane at the bottom are typically used to establish an ALI. ALIs are widely utilized in commercially available skin models such as EpiDerm4, Phenion5, and Episkin6, for the culture of skin models with sizes from 96-well (4.26 mm in diameter) up to 12-well (12.2 mm in diameter) plates. The method described here determines the permeation of substances in a membrane insert system.
The permeability coefficient is a significant parameter for evaluating the quality of any cultured skin-model compared to native skin5, and is used to assess how quickly active substances migrate through the skin. Especially if drugs or cosmetics products need to be applied to the skin, this parameter is essential to understand when precisely the active agents pass through it. A simulation can further help to predict the behavior of the system and to subsequently reduce the necessary time-consuming experimental effort, especially when a large set of substances is involved.
The Franz diffusion cell is state-of-the-art for permeation experiments with skin and skin models5,6,7,8,9. This device consists of two compartments with a fixed sample (diffusion barrier) in between. The substance to be tested is applied directly to the top of the sample (donor compartment) and the concentration of the permeating compound can be detected on the opposite (acceptor) compartment. On the acceptor side, constant temperature and homogeneous substance concentration are ensured through a temperature chamber and a magnetic stirrer. Samples can be taken from a sampling arm on the acceptor side of the Franz cell. With a height range between 19 cm and 179 cm, this system is relatively large10,11. Another method for determination of diffusion coefficients in gel-like substances and tissues is FRAP. This technique uses the principle of bleaching fluorescently labeled particles in the gel and then determining the recovery time of the bleached area to calculate the diffusion coefficient12,13,14.
Furthermore, Fourier-transform-infrared (FTIR) spectroscopy can be used to detect particle movement with infrared light absorbance in order to determine the permeation process of substances in skin15,16. However, these or other imaging methods (e.g., two-photon fluorescence correlation spectroscopy17) need cost intensive instruments.
In this article, a method is presented to directly measure the permeability of a barrier within a membrane insert system, where a skin model can be cultivated. This method enables permeability experiments to be run with a large number of small samples (well size up to 4.26 mm) in a compact system. This is in contrast to the Franz diffusion cell, where a separate device is needed for each probe, which has to be mounted on the device and is difficult to realize for small samples (size of 4.26 mm). Furthermore, since the method does not require major instrumentation (e.g., a confocal or multiphoton microscope), a reduction in both time and cost is achieved.
All the experiments were performed in microporous membrane insert systems with a sample (barrier) consisting of agarose gel or a collagen cell model established on the membrane. Fluorescent substances (donor) with varying molecular sizes were applied to the top of the sample, and the concentration of permeated substance was detected on the bottom (acceptor) using a fluorescence plate reader (see Figure 1). In order to validate the method and test the accuracy of this simulation, agarose gels were produced and used as a barrier. Hydrogels are generally used for the investigation of diffusion and permeation processes in porous medium in the biological sciences13. The method was then tested in a cell-seeded system consisting of a collagen matrix of primary fibroblasts and Human adult low Calcium high Temperature keratinocytes (HaCaT) cells (cell-matrix model), which is a simplified skin model18,19.
Additionally, the permeation process was simulated by means of flow simulations with computational fluid dynamics. It was found that, by means of parameter optimization, the diffusion coefficient could be calculated from the experimental data. In general, this simulation offers different applications; for instance, it is possible to predict a permeation process based on short experiments and the simulation can significantly reduce the number of experiments.
Experimental method and simulation were designed for application to an organ-on-a-chip system1,20,21, specifically the 2-organ-chip (2-OC) developed commercially1,22,23,24,25. In principle, the permeation process of any organ model based on membrane insert systems can be described in this way.

<table width="883">
	<tbody>
		<tr height="20">
			<td height="20" style="width:236px;height:20px;">Agarose</td>
			<td style="width:248px;">Carl Roth</td>
			<td style="width:112px;">K297.2</td>
			<td style="width:287px;">High Resolution Powder</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Collagen&#160;</td>
			<td>Serva</td>
			<td>47256.01</td>
			<td>Collagen R solution 0.4 %</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">DMEM</td>
			<td>Lonza (Biozym Scientific GmbH)</td>
			<td>880010-12</td>
			<td>High Glucose with L-Glutamine</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">FCS</td>
			<td>Biochrom GmbH</td>
			<td>S0615 0114F</td>
			<td>Fetal Calf Serum</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Fluorescein Sodium Salt</td>
			<td>Sigma-Aldrich</td>
			<td>46960-25G-F</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Fluorescein Isothiocyanate-dextran</td>
			<td>Sigma-Aldrich</td>
			<td>46944-500MG</td>
			<td>4000 g/mol</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Fluorescein Isothiocyanate-dextran</td>
			<td>Sigma-Aldrich</td>
			<td>FD10S-250MG</td>
			<td>10 000 g/mol</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Fluorescein Isothiocyanate-dextran</td>
			<td>Sigma-Aldrich</td>
			<td>FD20S-250MG</td>
			<td>20 000 g/mol</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Fluorescein Isothiocyanate-dextran</td>
			<td>Sigma-Aldrich</td>
			<td>FD40S-250MG</td>
			<td>40 000 g/mol</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">HBSS</td>
			<td>ThermoFisher Scientific</td>
			<td>14170120</td>
			<td>no calcium, no magnesium , with phenol red</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">NaOH</td>
			<td>Merck</td>
			<td>1.06467.9010</td>
			<td>granulated</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">PBS&#160;</td>
			<td>Gibco</td>
			<td>18912-014</td>
			<td>tablets</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Transwell Cell Culture Inserts</td>
			<td>Corning</td>
			<td>3391</td>
			<td>96 well, 0.4 &#181;m pore size</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Transwell Cell Culture Inserts</td>
			<td>Corning (VWR)</td>
			<td>734-1563</td>
			<td>12 well, 0.4 &#181;m pore size</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Trypsin</td>
			<td>Biochrom GmbH</td>
			<td>L2143</td>
			<td>with EDTA</td>
		</tr>
	</tbody>
</table>

a method for determination and simulation of permeability and diffusion in a 3d tissue model in a membrane insert system for multi-well plates

In vitro cultivated skin models have become increasingly relevant for pharmaceutical and cosmetic applications, and are also used in drug development as well as substance testing. These models are mostly cultivated in membrane-insert systems, their permeability toward different substances being an essential factor. Typically, applied methods for determination of these parameters usually require large sample sizes (e.g., Franz diffusion cell) or laborious equipment (e.g., fluorescence recovery after photobleaching (FRAP)). This study presents a method for determining permeability coefficients directly in membrane-insert systems with diameter sizes of 4.26 mm and 12.2 mm (cultivation area). The method was validated with agarose and collagen gels as well as a collagen cell model representing skin models. The permeation processes of substances with different molecular sizes and permeation through different cell models (consisting of collagen gel, fibroblast, and HaCaT) were accurately described.
Moreover, to support the above experimental method, a simulation was established. The simulation fits the experimental data well for substances with small molecular size, up to 14 x 10-10 m Stokes radius (4,000 MW), and is therefore a promising tool to describe the system. Furthermore, the simulation can considerably reduce experimental efforts and is robust enough to be extended or adapted to more complex setups.

Permeability experiments in a 96-well membrane insert system with 2% agarose gel as a barrier were conducted in order to evaluate the accuracy of a simulation. Fluorescein sodium salt (NaFl) and fluorescein isothiocyanate-dextranes (FD) were used to verify the impact of the molecular size of the diffusing substance from 5 x 10-10 m up to 45 x 10-10 m Stokes radius (376.27-40,000 mol wt). The simulation&#39;s native parameter optimization was used to fit the simulation to experimental data.
To that end, slopes of only the linear parts of the simulated permeability were compared to the experimental outcomes. For small molecular sizes, simulation and experimental data were in good agreement with 99.2% for NaFl and 80.2% for FD 4,000 (see Figure 4a and Figure 4b). Larger molecular size generated higher deviations showing correlations of 50.5% for FD 10,000, 79.7% for FD 20,000, and 53.6% for FD 40,000. Curve progression in the simulations showed a delay at the beginning and a stronger rise in the further course of the graphs (see Figure 4c-4e).
Permeability coefficients and simulated diffusion coefficients are shown in Table 4. The permeation coefficient decreases with increasing molecular size. Standard deviation was between 0.08 x 10-8 m/s and 0.47 x 10-8 m/s (N = 7), which corresponded to an absolute error of between 4.18% and 46.15%. Experiments with larger molecules showed a larger absolute error. The simulated diffusion coefficients behaved very similarly to experimental permeability coefficients. Substances with larger Stokes radii showed decreasing diffusion coefficients, and the absolute error ranged between 9.09% and 18.46% (N = 3).
In additional permeation experiments, four different collagen cell model types were used as barriers in a 12-well membrane insert system. These models comprise a cell-free model and a cell model with different combinations of primary fibroblasts in the collagen gel and HaCaT on the surface. The following combinations were used: Collagen (Col.) as a cell-free model, Collagen + Fibroblasts (Col.+F.), Collagen + HaCaT (Col.+H.), and Collagen + Fibroblasts + HaCaT (Col.+F.+H.). Fluorescein sodium salt with DMEM + 10% FCS was used as donor substance. For image analysis of the collagen cell model, staining with hematoxylin and eosin (HE) was used. This staining was done using the manufacturer&#39;s protocol. In Figure 5, such a stain with a representative Col.+F.+H. model is shown. The HE slightly stains the tissue structure of the collagen matrix. The fibroblasts are located in the matrix, and the nuclei of the fibroblast and HaCaT cells are stained in dark violet. On top of the collagen matrix, there is a layer containing many nuclei, which should be the nuclei of the HaCaTs, building an enclosing layer on the top of the model.
In Table 5, experimental permeation coefficients and simulated diffusion coefficients are listed. A trend can be seen for most of the models with HaCaT, which have lower permeation/diffusion coefficients in comparison to the models without HaCaT. The absolute error of the permeation coefficients is 10.9-24.4%, and for the diffusion coefficients 5.2%-12.9%.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/56412/56412fig1.jpg" /> 
Figure 1: Side view of the permeability experiment in a membrane insert system. <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/56412/56412fig2.jpg" /> 
Figure 2: Exemplary graph of a permeability experiment. The concentration of the acceptor is plotted over time. Two dashed lines bracket the nearly linear part of the graph. The slope of the linear part is used to determine the permeability coefficient. <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/56412/56412fig3.jpg" /> 
Figure 3: Geometry and mesh of the membrane insert system in the simulation. (a) Geometry of the 96-well membrane insert system. (b) Geometry of the 12-well membrane insert system. (c) Mesh of the 96-well membrane insert system. (d) Mesh of the 12-well membrane insert system. (e) Cross-section and parameters of the membrane insert system. <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/56412/56412fig4.jpg" /> 
Figure 4: Comparison of the experimental data from a permeation experiment to the optimized simulation. (a) fluorescein sodium salt, (b) fluorescein isothiocyanate-dextran 4,000 mol wt., (c) 10,000 mol wt., (d) 20,000 mol wt., and (e) 40,000 mol wt. <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/56412/56412fig5.jpg" /> 
Figure 5: Representative HE staining of a collagen cell model (Collagen + Fibroblasts + HaCaT). <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/56412/56412fig6.jpg" /> 
Figure 6: Permeability coefficient as a function of the 1/Stokes radius using fluorescein sodium salt and fluorescein isothiocyanate-dextran in a 96-well membrane insert system. <a href="https://cloudflare.jove.com/files/ftp_upload/56412/56412fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Name</td>
			<td>Experession for 96 well System in mm</td>
			<td>Experssion for 12-well System in mm</td>
			<td>Description</td>
		</tr>
		<tr>
			<td>d_tran</td>
			<td>5.65 [mm]</td>
			<td>14.7 [mm]</td>
			<td>Diameter of the well</td>
		</tr>
		<tr>
			<td>d_a</td>
			<td>4.26 [mm]</td>
			<td>12.1 [mm]</td>
			<td>Diameter of the Membrane</td>
		</tr>
		<tr>
			<td>d_w</td>
			<td>8.79 [mm]</td>
			<td>21.97 [mm]</td>
			<td>Diameter of the Acceptor</td>
		</tr>
		<tr>
			<td>h_b</td>
			<td>2 [mm]</td>
			<td>2 [mm]</td>
			<td>Heigh of the Barrier</td>
		</tr>
		<tr>
			<td>h_sp</td>
			<td>1 [mm]</td>
			<td>1 [mm]</td>
			<td>Distance between well and Bottom</td>
		</tr>
		<tr>
			<td>h_a</td>
			<td>4.73 [mm]</td>
			<td>5.24 [mm]</td>
			<td>High of the Acceptor</td>
		</tr>
		<tr>
			<td>b</td>
			<td>h_b/2</td>
			<td>-</td>
			<td>Immersion Depth</td>
		</tr>
		<tr>
			<td>r</td>
			<td>((d_a)^2+4*b^2)/(8*b)</td>
			<td>-</td>
			<td>Radius of Immersion Ball+</td>
		</tr>
		<tr>
			<td>r_z</td>
			<td>r+h_b</td>
			<td>-</td>
			<td>z-Position of the Immersion Ball+</td>
		</tr>
	</tbody>
</table>
Table 1: Geometry parameters for &#34;Chemical Species Transport&#34; simulation. +Only to be used for the simulation of agarose gel in 96 well membrane insert system.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Name</td>
			<td>Expression</td>
			<td>Value</td>
			<td>Description</td>
		</tr>
		<tr>
			<td>C_fl</td>
			<td>0.1 [mg/ml]/376.28 [g/mol]</td>
			<td>0.26576 mol/m2</td>
			<td>Concentration of Fl.So.</td>
		</tr>
		<tr>
			<td>C_4</td>
			<td>2 [mg/ml]/4000 [g/mol]</td>
			<td>0.5 mol/m2</td>
			<td>Concentration of FD 4.000</td>
		</tr>
		<tr>
			<td>C_10</td>
			<td>2 [mg/ml]/10000 [g/mol]</td>
			<td>0.2 mol/m2</td>
			<td>Concentration of FD 10.000</td>
		</tr>
		<tr>
			<td>C_20</td>
			<td>2 [mg/ml]/20000 [g/mol]</td>
			<td>0.1 mol/m2</td>
			<td>Concentration of FD 20.000</td>
		</tr>
		<tr>
			<td>C_40</td>
			<td>2 [mg/ml]/40000 [g/mol]</td>
			<td>0.05 mol/m2</td>
			<td>Concentration of FD 40.000</td>
		</tr>
		<tr>
			<td>Dif_w</td>
			<td>1e-9 [m^2/s]</td>
			<td>1E-9m2/s</td>
			<td>Diffusion Coefficient of mixing water</td>
		</tr>
	</tbody>
</table>
Table 2: Physical parameters for &#34;Chemical Species Transport&#34; simulation.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Name</td>
			<td>Expression</td>
			<td>Description</td>
		</tr>
		<tr>
			<td>C</td>
			<td>Acceptor(c)</td>
			<td>Definition of the acceptor concentration</td>
		</tr>
		<tr>
			<td>D</td>
			<td>D_search*1e-10</td>
			<td>Factor change for D</td>
		</tr>
	</tbody>
</table>
Table 3: Parameters for &#34;Optimization&#34; simulation.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Permeate</td>
			<td>Permeability coefficient (m/s)x10-8</td>
			<td>Diffusion coefficient (m/s2)x10-10</td>
			<td>Stokes radius of permeate (m)x10-10</td>
		</tr>
		<tr>
			<td>Fl.So.</td>
			<td>4.79 &#177; 0.20</td>
			<td>1.94 &#177; 0.34</td>
			<td>5</td>
		</tr>
		<tr>
			<td>FD 4,000</td>
			<td>2.37 &#177; 0.31</td>
			<td>0.65 &#177; 0.12</td>
			<td>14</td>
		</tr>
		<tr>
			<td>FD10,000</td>
			<td>1.67 &#177; 0.47</td>
			<td>0.22 &#177; 0.02</td>
			<td>23</td>
		</tr>
		<tr>
			<td>FD 20,000</td>
			<td>0.65 &#177; 0.30</td>
			<td>0.29 &#177; 0.04</td>
			<td>33</td>
		</tr>
		<tr>
			<td>FD 40,000</td>
			<td>0.27 &#177; 0.08</td>
			<td>0.14 &#177; 0.02</td>
			<td>45</td>
		</tr>
	</tbody>
</table>
Table 4: Permeability and diffusion coefficient of substances with different Stokes radius through 2% Agarose gel + membrane in a 96-well membrane insert system. (fluorescein sodium salt = Fl. So., fitc dextran = FD).
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Model</td>
			<td>Permeability coefficient (m/s)x10-8</td>
			<td>Diffusion coefficient (m/s2)x10-10</td>
		</tr>
		<tr>
			<td>Col.</td>
			<td>2.18 &#177; 0.29</td>
			<td>1.22 &#177; 0.06</td>
		</tr>
		<tr>
			<td>Col.+F.</td>
			<td>1.77 &#177; 0.38</td>
			<td>0.93 &#177; 0.12</td>
		</tr>
		<tr>
			<td>Col.+H.</td>
			<td>1.64 &#177; 0.40</td>
			<td>0.96 &#177; 0.05</td>
		</tr>
		<tr>
			<td>Col.+F.+H.</td>
			<td>1.65 &#177; 0.18</td>
			<td>0.88 &#177; 0.11</td>
		</tr>
	</tbody>
</table>
Table 5: Permeability and diffusion coefficient of fluorescein sodium salt through a collagen cell model in a 12-well membrane insert system (Col. = Collagen, F. = Fibroblast, H. = HaCaT).

Watch this Scientific Journal Video about A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates at JoVE.com

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

A method for determination of permeability in a membrane insert system for multi-well plates and in silico parameter optimization for the calculation of diffusion coefficients using simulation are presented.

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