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.

In vitro cultivated skin models have become increasingly relevant for pharmaceutical and cosmetic applications, and are also used in drug development as ...

a-method-for-determination-simulation-permeability-diffusion-3d

Universidad de Cartagena UDEC

Research

JoVE Journal

Bioengineering

25.0K Views.  Hamburg University of Technology. 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.

Video: 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 Ovarian Follicle Encapsulation and Culture in a Proteolytically Degradable 3 Dimensional System

The ovarian follicle is the functional unit of the ovary that secretes sex hormones and supports oocyte maturation. In vitro follicle techniques provide a tool to model follicle development in order to investigate basic biology, and are further being developed as a technique to preserve fertility in the clinic1-4. Our in vitro culture system employs hydrogels in order to mimic the native ovarian environment by maintaining the 3D follicular architecture, cell-cell interactions and paracrine signaling that direct follicle development 5. Previously, follicles were successfully cultured in alginate, an inert algae-derived polysaccharide that undergoes gelation with calcium ions6-8. Alginate hydrogels formed at a concentration of 0.25% w/v were the most permissive for follicle culture, and retained the highest developmental competence 9. Alginate hydrogels are not degradable, thus an increase in the follicle diameter results in a compressive force on the follicle that can impact follicle growth10. We subsequently developed a culture system based on a fibrin-alginate interpenetrating network (FA-IPN), in which a mixture of fibrin and alginate are gelled simultaneously. This combination provides a dynamic mechanical environment because both components contribute to matrix rigidity initially; however, proteases secreted by the growing follicle degrade fibrin in the matrix leaving only alginate to provide support. With the IPN, the alginate content can be reduced below 0.25%, which is not possible with alginate alone 5. Thus, as the follicle expands, it will experience a reduced compressive force due to the reduced solids content. Herein, we describe an encapsulation method and an in vitro culture system for ovarian follicles within a FA-IPN. The dynamic mechanical environment mimics the natural ovarian environment in which small follicles reside in a rigid cortex and move to a more permissive medulla as they increase in size11. The degradable component may be particularly critical for clinical translation in order to support the greater than 106-fold increase in volume that human follicles normally undergo in vivo .

A new method for ovarian follicle encapsulation in a 3D fibrin-alginate interpenetrating network is described. This system combines structural support with proteolytic degradation to support the development of immature follicles to produce mature oocytes. This method may be applied to culture cell aggregates to maintain cell-cell contacts without limiting expansion.

The ovarian follicle is the functional unit of the ovary that secretes sex hormones and supports oocyte maturation. In vitro  follicle techniques provide ...

Creating Two-Dimensional Patterned Substrates for Protein and Cell Confinement

Microcontact printing provides a rapid, highly reproducible method for the creation of well-defined patterned substrates.1 While microcontact printing can be employed to directly print a large number of molecules, including proteins,2 DNA,3 and silanes,4 the formation of self-assembled monolayers (SAMs) from long chain alkane thiols on gold provides a simple way to confine proteins and cells to specific patterns containing adhesive and resistant regions. This confinement can be used to control cell morphology and is useful for examining a variety of questions in protein and cell biology. Here, we describe a general method for the creation of well-defined protein patterns for cellular studies.5 This process involves three steps: the production of a patterned master using photolithography, the creation of a PDMS stamp, and microcontact printing of a gold-coated substrate. Once patterned, these cell culture substrates are capable of confining proteins and/or cells (primary cells or cell lines) to the pattern.
The use of self-assembled monolayer chemistry allows for precise control over the patterned protein/cell adhesive regions and non-adhesive regions; this cannot be achieved using direct protein stamping. Hexadecanethiol, the long chain alkane thiol used in the microcontact printing step, produces a hydrophobic surface that readily adsorbs protein from solution. The glycol-terminated thiol, used for backfilling the non-printed regions of the substrate, creates a monolayer that is resistant to protein adsorption and therefore cell growth.6 These thiol monomers produce highly structured monolayers that precisely define regions of the substrate that can support protein adsorption and cell growth. As a result, these substrates are useful for a wide variety of applications from the study of intercellular behavior7 to the creation of microelectronics.8
While other types of monolayer chemistry have been used for cell culture studies, including work from our group using trichlorosilanes to create patterns directly on glass substrates,9 patterned monolayers formed from alkane thiols on gold are straight-forward to prepare. Moreover, the monomers used for monolayer preparation are commercially available, stable, and do not require storage or handling under inert atmosphere. Patterned substrates prepared from alkane thiols can also be recycled and reused several times, maintaining cell confinement.10

Self-assembled monolayers (SAMs) formed from long chain alkane thiols on gold provide well-defined substrates for the formation of protein patterns and cell confinement. Microcontact printing of hexadecanethiol using a polydimethylsiloxane (PDMS) stamp followed by backfilling with a glycol-terminated alkane thiol monomer produces a pattern where protein and cells adsorb only to the stamped hexadecanethiol region.

Microcontact printing provides a rapid, highly reproducible method for the creation of well-defined patterned substrates.1  While microcontact printing ...

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis

The metabolism of fatty acids, such as arachidonic acid (AA) and linoleic acid (LA), results in the formation of oxidized bioactive lipids, including numerous stereoisomers1,2. These metabolites can be formed from free or esterified fatty acids. Many of these oxidized metabolites have biological activity and have been implicated in various diseases including cardiovascular and neurodegenerative diseases, asthma, and cancer3-7. Oxidized bioactive lipids can be formed enzymatically or by reactive oxygen species (ROS). Enzymes that metabolize fatty acids include cyclooxygenase (COX), lipoxygenase (LO), and cytochromes P450 (CYPs)1,8. Enzymatic metabolism results in enantioselective formation whereas ROS oxidation results in the racemic formation of products.
While this protocol focuses primarily on the analysis of AA- and some LA-derived bioactive metabolites; it could be easily applied to metabolites of other fatty acids. Bioactive lipids are extracted from cell lysate or media using liquid-liquid (l-l) extraction. At the beginning of the l-l extraction process, stable isotope internal standards are added to account for errors during sample preparation. Stable isotope dilution (SID) also accounts for any differences, such as ion suppression, that metabolites may experience during the mass spectrometry (MS) analysis9. After the extraction, derivatization with an electron capture (EC) reagent, pentafluorylbenzyl bromide (PFB) is employed to increase detection sensitivity10,11. Multiple reaction monitoring (MRM) is used to increase the selectivity of the MS analysis. Before MS analysis, lipids are separated using chiral normal phase high performance liquid chromatography (HPLC). The HPLC conditions are optimized to separate the enantiomers and various stereoisomers of the monitored lipids12. This specific LC-MS method monitors prostaglandins (PGs), isoprostanes (isoPs), hydroxyeicosatetraenoic acids (HETEs), hydroxyoctadecadienoic acids (HODEs), oxoeicosatetraenoic acids (oxoETEs) and oxooctadecadienoic acids (oxoODEs); however, the HPLC and MS parameters can be optimized to include any fatty acid metabolites13.
Most of the currently available bioanalytical methods do not take into account the separate quantification of enantiomers. This is extremely important when trying to deduce whether or not the metabolites were formed enzymatically or by ROS. Additionally, the ratios of the enantiomers may provide evidence for a specific enzymatic pathway of formation. The use of SID allows for accurate quantification of metabolites and accounts for any sample loss during preparation as well as the differences experienced during ionization. Using the PFB electron capture reagent increases the sensitivity of detection by two orders of magnitude over conventional APCI methods. Overall, this method, SID-LC-EC-atmospheric pressure chemical ionization APCI-MRM/MS, is one of the most sensitive, selective, and accurate methods of quantification for bioactive lipids.

This protocol will demonstrate the extraction and analysis of free and esterified bioactive fatty acids from cells. Fatty acids are accurately quantified using stable isotope dilution, chiral liquid chromatography, electron capture atmospheric chemical ionization multiple reaction monitoring mass spectrometry (SID-LC-ECAPCI-MRM/MS).

The metabolism of fatty acids, such as arachidonic acid (AA) and linoleic acid (LA), results in the formation of oxidized bioactive lipids, including ...

Tissue Engineering of a Human 3D in vitro Tumor Test System

Cancer is one of the leading causes of death worldwide. Current therapeutic strategies are predominantly developed in 2D culture systems, which inadequately reflect physiological conditions in vivo. Biological 3D matrices provide cells an environment in which cells can self-organize, allowing the study of tissue organization and cell differentiation. Such scaffolds can be seeded with a mixture of different cell types to study direct 3D cell-cell-interactions. To mimic the 3D complexity of cancer tumors, our group has developed a 3D in vitro tumor test system.	
	Our 3D tissue test system models the in vivo situation of malignant peripheral nerve sheath tumors (MPNSTs), which we established with our decellularized porcine jejunal segment derived biological vascularized scaffold (BioVaSc). In our model, we reseeded a modified BioVaSc matrix with primary fibroblasts, microvascular endothelial cells (mvECs) and the S462 tumor cell line. For static culture, the vascular structure of the BioVaSc is removed and the remaining scaffold is cut open on one side (Small Intestinal Submucosa SIS-Muc). The resulting matrix is then fixed between two metal rings (cell crowns).	
	Another option is to culture the cell-seeded SIS-Muc in a flow bioreactor system that exposes the cells to shear stress. Here, the bioreactor is connected to a peristaltic pump in a self-constructed incubator. A computer regulates the arterial oxygen and nutrient supply via parameters such as blood pressure, temperature, and flow rate. This setup allows for a dynamic culture with either pressure-regulated pulsatile or constant flow.	
	In this study, we could successfully establish both a static and dynamic 3D culture system for MPNSTs. The ability to model cancer tumors in a more natural 3D environment will enable the discovery, testing, and validation of future pharmaceuticals in a human-like model.

Tissue Engineering of a Human 3D in vitro Tumor Test System

Methods to create human 3D tumor tissues as test systems are described. These technologies are based on a decellularized Biological Vascularized Scaffold (BioVaSc), primary human cells and a tumor cell line, which can be cultured under static as well as under dynamic conditions in a flow bioreactor.

Cancer is one of the leading causes of death worldwide.  Current therapeutic strategies are predominantly developed in 2D culture  systems, which ...

Systematic Analysis of In Vitro Cell Rolling Using a Multi-well Plate Microfluidic System

A major challenge for cell-based therapy is the inability to systemically target a large quantity of viable cells with high efficiency to tissues of interest following intravenous or intraarterial infusion. Consequently, increasing cell homing is currently studied as a strategy to improve cell therapy. Cell rolling on the vascular endothelium is an important step in the process of cell homing and can be probed in-vitro using a parallel plate flow chamber (PPFC). However, this is an extremely tedious, low throughput assay, with poorly controlled flow conditions. Instead, we used a multi-well plate microfluidic system that enables study of cellular rolling properties in a higher throughput under precisely controlled, physiologically relevant shear flow1,2. In this paper, we show how the rolling properties of HL-60 (human promyelocytic leukemia) cells on P- and E-selectin-coated surfaces as well as on cell monolayer-coated surfaces can be readily examined. To better simulate inflammatory conditions, the microfluidic channel surface was coated with endothelial cells (ECs), which were then activated with tumor necrosis factor-&#945; (TNF-&#945;), significantly increasing interactions with HL-60 cells under dynamic conditions. The enhanced throughput and integrated multi-parameter software analysis platform, that permits rapid analysis of parameters such as rolling velocities and rolling path, are important advantages for assessing cell rolling properties in-vitro. Allowing rapid and accurate analysis of engineering approaches designed to impact cell rolling and homing, this platform may help advance exogenous cell-based therapy.

Systematic Analysis of In Vitro Cell Rolling Using a Multi-well Plate Microfluidic System

This study used a multi-well plate microfluidic system, significantly increasing throughput of cell rolling studies under physiologically relevant shear flow. Given the importance of cell rolling in the multi-step cell homing cascade and the importance of cell homing following systemic delivery of exogenous populations of cells in patients, this system offers potential as a screening platform to improve cell-based therapy.

A major challenge for cell-based therapy is the inability to systemically target a large quantity of viable cells with high efficiency to tissues of ...

Generation of a Three-dimensional Full Thickness Skin Equivalent and Automated Wounding

In vitro models are a cost effective and ethical alternative to study cutaneous wound healing processes. Moreover, by using human cells, these models reflect the human wound situation better than animal models. Although two-dimensional models are widely used to investigate processes such as cellular migration and proliferation, models that are more complex are required to gain a deeper knowledge about wound healing. Besides a suitable model system, the generation of precise and reproducible wounds is crucial to ensure comparable results between different test runs. In this study, the generation of a three-dimensional full thickness skin equivalent to study wound healing is shown. The dermal part of the models is comprised of human dermal fibroblast embedded in a rat-tail collagen type I hydrogel. Following the inoculation with human epidermal keratinocytes and consequent culture at the air-liquid interface, a multilayered epidermis is formed on top of the models. To study the wound healing process, we additionally developed an automated wounding device, which generates standardized wounds in a sterile atmosphere.

The goal of this protocol is to build up a three-dimensional full thickness skin equivalent, which resembles natural skin. With a specifically constructed automated wounding device, precise and reproducible wounds can be generated under maintenance of sterility.

In vitro models are a cost effective and ethical alternative to study cutaneous wound healing processes. Moreover, by using human cells, these models ...

Production, Characterization and Potential Uses of a 3D Tissue-engineered Human Esophageal Mucosal Model

The incidence of both esophageal adenocarcinoma and its precursor, Barrett&#8217;s Metaplasia, are rising rapidly in the western world. Furthermore esophageal adenocarcinoma generally has a poor prognosis, with little improvement in survival rates in recent years. These are difficult conditions to study and there has been a lack of suitable experimental platforms to investigate disorders of the esophageal mucosa.
A model of the human esophageal mucosa has been developed in the MacNeil laboratory which, unlike conventional 2D cell culture systems, recapitulates the cell-cell and cell-matrix interactions present in vivo and produces a mature, stratified epithelium similar to that of the normal human esophagus. Briefly, the model utilizes non-transformed normal primary human esophageal fibroblasts and epithelial cells grown within a porcine-derived acellular esophageal scaffold. Immunohistochemical characterization of this model by CK4, CK14, Ki67 and involucrin staining demonstrates appropriate recapitulation of the histology of the normal human esophageal mucosa.
This model provides a robust, biologically relevant experimental model of the human esophageal mucosa. It can easily be manipulated to investigate a number of research questions including the effectiveness of pharmacological agents and the impact of exposure to environmental factors such as alcohol, toxins, high temperature or gastro-esophageal refluxate components. The model also facilitates extended culture periods not achievable with conventional 2D cell culture, enabling, inter alia, the study of the impact of repeated exposure of a mature epithelium to the agent of interest for up to 20 days. Furthermore, a variety of cell lines, such as those derived from esophageal tumors or Barrett&#8217;s Metaplasia, can be incorporated into the model to investigate processes such as tumor invasion and drug responsiveness in a more biologically relevant environment.

This manuscript describes the production, characterization and potential uses of a tissue engineered 3D esophageal construct prepared from normal primary human esophageal fibroblast and squamous epithelial cells seeded within a de-cellularized porcine scaffold. The results demonstrate the formation of a mature stratified epithelium similar to the normal human esophagus.

The incidence of both esophageal adenocarcinoma and its precursor, Barrett&#8217;s Metaplasia, are rising rapidly in the western world. Furthermore ...

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

The importance of cell migration can be seen through the development of human life. When cells migrate, they generate forces and transfer these forces to their surrounding area, leading to cell movement and migration. In order to understand the mechanisms that can alter and/or affect cell migration, one can study these forces. In theory, understanding the fundamental mechanisms and forces underlying cell migration holds the promise of effective approaches for treating diseases and promoting cellular transplantation. Unfortunately, modern chemotaxis chambers that have been developed are usually restricted to two dimensions (2D) and have complex diffusion gradients that make the experiment difficult to interpret. To this end, we have developed, and describe in this paper, a direct-viewing chamber for chemotaxis studies, which allows one to overcome modern chemotaxis chamber obstacles able to measure cell forces and specific concentration within the chamber in a 3D environment to study cell 3D migration. More compelling, this approach allows one to successfully model diffusion through 3D collagen matrices and calculate the coefficient of diffusion of a chemoattractant through multiple different concentrations of collagen, while keeping the system simple and user friendly for traction force microscopy (TFM) and digital volume correlation (DVC) analysis.

Cell migration is an important part of human development and life. In order to understand the mechanisms that can alter cell migration, we present a planar gradient diffusion system to investigate chemotaxis in a 3D collagen matrix, which allows one to overcome modern diffusion chamber limitations of existing assays.

The importance of cell migration can be seen through the development of human life. When cells migrate, they generate forces and transfer these forces to ...

A Combined 3D Tissue Engineered In Vitro/In Silico Lung Tumor Model for Predicting Drug Effectiveness in Specific Mutational Backgrounds

In the present study, we combined an in vitro 3D lung tumor model with an in silico model to optimize predictions of drug response based on a specific mutational background. The model is generated on a decellularized porcine scaffold that reproduces tissue-specific characteristics regarding extracellular matrix composition and architecture including the basement membrane. We standardized a protocol that allows artificial tumor tissue generation within 14 days including three days of drug treatment. Our article provides several detailed descriptions of 3D read-out screening techniques like the determination of the proliferation index Ki67 staining&#39;s, apoptosis from supernatants by M30-ELISA and assessment of epithelial to mesenchymal transition (EMT), which are helpful tools for evaluating the effectiveness of therapeutic compounds. We could show compared to 2D culture a reduction of proliferation in our 3D tumor model that is related to the clinical situation. Despite of this lower proliferation, the model predicted EGFR-targeted drug responses correctly according to the biomarker status as shown by comparison of the lung carcinoma cell lines HCC827 (EGFR -mutated, KRAS wild-type) and A549 (EGFR wild-type, KRAS-mutated) treated with the tyrosine-kinase inhibitor (TKI) gefitinib. To investigate drug responses of more advanced tumor cells, we induced EMT by long-term treatment with TGF-beta-1 as assessed by vimentin/pan-cytokeratin immunofluorescence staining. A flow-bioreactor was employed to adjust culture to physiological conditions, which improved tissue generation. Furthermore, we show the integration of drug responses upon gefitinib treatment or TGF-beta-1 stimulation - apoptosis, proliferation index and EMT - into a Boolean in silico model. Additionally, we explain how drug responses of tumor cells with a specific mutational background and counterstrategies against resistance can be predicted. We are confident that our 3D in vitro approach especially with its in silico expansion provides an additional value for preclinical drug testing in more realistic conditions than in 2D cell culture.

A Combined 3D Tissue Engineered In Vitro/In Silico Lung Tumor Model for Predicting Drug Effectiveness in Specific Mutational Backgrounds

We present a three-dimensional (3D) lung cancer model based on a biological collagen scaffold to study sensitivity towards non-small-cell-lung-cancer-(NSCLC)-targeted therapies. We demonstrate different read-out techniques to determine the proliferation index, apoptosis and epithelial-mesenchymal transition (EMT) status. Collected data are integrated into an in silico model for prediction of drug sensitivity.

In the present study, we combined an in vitro 3D lung tumor model with an in silico model to optimize predictions of drug response based on a specific ...

Fabrication of Custom Agarose Wells for Cell Seeding and Tissue Ring Self-assembly Using 3D-Printed Molds

Engineered tissues are being used clinically for tissue repair and replacement, and are being developed as tools for drug screening and human disease modeling. Self-assembled tissues offer advantages over scaffold-based tissue engineering, such as enhanced matrix deposition, strength, and function. However, there are few available methods for fabricating 3D tissues without seeding cells on or within a supporting scaffold. Previously, we developed a system for fabricating self-assembled tissue rings by seeding cells into non-adhesive agarose wells. A polydimethylsiloxane (PDMS) negative was first cast in a machined polycarbonate mold, and then agarose was gelled in the PDMS negative to create ring-shaped cell seeding wells. However, the versatility of this approach was limited by the resolution of the tools available for machining the polycarbonate mold. Here, we demonstrate that 3D-printed plastic can be used as an alternative to machined polycarbonate for fabricating PDMS negatives. The 3D-printed mold and revised mold design is simpler to use, inexpensive to produce, and requires significantly less agarose and PDMS per cell seeding well. We have demonstrated that the resulting agarose wells can be used to create self-assembled tissue rings with customized diameters from a variety of different cell types. Rings can then be used for mechanical, functional, and histological analysis, or for fabricating larger and more complex tubular tissues.

This protocol describes a platform for fabricating self-assembled tissue rings in variable sizes using a customized 3D-printed plastic mold. PDMS negatives are cured in the 3D-printed mold; then agarose is cast in the cured PDMS negatives. Cells are seeded into the resulting agarose wells where they aggregate into tissue rings.

Engineered tissues are being used clinically for tissue repair and replacement, and are being developed as tools for drug screening and human disease ...

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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Chapters in this video

A Method for Ovarian Follicle Encapsulation and Culture in a Proteolytically Degradable 3 Dimensional System

Creating Two-Dimensional Patterned Substrates for Protein and Cell Confinement

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis

Tissue Engineering of a Human 3D in vitro Tumor Test System

Systematic Analysis of In Vitro Cell Rolling Using a Multi-well Plate Microfluidic System

Generation of a Three-dimensional Full Thickness Skin Equivalent and Automated Wounding

Production, Characterization and Potential Uses of a 3D Tissue-engineered Human Esophageal Mucosal Model

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

A Combined 3D Tissue Engineered In Vitro/In Silico Lung Tumor Model for Predicting Drug Effectiveness in Specific Mutational Backgrounds

Fabrication of Custom Agarose Wells for Cell Seeding and Tissue Ring Self-assembly Using 3D-Printed Molds