Diffusion of a drug in skin (multiphasic material)

[Dimitris Samaras]

Hello!
I am trying to model the diffusion of a drug (for instance DXM) on a 2 layer skin. At first I'm working on a single layer of skin and I used all the boundaries conditions which you suggested on https://forums.febio.org/forum/febio...rged-diffusion. But the program couldn't run. Why is that? I assigned the prescribed concentration on top of the cube. Do you have any other suggestions for me in order to make my model more reliable and more realistic? I attach to you my model in order to see it and make any suggestions/changes/corrections.
Thank you a lot in advance

[ateshian]

Hi,

The file you attached is a binary file, not a text file (as .feb files should be). Can you please upload the correct file?

Best,

Gerard

[maas]

It looks like this is actually an fsm file. If I change the extension to fsm, FEBio Studio seems to load the file fine.

Best,

Steve

[Dimitris Samaras]

Yes it's an fsm file, but I wasn't able to upload it, that's why I sent to you a .feb file

[ateshian]

Hi Dimitris,

1. Since you are running a diffusion problem by prescribing concentration on one of the faces of this cube, I recommend that you use a biased mesh in the direction normal to that face. That's because diffusion problems exhibit narrow boundary layers in the early time response of diffusion. If your mesh is too coarse relative to the thickness of this boundary layer, the analysis will not converge.
2. Since you followed the recommendations for performing a pure diffusion analysis using a multiphasic mixture (i.e. fixing displacement and effective fluid pressure DOFs), I recommend that you set the convergence tolerances to zero for these degrees of freedom, so let dtol=ptol=etol=0, and only keep a non-zero ctol (for the concentration degrees of freedom).
3. Since you have prescribed the concentration on one face of the cube, you cannot also prescribe zero molar flux on the same face. These are contradictory boundary conditions, so please delete that molar flux load from your model.

By making these changes I was able to get your model to run.

Best,

Gerard

[Dimitris Samaras]

Profesor Ateshian,
Thank you a lot for your guiding information. I would like to ask you how should I make my mesh more biased? Which geometries should I use? and with what properties.
I am so sorry for wasting your time, but I'm trying to do my best for my MSc Thesis, and I am a kind of lost.
Thank you in advance

[ateshian]

Hi Dimitris,

When you create the cube geometry in FEBioStudio and meshed it, there was an option to specify X-bias, Y-bias and Z-bias. In your case you can use the Z-bias value (pick a number greater than 1 to make the mesh become coarser as Z increases, e.g., use Z-bias=1.5 with Nz=10).

Best,

Gerard

[Dimitris Samaras]

Thank you. I'll try everything you said and if I come up with any difficulties I'll reach back to you.

[Dimitris Samaras]

Hello again,

I wish you are doing well and also having a wonderful time on your holidays.
I came up with a different approach regarding to my model. This time I'm trying a more precise contact with the cube. My goal at the beginning is to apply the boundary condition of prescribed effective concentration in only 4 nodes, in order to simulate the injection of the drug locally and not on the whole surface as before. Therefore at t = 0 we want the concentration of the drug at that point to be 0 (on the surface of the cube- surface of the skin). Then, we want the drug to diffuse throughout the cube (as is the case with the skin after injecting a drug). What should I change concerning the boundary conditions, time steps, and properties of the model? I attach you my current model at this time. (.fsm)

Thank you very much and I wish you a happy new year.

[ateshian]

Hi Dimitris,

Modeling drug injection in a tissue can be challenging, depending on what you want to learn from the model. It will be hard for me to give you meaningful advice unless you give me a more general sense of the purpose of your model. For example, are you trying to figure out how far the drug will diffuse in a tissue over a given period of time? Or are you trying to figure out the influence of drug concentration on transport? Do you need to know how much volume of drug must be injected for a specific purpose? Or how much pressure needs to be prescribed to inject the drug in a specific tissue? Do you expect that the drug will flow into capillaries and be transported by blood? There are many questions that need to be clarified in order for me to tell you what FEBio can do (or not do) and how to do it. If you need fundamental background information on mass transport in biological tissues, I suggest that you look up this book.

Best,

Gerard

[Dimitris Samaras]

Hello again,

I took into consideration what you told me during our last communication and I came up to the following:
First of all, I was interested in the effect of concentration on how the drug diffuses. That is, at a high concentration the drug diffuses more easily than at a lower concentration. Therefore, in the first phase, I would like to simulate this phenomenon in which we are not interested in either the volume of the drug or the pressure exerted.
Also, note that the study focuses initially on the first layer of the skin, and then can be extended to 2 layers, which means that the geometry used will be a cube that will resemble the first layer of the skin.
Finally, I would like your help in injecting the drug. I would like to study the injection both on the entire upper surface of the cube and also locally as when the needle enters the skin.

Thank you very much in advance,

Dimitris

[Dimitris Samaras]

Hello again,

So far I have reached to this point. I attached my .feb model. Any suggestions?

[ateshian]

Hi Dimitris,

I haven't looked at your model but here are my suggestions for your previous response:

- When you perform a diffusion analysis and prescribe a solute concentration at a surface, the mesh of the material through which the solute will diffuse needs to be biased such that you have thin elements right underneath the surface where the concentration is prescribed, while the mesh can become coarser further away from the surface. So make sure to create a biased mesh to analyze solute transport. For example, if the face on which you want to prescribe the concentration is in the XY-plane, the mesh needs to be biased along the Z-direction.

- You need to have a fundamental understanding of mass transport in porous media to determine what size mesh and what time increments to use in an analysis. If the solute diffusivity is D, and if the characteristic dimension of the domain through which the solute will transport is L, then the characteristic time for the transport is going to be on the order of T ~ L^2/D. That means that your time increments must start out much smaller than T, e.g., dt~T/100 or dt~T/1000 initially, then they can increase to roughly T/10 as the transport reaches steady state. Then it follows that your biased mesh should have its thinnest element (right underneath the boundary surface where the concentration is prescribed) to have a characteristic size dL ~ sqrt(D dt).

- If you want to prescribe the concentration on a small region representing the needle insertion, you need to have a highly refined mesh in the XY-plane at that location, which can become coarser as you move away radially in the XY-plane. This means that your mesh needs to be biased both in the XY-plane and along the Z-direction. It may be easier to do this with a cylindrical geometry rather than a cubic geometry, but either way is doable (as long as you have suitable software to create biased meshes as desired).

If your mesh is very coarse (such as the very first model you shared with us), it would be inappropriate to apply the desired concentration at just four nodes while expecting to get accurate results. Your results will be very dependent on the mesh size, which is not going to be acceptable to you. Once you have created the desired mesh and imported it in FEBioStudio, you may need to partition the surface on which you will prescribe the concentration, such as the small circular region simulating the needle injection (check the Mesh tab and Partition tool).

Best,

Gerard

[Dimitris Samaras]

Hello again,

I'm sorry for wasting your time with all these question, but your advice is vital.
How can I prescribe the concentration going downwards on the z-axis, with maximum concentration on the top surface of the cube and minimum at the bottom of the cube. As time goes, I would like the concentration to be reduced smoothly downwards. Something like your post "How to perform a simple solute transport analysis using a multiphasic material" but in my case with a cube.

Thank you very much,

Dimitris

[Dimitris Samaras]

Hello,

At this point, I am trying to solve a diffusion problem between two multiphasic materials. I would like my solute to be diffused from the top cube to the bottom cube as time goes, but my model don't converge. What am I doing wrong? I'm attaching my .feb model to take a look. I think that I am doing something wrong to the curve editor. What's your opinion?

Thank you very much,

Dimitris