Answers.Body: <p>The next step depends heavily on what your question is. Some general ideas, not specific to tumor particle penetration.</p>
  <ol>
  <li><p>Your current visualization seems OK to me, if you want to make some features more obvious you can try density estimation.</p>
  </li>
  <li><p>If you have a generative model (for example you believe this is a mixture of a &quot;shallow&quot; and &quot;deep&quot; Gaussian distribution, or you have reason to believe the particles follow an exponential distribution), you can fit your data to this distribution and estimate its parameters.</p>
  </li>
  <li><p>If you want to compare conditions without too strong assumptions on the distributions, you could compute the cumulative distribution of the particles. There are statistical approaches to compare such curves.</p>
  </li>
  <li><p>To compare conditions, you might even be able to come up with a simpler metric, for example &quot;total fluorescence in the core of the spheroid&quot; normalized by &quot;total fluorescence in its periphery&quot;.</p>
  </li>
  </ol>
  <p>Ultimately it all depends on your research question (are there treatments to compare to each others, biological replicates whose consistency you want to check, known structure within the tumor spheroid, a time course, ...). My suggestions above would be easier to implement in R/Matlab/Python than pure ImageJ.</p>
  
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Answers.Text: I want to compute the cumulative distribution of the particles. But I don't know how to do this with a z-stack as the distribution across z-direction will not be the same as in x and y-directions. I also don't have any knowledge of programming, that's why I was wondering if anyone knows a guide or course that can help in this regard. I did find a matlab script, but I get the same errors and I asked several people to help me with that and we didn't manage to solve it.
Answers.UserDisplayName: Timi
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Answers.UserDisplayName: Alexlok
Answers.Body: <p>I am not sure if this is exactly what you're looking for, but I was able to find <a href="https://github.com/yakavetsiv/distribution-macro" rel="nofollow noreferrer">this ImageJ script</a> that estimates a penetration profile in tumor spheroids.</p>
  <p>I am not an ImageJ person but I suspect that with some minimal changes this could be used to answer your question.</p>
  
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Answers.Text: This is actually what I was using to determine the intensity profile of my particles. However, I am not sure what to do next, because I have the intensity profile of a spheroid over z-axis and don't know how to put the information together or to visually represent the quantification of the penetration profile.
Answers.UserDisplayName: Timi
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Answers.Text: @Timi thanks for clarification. Can you post what your data look like (just a snippet is probably enough)? That might be something we can help with.
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Answers.Text: I added a screenshot of how to profile intensities look across a z-stack (1st image) and how the average profile intensity looks like in the last 5 focal planes in the z-stack. This is what we are aiming to get. 
  The papers that I found that do something similar are: https://www.sciencedirect.com/science/article/pii/S0168365921006672
  https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7824314/
  , but they also don't go into details, and the script in Matlab is not working for me.
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Answers.Text: @Timi Can you show the original raw data (text, not plots) output of the imagej protocol, rather than plotted summaries? As in, what is the data that you used to make those plots. It seems that you want to make better or more informative plots similar to some that you are seeing in those papers (which figures? maybe include them in the question). Just a subset of the data is fine, to show what the format is, or even faked data that is in the same format if you don't feel comfortable posting raw data. I don't see the matlab script you are talking about, a direct link might help.
Answers.UserDisplayName: Maximilian Press
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Answers.Text: I don't know how to attach a table to this post. Would it be possible to send you an Excel sheet in an email or private message?
Answers.UserDisplayName: Timi
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Answers.Text: @Timi What I'd suggest doing is using [table markdown](https://meta.stackoverflow.com/questions/302471/how-to-put-tables-in-stack-overflow) or similar to embed a table in your question. There are [web converters](https://tabletomarkdown.com/convert-spreadsheet-to-markdown/) for converting spreadsheet to markdown. Alternately you could use a google drive link, [pastebin](https://pastebin.com/), dropbox, box, etc. In each case I'd suggest embedding the link directly in your question so that anyone who needs to can look at it.
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Answers.UserDisplayName: Maximilian Press
Body: <p><a href="https://i.sstatic.net/bf0BC.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bf0BC.png" alt="enter image description here" /></a>0</p>
  <p>I have to establish the penetration profile of particles in tumour spheroids.</p>
  <p>For this I have spheroids composed of cells which were exposed to particles, both of which are fluorescently labeled. The spheroids were then imaged using a confocal microscope by taking z-stacks of all spheroids. For analysis, I determined the intensity profile of each focal plane using an ImageJ plugin, namely &quot;distribution_shapes&quot;.</p>
  <p>What should be done next?</p>
  <p>I currently did not find any step-by-step guide for this analysis for manual assessment and any type of help would be greatly appreciated.</p>
  <p><a href="https://i.sstatic.net/uzcq2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/uzcq2.png" alt="enter image description here" /></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-09-07T23:48:50.403Z
Comments.Text: This looks like an interesting image analysis question, which is great because we don't get as many of those here. Could you be more specific about what you mean by "penetration profile"? Can you point to any publications that use a similar analysis? I find one possibly related paper [here](https://opg.optica.org/boe/fulltext.cfm?uri=boe-12-10-6545&id=459855) but they don't go into any detail unfortunately.
Comments.UserDisplayName: Maximilian Press
Tags: <3d-structure>
Title: How to analyse qualitatively the penetration ability of particles in spheroids using fluorescent z-stacks?
ThreadText: # How to analyse qualitatively the penetration ability of particles in spheroids using fluorescent z-stacks?
  
  (Asked by: username_0 on 2023-09-04)
  
  [![enter image description here](https://i.sstatic.net/bf0BC.png)](https://i.sstatic.net/bf0BC.png)0
  
  I have to establish the penetration profile of particles in tumour spheroids.
  
  For this I have spheroids composed of cells which were exposed to particles, both of which are fluorescently labeled. The spheroids were then imaged using a confocal microscope by taking z-stacks of all spheroids. For analysis, I determined the intensity profile of each focal plane using an ImageJ plugin, namely "distribution\_shapes".
  
  What should be done next?
  
  I currently did not find any step-by-step guide for this analysis for manual assessment and any type of help would be greatly appreciated.
  
  [![enter image description here](https://i.sstatic.net/uzcq2.png)](https://i.sstatic.net/uzcq2.png)
  
  **Tags:** 3d-structure
  
  > **Comments:**
  > **username_1**: This looks like an interesting image analysis question, which is great because we don't get as many of those here. Could you be more specific about what you mean by "penetration profile"? Can you point to any publications that use a similar analysis? I find one possibly related paper [here](https://opg.optica.org/boe/fulltext.cfm?uri=boe-12-10-6545&id=459855) but they don't go into any detail unfortunately.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2023-11-02. Score: 1
  
  The next step depends heavily on what your question is. Some general ideas, not specific to tumor particle penetration.
  
  1. Your current visualization seems OK to me, if you want to make some features more obvious you can try density estimation.
  2. If you have a generative model (for example you believe this is a mixture of a "shallow" and "deep" Gaussian distribution, or you have reason to believe the particles follow an exponential distribution), you can fit your data to this distribution and estimate its parameters.
  3. If you want to compare conditions without too strong assumptions on the distributions, you could compute the cumulative distribution of the particles. There are statistical approaches to compare such curves.
  4. To compare conditions, you might even be able to come up with a simpler metric, for example "total fluorescence in the core of the spheroid" normalized by "total fluorescence in its periphery".
  
  Ultimately it all depends on your research question (are there treatments to compare to each others, biological replicates whose consistency you want to check, known structure within the tumor spheroid, a time course, ...). My suggestions above would be easier to implement in R/Matlab/Python than pure ImageJ.
  
  > **Comments:**
  > **username_0**: I want to compute the cumulative distribution of the particles. But I don't know how to do this with a z-stack as the distribution across z-direction will not be the same as in x and y-directions. I also don't have any knowledge of programming, that's why I was wondering if anyone knows a guide or course that can help in this regard. I did find a matlab script, but I get the same errors and I asked several people to help me with that and we didn't manage to solve it.  
  
  ---
  
  ### Answer by username_1 on 2023-09-07. Score: 1
  
  I am not sure if this is exactly what you're looking for, but I was able to find [this ImageJ script](https://github.com/yakavetsiv/distribution-macro) that estimates a penetration profile in tumor spheroids.
  
  I am not an ImageJ person but I suspect that with some minimal changes this could be used to answer your question.
  
  > **Comments:**
  > **username_0**: This is actually what I was using to determine the intensity profile of my particles. However, I am not sure what to do next, because I have the intensity profile of a spheroid over z-axis and don't know how to put the information together or to visually represent the quantification of the penetration profile.  
  > **username_1**: @username_0 thanks for clarification. Can you post what your data look like (just a snippet is probably enough)? That might be something we can help with.  
  > **username_0**: I added a screenshot of how to profile intensities look across a z-stack (1st image) and how the average profile intensity looks like in the last 5 focal planes in the z-stack. This is what we are aiming to get.  The papers that I found that do something similar are: https://www.sciencedirect.com/science/article/pii/S0168365921006672 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7824314/ , but they also don't go into details, and the script in Matlab is not working for me.  
  > **username_1**: @username_0 Can you show the original raw data (text, not plots) output of the imagej protocol, rather than plotted summaries? As in, what is the data that you used to make those plots. It seems that you want to make better or more informative plots similar to some that you are seeing in those papers (which figures? maybe include them in the question). Just a subset of the data is fine, to show what the format is, or even faked data that is in the same format if you don't feel comfortable posting raw data. I don't see the matlab script you are talking about, a direct link might help.  
  > **username_0**: I don't know how to attach a table to this post. Would it be possible to send you an Excel sheet in an email or private message?  
  > **username_1**: @username_0 What I'd suggest doing is using [table markdown](https://meta.stackoverflow.com/questions/302471/how-to-put-tables-in-stack-overflow) or similar to embed a table in your question. There are [web converters](https://tabletomarkdown.com/convert-spreadsheet-to-markdown/) for converting spreadsheet to markdown. Alternately you could use a google drive link, [pastebin](https://pastebin.com/), dropbox, box, etc. In each case I'd suggest embedding the link directly in your question so that anyone who needs to can look at it.  
  
  ---
  
  