It very much depends on what cells are studying. I have been trying to determine the volume of bacteria such as E. coli and L. lactis with flow cytometry and microscopy. I can help you here if needed.

Cheers!

Dear Sundarammal and Kaspar, thank you very much for your replies. Indeed, I have developed a mathematical equation for biovolume estimation, which is more accurate than the conventional approaches based on two linear measures or on pre-determined geometrical shapes. I am not sure, however, whether it is something worthwhile or, on the contrary, useless. I am then wondering how valuable it would be for those colleagues concerned with this matter. As for the kind of cells, Kaspar, all types of (not filamentous) bacteria are ok, but also algae, protozoa and other more or less irregularly shaped organisms (and cells), as long as they have an approximate radial symmetry.

Any kind of reply is the welcome. If you do not have a definite opinion, please tell me what equation, software, or procedure you do typically employ: it will be very useful to me in order to better understand the issue and draw a conclusion.

Following the link below you will find a graph showing the %error in the volume estimation of a rod with rounded ends. It compares the "new" approach vs. the "classic" method based on two linear dimensions and the prolate spheroid volume equation.

Cheers. Alessandro.

http://alessandrosacca.altervista.org/original-methods/biovolume-estimation

Thanks for the response, Alessandro.

I have used the very simple formula of volume=pi*width^2*(length-width/3)/4 for calculating cell volume from microscopy data.

Dear Kaspar,

yes, that is the formula for a rod with rounded ends, suitable for bacillus-like bacteria. If the shape of the organism were exactly like that, the formula would work perfectly. Anyway, in my simulation I took that geometrical shape in order to calculate the exact volume (with your formula), and then I tested my formula against a more general formula, which is used, for example, for many ciliated protozoa:

4/3 π(W/2)^2 (L/2)

Well, mine worked much better, as you can see looking at the graph in my website, and I suppose that even for bacillus-like bacteria it would be more precise, as bacteria are not exactly “geometrical”.

Do you think many researchers employ the formula used by you? How many people use, instead, automated or semi-automated software? Do those software employ much different approaches? These are few of my questions.

Cheers

Alessandro

Hi Alessandro,

I can see from the graph indeed that your more general formula gives a smaller error. This is definitely good news and I will test it on my data.

I am afraid I am not the best person to answer your last questions since I am a PhD student and, hence, not an expert in this field at all. I have seen this formula being used in many articles and I used the same formula since I had no evidence which would not enable me to make the assumption that E. coli cells that they are rods with perfectly rounded ends.

I, myself, have not used any software so far, but calculated the volume from raw data.

I hope this help at least someway.

Cheers!

Dear Kaspar,

I am sorry for the misunderstanding. The one I posted is not my original formula. It is the one used to calculate the volume of a “prolate spheroid”, that is an “elongated” sphere. I think it is used in several circumstances when the cell is somewhat “ellipsoidal”, but not similar to a rod with rounded ends. Indeed, my “formula” is more complex and requires an additional input: the 2D surface area of the cell, that can be obtained through a microscope snapshot and an imaging software (there are free ones such as ImageJ). I am sure it is a fine invention, but my question is: will it be practical or modern automated or semi-automated imaging software can do better?

Cheers

Alessandro

Dear Alessandro,

In this case, I have to say that I am not competent to answer this since I have not used these kind of software for this purpose.

I advise you to contact some experts in this field. One of the people who I contacted some time ago regarding microscope analysis and got excellent help was Anders Elfwing aelf [at] ifm.liu.se. Maybe try to contact him!

Good luck!

Hi Alessandro!

Would your method be applicable to calculating the volume of a C. elegans from a single (saggital plane) image, if we can assume the transverse cross-section of the nematode is circular?

Cheers!

Zuzana

Hi, Zuzana,

yes, it's possible! Indeed the method can be employed also for plain shaped metazoa, all you need is a good picture and a software that makes certain measurements. Please let me know if you need additional information (I am completing a manuscript describing the method just now) or if you wish me to try with a sample image. Thanks for the interest.

Cheers

ALessandro

Dear Alessandro,

I attached an average image like those for which I am calculating volume of the animal. I can get a pretty good area measurement from ImageJ, but have not found a good way to calculate volume without arbitrarily choosing one point on the animal for a radius measurement. Does your method require a particular software that one would need to obtain?

Cheers,

Zuzana

Dear Zuzana,

in its original form, my method does not require any additional software besides an application which permits to make linear as well as surface measurements, such as ImageJ. I admit that while choosing a proper point for measuring the cell radius is relatively straightforward in unicellular organisms, it may be indeed arbitrary in metazoa such as Caenorabditis. Nevertheless, with my method you only have to find the maximum width of the organism (perpendicular to the symmetry axis). I am including additional information in the next post, as soon as I complete a test with your image of the nematodes.

Cheers

Alessandro

Dear Zuzana,

I have tested my method for the biovolume estimation with the picture of Caenorabtitis you sent me. Unfortunately, I forgot to ask you for the scale conversion factor, so my results are in pixels, squared pixels and cubic pixels.

I used ImageJ 1.48t and I have estimated the total length as the length of a segmented line running roughly midway along the organism (segmented line – analyze – measure), while for the width I measured what seemed to me the largest section of the nematode (straight line – analyze – measure). I know these measures are arbitrary, but I have developed only the core of a method for biovolume estimation. Exact - or at least reproducible - measurements can possibly be obtained through algorithms intended for this purpose.

Surface area estimation was somewhat more automated: after thresholding the picture, I have selected the entire organism (edit – selection – create selection) and then measured its area (analyze – measure). A critical step was represented by the image pre-treatment, for which I had to manually fill the “white holes” due to the different densities to transmitted light (see the resulting picture). Perhaps some software already exists for this purpose too.

These are my outcomes:

Length: 1023.15 pxs

Width: 52.90 pxs

Area: 4.14*10^4 squared pxs

Volume: 1.44*10^6 cubic pxs (vs. 1.50*10^6 pxs obtained with the “classic” method)

Unfortunately I can’t provide the equation I used for the biovolume estimation because I am currently writing a manuscript with a thorough assessment of the method, which will hopefully be published by the end of this year.

Please let me know your reaction and also your outcome, if you tried with an established biovolume estimation method.

Cheers

Alessandro

Dear Alessandro,

I really appreciate your help with biovolume estimation.

I am using ImageJ 1.47v, and did not fill in white spaces by hand. I used Image - Adjust - Threshold, and then Analyze - Analyze Particles to get the area (42988 sq pixels, very close to what you got). I obtained length and width using segmented and straight lines, also.

I re-did my volume calculation with your width, and area measurements instead and got 1.71x10^6 cubic pixels. I used volume(cylinder) = area*width*.25*pi. It appears that any "classic" methods over-estimate volume by using a single width measurement and not being able to account for tapering-off. Using area instead of working entirely from length and width accounts for some tapering, because volume(cylinder)=length*width^2*.25*pi over-estimates the volume further (2.24x10^6 cubic pixels in this example).

Does your model "look at" the image to determine how much taper to account for, or is this a user-input of some sort? I would be really interested in reading your paper once you publish it.

Cheers,

Zuzana

Dear Zuzana,

thanks for your interest in my work. Indeed I think I have developed an interesting method for the biovolume estimation of simple shaped organisms, which probably needs to be coupled with an image pre-processing stage, either manual or automated. With this regard, I tried to use the function “Analyze Particles”, as you suggested, and it worked fine, although I had to close the outline manually in a few points (pencil tool) after the thresholding step, otherwise certain “white spaces” would have not been computed in the surface area.

The “classic” method I employed for comparison was indeed one which calculates the volume of a “prolate spheroid”, whose three radii are respectively: half length, half maximum width and again half maximum width. The equation is: V=1/6*pi*length*width^2. The latter actually accounts for the shape tapering-off and hence gives smaller results than the equation based on the area of a cylinder. In truth, I think that the shape of the nematode is more similar to a spheroid than to a cylinder because its sagittal section resembles more an ellipse rather than a rectangle, and even considering the actual surface area, as you did, reduces only in part the overestimation.

My model, though simple, is even more precise and performs well with a variety of shapes, as I am going to demonstrate with my manuscript - and it does only “look at” the image, without any sort of user-input. For example, if I use it to estimate the volume of a cone or of a cylinder, I get errors respectively of 1.59% and 4.22%, while with the equation of the prolate spheroid the errors are respectively of 100% and 33.33%.

Cheers

Alessandro

Dear Alessandro,

Thank you so much for taking the time to explain the different methods for estimating biovolume from images and for running your model on the nematode image. I will be interested to read your paper.

I just found out about a tool made specifically for nematodes that automatically measures the length and several width measurements to obtain a rotational volume by integration. It is called WormSizer: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0057142

WormSizer has been working pretty well for me this past week, although it misses some worms and all embryos without having a way to force recognition of an object (that I know of). Also I do not know how well it could work for embryos, so I still need a second method for estimating their volume, but at least I can get larval and adult nematode volumes now.

Cheers,

Zuzana

Dear Zuzana,

it was an interesting discussion for me too. Thank you very much for the new information, I am checking the tool as soon as I can.

Cheers

Alessandro

Hi Zuzana,

I checked WormSizer. It seems quite a powerful tool for detecting and measuring wormlike organisms, yet it is not suitable for non-elongated shapes.

Meanwhile, I have found YABBA, a software designed for bacteria, but working fine also with protozoa. I tried it with your Caenorabditis image and it failed, but perhaps it is good for nematode embryos, provided that the source image is appropriate for the algorithm, i.e. inverted image, few or no “holes” etc. In fact, I have found that YABBA works better with inverted images, probably because it is designed for bacteria viewed through epifluorescence microscopy.

The YABBA software can be downloaded here: http://www.technobiology.ch/index.php?id=software

I hope it will be helpful

Cheers

Alessandro

Hi Emanuele,

I am glad for your interest in my finding. In truth, I am delaying the submission of a manuscript because I am not sure of what is the best thing to do with my method. For this reason, I don’t have a preprint yet, but only a manuscript draft.

The idea behind it is simple: while the former methods employed fixed geometrical equations (inaccurate) and the recently developed algorithms seek to follow as precisely as possible the cell outline (complicated), I use somehow a “fuzzy” geometrical approach, which is both simple and accurate.

Cheers

Alessandro

Hi Emanuele,

I must hilight here a limitation of my method: it assumes that the cell has approximate radial symmetry, hence it is suitable especially for microorganisms. That said, if you are still interested, we may continue this discussion privately.

Best

Alessandro

Hi everybody interested in this question, please follow the link below if you want to read my paper regarding a simple, yet accurate method for the estimation of microbial cell biovolume. Glad for your interest.

Alessandro 

Article A Simple yet Accurate Method for the Estimation of the Biovo...