Alternative Methods to Calculating Volume

In brain research that seeks to determine the volume of an effect, such as in cerebral stroke or the volume of a feature of interest, the volume can be determined quite accurately using a number of different procedures including contemporary stereology. If such measures are done frequently then the methods of contemporary stereology embodied in different commercially available software and equipment packages can make this an efficient process. However, when stereologic resources are not readily available or this level of effort (10 or more uniformly spaced levels are required) and accuracy are not required or desired there are alternative techniques that can yield data that is an "index" of effect and provide a means of rank ordering the cases. Described below are three types of measures. The first two provide 'ball park' indices of effect while the third is more exact and comparable to stereologic results.

Method 1: Area Ratios

This method is the fastest of the three methods being presented. If it does not provide sufficient data to discriminate experimental groups then the measurements compiled may be reused and applied to the second slightly more involved volume assessment.

Step 1: Pick two to four suitably spaced coronal levels that are easily identified anatomically (e.g. one containing the anterior commissure) to be consistent across all brains.

Step 2: Measure the area involved and the total area of the section using NIH Image or other software packages.

Step 3: Calculate the ratio for each level for each case.

Step 4: From the resulting table create a rank order of ratios and determine if the experimental groups are distinguished.

Method 2: Ellipsoid Volume

If Method 1 lacked the desired rigor, then this approach may be used with the addition of just a few more measurements. Any given lesion (or area of interest that is not too irregularly shaped) has rostral-caudal limits as well as medio-lateral and dorsomedial limits. In effect then, the lesion is somewhat ellipsoidal. By obtaining measures of the long and short axes a volume can be computed.

From: http://www.fh-lueneburg.de/u1/gym03/expo/jonatur/wissen/mathe/analysis/ellipsoid.jpg	Modified from: http://www.pimath.de/geo/image/ellipsoid.gif

Ellipsoid volume = 4/3*pi*0.5H*0.5W*0.5L Where H & W are the two minor axes and L is the major (if H and W are equal, the result is a sphere).

Assumptions:

• The lesion is approximated to be ellipsoidal in shape.

Conventions:

Step 1: Calculate L: The long axis is determined from the number of slides between the beginning and end of the lesion. The number of slides multiplied by the interval between each slide (e.g. 320µ) equals the length, L.

Step 2: Calculate H: Short or minor axes:

• Two levels are chosen to be measured to obtain the two minor axes. For example, one slide on either side of the slide of the midpoint of the lesion can be measured.

• The height and width of the lesion was measured on each of the two slides. The average of the height and width was then used to determine the radius (e.g H/2) for the two minor axes.

Step 3: Use the values to calculate the ellipsoid volume.

A spreadsheet can be downloaded from our website to aid in gathering data and obtaining the calculations: www.nsalabs.com/Templates/EllipsoidCalc.xls

Method 3: Exact Volume

The more exact measure of volume calls for using an application such as NIH Image to measure the areas of interest. Eleven (or more but an odd number of) uniformly spaced measures must be made to comply with the application of Simpson's rule. More levels yields greater accuracy. A spreadsheet for data entry and auto-calculations can be downloaded: www.nsalabs.com/Documents/Templates/VolumeCalc.xls The area of the lesion in each of the eleven uniformly spaced sections is determined and entered in the spreadsheet. Simpson's rule is a power series used to approximate definite integrals as well as areas under curves. See this website for a graphic demonstration of accuracy of Simpson's rule: http://www-math.mit.edu/18.013A/HTML/chapter25/section02.html

Historical note of interest: Prior to the existence of spreadsheets, volumes could be graphically determined. On graph paper in between the established beginning (ordinate, 0,0) and end of the lesion or structure, the area of 10 uniformly spaced section levels were plotted on graph, paper. Using a planimeter (a device hardly known now) the area under the curve could be measured which translates into the volume. Without a planimeter, the curve on the graph paper could be cut out and weighed and the volume determined from the calibrated unit area of the graph paper.

NSALabs® routinely supplies researchers with the neurohistology services that yield slides ready for any of the above analysis. Additionally, the NIH Image tool and the follow-on analysis described above in Method 3 is utilized to deliver to the researcher beautiful pictorial graphs of the results of their study. Contact us today to discuss your needs and to receive a custom quote.

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