Derived Measurements

Suppose you've measured the area of each nucleus and, with a second engine, the area of its cytoplasm. Neither number is the size of the cell. Their sum is, and that is the first example in the Engines Reference: a derived measurement called Total Cell Area, built from the nucleus and cytoplasm areas.

Derived Measurements sits under the layer's Measurements, Add Measurements (advanced). It generates new measurements from existing ones using basic arithmetic, in two combinations: measurement and measurement, or measurement and a user-defined value. Its controls manage a list: New defines a derived measurement, Edit changes one, Remove deletes one and Remove All clears them all.

The second example converts units. Event distances are usually computed in pixels, and multiplying by the pixel size gives micrometers. You can find or edit the pixel size in the FOV Size window, in the project's Properties list in the Main Window.

The reference doesn't list the operators by name; its examples use addition and multiplication. It describes no functions such as log or square root and no formulas of more than two terms, and it doesn't say whether one derived measurement can feed another. For arithmetic on images pixel by pixel, rather than on measurements, use the Arithmetic operationsLoading... of the Basic Operations Module. The Statistics Report's Derived Statistics do the same kind of arithmetic one level up, on whole-sample statistics.

Source: StrataQuest 8.1 Engines Reference, ch. 13 (pp. 403–404), ch. 6.1 (p. 22); User Manual (p. 234).

Arithmetic as signal combination. In image processing generally, subtraction reveals differences and division normalizes. The same operations applied to per-cell numbers rather than pixels do the same jobs. A difference between a marker's nuclear and cytoplasmic intensity can show where it sits in the cell, and a ratio can strip out what two measurements share.

Ratios, a lesson from fluorescence. Ratiometric dyes for calcium and pH are read at two wavelengths, and the ratio doesn't depend on how much dye a cell took up. The same logic applies to two markers in one cell: whatever scales both signals equally, such as section thickness or illumination, largely cancels. What it can't cancel is anything that affects one marker and not the other, such as a stain that penetrates unevenly.

Watch the units. Converting a distance from pixels to micrometers takes one multiplication by the pixel size. An area scales with the square of length, so converting it takes the pixel size squared: multiply by a value you've squared yourself. Get this wrong and the numbers look plausible while being off by a factor of the pixel size.

Small denominators. Dividing by a value near zero produces extreme outliers. If the denominator can get very small, as a marker does in cells that barely express it, the ratio becomes unstable. In ratiometric work generally, the remedies are to add a small constant to the denominator, or to exclude cells whose denominator falls below a minimum before reading the ratio.

Here is a per-nucleus HER2/CEP17 ratio from FISH, built from documented engines.

1. Detect nuclei, then detect HER2 dots and CEP17 dots with Dots (FISH/CISH)Loading....
2. Add Dot MeasurementsLoading... twice, once per probe, each reporting Dots Count for every nucleus.
3. In Derived Measurements, click New and divide the HER2 Dots Count by the CEP17 Dots Count.
4. Plot the new measurement on a histogram and place a cutoffLoading... to find nuclei above a chosen ratio.

Two cautions. A nucleus with no CEP17 dots gives a zero denominator, and the reference doesn't say what the engine returns then, so exclude those nuclei with a gate before reading the ratio. And the published HER2 scoring convention averages counts over many nuclei before dividing; a per-nucleus ratio shows which cells drive that result.