The hyperbolic arcsine (arcsinh) is a function used in Cytobank for transforming data. It serves a similar purpose as transformation functions such as biexponential, logicle, hyperlog, etc.
One principle reason for using these equations to transform data is that flow cytometry data are traditionally displayed on a log scale. On older instruments, data would only be exported with positive numbers and scaled by base 10 log. However, data from newer digital machines (e.g. LSRII) can have negative numbers. Our current mathematical laws don't allow taking the log of a negative number, so different transforms are used that can accommodate negative numbers while also displaying data in a log-like fashion.
Another feature of current transformation equations is that they can be tweaked by user-controlled settings to behave differently for regions around zero. For arcsinh scales, this user-controlled setting is called the scale argument. For data values on either side of zero to the magnitude of the scale argument, data are displayed in an linear-like fashion tracking with the raw data values. For values beyond the scale argument, data are displayed in a log-like fashion.
Arcsinh values are calculated by applying the arcsinh equation divided by the scale argument to the measured intensity value. The scale argument defines the size of the linear region around 0. You can adjust the values for this in Cytobank by using the Scale Editor. You can get the same answer in Excel by taking an intensity value and using the function ASINH. The syntax is "=ASINH(value/cofactor)".
For more reading on setting scales, check out our blog post on making beautiful plots.