Background subtraction in calcium imaging

"For analysis of calcium transients, the fluorescence background was subtracted from the fluorescence intensity averaged over the line" -- XXX et al., XXXX, 2005

2-photon calcium imaging became popular as a tool to quantify calcium signaling in neurons. In a lot of papers published, fluorescence signal is subtracted by surrouding background fluorescence. However, generally this is a WRONG idea.

----Quote from Yasuda et al., 2004 Science STKE ------
Relating fluorescence and [Ca²⁺] requires subtraction of background from the fluorescence signal. Because neuronal compartments such as spines and boutons are typically smaller than the excitation volume of 2PLSM, the background calculation is complicated. Background fluorescence is commonly estimated by measuring fluorescence far from the spine, F_B. ΔF/F_o is defined by Eq. 12, where F and F_{o, raw} are the raw fluorescence signals during the response and baseline periods.

ΔF/F_o = (F-F_o,raw)/(F_o,raw - F_B)) (Eq.12)

Because the spine volume is smaller than the excitation volume, F, F_o,raw, F_raw, and F_B can be expressed by Eq. 13, where V_sp and V_ex are the spine volume and the excitation volume outside the compartment, b_sp and b_ex are background fluorescence intensities inside and outside the compartment per unit volume, respectively, and f_o and f are the fluorescence intensities from fluorophore in the compartment per unit volume before and after the stimulation.

F = (f+b_sp)V_sp + b_exV_ex
F_{o, raw} = (f_o + b_sp)V_sp+b_exV_ex
F_B=b_ex (V_sp + V_ex)

Because the excitation volume is V_sp+ V_ex, F/F_o is defined by Eq. 14.

ΔF/F_o = (f-f_o)/(f_o-(b_ex-b_sp)) (Eq.14)

Therefore, this type of background subtraction gives the correct value only if b_sp = b_ex, that is, if background is exactly the same inside and outside spine. Unfortunately, this is rarely the case. Under some conditions, depending on the excitation wavelength, spatially heterogeneous background fluorescence is excited. More importantly, it is often the case that small quantities of indicator spilled in the extracellular space during patching produce substantial background fluorescence in the brain slice. In this case, background subtraction always results in an underestimate of F_o and a resulting overestimate of F/F_o. Moreover, this error depends on the size of the compartment; it is larger for smaller compartments. In our view, quantitative measurements demand conditions in which the background is not significantly different from the dark noise of the PMT. If background fluorescence is higher than the dark noise of the PMT, the data are severely compromised for analysis of the amplitudes and time-courses of transient changes in [Ca²⁺].