Calculating irradiance depth
After some sleuthing, I found that Diesseroth based his calculator off a paper from 2007 by Aravanis1. It predicts the spread of light through tissue based on two major factors:
- Geometric spread – how much the light spreads out the end of the fibre, which for the multimode fibres used for in vivo opto’s will be mainly determined by the NA
- Tissue scatter – light absorption and scatter by the (brain) tissue the light is penetrating
Here is the relevant section from the paper:
The important equation is the bottom one, which calculates the irradiance (I) at distance (z), relative to the starting irradiance. The user can therefore input optical power (I at z=0), threshold irradiance (I at z), fibre radius (r) and numerical aperture (NA).
Apart from that, there are two more variables that are determined by experiment: the index of refraction of the tissue (n) and the scatter coefficient (S). I have used the same values as Aravanis, which are based on mouse brain grey matter.
Scattering of different wavelengths
A quick note on wavelengths of light. The astute among you will likely have noticed that my depth calculator does not allow you to pick the wavelength of light to use in the calculator, whereas Diesseroth’s does. The reason for this is that wavelength has little impact on the scattering of light in the visible range (Figure 1).
In fact, by far the biggest impact on predicted scattering comes from the difference between white and grey matter, or even who did the measurements! Which bring me to the caveats for using my depth calculator:
- It is an estimate predictor of optogenetics irradiance depth, so take the output values as a guide rather than absolute truth
- The calculator assumes you are targeting grey matter, so if you place your fibres in denser white matter regions (such as the brainstem), the predictions will no longer be accurate.
Despite the caveats, I do believe my depth calculator tool is useful, and hopefully people will find it easier to decipher than Karl Diesseroth’s.
1. Aravanis et al. J Neural Eng 4, S143-S156 (2007) An optical neural interface: in vivo control of rodent motor cortex with integrated fiberoptic and optogenetic technology
2. Yaroslavsky et al. Phys Med Biol 47, 2059 (2002) Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range