Predicted irradiance values
- For blue light, you can also use this Excel spreadsheet to calculate the intensity loss for blue light away from the fiber end (based on ).
Measurements and Theoretical Calculations
Aravanis et al. J. Neural Eng. 4 (2007) S143–S156
Aravanis et al.  cut acute brain slices (rat and mouse cortex) of thickness 200 μm-1 mm. The slices were placed in a Petri dish over the photodetector of a power meter (ThorLabs; S130A). The tip of a 200 μm diameter optical fiber (BFL37–200; Thorlabs) coupled to a blue diode-pumped solid-state laser (473 nm, CrystaLaser) was mounted on a micromanipulator and positioned over the slice perpandicularly. The fiber tip was submerged into the solution and moved to 1 mm above the slice surface. The transmission fraction was calculated as the power with tissue present divided by the power with no tissue present. The total transmitted light power was reduced by 50% after passing through a 100 μm slice, and by 90% through a 1 mm slice (Fig. 3b). Similar results were obtained in rat and mouse tissue, and both datasets corresponded very well with the Kubelka–Munk model for diffuse scattering media, with best fit values for S of 11.2 mm−1 for mouse and 10.3 mm−1 for rat (S: scatter coefficient per unit thickness, see details below).
The amount of light transmitted through a slice of brain tissue is dependent on 1) light scattering inside the slice, 2) light absorption by the tissue, and on 3) the conical spreading of light after it exits the optical fiber ("Geometric decrease"). This can be formalized using the Kubelka-Munk theory of light propagation in scattering and absorptive media.
- Diffuse reflection on Wikipedia.
- The Kubelka-Munk Theory of Reflectance.
- Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media.
and r = radius of the optical fiber; NA = numerical aperture of the optical fiber; n = refractive index of the tissue (1.36 for gray matter).
Total decrease in intensity
The total decrease in intensity takes into account both the geometric loss and the scattering.
where S is the scatter coefficient per unit thickness (z). S = 11.2 mm-1 for mouse and 10.3 mm-1 for rats .
Yizhar et al., Neuron 71, 9-34
The team of K. Deisseroth has repeated its measurements using a slightly different method: an optical fiber was inserted into a block of fresh (unfixed) brain tissue and optical power (i.e. intensity) was measured on the underside of the block. Light transmission was assessed for a range of tissue thickness by stepping the fibre through the block. These measurements were used to elaborate a mathematical model of light propagation in brain tissue taking into account light absorption, sattering and geometric dispersion, using the formalism of Kubelka–Munk (like in ). The model predicts the power density (in mW/mm2, i.e. irradiance) at any given distance from the fiber tip (see http://www.stanford.edu/group/dlab/cgi-bin/graph/chart.php for an online calculator of irradiance). To resolve the 3D extension of light intensity below the fiber tip, the two-dimensional pattern of illumination at the bottom of the block of tissue was imaged for various fiber depth by placing the block on a thin diffusive film. The same method was used to assess the pattern of light propagation in saline (the fiber was immersed in saline at various distances from the film). The reconstructed 3D intensity patterns shows that light propagation in the brain in more bulky (more symmetrical and less oriented) than in saline.
Huber et al., Nature 451, 61-64
The Svoboda Lab has explicitly measured the transmission of light through mouse cortex (Huber et al., 2008) by cutting coronal brain slices, mounting an LED over an artificial craniotomy, and imaging the surface of the tissue. They found that the light intensity profile approximately 250 microns beneath the cortical surface (red line) is significantly wider than the intensity profile at the surface (blue line), due to light scatter. Still, the light was relatively well-localized, dropping to 10% of the maximum about 2 mm away from the center of the LED. Electrophysiological experiments showed that ChR2-positive dendrites are much more excitable than axons, at least for the diffuse illumination provided by LEDs. Thus, the majority of light-driven activity presumably occurred local to the light stimulation, rather than in cells with axons passing through the illuminated area.
The following methods are described in the supplementary material:
- Absolute light intensity calibrated using a power meter (Coherent Fieldmaster, with an LM-2 VIS)
- Light profile 500 microns from the LED measured with a Dataray WinCamD
- Brain surface imaged with a Qimaging QICAM cooled CCD camera
The Boyden Lab  has performed Monte Carlo simulations of how blue (left) and yellow (right) photons emitted by LEDs travel through the brain. The images depict a slice through a simulated 4 x 4 x 4 mm cube of neural tissue. Beyond the boundaries of a cube with sides of approximately 1 mm, light intensity drops to below 1% of the maximum.
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