Living Image 3.1

G. Planar Spectral Imaging
Figure G.1 Optical Properties of Mouse Tissue and Firefly Luciferase Spectra
The bioluminescent signal from firefly luciferase (right) is emitted from wavelengths of 500-700 nm, which spans a region of
the spectrum where there are major contrasts in the optical properties of mouse tissue (left). The firefly spectrum was
measured at 37°C using PC3M cells.
Diffusion Model of
Light Propagation
Through Tissue
226
Light propagating through tissue undergoes scattering and absorption. The diffusion
model assumes that scattering is the predominant phenomenon and the reduced scattering
coefficient µ' s >> absorption coefficient µ a. This is valid mostly for wavelengths in the red
and near infrared part of the spectrum. The model also assumes that the light is produced
by a single point source and that the tissues are optically homogeneous.
Under these conditions, if we model the animal surface as flat and infinite in extent and
integrate the light that is collected over the animal surface, the total integrated intensity
I(λ) is reduced to a relatively simple expression:
I(λ) = SK(λ) exp(-μ eff d) (1)
where S is the absolute total photon flux emitted by the bioluminescent source and d is the
source depth.
The term µ eff is the effective attenuation coefficient. It is determined by the tissue
coefficient of absorption (µ a ) and reduced scattering (µ' s ) that quantify the two main
phenomena light undergoes in tissue.
The function K(λ) is a more complex expression that is derived from the model and
includes terms that describe the effect of the tissue-air boundary on the light propagation.
Both µ eff and the function K are dependent on the wavelength, λ.
Equation 1 shows that if the total integrated intensity (ROI measurement) is measured at
several wavelengths, it is proportional to an exponential function of the product of the
depth and the optical property, µ eff . Therefore, the steps to planar spectral image analysis
include:
• Acquire two or more images at different wavelengths.
• Measure the total integrated intensity on each image.
• Fit the measured values to the exponential function of Equation 1.