Living Image 3.1

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H. 3D Reconstruction of Light Sources Finding the Best Approximate Solution to the Linear System 236 The reconstruction method is based on the principle that there is an approximately linear relationship between the source strength in each voxel (Si ) and the photon density (ρj ) at each surface element described by a Green’s function Gij . The photon density at the jth surface element is the sum of the contributions from all the voxels: ρj ≅ ∑G ijSi (1) i The Green's function contains information about the transport of photons through the tissue and the effects of the tissue-air boundary. By using a planar boundary approximation, the Green's function can be calculated analytically as a solution to the diffusion equation. Having an analytic expression for G allows Equation 1 to be computed very rapidly. Once the Green's functions, G ij , are known, the goal is to solve Equation 1 for the source strength S i in each voxel. The DLIT algorithm attempts to minimize χ 2 (Equation 2) while requiring that the source strength in each voxel is positive (Equation 3). χ ∑---- 2 σj ρ = j – Gij 2 1 j Si ≥ 0 ∑ S i A combination of methods called Simplex and Non-Negative Least Squares are used to find the approximate solution which minimizes χ 2. In order to reduce the number of variables in the problem, the code only uses surface elements with signal above a certain threshold (minimum radiance) and only keeps the voxels that contribute significantly to these surface elements. i 2 (2) (3)
<strong>Living</strong> <strong>Image</strong> ® Software User’s Manual Source & Tissue Properties DLIT analysis of spectrally filtered images requires knowledge of the spectral dependence of bioluminescent light emission. Table H.1 shows the factory set source spectra provided by the software. NOTE The source spectra is not an input to the 3D reconstruction of fluorescent sources. Select a bioluminescent source spectrum. Figure H.4 DLIT 3D reconstruction tools, Properties tab Table H.1 Source spectra Source Spectrum Description Bacteria Bacterial luciferase CB Green Click beetle green luciferase CB Red Click beetle red luciferase Firefly Firefly luciferase XPM-2-LED LED in the XPM-2 mouse phantom. hRenilla Sea pansy (Renilla reniformis) luciferase NOTE Select a tissue or organ from the drop-down list. The associated internal medium index of refraction is automatically entered. Choose the Source Spectrum from the Plot drop-down list to display the selected spectrum. The firefly luciferase spectrum is dependent on temperature and pH. The data provided are valid only for measurements performed at 37° C and at pH 7.0-7.5. Selecting other temperature and pH conditions for a specific experiment requires the use of the associated spectral curve for the spectral analysis. For more information about pH and temperature dependence of the luciferase spectrum, please contact Caliper Life Sciences technical support. 237
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Living Image 3.1

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