Measurement of three-dimensional anisotropic diffusion by multiphoton fluorescence recovery after photobleaching.

The multiphoton fluorescence recovery after photobleaching (MP-FRAP) technique has been developed to measure the three-dimensional (3D) solute diffusion within biological systems. However, current 3D MP-FRAP models are based on isotropic diffusion and spatial domain analysis. The 3D anisotropic diffusion and frequency domain analysis for MP-FRAP measurements are rarely studied. In this study, a new technique is demonstrated for the quantitative and non-destructive determination of 3D anisotropic solute diffusion tensors within biological fibrosis tissues by multiphoton photobleaching and spatial Fourier analysis (SFA). Compared to the spatial domain analysis based MP-FRAP techniques, this SFA-based method has the capability for determining the 3D anisotropic diffusion tensors as well as the flexibility for satisfying initial and boundary conditions. First, a close-form solution of the 3D anisotropic diffusion equation is derived by solely using SFA. Next, this new method is validated by computer-simulated MP-FRAP experiments with pre-defined 3D anisotropic diffusion tensors as well as experimental diffusion measurements of FITC-Dextran (FD) molecules in aqueous glycerol solutions. Finally, this MP-FRAP technique is applied to the measurement of 3D anisotropic diffusion tensors of FD molecules within porcine tendon tissues. This study provides a new tool for complete determination of 3D anisotropic solute diffusion tensor in biological tissues.