Measurement of three-dimensional anisotropic diffusion by multiphoton fluorescence recovery after photobleaching - PubMed (original) (raw)

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

Changcheng Shi et al. Ann Biomed Eng. 2014 Mar.

Abstract

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.

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Conflict of interest statement

CONFLICT OF INTEREST

None of the authors of this paper have a conflict of interest that might be construed as affecting the conduct or reporting of the work presented.

Figures

Figure 1

Figure 1

An illustration of the SFA and averaging the diffusivity in the frequency domain over a shell. In the SFA, the solute concentration distribution is transformed from the spatial domain (a) to the frequency domain (b) by using the Fourier transform. In the frequency domain, the diffusivity D(u,v,w) is averaged over a shell of a spherical surface to obtain all components of the 3D diffusion tensor. The level of shell is defined by the radius a (i.e., commonly positive integers) and the range of shell is determined by azimuthal angle φ and polar angle θ.

Figure 2

Figure 2

Two observation protocols for fluorescent solute diffusion measurements in the porcine tendon tissues. X-Y coordinates represent the microscopy coordinates fixed on the microscope sample stage. (a) In the protocol of X-Alignment, the main fiber orientation is aligned with the X-axis. (b) In the protocol of Y-Alignment, the main fiber orientation is aligned with the Y-axis.

Figure 3

Figure 3

The 3D isotropic diffusion of FD500 molecule in glycerol/PBS solutions. (a) Typical time series of 3D MP-FRAP Z-stack image of fluorescent solutes for the experimental diffusion measurements in the glycerol/PBS solutions. For each experiment, typically, 40 stacks of post-bleaching images, plus 1 stack prior to photobleaching, are acquired at an approximate rate of 18 seconds/stack. The central region of the observation volume is photobleached by the multiphoton laser and fluorescence recovers completely in the last Z-stack image series (t=720s). (b) The results of 3D diffusion tensors (mean±SD). In each concentration group, there were no significant differences between the diagonal diffusion components (i.e., Dxx, Dyy, and Dzz), while the off-diagonal diffusion components were significantly smaller than the diagonal diffusion components (p<0.0001). Additionally, the nominal diffusivities (tr(D)/3) of FD500 significantly decreased (ANOVA, p<0.0001) with the increasing glycerol concentrations.

Figure 3

Figure 3

The 3D isotropic diffusion of FD500 molecule in glycerol/PBS solutions. (a) Typical time series of 3D MP-FRAP Z-stack image of fluorescent solutes for the experimental diffusion measurements in the glycerol/PBS solutions. For each experiment, typically, 40 stacks of post-bleaching images, plus 1 stack prior to photobleaching, are acquired at an approximate rate of 18 seconds/stack. The central region of the observation volume is photobleached by the multiphoton laser and fluorescence recovers completely in the last Z-stack image series (t=720s). (b) The results of 3D diffusion tensors (mean±SD). In each concentration group, there were no significant differences between the diagonal diffusion components (i.e., Dxx, Dyy, and Dzz), while the off-diagonal diffusion components were significantly smaller than the diagonal diffusion components (p<0.0001). Additionally, the nominal diffusivities (tr(D)/3) of FD500 significantly decreased (ANOVA, p<0.0001) with the increasing glycerol concentrations.

Figure 4

Figure 4

The 3D anisotropic diffusion of FD molecules in the porcine tendon tissues. (a) Typical time series of 3D MP-FRAP Z-stack image of fluorescent solutes for the experimental diffusion measurements in the porcine tendon tissues. For each experiment, typically, 40 stacks of post-bleaching images, plus 1 stack prior to photobleaching, are acquired at an approximate rate of 18 seconds/stack. The central region of the observation volume is photobleached by the multiphoton laser and fluorescence recovers completely in the last Z-stack image series (t=720s). (b) The results of 3D diffusion tensors (mean±SD). The diffusion of FD70 and FD150 along the major fiber orientation was significantly faster than the other two diffusions transverse to the fiber direction in both the X- and Y-Alignment observation protocols.

Figure 4

Figure 4

The 3D anisotropic diffusion of FD molecules in the porcine tendon tissues. (a) Typical time series of 3D MP-FRAP Z-stack image of fluorescent solutes for the experimental diffusion measurements in the porcine tendon tissues. For each experiment, typically, 40 stacks of post-bleaching images, plus 1 stack prior to photobleaching, are acquired at an approximate rate of 18 seconds/stack. The central region of the observation volume is photobleached by the multiphoton laser and fluorescence recovers completely in the last Z-stack image series (t=720s). (b) The results of 3D diffusion tensors (mean±SD). The diffusion of FD70 and FD150 along the major fiber orientation was significantly faster than the other two diffusions transverse to the fiber direction in both the X- and Y-Alignment observation protocols.

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