Determining diffusion coefficients in inhomogeneous tissues using fluorescence recovery after photobleaching.

Diffusion plays an important role in the transport of nutrients and signaling molecules in cartilaginous tissues. Diffusion coefficients can be measured by fluorescence recovery after photobleaching (FRAP). Available methods to analyze FRAP data, however, assume homogeneity in the environment of the bleached area and neglect geometrical restrictions to diffusion. Hence, diffusion coefficients in inhomogeneous materials, such as most biological tissues, cannot be assessed accurately. In this study, a new method for analyzing data from FRAP measurements has been developed, which is applicable to inhomogeneous tissues. It is based on a fitting procedure of the intensity recovery after photobleaching with a two-dimensional finite element analysis, which includes Fick's law for diffusion. The finite element analysis can account for distinctive diffusivity in predefined zones, which allows determining diffusion coefficients in inhomogeneous samples. The method is validated theoretically and experimentally in both homogeneous and inhomogeneous tissues and subsequently applied to the proliferation zone of the growth plate. Finally, the importance of accounting for inhomogeneities, for appropriate assessment of diffusivity in inhomogeneous tissues, is illustrated.

[1]  William M. Deen,et al.  Diffusivities of macromolecules in composite hydrogels , 2004 .

[2]  J. D. Gregory,et al.  Effect of proteoglycan removal on solute mobility in articular cartilage. , 1997, Journal of biomechanics.

[3]  T. Tsay,et al.  Spatial Fourier analysis of video photobleaching measurements. Principles and optimization. , 1991, Biophysical journal.

[4]  H. Kronenberg,et al.  Developmental regulation of the growth plate , 2003, Nature.

[5]  Farshid Guilak,et al.  Site-Specific Molecular Diffusion in Articular Cartilage Measured using Fluorescence Recovery after Photobleaching , 2003, Annals of Biomedical Engineering.

[6]  R K Jain,et al.  Direct in vivo measurement of targeted binding in a human tumor xenograft. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Z. Werb,et al.  Matrix remodeling during endochondral ossification. , 2004, Trends in cell biology.

[8]  W. Press.  Numerical recipes in Fortran 77 : the art of scientific computing : volume 1 of fortran numerical recipes , 1996 .

[9]  Gustavo Carrero,et al.  Using FRAP and mathematical modeling to determine the in vivo kinetics of nuclear proteins. , 2003, Methods.

[10]  A. Grodzinsky,et al.  Contributions of fluid convection and electrical migration to transport in cartilage: relevance to loading. , 1996, Archives of biochemistry and biophysics.

[11]  G. Zacchi,et al.  Use of holographic laser interferometry to study the diffusion of polymers in gels. , 2000, Biotechnology and Bioengineering.

[12]  R K Jain,et al.  Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media. , 1993, Biophysical journal.

[13]  W. Webb,et al.  Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. , 1976, Biophysical journal.

[14]  Jan Ellenberg,et al.  Dynamics and retention of misfolded proteins in native ER membranes , 2000, Nature Cell Biology.

[15]  K. Braeckmans,et al.  Three-dimensional fluorescence recovery after photobleaching with the confocal scanning laser microscope. , 2003, Biophysical journal.

[16]  Jean-Jacques Meister,et al.  Preservation and analysis of nonequilibrium solute concentration distributions within mechanically compressed cartilage explants. , 2002, Journal of biochemical and biophysical methods.

[17]  Alice Maroudas,et al.  Diffusion and partition of solutes in cartilage under static load. , 2003, Biophysical chemistry.

[18]  J. Meister,et al.  Static compression of articular cartilage can reduce solute diffusivity and partitioning: implications for the chondrocyte biological response. , 2001, Journal of biomechanics.