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Research Papers

Microstructural Parameter-Based Modeling for Transport Properties of Collagen Matrices

[+] Author and Article Information
Seungman Park

School of Mechanical Engineering,
College of Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: park382@purdue.edu

Catherine Whittington

Weldon School of Biomedical Engineering,
College of Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: cfwhitti@purdue.edu

Sherry L. Voytik-Harbin

Weldon School of Biomedical Engineering,
Department of Basic Medical Sciences,
Purdue University,
West Lafayette, IN 47907
e-mail: harbins@purdue.edu

Bumsoo Han

School of Mechanical Engineering,
Weldon School of Biomedical Engineering,
Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907
e-mail: bumsoo@purdue.edu

1Corresponding author.

Manuscript received September 26, 2014; final manuscript received February 18, 2015; published online March 18, 2015. Assoc. Editor: Ram Devireddy.

J Biomech Eng 137(6), 061003 (Jun 01, 2015) (9 pages) Paper No: BIO-14-1479; doi: 10.1115/1.4029920 History: Received September 26, 2014; Revised February 18, 2015; Online March 18, 2015

Recent advances in modulating collagen building blocks enable the design and control of the microstructure and functional properties of collagen matrices for tissue engineering and regenerative medicine. However, this is typically achieved by iterative experimentations and that process can be substantially shortened by computational predictions. Computational efforts to correlate the microstructure of fibrous and/or nonfibrous scaffolds to their functionality such as mechanical or transport properties have been reported, but the predictability is still significantly limited due to the intrinsic complexity of fibrous/nonfibrous networks. In this study, a new computational method is developed to predict two transport properties, permeability and diffusivity, based on a microstructural parameter, the specific number of interfibril branching points (or branching points). This method consists of the reconstruction of a three-dimensional (3D) fibrous matrix structure based on branching points and the computation of fluid velocity and solute displacement to predict permeability and diffusivity. The computational results are compared with experimental measurements of collagen gels. The computed permeability was slightly lower than the measured experimental values, but diffusivity agreed well. The results are further discussed by comparing them with empirical correlations in the literature for the implication for predictive engineering of collagen matrices for tissue engineering applications.

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Figures

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Fig. 1

Schematic illustrations of the image-based reconstruction. (a) Flow chart for model reconstruction, permeability, and diffusivity calculations: confocal image acquisition (confocal reflectance/fluorescence microscopy), data acquisition (Imaris Filament Tracer), 3D reconstruction (PTC Creo parametric 2.0), mesh generation (icem-cfd, ansys 14.0), and FEA to determine permeability and diffusivity values. (b) Image-based reconstruction of monomer matrix. (c) Representative mesh generation of monomer matrix.

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Fig. 2

Schematic illustrations of the parameter-based reconstruction. (a) Flow chart for model reconstruction, permeability, and diffusivity calculations: generation of random points (experimental data), generation of fibrils and 3D reconstruction (TNPC algorithm), computational mesh generation, and FEA to determine permeability and diffusivity values. (b) TNPC method which connects each point with its two closest neighboring points to form a fibril. (c) Close-up image of 3D fibril network with 100 nm diameter fibril. (d) SEM image of rat tail collagen [30].

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Fig. 3

Collagen networks generated by the parameter-based method (top-view). There is a clear difference in microstructure among 0:100, 50:50, and 100:0 ratios.

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Fig. 4

Representative computational results for permeability calculation (oligomer:monomer 0:100). (a) Velocity vectors. (b) Velocity contour. The fibril surface was assumed as having the nonslip boundary condition, and the velocity magnitude on the fibril surface is held at zero. All computed velocity values were averaged for permeability calculation.

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Fig. 5

Comparison of permeability values generated from computational methods with different diameters (d = 100 nm and d = 400 nm), and predictive models for 0:100, 50:50, and 100:0, and previously conducted experiments for 0:100 and 100:0 [24]. Computational and predicted values are lower than experimental values. The developed models (image- and parameter-based) generated values closer to the experimental data than other predictive models.

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Fig. 6

Diffusivity values of FITC-labeled dextran with four different sizes (4 kDa, 10 kDa, 40 kDa, and 500 kDa) for 0:100 and 100:0. The effect of molecular size on the diffusivity is clearly observed for both 0:100 and 100:0. However, there is no significance difference between the two formulations (p > 0.05), except for 500 kDa (p < 0.05).

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Fig. 7

Representative results for diffusivity calculation of 40 kDa dextran using the parameter-based model. (a) Particle random motion (0:100). (b) Particle displacement distribution (0:100, 50:50, and 100:0). All matrices show a typical Gaussian distribution of particle displacements with no notable difference in displacement frequency among 0:100, 50:50, and 100:0.

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Fig. 8

Diffusivity values obtained by computational methods (image-based model and parameter-based models) and IOI experiments. No significant differences were noted between the diffusivity values among 0:100, 50:50, and 100:0. Experimental values are approximately twice higher than computational values.

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