Computational and Experimental Comparison on the Effects of Flow-Induced Compression on the Permeability of Collagen Gels

Abstract

Collagen is a fibrous material and is ubiquitous throughout the human body. It is a biphasic material, consisting of a solid fibrous matrix and interstitial fluid. Collagen is one of the primary components within the extracellular matrix, which plays a vital role in the physiological, mechanical, and transport functions of various systems and processes of the body. Understanding the mechanical and transport properties of collagen can help us understand the roles and processes of the extracellular matrix. Additionally, understanding these properties may lead to more rational design choices in tissue engineering, where the permeability of the biomaterial in tissue engineering is critical for the transport of nutrients. The underlying goal of this study is to experimentally determine and to develop a finite element model showing the effect of concentration and compression of collagen gels on permeability. In this study, two methods to determine the permeability of collagen gels was developed. With both methods, the interstitial fluid of collagen gels was expelled under a pressure load, resulting in compressed collagen gels that were denser than the starting gels. The permeability of collagen gels was determined using Darcy’s Law. In the vertical apparatus, a changing height of fluid pushed water through and compressed a collagen sample. In the horizontal apparatus, a syringe pump delivered water through three collagen concentrations (1.98 mg/mL, 3.5 mg/mL, 5 mg/mL) at a constant volumetric flow rate of 0.85 ml/min. Instantaneous permeability values were obtained at various points of compression and fitted to the α and M values of the strain-dependent Holmes-Mow permeability model where α and M are defined as intrinsic permeability parameters. A finite element model was developed to model the biphasic compression of the collagen gels using FEBio. A neo-Hookean material was used to model the solid matrix and Young’s modulus was changed to match the degree of compression. The vertical apparatus found a higher permeability compared to the horizontal apparatus. The vertical apparatus showed a permeability of 2.37 x 10-11 ± 2.4 x 10-11 m2. The initial permeability doubled as the collagen went from a starting concentration of 5 mg/mL to a starting concentration of 1.98 mg/mL. Each concentration compressed to a final concentration of about 12 mg/mL, resulting in no dependence on starting concentration for the permeability of compressed samples. The M values of the Holmes-Mow model increased from 2.4 to 5 with increasing concentration, while the α value decreased from 1.3 to 0.5 with increasing concentration. The Young’s modulus found by the finite element model increased from 200 to 3700 Pa with increasing initial collagen concentration. The Young’s modulus determined in the current study was similar to the short-time modulus of other published works.