Constitutive modeling of compressible type-I collagen hydrogels
Introduction
Collagen is a naturally occurring polymer that provides a low immunogenic and biologically compatible platform for cellular attachment [1], [2]. Type-I collagen, the most abundant of the collagens, endows a diverse group of mammalian tissues with their mechanical properties [3], [4]. This material can be processed from primary tissue sources into acidic solutions, molded into a variety of shapes, and reconstituted into gels using pH neutralization [5]. As such, its applications in biomedical engineering are vast. These applications include scaffolding for tissue engineering, biomimetics, and drug delivery [2], [6], [7], [8]. Clinically, collagen hydrogels have been used as one of the major constituents of bioactive skin substitutes, corneal shields, and as drug-loaded wound dressings that enhance the healing and recovery processes [9], [10]. Injectable collagen hydrogels are currently being investigated to stabilize and improve ventricle remodeling after myocardial infarction [11]. When physically loaded, (e.g., following implantation or when seeded with contractile cells) collagen gels undergo compression and compaction due to the collapse of aqueous voids within the material [12], [13], [14], [15]. Accurate interpretation of the response of these materials to applied loads (e.g., using finite element analysis), requires an appropriate constitutive model that captures the complex mechanical behavior.
Diverse testing techniques have been employed to measure the mechanical properties of collagen hydrogels (e.g., shear rheometry, tension/compression, indentation, dynamic mechanical analysis). The best experimental tool is selected based on the range of anticipated material behavior, conditions of interest, availability of equipment, and intended material application [5], [16], [17], [18], [19], [20]. In simple unconfined axisymmetric compression tests, as performed here, two impermeable and rigid parallel plates compress a specimen submerged in an aqueous solution while permitting lateral deformation to occur [5], [21]. With the direct measurement of deformed cross-sectional area and force, the Cauchy stress can be calculated at each experimental state and a relationship between the lateral extension and axial compression (Poisson's ratio) easily formulated [17], [22], [23].
Assuming the orientation of the collagen fibers are random (cf., Fig. 1) and the time-scale of experimentation is such that viscoelastic and plastic effects are negligible, the material can be modeled within the finite strain theory as being nonlinearly-elastic and isotropic [5], [13], [24], [25], [26]. To encompass the salient features of these compressible collagen hydrogels within a mechanical formulation on the continuum scale, we employ an uncommon strain-energy function developed by Blatz and Ko in 1982 [27]. In its full form the model is called the General Blatz–Ko, aptly named after the pioneering work of these two investigators whose original experiments were used to explain a class of foamed polyurethane rubbers in uniaxial and biaxial tension [27]. Despite previous validation in both tension and compression by Beatty and others [27], [28], [29], this framework has been used sparingly to model biological tissues. An immediate advantage to this model is that, at most, only three material parameters are needed; one of which is measured directly, another can be measured or prescribed, and the last is related to the fraction of voids within the material. From the General form of the Blatz–Ko, the popular compressible Neo–Hookean and incompressible Mooney–Rivlin models can be derived [30]. A further reduced form, called the Special Blatz–Ko, has only a single fitted parameter thereby greatly simplifying the required mechanical measurements and facilitating comparisons between groups of gels with different material characteristics.
In this work we prepared hydrogels using collagen processed from a bovine corium and modified the hydrogel's mechanical properties through manipulations of concentration, UV crosslinking, and enzymatic degradation. We then tested the hypothesis that the lesser-known Blatz–Ko material model could provide a better, and simpler, representation of a diverse group of collagen hydrogels under compressive loading compared to the popular Neo–Hookean or Mooney–Rivlin models. As a representative example of the model's utility, we applied these findings to the gel contraction assay using neonatal rat cardiac fibroblasts (NCFs) and calculated the acute energy required to deform this material in culture. In doing so, a constitutive model for hydrogel mechanics was developed and validated that can easily be used to interpret clinical or experimental results.
Section snippets
Collagen isolation and preparation
Type-I collagen was isolated from a bovine corium through mechanical separation of the dermis and epidermis following the procedure outlined in Yost et al. 2004 [6]. Briefly, hair follicles and non-collagenous proteins were removed using Ca(OH)2 and a solution of NaHS and subsequently treated with pepsin, grinded with ice, and mixed with acetic acid to create a gel solution. Collagen proteins were then salted out of the solution, collected via centrifugation, and then dialyzed against dH2O to
Results
Confocal reflectance micrographs of a 3% (w/w) gel demonstrate both the initially random microstructural organization of collagen fibers and the inherent material porosity contained therein (Fig. 1). The nonlinear form of the Poisson's ratio described by Eq. (8) yielded an excellent fit to all experimental data (Fig. 3; R2 > 0.976). No significant differences in nonlinear Poisson's ratio were observed between any experimental groups resulting in an average value of ν= 0.29 ± 0.06. Material
Discussion
Working within the finite strain theory of continuum mechanics, the present work describes the macroscopic mechanical response of collagen hydrogels under unconfined compression testing using collagen harvested and processed from a bovine corium. As expected the shear modulus μ was readily tunable using different collagen treatments and formulations thereby emphasizing the diverse application of this material for a variety of biomedical applications. A nonlinear form of the Poisson's ratio was
Acknowledgments
The authors would like to acknowledge the contributions of undergraduate researchers Andrew Shuler, Michael Hendley, Alex Ruppe, and Mary Kay Matula for aid in the processing of collagen from the bovine corium.
Competing interests
None declared
Funding
NIH South Carolina IDeA Networks of Biomedical Research Excellence (INBRE) P20GM103499.
Ethical approval
Not required.
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