Constitutive modeling of compressible type-I collagen hydrogels

https://doi.org/10.1016/j.medengphy.2018.01.003Get rights and content

Highlights

  • Diverse type-I collagen hydrogel disks were tested using unconfined compression.

  • A nonlinear form of Poisson's ratio was consistent for all hydrogel formulations.

  • The Special Blatz–Ko model best represented the mechanics of hydrogel compression.

  • Using this model, the shear modulus was the only fitted-parameter.

  • Hydrogel mechanics are greatly simplified using the Special Blatz–Ko.

Abstract

Collagen hydrogels have been used ubiquitously as engineering biomaterials with a biphasic network of fibrillar collagen and aqueous-filled voids that contribute to a complex, compressible, and nonlinear mechanical behavior - not well captured within the infinitesimal strain theory. In this study, type-I collagen, processed from a bovine corium, was fabricated into disks at 2, 3, and 4% (w/w) and exposed to 0, 105, 106, and 107 microjoules of ultraviolet light or enzymatic degradation via matrix metalloproteinase-2. Fully hydrated gels were subjected to unconfined, aqueous, compression testing with experimental data modeled within a continuum mechanics framework by employing the uncommon Blatz–Ko material model for porous elastic materials and a nonlinear form of the Poisson's ratio. From the Generalized form, the Special Blatz–Ko, compressible Neo–Hookean, and incompressible Mooney–Rivlin models were derived and the best-fit material parameters reported for each. The average root-mean-squared (RMS) error for the General (RMS = 0.13 ± 0.07) and Special Blatz–Ko (RMS = 0.13 ± 0.07) were lower than the Neo–Hookean (RMS = 0.23 ± 0.10) and Mooney–Rivlin (RMS = 0.18 ± 0.08) models. We conclude that, with a single fitted-parameter, the Special Blatz–Ko sufficiently captured the salient features of collagen hydrogel compression over most examined formulations and treatments.

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.

References (47)

  • DJ Prockop et al.

    Collagens: molecular biology, diseases, and potentials for therapy

    Ann Rev Biochem

    (1995)
  • E Abou Neel et al.

    Use of multiple unconfined compression for control of collagen gel scaffold density and mechanical properties

    Soft Matter

    (2006)
  • MJ Yost et al.

    A novel tubular scaffold for cardiovascular tissue engineering

    Tissue Eng

    (2004)
  • SV Biechler et al.

    The impact of flow-induced forces on the morphogenesis of the outflow tract

    Front Physiol

    (2014)
  • RS Jones et al.

    Design and fabrication of a three-dimensional in vitro system for modeling vascular stenosis

    Microsc Microanal

    (2017)
  • A Hasan et al.

    Injectable hydrogels for cardiac tissue repair after myocardial infarction

    Adv Sci

    (2015)
  • DD Simon et al.

    Mechanical restrictions on biological responses by adherent cells within collagen gels

    J Mech Behav Biomed Mater

    (2013)
  • KD Costa et al.

    Creating alignment and anisotropy in engineered heart tissue: role of boundary conditions in a model three-dimensional culture system

    Tissue Eng

    (2003)
  • LiuX et al.

    Human bronchial epithelial cells can contract type I collagen gels human bronchial epithelial cells can contract type I collagen gels

    Am J Physiol - Lung Cell Mol Physiol

    (1998)
  • Gourdie RG, Myers T a, McFadden a, Li YX, Potts JD. Self-organizing tissue-engineered constructs in collagen hydrogels....
  • ML Oyen

    Mechanical characterisation of hydrogel materials

    Int Mater Rev

    (2014)
  • DM Knapp et al.

    Rheology of reconstituted type I collagen gel in confined compression

    J Rheol (N Y N Y)

    (1997)
  • BA Roeder et al.

    Tensile mechanical properties of three-dimensional type i collagen extracellular matrices with varied microstructure

    J Biomech Eng

    (2002)
  • Cited by (0)

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