A Mathematical Model for Analyzing the Elasticity, Viscosity, and Failure of Soft Tissue: Comparison of Native and Decellularized Porcine Cardiac Extracellular Matrix for Tissue Engineering

Abstract

The clinical success of tissue-engineered constructs commonly requires mechanical properties that closely mimic those of the human tissue. Determining the viscoelastic properties of such biomaterials and the factors governing their failure profiles, however, has proven challenging, although collecting extensive data regarding their tensile behavior is straightforward. The easily calculated Young's modulus remains the most reported mechanical measure, regardless of its limitations, even though single-relaxation-time (SRT) models can provide much more information, which remain scarce due to a lack of manageable tools for implementing these models. We developed an easy-to-use algorithm for applying the Zener SRT model and determining the elastic moduli, viscosity, and failure profiles of materials under different mechanical tests in a user-independent manner. The algorithm was validated on the data resulting from tensile tests on native and decellularized porcine cardiac tissue, previously suggested as a promising scaffold material for cardiac tissue engineering. This analysis yields new and more accurate measurements such as the elastic moduli and viscosity, the model's relaxation time, and information on the factors governing the materials' failure profiles. These measurements indicate that the viscoelasticity and strength of the decellularized acellular extracellular matrix (ECM) are similar to those of native tissue, although its elasticity and apparent viscosity are higher. Nonetheless, reseeding and culturing the ECM with mesenchymal stem cells was shown to partially restore the mechanical properties lost after decellularization. We propose this algorithm as a platform for soft-tissue analysis that can provide comparable and unbiased measures for characterizing viscoelastic biomaterials commonly used in tissue engineering.

Control of collagen gel mechanical properties through manipulation of gelation conditions near the sol–gel transition

“…The observation that the time dependent rheological properties of the collagen matrix adhere to the Fractional Maxwell Model with a = 0.3 and b = 0.05 is both novel and important in modelling and simulation of the extracellular matrix, which have previously employed traditional mechanical models involving springs and dashpots. [25][26][27][28] These findings suggest that a more appropriate mechanical model may include the spring-pot and draw on fractional calculus based descriptions of extracellular matrix viscoelasticity.…”

“…and dashpots). [25][26][27][28] The work presented herein suggests that a more appropriate approach will involve the use of spring-pots which accurately capture the relaxation/retardation properties of the collagen gel network using minimal parameters.…”

Decellularized Extracellular Matrix Materials for Cardiac Repair and Regeneration

“…The basement membranes of cECM show complete assembly of laminin and collagen IV in thick microfibers, possibly due to the basement membrane forming around vasculature. While the mechanical properties of both solid and soluble dECM are much different than native myocardium, the mechanical modulus of healthy myocardium has been measured as anywhere from 3 to 100 kPa, based on method of analysis and location of measurement within the myocardium itself . This heterogeneity in tissue mechanics is seen within dECM as well and studies are needed to better understand how changes in various ECM and cellular components, such as collagen and titin, modulate myocardial stiffness …”

Mathematical modeling of bioactive arterial wall

“…The model is a modified viscoelastic Zener model with one active element. Passive Zener model is widely used for interpretation of the experimental data obtained on single cells by atomic force microscopy or optical tweezers [14,15]. The rheological equation for the model is [13] :…”

“…The isotonic, isometric and oscillatory experiments with model (7) have been studied in [12,13]. Let us consider the linear extension in the form (5) applied to (14) with the same initial conditions (6); then to solution reads…”