A linear systems model of the hydrothermal isometric tension test for assessing collagenous tissue quality

Collagen is the most abundant structural protein in the animal kingdom. Its thermal and thermomechanical properties are often measured using differential scanning calorimetry (DSC) and hydrothermal isometric tension (HIT) tests, respectively. In living tissues, not all collagenous structures (molecules, fibrils, etc.) have the same "quality," and the heterogeneity among these structures in specific tissues increases with remodeling, aging, and/or disease states. In this paper, first, a peak-fitting analysis is carried out to separate and distinguish the sequential denaturation events in a DSC endotherm, which presumably stem from heterogeneity in the collagen fibrils. The fitting analysis uses one of two functions: a Gaussian function or a function proposed by Miles. The individual endotherms were then convolved with a physics-based parametric function, J(T), proposed by the authors, to model the development of the isometric tension in two stages: 1) tension development due to a sudden increase in conformational entropy as each collagen packet denatures, and 2) additional isometric tension development due to increasing temperature, consistent with rubber thermo-elasticity. The proposed function parameters were then found by fitting to actual HIT curves using a global optimization technique. This model provides a decoupling of the effects of denaturation kinetics and collagen network connectivity and therefore an improved interpretation of HIT test results during the temperature ramp from ambient temperature to 90 °C. The simple model outputs are two parameters, α and β, that have physical meaning and aid in assessing collagenous tissue quality in terms of connectivity and integrity.