Kevin Linka

T2 MR imaging vs. computational modeling of human articular cartilage tissue functionality

The detection of early stages of cartilage degeneration remains diagnostically challenging. One promising non-invasive approach is to functionally assess the tissue response to loading by serial magnetic resonance (MR) imaging in terms of T2 mapping under simultaneous mechanical loading. As yet, however, it is not clear which cartilage component contributes to the tissue functionality as assessed by quantitative T2 mapping. To this end, quantitative T2 maps of histologically intact cartilage samples (n=8) were generated using a clinical 3.0-T MR imaging system. Using displacement-controlled quasi-static indentation loading, serial T2 mapping was performed at three defined strain levels and loading-induced relative changes were determined in distinct regions-of-interest. Samples underwent conventional biomechanical testing (by unconfined compression) as well as histological assessment (by Mankin scoring) for reference purposes. Moreover, an anisotropic hyperelastic constitutive model of cartilage was implemented into a finite element (FE) code for cross-referencing. In efforts to simulate the evolution of compositional and structural intra-tissue changes under quasi-static loading, the indentation-induced changes in quantitative T2 maps were referenced to underlying changes in cartilage composition and structure. These changes were parameterized as cartilage fluid, proteoglycan and collagen content as well as collagen orientation. On a pixel-wise basis, each individual component correlation with T2 relaxation times was determined by Spearmans ρs and significant correlations were found between T2 relaxation times and all four tissue parameters for all indentation strain levels. Thus, the biological changes in functional MR Imaging parameters such as T2 can further be characterized to strengthen the scientific basis of functional MRI techniques with regards to their perspective clinical applications.

Multi-scale modeling of soft fibrous tissues based on proteoglycan mechanics

Collagen in the form of fibers or fibrils is an essential source of strength and structural integrity in most organs of the human body. Recently, with the help of complex experimental setups, a paradigm change concerning the mechanical contribution of proteoglycans (PGs) took place. Accordingly, PG connections protect the surrounding collagen fibrils from over-stretching rather than transmitting load between them. In this paper, we describe the reported PG mechanics and incorporate it into a multi-scale model of soft fibrous tissues. To this end, a nano-to-micro model of a single collagen fiber is developed by taking the entropic-energetic transition on the collagen molecule level into account. The microscopic damage occurring inside the collagen fiber is elucidated by sliding of PGs as well as by over-stretched collagen molecules. Predictions of this two-constituent-damage model are compared to experimental data available in the literature.

Mechanics of collagen fibrils: A two-scale discrete damage model

Collagen is one of the most important structural proteins of biological tissues. Recently, a new damage phenomena caused by a mechanical overloading of the tendon has been revealed on the collagen fibril level by means of scanning electron microscopy (Veres et al., 2013). In order to describe this phenomena we propose in the present paper a constitutive damage model for single collagen fibrils. It utilizes a statistical framework in order to incorporate a physically motivated transition from the entropic- to the intrinsic-elasticity range of single tropocollagen molecules. In this two-scale approach a bridging relation between the tropocollagen and fibril level as well as a failure criterion after exceeding a critical stretch limit are introduced. The final constitutive relations are validated against experimental data available in literature for both, the reversible and the irreversible, stress-strain response.

Fatigue of soft fibrous tissues: Multi-scale mechanics and constitutive modeling

In recent experimental studies a possible damage mechanism of collagenous tissues mainly caused by fatigue was disclosed. In this contribution, a multi-scale constitutive model ranging from the tropocollagen (TC) molecule level up to bundles of collagen fibers is proposed and utilized to predict the elastic and inelastic long-term tissue response. Material failure of collagen fibrils is elucidated by a permanent opening of the triple helical collagen molecule conformation, triggered either by overstretching or reaction kinetics of non-covalent bonds. This kinetics is described within a probabilistic framework of adhesive detachments of molecular linkages providing collagen fiber integrity. Both intramolecular and interfibrillar linkages are considered. The final constitutive equations are validated against recent experimental data available in literature for both uniaxial tension to failure and the evolution of fatigue in subsequent loading cycles. All material parameters of the proposed model have a clear physical interpretation. STATEMENT OF SIGNIFICANCE Irreversible changes take place at different length scales of soft fibrous tissues under supra-physiological loading and alter their macroscopic mechanical properties. Understanding the evolution of those histologic pathologies under loading and incorporating them into a continuum mechanical framework appears to be crucial in order to predict long-term evolution of various diseases and to support the development of tissue engineering.

Worm-like chain model extensions for highly stretched tropocollagen molecules

Tropocollagen plays a very important role in the load bearing functionality of soft tissues. In the context of multi-scale modeling the response of tropocollagen molecules to stretch should be very carefully predicted in order to describe the mechanical behavior of soft tissues. To this end, the worm-like chain (WLC) model is often applied, although it is restricted to the entropic force regime which is essential at moderate deformations. To describe molecular forces under larger stretches several extensions of the WLC have been proposed for deoxyribonucleic acid (DNA). This contribution aims to investigate the applicability of these models in the context of tropocollagen and discusses the feasibility of their application. Finally, the models are validated in comparison to experimental data available in the literature.

Multiparametric MRI and Computational Modelling in the Assessment of Human Articular Cartilage Properties: A Comprehensive Approach

Quantitative magnetic resonance imaging (qMRI) is a promising approach to detect early cartilage degeneration. However, there is no consensus on which cartilage component contributes to the tissues qMRI signal properties. T1, T1ρ, and T2⁎ maps of cartilage samples (n = 8) were generated on a clinical 3.0-T MRI system. All samples underwent histological assessment to ensure structural integrity. For cross-referencing, a discretized numerical model capturing distinct compositional and structural tissue properties, that is, fluid fraction (FF), proteoglycan (PG) and collagen (CO) content and collagen fiber orientation (CFO), was implemented. In a pixel-wise and region-specific manner (central versus peripheral region), qMRI parameter values and modelled tissue parameters were correlated and quantified in terms of Spearmans correlation coefficient ρs. Significant correlations were found between modelled compositional parameters and T1 and T2⁎, in particular in the central region (T1: ρs ≥ 0.7 [FF, CFO], ρs ≤ −0.8 [CO, PG]; T2⁎: ρs ≥ 0.67 [FF, CFO], ρs ≤ −0.71 [CO, PG]). For T1ρ, correlations were considerably weaker and fewer (0.16 ≤ ρs ≤ −0.15). QMRI parameters are characterized in their biophysical properties and their sensitivity and specificity profiles in a basic scientific context. Although none of these is specific towards any particular cartilage constituent, T1 and T2⁎ reflect actual tissue compositional features more closely than T1ρ.