Multiscale Elastic Models of Collagen Bio-structures: From Cross-Linked Molecules to Soft Tissues - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 96

Figure 13 clearly shows that proposed model is able to reproduce the
mean experimental p-r i curves associated with young (20-24 years), middle-age
(36-42 years), and old (71-78 years) subjects. Although values of model
parameters are chosen only in agreement with well-established trends and there is
no quantitative relationships with the available experiments, the model reveals to
be attractive and potentially effective in relating tissue structure at different scales
and its evolution to the tissue macroscopic mechanical behavior.
8 Conclusions
In the present paper, a structural multiscale elastic formulation for modeling soft
collagenous tissues has been presented, based on the approach proposed and
applied by authors in [ 8 , 51 ]. To this aim, single-scale models of collagenous bio-
structures at very different length scales have been introduced, addressing mole-
cules (nanoscale), fibrils (mesoscale) and crimped fibers (microscale). Following a
multiscale structural rationale, that allows to account for the hierarchical multiscale
arrangement of the constituents within tissues, these models have been integrated
by means of consistent inter-scale relationships and homogenization arguments,
leading to an accurate macroscale description of soft collagenous tissues.
Soundness and effectiveness of the present approach have been proved by
recovering a number of well-established evidences at different length scales,
without the use of phenomenological descriptions. It is shown that proposed sin-
gle-scale models are able to reproduce the transition from entropic-to-energetic
mechanisms at the nanoscale, the effects of inter-molecular cross-links on fibril
mechanics, and the coupling between material and geometric non-linearities
affecting the deformation process of crimped collagen fibers. Moreover, available
experimental data on the biomechanical response of tendons and aortas have been
compared with the numerical results obtained by the macroscale model, high-
lighting an excellent agreement. Such a capability arises from the structural
multiscale approach herein adopted, that allows to account for material and
geometrical non-linearities at different scales, as well as for nanoscale mecha-
nisms. In fact, as proved in [ 8 ], a structural approach involving only microscale
mechanisms is generally not able to recover accurately, for different strain levels,
the non-linear mechanical response of soft collagenous tissues.
Following the proposed approach, few and experimentally measurable model
parameters are introduced. Thereby, the effects of altered histological features on
tissue mechanics can be straightforwardly investigated. For instance, different
microscale fiber geometric features allow to explain the variability in constitutive
response experienced when data measured on different specimens of rat tail
tendons are compared. Moreover, the age-dependent evolution of aortic mechan-
ical behavior has been accurately reproduced, simply by incorporating the well-
documented features of age-dependent tissue remodeling.