Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 104

their organization. Section 3 provides a detailed review of the available data on
material characterization of ligaments and tendons at different scales. Section 4
reviews the mathematical fundamentals behind nonlinear continuum mechanics
and homogenization theory. Finally, Sect. 5 critically reviews the state of the art in
multiscale modeling of ligaments and tendons, and identifies directions for future
research.
2 Ligament and Tendon Structure
2.1 Ligament
Ligaments are soft, fibrous tissues that connect bone to bone at the joints. They
help to guide and limit the motion of the bones so that the joint articulates with no
separation or only a limited separation of the bones. Ligaments are passive sta-
bilizers and work in conjunction with other passive stabilizers, including the
articulating surfaces of the bones and, in most diarthrodial joints (major joints—
knee, hip and shoulder), other soft tissues such as the meniscus in the knee and the
labrum in the shoulder and hip. In diarthrodial joints, ligaments are primarily
banded or cordlike. For instance, the medial collateral ligament (MCL) of the knee
is a banded ligament, while the anterior cruciate ligament (ACL) is a cordlike
ligament. These knee ligaments resist motion along a single line of action and
transmit tensile load, but also experience shear, transverse and compressive loads
[ 5 , 6 , 20 , 29 , 33 , 41 , 49 , 65 , 75 , 76 , 233 , 240 , 242 , 245 ]. The MCL, for example,
primarily resists valgus knee motion, which loads the MCL in tension [ 3 , 11 , 87 ,
113 , 115 , 142 , 157 , 160 ]. However, articulation of the joint and contact with the
bones will also generate shear, transverse and compressive loads [ 49 , 65 , 75 , 76 ].
The ligaments in the shoulder and hip form thin, dense bands of tissue around the
joint capsule and are known as capsular ligaments. The inferior glenohumeral
ligament (IGHL), for example, is a capsular ligament in the shoulder. While it can
be argued that capsular ligaments resist motion primarily in one direction, they are
thought to constrain more complex motions than knee ligaments through their
connection with the rest of the capsule [ 51 , 52 , 56 , 57 , 63 , 64 , 164 ].
Although ligaments are considered passive stabilizers, there are stresses in the
tissue when the joint is in a neutral position [ 1 ]. These in situ stresses are
responsible for the stability of the joint when muscle forces are not acting across
the joint. Due to the difficulty in measuring in situ stresses, in situ strains are
usually measured [ 75 , 244 ]. Ligament in situ strains are inhomogenous, subject-
specific, and vary depending on joint position [ 75 , 244 ]. Previous research has
shown that ligament in situ strains must be measured in order to accurately
measure or predict ligament strains and stresses due to external loading [ 75 ].
Ligaments attach to bone at insertion sites. There are two types of insertion
sites: direct and indirect insertions. Direct insertion sites occur over a distance of