Page 187 - Advances in Biomechanics and Tissue Regeneration

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circumferentially oriented in the bulk of the tissue in between these surfaces [61]. In addition, radial tie fibers are pre-
sent that increase the tensile resistance of the meniscus [62]. Similar to the articular cartilage, the structural inhomo-
geneity and anisotropy of menisci dominate its tensile behavior [63].
Primary meniscal functions include the uniform transfer of the joint load across the cartilage [64], shock absorption
[63, 65], augmentation of the stiffness—stability—of the joint [66, 67], assistance in joint lubrication and articulation,
prevention of hyperextension, and protection of the joint [68, 69]. Pressure measurements have shown that 45%–70% of
the applied compression force is transmitted through the menisci [63, 68, 70, 71]. In joints after total meniscectomy,
contact stresses could double with a 50%–70% reduction in contact areas [72]. A 10% reduction in meniscal contact
area secondary to the partial meniscectomy produces 65% increase in peak contact stresses [72], leading likely to
early development of OA [73–75].
The mechanical properties of menisci have been extensively studied under compressive, tensile, and shear load con-
ditions [63, 76–78]. Tensile properties, as in articular cartilage, vary with tissue depth and from a direction to another,
depending on the spatial organization of collagen fibrils within the tissue [77].

9.2.2 Knee Joint Passive Finite Element (FE) Model
Numerous FE models with different degrees of complexity and accuracy have been developed to study the knee
joint biomechanics under various loads and movements [79]. The first comprehensive FE model of the TF joint is that of
Bendjaballah et al. [11] with the model reconstructed from CT images and direct measurements of a cadaver knee.
Menisci were simulated as a nonlinear nonhomogeneous composite of an isotropic bulk reinforced by collagen fibrils
with strain-dependent nonlinear material properties [80], ligaments as nonlinear elements with initial strains in dif-
ferent bundles, and articular cartilage layers as a simple isotropic homogeneous elastic material. Each bony structure
was taken as a rigid body represented by a primary reference node. The material properties were derived from the data
available in the literature [11, 81, 82]. Each meniscus matrix was stiffened by a higher modulus of 15 MPa at both ends
( 5mm length), which was inserted into the tibial eminence to simulate its horns [83]. Articulations at the cartilage–
cartilage (i.e., uncovered areas) and cartilage–meniscus (i.e., covered areas) were simulated as large displacement fric-
tionless contact [83, 84].
In later refinements and developments of this model, the articular cartilage layers at both TF and PF joints were also
representedasadepth-dependentnonhomogeneousnonlinearcompositeofincompressiblebulkmatricesreinforcedby
collagen fibril networks [85–87]. In superficial zones of all cartilage layers and bounding surfaces of menisci, membrane
elements were used to represent homogeneous in-plane distribution of fibrils with random orientations [78]. Despite
such isotropic distribution, however, a direction-dependent response prevails due to the strain dependency in fibril
material properties and anisotropy in strain field. The collagen fibril properties (types I and II) were taken nonlinear
based on earlier studies [88]. In the transitional zone with random fibrils (i.e., no dominant orientations), continuum
brickelementsthat takethe principal straindirectionsasthe materialprincipalaxesrepresentcollagenfibrils.Inthedeep
zone, however, vertical fibrils were modeled with vertical membrane elements similar to horizontal superficial ones
except in offering resistance only in local fibril directions [86]. In the bulk region of each meniscus in between peripheral
surfaces, collagen fibrils that are dominant in the circumferential direction were represented by membrane elements
with local material principal axes defined initially in orthogonal circumferential and radial directions.
Thickness of membrane elements in different regions of cartilage and menisci was computed based on fibril volume
fraction in each zone. In the cartilage, the equivalent collagen fibril content in the superficial zone was estimated based
on reported tissue properties in tension [89–91] and type II collagen stress-strain curve [85]. A total volume fraction of
15% was estimated in the superficial zone in agreement with the mean value of 14% reported for its wet weight.
In accordance with earlier investigations [92, 93], the transient response of water-saturated articular cartilage and
meniscus under higher strain rates could be computed either by a biphasic approach or equivalently by an incompress-
ible elastic analysis using bulk equilibrium moduli. Examining this equivalency at various Poisson’s ratios using our
earlier nonhomogeneous axisymmetric model of cartilage [86], indentation results at 20% strain applied in 0.5s dem-
onstrated a significant sensitivity in transient reaction force [86, 87]. Nearly incompressible Poisson’s ratios in the range
of 0.4999–0.5 could yield results identical to those computed with biphasic simulations. Since loading cycles of daily
activities like walking and running last for only a fraction of second, an incompressible elastic model can hence alter-
natively be employed with no loss of accuracy to compute the transient response. In this case, the hydrostatic pressure
in the elastic model represents the transient pore pressure in its equivalent poroelastic model. An equivalent compress-
ible elastic material can also be employed in which case greater equilibrium moduli should be used depending on the
Poisson’s ratio considered.

I. BIOMECHANICS