Introduction to biomechanics


Applications of biomechanics

It is often appropriate to model livingcan be voluntary controlled. Hill's Model is
tissues as continuous media. For example, atthe most popular model used to study muscle.
the tissue level, the arterial wall can be
modeled as a continuum. This assumptionCardiac muscle (striated): Cardiomyocytes are
breaks down when the length scales ofa highly specialized cell type. These
interest approach the order of theinvoluntarily contracted cells are located in
microstructural details of the material. Thethe heart wall and operate in concert to
basic postulates of continuum mechanics aredevelop synchronized beats. This is
conservation of linear and angular momentum,attributable to a refractory period between
conservation of mass, conservation of energy,twitches.
and the entropy inequality. Solids are
usually modeled using "reference" orSmooth muscle (smooth - lacking striations):
"Lagrangian" coordinates, whereas fluids areThe stomach, vasculature, and most of the
often modeled using "spatial" or "Eulerian"digestive tract are largely composed of
coordinates. Using these postulates and somesmooth muscle. This muscle type is
assumptions regarding the particular probleminvoluntary and is controlled by the enteric
at hand, a set of equilibrium equations cannervous  system.
be established. The kinematics and
constitutive relations are also needed toBiomechanics  of  Soft  Tissues
model  a  continuum.
Soft tissues such as tendon, ligament and
Second and fourth order tensors are crucialcartilage are combinations of matrix proteins
in representing many quantities inand fluid. In each of these tissues the main
biomechanics. In practice, however, the fullstrength bearing element is collagen,
tensor form of a fourth-order constitutivealthough the amount and type of collagen
matrix is rarely used. Instead,varies according to the function each tissue
simplifications such as isotropy, transversemust perform. Elastin is also a major
isotropy, and incompressibility reduce theload-bearing constituent within skin, the
number of independent components.vasculature, and connective tissues. The
Commonly-used second-order tensors includefunction of tendons is to connect muscle with
the Cauchy stress tensor, the secondbone and is subjected to tensile loads.
Piola-Kirchhoff stress tensor, theTendons must be strong to facilitate movement
deformation gradient tensor, and the Greenof the body while at the same time remaining
strain tensor. A reader of the biomechanicscompliant to prevent damage to the muscle
literature would be well-advised to notetissues. Ligaments connect bone to bone and
precisely the definitions of the varioustherefore are stiffer than tendons but are
tensors which are being used in a particularrelatively close in their tensile strength.
work.Cartilage, on the other hand, is primarily
loaded in compression and acts as a cushion
Biomechanics  of  Circulationin the joints to distribute loads between
bones. The compressive strength of collagen
Under most circumstances, blood flow can beis derived mainly from collagen as in tendons
modeled by the Navier-Stokes equations. Wholeand ligaments, however because collagen is
blood can often be assumed to be ancomparable to a "wet noodle" it must be
incompressible Newtonian fluid. However, thissupported by cross-links of
assumption fails when considering flowsglycosaminoglycans that also attract water
within arterioles. At this scale, the effectsand create a nearly incompressible tissue
of individual red blood cells becomescapable  of  supporting  compressive  loads.
significant, and whole blood can no longer be
modeled  as  a  continuum.Recently, research is growing on the
biomechanics of other types of soft tissues
Biomechanics  of  the  bonessuch as skin and internal organs. This
interest is spurred by the need for realism
Bones are anisotropic but are approximatelyin  the  development  of  medical simulation.
transversely isotropic. In other words, bones
are stronger along one axis than across thatViscoelasticity
axis, and are approximately the same strength
no matter how they are rotated around thatViscoelasticity is readily evident in many
axis.soft tissues, where there is energy
dissipation, or hysteresis, between the
The stress-strain relations of bones can beloading and unloading of the tissue during
modeled using Hooke's Law, in which they aremechanical tests. Some soft tissues can be
related by linear constants known as thepreconditioned by repetitive cyclic loading
Young's modulus or the elastic modulus, andto the extent where the stress-strain curves
the shear modulus and Poisson's ratio,for the loading and unloading portions of the
collectively known as the Lamé constants.tests  nearly  overlap.
The constitutive matrix, a fourth order
tensor,  depends on the isotropy of the bone.Nonlinear  Theories
Biomechanics  of  the  MuscleHooke's law is linear, but many, if not most
problems in biomechanics, involve highly
There  are  three  main  types  of  muscles:nonlinear behavior. Proteins such as collagen
and elastin, for example, exhibit such a
Skeletal muscle (striated): Unlike cardiacbehavior. Some common material models include
muscle, skeletal muscle can develop athe Neo-Hookean behavior, often used for
sustained condition known as tetany throughmodeling elastin, and the famous Fung-elastic
high frequency stimulation, resulting inexponential model. Non linear phenomena in
overlapping twitches and a phenomenon knownthe biomechanics of soft tissue arise not
as wave summation. At a sufficiently highonly from the material properties but also
frequency, tetany occurs, and thefrom the very large strains (100% and more)
contracticle force appears constant throughthat are characteristic of many problems in
time. This allows skeletal muscle to developsoft tissues.
a wide variety of forces. This muscle type



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