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