Biomechanics

Biomechanics is the analysis of the mechanics of living organisms. The analysis can be carried forth on multiple levels, from the molecular, wherein molecular biomaterials such as collagen and elastin are considered, to the macroscopic level, all the way up to the tissue and organ level. Some simple applications of Newtonian Mechanics can supply correct approximations on each level, but precise details demand the use of Continuum Mechanics.

Some simple examples of biomechanics research include the investigation of the forces that act on limbs, the aerodynamics of bird and insect flight, the hydrodynamics of swimming in fish and locomotion in general across all forms of life, from individual cells to whole organisms. The biomechanics of human beings is a core part of kinesiology.

Applied mechanics, most notably thermodynamics and continuum mechanics and mechanical engineering disciplines such as fluid mechanics and solid mechanics, play prominent roles in the study of biomechanics. By applying the laws and concepts of physics, biomechanical mechanisms and structures can be simulated and studied.

Relevant mathematical tools include linear algebra, differential equations, vector and tensor calculus, and computational techniques such as the finite element method.

The study of biomaterials is of crucial importance to biomechanics. For example, the various tissues within the body, such as skin, bone, and arteries each possess unique material properties. The passive mechanical response of a particular tissue can be attributed to the various proteins, such as elastin and collagen, living cells, ground substances such as proteoglycans, and the orientations of fibers within the tissue. For example, if human skin were largely composed of a protein other than collagen, many of its mechanical properties, such as elastic modulus, would be different.

Chemistry, molecular biology, and cell biology have much to offer in the way of explaining the active and passive properties of living tissues. For example, the binding of myosin to actin is based on the biochemical reaction, where Ca^{2 +} and ATP move the troponin and tropomyosin to allow for the crossbridges to bind to the activation sites on the actin.

It has been shown that applied loads and deformations can affect the properties of living tissue. There is much research in the field of growth and remodeling as a response to applied loads. For example, the effects of elevated blood pressure on the mechanics of the arterial wall, the behavior of cardiomyocytes within a heart with a cardiac infarct, and bone growth in response to exercise have been widely regarded as instances in which living tissue is remodeling as a direct consequence of applied loads.

Applications

Biomechanisms include all higher-class forms of life. The study of biomechanics ranges from the inner workings of a cell to the movement and development of limbs, the vasculature , and bones. An understanding of the physiological behavior of living tissues would allow researchers to advance the field of tissue engineering, as well as develop improved treatments for a wide array of pathologies.

Continuum Mechanics

It is often appropriate to model living tissues as continuous media. For example, at the tissue level, the arterial wall can be modeled as a continuum. This assumption breaks down when the length scales of interest approach the order of the microstructural details of the material. The basic postulates of continuum mechanics are conservation of linear and angular momentum, conservation of mass, conservation of energy, and the entropy inequality. Solids are usually modeled using a Lagrangian or reference coordinates, whereas fluids are often modeled using spatial or Eulerian coordinates. Using these postulates and some assumptions regarding the particular problem at hand, a set of equilibrium equations can be established. The kinematics and constitutive relations are also needed to model a continuum.

Second and fourth order tensors are crucial in representing many quantities in biomechanics. In practice, however, the full tensor form of a fourth order constitutive matrix is rarely used. Instead, simplifications such as isotropy, transverse isotropy, and incompressibility reduce the number of independent components. Commonly used second order tensors include the Cauchy stress tensor, the second Piola-Kirchhoff stress tensor, the deformation gradient tensor, and the Green strain tensor. A reader of the biomechanics literature would be well-advised to note precisely the definitions of the various tensors which are being used in a particular work.

Biomechanics of Circulation

Under most circumstances, blood flow can be modeled by the Navier-Stokes equations. Whole blood can often be assumed to be an incompressible Newtonian fluid. However, this assumption fails when considering flows within arterioles. At this scale, the effects of individual red blood cells becomes significant, and whole blood can no longer be modeled as a continuum.

Biomechanics of the bones

Bones are anisotropic but are approximately transversely isotropic. The stress-strain relations of bones can be modeled using Hooke's Law, in which they are related by linear constants known as the Young's modulus or the elastic modulus, and the shear modulus and poission ratio, collectively known as the Lam constants. The constitutive matrix, a fourth order tensor, depends on the isotropy of the bone.

σ_ij = C_ijklε_kl

Biomechanics of the Muscle

There are three main types of muscles:

• Skeletal Muscle (striated) Unlike cardiac muscle, skeletal muscle can develop a sustained condition known as tetany through high frequency stimulation, resulting in overlapping twitches and a phenomenon known as wave summation. At a sufficiently high frequency, tetany occurs, and the contracticle force appears constant through time. This allows skeletal muscle to develop a wide variety of forces. This muscle type can be voluntary controlled. Hill's Model is the most popular model used to study muscle.

• Cardiac Muscle (striated) Cardiomyocytes are a highly specialized cell type. These involuntarily contracted cells are located in the heart wall and operate in concert to develop synchronized beats. This is attributable to a refractory period between twitches.

• Smooth Muscle (smooth - lacking striations) The stomach, vasculature, and most of the digestive tract are largely composed of smooth muscle. This muscle type is involuntary and is controlled by the enteric nervous system.

Viscoelasticity

Viscoelasticity is readily evident in many soft tissues, where there is energy dissipation, or hysteresis, between the loading and unloading of the tissue during mechanical tests. Some soft tissues can be preconditioned by repetitive cyclic loading to the extent where the stress-strain curves for the loading and unloading portions of the tests nearly overlap.

Nonlinear Theories

Hooke's law is linear, but many, if not most problems in biomechanics, involve highly nonlinear behavior. Proteins such as collagen and elastin, for example, exhibit such a behavior. Some common material models include the Neo-Hookean behavior, often used for modeling elastin, and the famous Fung-elastic exponential model.

See also

• Mechanics
• orthosis
• physiology
• anatomy
• Important publications in biomechanics

References

• Fung, Y.C. "Biomechanics: Mechanical Properties of Living Tissue" (2nd ed.). New York: Springer. ISBN 0-387-97947-6.
• Humphrey, Jay D. "Cardiovascular Solid Mechanics: Cells, Tissues, and Organs." New York: Springer. ISBN 0-387-95168-7.
• Vogel, Steven. (2003). Comparative Biomechanics: Life's Physical World. Princeton: Princeton University Press. ISBN 0691112975