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