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