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