Soft tissue is all the tissue in the body that is not hardened by the processes of ossification or calcification such as bones and teeth. [1] Soft tissue connects, surrounds or supports internal organs and bones, and includes muscle, tendons, ligaments, fat, fibrous tissue, lymph and blood vessels, fasciae, and synovial membranes. [1] [2]
It is sometimes defined by what it is not – such as "nonepithelial, extraskeletal mesenchyme exclusive of the reticuloendothelial system and glia". [3]
The characteristic substances inside the extracellular matrix of soft tissue are the collagen, elastin and ground substance. Normally the soft tissue is very hydrated because of the ground substance. The fibroblasts are the most common cell responsible for the production of soft tissues' fibers and ground substance. Variations of fibroblasts, like chondroblasts, may also produce these substances. [4]
At small strains, elastin confers stiffness to the tissue and stores most of the strain energy. The collagen fibers are comparatively inextensible and are usually loose (wavy, crimped). With increasing tissue deformation the collagen is gradually stretched in the direction of deformation. When taut, these fibers produce a strong growth in tissue stiffness. The composite behavior is analogous to a nylon stocking, whose rubber band does the role of elastin as the nylon does the role of collagen. In soft tissues, the collagen limits the deformation and protects the tissues from injury.
Human soft tissue is highly deformable, and its mechanical properties vary significantly from one person to another. Impact testing results showed that the stiffness and the damping resistance of a test subject’s tissue are correlated with the mass, velocity, and size of the striking object. Such properties may be useful for forensics investigation when contusions were induced. [5] When a solid object impacts a human soft tissue, the energy of the impact will be absorbed by the tissues to reduce the effect of the impact or the pain level; subjects with more soft tissue thickness tended to absorb the impacts with less aversion. [6]
Soft tissues have the potential to undergo large deformations and still return to the initial configuration when unloaded, i.e. they are hyperelastic materials, and their stress-strain curve is nonlinear. The soft tissues are also viscoelastic, incompressible and usually anisotropic. Some viscoelastic properties observable in soft tissues are: relaxation, creep and hysteresis. [7] [8] In order to describe the mechanical response of soft tissues, several methods have been used. These methods include: hyperelastic macroscopic models based on strain energy, mathematical fits where nonlinear constitutive equations are used, and structurally based models where the response of a linear elastic material is modified by its geometric characteristics. [9]
Even though soft tissues have viscoelastic properties, i.e. stress as function of strain rate, it can be approximated by a hyperelastic model after precondition to a load pattern. After some cycles of loading and unloading the material, the mechanical response becomes independent of strain rate.
Despite the independence of strain rate, preconditioned soft tissues still present hysteresis, so the mechanical response can be modeled as hyperelastic with different material constants at loading and unloading. By this method the elasticity theory is used to model an inelastic material. Fung has called this model as pseudoelastic to point out that the material is not truly elastic. [8]
In physiological state soft tissues usually present residual stress that may be released when the tissue is excised. Physiologists and histologists must be aware of this fact to avoid mistakes when analyzing excised tissues. This retraction usually causes a visual artifact. [8]
Fung developed a constitutive equation for preconditioned soft tissues which is
with
quadratic forms of Green-Lagrange strains and , and material constants. [8] is the strain energy function per volume unit, which is the mechanical strain energy for a given temperature.
The Fung-model, simplified with isotropic hypothesis (same mechanical properties in all directions). This written in respect of the principal stretches ():
where a, b and c are constants.
For small strains, the exponential term is very small, thus negligible.
On the other hand, the linear term is negligible when the analysis rely only on big strains.
where is the shear modulus for infinitesimal strains and is a stiffening parameter, associated with limiting chain extensibility. [10] This constitutive model cannot be stretched in uni-axial tension beyond a maximal stretch , which is the positive root of
Soft tissues have the potential to grow and remodel reacting to chemical and mechanical long term changes. The rate the fibroblasts produce tropocollagen is proportional to these stimuli. Diseases, injuries and changes in the level of mechanical load may induce remodeling. [11] [12] An example of this phenomenon is the thickening of farmer's hands. The remodeling of connective tissues is well known in bones by the Wolff's law (bone remodeling). Mechanobiology is the science that study the relation between stress and growth at cellular level. [7]
Growth and remodeling have a major role in the cause of some common soft tissue diseases, like arterial stenosis and aneurisms [13] [14] and any soft tissue fibrosis. Other instance of tissue remodeling is the thickening of the cardiac muscle in response to the growth of blood pressure detected by the arterial wall.
There are certain issues that have to be kept in mind when choosing an imaging technique for visualizing soft tissue extracellular matrix (ECM) components. The accuracy of the image analysis relies on the properties and the quality of the raw data and, therefore, the choice of the imaging technique must be based upon issues such as:
The collagen fibers are approximately 1-2 μm thick. Thus, the resolution of the imaging technique needs to be approximately 0.5 μm. Some techniques allow the direct acquisition of volume data while other need the slicing of the specimen. In both cases, the volume that is extracted must be able to follow the fiber bundles across the volume. High contrast makes segmentation easier, especially when color information is available. In addition, the need for fixation must also be addressed. It has been shown that soft tissue fixation in formalin causes shrinkage, altering the structure of the original tissue. Some typical values of contraction for different fixation are: formalin (5% - 10%), alcohol (10%), bouin (<5%). [15]
Imaging methods used in ECM visualization and their properties. [15] [16]
Transmission Light | Confocal | Multi-Photon Excitation Fluorescence | Second Harmonic Generation | ||
Resolution | 0.25 μm | Axial: 0.25-0.5 μm Lateral: 1 μm | Axial: 0.5 μm Lateral: 1 μm | Axial: 0.5 μm Lateral: 1 μm | Axial: 3-15 μm Lateral: 1-15 μm |
Contrast | Very High | Low | High | High | Moderate |
Penetration | N/A | 10 μm-300 μm | 100-1000 μm | 100-1000 μm | Up to 2–3 mm |
Image stack cost | High | Low | Low | Low | Low |
Fixation | Required | Required | Not required | Not required | Not required |
Embedding | Required | Required | Not required | Not required | Not required |
Staining | Required | Not required | Not required | Not required | Not required |
Cost | Low | Moderate to high | High | High | Moderate |
Soft tissue disorders are medical conditions affecting soft tissue. Soft tissue injuries are some of the most chronically painful and difficult conditions to treat because it is very difficult to see what is going on under the skin with the soft connective tissues, fascia, joints, muscles and tendons.
Musculoskeletal specialists, manual therapists and neuromuscular physiologists and neurologists specialize in treating injuries and ailments in the soft tissue areas of the body. These specialized clinicians often develop innovative ways to manipulate the soft tissue to speed natural healing and relieve the mysterious pain that often accompanies soft tissue injuries. This area of expertise has become known as soft tissue therapy and is rapidly expanding as technology continues to improve the ability of these specialists to identify problem areas.
A promising new method of treating wounds and soft tissue injuries is via platelet-derived growth factor. [17]
There is a close overlap between the term "soft tissue disorder" and rheumatism. Sometimes the term "soft tissue rheumatic disorders" is used to describe these conditions. [18]
Soft tissue sarcomas are many types of cancer that can develop in the soft tissues.
In physics, Hooke's law is an empirical law which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring, and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis. Hooke states in the 1678 work that he was aware of the law since 1660.
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
Yuan-Cheng "Bert" Fung was a Chinese-American bioengineer and writer. He is regarded as a founding figure of bioengineering, tissue engineering, and the "Founder of Modern Biomechanics".
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations.
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue.
In continuum mechanics, a Mooney–Rivlin solid is a hyperelastic material model where the strain energy density function is a linear combination of two invariants of the left Cauchy–Green deformation tensor . The model was proposed by Melvin Mooney in 1940 and expressed in terms of invariants by Ronald Rivlin in 1948.
In the mathematical fields of Riemannian and pseudo-Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a Riemannian or pseudo-Riemannian manifold into pieces with special algebraic properties. This decomposition is of fundamental importance in Riemannian and pseudo-Riemannian geometry.
Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity.
A hyperelastic or Green elastic material is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function. The hyperelastic material is a special case of a Cauchy elastic material.
A strain energy density function or stored energy density function is a scalar-valued function that relates the strain energy density of a material to the deformation gradient.
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness tensor. Common symbols include and .
The Ogden material model is a hyperelastic material model used to describe the non-linear stress–strain behaviour of complex materials such as rubbers, polymers, and biological tissue. The model was developed by Raymond Ogden in 1972. The Ogden model, like other hyperelastic material models, assumes that the material behaviour can be described by means of a strain energy density function, from which the stress–strain relationships can be derived.
In continuum mechanics, an Arruda–Boyce model is a hyperelastic constitutive model used to describe the mechanical behavior of rubber and other polymeric substances. This model is based on the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material is assumed to be incompressible. The model is named after Ellen Arruda and Mary Cunningham Boyce, who published it in 1993.
The Gent hyperelastic material model is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, the strain energy density function is designed such that it has a singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value .
The acoustoelastic effect is how the sound velocities of an elastic material change if subjected to an initial static stress field. This is a non-linear effect of the constitutive relation between mechanical stress and finite strain in a material of continuous mass. In classical linear elasticity theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised Hooke's law. The linear elastic theory involves second order elastic constants and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand include higher order expansion of the constitutive relation between the applied stress and resulting strain, which yields longitudinal and shear sound velocities dependent of the stress state of the material. In the limit of an unstressed material the sound velocities of the linear elastic theory are reproduced.
Plasticity theory for rocks is concerned with the response of rocks to loads beyond the elastic limit. Historically, conventional wisdom has it that rock is brittle and fails by fracture while plasticity is identified with ductile materials. In field scale rock masses, structural discontinuities exist in the rock indicating that failure has taken place. Since the rock has not fallen apart, contrary to expectation of brittle behavior, clearly elasticity theory is not the last word.
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate. The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame-indifferent (objective). If the stress and strain measures are material quantities then objectivity is automatically satisfied. However, if the quantities are spatial, then the objectivity of the stress-rate is not guaranteed even if the strain-rate is objective.
The fracture of soft materials involves large deformations and crack blunting before propagation of the crack can occur. Consequently, the stress field close to the crack tip is significantly different from the traditional formulation encountered in the Linear elastic fracture mechanics. Therefore, fracture analysis for these applications requires a special attention. The Linear Elastic Fracture Mechanics (LEFM) and K-field are based on the assumption of infinitesimal deformation, and as a result are not suitable to describe the fracture of soft materials. However, LEFM general approach can be applied to understand the basics of fracture on soft materials. The solution for the deformation and crack stress field in soft materials considers large deformation and is derived from the finite strain elastostatics framework and hyperelastic material models.
In materials science and solid mechanics, biaxial tensile testing is a versatile technique to address the mechanical characterization of planar materials. It is a generalized form of tensile testing in which the material sample is simultaneously stressed along two perpendicular axes. Typical materials tested in biaxial configuration include metal sheets, silicone elastomers, composites, thin films, textiles and biological soft tissues.