Soft tissue

In anatomy, soft tissues are the tissues that connect, support, or surround other structures and organs of the body, not being bone. Soft tissue includes tendons, ligaments, fascia, skin, fibrous tissues, fat, and synovial membranes (which are connective tissue), and muscles, nerves and blood vessels (which are not connective tissue).[1]

It is sometimes defined by what it is not. Soft tissue has been defined as "nonepithelial, extraskeletal mesenchyme exclusive of the reticuloendothelial system and glia".[2]


The characteristic substances inside the extracellular matrix of this kind of 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.[3]

Mechanical characteristics

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.[4] When solid object impact a human soft tissues, the energy of the impact will be absorbed by the tissues to reducing effect of the impact or the pain level, therefore; subjects with more soft tissue thickness tended to absorb the impacts with less aversion.[5]

File:Pseudoelastic response (stress vs stretch ratio).png
Figure 1: Graph of lagrangian stress (T) versus stretch ratio (λ) of a preconditioned soft tissue.

Soft tissues have the potential to undergo big deformations and still come back to the initial configuration when unloaded. The stress-strain curve is nonlinear, as can be seen in Figure 1. The soft tissues are also viscoelastic, incompressible and usually anisotropic. Some viscoelastic properties observable in soft tissues are: relaxation, creep and hysteresis.[6][7]


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.

<math>\mathbf{S}=\mathbf{S}(\mathbf{E},\dot{\mathbf{E}}) \quad\rightarrow\quad \mathbf{S}=\mathbf{S}(\mathbf{E})</math>

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 (see Figure 1). 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.[7]

Residual stress

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.[7]

Fung-elastic material

Fung developed a constitutive equation for preconditioned soft tissues which is

<math>W = \frac{1}{2}\left[q + c\left( e^Q -1 \right) \right]</math>


<math>q=a_{ijkl}E_{ij}E_{kl} \qquad Q=b_{ijkl}E_{ij}E_{kl}</math>

quadratic forms of Green-Lagrange strains <math>E_{ij}</math> and <math>a_{ijkl}</math>, <math>b_{ijkl}</math> and <math>c</math> material constants.[7] <math>w</math> is the strain energy function per volume unit, which is the mechanical strain energy for a given temperature.

Isotropic simplification

The Fung-model, simplified with isotropic hypothesis (same mechanical properties in all directions). This written in respect of the principal stretches (<math>\lambda_i</math>):

<math>W = \frac{1}{2}\left[a(\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3) + b\left( e^{c(\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3)} -1 \right) \right]</math> ,

where a, b and c are constants.

Simplification for small and big stretches

For small strains, the exponential term is very small, thus negligible.

<math>W = \frac{1}{2}a_{ijkl}E_{ij}E_{kl}</math>

On the other hand, the linear term is negligible when the analysis rely only on big strains.

<math>W = \frac{1}{2}c\left( e^{b_{ijkl}E_{ij}E_{kl}} -1 \right)</math>

Gent-elastic material

Further information: Gent (hyperelastic model)
<math>W = - \frac{\mu J_m}{2} \ln \left(1 - \left( \frac{\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3}{J_m} \right) \right)</math>

where <math>\mu > 0</math> is the shear modulus for infinitesimal strains and <math>Jm > 0</math> is a stiffening parameter, associated with limiting chain extensibility.[8] This constitutive model cannot be stretched in uni-axial tension beyond a maximal stretch <math>Jm</math>, which is the positive root of

<math>\lambda_m^2 + 2\lambda_m - J_m - 3 = 0 </math>

Remodeling and growth

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. 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.[6]

Growth and remodeling have a major role in the etiology of some common soft tissue diseases, like arterial stenosis and aneurisms [9][10] 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.

See also


  1. ^ Definition at National Cancer Institute
  2. ^ Skinner, Harry B. (2006). Current diagnosis & treatment in orthopedics. Stamford, Conn: Lange Medical Books/McGraw Hill. p. 346. ISBN 0-07-143833-5. 
  3. ^ Junqueira, L.C.U.; Carneiro, J.; Gratzl, M. (2005). Histologie. Heidelberg: Springer Medizin Verlag. p. 479. ISBN 3-540-21965-X. 
  4. ^ Amar, M., Alkhaledi, K., and Cochran, D., (2014). Estimation of mechanical properties of soft tissue subjected to dynamic impact. Journal of Eng. Research Vol. 2 (4), pp. 87-101
  5. ^ Alkhaledi, K., Cochran, D., Riley, M., Bashford, G., and Meyer, G. (2011). The psycophysical effects of physical impact to human soft tissue. ECCE '11 Proceedings of the 29th Annual European Conference on Cognitive Ergonomics Pages 269-270
  6. ^ a b Humphrey, Jay D. (2003). The Royal Society, ed. "Continuum biomechanics of soft biological tissues" (PDF). Proceedings of the Royal Society of London A 459 (2029): 3–46. Bibcode:2003RSPSA.459....3H. doi:10.1098/rspa.2002.1060. 
  7. ^ a b c d Fung, Y.-C. (1993). Biomechanics: Mechanical Properties of Living Tissues. New York: Springer-Verlag. p. 568. ISBN 0-387-97947-6. 
  8. ^ Gent, A. N. (1996). "A new constitutive relation for rubber". Rub. Chem. Tech. 69: 59–61. 
  9. ^ Humphrey, Jay D. (2008). Springer-Verlag, ed. "Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels". Cell Biochemistry and Biophysics 50 (2): 53–78. PMID 18209957. doi:10.1007/s12013-007-9002-3. 
  10. ^ Holzapfel, G.A.; Ogden, R.W. (2010). The Royal Society, ed. "Constitutive modelling of arteries". Proceedings of the Royal Society of London A 466 (2118): 1551–1597. Bibcode:2010RSPSA.466.1551H. doi:10.1098/rspa.2010.0058.