1. Soft Tissues Unlike bone, most solid tissues are soft
they can undergo large deformations without failing
Soft tissues with obvious mechanical functions:
skin – blood vessels
ligaments – tendons
pericardium – heart valves
muscle – myocardium
Other soft tissues:
stomach – intestines
esophagus – kidney
liver – lung
Feb 2000: I only got half way through this. One way to make it smoother and easier would be to make hyperlinks from the overview slides to the examples, showing preconditioning etc. The kinematics should either be more complete or more simple. They have not seen it before, so really it should be more complete. Use extra slides from BE250A topic 4. I have now edited these and saved them as be112a topic 8a. Then turn this in to two lectures instead of one. Also current topic 9 should go after current topic 7 and not be separated by topic 8.

2. References Textbook sections 7.5, 7.7-7.10, 7.12
Y-C Fung (1981) Chapter 1 in Handbook of Bioengineering (Skalak and Chien, Eds)
Y-C Fung (1973) Biorheology of Soft Tissues. Biorheology 10:

3. Basic Properties of Soft Tissues
Can be classified as:
“Biological”
Structural
Mechanical
Elastic
Anelastic

4. “Biological” Properties
Dynamic
growth, remodeling and adaptation
injury and healing
hypertrophy, proliferation, necrosis, apoptosis
active cell contraction and cell motion
Compartmentalized
intracellular structures and organelles
cell-matrix units
electrochemical balance
Responsive and sensitive to environment
homeostasis
signal transduction

5. Structural Properties
Complex composites
cells and basic functional units
extracellular matrix
vasculature and lymphatics
Hydrated
65-85% water
intracellular, interstitial, vascular & lymphatic
hydrostatic pressure and fluid flow
Organized hierarchical microstructure
Irregular three-dimensional geometry
Difficult to test

6. Elastic Properties Large (finite) deformations
Nonlinear stress-strain relations
Anisotropy – multiaxial material properties
Inhomogeneity – properties that varying with location in the tissue
Microstructural determinants of material properties

7. Anelastic Properties
Hysteresis – energy dissipation during loading and unloading
Creep – time-dependent increase in strain following a step increase in stress
Stress relaxation – time-dependent relaxation in stress following a step increase in strain
Strain-rate dependence (small)
Viscoelasticity – stress depends on the time-history of strain with a fading memory
– models all the above properties
Pseudoelasticity approximation
Preconditioning behavior
Strain softening – stress depends on the history of maximum strain

8. Large elastic deformations: Maximum physiological stretches
Lung 100%
Heart muscle 50% (thickening)
Mesentery %
Ureter 60%
Arteries/Veins 60%
Skin 40%
Tendons 2-5%
Ligaments 5-10%

9. Tangent Modulus vs. Stress
Nonlinear Elasticity
Stress-strain curves of soft tissues are nonlinear
Tangent Modulus vs. Stress
Tangent modulus (slope of the stress-strain curve) is often proportional to the stress

10. Exponential Elasticity
Exponential stress-strain relations often work well (e.g. cardiac muscle, skin, ureter), but not always (e.g. aorta).

11. Exponential Elasticity
Cornea under uniaxial tension
Table 7.5:1 in textbook

12. Incremental Elasticity
Incremental Elasticity – assume linear elasticity and solve for small increments of strain, updating the "incremental elastic modulus" for each step
In viscoelastic tissues, incremental modulus must be measured by incremental testing
Rabbit mesentary
Fig. 7.7:1 in text

13. Anisotropy
Ligaments, tendons and muscles are fibrous with greatest strength and stiffness along their axes
Blood vessels are orthotropic (like bone), with different properties axially, radially and circumferentially
Requires simultaneous multiaxial testing, e.g. biaxial testing
unlike bone, multiple uniaxial tests are insufficient due to nonlinear interactions, e.g. axial strain in arteries alters the circumferential stress-strain curve

14. x-axis = caudal-cranial
Anisotropy
Biaxial testing rig
(Fig. 7.9:1 in textbook)
Rabbit abdominal skin
x-axis = caudal-cranial
(Fig. 7.12:2 in textbook)

15. Inhomogeneity Blood vessels have three transmural layers:
intima (endothelial cell layer)
media (muscular middle layer)
adventitia (outer connective tissue layer)
Properties vary along arterial tree:
from proximal ascending aorta (high elastin, low smooth muscle)
to descending abdominal aorta (less elastin)
to smaller arterioles (more smooth muscle)
Artery Wall

16. Hysteresis
Difference in the stress-strain relation between loading and unloading
Area of the hysteresis loop represents energy dissipation as heat during the load cycle
Hysteresis is a property of viscoelastic materials
It is associated with tissue fluid motion, e.g. synovial fluid in cartilage
Varies between tissues
high in smooth muscle and cartilage
low in ligament and tendon
higher in arterioles; lower in aorta
Human vena cava
Fig 8.11:3 in text

17. Hysteresis
Guinea pig jejunum (Gregerson et al., 1998)

18. Creep
Creep is the strain response over time to a step change in the stress

19. Stress Relaxation
Stress relaxation is the stress response over time to a step change in the strain
Creep and relaxation are viscoelastic properties, e.g. they are sufficient to predict hysteresis response quite well
Bovine coronary artery

20. Strain-rate dependence
Rabbit papillary muscle
(Fig 7.5:2 in text)
A viscoelastic property of materials
Changes in hysteresis loop and stiffness with strain-rate are relatively small (<100%) for strain rates spanning the physiological range (e.g. <1000-fold)
Soft tissues are therefore similar to to bone in this respect — they do exhibit strain-rate dependence but not very much over the physiological range of rates

21. Pseudoelasticity Concept
Since the properties of soft tissues are only weakly dependent on strain-rate, we approximate their response to loading and unloading by two stress-strain relations that are assumed to be independent of strain rate
Thus we can approximate the viscoelastic hysteresis behavior of soft tissues within the more tractable framework of elasticity, provided we allow that the elastic properties can be different for loading and unloading

22. Preconditioning Behavior
Stress-strain curve changes between 1st, 2nd and subsequent repetitions of loading-unloading. But with sufficient repetitions test becomes repeatable and tissue is preconditioned
Preconditioned state is regarded as most representative of the in-vivo (homeostatic) state
Required preconditioning cycles varies with tissue and conditions from 2-3 cycles to >15
Testing system itself can contribute to preconditioning behavior, e.g. tethering damage
passive bovine coronary artery
STRESS, kPa
Characteristic uniaxial preconditioning behavior during cyclic testing (data from Humphrey JD, Salunke N, Tippett B, 1996)

23. Strain Softening
Strain softening (Mullins effect) contributes to preconditioning
Strain softening is a property of many elastomers
Material is stiffer during the first loading to a new maximum strain than during subsequent loading to that strain
Emery et al (1995) and Gregersen et al (1998) demonstrated that this is the major cause of preconditioning in passive ventricular muscle and small intestine
Damage: injury, tearing can all occur in tissues loaded beyond normal limits

24. Strain Softening
Guinea pig jejunum (Gregerson et al., 1998)

25. Soft Tissues: Summary of Key Points
Soft tissues are structurally complex, hydrated composites of cells and extracellular matrices
Their characteristic mechanical properties include:
Finite deformations, nonlinearity, anisotropy, inhomogeneity
Viscoelastic properties including creep, stress relaxation and hysteresis
Other anelastic properties such as strain softening
Because soft tissues exhibit load-history dependent behavior, mechanical tests must be repeated until the tissue is “preconditioned”.