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

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 10:139-155

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) deformationsfinite Nonlinear stress-strain relationsNonlinear Anisotropy – multiaxial material propertiesAnisotropy Inhomogeneity – properties that varying with location in the tissueInhomogeneity Microstructural determinants of material properties

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

8. Large elastic deformations: Maximum physiological stretches Lung100% Heart muscle50% (thickening) Mesentery100-200% Ureter60% Arteries/Veins60% Skin40% Tendons2-5% Ligaments5-10%

9. 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 Table 7.5:1 in textbook Cornea under uniaxial tension

12. 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

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

14. 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

15. 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

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

17. 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

18. 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

19. 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

20. 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 STRESS, kPa passive bovine coronary artery Characteristic uniaxial preconditioning behavior during cyclic testing (data from Humphrey JD, Salunke N, Tippett B, 1996)

21. 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

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

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