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.

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

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

“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

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

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

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

Large elastic deformations: Maximum physiological stretches Lung 100% Heart muscle 50% (thickening) Mesentery 100-200% Ureter 60% Arteries/Veins 60% Skin 40% Tendons 2-5% Ligaments 5-10%

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

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

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

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

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

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)

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

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

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

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

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

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

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

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)

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

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

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”.