Viscoelasticity and Biological Tissues

Viscoelasticity and Biological TissuesBIOE 3200 Biomechanics

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Define viscoelastic stress/strain and time dependent relationships, and compare for different materials Define viscoelastic behaviors (creep and stress relaxation) and compare for different biologic materials (muscle, ligament, tendon, cartilage)Identify tissue structures and components that contribute and/or explain viscoelastic properties for different biologic materials

Learning Objectives:

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Review: Constitutive Relationships

Stress/strain curves for metal, soft tissue and rubber/elastomers(from pp. 81-87 in text); strains are orders of magnitude higher for soft tissues and elastomers

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Examples:Instant deformation under loadDeformation is recovered

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Elastic behavior

An instantaneous increase in applied force is known as a step-function (See force-time curve for step function above); resulting deformation curve is also a step function for elastic materialsMechanical analogy for elastic material: springCharacterized by straight stress/strain curve, elasticity (constant elastic modulus, or slope of stress/strain curve), no energy loss when loaded and unloadedMetal is linear (direct relation between stress and strain) and elastic it responds almost instantaneously under load and there is no energy dissipated when it deforms. Bone and teeth are linear under small strains (within physiologic ranges); there are no changes in microstructure, so no change in properties.

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Not instantaneous deformationDeformation not recovered

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Viscous behavior

Force-time curve for step function on top; below is resulting deformation curve for viscous material (linearly increasing deformation from t0 to t1, flat line after t1)Mechanical analogy for viscous material: dashpotCurved stress/strain curve; typically shown as stress and strain rate (change in strain with time); viscous materials have a constant strain rate under constant load5

Viscoelastic = viscous + elastic behaviorInstantaneous and delayed deformationSome deformation is recovered, some is not

Viscoelasticity defined

- Soft tissues and elastomers are non-linear under stress with no permanent change in structure; this is due to their long-chain polymeric structure. Specific behavior of different tissue types depends on underlying conformations of molecules (inherent order or disorder). Elastin and collagen dominate soft tissue behavior; soft tissue is nearly elastic or pseudoelastic, meaning it responds almost instantaneously under load, but exhibits hysteresis (different loading and unloading curves due to energy loss). Hysteresis is due to movement of the structural proteins within the viscous ground substance (dominated by proteoglycans). Bones experience small strains (less than .001 during walking) which are necessary for balanced osteoblast/osteoclast activity (compressive strain); higher strain = higher bone production and lower removal of bone, eventually leading to microdamage, which may stimulate growth/healing response. Extremely low strains (unloading) leads to net loss of bone.Strain response to applied stress depends on strain rate (similar to loading rate); strain rate sensitivity is a characteristic of time-dependent behavior of viscoelastic materials.

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Time-dependent behaviorViscoelasticity: Creep and Stress Relaxation Behaviors

Refer to Humphrey and Delange Ch 11.4 for a thorough explanation of creep and stress relaxation curves.Creep: apply a constant force, and resulting deformation is time-dependent.Stress relaxation: apply a constant deformation, and resulting stress within the material is time-dependent.7

Difference in creep behavior of rubber band and electrical tape demonstrates the conceptCreep behavior can be demonstrated experimentally

Rubber bandElectrical tapeWeights (apply constant force)

Test set up for measuring creep (known load, measure deformation over time); different for electrical tape vs. rubber bandApply a constant stress and measure resulting strainStrain (creep) will grow with time Modulus is time-dependentUnlike elastic materials - under fixed stress elastic materials will reach a fixed strain and stay at that level8

Creep time-dependent deformation under a constant load; (Sort of the inverse of stress relaxation); refers to the general characteristic of viscoelastic materials to undergo increased deformation under a constant stress, until an asymptotic level of strain is reached9

Creep constant load (step function for force-time curve); increased deformation to asymptotic level of strain, as shown in stress/strain figure

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Force gauge (like a fish scale) applies constant displacement, measures resulting loadStress relaxation behavior can be demonstrated experimentally

Rubber bandElectrical tapeForce gauge (apply constant displacement)

Test set up for measuring stress relaxation (known deformation, measure change in force over time)Apply constant strain and measure resulting stressStress decreases with time (material relaxes) Modulus is time-dependentUnlike elastic materials - under fixed strain, elastic materials will reach a fixed stress and stay at that level with no relaxation11

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Stress Relaxation Behavior of Biological Materials (Soft Tissues)

Stress relaxation time-dependent decrease in load at a constant deformation; refers to the behavior of stress reaching a peak and then decreasing or relaxing over time under a fixed level of strain, as shown in stress/strain figure

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All biological tissues exhibit viscoelastic behaviors (hysteresis, creep, stress relaxation)Elastin fibersCollagenSmooth MuscleDifferent tissues contain different amounts or fractions of collagen and elastic fibers resulting in different mechanical propertiesTendonLigamentIntestinal wallComparing viscoelastic behaviors of different tissues

The more viscous a material, the more it relaxes and creeps; more strain rate dependency Different relative fractions of collagen and elastin in each tissueTendons (muscle bone) more collagen than elastin by weight compared to ligamentLigaments (bone bone) more elastin than collagen by weight compared to tendon

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Different tissues contain different amounts or fractions of collagen and elastic fibers resulting in different mechanical properties (tendon, ligament, arteries)

Tissue components that contribute to viscoelastic behavior

Collagen in tendon, ligament, skin, cartilage, bone, cornea, blood vessels most abundant protein in the body (~25-30%)Not all collagen is the same (29 types or more!); most common are I, II, III and IVI and III fibers structural support in tension; found in tendons, skin, bone, hear, arteries and corneaII fibrils cartilage (which also has lots of proteoglycans)IV sheet; porous network that forms basement membrane scaffolding for epithelial and endothelial cells inner layer of blood vessels

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Triple-helical structure stabilized by hydrogen bonds (see Fig 1.8 in textbook)Individual fibers surrounded by gel-like ground substance (mainly water) Combination results in viscoelastic behavior Fibers are crimped; crimp stretches out under load

Collagen

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Collagen

From http://cdn.intechopen.com/pdfs/22189/InTech-Biomechanics_and_modeling_of_skeletal_soft_tissues.pdf

Three distinct regions of stress-strain curve for collagen1 Toe region non-linear, physiological level loading2 Linear elastic3 Yield 4 - FailureAt rest: randomly oriented molecules high disorder, higher entropyUnder stretch: more oriented lower disorder, lower entropy, increased stress (like a spring energy is stored in stretched fiber, which is released to restore crimp when load is removed)

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Elastin + microfibrillar proteins = elastin fibersBehave like rubber Low modulus (lower than collagen)Elastic behavior: very extensible and reversible deformation even under high strains Found in Blood vesselsLungsSkinElastin

From http://helpfromthedoctor.com/blog/2010/07/27/what-is-a-protein/

- Damage to elastin:- in blood vessels aneurysm- in skin wrinkles (often due to sun damage)- in lung - emphysema

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Combined effects in biological structures

From http://www.astarmathsandphysics.com/a_level_physics_notes/medical_physics/a_level_physics_notes_medical_physics_stress_and_strain_in_blood_vessels.html

Elastin contributes to toe regionCollagen contributes to stiffer slope of stress-strain curve22