Biofluids & Dynamics

Studies the way that fluids move in the human body

BLOOD

Amniotic fluid

Gastric acid/Juice Pericardial

fluid

Mucus

PusSaliva

Synovial fluid

Urine

Blood Flow

• Obstructions in blood passageways • Smallest transport lines for blood/some

point allows individual RBC’s

Understanding the relationship between

blood and its containing vessels

• Research on small blood passages in cancer cells Treatment of Cancer

Biofluid mechanics

Biofluids Mechanics Biomechanics

Study of Fluid Movement in the

BodyAnalysis of any

Dynamic System

Mechanics applied to

Biological entity

Biofluid Mechanics

Newton’s Laws

First Law: An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Second Law:When a force is applied to an object, it accelerates.

The acceleration takes place in the direction of the applied force, and is proportional to the magnitude of the force. It is also inversely proportional to the mass of the object.F = ma Where F is the force (N), m is the mass in kg, and a is the acceleration in metres per second squared. F and a are vectors.

Third Law: To every action there exists an equal and opposite reaction

Stress

Stress = Load applied / Sectional Area

Normal Stress: Force acting perpendicular to the plane

Shear Stress: Force acting tangential to the plane

Strain = Change in length / Original length

E = Stress / Strain

Hook’s Law

Strain

Hook’s Law: The ratio of stress to strain is a constant

Hook’s Law does not depend on time

Elasticity

Physical property of materials which return to its original shape after they are deformed

Stress-Strain Curve

Hook’s Law

Materials E (GPa)

Mild Steel 200

Oil Paint 1.66

Rubber 0.01-0.1

Collagen 6

Which one is Elastic??

Collagen

Triple Helix

Madras Model

Linear Elasticity Pseudo Elasticity

Study of how solid objects deform and become internally stressed due to loading conditions

Elastic response to an applied stress, caused by phase transformation (austenite and martensite) of a crystal

Elasticity exhibit in Fluids

Fluid is a substance which deforms continuously when subjected to shear forces

• Newtonian Fluids• Non- Newtonian

Fluids

Newtonian Fluids : Fluids which obey Newton’s law of Viscosity

• Water

• Air

Non-Newtonian Fluids : Fluids which do not obey Newton’s law of Viscosity

• Pastes• Gels• Polymer

solutions

Various Non-Newtonian behaviors:

Time Independent

• Bingham –plastic

• Pseudo plastic• Dilatant fluids

Resist small shear stress but flow easily under large shear stress. Eg: tooth paste, jellies

Viscosity decreases with increase in velocity gradient (Shear Thinning Fluids). Eg:

Polymer solutions, Blood

Viscosity increases with increase in velocity gradient (Shear Thickening Fluids).

Time dependent

• Thixotropic fluids

• Rheopectic fluids

• Viscoelastic fluids

Viscosity decreases as the duration of stress increases

Eg: Honey

Viscosity increases as the duration of stress increasesEg: Gypsum suspension in

water

Fluids which exhibits both elastic and viscous

characteristics Eg: biopolymers

Newton’s Law of Viscosity

States that “Shear stress between adjacent fluid layers is proportional to the negative value of the velocity gradient between the two layers”

ViscosityMeasure of resistance of a fluid which is being deformed either by shear stress or tensile stress

“Thickness or internal friction”

Water

Honey

Viscoelastic materials

Materials for those the relationship between stress and strain depends on time

Materials that exhibit both viscous and elastic characteristics when undergoing deformation

Properties : • Hysteresis is seen in the stress-strain curve• Stress relaxation occurs: constant strain

causes decreasing stress• Creep occurs : constant stress causes

increasing strain

Hysteresis: If a body is subjected to a cyclic loading, the stress-strain relationship in the loading process usually different from the unloading process and this phenomenon is called hysteresis

Stress Relaxation: When a body is suddenly strained and then the strain is maintained constant afterward, the corresponding stresses induced in the body decrease with time

Creep: If the body is suddenly stressed and then the stress is maintained constant afterward, the body continue to deform and the phenomenon is called Creep

Elastic Vs Viscoelastic materials

a) Elastic materialb) Viscoelastic material

Elastic Viscoelastic

Elastic component Elastic and viscous components

Do not dissipate energy Losses energy

No hysteresis Hysteresis

Types of Viscoelasticity

• Linear Viscoelasticity• Non-linear

Viscoelasticity

Function is separable in both creep response and loadApplicable only for small

deformations

Function is not separable. Applicable for large

deformations

Models : Linear Viscoelasticity

Viscoelastic Materials can be modeled to determine the stress or strain interactions and their temporal dependencies

Modeled

Models :

• Maxwell model• Kelvin-Voigt model• Standard Linear Solid model

“To predict a materials response under different loading conditions”

Viscoelastic material

Elastic Viscous

Springs Dashpots

“Electrical circuits”

Elements and their electrical equivalence

Elements Electrical

Stress Voltage

Derivative of strain Current

Elastic modulus of spring (E) Capacitance

Viscosity resistance

Elastic component Springs

Viscous component Dashpots

σ - stress, η - viscosity of the material, and dε/dt - time derivative of strain

σ - stress, E - elastic modulus of the material, and ε - strain that occurs under the given stress

Maxwell Model

Viscous Elastic

“Viscous damper and elastic spring connected in series”

“It predict that stress decays exponentially with time, accurate for most polymers”

Limitation: “It does not predict creep accurately”

Kelvin-Voigt Model

“Viscous damper and elastic spring connected in parallel”

“Extremely good in modeling creep in materials but less accurate in modeling relaxation”

Applications: Organic polymers, rubber, wood when load is not high

Standard Linear Solid Model (Kelvin model)

“Combines Maxwell model and Spring in parallel”

“Accurate in predicting material responses compared to Maxwell and Voigt’s model but the results for strain under specific loading conditions are inaccurate”

Biological tissues: Cartilage, bone, skeletal muscle, cardiovascular tissue, tendon and ligament

Use of Viscoelastic models

“Biomechanics” – Biological tissues have Viscoelastic properties

Vascular Tree

Blood Flow, Blood Pressure and Resistance

Blood Flow: Volume of blood flowing through a vessel, organ or entire circulation in a given period (ml/min)Blood flow of entire circulation is equal to cardiac output

Blood Pressure: Force per unit area exerted by blood against a vessel wall (mm Hg)

Resistance: It is a measure of the friction between blood and the vessel wall

a) Blood Viscosityb) Blood Vessel Lengthc) Blood Vessel Diameter Radius increases: resistance drops

exponentially

Total Peripheral Resistance: Resistance throughout the entire systemic circulation

Relationship between Flow, Pressure and Resistance

Blood flow

Q = A x V A – area, V - velocity

P1 V1

P2 V2 P1 – 5 barV1 – 2 m/sP2 - ?V2 – 3 m/s

P1-P2 = 0.5 x (V22 – V1

2)

P2 = 2.5 bar

Bio-Viscoelastic FluidsBiological fluids that exhibits both viscous and elastic characteristics

Biological Viscoelastic Fluids: Saliva, mucus and synovial fluid

Saliva

Function:a) Protect hard and soft oral tissues from wear, dehydration,

demineralization, chemical insult and microbial imbalanceb) Lubricative function

Mucins Proline

• High & low molecular

weight, secreted from sub

mandibular – sublingual

salivary glands

• Secreted from parotid

glands

Saliva is a dilute Viscoelastic polymer solution with very low shear modulus

Synovial Fluid

• Pale, yellow viscous fluid, non-Newtonian • Lubrication and

Nutrition of joint tissues • Hyaluronic acid

High-molecular weight polysaccharide

Volume of normal synovial fluid in the Knee joint is estimated around 0.5 to 2 ml

Viscosity depends on rate of shear

Thixotropic (time dependent)

Synovial resembles to egg albumin

MucusSlippery secretion

covered by mucus membrane

Viscous colloid containing antiseptic enzymes (lysozyme), immunoglobulins, inorganic salts, proteins (lactoferrin) and

glycoproteins (mucins)

Serve to protect epithelial cells in the respiratory, gastrointestinal, urogenital, visual and auditory

systems

Mucus from the respiratory tract

Aid in the protection of the lungs by trapping foreign particles

“Phlegm”

Nasal mucus is produced by nasal mucosa

Small particles, such as dust, particulate pollutants, allergens and infectious agents such as bacteria

The body’s natural reaction is to increase mucus production

Aids in moisturizing the inhaled air and prevents tissue (nasal and airway epithelia) drying out

Increased mucus production in the respiratory track is a symptom of many common illnesses. i.e common cold and influenza

Hyper secretion in case of inflammatory respiratory diseases i.e allergic reaction, asthma and chronic bronchitis

Mucus in the Digestive system

Mucus acts as lubricant for

materials that must pass over

membranes

A layer of mucus along the inner wall of stomach is vital to protect the cell linings of that organ from the highly acidic environment

within it

Protoplasm

Living content of a cell surrounded by plasma membrane

Cytoplasm

Composed of mixture of small molecules such as

ions, amino acids, monosaccharides, water

and macromolecules such as nucleic acid, proteins,

lipids and polysaccharides

1) Significant features of non-Newtonian fluids?

2) How mucus play an important role in controlling antigen present in the system?

3) What is meant by Pseudo-elasticity?

4) Short notes on i) Hookes law, ii) Newtonian and non-Newtonian fluids, iii) Resistance against flow

5) What is bioviscoelastic fluid? Explain its biological functions with example

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