Biofluids & Dynamics Studies the way that fluids move in the human body Gastric acid/Juice Pericardial fluid Amniotic fluid BLOOD Urine Mucus Synovial fluid Pus Saliva

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 Biomechanics Mechanics Biofluids Biofluid Mechanics Study of Fluid Movement in the Body Analysis 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.

To every action there exists an equal and opposite reaction 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 Strain = Change in length / Original length Hook’s Law E = Stress / 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

Which one is Elastic?? Materials E (GPa) Mild Steel 200 Oil Paint 1.66 Rubber 0.01-0.1 Collagen 6

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 Resist small shear stress but flow easily under large shear stress. Eg: tooth paste, jellies Bingham –plastic Pseudo plastic Dilatant fluids 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 Viscosity decreases as the duration of stress increases Eg: Honey Thixotropic fluids Rheopectic fluids Viscoelastic fluids Viscosity increases as the duration of stress increases Eg: 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” Viscosity Measure 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 that exhibit both viscous and elastic characteristics when undergoing deformation Materials for those the relationship between stress and strain depends on time 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 Elastic component Elastic and viscous components Do not dissipate energy Losses energy No hysteresis Hysteresis

Types of Viscoelasticity Function is separable in both creep response and load Applicable only for small deformations Linear Viscoelasticity Non-linear Viscoelasticity 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

Models : “Electrical circuits” Maxwell model Kelvin-Voigt model Standard Linear Solid model “To predict a materials response under different loading conditions” Viscoelastic material Elastic Viscous Modeled Springs Dashpots

Elastic modulus of spring (E) Elements and their electrical equivalence Elements Electrical Stress Voltage Derivative of strain Current Elastic modulus of spring (E) Capacitance Viscosity resistance Elastic component Springs σ - stress, E - elastic modulus of the material, and ε - strain that occurs under the given stress Viscous component Dashpots σ - stress, η - viscosity of the material, and dε/dt - time derivative of strain

Maxwell Model “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”

Use of Viscoelastic models “Biomechanics” – Biological tissues have Viscoelastic properties Biological tissues: Cartilage, bone, skeletal muscle, cardiovascular tissue, tendon and ligament

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 Blood Viscosity Blood Vessel Length Blood Vessel Diameter Radius increases: resistance drops exponentially

Relationship between Flow, Pressure and Resistance Blood flow Total Peripheral Resistance: Resistance throughout the entire systemic circulation Relationship between Flow, Pressure and Resistance

Q = A x V A – area, V - velocity P1-P2 = 0.5 x (V22 – V12) P2 V2 P1 – 5 bar V1 – 2 m/s P2 - ? V2 – 3 m/s P1-P2 = 0.5 x (V22 – V12) P2 = 2.5 bar

Bio-Viscoelastic Fluids Biological fluids that exhibits both viscous and elastic characteristics Biological Viscoelastic Fluids: Saliva, mucus and synovial fluid

Secreted from parotid glands Saliva Function: Protect hard and soft oral tissues from wear, dehydration, demineralization, chemical insult and microbial imbalance Lubricative function Mucins Proline Secreted from parotid glands High & low molecular weight, secreted from sub mandibular – sublingual salivary 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 Viscosity depends on rate of shear Thixotropic (time dependent) High-molecular weight polysaccharide Volume of normal synovial fluid in the Knee joint is estimated around 0.5 to 2 ml

Synovial resembles to egg albumin

Slippery 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 acts as lubricant for materials that must pass over membranes 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

Living content of a cell surrounded by plasma membrane Cytoplasm Protoplasm Living content of a cell surrounded by plasma membrane Composed of mixture of small molecules such as ions, amino acids, monosaccharides, water and macromolecules such as nucleic acid, proteins, lipids and polysaccharides

Previous year Q’s 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