Suman Science Living System Lect Concise

8/4/2019 Suman Science Living System Lect Concise

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Indian Institute of Technology Kharagpur, IndiaIndian Institute of Technology Kharagpur, India -- 721302721302

Science of Living Systems:Science of Living Systems: BioBio--ThermalThermal--Fluid SciencesFluid Sciences

Lecture By

Prof.Prof. SumanSuman ChakrabortyChakrabortyDepartment of Mechanical Engineering

Autumn 2010




Major Differences in Transport Phenomena inMajor Differences in Transport Phenomena in

Engineering and PhysiologyEngineering and Physiology

• Wide Range of Reynolds Number:

– Majority of flow in physiological system is laminar

– High and low Reynolds Number Laminar regime

• High Re: Large Arteries

and airways in lungs

• Low Re: Small capillaries and Interstitial Flow

– There are localized bursts of turbulence as well

Artery

Interstitial Flow (IF)

Blood vessels that carry blood away from the heart

into the tissue. This blood is normally oxygenated.

Percolating fluid flow through a 3D tissue spaces,

around embedded cells. IF drains out of blood vessels.

Interstitial Flow

Local Vortices in Bifurcation

Glossary




Hierarchy of Blood VesselsHierarchy of Blood Vessels




• Unusual Multiplicity of Tube Branching –

The branched

networks of tubes from the cardiovascular system

andlungs are extremely intricate and complex.

• Unusual Wall Properties of Containing Vessels –

Networks of vessels containing blood flow and air flows

exhibit complicated distensibility. Walls of arteries arecomplicated by viscoelasticity

and non-linear features.

Major DifferencesMajor Differences ……..

Cardiovascular System

Viscoelasticity

GlossaryThe circulatory system which includes the heart and the blood vessels and is

responsible for the transport of blood, dissolved oxygen, nutrient, metabolic

wastes throughout the body

Property of materials that exhibit both viscous (fluid) and elastic (solid)

characteristics when undergoing deformation





• Unusual Fluid Properties

– Whole blood contains a suspension of 40-50% by

volume (hematocrit) of deformable bodies (mainly red

blood cells or RBCs) in a transparent plasma.

– While the plasma obeys Newtonian behavior, thewhole blood is described by an effective viscosity

which increases substantially with decreasing rate of

strain due to increased formation of RBC aggregates

– Air inhaled into lung is also a suspension of dust

particles which deposit at different levels in the

bronchial tree

depending upon particle size

Bronchial Tree

Blood Plasma

Bronchial Tree

GlossaryBlood plasma is the yellow liquid component of blood in which the blood cellsin whole blood are normally suspended. It makes up about 55% of the total

blood volume.

The branching of the bronchi (airway passages) of the lung, considered as a

structural and functional unit and designed to spread air over wide area.




Major DifferencesMajor Differences ……..• Unusual Pulsatility

– Pulmonary

inspiration and expiration cause regular flow reversal in the

respiratory system

– In the circulatory system, however, the arterial blood flow exhibits a

pulsatile characteristics

– Attenuation of the pulse waves, due to deformable vessel walls, makes

such pulsatility

less important in microcirculation

and veins

Pulmonary

Microcirculation

GlossaryRelated to lungs

Describes the small vessels in the vasculature which are embedded within

organs and are responsible for the distribution of blood within tissues; as

opposed to larger vessels in the macrocirculation

which transport blood to and

from the organs.





• Unusually Low Conduction of Heat Flux

– In human body, maximum temperature is around37ºC in the core region while minimum

temperature is around 34ºC at extremities

– The temperature gradient is 0.1ºC/cm

– Thermal conductivity of tissue is quite low ~ 0.06

W/m.K

– The conduction heat flux ( ) ~ 0.06 W/m2

is

low to disperse the BMR (Basal Metabolic Rate

~

72 kcal/hour) over our body surface area of 1.8 m2

(for a normal 70kg adult)

T k q ~

Basal Metabolic Rate

GlossaryThe minimum calorific requirement needed to sustain life in a resting

individual. It is the amount of energy expended while at rest in

a neutrally

temperate environment, in the post-absorptive state (i.e. the digestive system is

inactive, which requires about twelve hours of fasting in humans)





• Unusual Blood Cooling

– When blood flows through tissues or organs, it functions not only as a carrier of nutrients

and metabolic

wastes but also as a coolant to remove the heat produced by metabolism

– Blood gains heat which is transferred by circulation to the skin

where it is dissipated to the

environment

– For maintaining body core temperature in the normal range, the blood transfusion cooling is

vital, because of the poor conduction flux

– The blood cooling rate per unit volume may be estimated as

– The unusual feature of blood cooling is the variability range of

cooling rate with mass flow

mass can be regulated by the vasomotor activity

of tissue vessels

– For example, vasoconstriction

decreases the mass flux while vasodilation

increases it

tissuebloodarterial~ T T C mq pbvol

Metabolism

Glossary

Vasomotor

Vasoconstriction/dilation

The chemical processes occurring within a living cell or organism that are

necessary for the maintenance of life.

Vasomotor refers to actions upon a blood vessel which alter its diameter.

Vasoconstriction is the narrowing of the blood vessels resulting

from

contraction of the muscular wall of the vessels, particularly the large arteries,

small arterioles and veins. Vasodilation

refers to the widening of blood vessels

resulting from relaxation of smooth muscle cells within the vessel walls.




Major DifferencesMajor Differences ……..• Unusual Thermoregulatory Mechanisms

– Skin Temperature (Ts

) is one of the most important factors in the regulation

of body temperature and it varies with a change in the environmental

conditions.

– For a resting person in thermally steady state, metabolic heat generation

balances the heat loss by convection and radiation

– However for sudden change in ambient temperature (Tamb

), Ts

and Tcore

change, activating peripheral and central thermoreceptors

respectively.

– Signals from thermoreceptors

are integrated by the thermorgulator

centers

(mainly located in Hypothalamus), which trigger the necessary regulatory

mechanisms.

– The control mechanisms include –

• Vasomotor Systems (induce either vasodilation

or vasoconstriction)

• Active regulation: sweating for Tamb

>Ts

and cold induced metabolic

heat generation (including shivering and non-shivering) for Tamb

<Ts

Thermoreceptor

Hypothalamus

GlossaryA thermoreceptor

is a sensory receptor, or more accurately the receptive

portion of a sensory neuron, that codes absolute and relative changes in

temperature.

Hypothalamus is an area of the brain that produces hormones that

control

body temperature, hunger, moods etc.





• Unusual Thermal Properties

– Tissue thermal properties

are inhomogeneous,

anisotropic and age

dependent

• Unusual Range of System

Size for Heat Transfer

– Ranges from microheat transfer in cellular scale

to

macro heat transfer on

system scales

Tissue –

OrganizedCluster of Cells

Hierarchical Organization

of Life

Inner Architecture of a

Typical Animal Cell

Cellular Scale

GlossaryTypical length scale of an animal cell is 5-10 µm. Mass Transport processes at

this scale is dominated by diffusion while heat transfer is dictated by the

enhanced surface area to volume ratio which scales as the inverse of the

characteristic length scale




Blood RheologyBlood Rheology – – Blood PropertiesBlood Properties

• Human Plasma is transparent, slightly yellowish with ρ

= 1.035

g/ml• It contains a solution of plasma proteins is an aqueous

medium

• Proteins contain about 7% of total plasma volume and can be

classified into three major groups –

Albumin, Globulin and

Fibrinogen• Plasma also contains emulsified fats (or lipids), cholesterol,

free fatty acids, hormones (adrenalin), dissolved O2

, dissolved

CO2

• Whole blood consists of a suspension of RBCs

(erythrocytes),

WBCs

(White Blood Cells or Leukocytes) and Platlets

in an

aqueous solution

• RBC count is approximately 5 million/mm3

40-45% by

volume of whole blood Hematocrit

• Typical dimensions of RBC 7.8 µm in diameter (Biconcave

Disc), 2 µm thick and 88 µm3

in volume

• Function Transport of Oxygen

• Less number of RBC Anaemia




Blood PropertiesBlood Properties ……..

• Size of WBC varies from 16-22 µm for

monocytes

to 6-12 µm for lymphocytes and

granulocytes

• WBC protects body from disease

• Normal WBC:RBC concentration = 1:1000

• Abnormal rise in WBC number ~ Leukemia

• Platelets are smaller than RBC and WBC:

Diameter ~ 2-3 µm

• Platelet : RBC = 1 : 10 (number

concentration)

• Platelets and WBCs

are actively ordinarily

not enough to influence the flow

characteristics• However, platelets play important role in

forming blood clots that may severely

interfere with flow

RBC

WBC

Platlets




Standard Rheological BehaviorsStandard Rheological Behaviors

Bingham Plastic B 0

Newtonian

Power law 1; nn

Power law 1; nn

Stress

Strain Rate

µ = Viscosity

Apparent Viscosity (µapp

):

app




Blood PropertiesBlood Properties – – Unusual HydrodynamicsUnusual Hydrodynamics• Fahraeus

–

Lindquist Effect: Tendency of blood cells to move away

from the wall• At wall, they leave a layer of low viscosity

• The effect is more pronounced for reduced capillary diameter (d)

• Hence, apparent viscosity decreases with the reduction in capillary

diameter • Apparent Viscosity increases with increasing volume percentage of

RBC (Hematorcrit)




Unusual HydrodynamicsUnusual Hydrodynamics ……. Disease. Disease

• Shape of RBC changes with flow

rate

• At abnormally high flow rate and

in constricted region of

circulatory system, RBCs

maydeform and burst

• Change in effective/apparent viscosity with volume

percentage of RBC (also Packed Cell Volume or PCV) is manifested in several diseases like Anaemia

or Polycythaemia

• Anaemia: A decrease in normal number of red blood

cells (RBCs) or less than the normal quantity of

hemoglobin in the blood.

• Polycythaemia: A disease state in which the

proportion of blood volume that is occupied by red

blood cells i.e. hematocrit

increases.




Blood PropertiesBlood Properties – – Unusual RheologyUnusual Rheology

• Often Represented by a Pseudoplastic

behavior (apparent viscosity

decreases with increasing shear rate)

• Blood is also sometimes modeled as a Bingham plastic fluid withτ

0 ~ 0.1 dyn/cm2

• However, the deviation from this model may be significant, typically at

low shear rates

• Casson

model is an empirically modified Bingham plastic model to

give a better fit to measured µapp

data for lower shear rates. As per the

model

0 ck

Casson’s Viscosity




Lump Parameter Modeling of CompartmentalLump Parameter Modeling of Compartmental

System with Flow RegulationSystem with Flow Regulation

Compartment = An organ or tissue

Q Volumetric Flow Rate

C Concentration

V VolumemMass = C×V

V

C(t)

Q

Ci

(t)

Q

Ce

(t)

Control Volume (CV)

eiCV mmdt

dm ei QC QC V C

dt

d

NoteNote

i. V = Const. (Const. volume of organ)i. V = Const. (Const. volume of organ)

ii.ii. CCee

== C(tC(t)) QCQCee

== QC(tQC(t))

0)0(conditioninitialwith)(

)(

C t C C Qdt

t dC

V i

tCompartmentheof ConstantTime /

1)( :soln. /

QV

eC t C t

i




Compartmental Systems in Parallel and SeriesCompartmental Systems in Parallel and Series

V1

C1

(t)

V2

C2

(t)

Q

Ci

(t)

Q

Ce

(t)

Q1

, Ci1

(t) Q1

, Ce1

(t)

Q2

, Ci2

(t) Q2

, Ce2

(t)

)()(

111

1

1

t C C Qdt

t dC V

i

)()(

2222

2 t C C Qdt

t dC V i

21 QQQ 2211 iii C QC QQC

)()( 2211

2211

t C Qt C QQC

C QC QQC

e

eee

Q

Ci

(t)

Q

C2

(t)

V1

C1

(t)

V2

C2

(t)

Q

C1

(t)

)()(

11

1 t C C Qdt

t dC V i

)()()(21

22 t C t C Q

dt t dC V




Compartmental Systems in BodyCompartmental Systems in Body

During systolic phase of a heartbeat cycle, blood is

pumped from the heart to one end of the aorta and

walls of the aorta stretch to accommodate the blood

Assume: apV pV 0)(

Volume of Aorta Pressure of Blood

bpQeand

During the diastolic phase, there is

no blood flow into the aorta. Thewalls of the aorta contract, squeezing

blood out of the aorta around the

circulatory network of the body

Heart

Qi

Aorta

V,p

Qe

Circulatory Network

For Illustration of the Cardiac Cycle, please see Next Slide




Cardiac CycleCardiac Cycle




Mass Conservation

of Aorta: ei QQdt

dV

bpQdt

dV

i

bpQdt

dp

a i

Assume: apV pV 0)(

Volume of Aorta Pressure of Blood

bpQeand

Assume:

phasesystolicduring,sin

phasediastolicduring,0

t AQi

Assume: 0)0( pt p 11 ) / ( pt t p

Aortic pressure at the

beginning of systolic phase

Aortic pressure at the end of

systolic phase

Solution: 2220cossin / exp / exp

abt at babt a Aabt p psystolic

at t b p psystolic / exp 11

Compartmental Systems in BodyCompartmental Systems in Body




Some Diseases with Fluid Mechanics RelevanceSome Diseases with Fluid Mechanics Relevance

• Air Embolism: Cavitation

of Bubbles creates

destructive action to the blood components

(RBCs

typically). This can trigger coagulation

mechanisms that produce blood clots

• Thrombus is stationary clot while Embolus is

moving clot

• Hemolysis: Refers to loss (damage) of RBCs

and is a measure of cell trauma. This may be

due to the diseased condition or in presence

of prosthetic devices such as valves.

Hemolysis

is triggered by

– Wall-RBC interaction

– Prolonged Exposure to intermediate shear stress (1000-2000 dynes/cm2)

– Short Exposure to high shear stress (> 40,000

dynes/cm2)




DiseasesDiseases ……. Thrombosis. Thrombosis

• Thrombosis: Formation of a clot or thrombus (an

abnormal clot) in ant part of the vascular or lymphatic system. The thrombus bump or clot is a

coagulation of blood elements or a growth of cells

formed in the heart, blood vessel or lymphatic

system.• Once a clot has developed, the continued flow of

blood past the clot may break it away from its

attachment. Such freely flowing clots are called

Emboli (Embolus in singular). These may continueflowing until coming to a narrow point in the

circulatory system

• Formation of thrombus or embolus is favored by

– Any roughened endothelial surface of a vascular or lymphatic vessel which may be caused by

Atherosclerosis, Infection or Trauma

– Very slow rate of Blood Flow




DiseasesDiseases ……. Atherosclerosis. Atherosclerosis• Atherosclerosis: Disease of large arteries in which lipid deposits called Atheromatous

plaques

appear in the subintimal

layer

of the arteries. These plaques are rich in

Cholesterol.• Calcium often precipitates with lipids to form calcified plaques.

• In later stage, progressive sclerosis

of the arteries occurs due to the infiltration of

fibroblasts

in the degenerative area. When both reactions take place, arteries become

extremely hard Arteriosclerosis (Hardening of Arteries).

• These plaques often protrude into the flowing blood and their surface roughness maycause clots to develop. When a small clot has developed, platelets become entrapped and

cause more clots to develop (thrombus) or the clot breaks away (Embolus) and plugs a

smaller vessel further downstream.

• This is the mechanism for most coronary occlusions.

• Interestingly, the presence of flow separation at branching points and bifurcation is

considered to be one form of hydrodynamic disturbance that contributes to Atherogenesis

at these sides.

Subintimal PlaqueGlossary

Sclerosis Fibroblast

The layer situated beneath the intima

i.e. the innermost layer of an artery or vein.

A deposit of fat and other substances that accumulate in the lining of the artery

wall.

Sclerosis or sclerotization

is a hardening of tissue and other anatomical

features.

A fibroblast is a type of cell that synthesizes and maintains the structural

framework (stroma) for connective tissues such as skin, tendons, ligaments etc.




Illustration of AtherosclerosisIllustration of Atherosclerosis







DiseasesDiseases …….. StenosisStenosis from Atherosclerosisfrom Atherosclerosis• Abnormal narrowing of lumen is

called as Stenosis

• There are three primary methods of

treating Atherosclerosis

– Arterial Bypass: This is created to

restore flow to distal tissue by

bypassing the obstraction. The graft

may be synthetic (made from polymer

materials such as Dacron) or natural

(uses arteries or veins from other vascular parts of the patient)

– Balloon Angioplasty: Dilatation of a

balloon-tipped catheter within the

stenosis

to expand the lumen

– Stenting: To hold open the diseased

region by using a metallic stent

Arterial Bypass

Balloon AngioplastyStenting




Blood Flow and Cell AdaptationBlood Flow and Cell Adaptation

• Endothelial Cells (ECs) that line the inner (Luminal)

surface of the vasculature are sensitive to flow inducedshear stress

• Large arteries appear to vasoconstrict

or vasodilate

via

smooth muscle contraction and relaxation so as to

maintain wall shear stress (τ

w

) of 1.5 Pa under allconditions

• The vasomotion

is controlled partly by endothelial

productions of vasoactive

molecules such as

– Vasodilators: Nitric Oxide (NO), Prostacyclin

(PGI

2

)

– Vasoconstrictors: Endothelin-1 (ET-1) and

Thromboxene

(TXA2

)

– An important research goal is to correlate the

endothelial production of these molecules with τw

• In general as τw

is increased (e.g. during exercise), the

endothelium produces more vasodilators to increase the

lumen area and thereby restores τw

to its normal value.

The converse occurs when shear stress is decreased by

a decreased flow




F

l o w f i e

l d

Cell

Cell

Membrane

Cell-Substrate

Adhesiony

xz

Fluid Shear StressFluid Shear Stress – – Schematic DepictionSchematic Depiction




Cell Culture in Parallel Plate Channel: The Flow PhysicsCell Culture in Parallel Plate Channel: The Flow Physics

Fully developed flow is non-accelerating:

0

0

y x p

dxdy y

dxdydx x

p p pdy

Assume Newtonian Fluid: flow)developed(fully0 as

v yu

y

u

x

v

Combining two relations:

y

u

y x

p

Function of x only Function of y only

Hence, each term = const. = C

Also µ

= const.




y

u

y x

p

The Flow PhysicsThe Flow Physics ……..

Integrating With boundary conditions H yu

yu

at0

0at0

Hy y

dx

dp yu 2

2

1)(

Poiseuille

Flow

(named in honor of French physician J. Poiseuille

who studied pressure-flow relations for blood flow)

H

H

dx

dpudy

H u

H

avg

6 /

2

113

0

2

12

H

u

dx

dp avg

Wall Shear Stress: H

u

H

u H

dx

dp H

dy

du avgavg

yw

612

22 20

Re66

2

2

H H

H u

H

avg

w

NumberReynoldsRe

H uavg

Average Velocity:




AdaptivityAdaptivity of Adhering Cellsof Adhering Cells•• Prima Foci of Shear Stress Prima Foci of Shear Stress

– – Apical Cell MembraneApical Cell Membrane – – Focal Adhesion Points atFocal Adhesion Points at

Basal SurfaceBasal Surface

– – Events related to these areEvents related to these areinter inter --connected !!!connected !!!

Apical Cell Membrane

Focal Adhesion Points at Basal Surface

Rearrangement of Focal Adhesion

Points Elicits Changes in Apical

Cell Membrane, which leads to

Reduction of Lipid Rafts

(Relatively Rigid Nanodomains

of Cell Membrane)

Increase in Membrane

Fluidity Stress Adaptation

Open Question: What are the distinctive features of shear-adaptive

process kinetics of cancer cells in very narrow confinements like inside microchannels?

Lipid Raft

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Suman Science Living System Lect Concise