INTRODUCTION

HUMAN BIOFLUID DYNAMIC SHOW

Biofluid Mechanics

MCG3143

Marianne FenechMechanical engineering

mfenech@uOttawa.caRoom: A328 C.BY (mezzanine)Ext 1924

What is a Biofluid? Medical definition :A biological fluid. Biofluids can be excreted (such as urine or sweat), secreted (such as breast milk or bile), obtained with a needle (such as blood or cerebrospinal fluid), or develop as a result of a pathological process(such as blister or cyst fluid). The term biofluid is employed as both a noun and an adjective (as in biofluid dynamics and biofluid mechanics). (www.medecinenet.com)

‘There are numerous processes in the body under healthy and pathologic conditions in which biofluid mechanics play a central role. The delivery of various substances to and from tissues is accomplished through a combination of complex active and passive mass transfer processes. Biofluid mechanics also play a central role in locomotion, from water-bound amoeba and fish to the soaring of birds. ‘

Biofluid mechanics

Extracted from’ D. Bluestein and JE. Moore Jr. Biofluids Educational Issues: An Emerging Field Aims to Define Its Next Generation’, Annals of Biomedical Engineering 33 12 2005

Complex flows the cardiovascular system

Arteriovenous fistula is specific vessels created by a vascular operation in order to provide sufficient blood access for extra-corporeal circulation. (Karboutly et al.)

Modelisation of the turbulent flow through a femoral stenosis using Fluent sofware (Garcia et al.)

Complex unsteady velocity profile in the blood vessel: The Wormsley profile.

Pulsatile flow in a curved artery :fluid structure interactionNote. The displacements are exaggerated. Color scale represents the pressure. http://www.csc.fi/english/pages/elmer/examples/Coupled_problems/hemodyn

1

3

2

Microcirculation

Intravital microscopy of the microcirculation of the mouse’s cremaster , Chayer B, LBUM, CRCHUM & IRCM

Microcirculation in the human body, which is composed of numerous vessels with diameters less than 50 micrometers, is the main exchange site between blood and tissues.

Blood behavior in the microcirculation is very complex because it cannot be considered as a liquid flow, but rather as a collection of interacting particles.

Red blood cell deformation in a microvessel

4

5

Renal circulation

The kidneys are an amazingly efficient pair of filter and regulator!Every 40 minutes or so the entire blood volume is cleared:

-Homeostasis balance-Ph control -Blood pressure control

An animation here : http://www.footprints-science.co.uk/flash/kidney.swf

The tubular walls act like semi-permeable membranes:

From: Maintaining the Body's Chemistry: Dialysis in the Kidneys. Department of Chemistry, Washington University. (http://www.chemistry.wustl.edu)

6

A exceptional swimmer: the Spermatozoa

It use just the viscous force to swim it is the particularity of this exceptional swimmer

What does it mean?Looks the difference between moving with inertial propulsion and viscous

propulsion:

2 self-propelled objects:

Inertial propulsion in the water

Inertial propulsion in a viscous fluid:It doesn’t work!

Viscouspropulsion

Inertial propulsion

viscous propulsion in a viscous fluid:It is working!

As spermatozoa!

From Multimedia Fluid mechanics

7 8

9 10

The respiratory system

- Because bronchiole inflammation and asthma are directly linked to air pollution and to the deposition of particle of pollutants in the lungs.

- Because drugs are delivered into the lungs in the form of aerosol. The efficacy and efficiency of such treatments depend on the size of the particles, and on their transport and deposition in the bronchial tree.

Why study the air flow in the respiratory system and particle transport and deposition?

11

Gastro-intestinal flow

The flow is generated by peristaltic reflex

Linear peristaltic pump

Rotational peristaltic pump for medical applications

the gastrointestinal tract, smooth muscles contract in sequence to produce a peristaltic wave which forces a ball of food (called a bolus while in the esophagus and gastrointestinal tract and chyme in the stomach) along the gastrointestinal tract.

Total Artificial Heart

CardioWest12

CHAPTER 1

CARDIOVASCULAR SYSTEM

Biofluid Mechanics

MCG3143

Marianne FenechMechanical engineering

mfenech@uOttawa.caRoom: A328 C.BY (mezzanine)Ext 1924

11

Cardiovascular System• Cardiovascular system consists of:

• Blood• Heart (pump),• Blood vessels (flexible pipes)

• Circulatory System: The Circle of Blood• pulmonary circulation• coronary circulation• systemic circulation

• Blood vessels • Arteries, arterioles, capillaries, venules, veins

12

THE HEART

13

Heart• Consists in two pumps in series circulating blood through the pulmonary and systemic circulation, respectivly.

• Is controlled by an internal electrical system

• Pumps about 5 liters of blood every minute, or 7000 liters of blood every day!

14

Heart Wall• The heart wall is made up of three layers:

• Inner layer – endocardium - thin layer of epithelial tissue

• Middle layer – myocardium – thick layer of muscle tissue

• Outer layer – epicardium – thin layer of epithelial tissue

• The heart is enclosed in a sac called the pericardium

• The inner layer of the pericardium is attached to the heart

• The outer layer of the pericardium is attached to the diaphragm

• These two layers are separated by pericardial fluid

15

Structure of the HeartChamber

• The heart consists of 4 chambers:• Upper chambers:

- left and right atria (LA, RA)- separated by interatrial septum

• Lower chambers :- left and right ventricles (LV, RV)- separated by interventricular septum

• Left and right is denoted by how you view your own heart

16

Structure of the HeartChamber

• Chamber wall thickness depends on function:

• Atria have thin walls – only pump blood to ventricles

• Ventricles have thicker walls – must pump blood further• LV wall thicker due to increased flow

resistance (both chambers must pump same amount of blood)

17

Cardiac Cycle - Definitions

• Cardiac cycle = heartbeat

• One heartbeat takes approximately 0.8 s

• Systole – contraction of a chamber

• Diastole – relaxation of a chamber

18

Cardiac pressures

19

Cardiac Cycle - Steps1. Atrial contraction

• AV valves open, SL valves closed• Blood flows from atria to ventricles

2. Isovolumetric ventricular contraction• All four valves closed

3. Ventricular contraction (ejection)• SL valves open• Blood exits ventricles

4. Isovolumetric ventricular relaxation• All four valves closed

5. Passive ventricular filling• AV valves open• Blood flows from atria to ventricles

http://www.nhlbi.nih.gov/health/dci/Diseases/hhw/hhw_pumping.html

13

20

Structure of the Heart - Valves• The heart contains 4 one-way valves to control flow direction:

• The aortic valve separates the LV and the aorta• The pulmonary valve separates the RV and the pulmonary trunk• The mitral (bicuspid) valve separates the LA and the LV• The tricuspid valve separates the RA and the RV

Heart Valves (From Tortora, 2002).

21

Blood Circulation

• Blood flows through two loops• systemic circulation (body)• pulmonary circulation (lungs)

• Red denotes oxygenated blood

• Blue denotes deoxygenated blood

Systemic capillaries

Pulmonary capillaries

Blood Circulation.

22

Blood Circulation Path

1. Deoxygenated blood flows from RA to RV2. Deoxygenated blood is pumped from the RV to the lungs3. Gas exchange in the lungs (CO2 leaves blood, O2 enters)4. Oxygenated blood from the lungs enters the LA5. Oxygenated blood flows from LA to LV6. Oxygenated blood pumped from LV through body7. Gas exchange in capillaries (O2 leaves blood, CO2 enters)8. Deoxygenated blood returns from body to RA

23

Coronary Circulation

• The heart, like all organs, requires oxygen and nutrients from blood• These nutrients cannot diffuse through the

heart walls• Therefore, the heart requires its own blood

vessels (coronary vessels)

• Circulation of blood to and from the heart is known as the coronary circulation

24

Conduction – Action Potential

• Blood is pumped through the body due to heart muscle contractions• These contraction are caused by the propagation of a

voltage, called the action potential, through the heart muscle cells

• All cells have a membrane potential• Voltage difference across the cell membrane• When this potential exceeds a certain threshold value, it

is known as action potential• In the case of muscles, action potential causes the

muscle cells to contractGreat animation here:

http://www.nhlbi.nih.gov/health/dci/Diseases/hhw/hhw_electrical.html14

25

Conduction

• The conduction system describes the propagation of the action potential through the heart

• An electrocardiogram (ECG) measures the voltage in the heart during this propagation

26

Pacemakers• The SA node is the first natural pacemaker

• Generates action potential at a rate which controls the rate the heart beats

• If the SA node fails, the AV node becomes the pacemaker of the heart

• If both of these nodes fail, the heart will continue to beat, but at a rate too low for normal function• In this case, artificial pacemakers are implanted

27

Electrocardiogram (ECG)• P wave represents the propagation of the action potential from

the sinoatrial (SA) node to the atria• Atrial contraction occurs just after the P wave

• QRS wave represents the propagation of the action potential from the atria through the ventricles• Ventricular contraction occurs just after the QRS wave

• T wave corresponds to ventricular relaxation

ECG.

Velocity and pressures

Mean average pressure (MAP)

MAP= (ps+2pd)/3

As Systole last for about a 1/3 of the cardiac cycle.

Velocity at the end of the pressure pulse is about• 3-5m/s in aorta• 7-10m/s in large arteries• 35m/s in small arteriesIncreasing as wall stiffness increasing

Volume and flow• Diastole: cardiac muscle relaxing (blood flow in

chambers)• Systole: cardiac muscle contracting (flow flow out)

• End diastolic volume (ml) :EDV• End systolic volume (ml) :ESV

• Heart beat beat/minutes : HR

• Cardiac output CO(mL/min) = SV.HR

Stroke volume (ml/beat) : EDV-ESV

30

BLOOD VESSELS

31

Types of Blood Vessels

• Blood vessels can be divided into five groups:• Arteries – take blood away from the heart• Arterioles – small arteries• Capillaries – microscopic vessels gas

exchange• Venules – small veins• Veins – return blood to the heart

32

Blood Vessel Properties

Single Vessel Diameter

Cross-sectional Area

Volume

Aorta Arterioles VenulesCapillaries

Vena Cava

Comparison of vessel diameters, areas, and

volumes.

33

Definitions – Compliance & Resistance

• Compliance - a measure of the elastic properties of a blood vessel wall. The compliance measures how much the vessel wall will expand for a given pressure.C = dV/dP, where V is volume and P is pressure

• Resistance –

• From Hangen Poiseuille, hydraulic resistance can be defined as

• This equation shows that the resistance to flow in a vessel depends on the fluid viscosity, vessel radius, and length

4

8rLR

QPR

34

Definitions – Pressure

• Systolic pressure – Arterial pressure during systole

• Diastolic pressure – Arterial pressure during diastole

• Blood pressure can be measured by plethysmography (cuff attached to your arm)

• Blood pressure of 120/80 means Psys= 120 mm Hg,

Pdia = 80 mm Hg

Pressures in the systemic circulation

Theoretical development of the Windkessel effect

We will consider here the simplest form of the Windkessel effect. This model called Windkessel 2-element considers only the arterial compliance (C) and the peripheral resistance (R).

Hypotheses

1-Unsteady flow.

2-The pressure difference across the resistance is a linear function of the flow rate.

3-The working fluid is incompressible.

4-The flow is constant throughout the ejection phase.

Symbols

P:pressure generated by the heart (N m-2) [mmHg]Q: blood flow in the aorta (m3 s-1) [l mn-1R: peripheral resistance (N s m-5) [dyne s cm-5] C: arterial or systemic compliance (m5 N-1) [ml mmHg-1]t: time [(s)T: period (s) Ts: ejection time (s)

Theoretical development

Conservation of mass

Qcc is the flow to the compliance chamber.

Thus

Hyp: P-Pcv= R×Q1Pcv is the central veinus pressurePcv << P [Pcv≅5 mmHg vs. P≅100 mmHg ])

Hyp: Q=Cte throughout the systolic phase.

Therefore

Then

Systolic phase (valve in open position) 0≤t≤Ts

Finally the equation to be solved for the systolic phase is

Initial condition: P(t=0)=P0

Solving eq. I

a) Particular solution (Q=Cte=0)

Systolic phase (valve in open position) 0≤t≤Ts

Theoretical development

Systolic phase (valve in open position) 0≤t≤Ts

Theoretical development

b) Method of variation of the paramter(α1= α1(t))replace in eq.I

To be replaced in the particular solution

Systolic phase (valve in open position) 0≤t≤Ts

Theoretical development

c) The general solution for the systolic phase is therefore:

To determine the constant α2 we use the initial condition:

Finally, the pressure waveform for the systolic phase can be written as:

Theoretical developmentDiastolic phase (valve in closed position) Ts ≤ t ≤ T

It is same thing as for the systolic phase but with Q=Cte=0

Therefore;

The solution for this equation is under the following form:

Initial condition: P(t =Ts) = Ps(Ts) α3 is determined using the initial condition

Then,

Theoretical developmentDiastolic phase (valve in closed position) Ts ≤ t ≤ T

Finally, the pressure waveform for the diastolic phase can be written under the form:

Theoretical developmentSystolic / Diastolic phase

(valve in open position) / (valve in closed position) 0 ≤ t ≤ Ts / Ts ≤ t ≤ T

To compute the solution, we need to know: P0; Q; R; C; T; Ts.However, it is convenient to use a condition of recurrence to compute P0: P(0)=P(T)

Analysis of the solution

• We can notice from the analytical solution of the Windkessel2-element model the importance of the term (R×C) because it determines the “speed”of the exponential rise or decay. This product is called the characteristic time and is usually noted ().

No resistance Higth resistancecirculation in the veins, venules, capilary

Analysis of the solution

(Stiffer)

dPdVC

46

Blood Vessel Wall Layers

• Intima • a layer of epithelial

cells called the endothelium and a basement membrane

• Media• smooth muscle cells,

elastin and collagen fibres

• Adventitia• elastin and collagen

fibres

Wall Layers (From Tortora, 2002).

47

Arteries• Can be divided into two groups, elastic and muscular

• Elastic arteries • larger diameters• located closer to the heart• more elastin in media

• Muscular arteries• So named, due to increase in smooth muscle cells in the media

compared to elastic arteries

48

Arterioles• Small arteries

• Transition between arteries and capillaries

• Wall properties near arteries similar to muscular arteries, wall properties near capillaries similar to capillaries

• Important in determining flow resistance – recall

• Small change in vessel radius large change in resistance4

1r

R

49

Control of Blood Flow

• Passive control – compliant blood vessel walls expand and contract due to pressure differences

• Active control – nervous signals cause smooth muscle cells in vessel walls to contract, leading to a decrease in

vessel diameter –Vasoconstriction decrease in R

• Vasodilation – increase in vessel diameter due to relaxation of smooth muscle cells

increase in R

50

Capillaries

• Microscopic vessels responsible for exchange of gases, nutrients, and wastes

• Capillary walls have only the tunica intima• Allows for molecules to pass through vessel walls

• Small diameter, large number large surface area

51

Venules

• Small veins

• Transition between capillaries and veins

• Venules close to capillaries do not have a tunica adventitia• This layer forms in venules that are close to veins

52

Veins

• Tunica intima and tunica media are thinner in veins than in arteries

• Tunica adventitia is thicker in veins

• Elastic laminae is not found in veins

• Veins are more compliant than arteries and are capable of collapsing

53

Venous Valves• Veins, especially those in the lower limbs, contain one-way valves

• Venous pressure is much lower than arterial pressure

• Force needed for blood to flow back to the heart is only slightly larger than gravitational force

• Valves are needed to prevent backflow

• Skeletal muscle contraction helps move blood in veins

55

BLOOD

56

Blood

Blood cells 45%Red blood cellsWhite blood cells (leukocytes )Platelets (Thrombocytes)

Plasma 55%

Hematocrit (Ht or HCT) is the proportion of blood volume that is occupied by red blood cells45%

Blood volume in humans is 4 – 6 L

Blood makes up 8 % of total body weight

57

Blood Functions• Transportation

• oxygen, carbon dioxide, nutrients, wastes, hormones, enzymes

• Regulation• pH, body temperature, water content of cells

• Protection• clotting to prevent excessive blood loss• protect against diseases

58

Plasma• liquid component of blood, in which the blood cells in whole

blood would normally be suspended.

• plasma being the main medium for excretory product transportation

• Composition: 90 - 92 % water, 8-10 % solutes

• solutes include:• Proteins• Electrolytes• Metabolic wastes• Nutrients• Respiratory gases (O2, CO2, N2)• Regulatory substance (hormones, enzymes)

59

Red Blood Cells

• No nucleus in the cell

• Life cycle : 120 days

• 99 % of formed elements in blood

• 5-6×106 red blood cells per mm3

• Responsible for oxygen transport

• Biconcave disc shape Red Blood Cells (From wikipedia)

60

Red blood cells

7 µm

2 µm

Also called erythrocytes

Properties:

Aggregation

Deformation

5 µm

5

61

•Physiological and reversible phenomena

•Increase the blood viscosity

•Hyper-aggregation is associated with the cardiovascular disease pathologies

Red blood cell aggregation

2

Time

Porcine blood

Human Blood

15

62

White Blood Cells (Leukocytes)

• Responsible for defense

• Contain nuclei

• 1% of blood

• 5-10×103 white blood cells per mm3

• 8-20 m diameter (depends on type)

• Life cycle – few days (depends on type)

• Rolling and extravasation / Phagocytosis 16 17

63

64

Platelets (Thrombocytes)

• Responsible for blood clotting

• Cell fragments - no nuclei

• 1.5-4×105 platelets per mm3

• 2-4 m diameter

• Life cycle – 5-9 days

65

Blood Properties• Temperature: 38°C

• pH: 7.35 – 7.45

• Density: = 1057 kg/m3

• Viscosity: • blood is a non-Newtonian fluid• If assumed Newtonian, = 4×10-3 kg/m·s

• Recall, for a Newtonian fluid,

where is shear stress and du/dy is velocity gradientdydu

66

Blood Viscosity

67

Blood Viscosity

• Blood viscosity depends on three factors:• Shear rate• Percentage of cells in plasma• Vessel diameter

68

Factors Affecting Blood Viscosity

• Shear rate• At low shear rates, apparent viscosity increases. • Yield stress required to start fluid motion (Bingham Fluid)

• Cell concentration• Plasma is generally considered to be a Newtonian fluid at

physiological conditions ( = 1.6×10-3 kg/m·s)• Increasing RBC concentration increases viscosity linearly

(over a physiological range)

• Vessel diameter• Apparent viscosity is lower in small vessels (d < 0.3 mm)• Apparent viscosity approx. constant in vessels above 0.3

mm