IF YOU WANT PEOPLE TO SMILE, YOU SMILE FIRST

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IF YOU WANT PEOPLE TO SMILE, YOU SMILE FIRST!
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BIOFLUID DYNAMICS OF THE HUMAN CIRCULATORY SYSTEM
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CONTRIBUTORS
LEFT TO RIGHT 1. Human Arjomandi 3.
Siobhain L. Gallocher 2.
Stephanie S. Barcelona 4. Martha Vallejo
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OBJECTIVES

• Describe the circulatory system and its
  conceptual model.
• 2. Describe the biological, chemical, and
  physical properties of the biofluids present
• in the circulatory system.
• 3. Describe the rheology of blood.
• 4. Describe flow in the
• - Arteries
• - Veins
• - Capillaries

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CONCEPTUAL MODEL OF THE CIRCULATORY SYSTEM
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CIRCULATORY SYSTEM
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BLOOD FLOW
Path of Blood Flow Left ventricle ?
Arteries ? Arterioles ? Capillaries ? Venules ?
Veins ? Right Atrium.
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DISTRIBUTION OF BLOOD

• Total blood volume 5 L
• Systemic circulation 84
• 64 Veins.
• 13 Arteries.
• 7 Systemic
• arterioles
• capillaries.
• Heart and lungs 16
• 7 Heart.
• 9 Pulmonary
• vessels.

Guyton, 145
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BLOOD COMPOSITION
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BLOOD FORMED ELEMENTS
TYPES OF LEUKOCYTES
PLATELETS
RBCs
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PHYSICAL PROPERTIES OF BLOOD
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KINEMATIC VISCOSITY vs SHEAR RATE
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BLOOD NON-NEWTONIAN BEHAVIOR
Blood
Newtonian fluid
Newtons law of viscosity
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NON- NEWTONIAN BLOOD

• Blood is non-Newtonian due to presence of various
  cells.
• Power Law can describe the bloods flow behavior.

t Stress. du/dy Strain rate. K
Material dependent
parameter. n Material-dependent
index. ty Yield stress.
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THE YIELD STRESS OF BLOOD
H Hematocrit expressed as a fraction CF
Plasma concentration of fibrinogen, grams
per 100 mL.
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BLOOD VISCOSITY vs HEMATOCRIT

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RELATIVE VISCOSITY vs SHEAR RATE
Aggregated RBC

• Blood viscosity when shear rate (RBC
  aggregations breaks up)

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FLUID DYNAMICS
Re gt 4000 Turbulent

• Reynolds Number
• v Velocity
• D Vessel diameter
• Blood density
• Blood viscosity

2100 ltRelt 4000 Undefined
Re lt 2100 Laminar
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HAGEN - POISEUILLES LAW
F Volume flow rate. r Vessel
radius Pressure gradient L Length
of vessel Viscosity R Flow
resistance
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RELATIVE FLOW vs RELATIVE RADIUS

• F r4

R 1/r4
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REGULATING BLOOD FLOW TO DIFFERENT PARTS OF THE
BODY
Vasodilatation If r ? 1.5 rThen F ?
(1.5)4 F 5.06 F Where r
Radius F Flow rate
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VESSELS IN SERIES OR PARALLEL

• For vessels in series
• For vessels in parallel

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CAPILLARY STRUCTURE

• Thin walled with 8 µm in diameter
• Exchange between the blood and the interstitial
  fluid.
• Three types - Continuous - Discontinuous
  - Fenestrated.

Martini,696
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MECHANISM OF EXCHANGE ACROSS CAPILLARIES

LEGEND a Diffusion d, e, f
Bulk flow (convection) b Vesicular
transport
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EXCHANGE ACROSS CAPILLARIES
Reflection coefficient that represents
the permeability of the capillary barrier.
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HYDROSTATIC PRESSURE
Martini, 709
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CONCLUSIONS

• The cardiovascular system consists of the heart
  and blood vessels.
• The cardiovascular system transports nutrients,
  waste products, respiratory gases, and cells
  within the body
• Blood behaves like a nonNewtonian fluid at low
  strain rates.

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CONCLUSIONS Contd

• The viscosity of blood is decreased with -
  Increasing the strain rate - Decreasing
  hematocrit - Decreasing vessel size -
  Increasing temperature.
• Fluid exchange across capillaries -
  Diffusion - Convection (Bulk flow) -
  Vesicular transport

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ACKNOWLEDGMENTS

• Dr. James E. Moore Jr Dr. Megh R. Goyal
  May the seeds of your burning passion for
  this subject germinate in the impressionable
  minds of your students and may the resulting
  yield be fruitful

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Nothing is a waste of time if you use the
experience wisely - - - Rodin
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QUESTIONS

• ? ? ?

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The Circulatory System Represented as a
Closed-loop System with Two Pumps
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Cardiovascular System Overview

• BLOOD FLOW
• Heart ? Arteries ? Arterioles ? Capillaries ?
  Veins ? Heart

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Percentage Distribution of Body Fluids
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Lymphatic Fluid

• Flows through the vessels and enters bloodstream
• Relies on the movements of muscles and the
  rhythmic contraction of the arteries squeezing
  the lymph vessels to push lymph along
• Total lymph flow is 2 to 4 L/day

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Lymphatic Fluid

• What is it? It is a fluid that resembles plasma
  but with a much lower concentration of suspended
  proteins
• Functions?
• Transports hormones, nutrients, and waste
  products from peripheral tissues to the general
  circulation
• Returns fluid and solute from peripheral tissues
  to the blood
• Maintains blood volume and eliminates local
  variations in the composition of the interstitial
  fluid

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Newtonian Behavior

• Newtonian fluid constant viscosity at all shear
  rates at a constant pressure and temperature.
  Relationship between shear stress and shear rate
  is linear.

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Capillaries in the Intestinal Mucosa Promote
Absorption of Fluid at the Venular End
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Capillaries in the Renal Glomerulus Exhibit
Filtration Over Entire Length
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Example of a Wave Propagation Pressure Pulse
with Distance
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An Example of a CFD of the Lumen on Flow Patterns
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Variation of Relative Viscosity of Blood and
Suspension With Rigid Spheres
n.b Shear rates are lt 100 s-1
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Windkessel Model of Aorta
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Electric Analog for Blood Flow in a Compliant
Vessel
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Lumped-parameter Electrical Analog Model of a
Multi-compartment Arterial Segment
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Pressure and Flow Waves
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Shear Thinning Behavior of Blood
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Conclusions

• The Windkessel model showed that flow was
  dependent on the following
• pressure change with time
• compliance of the elastic vessel
• resistance of the peripheral vessels

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Conclusions

• Electrical models were developed as well to
  further understand blood flow
• Using Kirchoffs Law of Currents, pressure, flow,
  compliance, resistance, and fluid inertial
  effects were each given electrical analogs

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Conclusions

• PROBLEM None of the mathematical, mechanical,
  nor electrical models could encompass all
  properties of the arteries and blood

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Hydrostatic Forces within the Capillaries
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Pulsatile Flow in a Tube
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Research Advances

• Biologists at Cal Tech have uncovered that cells
• destined to form arteries and veins are
  genetically
• distinct from each other even at the earliest
  stages
• of blood vessel formation in the embryo. This
  could
• lead to the development of new artery- or
  vein-specific drugs that could potentially
  enhance the efficacy or specificity of blood
  vessel-directed anticancer drugs

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• Rate of exchange across capillaries is determined
  by hydrostatic pressure and oncotic pressure
• Starling hypothesis shows relationship between
  hydrostatic and oncotic pressure and their role
  in regulating fluid exchange across capillaries
• No one model can accurately describe the
  circulatory system since not all variables are
  known
• To include all known variables would result in a
  complex model that is difficult to solve

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Blood Flow Distribution
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Comparison of Newtonian Plasma Viscosity and
Shear-Thinning Whole Blood Viscosity
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Blood Flow Characteristics of Blood Vessels

• Blood flow velocity decreases as the total cross
  sectional area of the vessel increases.

Martini, 704
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Shear Stress at the Vessel Wall
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Flow Profiles of an Oscillating Flow
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Wave Propagation in Arteries
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Capillary Fluid Mechanics Contd

• Filtration Coefficient
• Ap Capillary area.
• S Total circumferential surface area of the
  capillary wall.
• r Capillary radius.

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Capillary Fluid Mechanics

• Starling Equation
• Lp Hydraulic conductance.
• J Volumetric fluid transfer rate.
• S Total circumferential surface area of the
  capillary wall.
• ?P Effective pressure.

• Womersley Number
• D Blood vessel diameter.
• ? Blood kinematic viscosity.
• ? Circular frequency of oscillation of the
  blood velocity fluctuations.