Good
Morning
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Circulatory Hemodynamics-1
Physical laws governing blood
Flow & Pressure & Resistance
Prof. Dr. Faten Mahmoud A. Diab
Professor of Medical physiology
Egypt
www.gmu.ac.ae
COLLEGE OF MEDICINE
Learning Objectives
➢ State Ohm's law of hemodynamics
➢ State the Poiseuille's – Hagan Formula for the resistance.
➢ Describe the factors controlling the resistance
➢ Describe the interrelationship between the flow & pressure & resistance in the
systemic and the pulmonary circulation.
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FLOW – PRESSURE - RESISTANCE
The physical laws that describe the blood flow through the cardiovascular
system are similar to that describe the flow of any liquid through a pipe system.
Flow rule = Ohm's law of hemodynamics
Flow (F) = pressure gradient (∆P) / resistance (R)
F=
∆P / R
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Circulation Hemodynamics
Flow = ∆ P/ R
The heart and blood vessels, in turn, are controlled to
provide the cardiac output and arterial pressure needed
to supply adequate tissue blood flow.
▪ The heart provides the cardiac output (COP)= Flow
▪ The heart provides the driving force = the pressure =
arterial blood pressure (ABP)
▪ The blood vessels responsible for the resistance (R) by
changing the diameter Vasodilation= VD with
decreasing the resistance & vasoconstriction = VC with
increasing the resistance (vascular resistance)
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Relationship between Flow & Pressure & Resistance
Flow = ∆ pressure (P)/ resistance (R)
What is the
Flow?
Flow = ∆ P/ R
What is the
∆ Pressure ?
What is the
Resistance?
Flow (Q) = Blood flow rate means the volume of blood that passes a given point in the
circulation in a given period of time (ml/min). Measured by Ultrasonic Doppler Flowmeter.
∆ pressure (P)= pressure difference between the 2 ends of the vessel.
Resistance (R)= impedance offered against the flow.
Interrelationships between Flow & Pressure & Resistance
Blood flow through a blood vessel is determined by two factors:
❑ The pressure difference of the blood between the two ends of the vessel, also
sometimes called the pressure gradient along the vessel, which pushes the blood through
the vessel;
❑ The impediment to blood flow through the vessel, which is called vascular resistance.
Relationship between Flow & Pressure & Resistance
Flow (Q) = ∆ pressure (P)/ resistance (R)
Q α
P
Q α
P
The increase in
pressure gradient,
increases the flow
(direct relationship)
Relationship between Flow & Pressure & Resistance
Flow (Q) = ∆ pressure (P)/ resistance (R)
Q α 1/R
Q α 1/R
The decrease in
resistance (VD), the
flow increases
(indirect relationship)
VC= high resistance
With the same
pressure gradient
VD
VD= low resistance
Circulation Hemodynamics
Pulmonary Circulation
Systemic circulation
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Pressure Gradient (∆ pressure)
1. Pressure gradient across the systemic circulation:
❖ At the start of the circuit: the mean arterial blood pressure (MAP), the average
pressure in the aorta throughout the cardiac cycle is about ~90 mmHg.
❖ At the other end of the circuit: the central venous pressure (CVP), the average
pressure in the great veins entering the heart is about ~4 mmHg (it is close to zero).
❖ The difference between MAP and CVP is the pressure gradient that derives blood flow
through the systemic circuit.
∆P = MAP - CVP
∆P = 90 - 0
∆P = 90 mmHg
Pressure Gradient (∆ pressure)
2. Pressure gradient across the pulmonary circulation:
❖ At the start of the circuit: the average pressure in the pulmonary arteries throughout
the cardiac cycle is about ~15 mmHg.
❖ At the other end of the circuit: the average pressure in the pulmonary veins entering
the heart is like CVP (it is close to zero).
❖ The difference between mean pulmonary arterial pressure and the pressure in the
pulmonary veins is the pressure gradient that derives blood flow through the
pulmonary circuit
∆P = mean pr in pulmonary arteries - pr in pulmonary veins
∆P = 15 - 0
∆P = 15 mm Hg
Resistance
The resistance of any tube (including a blood vessel) is a measure of the degree
to which the tube hinders or resists the flow of the liquid through it.
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Resistance
❖ A fluid flowing through a tube, or a blood vessel encounters
resistances:
✓ Some of which is due to frictional forces acting between the fluid and
the wall of the tube or the vessel.
✓ Some of which is due to frictional forces within the fluid itself.
❖ Therefore, the resistance depends on the physical dimensions of the
tube (tube's radius and tube's length) and the properties of the fluid
flowing through it (fluid viscosity).
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Resistance
❖For a fluid moving smoothly through a cylindrical tube, the resistance (R) is given by the
equation of Poiseuille's law:
Poiseuille – Hagan law:
8ηL
Resistance (R) =
π r4
R has direct relationship with
Viscosity of the blood= η
R has direct relationship with
Length of the vessel= L
R has indirect relationship with
radius of the vessel= r 4
Poiseuille law is used to calculate TPR (total peripheral resistance) in the systemic circulation in regulation
ABP & PVS (pulmonary vascular resistance & also airway resistance).
Resistance
❖ Factors affecting the resistance in the CVS:
8ηL
Resistance (R) =
π r4
1. The resistance is directly related with viscosity of the blood (η)
➢ Direct relation (increasing blood viscosity
increasing resistance).
➢ Major determinants of the blood viscosity are the concentration of blood cells:
septically the hematocrit value and the plasma proteins.
➢ However, blood viscosity does not change appreciably under normal condition.
➢ It is increased in pathological conditions e.g., polycythemia and multiple myeloma…
2. The resistance is directly related with length of the tube (L)
➢ Direct relation (increasing vessel length
increasing resistance).
➢ The changes in the vascular resistance due to change in vessel length are rare;
vessels don't change in length except as a person grows.
Resistance
❖ Factors affecting the resistance in the CVS:
8ηL
Resistance (R) =
π r4
The resistance is indirectly relation to the radius of the vessel= r 4
➢ Indirect relation: The resistance is inversely related to the internal diameter of the tube,
increase the radius of the vessel
decrease the resistance.
o An increase in a blood vessel radius is called vasodilation (VD).
o A decrease in a blood vessel radius is called vasoconstriction (VC).
➢The resistance is strongly affected by the tube's internal diameter
because it depends on the fourth power of the radius (r4).
If r=1 so, 14 = 1x1x1x1 =1
If r=2 so, 24 = 2x2x2x2 =16
Resistance
VD
VC
1
2
R
R
Flow = ∆ P/ R
R
by16 times
R
by16 times
F
by16 times
F
by16 times
Resistance
For simplification: R α L/ r4
R has direct relationship with length of the vessels (L)
R has indirect relationship with fourth power of the radius (r4 ).
Fourth power of
the radius (r 4) ??
When the radius of the vessel is doubled (VD):
➢ The resistance (R) will decrease by (1/16)
➢ The flow (F) will increase by 16
Resistance
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Resistance
8ηL
Resistance (R) =
π r4
❖ The blood flow (F) from the ventricle per minute is called the cardiac output (COP).
❖ This flow (=COP) is driven by the pressure gradient across the circulation.
❖ This flow (=COP) is hindered by the total peripheral resistance.
F
= ∆P / R
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Resistance
1. Resistance of systemic circulation (total peripheral resistance):
❖ The blood flow (F) from the left ventricle per minute is called the cardiac output (COP).
[The flow: the volume of blood pumped by the left ventricle to the aorta per minute = COP
= 5 liters/min.]
➢ This flow (COP) is driven by the mean arterial pressure (MAP), which is the pressure
gradient between the (MAP-CVP).
[Pressure gradient in the systemic circuit = MAP – CVP = 90 – 0 = 90 mmHg].
➢ This flow (COP) is hindered by the total peripheral resistance (TPR) of the systemic circuit.
F = ∆P / R
5 = 90 / TPR
TPR= ~ 18
Resistance
1. Resistance of pulmonary circulation (pulmonary vascular resistance):
❖ The blood flow (F) from the right ventricle per minute is called the cardiac output (COP).
[The flow: the volume of blood pumped by the right ventricle to the pulmonary trunk per
minute = COP = 5 liters/min.]
➢ This flow (COP) is driven by the Pressure gradient in the pulmonary circuit = mean
arterial pulmonary pressure – pulmonary venous pressure = 15 – 0 = 15 mmHg.
It is lower than that in the systemic circuit.
➢ This flow (COP) is hindered by the pulmonary vascular resistance (PVR) of the pulmonary
circuit.
F = ∆P / R
5 = 15 / PVR
PVR= ~ 3
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Relationship between Flow & Pressure & Resistance
Systemic circulation
▪
▪
▪
▪
▪
Systemic systolic pressure
= 120 mmHg
Systemic diastolic pressure
= 80 mmHg
Mean systemic arterial pressure
= 90 mmHg
Systemic circulation characterized
by being a high-pressure system.
Systemic circulation characterized
by having high-resistance compared
to the pulmonary circulation.
Pulmonary circulation
▪
▪
▪
▪
▪
Pulmonary systolic pressure
= 25 mmHg
Pulmonary diastolic pressure
= 10 mmHg
Mean pulmonary arterial pressure
= 15 mmHg
Pulmonary circulation characterized
by being a low-pressure system.
Pulmonary circulation characterized
by having low-resistance compared
to the systemic circulation.
Therefore, the pulmonary circuit, which has lower pressure gradient and lesser pulmonary vascular resistance, can
achieve the same flow (COP) like the systemic circuit that has higher pressure gradient and higher vascular resistance.
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Relationship between Flow & Pressure & Resistance
Flow = ∆ pressure (P)/ resistance (R)
8ηL
Resistance (R) =
π r4
When the radius of the vessel is doubled (VD):
➢flow will (Q) increase by 16 times.
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Learning Resources
➢ https://usmle-rx.scholarrx.com/rx-bricks/brick/CP_CAR0039
➢ Textbook: Guyton and Hall Textbook of Medical Physiology, Fourteenth Edition ISBN:
978-0-323-59712-8. International Edition ISBN: 978-0-323-67280-1. Chapter 14, 171181
➢ https://www-clinicalkey-com.gmulibrary.com/#!/content/book/3-s2.0B978032359712800014X
➢ Power-point presentation in the moodle.
www.gmu.ac.ae
COLLEGE OF MEDICINE
Thank you