Transcript Physical principlesx

THE AUSTRALIAN NATIONAL UNIVERSITY
Overview of
Physical Principals in Physiology
Christian Stricker
Associate Professor for Systems Physiology
ANUMS/JCSMR - ANU
[email protected]
http://stricker.jcsmr.anu.edu.au/Physical_principles.pptx
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Aims
At the end of this lecture students should be able to
• state what the elementary SI units are;
• explain the concept of SI units and give examples;
• interpret relevant symbols for multiples/fractions of units;
• define frequency, temperature, distance, velocity,
acceleration, volume, mass density, concentration, force,
weight, tension, pressure, torque, lever, energy and
power and assign the correct units;
• state which special dimensions are used in medicine; and
• name and estimate some different forms of energy.
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Contents
• Importance of the concepts covered
• SI units, and derived dimensions
• Multiples and fractions of units
• Frequency, Temperature
• Distance, velocity, acceleration
• Volume, density, concentration
• Force, weight, tension, pressure
• Torque and lever types
• Energy and power
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Importance
• How to document a patient’s
state?
– Inspection
– History
– Measurements
• Become more and more important as
“objective”.
• Examples: BP, Temperature, pH,
cardiac output, hearing sensitivity, …
• Without unit, a number is meaningless!
• Patient data
• We have to refresh
– units / dimensions
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Elementary Units (SI)
• SI units refer to Système international d'unités”.
• kg is special case as it has a “multiple” in front
(see next).
• Follows “meter-kilogram-seconds” system (MKS).
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Some Derived Dimensions
• List incomplete (some physiologically relevant ones…)
• It is possible to describe all measurements using the
7 elementary SI units.
– Dependency often established via the energy associated.
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Multiples and Fractions of Units
• Multiples are typically upper, fractions lower case.
• Because of inability to print Greek character µ,
sometimes people use ‘mu’ or ‘u’ for it.
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How Often Does Your …?
• Frequency (f) [Hz] used to
describe a periodic event.
• In medicine, as 1 s is mostly too
short, the base is often 1 min
(beats per min; bpm).
• Useful to determine the time
interval between the events: 1/f
– 10 Hz → 100 ms
– 80 bpm → 0.75 s = 750 ms (60/bpm)
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Temperature
• Kelvin is SI unit.
– 0 K = absolute zero (in space…)
• Conversion: ºC = K - 273.15
• In medicine, typically ºCelsius.
– 0º: triple point of water (solid, fluid,
gaseous) at sea level
– 100º: boiling point at sea level
– 37º: average body temperature
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Distance, Velocity
• Distance [m] = length or equivalent
• Velocity [m/s] = distance travelled per
unit time.
• How fast does a pulse wave travel?
– Distance (heart → wrist) in m: 1.50 m.
– Delay to periphery: 210 ms
∴ V = 1.50 / 0.21 = 7.1 m/s.
• You are going to measure this in
context of the ECG in Block 2.
• Similarly for nerve conduction velocity
in Block 6.
Modified from Nam et al. (2013), Sensors 13:4714
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Distance, Velocity, Acceleration
• Acceleration = change in velocity per
unit time [m/s2].
• Acceleration +-ve; deceleration –-ve.
• Velocity can be inferred from
acceleration as area under that curve.
• Distance can be inferred from velocity
as area under that curve.
• Acceleration can be inferred from the
velocity as its differential in time.
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Volume - Density
• Volume in SI units [m3], however this
is an impractical size.
• Volume is typically in litres;
i.e. 1000 (l or L) = 1 m3.
• In medicine, it is customary to
abbreviate litre in L instead of l as the
latter could be mistaken as number.
• Density [kg / L] = mass per volume.
At 4ºC, H2O density is 1 kg/L.
– At this density, 1 mL = 1 g
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Concentration
• Molar concentration [ ] = amount of
substance s per unit volume [mol/L ≡ M]
= molarity.
amount of s = [s] × Vol
• Molal concentration = amount of
substance per unit mass of solvent
[mol/kg H2O].
– At 4ºC molar conc. = molal conc.
– Otherwise molar conc. ≈ molal conc.
– Deviations at high concentrations
• 1 mol contains 6.022∙1023 molecules
• Mass of a molecule expressed in
daltons (Da)
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Force – Weight – Tension
• Force equals mass * acceleration [N].
Because acceleration has a direction,
force is directional (vector).
• Weight is a special case, where acceleration is caused by gravity (9.81 m/s2).
• For every force (“action”), there is a
counter force (“reaction”, resistance, etc.)
• Tension is a special force that develops in
a muscle (string, cable, vessel wall, etc.)
after a force has been applied to it
(muscle contraction,…).
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Pressure
• Pressure = Force per unit area
• Does not have a direction, but if in a
container (vessel), exerts force in all
directions.
• = fluid column height.
• Unit Pa = N/m2; unfortunately area is very
big. In medicine, mostly kPa for most,
except body fluids, which are in torr
(mmHg; BP) or cmH2O (for small
pressures like CSF, lung).
• 1 torr = 0.133 kPa.
• Mercury manometers are unsafe.
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Force – Torque – Lever Types
• Head on spinal column.
• Triceps on ulna
• Achilles tend. / forefoot
• Molar crushing
• Biceps, biting with
incisives, etc.
• To explain, torque is introduced: Torque = Force * radius.
• Torque causes a rotation / movement.
• Fulcrum / pivot is at center of rotation.
• Applies to muscles and sesamoid bodies, like patella, etc.
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Modified after Rhodes & Pflanzer 2003
Muscle Tension
• Large forces at work equivalent to weights of masses of
several 100 kg.
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Energy – Work – Power
• Energy = Work [J]
• Energy can take different forms
– Heat (“internal” work)
– Kinetic energy
– Potential energy
– Electrical energy
– PV work
1
æ
2ö
E
=
mv
çè
÷ø
2
( E = mDh)
( E = RI )
2
( E = PV )
– Chemical energy
– …
• Different forms sum to total energy;
can be converted into other forms.
• Metabolic energy in medicine still
often measured in cal (old…)
– 1 cal = 4.185 J
• Power = Work per time unit [W]CS 2017
Take-Home Messages
• Numbers without dimensions have little meaning.
• In medicine, frequency is often based on minute.
• Weight is a special force caused by mass * gravity.
• Tension is a force that develops in a muscle.
• Pressures are measured in kPa, except body fluids.
• Torque is the product of radius and force to causes rotation.
• Muscles produce large forces when contracting.
• Energy takes different forms, summing to the total and can
be converted into others.
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MCQ
The force of 1 N on a standard mass causes which of the following
accelerations?
A. 9.81 m/s2
B. 0.981 m/s2
C. 10 m/s2
D. 1 m/s2
E. 0.1 m/s2
How large is the energy of 1 mg of blood moving at a speed of 20 µm/min?
A. 20·10-12 kg*m2/s2
B. 5.6·10-12 kg*m2/s2
C. 5.6·10-20 kg*m2/s2
D. 0.56·10-15 kg*m2/s2
E. 5.6·10-20 kg*m/s2
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That’s it folks…
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MCQ
The force of 1 N on a standard mass causes which of the following
accelerations?
A. 9.81 m/s2
B. 0.981 m/s2
C. 10 m/s2
D. 1 m/s2
E. 0.1 m/s2
How large is the energy of 1 mg of blood moving at a speed of 20 µm/min?
A. 20·10-12 kg*m2/s2
B. 5.6·10-12 kg*m2/s2
C. 5.6·10-17 kg*m2/s2
D. 0.56·10-15 kg*m2/s2
E. 5.6·10-20 kg*m/s2
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Elementary Units (SI)
Dimension
Unit
Abbreviation
Length
meter
m
Mass
kilogram
kg
Time
second
s
Amount of substance
mole
mol
Current
ampere
A
Temperature
kelvin
K
Luminous intensity
candela
cd
• SI units refer to Système international d'unités”.
• Follows “meter-kilogram-seconds” system (MKS).
• kg is special case as it has a “multiple” in front
(see next).
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Some Derived Dimensions
Derived dimension
Unit
Abbrev.
Unit
Frequency
Hertz / …
Hz / bpm
s-1 / min-1
Force
Newton
N
kg·m·s-2
Pressure
Pascal / torr
Pa
N·m-2 = kg·m-1·s-2
Heat / Energy / Work Joule
J
N·m = kg·m2·s-2
Power
Watt
W
J·s-1 = kg·m2·s-3
Electric potential
Volt
V
W·A-1 = kg·m2·s-3·A-1
Electric resistance
Ohm
Ω
V·A-1 = kg·m2·s-3·A-2
Conductivity
Siemens
S
Ω-1 = kg-1·m-2·s3·A2
…
• List incomplete (some physiologically relevant ones…)
• It is possible to describe all measurements using the
7 elementary SI units.
– Dependency often established via the energy associated.
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Multiples and Fractions of Units
Factor
Prefix
Symbol
Factor
Prefix
Symbol
101
deca-
da
10-1
deci-
d
102
hecto-
h
10-2
centi-
c
103
kilo-
k
10-3
milli-
m
106
mega-
M
10-6
micro-
µ
109
giga-
G
10-9
nano-
n
1012
tera-
T
10-12
pico-
p
1015
peta-
P
10-15
femto-
f
1018
exa-
E
10-18
atto-
a
• Multiples are typically upper, fractions lower case.
• Because of inability to print Greek character µ early
on, sometimes people use ‘mu’ or ‘u’ for it.
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