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Osmotic pressure – van’t Hoff equation:
=gCRT
Where:
 - osmotic pressure (atm or mm
Hg)
g – number of particles per mole
in solution (Osm/mol)
C – concentration (mmol/L)
 - reflection coefficient (varies
from 0 to 1, where 0 means that the
membrane is freely permeable to that
substance; and 1 means the membrane is
totally reflective or impermeable to the
substance)
R – gas constant
T – absolute temperature (K)
Fick’s law (diffusion/ conservation of
mass)
Flux = P A (Cout – Cin)
Where:
P = permeability factor; P is a
combination of 3 factors:
Diffusion coefficient – the ease with which
a substance moves through the
membrane once it is in it; e.g. size and
shape of the substance as well as
membrane properties;
Partition coefficient – the lipid solubility of
the substance
Membrane thickness
A = the cross sectional area available for
diffusion
C = concentrations of the substance on
either side of the separating membrane
Starling’s law of the capillaries is: The volume of fluid & solutes
reabsorbed is almost as large as the volume filtered
Ans: Apply Starling’s law (draw a picture to visualize)
J = k [(BHP-IFHP) – (BOP-IFOP)]
Where
J = fluid movement (ml/min)
k = hydraulic constant (ml/min); k depends on permeability of capillaries,
e.g fenestration; larger k means greater permeability
J = k [(30—1) – (26-3)] = k (30 – 1 – 26 + 3) = k x (6 mm Hg)
Therefore, net filtration will take place under 6 mm Hg pressure
(If you are given a value for the constant, e.g. 0.5 ml/min, then fluid flow will
be 0.5 x 6 = 3 ml/min)
Volume of Blood Flow
• Cardiac output = stroke volume x heart
rate CO = SV x HR
• Other factors that influence CO
– blood pressure
– resistance due to friction between blood cells
and blood vessel walls
• blood flows from areas of higher pressure to areas
of lower pressure
Pulse pressure= systolic pressure – diastolic pressure
120-80 =40 3:2:1
• Mean Arterial Blood Pressure (MABP) = average pressure in
arteries (not an arithmetic average)
• MABP = diastolic BP + 1/3(systolic BP – diastolic BP)
• For example, if one has 140/80 BP, then MABP is
• MABP = 80 + 1/3(140 – 80) = 80 + 1/3 (60) = 80 + 20 = 100
• Recall that MABP can also be expressed as
• MABP = CO x TPR
• (cardiac output times total peripheral resistance)
Blood Flow, Poiseuille’s Law
and Viscosity, Laplace’s Law and
Compliance
• Blood flow
– Amount of blood moving through a vessel in a given time period
– Directly proportional to pressure differences, inversely
proportional to resistance
• Poiseuille’s Law
– Flow decreases when resistance increases
– Flow resistance decreases when vessel diameter increases
• Viscosity
– Measure of resistance of liquid to flow
– As viscosity increases, pressure required to flow increases
Relationship between Pressure, Flow and
Resistance
Ohm’s Law I = V/R
Similarly,
Q = P/R or P = Q x R
Where
Q – flow (ml/min)
P – pressure difference
(mm Hg)
R – resistance (mm
Hg/ml/min)
Magnitude of Q is:
directly proportional to P. Flow is always
from high to low pressure.
Inversely proportional to resistance;
increasing resistance decreases flow.
This formula can be used to calculate flow
or resistance across a single organ or to
calculate total peripheral resistance (TPR).
Poiseuille’s Law
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The flow of (Newtonian) fluid through rigid tubes is governed by
pressure gradient and resistance to flow
Q = P/R,
where R = 8l / (r4)
(Ohm’s law)
(Poiseuille’s equation)
Properties of the fluid and tube affect resistance to flow.
Length of tube (l)
R = 8l / (r4)
Radius of tube (r)
Viscosity of fluid ()
>>Viscosity> the resistance to flow again direct relationship
>Radius < resistance inverse relationship
SO SMALLER THE
RADIUS GREATER THE RESISTANCE
P1 V1 = P2 V2
Boyle’s law – a special case of the gen’l gas law
The pressure times volume (at a given t) is constant (diaphragm movement
changes lung volume which changes P)
Dalton’s law - Partial pressure
–The pressure exerted by each type of gas in a mixture
Water vapor pressure
Henry’s law - Diffusion of gases through liquids
Concentration of a gas in a liquid is determined by its partial pressure
and its solubility coefficient
Dalton’s Law
• Each gas in a mixture of gases exerts its own
pressure
– as if all other gases were not present
– partial pressures denoted as ‘P’
• Total pressure is sum of all partial pressures
– atmospheric pressure (760 mm Hg) = pO2 + pCO2 +
pN2 + pH2O
– to determine partial pressure of O2 - multiply 760 by
% of air that is O2 (21%) = 160 mm Hg
Henry’s Law
• Quantity of a gas that will dissolve in a liquid
depends upon the amount of gas present and its
solubility coefficient
– Breathing compressed air while scuba diving
• N2 has very low solubility unlike CO2 (soda cans)
• dive deep & increased pressure forces more N2 to dissolve in
the blood (nitrogen narcosis)
• decompression sickness if come back to surface too fast or
stay deep too long
• Breathing O2 under pressure dissolves more O2
in blood
Turbulent flow – generates vibrations that
can be heard with a stethoscope (murmurs
and bruits)
Pathologic changes in cardiac valves or
narrowing of arteries, which raises flow
velocity, often induce turbulent flow
Reynold’s number (dimensionless) is used
to predict whether blood flow will be
laminar or turbulent. If value is less than
2,000, blood flow will be laminar, greater
than 3000 - turbulent.
NR =  d v / 
NR is Raynold’s number
Anemia (decreases viscosity)
is density of blood
Thrombi (decrease diameter)
d is diameter of blood vessel
v is velocity of blood flow and
 is blood viscosity
Compliance of blood vessels
V/P
C=
The higher the compliance of a vessel –
the more volume it can hold at a given
pressure
Aging decreases compliance of vessels
which decreases the volume of blood that
a vessel can hold
Changes in compliance causes
redistribution of blood between arteries and
veins.
If the compliance of veins decreases (e.g.
by venoconstriction), the volume of blood
they can hold decreases and is moved to
arteries.
Capacitance = ability to distend, hold a
volume of blood at a given pressure
Critical Closing Pressure, Laplace’s
Law and Compliance
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Laplace’s law – relate pressure, radius
of vessel, and tension on vessel wall:
Pv=T(1/r1+1/r2) where Pv is
ventricular pressure
For a cylindrical vessel, P=T/r
The larger the radius, the greater the
tension needed to
reach a
given pressure.
For a dilated heart
(radius is increased),
greater tension must be developed to
reach
any given pressure.
Capillaries and alveoli – importance of
Laplace’s law
P = T/r which is same as T = P x r
Small cap’s have small radius, thus can
withstand high internal pressures without
bursting.
If pressure is reduced, radius has to
increase to maintain tension (which keeps
a vessel open).
Under low enough pressure, the capillary
or alveoli will collapse = CRITICAL
CLOSING PRESSURE.
(alveolar surfactants decrease tension in
alveoli helping in preventing alveolar
collapse)
Einthoven’s law = if any two bipolar limb
potentials are known, one can find the third
(keep correct signs), e.g. lead I + lead III =
lead II
Einthoven’s law can be used to measure
the electrical axis of the heart.
Axis of the heart provides information on
changes of:
heart position within chest cavity (left or
right shift)
Hypertrophy of one ventricle, which is
related to hypertension, systemic or
pulmonary
Bundle branch block (left or right)
Please, see Ch. 12, figures 12 through 15
in Guyton for examples
One Cardiac Cycle
• At 75 beats/min, one cycle requires 0.8 sec.
– systole (contraction) and diastole (relaxation) of both
atria, plus the systole and diastole of both ventricles
• End diastolic volume (EDV)
– volume in ventricle at end of diastole, about 130ml
• End systolic volume (ESV)
– volume in ventricle at end of systole, about 60ml
• Stroke volume (SV); a.k.a. ejection fraction
– the volume ejected per beat from each ventricle,
about 70ml; normal ~ 65%, below 35% = leading
cause of sudden cardiac arrest (need defibrilator)
SV = EDV - ESV
Mean Arterial Pressure (MAP)
• Average blood pressure in aorta
• MAP = CO x PR
– CO is amount of blood pumped by heart per minute
• CO=SV x HR
– SV: Stroke volume of blood pumped during each heart beat
– HR: Heart rate or number of times heart beats per minute
• Cardiac reserve: Difference between CO at rest and
maximum CO
– PR is total resistance against which blood must be
pumped
Regulation of the Heart
• Intrinsic regulation: Results from normal
functional characteristics, not on neural or
hormonal regulation
– Starling’s law of the heart- (Frank Starling’s
contractibility of the heart)
• Extrinsic regulation: Involves neural and
hormonal control
– Parasympathetic stimulation
• Supplied by vagus nerve, decreases heart rate, acetylcholine
secreted
– Sympathetic stimulation
• Supplied by cardiac nerves, increases heart rate and force of
contraction, epinephrine and norepinephrine released
Pharmocology at NMJ
• Botulinum toxin blocks release of neurotransmitter at
the NMJ so muscle contraction can not occur
– bacteria found in improperly canned food
– death occurs from paralysis of the diaphragm
• Curare (plant poison from poison arrows)
– causes muscle paralysis by blocking the ACh receptors
– used to relax muscle during surgery
• Neostigmine (anticholinesterase agent)
– blocks removal of ACh from receptors - strengthens weak
muscle contractions (as in myasthenia gravis)
– also an antidote for curare after surgery is finished
Acidity & Oxygen Affinity for Hb
As acidity increases, O2 affinity for
Hb decreases
Bohr effect
H+ binds to hemoglobin & alters it
O2 left behind in needy tissues
Transport of Carbon Dioxide
in tissue capillaries
Carbon dioxide is transported as:
1.
bicarbonate ions (70%)
2.
in combination with
blood proteins (23%)
3.
in solution with plasma
(7%)
Haldane effect - Hemoglobin that has
released oxygen binds more readily to
carbon dioxide than hemoglobin that has
oxygen bound to it
In tissue capillaries, carbon dioxide
combines with water inside RBCs to form
carbonic acid which dissociates to form
bicarbonate ions and hydrogen ions
H20 + CO2 < > H2CO3> H+ + HCO3REMEMBER
P1V1=P2V2 Boyles Law
As the size of closed container decreases, pressure inside is
increased (inverse relationship)
The molecules have less wall area to strike so the pressure on each
inch of area increases.
Law of Laplace (P = 2T/r). Note the inverse relationship between
pressure and radius. The greater the radius the lesser the pressure
needed to keep the alveoli open. Surfactant effect…
Smaller the radius the greater the tension so the baby’s lung is more likely to collapse
compared to an adults
Physical Principles of Gas
Exchange
• General gas law (PV = nRT or P = nRT/V)
Where
P – pressure
V – volume
n – moles
R – gas constant
T – temperature (K); 310K for
body temperature of 37C
CO2 and Chloride (Hamburger) Shift
Summary of Gas Exchange & Transport
Inflation Reflex
(Hering-Breuer
reflex)
big deep breath
stretches
receptors in
bronchi and
bronchioles
producing urge
to exhale
pH
Henderson-Hasselbalch equation
pH = pKa + log ([base]/[acid])
Measurement pH
pH = -log[H+] = log 1/ [H+]
pH scale:
1-14;
pH 7 = neutral;
change of 1 pH unit is a 10 fold
change in proton concentration
Nernst Equation
• The diffusion potential level across a membrane that exactly
opposes the net diffusion of a particular ion through the membrane
is the Nernst Potential for that ion
• The magnitude of this Nernst potential is determined by the ration of
the concentration of that specific ion on the two sides of the
membrane.
• The greater this ratio, the greater the tendency for that ion to diffuse
in one direction
• Eion= RT ln [ion] out
ZF
[ion]in
Goldman-Hodgkin-Katz
• This is used when the membrane is permeable
to several different ions
• The diffusion potential that develops depends on
3 factors:
– The polarity of the electrical charge of each ion
– The permeablility of the membrane to each ion
– The concentration of the respective ions on the inside
and the outside of the membrane
• The equation gives the membrane potential for the
inside of the membrane when two univalent positive
ions, Na+ and K+ and one univalent negative ion, Clare involved.