Osmotic pressure – van’t Hoff equation:

= g C R TWhere:

- 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 constantT – 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)]WhereJ = fluid movement (ml/min)k = hydraulic constant (ml/min); k depends on permeability of capillaries, e.g fenestration; larger k means greater permeabilityJ = 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 Lawand 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 ResistanceOhm’s Law I = V/RSimilarly, Q = P/R or P = Q x RWhere 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

• The flow of (Newtonian) fluid through rigid tubes is governed by pressure gradient and resistance to flow

• Q = P/R, where R = 8l / (r4)• (Ohm’s law) (Poiseuille’s equation)• Properties of the fluid and tube affect resistance to flow.• Length of tube (l) R = 8l / (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 lawThe 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 mixtureWater vapor pressure

Henry’s law - Diffusion of gases through liquidsConcentration 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 vesselv is velocity of blood flow and is blood viscosity

Compliance of blood vessels C = V/P

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

• 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 lawP = 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 pulmonaryBundle 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 decreasesBohr effectH+ binds to hemoglobin & alters itO2 left behind in needy tissues

Transport of Carbon Dioxidein 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 itIn tissue capillaries, carbon dioxide combines with water inside RBCs to form carbonic acid which dissociates to form bicarbonate ions and hydrogen ionsH20 + CO2 < > H2CO3> H+ + HCO3- REMEMBER

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 equationpH = pKa + log ([base]/[acid])

Measurement pHpH = -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, Cl- are involved.