Osmotic pressure – van’t Hoff equation : = g C  R T Where:  - osmotic pressure (atm or mm Hg)

1. Osmotic pressure – van’t Hoff equation: = g C  R T 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)

2. 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

3. 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)

4. 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

5. 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)

6. 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

7. 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).

8. 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 = 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

9. 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

10. 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

11. 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

12. 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

13. 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.

14. Capacitance = ability to distend, hold a volume of blood at a given pressure

15. 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. Critical Closing Pressure, Laplace’s Law and Compliance

16. 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)

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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 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+ + HCO3- REMEMBER

25. 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.

26. 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

27. 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

28. CO2 and Chloride (Hamburger) Shift

29. Summary of Gas Exchange & Transport INTERNAL RESPIRATION ABOVE (top) hco3- VERY GOOD BUFFER BUT IT HAS A CHARGE FOR EVERY ONE OUT A Cl- shift AKA a Hamburger shift. Bottom shift equation to the left Remember Cl- follows CO2 in top case, follows O2 is other case

30. Inflation Reflex (Hering-Breuer reflex) • big deep breath stretches receptors in bronchi and bronchioles producing urge to exhale

31. 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

32. 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

33. 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.