Pressure and Flow - Tagged PDF

In a lifetime: ~250 million beats, ~17 million litres pumped  MBBS1:FPP FLOW AND PRESSURE (flow through tubes and its relevance to the cardiovascular system) Dr Greg Knock [email protected]  Flow and Pressure After s...

In a lifetime: ~250 million beats, ~17 million litres pumped  MBBS1:FPP FLOW AND PRESSURE (flow through tubes and its relevance to the cardiovascular system) Dr Greg Knock [email protected]  Flow and Pressure After studying this lecture, you should be able to: Describe the factors that influence flow through tubes, including: Pressure differences, tube calibre, resistance to flow and viscosity Describe Darcy's Law and Pouseuilles' Law Distinguish between laminar and turbulent flow Explain the influence of tubes in series vs. tubes in parallel on total resistance Apply the above to an understanding of the cardiovascular system  The cardiovascular system: Why do we need it? Only in single-celled and simple multi-cellular organisms is diffusion alone sufficient to deliver oxygen and nutrients and remove waste products Complex multicellular organisms require a circulatory system to transport these substances around the body by bulk flow We also need to be able to REGULATE the delivery/transport of substances in response to the changing environment or the changing needs of the organism (homeostasis) Substances are transported in blood, so we need to regulate blood flow ARTERIES VEINS  The circulation is a closed system, with two pumps in series - But why do we Pulmonary Circulation: need two pumps? Low resistance & low pressure (~16mmHg), In series with the systemic Right ventricle pumps Blood through lungs Left ventricle Systemic Circulation: pumps High resistance Blood through body high pressure (~92mmHg) Mostly in parallel with each other  Head & Neck O2 Pulmonary Bronchial CO2 Coronary Trunk Gut, Pancreas & Liver Nutrients - Hepatic portal system Metabolites Renal Pelvis and legs Terminology Flow out of heart: Flow in to heart: Volume per beat: - Stroke Volume (~70mls) Volume per minute: Volume per minute: - Venous return (~5L/min) - Cardiac output (~5L/min) So: Must equal CO So: CO = SV  Heart rate Filling of heart: Resistance to flow: Determined by Total peripheral resistance Central Venous Pressure - TPR - CVP This determines pressure This Filling Pressure is load on left heart - PRELOAD - AFTERLOAD Movement of substances in the blood and to the cells Bulk flow – Transport within blood or air due to pressure differences Passive diffusion – Movement down a concentration gradient Transport of gases requires BOTH How does diffusion differ from bulk flow? = O2 Lungs Bulk Flow Respiring tissue Diffusion = CO2  Rate of diffusion in a solution: Fick’s law This depends on: – Area over which diffusion occurs (A) – Thickness of the diffusion barrier (T) – Difference in concentration of diffusing substance (C1-C2) (or partial pressure if a gas, P1-P2) – How easily a substance diffuses is also affected by: Solubility of the substance Square root of molecular weight of substance (+ temperature, usually constant at 37°C)  What determines the rate of diffusion between air and blood? Fick’s Law of diffusion airflow Diffusion is driven by: The concentration (or partial pressure) difference (C1 – C2) Diffusion is limited by: The thickness (T) and surface area (A) of the diffusion barrier and: O2 The Solubility and MW of the Alveolar substance Type I pneumocyte Therefore, rate of diffusion = Capillary CO2 endothelium (C1-C2) x A x solubility x 1 T √Mol. Wt. blood flow  Fick’s Law of diffusion Rate of diffusion = (P1-P2) x A x solubility x 1 T √Mol. Wt. Physical properties of the diffusion barrier and of the diffusing substance influence the permeability of the substance This is why Diffusion is too slow over large distances FLOW is required to transport substances around body  Flow in tubes The Law of Flow (or Darcy’s Law): P1 P2 Flow proportional to pressure difference (P1-P2) and inversely proportional to the resistance to flow (P1-P2) V Flow = I= (Ohm’s Law) Independent variable R R P = pressure (equivalent to) V = voltage; Flow (equivalent to) I = current R = resistance to flow / current flow What determines resistance to flow? 8VL R= Poiseuille’s Law r 4 (P1-P2) (P1-P2) r4 Flow = = R 8VL Length of tube (L) Radius of tube (r) Viscosity of fluid (V)  What determines resistance to flow? Vessel radius Flow  r4 R  1/r4 A small change in radius causes a large change in resistance and flow E.g. a 20% reduction in radius causes a 60% increase in resistance, therefore a 60% reduction in flow Why? 0.8 x 0.8 x 0.8 x 0.8 = 0.41  Arterioles can actively adjust their radius (and therefore, their resistance) through vasoconstriction or vasorelaxation Vasoconstriction Vasodilation more smooth constriction muscle relaxation Reduces radius Increases radius Increased resistance Reduced resistance Vasoconstrictor stimuli: At rest: Vasodilator stimuli: noradrenaline (SNS) partially Adrenaline Adrenaline constricted Atrial natriuretic peptide Angiotensin II (RAAS) Histamine Vasopressin (ADH) Flow Pressure  What determines resistance to flow? Viscosity P1 P2 The “thicker” the fluid, the higher the viscosity Red cell mass and plasma proteins make blood very viscous Blood is thicker than water (by 3-4 times) This alone would reduce flow… But – Blood is a non-Newtonian Fluid What difference does this make?  Flow in tubes Laminar flow P1 P2 Viscous drag at the sides of the tube slows the fluid, so the fastest movement (flow) is in the centre This becomes more apparent as the radius becomes smaller Cells tend to becomes aligned in the fastest moving fluid: AXIAL STREAMING In small vessels this effectively reduces viscosity The Fåhraeus-Lindqvist effect  Flow in capillaries P1 P2 Red cells are ~7m in diameter – Capillaries are ~6 m in diameter- Cells fit capillary like a plug, but they are very deformable And slip easily through – viscosity is therefore similar to plasma Why is this important? Very high viscosity (eg ↑ red cell count) → increased TPR → increased MAP (hypertension)  Flow in tubes Turbulence P1 P2 High velocity, sharp edges and branch points, especially in large tubes, can disrupt laminar flow, leading to turbulence  Flow in tubes Turbulence P1 P2 High velocity, sharp edges and branch points, especially in large tubes, can disrupt laminar flow, leading to turbulence This significantly increases resistance High velocity blood flow due to narrowed heart valves, or High velocity air flow due to narrowed airways therefore causes murmurs and wheezes respectively It can also cause damage to the vessel wall and/or activation of clotting mechanisms  Flow in (flexible) tubes Distensible vessel Rigid tube (Poiseuille) Distensible vessel Flow + myogenic tone Distensible E.g. pulmonary Myogenic E.g. cerebral Pressure  Flow in tubes Resistances in series and in parallel (P1-P2) V (Ohm’s Law) Flow = I= R R R1 R2 SERIES RTotal = R1 + R2 + … R1 1 1 1 PARALLEL = + + …. R2 RTotal R1 R2  Simple(st) model P1-P2 constant (controlled) thus Flow  1/Total resistance A Artery of resistance R P1 P2 As we have flow through a P1 resistor from a region of high pressure on the left to a region of lower pressure Pressure on the right, the pressure of the flowing fluid drops as it flows from left to right P2  Simple model P1-P2 constant (controlled) thus Flow  1/Total resistance A Total RA= R1+ R2 R1 R2 P1 P2 If R2 = 2 x R1, Then pressure drop over R1 P1 PX must be 1/2 of that over R2 R1 (Or 1/3 of total pressure drop) Pressure R2 NOTE: R1