BMS100_PHL1-21 PreLearn (F2022) PDF

Flow down gradients – overview • Flow = movement of a substance from one point in a system (A) to another point in the system (B) ▪ Flow is measured by the amount of substance (volume, moles, charge) that moves over time (seconds, minutes) ▪ The driving force for the flow of a substance is the energ...

Flow down gradients – overview • Flow = movement of a substance from one point in a system (A) to another point in the system (B) ▪ Flow is measured by the amount of substance (volume, moles, charge) that moves over time (seconds, minutes) ▪ The driving force for the flow of a substance is the energy gradient between point A and point B ▪ The amount of flow is directly related to the size of the energy gradient between A and B ▪ The greater the gradient, the greater the flow • Every system will have factors that resist this flow Why is this concept important? Life depends on the movement of substances from one point in the body to another • Fluids and gases must constantly be moving from one point in the body to another ▪ Example – flow of gases and fluid through “large tubes” is determined by certain variables • described by Pouiseille’s law ▪ Example – molecular flow of gases, water, and solutes can be driven by diffusion, by electrostatic interactions, or by pressure gradients • described by Fick’s law, Ohm’s law, and others Flow down gradients – movement of gases and liquids through a vessel • Movement of a gas or liquid through a tube can be described with the following parameters in the model: ▪ Hydrostatic pressure causes gas or liquid to flow from point A to B ▪ Physical structures resist flow (resistance): • the dimensions of the tube that the substance flows through ▪ Substance characteristics that impact flow: • viscosity of the fluid ▪ The rate of flow is determined by Poiseuille’s law: F = (P1 – P2) · 𝝅𝒓𝟒 𝟖𝝁𝒍 Poiseuille’s law - defined • F = flow ▪ volume of liquid that passes through a tube per unit time (i.e. L/min) • P = hydrostatic pressure ▪ the force that a substance exerts on the walls of its container • r = radius of the tube that the fluid is moving through • l = the length of the tube • 𝝁 = the viscosity of the fluid ▪ Less viscous fluids are more “runny” (i.e. water) and more viscous fluids are more “syrupy” (i.e. …. syrup) F = (P1 – P2) · 𝜋𝑟 4 8𝜇𝑙 Poiseuille’s law - defined • F = flow ▪ volume of liquid that passes through a tube per unit time (i.e. L/min) F = (P1 – P2) · 𝜋𝑟 4 8𝜇𝑙 • P = hydrostatic pressure ▪ the force that a substance exerts on the walls of its container • r = radius of the tube that the fluid is moving through • l = the length of the tube • 𝝁 = the viscosity of the fluid ▪ Less viscous fluids are more runny (i.e. water) and more viscous fluids are more “syrupy” (i.e. …. syrup) Flow increases when these increase Flow decreases when these increase Poiseuille’s law – take-home • Therefore, flow of… ▪ Water through a garden hose ▪ Blood or lymph through its vessels ▪ Air through an airway • … can be affected by the: ▪ difference in hydrostatic pressure between two points in the tube/vessel ▪ cross-sectional “size” of the tube/vessel (radius) ▪ distance between the two points in the tube/vessel (l) ▪ how viscous (“syrupy”) the flowing substance is Poiseuille’s law – take-home • For the respiratory tract and the cardiovascular system, it is clinically relevant to think of flow of gas or blood to tissues (in terms of mL/min) • The body controls flow through vessels by: ▪ Controlling the pressure in the large vessels ▪ Controlling the radius of the small vessels • NOTE: the resistance is inversely related to the 4th power of the radius ▪ What happens to the resistance if the radius decreases by half? Poiseuille’s law – take-home • Poiseuille’s law caveats: ▪ Accurate for rigid, simply-shaped tubes with non-turbulent fluid flow • As tubes become more branched or irregularly-shaped, harder to quantify resistance • If flow becomes turbulent, the resistance changes as well • If a tube is flexible – like an artery – Poiseuille’s law also is not exact ▪ For all of the above variations, radius of the tube is still the most important determinant of resistance A simplified equation that includes a measured (not calculated) resistance can also describe flow: Flow = ∆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (a variant of Ohm’s law) Poiseuille’s law – take-home • Poiseuille’s law caveats: ▪ As tubes become more branched or irregularlyshaped, harder to quantify resistance ▪ If flow becomes turbulent, the resistance changes as well ▪ If a tube is flexible – like an artery – Poiseuille’s law also is not exact ▪ Radius is most important determinant of resistance Flow down gradients - diffusion • Diffusion in biology: ▪ Movement of a solute or a gas in a gas mixture from an area of high concentration to low concentration • Usually this movement occurs across a barrier composed of a membrane(s) • Simplified equation - Fick’s law - quantifies how the rate of diffusion is affected by various parameters: ▪ Flow = flux = amount of solute moving across a barrier per unit time ▪ Force driving flux → concentration gradient (C2 – C1) • difference in concentration on either side of the membrane ▪ Resistances: • Membrane surface area and membrane thickness • Permeability of the membrane to the substance Flow down gradients - diffusion Fick’s law: 𝑭 = 𝒌 ∙ 𝑨(𝑪𝑨 −𝑪𝑩 ) 𝒕 Fick’s law - defined • F = flow/flux ▪ number of molecules of a substance diffusing from point A to point B over time • (𝐶𝐴 − 𝐶𝐵 ) = concentration gradient ▪ Difference in concentration on either side of the membrane • A = surface area of the membrane • 𝒌 = a constant that increases when: ▪ The substance is a smaller molecule that dissolves better in the barrier ▪ The permeability of the barrier to the substance increases • t = thickness of the membrane 𝑨(𝑪𝑨 − 𝑪𝑩 ) 𝑭=𝒌 ∙ 𝒕 Fick’s law - defined • F = flow/flux ▪ number of molecules of a substance diffusing from point A to point B over time • (𝐶𝐴 − 𝐶𝐵 ) = concentration gradient ▪ Difference in concentration on either side of the membrane • A = surface area of the membrane • 𝒌 = a constant that increases when: ▪ The substance is a smaller molecule that dissolves better in the barrier ▪ The permeability of the barrier to the substance increases • t = thickness of the membrane 𝐴(𝐶𝐴 − 𝐶𝐵 ) 𝐹=𝑘 ∙ 𝑡 Flow increases when these increase Flow decreases when this increases Fick’s law – take-home • Therefore, flow/flux of… ▪ Solutes through capillaries ▪ Substances through cell membranes ▪ Oxygen and carbon dioxide from alveolus to blood • … can be affected by the: ▪ Concentration difference ▪ Surface area available for the solute/gas to cross ▪ The permeability of the membrane ▪ Solubility and molecular size of the substance ▪ The distance between the two compartments Fick’s law – take-home Tissue/cellular structure has adapted to meet the constraints of Fick’s law: • The thickness of the membrane/barrier to diffusion needs to be very small - flux is very slow over distances greater than 0.1 mm • How have we adapted? • Membranes have channels or transporters in order to increase permeability of the membrane • The need for channels/transporters depends on the solubility of the substance in the membrane Fick’s law – take-home Tissue/cellular structure has adapted to meet the constraints of Fick’s law: • Cells that are specialized for transporting large amounts of solute have: ▪ more transporters ▪ structural features that increase the surface area:volume ratio • Our bodies manipulate concentration gradients all the time ▪ Metabolism ▪ Transporters that INCREASE gradients Fick’s law – take-home Fick’s law caveats: • There are many “versions” of Fick’s law – the one discussed here is the easiest to apply to clinically-relevant situations ▪ it’s mathematically accurate for gases diffusing across fluid barriers, and “close enough” for other situations ▪ Saturation of protein transporters will reduce flux • In most physiological situations diffusion happens so quickly that we don’t worry too much about the rate of flux ▪ Diffusion “failure” is a common theme in disease Flow down gradients – movement charged particles across a barrier • Movement of a dissolved, charged particle – i.e. an ion – across a barrier – i.e. a membrane – depends on: ▪ The charge of the particle ▪ The difference in “concentration” of charges across the membrane – this gradient is known as voltage • A type of potential energy → how much work it takes to move a charged particle through an electric field ▪ The permeability of the membrane to the charged particle • The rate of flow of charges across a membrane is known as current (I) and is simply defined by Ohm’s law: 𝑉 𝐼= 𝑅 Ohm’s law - defined • I = current ▪ the number of charges or charged particles that move across the membrane per unit time • 𝑽 = voltage ▪ For our purposes, this is the energy generated by separating charges across the cell membrane • R = resistance ▪ More channels for a charged particle → less resistance 𝑉 𝐼= 𝑅 Ohm’s law - defined • I = current ▪ the number of charges or charged particles that move across the membrane per unit time 𝑉 𝐼= 𝑅 • 𝑽 = voltage ▪ For our purposes, this is the energy generated by separating charges across the cell membrane Current increases when this increases • R = resistance ▪ More channels for a charged particle → less resistance Current decreases when this increases Ohm’s law – take-home • Opposites attract – like charges repel ▪ The particles move “down a gradient” of voltage according to their charge ▪ Electric field of the charged particle is responsible for establishing voltage ▪ Resistance is anything that impedes the movement of the particle 𝑉 𝐼= 𝑅 Ohm’s law – take-home • In biology, Ohm’s law is most useful when thinking about unequal distributions of charges very close on either side of a membrane ▪ Overall positive and negative charges are balanced in all physiologic compartments ▪ The electric field declines very rapidly as charges are separated by distance + + - + - - + + + + + + - + + + - - + - + + - + - + - + + + - Case 1 • Mary is a 64-year-old woman with a 17-year history of Type 2 diabetes mellitus controlled by metformin and diet. Today she presents with slowly progressive numbness and coldness in her feet. The right foot is worse than the left • On investigation, you note: ▪ Mary’s right foot is cooler and more pale than her left foot ▪ Her posterior tibial pulse is weaker on her right than on her left, and the dorsalis pedis pulse on her right is not detectable ▪ The capillary refill time on the right great toe is 15 seconds, and on the left it is 3 seconds ▪ She cannot disintguish between sharp and dull stimuli over her right foot Case 1 • Below are an arteriole and an elastic artery from a patient without vascular disease and one with type II diabetes Long-term DM | No vascular disease Small vessels (arterioles) Large vessels (elastic arteries) Case 1 – Questions to answer • Clearly correlate Mary’s findings on history and physical exam to the known vascular changes that accompany diabetes mellitus ▪ Use the physico-chemical laws that were discussed in the pre-learning and the lecture • How many of these laws are in play? How many are less important? ▪ Try to explain every clinical feature • are there some clinical features that are less likely to be due to vascular changes? What would these be? Case 2 • Robert is a 75-year-old gentleman with a long history of coronary artery disease and high blood pressure. He had been diagnosed with NYHA stage II heart failure 5 years ago. • Today he presents because: ▪ his foot swelling has been getting worse – at the end of the day he has a great deal of difficulty putting on his shoes ▪ He has become more short of breath in the last few days • On investigation you note: ▪ His blood pressure is 156/98 mm Hg – other vitals are within normal limits ▪ His feet are notably swollen, and this swelling continues part-way up the shin ▪ He is breathing quickly at rest – his respiratory rate is 25 breaths/min Case 2 – Questions to answer • What aspect(s) of Robert’s medical history best explain his foot swelling? How about his shortness of breath? • How does these relate to the physicochemical laws discussed in the pre-learning and during the lecture? Heart failure – some basics Most patients with heart failure develop two general types of problems: • Impaired “forward-flow” ▪ due to decreased cardiac output and worsening blood supply to important tissues like the brain, heart, kidneys ▪ The tissues with poor blood supply suffer impaired function • “fluid backup” ▪ Blood is not moved from the veins at its usual rate, since the ventricles have a worsened cardiac output ▪ Blood “backs up” in the venous system