ZOOL 463 Midterm 2

ZOOL 463 UofC

MODULE 6: OSMOTIC & IONIC REGULATION

Aquatic Environments: Salinity (2)

• Aquatic environments can vary in their salinity gradients (E.g. Chesapeake Bay where freshwater rivers dilute saltwater from the ocean)

• Saltwater has a greater concentration of ions relative to freshwater

2 Strategies to Function in Varied Environments

1. Regulators: Maintain tight control of internal environment (regardless of external environment)

2. Conformers: Maintain normal cellular function while matching external environment (match amount of dissolved solutes to internal environment)

3 Methods of Regulatory Control

1. Osmotic Regulation: Controlling total amount of dissolved solutes in internal environment to maintain water balance

2. Ionic Regulation: Regulation of specific ions, independent of total solute concentration

3. Volume Regulation: Organisms that are changing their physical size through precise regulation of water and salt balance

*Volume Regulation: Example

• Some crustaceans temporarily increase water uptake to swell and break out of their rigid carapace during molting, allowing them to grow before the new exoskeleton hardens

Graphing Osmotic Regulators vs. Conformers - Similarities (3)

• On the y-axis, blood osmotic pressure (total dissolved solutes in the blood) in mOsm is plotted

• On the x-axis, ambient osmotic pressure (solute concentration of the environment) in mOsm is plotted

• The dotted diagonal line represents the isoosmotic line, where blood osmotic pressure equals environmental osmotic pressure

Graphing Osmotic Regulators vs. Conformers - Differences (2)

• In the left graph, an osmotic regulator maintains a relatively constant blood osmotic pressure regardless of changes in the environment, reflected by a horizontal line (does not follow isoosmotic line)

• In the right graph, an osmotic conformer, whose internal osmotic pressure increases proportionally with environmental osmotic pressure, closely follows the isoosmotic line

*Graphing Osmotic Regulators vs. Conformers - Examples

• Shrimp is a regulator, mussel is a conformer, and the green crab is unique in which it tends to be a regulator until a high osmotic pressure (at which they become conformers)

Osmosis (2)

• Osmosis is the diffusion of water across a semipermeable membrane, where water moves from areas of low solute concentrations to high solute concentrations (areas of higher free water to less free water)

• This occurs because dissolved solutes bind surrounding water molecules, forming hydration shells that leave less “free water available

Osmolarity

• Refers to the total concentration of dissolved solutes in a solution and determines its osmotic pressure, which drives the movement of water during osmosis

Osmoticity: Osmotic Regulators (2)

• In freshwater, the external environment is hypoosmotic relative to body fluids, meaning it has a lower osmotic pressure (lower solute concentration)

• In saltwater, the external environment is hyperosmotic relative to body fluids, meaning it has a higher osmotic pressure (higher solute concentration)

• If the external and internal osmotic pressures are equal, the condition is described as isoosmotic

Osmoticity & Osmotic Regulators: Challenges to Freshwater Regulators (2)

• External environment is hypoosmotic, so water is constantly moving into the organism

• Constantly losing ions

Osmoticity & Osmotic Regulators: Challenges to Marine Regulators (2)

• External environment is hyperosmotic, so water is constantly moving out of organism

• Constantly loading ions

Organs of Salt/Water Balance: Gills (3)

• Gills are highly permeable structures with a large surface area and thin epithelium, adaptations that maximize gas exchange

• The extensive surface area increases osmotic water movement, and the high permeability allows ions to diffuse across the gill surface

• As a result, animals with high O₂ demands require larger gill surface areas, but this also increases water and ion exchange (osmoregulatory challenge)

Gill Anatomy: Two Types of Cells

1. Pavement Cells

• Make up most of the gills, and majority of the oxygen transport

2. Mitochondria-Rich Cells (MRCs - aka Chloride Cells)

• Specialized for ion regulation rather than gas exchange

Gill Cell Types: Mitochondria-Rich Cells (2)

• Uptake of Cl^-, Na⁺, and Ca²⁺ in freshwater (compensate ion loss), but excretion of Cl^- and Na⁺ in saltwater (counteract ion gain)

• The density and functional type of MRCs can change depending on environmental conditions, and are partially under hormonal control

Solution to Osmoticity Challenges: Active Transport (2)

• In freshwater fish, MRCs actively transport Na⁺ and Cl^- into the body to replace losses, while excess water is eliminated through production of large amounts of dilute urine

• In saltwater fishes, MRCs actively excrete excess ions, and water loss is compensated by drinking seawater

Ion Transport by Fish Gills: Anatomy

• The membrane facing the external environment is the apical membrane, while the membrane facing the blood supply is the basolateral membrane

Ion Transport by Fish Gills: Freshwater Gills - Apical Membrane (3)

• Ion uptake begins with a V-type (vacuolar) H⁺-ATPase in the apical membrane which actively pumps protons out of the cell into the surrounding water to create a negative electrical potential inside the cell

• This attracts positive ions such as Na⁺ & Ca²⁺ to enter passively through sodium channels & calcium channels respectively in the apical membrane

• Chloride uptake occurs through an electroneutral anion exchanger in the apical membrane, which exchanges external Cl^- for intracellular HCO₃^-

Ion Transport by Fish Gills: Freshwater Gills - Basolateral Membrane (3)

• The Na⁺/K⁺-ATPase actively pumps Na⁺ out of the cell into the blood while bringing K⁺ into the cell; the K⁺ that enters the cell leaks back into the blood, helping preserve the negative membrane potential

• Calcium can be transported across the basolateral membrane either by Ca²⁺-ATPase or by a Na⁺/Ca²⁺ exchanger (NCX) (uses inward Na⁺ gradient as driving force - created by Na⁺/K⁺-ATPase)

• As Cl^- accumulates in the cell, it can move across the basolateral membrane through channels such as the Cystic Fibrosis Transmembrane Regulator (CFTR) which is a passive channel

The Three Active Transporters During Ion Transport by Freshwater Fish Gills Are ___

• V-type pump, sodium-potassium pump, calcium-ATPase

Cystic Fibrosis (3)

• Caused by a genetic mutation in the CFTR gene, reducing Cl^- clearance from the cell, making the intracellular environment more negative than normal

• This reduces the movement of positively charged ions such as Na⁺ out of the cell, and the buildup of ions increases osmotic water movement into cells, contributing to thickened secretions and inflammation

• In epithelial tissues in the lungs and GI tract, this leads to mucosal buildup (and its associated complications)

Saltwater Fishes: Drinking Seawater (3)

• When seawater is consumed, the fluid in the gut becomes hyperosmotic relative to the blood plasma; as a result, water moves by osmosis out of the blood plasma into the gut lumen

• At the same time, Na⁺ and Cl^- diffuse from the gut into the bloodstream down their concentration gradients; later parts of the intestine continue to actively transport Na⁺ and Cl^- out of the gut and into the blood (allows animal to retain water despite ingesting a hyperosmotic fluid)

• Net result is concentrated (hyperosmotic) blood plasma which is why mammals cannot drink seawater to rehydrate (lack specialized transport mechanisms)

Saltwater Fishes: Drinking Seawater - Percentages (2)

• As Na⁺ and Cl^- are absorbed, water follows by osmosis and 50-85% of the ingested water can be absorbed into the blood

• For this process to be effective, 97% of Na⁺ and Cl^- must be transported into the blood plasma to maintain the gradient for water absorption

Ion Transport by Fish Gills: Marine Gills - Basolateral & Apical Membrane (4)

• The Na⁺/K⁺-ATPase at basolateral membrane actively pumps Na⁺ out of the cell and K⁺ into the cell (K⁺ leaks back into blood), maintaining a low intracellular Na⁺ and negative membrane potential

• This sodium gradient drives the NKCC cotransporter which brings 1 Na⁺, 1 K⁺, and 2 Cl^- into the cell from the blood with each cycle

• The accumulation of Cl- rises above that of seawater, allowing it to passively diffuse out across the apical membrane into the external environment

• Sodium follows paracellulary due to the electrical gradient, allowing marine fish to effectively excrete excess salts absorbed from seawater

Ion Transport by Fish Gills: Marine Gills - Calcium Transport

*Calcium transport in marine gills is same as freshwater gills

Terrestrial Organisms: Marine Birds/Reptiles (2)

• Live in close association with seawater and are hypoosmotic relative to seawater

• The two major challenges they face are water loss and salt loading

Terrestrial Organisms: Marine Birds/Reptiles - Challenges (2)

• Water tends to leave their bodies by osmosis, while salts enter through ingestion of seawater and consumption of marine prey

• Have less permeable integuments which helps reduce water loss across the body surface, but water loss still occurs through respiration

Marine Birds - Strategies for Salt Balance (2)

• Rely on specialized nasal salt glands that actively remove excess NaCl from the blood by producing a highly concentrated salt solution that is excreted through the nostrils

• This secretion is often more concentrated than seawater, allowing them to eliminate excess solutes while conserving water

*4 Marine Birds That Utilize Nasal Salt Glands

1. Gulls (Charadriiformes)

2. Penguins (Sphenisciformes)

3. Albatross (Procellariiformes)

4. Pelicans (Pelecaniformes)

Marine Birds: Physiology of Nasal Salt Glands (4)

• The nasal salt gland consists of highly vascularized secretory tubules surrounded by capillaries, separated by a single epithelial cell layer that allows efficient ion transport from blood to gland lumen

• On the basolateral membrane, the Na⁺/K⁺-ATPase pumps Na⁺ out of the cell and K⁺ into the cell (out through K+ leak channels to stabilize membrane potential), maintaining low intracellular Na⁺ for negative membrane potential

• This sodium gradient drives the NKCC cotransporter (same function as before), resulting in a highly concentrated NaCl solution in the tubule lumen

• The concentrated NaCl is then transported through a central duct and excreted through the nostrils

Marine Reptiles: Salt Glands

• Function similarly to that of the marine birds, but differ in anatomical location (e.g. lingual (tongue) salt gland, modified tear ducts, etc.,)

Marine Fish: Special Cases to Osmotic Balance - Elasmobranchii (3)

• Elasmobranchii (sharks, rays, skates) are marine osmoconformers/ionic regulators that take a unique approach to osmotic balance

• Instead of actively secreting large amounts of salt, they produce high concentrations of organic solutes in their blood, primarily urea and trimethylamine oxide (TMAO)

• The accumulation of organic osmolytes raises osmotic pressure of blood plasma to be nearly isosmotic with seawater, reducing osmotic water loss

Marine Fish: Special Cases to Osmotic Balance - Salmon

• Salmon are born in freshwater, migrate to seawater to grow, and return to freshwater to reproduce

Salmon: Behavioural Strategies (2)

• Salmon often spend time in brackish water (estuaries) that serve as a transitional environment between freshwater and full-strength seawater (reduces osmotic stress)

• Additionally, salmon can adjust drinking behaviour to reduce water intake when transitioning between environments

Salmon: Physiological Strategies (2)

• Kidney function changes as in freshwater salmon produce a high volume of dilute urine to eliminate excess water, whereas in seawater urine volume decreases

• Gill function also shifts through changes in MRCs, where in freshwater they specialize in ion uptake, while in seawater they switch to ion excretion

MODULE 7: TERRESTRIAL OSMOREGULATION & THE KIDNEY

The greatest challenge to terrestrial organisms is ___

• Water loss

3 Sources of Water Loss

1. Respiratory Water Loss: Water vapour lost during breathing

2. Evaporative Water Loss (EWL): Water loss across the skin/body surface

3. Excretory Water Loss: Water loss through urine and feces

Excretory Water Loss (3)

• EWL is necessary because organisms must remove metabolic waste products, particularly nitrogenous wastes produced from breakdown of proteins

• Nitrogen is initially generated as ammonia (toxic), and many terrestrial vertebrates convert it into urea for safer transport and excretion

• Eliminating these wastes requires water, so to prevent excessive dehydration organisms regulate the composition, concentration, and volume of urine

Urine Concentration Modification (2)

• During times of drought, organisms retain as much water as possible by producing highly concentrated urine

• During times of water loading, excess water is eliminated through production of large volumes of dilute urine

The degree of urine concentration is expressed as ___

• U/P ratio; concentration of substance in urine divided by its concentration in plasma (primarily reflected by adjustments in urine concentration)

U/P Ratio (3)

• U/P = 1; urine is isoosmotic to plasma

• U/P < 1; urine is hypoosmotic (dilute) relative to plasma (water excretion)

• U/P > 1; urine is hyperosmotic (concentrated) relative to plasma (water loading)

The U/P ratio in humans ranges from ___

• 0.1-4

The Mammalian Kidney

• Its concentrating ability regulates urine production, and thus H₂O and solute concentration

*Dotted line on left diagram is border between renal cortex and renal medulla

*Renal pyramid is the structure that carries a collection of nephrons (functional unit of water and salt balance for the kidneys - 1 million nephrons per kidney)

The Nephron (5)

• The nephron is the functional unit of the mammalian kidney and is responsible for filtering blood and forming urine

• It begins in the renal cortex with Bowman’s capsule, which surrounds the glomerulus and is where filtration occurs

• The filtrate then passes through the proximal tubule, where most reabsorption of water and solutes takes place

• It continues into the loop of Henle which extends into the medulla and consists of descending and ascending limbs that establish the osmotic gradient necessary for urine concentration

• The filtrate then moves into the distal tubule, and finally into the collecting duct (which runs through the renal medulla)

Bowman’s Capsule (3)

• Located in the cortex and surrounds the glomerulus, a network of capillaries that provides direct access to the blood

• This close association allows filtration of blood plasma under pressure, forming the initial filtrate (primary urine)

• Small solutes and water pass from the blood into Bowman’s capsule, while large molecules (proteins and cells) are retained in the blood

Glomerulus (2)

• Blood enters the glomerulus through the afferent arteriole and exits through the efferent arteriole

• Exit of blood in the capillary bed through an arteriole rather than a venule allows tight regulation of contraction through systole pressure (heart contraction)

Together, Bowman’s capsule and the glomerulus form the ___

• Renal corpuscle

Filtration at Glomerulus: Hydrostatic & Osmotic Forces (3)

• The primary force favouring filtration is the hydrostatic blood pressure within the glomerular capillaries which push fluid into the capsule

• Opposing this movement are two forces: colloid osmotic pressure of blood (generated by plasma proteins that remain in capillaries), and hydrostatic pressure of the capsular fluid within Bowman’s capsule

• The osmotic (oncotic) pressure of the blood is slightly higher than that of the filtrate, which pulls water back towards the capillaries

Glomerular Ultrafiltration (2)

• Ultrafiltration occurs at the glomerulus when hydrostatic pressure in the glomerular capillaries is greater than pressure within the tubule lumen of Bowman’s capsule

• This pressure difference (generated by cardiac systole) forces water and small solutes out of the blood and into the filtrate, but not large solutes

Glomerular Ultrafilter: 3 Components

1. Glomerular Capillaries

• Composed of a single endothelial layer containing fenestrations that allow water and small solutes to pass only

2. Basement Membrane

• On the outside of blood vessel; collagen-rich layer that acts as a selective barrier based on size and charge (restricting large proteins)

3. Podocytes

• Have a central cell body with extending foot processes that interlock to form openings known as slit diaphragms

Primary Urine (2)

• Primary urine consists of water and small solutes that first enter the nephron after filtration into the Bowman’s capsule

• Primary urine has a U/P ratio close to 1 (blood slightly higher osmotic pressure)

Definitive Urine (2)

• Is the final excreted product after reabsorption and secretion along the nephron

• Can have a much higher or lower osmotic concentration than plasma depending on whether the body is conserving water, or eliminating excess water

Glomerular Filtration Rate (GFR) (2)

• GFR is the rate of production of primary urine (approximately 120mL per minute)

• The kidneys filter a volume equivalent to the entire blood volume roughly every 30 minutes

Loop of Henle (3)

• The ability to change the concentration of urine starts with the Loop of Henle

• Nephrons are classified as long-loop (juxtamedullary) or short-loop (cortical) nephrons

• Long-loop nephrons have Loops of Henle that extend deep into the inner renal medulla; short-loop nephrons remain mostly in the cortex and outer renal medulla and do not contribute to urine concentration

Renal Medullary Thickness (2)

• Renal medullary thickness can be measured as the thickness of the inner renal medulla relative to the overall thickness of the kidney

• There is a positive relationship between relative medullary thickness (longer Loops of Henle) and maximum urine concentration

Primary Urine Flow: Loops of Henle (3)

• After filtration in Bowman’s capsule, primary urine flows into the proximal convoluted tubule and then into the Loop of Henle

• The filtrate first travels down into the inner renal medulla through the thin segment of the descending limb

• When the loop turns and ascends back toward the renal cortex, it enters the ascending limb (which is divided into a thick and thin segment)

Loops of Henle: Descending Thin Segments - Permeability

• The descending thin segments are highly permeable to water, and moderately permeable to solutes

Loops of Henle: Ascending Thin Segments - Permeability

• The ascending thin segment is impermeable to water, but moderately permeable to solutes

Loops of Henle: Ascending Thick Segments - Permeability

• The ascending thick segment is impermeable to water, and is involved in active transport of NaCl

___ can leave the descending limb, but not the ascending limb

• Water

Loops of Henle: Ascending Thick Segments - Active NaCl Transport (4)

• The Na⁺/K⁺-ATPase located on the basolateral membrane actively pumps Na⁺ out of the cell (into interstitium), while most of the K⁺ leaks back into the interstitium through leak channels

• This low Na⁺ level provides the driving force for the NKCC cotransporter on the apical membrane, which brings 1Na⁺, 1K⁺, and 2Cl^- ions into the cell from lumen of nephron

• The net effect is accumulation of Cl^- within the cell, which then diffuses passively through chloride channels into the interstitium

• Additionally, the movement of ions creates an electrical gradient that drives Na⁺ movement from lumen to interstitium through paracellular pathways

Two Osmotic Pressures in Loop of Henle

1. Single Effect

• Refers to the initial local change in concentration produced by active NaCl transport

2. Countercurrent Multiplication

• Occurs because fluid in the descending and ascending limbs flow in opposite directions, causing the single effect to be repeatedly applied along its length as new filtrate enters and moves through the loop

Single Effect: Scenario (4)

• Imagine starting with equal solute concentrations in the ascending limb, descending limb, and surrounding interstitium

• Active transport pumps NaCl out of the ascending limb into the interstitium, decreasing NaCl concentration in the ascending limb while increasing it in the interstitium

• As the interstitium becomes more concentrated, NaCl diffuses into the descending limb, and water moves out of the descending limb into the interstitium

• This single active transport process therefore creates concentration differences across the two limbs and the interstitium to establish a transverse (horizontal) osmotic pressure gradient between the limbs

Countercurrent Multiplication (2)

• Countercurrent multiplication transforms the transverse gradient created by the single effect into an axial osmotic pressure gradient within the renal medulla

• Osmotic pressure increases as you move deeper into the renal medulla, with solute concentrations becoming highest in the inner medulla

Collecting Ducts (2)

• The loop of Henle creates the osmotic gradient in the renal medulla, and is continuously removing NaCl making the tubular fluid dilute

• The concentration of urine primarily occurs in the collecting ducts

As fluid moves down the collecting duct toward the inner renal medulla, ___

• it encounters an interstitium with higher osmotic concentration

Antidiuresis: Concentrated Urine - Drought (2)

• During antidiuresis, the collecting duct is permeable to water, so kidney produces concentrated urine because water is reabsorbed from the collecting duct into the interstitium

• Most solutes remain in the duct, so fluid inside becomes increasingly concentrated as it descends

Diuresis: Dilute Urine - Water Loading (2)

• During diuresis, the collecting duct becomes impermeable to water

• As a result, the tubular fluid becomes progressively more dilute, and is excreted as large volumes of dilute urine

Water retention of the collecting duct is governed by ___

• hormonal control

Hormonal Control of Urine Concentration (3)

• Hormonal control of urine concentration is primarily regulated by antidiuretic hormone (ADH), aka vasopressin or arginine vasopressin

• ADH modulates the permeability of the collecting duct to water

• When ADH is present, it stimulates the insertion of aquaporin-2 water channels into the membrane of collecting duct cells, allowing water to move into the interstitium (antidiuresis)

Antidiuretic Hormone: Detection

• ADH release is upregulated by low levels of blood plasma, meaning the body needs to conserve water

Antidiuretic Hormone: Stimulation of Release - Baroreceptors (2)

• Low blood volume is detected by baroreceptors which are stretch-sensitive receptors located in the pulmonary venous system, cardiac atria, aortic arch, and carotid sinus

• When these receptors sense reduced stretch (indicating lower blood volume), they signal for increased ADH release

Antidiuretic Hormone: Stimulation of Release - Osmoreceptors (2)

• Osmoreceptors in the hypothalamus detect increases in blood osmolarity (when blood becomes more concentrated due to water loss)

• These receptors stimulate neurons in the hypothalamus that trigger the posterior pituitary to release ADH into the bloodstream

Aquaporin-2: Second-Messenger Signalling Pathway (4)

• ADH binds to V₂ receptors on the basolateral membrane of collecting duct cells which activates a G-protein (G_s)

• This activates adenylyl cyclase which converts ATP into cAMP, which then activates protein kinase A (PKA)

• PKA triggers exocytosis of aquaporin-containing vesicles (AQWCV), inserting aquaporin-2 channels into the apical membrane of the collecting duct (concentrated urine)

• When ADH is absent, the opposite occurs where aquaporin-2 channels are removed from the membrane by endocytosis (dilute urine)

Urea (2)

• Ammonia (NH₃) is a nitrogenous waste product formed during protein metabolism (toxic); the liver converts ammonia into urea, a less toxic compound that is transported to the kidneys for excretion

• Urea is freely filtered at the glomerulus as the concentration of urea in Bowman’s capsule is nearly equal to that of blood plasma

Urea Has Low Permeability In: (3)

1. Distal convoluted tubule

2. Thick ascending segment of Loop of Henle

3. Cortical and outer renal medulla

Urea Has High Permeability In: (2)

1. Collecting duct

2. Inner renal medulla

Urea Permeability: Urea Recycling (3)

• As fluid moves down the descending limb of the loop of Henle, the concentration of urea increases as water leaves into the interstitium, but then stabilizes as it enters the ascending limb and upper portion of the collecting duct

• In the lower portion of the collecting duct in the inner renal medulla, the epithelial cells contain high levels of UT-A1 and UT-A3, which are transporters that allow urea to diffuse out of the collecting duct into the interstitial fluid

• Once in the interstitium, some of the urea diffuses back into the thin segments of the loop of Henle (increasing urea concentration)

Urea transporter proteins are upregulated by ___

• ADH

Renal Medulla Blood Supply: Vasa Recta (3)

• The capillaries that supply the medulla (vasa recta) are highly permeable, allowing water and solutes to move easily between the blood and surrounding interstitial fluid

• As blood flows from the renal cortex down into the medulla, it encounters an environment with progressively higher osmotic pressure

• As a result, water diffuses out of the plasma into the interstitium, while the blood takes up NaCl and urea

Vasa Recta (2)

• The vasa recta supplies oxygen and nutrients to the medulla without destroying osmotic pressure gradients because of countercurrent exchange (minimizes washout of solutes)

• Only 1-2% of total renal blood flow passes through the vasa recta (also minimizes washout)

Vasa Recta: Countercurrent Exchange (3)

• As blood enters the descending limb of the vasa recta, it encounters increasingly concentrated interstitium, and water diffuses out of the blood vessel while solutes (NaCl and urea) diffuse into the blood

• When the blood turns and ascends back toward the cortex, the situation reverses as the blood inside the vessel is now more concentrated, so water moves back into the blood and solutes diffuse into the interstitium

• The blood leaves the vasa recta and returns to the venous circulation has a composition similar to the blood that entered, and this mechanism prevents the osmotic gradient of the renal medulla from being washed out

MODULE 8: CARDIOVASCULAR 1

Cadiovascular System

• Refers to the system involving the heart (cardio) and blood vessels (vascular) that circulate blood throughout the body

Lumen

• The hollow internal space within a blood vessel or heart chamber through which blood flows

Circulation (3)

• Refers to the pressure-driven bulk flow of blood through vessels and passages

• Mechanistically, it is the movement of blood caused by pressure differences generated by the heart

• Functionally, circulation transports commodities (oxygen, nutrients, wastes, hormones, etc.,) while also providing hydraulic pressure that supports organ function

Perfusion

• Refers to the forced flow of blood through blood vessels supplying tissues, ensuring that organs receive oxygen and nutrients

Convective Transport

• Refers to the movement of substances by bulk flow of fluid, meaning materials are carried along with flowing blood rather than diffusion

The circulatory system includes the ___, ___, ___, and ___

• Heart (blood pump)

• Blood vessels

• Circulatory passages

• Blood

Volumetric Flow Rate (Q) (2)

• Volumetric flow rate (Q) describes the volume of fluid that passes through a cross-section of a vessel per unit time (L/min or m²/min)

• It is calculated using the equation: Q = A x v where A is the cross-sectional area of the vessel (m²) and v is the velocity of the fluid (m/s)

Volumetric Flow Rate (Q): Continuity Principle (2)

• In a closed system, Q is conserved, meaning the same volume of fluid must pass through each section of the system per unit time

• If the radius of a vessel decreases, the cross-sectional area decreases; since flow must remain constant, the velocity of fluid must increase to compensate

*Volumetric Flow Rate (Q): Continuity Principle - Mathematical Approach (2)

• Because Q is constant: A₁V₁ = A₂V₂

• If A₂ < A₁, then V₂ > V₁; meaning fluid moves faster in narrow vessels

Volumetric Flow Rate (Q): Branching Vessels (2)

• When a vessel branches, the flow entering the branch must equal the sum of the flows in all downstream branches (Q_in = Q₁ = Q₂ + Q₃ + Q_n)

• This means the total flow entering a branching point equals the total flow leaving it

Volumetric flow rate explains ___ and ___

• Why blood velocity increases in narrower vessels

• Why flow from larger arteries is distributed among multiple smaller branches while maintaining conservation of flow

*Application Question: Volumetric Flow

5 Factors Affecting Q

1. Pressure Difference

• ΔP between the entrance and exit of the vessel is proportional to flow; larger pressure gradient produces greater flow (blood flows from high to low - P_in > P_out)

2. Vessel Radius (r)

• Larger radius increases flow; resistance to flow decreases

3. Vessel Length (l)

• Longer vessels increase resistance (reducing flow)

4. Viscosity of Fluid (v)

• Higher viscosity (thicker blood) increases resistance and reduces flow

5. Elasticity & Compliance

• Blood vessels that are more elastic and compliant can expand in response to pressure

*VELPR

Hagen-Poiseuille Law (3)

• Describes how flow (Q) through a cylindrical vessel depends on the pressure difference and resistance

• Where P1-P2 is the pressure difference between the entrance and exit of the vessel, and R is the resistance to flow

• This means that greater pressure differences increase flow, while greater resistance decreases flow

Resistance in a Vessel (3)

• Resistance depends on viscosity of the fluid (µ) length of the vessel (L), and radius of the vessel (r)

• Resistance increases with greater viscosity and longer vessel length, and decreases dramatically as radius increases (strongest effect)

• Viscosity is influenced by the number of red blood cells (hematocrit) and plasma proteins (affect how thick blood is)