SS Laplace - Fall23.pptx

Law of Laplace Clay Freeman, DNP, CRNA Science in Anesthesia 1 Objectives Readings: Nagelhout: Chap. 15 Davis: p.17-18, 187 • Detail Laplace’s Law & how it relates to: • Cylinders • Spheres • Describe Pascal’s Principle • Describe components of Surface Tension • Describe surfactant effects 2...

Law of Laplace Clay Freeman, DNP, CRNA Science in Anesthesia 1 Objectives Readings: Nagelhout: Chap. 15 Davis: p.17-18, 187 • Detail Laplace’s Law & how it relates to: • Cylinders • Spheres • Describe Pascal’s Principle • Describe components of Surface Tension • Describe surfactant effects 2 Law of Laplace Describes the relationship of fluids to Tension (T) based on the factors of Pressure (P), and Radius (r) Tension (T) is a stress force exerted over a given area measured in Newtons/cm T = Pr 2T = Pr Cylind er Sphe re 3 Pressure & Pascal’s Principle Pressure applied to a confined fluid is transmitted unchanged throughout the entire system 4 La-Pascal 5 T = Pr Law of Laplace -Cylinder 100 mmHg 2 cm 100 mmHg 4 cm 100 mmHg 2 cm PRESSURE (P) maintained along length of cylinder Normal Physiology T = 1.33 N/cm2 x 2 cm T = 2.66 N/cm Aneurysm T = 1.33 N/cm2 x 4 cm T = 5.32 N/cm 6 T = Pr Law of Laplace -Cylinder Fluid pathways are dependent on a balance between internal pressure and wall tension in order to maintain patency 7 Law of Laplace Sphere 2T = Pr Increased Pressure = Increased wall Tension Increased Radius = Increased wall Tension Increased Contractility = Increased wall Tension 8 Law of Laplace Sphere Another component is Afterload – the force opposing against heart ejection. Increased afterload requires the heart to create more force in order to maintain the pressure gradient • This increased tension is transmitted into ventricular wall stress Ultimately The heart adapts to sustained stress through a process of hypertrophy Wall stress is wall tension divided by wall thickness ventricular wall stress equation: P = pressure R = radius H = wall thickness σ = wall stress 9 Law of Laplace Sphere Clinical Scenario: ETT cuff vs Pilot balloon Ideal cuff pressure is 20-25mmHg Practitioners are inaccurate at reliably palpating for ideal cuff pressures This is due to the pilot balloon being smaller • Wall tension of Pilot balloon < ETT 10 cuff Law of Laplace Sphere Applicable to alveoli in the Absence of Surfactant Solve for Pressure (T is constant) P = 2T / r Small Alveoli 2 (2) / 1 = 4 r= 1 Larger Alveoli 2 (2) / 2 = 2 r= 2 Pressure gradient: smaller Radius alveolus empties into larger Radius 11 Law of Laplace Sphere Clinical Scenario: Anesthesia machine reservoir bag The distensibility of the bag serves as protection from high pressures in the breathing system - Therefore, risk of barotrauma is reduced 12 Surface Tension • Surface tension is the cumulative effect of intermolecular forces within a substance against the unbalanced forces at a fluid interface (Van Der Waal Forces) Net Movement Surfac e Inwar d • H2O exhibits effects of surface tension • Alveoli have thin H2O membrane • Surface tension = wall tension in alveolus 13 Surfactant: Anti-Laplace • Surfactant is secreted by alveolar epithelial cells • Long chain phospholipid • hydrophilic head & hydrophobic tail • Surfactant breaks Surface Tension • Net equal distribution of water molecules 14 All together now Surfactant is the Equalizer Amount of Surfactant remains the same in healthy tissue  What varies is the Concentration Normal Alveolus: (With Pressure constant) if radius decreases  Tension decreases (due to concentration of surfactant) 15