Physiology Formulae😍

Physiology Formulae

Reynolds' Number

Feature	Laminar flow	Turbulent flow
Pattern	Streamlined	Disordered
Velocity	• Highest at center • Lowest at walls	Velocity in multiple directions
Cell position	Cells in center	Random distribution
Vessel condition	Normal vessels	Compressed / obstructed vessels
Sound	Silent	Noisy ↳ Murmurs, Korotkoff sounds
Reynolds Number (Re)	< 2000: Always laminar	> 3000: Always turbulent

Determined by Reynolds Number (Re): 

• Re = (Density x Diameter x Velocity) / Viscosity

• Velocity:
• Most important determinant
• due to Critical Velocity

Laplace’s Law

Pressure = 2 x Tension / radius

• Tension α Radius

• Mnemonic: Place ( Radius, Laplace) vikkan ulla pressurum (Pressure) tension (Tension)

Poiseuille-Hagen Formula

• Calculates Vessel resistance

• R = 8 x Viscosity x Length / (π x Radius⁴)

ㅤ	Resistance	Flow
Directly proportional	Blood viscosity & vessel length	Radius (R⁴)
Inversely proportional	Radius (R⁴)	Length of vessel

Poiseuille's Law (Formula for Blood Flow)

• F = ΔP x r⁴ x π / 8hl
• F: Rate of blood flow
• ΔP: Pressure difference between vessel ends
• r: Radius of the vessel
• l: Length of the vessel
• h: Viscosity of the blood

Blood Pressure

Bernoulli's principle:

• Potential energy (Blood pressure) + Kinetic energy (Blood flow) = Constant.
• Therefore, BP + Blood flow = Constant.

• Mnemonic: Bernoulli Principe → BP

Formulas

Modes of Measurement

Indirect Blood Pressure Measurement

• Korotkoff Sounds
• Sounds heard during cuff deflation
• Used to determine BP.

Phase	Sound Description	Correlates To
Phase 1	Faint tapping sound	SBP
Phase 2	Murmur-like sound	ㅤ
Phase 3	Crisp & clear sound	ㅤ
Phase 4	Muffled sound	ㅤ
Phase 5	Sound disappears	DBP

Auscultatory Gap

• Silent interval
• Korotkoff sounds temporarily disappear
• then reappear during cuff deflation.

• Significance:
• Not recognizing it can lead to 
1. DBP being overestimated 
2. SBP being underestimated

Causes of False BP Recordings

• Small size cuff used

• Obesity

• Thick & calcified vessel

Riva Rocci Cuff

• For accurate measurement:

ㅤ	Cuff bladder should cover
Length	• 80% of arm circumference
Width	• 40% of arm circumference

Direct Blood Pressure Measurement

 

Indicator	CVP	PCWP or Occlusion Pressure
ㅤ	M/c used indicator	Best indicator, more accurate.
Purpose	Right heart function	Left heart function
Equipment	CVC – Central Venous Catheter	PAC – Pulmonary Artery Catheter (Swan-Ganz)
Normal Values	CVP: 0 – 5 cm H₂O.	PCWP: 4 – 12 mmHg.
Fluid Mx	↓ CVP + ↓ BP → Give fluid ↑ CVP + ↓ BP (pump failure) → no fluid.	↑ PCWP → LV dysfunction.
Long-Term Use	For TPN, inotropes, cardiac drugs.	ㅤ
Complication	Common: Arrhythmias.	Common: Arrhythmias. Dreaded: Pulmonary capillary rupture.
Image	• CV Catheter: Triple lumen, 7 Fr (20 cm)	Swan-Ganz catheter assembly

Bainbridge Reflex:

• Fluid overload → Activates SA node → Tachycardia (↑HR)

• Mnemonic: Stand above bridge → water rising → HR↑

• Receptor: Right Atrium wall.

• Activation: Increased stretch of RA wall
• from increased venous return

• Action: 
1. Increase in heart rate (inhibits parasympathetic)
2. ↑ANP secretion
3. ↓ADH secretion (Bridge to brain)

• Example: Congestive Cardiac Failure
• (due to Right atrium enlargement)

Bezold-Jarisch Reflex (Basilidis / Coronary Chemoreceptor Reflex):

• Mnemonic: Chest pain (MI) vannitt thala karangi (hypotension and bradycardia) → Jar of water eduth kudich

• MI → Serotonin release → Bradycardia & Hypotension

• Receptor:
• Chemoreceptors in Left Ventricular wall & Interventricular septum.

• Activation:
• Serotonin, Veratridine, Capsaicin

• Clinical:
• Coronary reperfusion/angiography dye
• High spinal anaesthesia
• Vaso-vagal syncope

• Triad: 
1. Severe Bradycardia
2. Severe Hypotension
3. Coronary Vasodilation

• Other:
• Apnea f/b hyperventilation → Dangerous.

Cushing's reflex:

• Head injury → ↑ICT (Intracranial pressure) → Bradycardia (↓HR).

Marys Law

• Baroreceptor reflex

• ↑ BP → ↓ HR (BP x HR = constant).

• Mnemonic: Maary cheyyumbo → BP kuudum, Rating ↓↓ (HR)

Fluid Compartments & Measurement

• Total Blood Volume:
• Approx. 8% of total body weight.
• Plasma → 5%
• RBC volume → 3%

• Total Body Water (TBW):

Demographic	% Total Body Weight (Water)
Children (General)	75%
Adult: Male	60%
Adult: Female	50-55%

Measurement of Body water

• Principle: Volume of Distribution

• Using dilution principle

Formula: V = (Q - E) / C

• V: Volume of distribution (compartment volume).
• Q: Amount of substance injected.
• E: Excreted or metabolized portion.
• C: Concentration of substance in plasma after distribution.

Total Blood Volume = Plasma Volume
(1-Hematocrit)

• Example (ECF): 500mg dose, 3mg/dL conc., 10% excreted → 450mg in body
• Volume = 15 L.

Other Physiological Formulae

Tetanizing Frequency

Gain (Physiological Control Systems)

Serum Osmolality

Respiratory Formulas

Factors Affecting Diffusion (Fick's Law)

Directly Proportional	Inversely Proportional
Concentration gradient (High → low)	Thickness respiratory membrane
Surface area of respiratory membrane	Size of particle
Lipid solubility of gas	ㅤ

Renal Physiology

• Clearance:
• Definition: Volume of plasma completely cleared of a substance per unit time.
• Clearance (C) = (U x V)
  P

ㅤ	ㅤ	ㅤ
U	Urinary concentration of substance	mg/mL
V	Urine flow rate (volume/minute)	mL/min
P	Plasma concentration of substance	ㅤ
(U x V)	Amount of substance excreted in urine per minute	mg/min

• Glomerular Filtration Rate (GFR):

Clearance	ㅤ	ㅤ
Creatinine	GFR + Tubular secretion	Overestimates GFR.
Urea	GFR - Tubular reabsorption	Underestimates GFR.
Inulin	= GFR ≈ 100-120 mL/min	Gold standard test

• Filtration Fraction (FF)
• Formula: FF = GFR / RPF = 0.1 to 0.2
• Renal Plasma Flow (RPF): 700 ml/min 
• (Clearance of PAH)
• Renal Blood Flow (RBF): 1200 ml/min.
• Importance of FF
• After filtration, peritubular capillaries has:
• ↑ Protein concentration
• ↑ Oncotic pressure
• Favors reabsorption of water + solutes from tubules
• Helps maintain medullary osmotic gradient
• Fractional Excretion of Sodium (FeNa)
• (Clearance of Sodium / GFR) OR 
• (Urine Sodium x Plasma Creatinine) / (Plasma Sodium x Urine Creatinine)

• Reabsorption Rate:
• Filtered Load - Excreted Load.

• Interpreting Clearance vs. GFR

Substance secreted [Clearance > GFR]	Clearance	ㅤ
PAH	• 625 ml/min d/t high secretion ↳ lower concentrations = RPF ↳ higher concentration = Falsely Low	= Renal Plasma Flow (RPF)
Creatinine	• Secreted	• < PAH clearance • > Inulin clearance
Neither secreted Nor absorbed	ㅤ	ㅤ
Inulin	• Freely filterable ↳ Urinary Amount = Filtration Rate • 125 ml/min • Constant regardless of plasma concentration	= GFR
Substance reabsorbed [Clearance < GFR]	ㅤ	ㅤ
• Urea • Sodium and Potassium • Glucose / Amino Acids	Glucose / Amino Acids • Completely reabsorbed • Clearance: Zero (Non diabetic)	Diabetic: High plasma levels → transporter saturation → substance in urine → positive clearance

• Net Filtration Pressure (NFP)
• (Glomerular Hydrostatic Pressure + Bowman's Osmotic Pressure) -
• (Bowman's Hydrostatic Pressure + Plasma Colloid Osmotic Pressure)

Cardiovascular Physiology (CVS)

MET (Metabolic Equivalent)