Formulae

Abbreviated strong ion difference

Abbreviated SID (Na⁺ − Cl⁻)

CWF-0131

$$Abbreviated \; SID = [Na^+] - [Cl^-]$$

Acid–Base G1.iv

1 answer

Absorption (First pass metabolism)

CWF-0013

$$F_{B} \; = \; F_{A} \; \times \; F_{G} \; \times \; F_{H}$$

Concepts in Pharmacology B1.iv

1 answer

Acetylcholine synthesis

CWF-0150

$$Choline + Acetyl{-}CoA \xrightarrow{Choline\ acetyltransferase} Acetylcholine + CoA$$

Musculoskeletal System I1.iii

1 answer

Airway resistance — pressure-flow relationship

Airway resistance from ΔP / flow

CWF-0058

$$AWR \; = \; {{\Delta \, P} \over {Q}}$$

Respiratory System C3.vi

1 answer

Alveolar gas equation

CWF-0043

$$P_AO_2 \; = \; FiO_2 (P_{ATM} \; – \; SVP_{H2O}) \; – \; {{P_aCO_2} \over {RER}}$$

Respiratory System Obstetrics and Neonatal C8.iii C6.iv P1.i

4 answers · 2 aliases

Alveolar ventilation relationship

CWF-0160

$$P_aCO_2 \propto \frac{\dot V_{CO_2}}{\dot V_A}$$

Obstetrics and Neonatal P1.i

1 answer

Ammonium–ammonia equilibrium

CWF-0109

$$NH_4^+ \rightleftharpoons NH_3 + H^+$$

Renal System E1.v

1 answer

Arrhenius equation

Arrhenius equation

CWF-0022

$$k = Ae^{-Ea \over RT}.$$

Concepts in Pharmacology Thermoregulation B2.i M1.iv

2 answers · 1 alias

Arterial oxygen content

CWF-0154

$$C_aO_2 = (1.34 \times [Hb] \times S_aO_2) + 0.003(P_aO_2)$$

Haematological and Immunological System Renal System N1.vi E1.i

2 answers · 1 alias

Arterial oxygen content — clinical coefficient

CWF-0096

$$C_aO_2 = 1.34 \times [Hb] \times S_aO_2 + 0.003 \times P_aO_2$$

Respiratory System Cardiovascular System C7.i D3.viii

4 answers

Bicarbonate buffer equilibrium

CWF-0135

$$H^+ \;+\; HCO_3^- \;⇌\; H_2CO_3 \;⇌\; H_2O \;+\; CO_2$$

Acid–Base G1.iii

1 answer

Blood oxygen content — ideal Hüfner coefficient

CWF-0068

$$O_2 \; concentration \; : \; (1.39 \; \times \; Hb \; \times \; sats) \; + \; (0.003 \; \times \; PO_2)$$

Respiratory System C7.ii

1 answer

Bohr equation

Bohr equation using alveolar PCO₂

CWF-0038

$${{V_D} \over {V_T}} = { {PA_{CO_2} \; - \; P\bar{E}_{CO_2}} \over {PA_{CO_2}}}$$

Respiratory System C6.ii

1 answer

Boyle’s Law

CWF-0001

$$P\;\propto\;{1\over V}$$

General / Historical

1 answer

Capillary pressure — resistance relationship

Capillary pressure vs resistance ratio

CWF-0126

$$P_{cap} \; \propto \; {{Post-capil\;resist} \over {Pre-capil \; resist}}$$

Cellular Physiology Cardiovascular System Body Fluids and Electrolytes A.iv D4.v F1.ii

4 answers

Carbonic acid–bicarbonate reaction

CWF-0119

$$CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons H^+ + HCO_3^-$$

Renal System E1.v

1 answer

Cerebral blood flow — determinants

CWF-0149

$$Cerebral \; Blood \; Flow \; (CBF) \; = {{CPP} \over {CVR}} = \; {{Cerebral \; Perfusion \; Pressure} \over {Cerebrovascular \; Resistance}}$$

Nervous System H2.ii

2 answers

Cerebral blood flow — perfusion-pressure form

CWF-0148

$$CBF \; = {{CPP} \over {CVR}} = \; {{MAP - (greater \; of \; CVP \; or \; ICP)} \over {CVR}}$$

Nervous System Cardiovascular System H2.i D5.i

2 answers · 1 alias

Coronary Perfusion Pressure

CWF-0094

$$CPP \; = \; ADP \; - \; (larger \; of \; LVEDP \; or \; RAP)$$

Cardiovascular System D4.iv D3.v

2 answers · 2 aliases

Dalton’s Law (of partial pressures)

CWF-0002

$$P_{total}\;=\;P_{1}\;+\;P_{2}\;+\;P_{3}\;+\;.\;.\;.\;+P_{n}\;\equiv\;\sum_{i=1}^{n}\;P_{i}$$

General / Historical

1 answer

Dead-space fraction identity

Dead-space fraction from Vₐ and Vₜ

CWF-0040

$${{V_D} \over {V_T}} = { {V_T \; - \; V_A} \over {V_T}}$$

Respiratory System C6.ii

1 answer

Diffusion coefficient — solubility and molecular weight

Diffusion coefficient

CWF-0046

$$D=Diffusion\;constant\;\propto\;{{Solubility}\over{\sqrt{Molecular\;Weight}}}$$

Cellular Physiology Respiratory System Obstetrics and Neonatal A.iv C7.i C7.vi P2.v

4 answers

Dissolved oxygen content

CWF-0041

$$C_dO_2 \; = \; a_{O_2} \; \times \; P_{O_2}$$

Respiratory System C7.i

1 answer

Dynamic compliance

CWF-0049

$$C_d \; ∼ \; {{\Delta volume} \over {initial \; \Delta transmural \; pressure}}$$

Respiratory System C3.iii

2 answers

Effective strong ion difference

Effective SID (SIDe)

CWF-0134

$$SIDe = [HCO_3^-] + [Alb^-] + [Pi^-]$$

Acid–Base G1.iv

1 answer

Enghoff modification

Enghoff modification using arterial PCO₂

CWF-0039

$${{V_D} \over {V_T}} = { {Pa_{CO_2} \; - \; P\bar{E}_{CO_2}} \over {Pa_{CO_2}}}$$

Respiratory System C6.ii

1 answer

Fick diffusion flux

Fick diffusion flux

CWF-0047

$$J\;={{D\;A\;\Delta C}\over{T}}$$

Cellular Physiology Respiratory System Obstetrics and Neonatal A.iv C7.i C7.vi P2.v

4 answers

Fick diffusion relationship

CWF-0156

$$Diffusion\;constant \; = \; {{Solubility \; \times \; Δ conc } \over {\sqrt{Molecular\;Weight}}} \; \times {{surf \; area} \over {thickness}}$$

Obstetrics and Neonatal P2.i

1 answer

Fick’s Law of Diffusion

CWF-0003

$$Diffusion \propto \;Diffusion\;Coefficient\;\:{(Concentration\;gradient\;×\;Surface\;area) \over Thickness}$$

General / Historical

1 answer

Filtered Load

CWF-0112

$$Filtered \; Load \; = \; GFR \; \times \; plasma \; concentration \; of \; substance \; (Px)$$

Renal System E1.iv

1 answer

Flow-pressure-resistance relationship

Pressure–flow–resistance relation

CWF-0104

$$Flow \; = \; {Pressure \over Resistance}$$

Cardiovascular System D4.iii

1 answer

Fractional oxyhaemoglobin saturation

CWF-0061

$$FO_2Hb \; = \; {{oxy-Hb} \over {oxy-Hb \; + \; deoxy-Hb \; + \; carboxy-Hb \; + \; met-Hb}}$$

Respiratory System C9.i

2 answers

Gas diffusion across a membrane — Fick relationship

CWF-0045

$$Flow \; of \; gas \; ∝ \; {{A} \over {T}} \; . \; D \; (P_1- P_2)$$

Respiratory System C7.v

1 answer

GFR — filtration coefficient relationship

GFR = Kf × net filtration pressure

CWF-0110

$$GFR \; = \; K_f \; \times \; NFP$$

Renal System E1.iv

3 answers

Gibbs – Donnan Effect

CWF-0008

$$[Na^+]_A \;\times\; [Cl^−]_A \;=\; [Na^+]_B \;\times\; [Cl^−]_B$$

Cellular Physiology A.iv

1 answer

Goldman-Hodgkin-Katz Equation

CWF-0010

$$E(mV) \;=\; {{R.T} \over {F}} \; \ln \; {{P_K[K^+]_o \; + \; P_{Na}[Na^+]_o \; + \; P_{Cl}[Cl^-]_i } \over { P_K[K^+]_i \; + \; P_{Na}[Na^+]_i \; + \; P_{Cl}[Cl^-]_o }}$$

Cellular Physiology A.iv

1 answer

Graham’s Law

CWF-0004

$$Diffusion\;\propto\;{1 \over \sqrt{MW}}$$

General / Historical

1 answer

Haemoglobin buffer — bicarbonate reaction

Haemoglobin–bicarbonate buffer reaction

CWF-0137

$$H.Hb \;+\; KHCO_3 \;⇌\; K.Hb \;+\; H_2CO_3$$

Acid–Base G1.iii

2 answers

Haemoglobin buffer — non-volatile acid reaction

Haemoglobin buffer reaction

CWF-0139

$$HA \;+\; K.Hb \; ⇌ \; H.Hb \;+\; KCl$$

Acid–Base G1.iii

2 answers

Haemoglobin buffer — proton dissociation

Haemoglobin acid dissociation

CWF-0138

$$H.Hb \;⇌\; H^+ \;+\; Hb^-$$

Acid–Base G1.iii

2 answers

Helium dilution (FRC)

CWF-0060

$$FRC = V_1 \left( \frac{F_{He,1}}{F_{He,2}} - 1 \right)$$

Respiratory System C4.ii

1 answer

Henry’s Law

CWF-0005

$$p\;=\;k_{H}\;c$$

General / Historical

1 answer

Hepatic clearance — extraction ratio

Flow × extraction ratio

CWF-0017

$$Cl_{Hep} \; = \; Q_{H} \; \times \; ER_{Hep}$$

Concepts in Pharmacology Gastrointestinal System B1.iv J2.ii

2 answers · 1 alias

Hepatic clearance — well-stirred model

Well-stirred model

CWF-0018

$$Cl_{Hep} \; = \; Q_{H} \; \times \; {{FU \; \times \; Cl_{Int}} \over {Q_{H} \; + \; FU \; \times \; Cl_{Int}}}$$

Concepts in Pharmacology B1.iv

1 answer

Hepatic Extraction Ratio

CWF-0016

$$ER_{Hep} \; = \; {{FU \; \times \; Cl_{Int}} \over {Q_{H} \; + \; FU \; \times \; Cl_{Int}}}$$

Concepts in Pharmacology B1.iv

1 answer

Kelvin–Celsius conversion

CWF-0153

$$K \; = \; °C \; + \; 273.15$$

Thermoregulation M1.iii

1 answer

Laplace relationship (alveolar model)

CWF-0055

$$P = \frac{2T}{r}$$

Respiratory System C3.ix

1 answer

Left ventricular wall stress

Preload relation

CWF-0085

$$Preload \; = \; {{{(LVEDP \; - \; ITP)} \times LVEDR} \over {2h}}$$

Cardiovascular System D3.ii

1 answer

Measurement of Volume of Distribution

Apparent Vd = dose / C₀

CWF-0020

$$Vd = {{Dose} \over {C^0_p}}$$

Concepts in Pharmacology B1.iii

1 answer

Michaelis–Menten elimination

CWF-0024

$${Rate\;of\;elimination}={{\delta P} \over {\delta t}}={{V_{max} \times S} \over {K_m + S}}$$

Concepts in Pharmacology B1.iv

1 answer

Modified Laplace equation — wall stress

CWF-0095

$$T \; = \; {{P \; R} \over {2 \; H}}$$

Cardiovascular System D3.ii

3 answers

Nernst equation

CWF-0124

$$E(mV) \;=\; {{R.T} \over {z.F}} \; \ln {{[ion]_{outside}} \over {[ion]_{inside}}}$$

Cellular Physiology Body Fluids and Electrolytes A.iv F1.v

2 answers

Net filtration pressure

Net filtration pressure

CWF-0111

$$NFP ={ [(P_{GC} - P_T) - \sigma \; (\pi_{GC} - \pi_T)]}$$

Renal System E1.iv

3 answers

Oxygen consumption — Fick principle

CWF-0099

$$VO_2 \; = \; CO \; \times (C_aO_2 \; - \; C_vO_2)$$

Respiratory System Cardiovascular System C9.i D3.viii

2 answers

Parallel vascular resistance

Parallel vascular resistances

CWF-0106

$${1 \over SVR} = {1 \over R_{1}} \; + \; {1 \over R_{2}}$$

Cardiovascular System D4.iii

1 answer

Passive diffusion determinants

CWF-0012

$$Diffusion\;\propto{{1\over\sqrt{Molecular Weight}} \times {Surface\;Area \over Thickness} \times \Delta concentration}$$

Concepts in Pharmacology Obstetrics and Neonatal B1.ii B1.iv P2.v

3 answers · 1 alias

Poiseuille flow

Hagen–Poiseuille flow equation

CWF-0006

$$\dot{Q} = {\Delta P \over R} = {(π\;r^4.\;\Delta P) \over{8\;η\;L}}$$

Renal System E2.i E1.i

3 answers · 3 aliases

Poiseuille resistance

Poiseuille resistance

CWF-0056

$$R\;=\;{8\;η\;l \over {π\;r^4}}$$

Respiratory System Cardiovascular System C3.vi D4.iii

3 answers · 1 alias

Pulse oximetry ratio-of-ratios

CWF-0069

$$R \; = \; { {Pulsatile_{660} \; / \; Non-Pulsatile_{660} } \over { Pulsatile_{940} \; / \; Non-Pulsatile_{940} } }$$

Respiratory System C9.i

1 answer

Regulation of Renal Blood Flow

CWF-0120

$$Renal \; Blood \; Flow \; = \; {{Renal \; arterial \; pressure \; - \; Renal \; venous \; pressure} \over {Renal \; vascular \; resistance}}$$

Renal System E1.i E1.iii

4 answers

Relative Humidity

CWF-0070

$$Relative \, Humidity \, = \, {{absolute \, humidity \, (actual) \, in \, the \, gas} \over {absolute \, humidity \, (saturated) \, at \, that \, temperature}}$$

Respiratory System C8.v

1 answer

Renal drug clearance

CWF-0025

$${Renal\;Drug\;Clearance} = { {Urine\; [Drug] \times V} \over {Plasma\; [Drug]} }$$

Concepts in Pharmacology B1.iv

1 answer

Renal oxygen delivery

Renal oxygen delivery

CWF-0114

$$Oxygen \; delivery \; = \; Renal \; Blood \; flow \; \times \; CaO_2$$

Renal System E1.i

1 answer

Renal sodium excretion

CWF-0123

$$Na \; excretion \; = \; Na^+ \; filtered \; - \; Na^+ reabsorbed$$

Body Fluids and Electrolytes F1.v

1 answer

Respiratory compliance

Compliance = ΔV / ΔP

CWF-0071

$$Compliance \; = \; {{\Delta \, V} \over {\Delta \, P}}$$

Respiratory System C3.iii

2 answers

Respiratory-system compliance

Combined respiratory compliance

CWF-0074

$${{1} \over {Respiratory \, Compliance}} \; = \; {{1} \over {Lung\, Compliance}} + {{1} \over {Chest \, Wall\, Compliance}}$$

Respiratory System C3.iii

2 answers

Reynolds number

CWF-0028

$$Re\;={\;2\;r\;ρ\;v\;\over η}={diameter\;\times\;density\;\times\;velocity\;\over viscosity}$$

Respiratory System C3.vi

2 answers

Right ventricular output

Right ventricular output

CWF-0086

$$Right \, Ventricular \, Output \, = \, CO$$

Cardiovascular System D3.ii

1 answer

Shunt equation

CWF-0075

$$Q_t (C_aO_2) \; = \; Q_{ns} (C_cO_2) \; + \; Q_s (C_{mv}O_2)$$

Respiratory System C6.iv

1 answer

Shunt mixing equation

CWF-0027

$$Q_t \times C_aO_2 \;\; = \;\; (Q_{t-s} \times C_cO_2) \;\; + \;\; (Q_s \times C_{MV}O_2)$$

Respiratory System C7.i

1 answer

Simplified equation for half life

CWF-0026

$$T_{1/2} = {{\ln(2)\; \times\; Vd} \over {Cl}}$$

Concepts in Pharmacology B1.iv

1 answer

Specific compliance — lung-volume normalised

CWF-0076

$$C_S \; = \; {{Static \; Compliance} \over {Lung \; Volume}}$$

Respiratory System C3.iii

2 answers

Specific lung compliance — FRC normalised

CWF-0057

$$C_S \; = \; {{C_{Tot}} \over {FRC}}$$

Respiratory System C3.iii

2 answers

Starling fluid flux

Starling fluid flux

CWF-0125

$$J_v={\kappa \; ([P_{capil} - P_{interstit}] - \sigma \; [\pi_{plasma} - \pi_{interstit}])}$$

Cellular Physiology Respiratory System Cardiovascular System Body Fluids and Electrolytes A.iv C5.i D4.v F1.ii

5 answers

Steady-state volume of distribution

Sum of compartment volumes

CWF-0019

$$V_{ss} = V_1 + V_2 + \cdots + V_n$$

Concepts in Pharmacology B1.iii

1 answer

Strong ion gap (SIG)

CWF-0147

$$SIG \; = \; SIDa - SIDe$$

Acid–Base G1.iv

1 answer

Systemic oxygen delivery

Systemic oxygen delivery

CWF-0098

$$DO_2 \; = \; CO \; \times C_aO_2$$

Respiratory System Cardiovascular System Cellular Physiology Haematological and Immunological System C9.i D3.viii A.i C7.i N1.vi

6 answers · 3 aliases

Systemic vascular resistance

SVR from MAP, CVP and CO

CWF-0105

$$SVR \; = \; {{MAP \; - \; CVP} \over CO}$$

Cardiovascular System D4.iii

1 answer

TBW distribution between ISF and intravascular compartments

CWF-0127

$$Net \; H_{2}O \; Flux = K_{f} \times { [(P_{CAP} - P_{ISF}) - \sigma \; (\pi_{CAP} - \pi_{ISF})]}$$

Body Fluids and Electrolytes F1.ii

1 answer

Thoracic gas volume — body plethysmography

Plethysmographic lung volume

CWF-0059

$$TGV = (P_B - P_{H_2O}) \frac{\Delta V}{\Delta P}$$

Respiratory System C3.vi

1 answer

Total work and efficiency of breathing

CWF-0077

$$\% \; Efficiency \; = \; {{Useful \, Work} \over {Total \, energy \, expended \, (O_{2} \, cost)}} \; \times \; {100 \, \%}$$

Respiratory System C3.x

1 answer

Transition-state rate constant (Eyring)

Free-energy form

CWF-0023

$$k = \frac{k_B T}{h} e^{-\Delta G^\ddagger/(RT)}$$

Concepts in Pharmacology B2.i

1 answer

Transpulmonary pressure

Transpulmonary pressure

CWF-0072

$$\Delta \, P \; = \; Alveolar \; - \; Intrapleural \; pressure$$

Respiratory System C3.iii

2 answers

Turbulent flow — pressure relationship

Turbulent flow relationship

CWF-0007

$$\dot{Q} \propto \sqrt{\Delta P \over {ρ \times l} }$$

General / Historical

1 answer

Turbulent flow — pressure-drop relationship

Turbulent resistance relationship

CWF-0078

$$R ∝ {ρ\;l \over {π\;r^5}}$$

Respiratory System C3.vi

2 answers

Urinary ammonium trapping

CWF-0128

$$NH_3 \;+\; H^+ \; ⇌ \; NH_4^+$$

Acid–Base G1.iii

1 answer

Urinary phosphate buffer

CWF-0143

$$HPO_4^{2-} + H^+ \rightleftharpoons H_2PO_4^-$$

Acid–Base G1.iii

1 answer

Uteroplacental blood flow

CWF-0159

$$UBF \; = \; {{(UAP \; - \; UVP)} \over {UVR} }$$

Obstetrics and Neonatal P2.i

1 answer

Van ’t Hoff osmotic pressure

CWF-0009

$$Osmotic \; pressure \; (\pi) \; = \; {{nRT \times c} \over {M}}$$

Cellular Physiology A.iv

1 answer

Vascular distensibility

CWF-0050

$$Vascular \; distensibility \; = {{increase \; in \; volume} \over {Increase \; in \; pressure\; \times \; original \; volume}}$$

Respiratory System C5.i

1 answer

Venous return — pressure-gradient relationship

Venous return pressure gradient

CWF-0088

$$VR \; = \; {{MSFP \; - \; RAP} \over {Venous \; Resistance}}$$

Cardiovascular System D3.ii

1 answer

Venous return — steady-state identity

Venous return = cardiac output

CWF-0087

$$VR \; = \; CO$$

Cardiovascular System D3.ii

1 answer

Volume of distribution

CWF-0014

$$Vd = {{Amount\;of\;drug\;in\;body} \over {Plasma\; concentration\;}}$$

Concepts in Pharmacology B1.iii

1 answer · 1 alias

West Zone 1

CWF-0079

$$P_A \; > \; P_a \; > \; P_v$$

Respiratory System C5.i

1 answer

West Zone 2

CWF-0080

$$P_a \; > \; P_A \; > \; P_v$$

Respiratory System C5.i

1 answer

West Zone 3

CWF-0081

$$P_a \; > \; P_v \; > \; P_A$$

Respiratory System C5.i

1 answer

West Zone 4

CWF-0082

$$P_a \; > \; P_i \; > \; P_v \; > \; P_A$$

Respiratory System C5.i

1 answer