Physiology & Pharmacology Calculations - Summative Revision Notes

Morning Rounds · Clinical Numericals · Summative Revision

Morning Rounds · Numerical Series · Clinical Physiology & Pharmacology

Clinical Numericals
Summative Revision Notes

Seven rounds · NEET-PG / INI-CET / UPSC CMS · Formulae, normal values, traps & the Editor's Ten

Physiology ABG Anion Gap Fluids & Electrolytes Renal Cardiovascular Drug Calculations

These notes consolidate all seven Clinical Numericals Morning Rounds. Written for rapid pre-exam revision, not first-time learning. Each section heading links to its quiz. Track units alongside every number — that is the single habit that prevents most errors in this series.

Round 01 · Clinical Numericals Series

Physiological Calculations ↗

Formula Reference

Cardiac Output (Fick) = VO2 / (CaO2 – CvO2) [units: mL/min / mL/L = L/min] GFR (Clearance) = (U x V) / P [U = urine conc, V = urine flow mL/min, P = plasma conc] Dead Space (Bohr) = VT x [(PaCO2 – PE'CO2) / PaCO2] Static Compliance = Tidal Volume / (Plateau Pressure – PEEP) Alveolar Ventilation = (VT – VD) x RR

Normal Values

Parameter	Normal range
Cardiac output	4-8 L/min
GFR (inulin)	~125 mL/min (male); ~110 mL/min (female)
VD/VT ratio	0.20-0.35; >0.6 = severe ventilatory failure
Static compliance	60-100 mL/cmH2O; <40 = stiff lungs (ARDS)

PEEP must be subtracted before dividing for compliance Inulin: filtered, not secreted, not reabsorbed Rapid shallow breathing: same minute ventilation, less alveolar ventilation

Open Round 01

Round 02 · Clinical Numericals Series

ABG Interpretation & Compensation Formulae ↗

Compensation Formulae — All Four Disorders

Disorder	Compensation formula	Expected change
Resp acidosis (acute)	HCO3 rises 1 mEq/L per 10 mmHg CO2 rise	CO2 up 20 → HCO3 = 26
Resp acidosis (chronic)	HCO3 rises 3.5 mEq/L per 10 mmHg CO2 rise	CO2 up 20 → HCO3 = 31
Resp alkalosis (acute)	HCO3 falls 2 mEq/L per 10 mmHg CO2 fall	CO2 down 12 → HCO3 = 21.6
Resp alkalosis (chronic)	HCO3 falls 5 mEq/L per 10 mmHg CO2 fall	CO2 down 12 → HCO3 = 18
Met acidosis	Winter's: PaCO2 = (HCO3 x 1.5) + 8 ±2	HCO3 = 9 → PaCO2 = 21.5
Met alkalosis	PaCO2 rises 0.7 mmHg per 1 mEq/L HCO3 rise	HCO3 up 14 → PaCO2 = 49.8

Winter's formula: multiply HCO3 by 1.5 THEN add 8 — never skip the +8 Met alkalosis: lung HYPOVENTILATES to retain CO2 Near-normal pH never means single simple disorder — always calculate expected compensation

Open Round 02

Round 03 · Clinical Numericals Series

Anion Gap & Mixed Acid-Base Disorders ↗

Formulae

AG = Na – (Cl + HCO3) Normal: 8-12 mEq/L Corrected AG = Measured AG + 2.5 x (4 – albumin g/dL) Delta-delta = delta-AG / delta-HCO3 = (AG-12) / (24-HCO3) Urine AG = Urine (Na + K) – Urine Cl

Delta-Delta Interpretation

Delta-delta ratio	Interpretation
<1	Concurrent non-AG metabolic acidosis pulling HCO3 down further
1-2	Pure HAGMA — AG rise matches HCO3 fall 1:1
>2	Concurrent metabolic alkalosis propping HCO3 up

Urine AG negative: GI cause (diarrhoea) — high NH4+ excretion Urine AG positive: RTA — impaired NH4+ excretion Hypoalbuminaemia masks HAGMA — always correct AG in ICU patients MUDPILES: Methanol, Uraemia, DKA, Propylene glycol, Isoniazid/Iron, Lactic acidosis, Ethylene glycol, Salicylates

Open Round 03

Round 04 · Clinical Numericals Series

Fluids & Electrolytes ↗

Formulae

Serum Osmolality = 2xNa + Glucose/18 + BUN/2.8 Normal: 275-295 mOsm/kg Osmol Gap = Measured Osm – Calculated Osm Normal: <10 mOsm/kg Corrected Na (hyperglycaemia) = Measured Na + 1.6 x [(Glucose-100)/100] Free Water Deficit = TBW x [(Na measured/140) – 1] TBW = 0.6 x wt (male), 0.5 x wt (female)

Key Clinical Rules

Elevated osmol gap (>10): toxic alcohols — methanol, ethylene glycol, ethanol, isopropanol. May precede AG elevation. Hypernatraemia correction: no faster than 0.5 mEq/L/hour or 10-12 mEq/L/day. Rapid correction causes cerebral oedema. Hyponatraemia correction: no faster than 8-10 mEq/L/day (risk of osmotic demyelination).

Serum K in DKA: normal or high despite total body depletion K falls after treatment: acidosis correction + insulin + osmotic diuresis Translocational hyponatraemia: water moves out, not sodium — corrects with glucose

Open Round 04

Round 05 · Clinical Numericals Series

Renal Calculations ↗

Formulae

CrCl (Cockcroft-Gault) = [(140-age) x weight] / (72 x Cr) x 0.85 (female) FENa = [(UNa/SNa) / (UCr/SCr)] x 100 Filtration Fraction = GFR / RPF Normal: 15-20% 24-hr protein estimate = Spot PCR (g/g) x 1 g/day creatinine

AKI Classification by Urine Indices

Index	Pre-renal	Intrinsic (ATN)
FENa	<1%	>2%
Urine Na	<20 mEq/L	>40 mEq/L
Urine Osm	>500 mOsm/kg	250-350 (isosthenuric)
U:P Cr ratio	>40	<20

FENa exceptions: low FENa (<1%) despite intrinsic AKI in contrast nephropathy, myoglobinuria, haemoglobinuria, hepatorenal syndrome, early obstruction. Nephrotic syndrome requires all four: proteinuria >3.5 g/day + hypoalbuminaemia + oedema + hyperlipidaemia. Proteinuria alone = nephrotic-range, not nephrotic syndrome.

FF rises in renal artery stenosis: efferent constriction preserves GFR as RPF falls ACEi in bilateral RAS: dilates efferent arteriole, abolishes compensation, GFR crashes

Open Round 05

Round 06 · Clinical Numericals Series

Cardiovascular Calculations ↗

Formulae

MAP = DBP + (1/3 x Pulse Pressure) = (SBP + 2xDBP) / 3 Target in sepsis: >=65 mmHg SVR = [(MAP – CVP) / CO] x 80 Normal: 800-1200 dynes/sec/cm5 Stroke Volume = EDV – ESV Ejection Fraction = SV/EDV x 100 Normal EF: 55-70% Cardiac Index = CO / BSA Normal: 2.5-4.0 L/min/m2; cardiogenic shock: <2.2

Shock Haemodynamic Patterns

Shock type	CO/CI	SVR	Example
Distributive	High	Low	Sepsis, anaphylaxis, neurogenic
Cardiogenic	Low	High	MI, acute HF
Hypovolaemic	Low	High	Haemorrhage, dehydration
Obstructive	Low	High	Massive PE, tamponade

Widened PP: AR, thyrotoxicosis, anaemia, AV fistula — raised SV or reduced diastolic runoff Narrow PP: tamponade, severe AS, cardiogenic shock SVR x80 converts Wood units to dynes/sec/cm5 — never omit this factor

Open Round 06

Round 07 · Clinical Numericals Series

Clinical Drug Calculations ↗

Formulae

Drip rate (drops/min) = [Volume (mL) x Drop factor] / Time (minutes) Volume per dose = (Dose required / Stock concentration) x Stock volume

The Five-Step Infusion Method — Apply to Every Weight-Based Infusion

Step	Action	Example (dopamine 5 mcg/kg/min, 70 kg, 200 mg/250 mL)
1	Dose needed	5 x 70 = 350 mcg/min
2	Convert units	350 mcg/min / 1000 = 0.35 mg/min
3	Solution conc	200 mg / 250 mL = 0.8 mg/mL
4	Volume rate	0.35 / 0.8 = 0.4375 mL/min
5	Convert time	0.4375 x 60 = 26.25 mL/hr

Drop factor 20: standard adult set; drop factor 60: microdrip/paediatric Time in MINUTES for drip rate — convert hours first Insulin 0.1 units/kg/hr in 70 kg / 100 units/mL = 0.06 mL/hr — correct despite appearing small Aminophylline: halve or omit loading dose if patient already on theophylline — NTI drug

Open Round 07

Curated Selection · Clinical Numericals Series

Editor's Ten — Questions Worth Returning To

Ten questions from across the series, selected because either the question itself or its debrief explanation is foundational enough that owning it changes how you approach an entire topic. At least one from each round. Exam relevance is the primary criterion.

R1 Q1

Fick Principle — Cardiac Output

The foundational formula of haemodynamics. The units trap (mL/min divided by mL/L gives L/min) is the same unit-cancellation logic that runs through every calculation in Rounds 06 and 07. Miss this and every downstream formula is on shakier ground.

R1 Q5

Alveolar Ventilation — Rapid Shallow Breathing Trap

The embedded calculation showing that increasing RR from 16 to 32 while halving tidal volume maintains minute ventilation but reduces alveolar ventilation from 5600 to 3200 mL/min is the physiological reason why rapid shallow breathing is dangerous. Directly examined in anaesthesia and critical care questions.

R2 Q2

Winter's Formula — The +8 Step

Expected PaCO2 = (HCO3 x 1.5) + 8 is the only simple numerical formula for any compensation calculation. Omitting the +8 produces a PaCO2 of 13.5 instead of 21.5 — making a well-compensated metabolic acidosis look like it has a superimposed respiratory acidosis. This error is common enough that it is tested by design.

R2 Q5

Triple Disorder — pH 7.42 Hiding Three Processes

The series' central clinical lesson: a near-normal pH is not a licence to stop the analysis. Sepsis plus vomiting produces respiratory alkalosis, high-AG metabolic acidosis, and metabolic alkalosis simultaneously, each nearly cancelling the others. Without calculating expected compensation and checking the delta-delta ratio, all three are invisible.

R3 Q2

Albumin Correction — Masked HAGMA in ICU Patients

A measured AG of 16 in a patient with albumin of 1.5 g/dL corrects to 22.5 — a true elevated AG process hidden entirely. In critically ill, malnourished, or hypoalbuminaemic patients, the uncorrected AG routinely underestimates severity. This is not a theoretical trap; it is a daily ward error.

R4 Q5

Potassium in DKA — Normal Serum K Hiding Total Body Depletion

Serum K of 5.5 mEq/L on DKA admission masks profound total body depletion. Three mechanisms drive the fall after treatment begins: acidosis correction, insulin, and osmotic diuresis. Knowing this prevents the catastrophic error of not replacing potassium early because the serum level looks adequate.

R5 Q2

FENa — Exceptions Where Low FENa Does Not Mean Pre-renal

FENa less than 1% is not a reliable pre-renal marker in contrast nephropathy, myoglobinuria, haemoglobinuria, hepatorenal syndrome, or early obstruction. Examiners test this directly. The clinical consequence of misclassifying intrinsic AKI as pre-renal and continuing aggressive fluid loading is renal and pulmonary harm.

R5 Q5

Nephrotic-Range Proteinuria vs Nephrotic Syndrome

Proteinuria above 3.5 g/day is nephrotic-range proteinuria, not nephrotic syndrome — which requires the full tetrad of proteinuria, hypoalbuminaemia, oedema, and hyperlipidaemia. This distinction is tested directly and its practical importance is high: treatment decisions, biopsy indications, and prognosis differ between the two labels.

R6 Q2

SVR — Shock Haemodynamic Patterns

SVR = [(MAP-CVP)/CO] x 80 with the four shock patterns placed side by side: distributive (high CO, low SVR) versus the three low-CO patterns (cardiogenic, hypovolaemic, obstructive each with high SVR). This is the most-examined haemodynamic framework in critical care and anaesthesia MCQs, and the x80 conversion is the most commonly omitted step.

R7 Q2

Dopamine Infusion — The Five-Step Method

The five-step method (dose needed, unit conversion, solution concentration, volume rate, time conversion) is not specific to dopamine — it applies to every weight-based infusion question regardless of drug. Candidates who internalise this sequence as a single procedure answer infusion questions reliably; those who attempt them ad hoc produce unit errors on approximately half.

Physiology & Pharmacology Calculations – Summative Revision Notes