Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

Which structure produces most of the cerebrospinal fluid?

  1. APineal gland
  2. BPia mater
  3. CChoroid plexus
  4. DArachnoid granulations
2.Human anatomyHard

Which muscle "unlocks" the fully extended knee by rotating the femur laterally on the tibia at the start of flexion?

  1. ABiceps femoris
  2. BPopliteus
  3. CSartorius
  4. DGastrocnemius
3.Human physiologyMedium

Which is a classic example of positive feedback in the body?

  1. ASweating when body temperature rises
  2. BOxytocin release during labour
  3. CInsulin release after a meal
  4. DADH release when plasma osmolality rises
4.Human physiologyHard

After a head injury, a patient passes large volumes of very dilute urine and plasma sodium rises. What is the most likely cause?

  1. AExcess aldosterone
  2. BExcess ADH release (SIADH)
  3. CLack of ADH release (cranial diabetes insipidus)
  4. DUncontrolled diabetes mellitus
5.MicrobiologyMedium

Cholera causes profuse "rice-water" diarrhoea. What is the most important treatment?

  1. AStopping all oral fluid intake so that the bowel can rest and recover
  2. BAntifungal drugs
  3. CAntiviral drugs
  4. DReplacing fluid and salts by oral or intravenous rehydration
6.MicrobiologyHard

A patient taking high-dose immunosuppressive drugs after a transplant is due for vaccinations. Which vaccine type is generally avoided?

  1. AToxoid vaccines
  2. BSubunit vaccines
  3. CInactivated whole-virus vaccines
  4. DLive attenuated vaccines
7.PharmacologyMedium

How should a topical corticosteroid cream usually be applied?

  1. AOn broken, infected skin to speed healing
  2. BAs a thick layer over the whole body
  3. CUnder a tight plastic dressing every night without advice
  4. DAs a thin layer to the affected area only, as directed
8.PharmacologyHard

A woman has received a high-dose oxytocin infusion with large volumes of hypotonic fluid for many hours. She now has a headache, confusion and a low serum sodium. What is the most likely cause?

  1. AWater intoxication from the antidiuretic effect of oxytocin
  2. BNormal tiredness after a long labour
  3. CAn allergic reaction to oxytocin causing brain swelling
  4. DExcessive salt in the infusion fluid
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 16 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 16 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 33 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 33 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus tachycardiajunctional rhythmfirst-degree AV blocksinus bradycardia

Interpret this lead II rhythm strip. Which rhythm is it? Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1sinus tachycardia
  2. 2junctional rhythm
  3. 3first-degree AV block
  4. 4sinus bradycardia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV

This lead II strip shows an AV block, so the atria and the ventricles beat at different rates. Measure the P–P interval and find the atrial rate in beats per minute (1500 method, whole number).

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
atrial rate = bpm
13.Evidence-based practice statisticsMedium
Se90%Sp96%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 90% and a specificity of 96%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 90%Sp = 96%
LR− =
14.Evidence-based practice statisticsHard
p (%)NPV (%)3%NPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 99% and a specificity of 99%. It is used in a population where the prevalence is 3%. Find the negative predictive value NPV as a percentage. Round to one decimal place.

Se = 99%Sp = 99%p = 3%
NPV = %

3Solutions

1.Human anatomy

Answer: C · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

C · Choroid plexus
2.Human anatomy

Answer: B · Popliteus

Why this is the answer

At full extension the knee locks by medial rotation of the femur. Popliteus laterally rotates the femur on the fixed tibia to unlock it so flexion can begin.

Answer

B · Popliteus
3.Human physiology

Answer: B · Oxytocin release during labour

Why this is the answer

Stretch of the cervix releases oxytocin, which strengthens contractions and causes more stretch. The loop ends with delivery. The other examples are negative feedback.

Answer

B · Oxytocin release during labour
4.Human physiology

Answer: C · Lack of ADH release (cranial diabetes insipidus)

Why this is the answer

Without ADH the collecting ducts stay impermeable to water, so dilute urine is produced and the patient loses free water, raising plasma sodium.

Answer

C · Lack of ADH release (cranial diabetes insipidus)
5.Microbiology

Answer: D · Replacing fluid and salts by oral or intravenous rehydration

Why this is the answer

Cholera toxin makes gut cells secrete large amounts of water and salt. Rapid rehydration saves most lives; antibiotics only shorten the illness.

Answer

D · Replacing fluid and salts by oral or intravenous rehydration
6.Microbiology

Answer: D · Live attenuated vaccines

Why this is the answer

Live vaccines contain weakened organisms that can cause disease when the immune system is severely suppressed. Inactivated, toxoid and subunit vaccines are safe, although the response may be weaker.

Answer

D · Live attenuated vaccines
7.Pharmacology

Answer: D · As a thin layer to the affected area only, as directed

Why this is the answer

Thin application to affected skin limits systemic absorption and skin atrophy. Occlusive dressings increase absorption and are used only when prescribed.

Answer

D · As a thin layer to the affected area only, as directed
8.Pharmacology

Answer: A · Water intoxication from the antidiuretic effect of oxytocin

Why this is the answer

Oxytocin has antidiuretic activity at high doses. With large volumes of fluid this can cause water retention and dilutional hyponatraemia, so fluid balance and sodium are monitored.

Answer

A · Water intoxication from the antidiuretic effect of oxytocin
9.Arterial blood gas interpretation

Answer: PaCO₂ = 32 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Winter’s formula

PaCO₂ = 1.5·16 + 8 = 32 mmHg
range: 30–34 mmHg

Answer

PaCO₂ = 32 mmHg
10.Arterial blood gas interpretation

Answer: PaCO₂ = 44.1 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected PaCO₂

0.7·33 + 21 = 44.1 mmHg

Answer

PaCO₂ = 44.1 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: first-degree AV block

Rhythm criteria (lead II): sinus rhythm has an upright P wave before every QRS, a constant PR of 0.12–0.20 s and a narrow QRS: normal sinus rhythm at 60–100/min, sinus bradycardia below 60, sinus tachycardia above 100. Atrial fibrillation: no P waves, a fibrillatory baseline and an irregularly irregular R–R. Atrial flutter: sawtooth flutter waves at about 250–350/min with a fixed conduction ratio such as 2:1 or 4:1. First-degree AV block: sinus rhythm with a constant PR above 0.20 s. Junctional rhythm: narrow QRS at 40–60/min with absent or inverted P waves (PR below 0.12 s, or P after the QRS). A PVC is an early, wide (0.12 s or more), bizarre QRS without a P wave, with the T wave in the opposite direction and usually a full compensatory pause; in bigeminy every second beat is a PVC.

Five steps

1. Rate: R–R = 25 small boxes, 1500 ÷ 25 ≈ 60 per minute.
2. Rhythm: regular, every R–R is 1.00 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.32 s, constant, longer than 0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

first-degree AV block

Answer

first-degree AV block
12.ECG rhythm strip interpretation

Answer: atrial rate = 83 bpm

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Atrial rate

P–P = 18 small boxes = 0.72 s → 1500 ÷ 18 = 83.33 ≈ 83 per minute

Ventricular rate

R–R = 45 small boxes = 1.80 s → 1500 ÷ 45 = 33.33 ≈ 33 per minute

Answer

atrial rate = 83 bpm

Answer

atrial rate = 83 bpm

Third-degree block with a wide-complex ventricular escape (usually 20–40 per minute).

13.Evidence-based practice statistics

Answer: LR− = 0.1

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Negative likelihood ratio

LR− = (1 − 0.9)/0.96 = 0.1042 ≈ 0.1

Answer

LR− = 0.1
14.Evidence-based practice statistics

Answer: NPV = 100 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

True and false negatives (per person)

Sp·(1 − p) = 0.99·0.97 = 0.9603
(1 − Se)·p = 0.01·0.03 = 0.0003

Negative predictive value

NPV = 0.9603/(0.9603 + 0.0003) = 0.9997 ≈ 100%

Answer

NPV = 100%

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