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 nerve is compressed in carpal tunnel syndrome?

  1. AMusculocutaneous nerve
  2. BMedian nerve
  3. CUlnar nerve
  4. DRadial nerve
2.Human anatomyHard

An ECG shows an infarct in leads II, III and aVF (inferior wall). Which coronary artery is most commonly blocked?

  1. ALeft main coronary artery
  2. BLeft anterior descending artery
  3. CRight coronary artery
  4. DFirst diagonal branch
3.Human physiologyMedium

In skeletal muscle, where does most of the calcium for contraction come from?

  1. AThe sarcoplasmic reticulum
  2. BThe mitochondria
  3. CThe nucleus
  4. DThe extracellular fluid
4.Human physiologyHard

Why does left ventricular failure cause pulmonary oedema?

  1. ARaised left atrial pressure increases pulmonary capillary hydrostatic pressure
  2. BPlasma oncotic pressure in the lungs rises sharply
  3. CThe bronchial arteries become blocked
  4. DThe right ventricle pumps less blood into the lungs
5.MicrobiologyMedium

Why are Gram-negative bacteria often harder to treat with antibiotics?

  1. ATheir outer membrane blocks many drugs
  2. BThey have no ribosomes
  3. CThey have a thicker peptidoglycan layer
  4. DThey divide much more slowly
6.MicrobiologyHard

A positive blood culture shows Gram-positive cocci in clusters. Which organism is most likely?

  1. ANeisseria
  2. BEnterococcus in short chains
  3. CStaphylococcus
  4. DStreptococcus
7.PharmacologyMedium

A patient with insulin-treated diabetes is found unconscious with very low blood glucose. There is no IV access. Which drug can a trained helper give?

  1. AGlucagon by injection or nasal spray
  2. BRapid-acting insulin under the skin
  3. CIntramuscular adrenaline
  4. DOral glucose gel poured into the mouth
8.PharmacologyHard

A patient with Parkinson's disease has nausea. Why should metoclopramide be avoided?

  1. AIt increases dopamine levels in the brain too much and causes psychosis
  2. BIt inhibits the absorption of all oral drugs
  3. CIt causes severe diarrhoea in Parkinson's disease
  4. DIt blocks dopamine receptors in the brain and can worsen the parkinsonism
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 63 mmHg (8.4 kPa). Use the rule that in chronic respiratory acidosis HCO₃⁻ rises by 3.5 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 63 mmHg (8.4 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard
pH7.357.457.19PaCO₂mmHg354546HCO₃⁻mmol/L222617appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.19, PaCO₂ 46 mmHg (6.1 kPa), HCO₃⁻ 17 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.19PaCO₂ 46 mmHg (6.1 kPa)HCO₃⁻ 17 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

This lead II strip shows sinus rhythm with one pause. Measure the pause, the R–R interval across it, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
pause = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVventricular paced rhythmdual-chamber (AV) paced rhythmsinus rhythm with wide QRSidioventricular rhythm

This patient has a pacemaker. Interpret the lead II strip. 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. 1ventricular paced rhythm
  2. 2dual-chamber (AV) paced rhythm
  3. 3sinus rhythm with wide QRS
  4. 4idioventricular rhythm
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment6496160abcontrol64256320cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 160 patients received a new treatment and 320 received the control treatment. The table shows how many in each group had a side effect. Find the relative risk RR of the event with treatment. Round to two decimal places.

treatment: 64/160control: 64/320
RR =
14.Evidence-based practice statisticsHard
pre-test40%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 40% for a disease. A test with sensitivity 66% and specificity 69% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 40%Se = 66%Sp = 69%negative
p′ = %

3Solutions

1.Human anatomy

Answer: B · Median nerve

Why this is the answer

The median nerve passes through the carpal tunnel under the flexor retinaculum; compression causes tingling in the thumb, index and middle fingers.

Answer

B · Median nerve
2.Human anatomy

Answer: C · Right coronary artery

Why this is the answer

The inferior wall is usually supplied by the right coronary artery through the posterior descending artery (right-dominant circulation), so inferior infarcts are mostly RCA occlusions.

Answer

C · Right coronary artery
3.Human physiology

Answer: A · The sarcoplasmic reticulum

Why this is the answer

Depolarisation of the T-tubules opens ryanodine receptors in the sarcoplasmic reticulum, releasing stored calcium into the cytoplasm.

Answer

A · The sarcoplasmic reticulum
4.Human physiology

Answer: A · Raised left atrial pressure increases pulmonary capillary hydrostatic pressure

Why this is the answer

A failing left ventricle backs up pressure into the left atrium and pulmonary veins. High capillary hydrostatic pressure pushes fluid into the lung interstitium and alveoli.

Answer

A · Raised left atrial pressure increases pulmonary capillary hydrostatic pressure
5.Microbiology

Answer: A · Their outer membrane blocks many drugs

Why this is the answer

The outer membrane of Gram-negative bacteria, with lipopolysaccharide and porins, keeps many antibiotics out and adds efflux and enzyme defences.

Answer

A · Their outer membrane blocks many drugs
6.Microbiology

Answer: C · Staphylococcus

Why this is the answer

Staphylococci grow in grape-like clusters; streptococci and enterococci in chains or pairs. Neisseria are Gram-negative diplococci.

Answer

C · Staphylococcus
7.Pharmacology

Answer: A · Glucagon by injection or nasal spray

Why this is the answer

Glucagon breaks down liver glycogen and raises blood glucose. Nothing is given by mouth to an unconscious patient because of the risk of choking and aspiration.

Answer

A · Glucagon by injection or nasal spray
8.Pharmacology

Answer: D · It blocks dopamine receptors in the brain and can worsen the parkinsonism

Why this is the answer

Metoclopramide crosses the blood–brain barrier and antagonises D2 receptors. In Parkinson's disease this worsens rigidity and bradykinesia, so antiemetics that do not block central dopamine receptors are preferred.

Answer

D · It blocks dopamine receptors in the brain and can worsen the parkinsonism
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 32.05 mmol/L

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.

Change in PaCO₂

|63 − 40| = 23 mmHg → 2.3 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 3.5·2.3 = 32.05 mmol/L

Answer

HCO₃⁻ = 32.05 mmol/L
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·17 + 8 = 33.5 → 31.5–35.5 mmHg

Compare

measured: 46 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: pause = 2.28 s

Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

Measure

57 small boxes from R to R across the pause

Convert

pause = 57 × 0.04 s = 2.28 s

Compare with P–P

2.28 ÷ 0.96 ≈ 2.4 P–P cycles, not a whole number

Answer

pause = 2.28 s

No P wave appears in the pause, and the pause is not a whole number of P–P cycles: sinus arrest. A pause of exactly two or three cycles would point to sinus exit block.

12.ECG rhythm strip interpretation

Answer: ventricular paced rhythm

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: R–R = 22 small boxes, 1500 ÷ 22 ≈ 68 per minute.
2. Rhythm: regular, every R–R is 0.88 s.
3. P waves: none visible; a sharp pacing spike comes just before every QRS.
4. PR interval: not measurable.
5. QRS: 0.14 s, wide, and every spike is followed by a QRS (capture).

Interpretation

ventricular paced rhythm

Answer

ventricular paced rhythm

The paced QRS is wide by nature; do not call it a bundle branch block or a ventricular rhythm.

13.Evidence-based practice statistics

Answer: RR = 2

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.

Event rates

EER = 64/160 = 0.4
CER = 64/320 = 0.2

Relative risk

RR = 0.4/0.2 = 2

Answer

RR = 2
14.Evidence-based practice statistics

Answer: p′ = 24.7 %

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.

Likelihood ratio

LR− = (1 − 0.66)/0.69 = 0.4928

Pre-test odds

0.4/(1 − 0.4) = 0.6667

Post-test odds

0.6667·0.4928 = 0.3285

Post-test probability

p′ = 0.3285/(1 + 0.3285) = 0.2473 ≈ 24.7%

Answer

p′ = 24.7%

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