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 cranial nerve supplies the trapezius and sternocleidomastoid muscles?

  1. AHypoglossal nerve (XII)
  2. BVagus nerve (X)
  3. CFacial nerve (VII)
  4. DAccessory nerve (XI)
2.Human anatomyHard

After a stroke, a patient speaks fluently but uses meaningless words and cannot understand speech. Where is the lesion most likely to be?

  1. ACerebellar hemisphere
  2. BPosterior superior temporal gyrus of the dominant hemisphere
  3. CInferior frontal gyrus of the dominant hemisphere
  4. DPrecentral gyrus of the non-dominant hemisphere
3.Human physiologyMedium

Which receptors respond mainly to a fall in arterial oxygen levels?

  1. APeripheral chemoreceptors in the carotid and aortic bodies
  2. BCentral chemoreceptors in the medulla
  3. CBaroreceptors in the carotid sinus
  4. DStretch receptors in the lungs
4.Human physiologyHard

Which adaptation develops over days to weeks at high altitude?

  1. AA fall in haematocrit
  2. BHigher erythropoietin levels and more red blood cells
  3. CLower ventilation to save oxygen
  4. DIncreased renal bicarbonate retention
5.MicrobiologyMedium

Which organism is a common cause of infection in burns and in people with cystic fibrosis, and can produce a green pigment?

  1. AStreptococcus pyogenes
  2. BHelicobacter pylori
  3. CClostridium tetani
  4. DPseudomonas aeruginosa
6.MicrobiologyHard

Staphylococcus aureus food poisoning starts only 1–6 hours after eating. Why so fast?

  1. AThe bacteria multiply very fast inside the gut and invade the intestinal wall
  2. BThe bacteria invade the bloodstream immediately
  3. CThe bacteria made a heat-stable toxin in the food before it was eaten
  4. DThe immune system reacts to the bacteria within minutes
7.PharmacologyMedium

How is adenosine given for supraventricular tachycardia?

  1. AAs an intramuscular injection into the outer thigh muscle
  2. BAs a slow infusion over one hour
  3. CAs a rapid IV push followed by a fast saline flush
  4. DAs a tablet under the tongue
8.PharmacologyHard

Codeine is converted to morphine by CYP2D6. What happens in a patient who is a CYP2D6 ultra-rapid metaboliser?

  1. ACodeine gives almost no pain relief because little morphine is formed
  2. BCodeine is converted to an inactive compound only
  3. CMore morphine is formed, increasing the risk of opioid toxicity
  4. DCodeine is excreted unchanged in the urine
9.Arterial blood gas interpretationMedium
pH7.357.457.37PaCO₂mmHg354564HCO₃⁻mmol/L222636uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.37, PaCO₂ 64 mmHg (8.5 kPa) and HCO₃⁻ 36 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.37PaCO₂ 64 mmHg (8.5 kPa)HCO₃⁻ 36 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.27PaCO₂mmHg354567HCO₃⁻mmol/L222630acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.27, PaCO₂ 67 mmHg (8.9 kPa), HCO₃⁻ 30 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.27PaCO₂ 67 mmHg (8.9 kPa)HCO₃⁻ 30 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Bazett’s formula QTc = QT/√RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVatrial fibrillationsupraventricular tachycardia (SVT)atrial flutter, 2:1 conductionventricular tachycardia

Identify the rhythm on this 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. 1atrial fibrillation
  2. 2supraventricular tachycardia (SVT)
  3. 3atrial flutter, 2:1 conduction
  4. 4ventricular tachycardia
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive158152310abnegative92508600cdtotal250660910

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the negative likelihood ratio LR−. Round to two decimal places.

a = 158b = 152c = 92d = 508
LR− =
14.Evidence-based practice statisticsHard
p (%)PPV (%)30%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 96% and a specificity of 92%. It is used in a population where the prevalence is 30%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 96%Sp = 92%p = 30%
PPV = %

3Solutions

1.Human anatomy

Answer: D · Accessory nerve (XI)

Why this is the answer

The accessory nerve (XI) supplies sternocleidomastoid and trapezius. Damage weakens head turning and shoulder shrugging.

Answer

D · Accessory nerve (XI)
2.Human anatomy

Answer: B · Posterior superior temporal gyrus of the dominant hemisphere

Why this is the answer

This is Wernicke's (receptive) aphasia, caused by damage to Wernicke's area in the posterior superior temporal gyrus. Broca's area in the inferior frontal gyrus causes non-fluent aphasia.

Answer

B · Posterior superior temporal gyrus of the dominant hemisphere
3.Human physiology

Answer: A · Peripheral chemoreceptors in the carotid and aortic bodies

Why this is the answer

The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.

Answer

A · Peripheral chemoreceptors in the carotid and aortic bodies
4.Human physiology

Answer: B · Higher erythropoietin levels and more red blood cells

Why this is the answer

Hypoxia stimulates EPO and red cell production, raising oxygen-carrying capacity. Hyperventilation causes alkalosis, which the kidneys compensate by excreting bicarbonate.

Answer

B · Higher erythropoietin levels and more red blood cells
5.Microbiology

Answer: D · Pseudomonas aeruginosa

Why this is the answer

Pseudomonas aeruginosa is an opportunistic pathogen of burns, ventilated patients and cystic fibrosis lungs. It is naturally resistant to many antibiotics.

Answer

D · Pseudomonas aeruginosa
6.Microbiology

Answer: C · The bacteria made a heat-stable toxin in the food before it was eaten

Why this is the answer

S. aureus produces enterotoxins in food left at warm temperatures. The toxin is already there when the food is eaten and survives reheating, so symptoms start quickly.

Answer

C · The bacteria made a heat-stable toxin in the food before it was eaten
7.Pharmacology

Answer: C · As a rapid IV push followed by a fast saline flush

Why this is the answer

Adenosine must reach the heart quickly, so it is pushed rapidly into a large vein and flushed. Patients are warned about brief flushing, chest tightness and a short pause in the heartbeat.

Answer

C · As a rapid IV push followed by a fast saline flush
8.Pharmacology

Answer: C · More morphine is formed, increasing the risk of opioid toxicity

Why this is the answer

Ultra-rapid metabolisers convert more codeine to morphine, which can cause respiratory depression. Poor metabolisers form little morphine and get poor pain relief. This is a classic example of pharmacogenetics.

Answer

C · More morphine is formed, increasing the risk of opioid toxicity
9.Arterial blood gas interpretation

Answer: fully compensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.37: within 7.35–7.45
PaCO₂ 64 mmHg: high (35–45)
HCO₃⁻ 36 mmol/L: high (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: acute on chronic

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 HCO₃⁻

acute: 24 + 1·2.7 = 26.7 mmol/L
chronic: 24 + 3.5·2.7 = 33.45 mmol/L

Compare

measured: 30 mmol/L → acute on chronic

Answer

acute on chronic
11.ECG rhythm strip interpretation

Answer: QTc = 0.454 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

QT = 12 × 0.04 = 0.48 s
RR = 28 × 0.04 = 1.12 s

Bazett’s formula

QTc = 0.48/√1.12 = 0.48/1.058 = 0.454 s

Answer

QTc = 0.454 s

Between the usual limits for men (about 0.45 s) and women (about 0.46 s): borderline, depending on the reference used. (454 ms)

12.ECG rhythm strip interpretation

Answer: ventricular tachycardia

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: R–R = 10 small boxes, 1500 ÷ 10 ≈ 150 per minute.
2. Rhythm: regular, every R–R is 0.40 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide (0.12 s or more).

Interpretation

ventricular tachycardia

Answer

ventricular tachycardia

In resuscitation guidelines VF and pulseless VT are the shockable rhythms. This is identification practice only.

13.Evidence-based practice statistics

Answer: LR− = 0.48

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.

Sensitivity and specificity

Se = 158/250 = 0.632
Sp = 508/660 = 0.7697

Negative likelihood ratio

LR− = (1 − 0.632)/0.7697 = 0.4781 ≈ 0.48

Answer

LR− = 0.48
14.Evidence-based practice statistics

Answer: PPV = 83.7 %

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.

True and false positives (per person)

Se·p = 0.96·0.3 = 0.288
(1 − Sp)·(1 − p) = 0.08·0.7 = 0.056

Positive predictive value

PPV = 0.288/(0.288 + 0.056) = 0.8372 ≈ 83.7%

Answer

PPV = 83.7%

The lower the prevalence, the lower the PPV of the same test.

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