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 type of epithelium lines the urinary bladder?

  1. ATransitional epithelium (urothelium)
  2. BSimple columnar epithelium
  3. CPseudostratified columnar epithelium
  4. DSimple squamous epithelium
2.Human anatomyHard

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

  1. ARight coronary artery
  2. BLeft main coronary artery
  3. CFirst diagonal branch
  4. DLeft anterior descending artery
3.Human physiologyMedium

Which cells in the stomach secrete hydrochloric acid?

  1. AG cells
  2. BParietal cells
  3. CChief cells
  4. DGoblet cells
4.Human physiologyHard

Why does breathing 100% oxygen correct hypoxaemia from a true right-to-left shunt only poorly?

  1. APure oxygen damages haemoglobin
  2. BThe shunted blood never comes into contact with alveolar gas
  3. CShunted blood is already fully saturated
  4. DThe extra oxygen is all exhaled as CO₂
5.MicrobiologyMedium

How does an mRNA vaccine produce immunity?

  1. ABody cells use the mRNA to make a viral protein that the immune system learns to recognise
  2. BThe mRNA is inserted permanently into human DNA
  3. CThe mRNA contains weakened live virus
  4. DThe mRNA kills the virus directly in the blood
6.MicrobiologyHard

Gram-positive cocci are found. Which test quickly separates staphylococci from streptococci?

  1. AThe acid-fast stain
  2. BGrowth on MacConkey agar
  3. CThe catalase test
  4. DThe coagulase test
7.PharmacologyMedium

An adult patient is due to receive digoxin. The apical pulse, counted for a full minute, is 52 beats per minute. What should the nurse do?

  1. AGive the dose and recheck the pulse in one hour
  2. BGive the dose with food to slow absorption
  3. CWithhold the dose and notify the prescriber
  4. DGive half the dose and document the pulse
8.PharmacologyHard

A drug has a half-life of 6 hours. Its plasma level is 80 mg/L. Assuming first-order elimination and no further doses, what is the level after 18 hours?

  1. A26.7 mg/L
  2. B20 mg/L
  3. C40 mg/L
  4. D10 mg/L
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 28 mmHg (3.7 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 28 mmHg (3.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 38 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 38 mmol/L
PaCO₂ = mmHg
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 Fridericia’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 flutter, 2:1 conductionsupraventricular tachycardia (SVT)torsades de pointesidioventricular rhythm

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 flutter, 2:1 conduction
  2. 2supraventricular tachycardia (SVT)
  3. 3torsades de pointes
  4. 4idioventricular rhythm
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment62768830abcontrol28252280cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 830 patients received a new treatment and 280 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 62/830control: 28/280
NNT =
14.Evidence-based practice statisticsHard
pre-test30%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 30% for a disease. A test with sensitivity 61% and specificity 68% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 30%Se = 61%Sp = 68%positive
p′ = %

3Solutions

1.Human anatomy

Answer: A · Transitional epithelium (urothelium)

Why this is the answer

Transitional epithelium can change shape from rounded to flattened cells as the bladder stretches, while staying watertight.

Answer

A · Transitional epithelium (urothelium)
2.Human anatomy

Answer: A · 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

A · Right coronary artery
3.Human physiology

Answer: B · Parietal cells

Why this is the answer

Parietal cells secrete HCl and intrinsic factor. Chief cells secrete pepsinogen and G cells secrete gastrin.

Answer

B · Parietal cells
4.Human physiology

Answer: B · The shunted blood never comes into contact with alveolar gas

Why this is the answer

Shunted blood bypasses ventilated alveoli and mixes deoxygenated blood into arterial blood. Extra inspired oxygen cannot reach it, unlike in V/Q mismatch or hypoventilation.

Answer

B · The shunted blood never comes into contact with alveolar gas
5.Microbiology

Answer: A · Body cells use the mRNA to make a viral protein that the immune system learns to recognise

Why this is the answer

The mRNA is translated by cells into an antigen, such as a coronavirus spike protein. The immune system responds to it. The mRNA is broken down and does not enter the nucleus.

Answer

A · Body cells use the mRNA to make a viral protein that the immune system learns to recognise
6.Microbiology

Answer: C · The catalase test

Why this is the answer

Staphylococci produce catalase, which breaks hydrogen peroxide into water and oxygen bubbles; streptococci do not. The coagulase test is then used to identify S. aureus among staphylococci.

Answer

C · The catalase test
7.Pharmacology

Answer: C · Withhold the dose and notify the prescriber

Why this is the answer

Digoxin is usually withheld in adults if the apical pulse is below 60 per minute, and the prescriber is informed. Bradycardia may be an early sign of toxicity.

Answer

C · Withhold the dose and notify the prescriber
8.Pharmacology

Answer: D · 10 mg/L

Why this is the answer

18 hours is three half-lives. The level halves three times: 80 → 40 → 20 → 10 mg/L.

Answer

D · 10 mg/L
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 21.6 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

|28 − 40| = 12 mmHg → 1.2 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·1.2 = 21.6 mmol/L

Answer

HCO₃⁻ = 21.6 mmol/L
10.Arterial blood gas interpretation

Answer: PaCO₂ = 47.6 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

0.7·38 + 21 = 47.6 mmHg

Answer

PaCO₂ = 47.6 mmHg

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

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 = 11.5 × 0.04 = 0.46 s
RR = 26 × 0.04 = 1.04 s

Fridericia’s formula

QTc = 0.46/∛1.04 = 0.46/1.013 = 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: torsades de pointes

More ventricular rhythms: torsades de pointes is a polymorphic ventricular tachycardia, usually 150–250/min, in which the wide complexes change in height and twist around the baseline, pointing up for a few beats and then down. Textbooks link it to a prolonged QT interval, and magnesium sulfate is the drug resuscitation guidelines name for it. An idioventricular rhythm is a ventricular escape rhythm: regular, wide QRS (0.12 s or more), no P waves, at 20–40/min (an accelerated idioventricular rhythm runs at 40–100/min). Monomorphic VT has identical wide complexes at more than 100/min. VF is chaotic, without any repeating complex.

Five steps

1. Rate: very fast, the complexes are about 7 small boxes apart (about 214 per minute).
2. Rhythm: fast and roughly regular, but the height and direction of the complexes change in a repeating spindle pattern.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: wide and polymorphic; the complexes twist around the baseline, pointing up for a few beats and then down.

Interpretation

torsades de pointes

Answer

torsades de pointes

Torsades de pointes is a polymorphic VT linked to a prolonged QT interval. This is identification practice only.

13.Evidence-based practice statistics

Answer: NNT = 40

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 = 62/830 = 0.0747
CER = 28/280 = 0.1

Number needed to treat

ARR = 0.1 − 0.0747 = 0.0253
NNT = 1/0.0253 = 39.52 → 40

Answer

NNT = 40

Treating 40 patients prevents about one event.

14.Evidence-based practice statistics

Answer: p′ = 45 %

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+ = 0.61/(1 − 0.68) = 1.906

Pre-test odds

0.3/(1 − 0.3) = 0.4286

Post-test odds

0.4286·1.906 = 0.817

Post-test probability

p′ = 0.817/(1 + 0.817) = 0.4496 ≈ 45%

Answer

p′ = 45%

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