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. AMedian nerve
  2. BUlnar nerve
  3. CRadial nerve
  4. DMusculocutaneous nerve
2.Human anatomyHard

During a lumbar puncture, which ligament is the last one pierced before the needle enters the epidural space?

  1. APosterior longitudinal ligament
  2. BSupraspinous ligament
  3. CLigamentum flavum
  4. DInterspinous ligament
3.Human physiologyMedium

Why do myelinated axons conduct action potentials faster than unmyelinated ones?

  1. AThe impulse jumps between nodes of Ranvier
  2. BMyelin contains more sodium channels
  3. CMyelin releases neurotransmitter along the axon
  4. DMyelin makes the axon thinner
4.Human physiologyHard

Why is severe hyperkalaemia dangerous for the heart?

  1. AIt blocks the binding of calcium to troponin
  2. BIt depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
  3. CIt hyperpolarises cardiac cells, so they can never fire
  4. DIt speeds up the SA node until tachycardia causes fainting
5.MicrobiologyMedium

Many antifungal drugs target ergosterol. Why does this work?

  1. AErgosterol is only found in viruses
  2. BErgosterol is in fungal cell membranes but not in human cells
  3. CHuman cells use ergosterol to make energy
  4. DErgosterol is the main structural component of bacterial cell walls
6.MicrobiologyHard

Which process can produce a completely new influenza A subtype that causes a pandemic?

  1. AAntigenic drift through gradual accumulation of point mutations
  2. BAntigenic shift through reassortment of gene segments
  3. CTransformation with free DNA
  4. DLysogenic conversion by a bacteriophage
7.PharmacologyMedium

Why is a spacer recommended with a metered-dose inhaler?

  1. AIt turns the inhaler into a nebuliser
  2. BMore drug reaches the lungs and less stays in the mouth
  3. CIt doubles the dose of drug released by each puff of the inhaler
  4. DIt removes the need to shake the inhaler
8.PharmacologyHard

A patient who used heroin a few hours ago is given a first dose of buprenorphine and quickly develops severe withdrawal. Why?

  1. ABuprenorphine causes an allergic reaction in heroin users
  2. BBuprenorphine is a pure antagonist like naloxone with no agonist effect
  3. CBuprenorphine has no effect at opioid receptors
  4. DBuprenorphine is a high-affinity partial agonist that displaces heroin
9.Arterial blood gas interpretationMedium
pH7.357.457.38PaCO₂mmHg354523HCO₃⁻mmol/L222613uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.38, PaCO₂ 23 mmHg (3.1 kPa) and HCO₃⁻ 13 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.38PaCO₂ 23 mmHg (3.1 kPa)HCO₃⁻ 13 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 138, Cl⁻ 113, HCO₃⁻ 15 mmol/L and albumin 35 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 138 mmol/LCl⁻ 113 mmol/LHCO₃⁻ 15 mmol/Lalbumin 35 g/L
AGc = mmol/L
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/mVventricular tachycardiasinus tachycardiaventricular fibrillationtorsades de pointes

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. 1ventricular tachycardia
  2. 2sinus tachycardia
  3. 3ventricular fibrillation
  4. 4torsades de pointes
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment194526720abcontrol70320390cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 720 patients received a new treatment and 390 received the control treatment. The table shows how many in each group had a side effect. Find the number needed to harm NNH: how many patients must be treated for one extra patient to have the side effect? Round up to a whole number of patients.

treatment: 194/720control: 70/390
NNH =
14.Evidence-based practice statisticsHard
p (%)PPV (%)3%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 79% and a specificity of 86%. It is used in a population where the prevalence is 3%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 79%Sp = 86%p = 3%
PPV = %

3Solutions

1.Human anatomy

Answer: A · 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

A · Median nerve
2.Human anatomy

Answer: C · Ligamentum flavum

Why this is the answer

The needle passes skin, supraspinous and interspinous ligaments, then ligamentum flavum into the epidural space, then dura and arachnoid into the subarachnoid space.

Answer

C · Ligamentum flavum
3.Human physiology

Answer: A · The impulse jumps between nodes of Ranvier

Why this is the answer

Myelin insulates the axon, so action potentials are only generated at the nodes of Ranvier. This saltatory conduction is much faster.

Answer

A · The impulse jumps between nodes of Ranvier
4.Human physiology

Answer: B · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias

Why this is the answer

High extracellular potassium makes the resting potential less negative. Many fast sodium channels then become inactivated, slowing conduction and risking fatal arrhythmias.

Answer

B · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
5.Microbiology

Answer: B · Ergosterol is in fungal cell membranes but not in human cells

Why this is the answer

Fungal membranes contain ergosterol, while human membranes contain cholesterol. Azoles block ergosterol synthesis and amphotericin binds ergosterol, so they target fungi selectively.

Answer

B · Ergosterol is in fungal cell membranes but not in human cells
6.Microbiology

Answer: B · Antigenic shift through reassortment of gene segments

Why this is the answer

When two different influenza A viruses infect the same cell, their segments can mix, giving new haemagglutinin or neuraminidase combinations. Few people are immune, so pandemics can follow. Drift causes the smaller yearly changes.

Answer

B · Antigenic shift through reassortment of gene segments
7.Pharmacology

Answer: B · More drug reaches the lungs and less stays in the mouth

Why this is the answer

A spacer holds the aerosol so it can be inhaled slowly, without precise coordination. This improves lung delivery and reduces mouth side effects such as thrush from inhaled steroids.

Answer

B · More drug reaches the lungs and less stays in the mouth
8.Pharmacology

Answer: D · Buprenorphine is a high-affinity partial agonist that displaces heroin

Why this is the answer

Buprenorphine binds mu receptors more strongly than heroin but activates them less, so it can precipitate withdrawal. Induction is started when the patient already has mild to moderate withdrawal signs.

Answer

D · Buprenorphine is a high-affinity partial agonist that displaces heroin
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 7.38: within 7.35–7.45
PaCO₂ 23 mmHg: low (35–45)
HCO₃⁻ 13 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 25.5–29.5 mmHg, so the measured 23 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: AGc = 11.25 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.

Anion gap

AG = 138 − (113 + 15) = 10

Correction for albumin

10 + 0.25·(40 − 35) = 11.25 mmol/L

Answer

AGc = 11.25 mmol/L

Still within about 8–12 after correction.

11.ECG rhythm strip interpretation

Answer: QTc = 0.394 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 = 9 × 0.04 = 0.36 s
RR = 19 × 0.04 = 0.76 s

Fridericia’s formula

QTc = 0.36/∛0.76 = 0.36/0.9126 = 0.394 s

Answer

QTc = 0.394 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (394 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: 0.14 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: NNH = 12

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 = 194/720 = 0.2694
CER = 70/390 = 0.1795

Number needed to harm

ARI = 0.2694 − 0.1795 = 0.08996
NNH = 1/0.08996 = 11.12 → 12

Answer

NNH = 12

About one in every 12 treated patients has the side effect because of the treatment.

14.Evidence-based practice statistics

Answer: PPV = 14.9 %

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 = 0.79·0.03 = 0.0237
(1 − Sp)·(1 − p) = 0.14·0.97 = 0.1358

Positive predictive value

PPV = 0.0237/(0.0237 + 0.1358) = 0.1486 ≈ 14.9%

Answer

PPV = 14.9%

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

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