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. AAccessory nerve (XI)
  2. BHypoglossal nerve (XII)
  3. CVagus nerve (X)
  4. DFacial nerve (VII)
2.Human anatomyHard

What is the correct order of structures that urine passes through after leaving the collecting ducts?

  1. ARenal pelvis, minor calyx, major calyx, ureter
  2. BMinor calyx, major calyx, renal pelvis, ureter
  3. CMajor calyx, minor calyx, renal pelvis, ureter
  4. DMinor calyx, renal pelvis, major calyx, ureter
3.Human physiologyMedium

What is the main effect of vagus nerve stimulation on the heart?

  1. AIt increases ventricular contractility strongly
  2. BIt slows the heart rate
  3. CIt increases the heart rate
  4. DIt constricts the coronary arteries
4.Human physiologyHard

Why is severe hyperkalaemia dangerous for the heart?

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

Which laboratory test separates Staphylococcus aureus from most other staphylococci?

  1. AThe acid-fast stain
  2. BThe coagulase test
  3. CThe catalase test
  4. DThe Gram stain
6.MicrobiologyHard

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

  1. AThe bacteria invade the bloodstream immediately
  2. BThe bacteria multiply very fast inside the gut and invade the intestinal wall
  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

Which blood test is used to monitor warfarin therapy?

  1. APlatelet count
  2. BINR (prothrombin time)
  3. CSerum albumin
  4. DActivated partial thromboplastin time (aPTT)
8.PharmacologyHard

An older patient who has taken omeprazole for many years has muscle cramps, tremor and an irregular heartbeat. Which lab finding is most likely linked to the drug?

  1. ALow serum magnesium
  2. BLow serum glucose
  3. CHigh serum calcium
  4. DHigh serum sodium
9.Arterial blood gas interpretationMedium
pH7.357.457.52PaCO₂mmHg354551HCO₃⁻mmol/L222640uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.52, PaCO₂ 51 mmHg (6.8 kPa) and HCO₃⁻ 40 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.52PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 40 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 142, Cl⁻ 105, HCO₃⁻ 19 mmol/L and albumin 26 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 142 mmol/LCl⁻ 105 mmol/LHCO₃⁻ 19 mmol/Lalbumin 26 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationfirst-degree AV blocknormal sinus rhythmsinus rhythm with PVCs

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. 1atrial fibrillation
  2. 2first-degree AV block
  3. 3normal sinus rhythm
  4. 4sinus rhythm with PVCs
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
eventno eventtotaltreatment97493590abcontrol63507570cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 590 patients received a new treatment and 570 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: 97/590control: 63/570
NNH =
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 87% and a specificity of 93%. 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 = 87%Sp = 93%p = 30%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Accessory nerve (XI)

Why this is the answer

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

Answer

A · Accessory nerve (XI)
2.Human anatomy

Answer: B · Minor calyx, major calyx, renal pelvis, ureter

Why this is the answer

Collecting ducts open at the renal papillae into minor calyces, which join to form major calyces, which empty into the renal pelvis and then the ureter.

Answer

B · Minor calyx, major calyx, renal pelvis, ureter
3.Human physiology

Answer: B · It slows the heart rate

Why this is the answer

The vagus releases acetylcholine on muscarinic receptors in the SA and AV nodes, slowing pacemaker firing and AV conduction.

Answer

B · It slows the heart rate
4.Human physiology

Answer: D · 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

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

Answer: B · The coagulase test

Why this is the answer

S. aureus produces coagulase, which converts fibrinogen to fibrin. All staphylococci are Gram-positive and catalase-positive, so those tests do not separate them.

Answer

B · The coagulase test
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: B · INR (prothrombin time)

Why this is the answer

Warfarin is monitored with the INR, a standardised prothrombin time. For most indications, such as atrial fibrillation or venous thrombosis, the target is usually 2–3.

Answer

B · INR (prothrombin time)
8.Pharmacology

Answer: A · Low serum magnesium

Why this is the answer

Long-term PPI use can cause hypomagnesaemia, which leads to cramps, tremor and arrhythmias. Other long-term risks include fractures, vitamin B12 deficiency and C. difficile infection.

Answer

A · Low serum magnesium
9.Arterial blood gas interpretation

Answer: partially 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 7.52: alkalaemia (above 7.45)
PaCO₂ 51 mmHg: high (35–45)
HCO₃⁻ 40 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: AGc = 21.5 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 = 142 − (105 + 19) = 18

Correction for albumin

18 + 0.25·(40 − 26) = 21.5 mmol/L

Answer

AGc = 21.5 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: sinus rhythm with PVCs

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: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: regular (0.76 s) except for the early beats and the pause after each of them.
3. P waves: upright before every narrow QRS; none before the early wide beats.
4. PR interval: 0.16 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s in the sinus beats; the early beats are wide (0.14 s) and bizarre, with the T wave pointing the other way.

Interpretation

sinus rhythm with PVCs

Answer

sinus rhythm with PVCs
12.ECG rhythm strip interpretation

Answer: atrial rate = 60 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 = 25 small boxes = 1.00 s → 1500 ÷ 25 = 60 ≈ 60 per minute

Ventricular rate

4 QRS complexes in 6 s × 10 = 40 per minute

Answer

atrial rate = 60 bpm

Answer

atrial rate = 60 bpm

Second-degree type I (Wenckebach): 3 P waves for every 2 QRS complexes.

13.Evidence-based practice statistics

Answer: NNH = 19

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 = 97/590 = 0.1644
CER = 63/570 = 0.1105

Number needed to harm

ARI = 0.1644 − 0.1105 = 0.05388
NNH = 1/0.05388 = 18.56 → 19

Answer

NNH = 19

About one in every 19 treated patients has the side effect because of the treatment.

14.Evidence-based practice statistics

Answer: PPV = 84.2 %

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 = 0.87·0.3 = 0.261
(1 − Sp)·(1 − p) = 0.07·0.7 = 0.049

Positive predictive value

PPV = 0.261/(0.261 + 0.049) = 0.8419 ≈ 84.2%

Answer

PPV = 84.2%

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

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