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 muscle is the main extensor of the elbow?

  1. ATriceps brachii
  2. BBrachialis
  3. CCoracobrachialis
  4. DBiceps brachii
2.Human anatomyHard

After an injury at the medial epicondyle of the elbow, a patient has numbness of the little finger and weakness of finger abduction. Which nerve is affected?

  1. AUlnar nerve
  2. BMedian nerve
  3. CMusculocutaneous nerve
  4. DRadial nerve
3.Human physiologyMedium

Cardiac output equals heart rate multiplied by:

  1. ABlood pressure
  2. BPeripheral resistance
  3. CEjection fraction
  4. DStroke volume
4.Human physiologyHard

Which adaptation develops over days to weeks at high altitude?

  1. ALower ventilation to save oxygen
  2. BIncreased renal bicarbonate retention
  3. CHigher erythropoietin levels and more red blood cells
  4. DA fall in haematocrit
5.MicrobiologyMedium

Which laboratory test separates Staphylococcus aureus from most other staphylococci?

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

In the 1840s Ignaz Semmelweis lowered deaths from puerperal fever in a Vienna maternity clinic. What did he introduce?

  1. AHandwashing with chlorinated lime before examining women
  2. BVaccination of all mothers before birth
  3. CKeeping mothers in separate isolation rooms after delivery
  4. DTreating mothers with penicillin
7.PharmacologyMedium

A person who has never been vaccinated against tetanus has a deep, dirty wound. What is usually given?

  1. ATetanus vaccine only, after the wound heals
  2. BNo treatment unless symptoms appear
  3. CTetanus vaccine and tetanus immunoglobulin
  4. DOral antibiotics only
8.PharmacologyHard

A patient on lisinopril for hypertension starts taking ibuprofen every day for knee pain. What is the main concern?

  1. AWeaker blood pressure control, kidney injury and high potassium
  2. BFaster liver metabolism of lisinopril, so it stops working
  3. CA large fall in blood pressure, with fainting and falls on standing up
  4. DA higher risk of a dry cough than with lisinopril alone
9.Arterial blood gas interpretationMedium
pH7.357.457.42PaCO₂mmHg354524HCO₃⁻mmol/L222615uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.42, PaCO₂ 24 mmHg (3.2 kPa) and HCO₃⁻ 15 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.42PaCO₂ 24 mmHg (3.2 kPa)HCO₃⁻ 15 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 40% oxygen shows PaO₂ 78 mmHg (10.4 kPa) and PaCO₂ 36 mmHg (4.8 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 40%PaO₂ 78 mmHg (10.4 kPa)PaCO₂ 36 mmHg (4.8 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationatrial flutter, 4:1 conductionatrial flutter, 2:1 conductionnormal sinus rhythm

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. 2atrial flutter, 4:1 conduction
  3. 3atrial flutter, 2:1 conduction
  4. 4normal sinus rhythm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
casescontrolsexposed3159abnot exposed279211cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 310 patients with a disease (cases) and 270 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 31b = 59c = 279d = 211
OR =
14.Evidence-based practice statisticsHard
CER10%EER?RRR 21%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 21% in relative terms (RRR = 21%). In a patient group the risk without treatment (CER) is 10% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 21%CER = 10%
NNT =

3Solutions

1.Human anatomy

Answer: A · Triceps brachii

Why this is the answer

Triceps brachii inserts on the olecranon of the ulna and extends the elbow. Biceps and brachialis are elbow flexors.

Answer

A · Triceps brachii
2.Human anatomy

Answer: A · Ulnar nerve

Why this is the answer

The ulnar nerve passes behind the medial epicondyle. It supplies most intrinsic hand muscles, including the interossei, and the skin of the little finger.

Answer

A · Ulnar nerve
3.Human physiology

Answer: D · Stroke volume

Why this is the answer

CO = HR × SV. At rest about 70 beats/min × 70 mL ≈ 5 L/min.

Answer

D · Stroke volume
4.Human physiology

Answer: C · 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

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

Answer: A · 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

A · The coagulase test
6.Microbiology

Answer: A · Handwashing with chlorinated lime before examining women

Why this is the answer

Semmelweis noticed higher mortality in the ward run by doctors who also did autopsies. Hand disinfection with chlorinated lime sharply reduced deaths, long before germ theory was accepted.

Answer

A · Handwashing with chlorinated lime before examining women
7.Pharmacology

Answer: C · Tetanus vaccine and tetanus immunoglobulin

Why this is the answer

Tetanus immunoglobulin gives immediate passive protection, while the vaccine starts active immunity. Thorough wound cleaning is also essential.

Answer

C · Tetanus vaccine and tetanus immunoglobulin
8.Pharmacology

Answer: A · Weaker blood pressure control, kidney injury and high potassium

Why this is the answer

NSAIDs block prostaglandins that dilate the afferent arteriole and promote sodium loss. With an ACE inhibitor this can reduce blood pressure control and cause kidney injury and hyperkalaemia, especially if a diuretic is also used.

Answer

A · Weaker blood pressure control, kidney injury and high potassium
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 7.42: within 7.35–7.45
PaCO₂ 24 mmHg: low (35–45)
HCO₃⁻ 15 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 162.2 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.4·713 − 36/0.8 = 285.2 − 45 = 240.2 mmHg

Gradient

A–a = 240.2 − 78 = 162.2 mmHg

Answer

A–a gradient = 162.2 mmHg
11.ECG rhythm strip interpretation

Answer: atrial flutter, 2:1 conduction

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: R–R = 10 small boxes, 1500 ÷ 10 ≈ 150 per minute.
2. Rhythm: regular, every R–R is 0.40 s.
3. P waves: none; regular sawtooth flutter waves every 0.20 s (300 per minute), 2 for each QRS.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

atrial flutter, 2:1 conduction

Answer

atrial flutter, 2:1 conduction
12.ECG rhythm strip interpretation

Answer: rhythm

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: irregularly irregular, R–R from 0.60 to 0.94 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s).

First abnormal step

rhythm → atrial fibrillation

Answer

rhythm
13.Evidence-based practice statistics

Answer: OR = 0.4

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.

Odds of exposure

cases: 31/279 = 0.1111
controls: 59/211 = 0.2796

Odds ratio

OR = (31·211)/(59·279) = 0.3974 ≈ 0.4

Answer

OR = 0.4

OR below 1: exposure is less common among the cases, which suggests a protective effect.

14.Evidence-based practice statistics

Answer: NNT = 48

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.

Absolute risk reduction

ARR = 0.1·0.21 = 0.021

Number needed to treat

NNT = 1/0.021 = 47.62 → 48

Answer

NNT = 48

The same relative effect gives a smaller NNT when the baseline risk is higher.

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