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 of these organs is retroperitoneal?

  1. ATransverse colon
  2. BStomach
  3. CKidney
  4. DSpleen
2.Human anatomyHard

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

  1. ALeft main coronary artery
  2. BRight coronary artery
  3. CLeft anterior descending artery
  4. DFirst diagonal branch
3.Human physiologyMedium

Why can cardiac muscle not be tetanised like skeletal muscle?

  1. AIt has no calcium in the sarcoplasmic reticulum
  2. BIts long refractory period lasts almost as long as the contraction
  3. CIt is controlled only by hormones
  4. DIt is not striated
4.Human physiologyHard

Why does ketoacidosis typically develop in untreated type 1 diabetes but rarely in type 2?

  1. AKetones are only made in children
  2. BType 1 patients have more glucagon receptors
  3. CType 2 patients cannot make ketones at all
  4. DEven low insulin levels suppress lipolysis and ketogenesis
5.MicrobiologyMedium

Why are pregnant women advised to avoid unpasteurised soft cheeses?

  1. AThey contain too much lactose for the fetus
  2. BThey often contain the hepatitis C virus, which crosses the placenta
  3. CThey may contain Listeria, which can harm the fetus
  4. DThey may contain tapeworm eggs
6.MicrobiologyHard

What is the key difference between bactericidal and bacteriostatic antibiotics?

  1. ABactericidal drugs work only on viruses; bacteriostatic drugs work on bacteria
  2. BBactericidal drugs work only outside the body
  3. CBactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
  4. DBacteriostatic drugs always work faster than bactericidal drugs
7.PharmacologyMedium

A patient is due the first dose of IV cefuroxime. Which question is most important before giving it?

  1. A"Have you eaten anything in the last two hours?"
  2. B"Have you taken paracetamol today?"
  3. C"Have you ever had a reaction to penicillin or another antibiotic?"
  4. D"Do you prefer the drip in your left arm or in your right arm?"
8.PharmacologyHard

An older patient with coronary artery disease is starting levothyroxine for hypothyroidism. Why is a low starting dose used?

  1. AOlder patients absorb levothyroxine much better, so small doses are all they need
  2. BHigh starting doses cause permanent hypothyroidism
  3. CFast replacement raises cardiac oxygen demand and can cause angina
  4. DLevothyroxine causes severe hypoglycaemia in older patients
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 31 mmHg (4.1 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 31 mmHg (4.1 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard
pH7.357.457.17PaCO₂mmHg354579HCO₃⁻mmol/L222628acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.17, PaCO₂ 79 mmHg (10.5 kPa), HCO₃⁻ 28 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 7.17PaCO₂ 79 mmHg (10.5 kPa)HCO₃⁻ 28 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/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
testdisease presentdisease absenttotalpositive147327474abnegative73883956cdtotal22012101430

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 positive likelihood ratio LR+. Round to two decimal places.

a = 147b = 327c = 73d = 883
LR+ =
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 80% and specificity 82% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 30%Se = 80%Sp = 82%negative
p′ = %

3Solutions

1.Human anatomy

Answer: C · Kidney

Why this is the answer

The kidneys lie behind the parietal peritoneum. The stomach, spleen and transverse colon are intraperitoneal and have a mesentery or ligaments.

Answer

C · Kidney
2.Human anatomy

Answer: B · 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

B · Right coronary artery
3.Human physiology

Answer: B · Its long refractory period lasts almost as long as the contraction

Why this is the answer

The plateau of the cardiac action potential gives a long refractory period, so the muscle relaxes before it can be excited again. This allows the heart to refill.

Answer

B · Its long refractory period lasts almost as long as the contraction
4.Human physiology

Answer: D · Even low insulin levels suppress lipolysis and ketogenesis

Why this is the answer

Insulin strongly inhibits lipolysis and hepatic ketone production. In type 1 there is almost no insulin, so fatty acids flood the liver and ketones build up.

Answer

D · Even low insulin levels suppress lipolysis and ketogenesis
5.Microbiology

Answer: C · They may contain Listeria, which can harm the fetus

Why this is the answer

Listeria monocytogenes can grow in chilled foods and cross the placenta. It can cause miscarriage, stillbirth or severe neonatal infection.

Answer

C · They may contain Listeria, which can harm the fetus
6.Microbiology

Answer: C · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them

Why this is the answer

Bacteriostatic drugs halt multiplication so host defences can eliminate the bacteria. Bactericidal drugs are preferred when defences are weak or hard to reach, such as in endocarditis or neutropenia.

Answer

C · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
7.Pharmacology

Answer: C · "Have you ever had a reaction to penicillin or another antibiotic?"

Why this is the answer

Allergy history must be checked before any first antibiotic dose. Cephalosporins share the beta-lactam ring with penicillins, so a history of severe penicillin allergy is important.

Answer

C · "Have you ever had a reaction to penicillin or another antibiotic?"
8.Pharmacology

Answer: C · Fast replacement raises cardiac oxygen demand and can cause angina

Why this is the answer

Thyroid hormone increases metabolic rate, heart rate and contractility. In older people and those with heart disease, the dose is started low and increased slowly to avoid ischaemia and arrhythmias.

Answer

C · Fast replacement raises cardiac oxygen demand and can cause angina
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 22.2 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

|31 − 40| = 9 mmHg → 0.9 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·0.9 = 22.2 mmol/L

Answer

HCO₃⁻ = 22.2 mmol/L
10.Arterial blood gas interpretation

Answer: acute

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 + 1·3.9 = 27.9 mmol/L
chronic: 24 + 3.5·3.9 = 37.65 mmol/L

Compare

measured: 28 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: QTc = 0.4 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 = 8 × 0.04 = 0.32 s
RR = 16 × 0.04 = 0.64 s

Bazett’s formula

QTc = 0.32/√0.64 = 0.32/0.8 = 0.4 s

Answer

QTc = 0.4 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (400 ms)

12.ECG rhythm strip interpretation

Answer: QRS duration

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: R–R = 22 small boxes, 1500 ÷ 22 ≈ 68 per minute.
2. Rhythm: regular, every R–R is 0.88 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.18 s, constant, within 0.12–0.20 s.
5. QRS: 0.14 s, wide (0.12 s or more).

First abnormal step

QRS duration → sinus rhythm with wide QRS

Answer

QRS duration
13.Evidence-based practice statistics

Answer: LR+ = 2.47

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 = 147/220 = 0.6682
Sp = 883/1210 = 0.7298

Positive likelihood ratio

LR+ = 0.6682/(1 − 0.7298) = 2.472 ≈ 2.47

Answer

LR+ = 2.47
14.Evidence-based practice statistics

Answer: p′ = 9.5 %

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− = (1 − 0.8)/0.82 = 0.2439

Pre-test odds

0.3/(1 − 0.3) = 0.4286

Post-test odds

0.4286·0.2439 = 0.1045

Post-test probability

p′ = 0.1045/(1 + 0.1045) = 0.09464 ≈ 9.5%

Answer

p′ = 9.5%

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