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 layer of the heart wall contains the cardiac muscle?

  1. AEpicardium
  2. BMyocardium
  3. CPericardium
  4. DEndocardium
2.Human anatomyHard

A patient with a large aneurysm of the aortic arch develops hoarseness. Which nerve is most likely compressed?

  1. ALeft phrenic nerve
  2. BExternal laryngeal nerve
  3. CRight recurrent laryngeal nerve
  4. DLeft recurrent laryngeal nerve
3.Human physiologyMedium

The Frank–Starling mechanism describes that:

  1. AContractility falls when temperature rises
  2. BHeart rate rises when arterial blood pressure falls suddenly
  3. CStroke volume rises when ventricular filling increases
  4. DThe atria contract after the ventricles
4.Human physiologyHard

A patient has taken high-dose prednisolone for a year. What is the state of the hypothalamic–pituitary–adrenal axis?

  1. AACTH is high and the adrenal cortex is enlarged
  2. BACTH is suppressed and the adrenal cortex has atrophied
  3. CACTH is normal and cortisol production is increased
  4. DThe adrenal medulla has stopped making adrenaline and noradrenaline
5.MicrobiologyMedium

Which organism is a common cause of infection in burns and in people with cystic fibrosis, and can produce a green pigment?

  1. APseudomonas aeruginosa
  2. BHelicobacter pylori
  3. CStreptococcus pyogenes
  4. DClostridium tetani
6.MicrobiologyHard

Joseph Lister reduced infection after surgery in the 1860s. What was his main innovation?

  1. AVaccinating surgeons against staphylococci
  2. BUsing carbolic acid (phenol) as an antiseptic on wounds and instruments
  3. CGiving sulfonamide antibiotics after every operation
  4. DUsing steam autoclaves to sterilise all surgical instruments before each operation
7.PharmacologyMedium

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

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

A patient on long-term prednisolone has been vomiting for two days and could not take her tablets. She is now hypotensive and confused, with low sodium and high potassium. What is the most urgent treatment?

  1. AOral prednisolone with a glass of water
  2. BIV hydrocortisone and IV fluids
  3. CIV insulin with glucose only
  4. DIV furosemide
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 6 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 6 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.32PaCO₂mmHg354530HCO₃⁻mmol/L222615added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.32, PaCO₂ 30 mmHg (4.0 kPa) and HCO₃⁻ 15 mmol/L, with Na⁺ 142 and Cl⁻ 90 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.32PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 15 mmol/LNa⁺ 142 mmol/LCl⁻ 90 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
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/mVpulseless electrical activity (PEA)asystolesinus bradycardiaventricular fibrillation

A monitored patient is found unresponsive and not breathing normally, and no carotid pulse can be felt. The monitor shows this organised rhythm. What is this situation called? 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. 1pulseless electrical activity (PEA)
  2. 2asystole
  3. 3sinus bradycardia
  4. 4ventricular fibrillation
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive133456589abnegative57744801cdtotal19012001390

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 negative likelihood ratio LR−. Round to two decimal places.

a = 133b = 456c = 57d = 744
LR− =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositivenegative?total10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 76% and specificity 82%. The prevalence of the disease is 8%. How many people with the disease are missed by the test (false negatives, FN)?

N = 10 000p = 8%Se = 76%Sp = 82%
FN =

3Solutions

1.Human anatomy

Answer: B · Myocardium

Why this is the answer

The myocardium is the thick muscular middle layer. The endocardium lines the chambers and the epicardium covers the outside.

Answer

B · Myocardium
2.Human anatomy

Answer: D · Left recurrent laryngeal nerve

Why this is the answer

The left recurrent laryngeal nerve loops under the aortic arch beside the ligamentum arteriosum. It supplies most laryngeal muscles, so compression causes hoarseness.

Answer

D · Left recurrent laryngeal nerve
3.Human physiology

Answer: C · Stroke volume rises when ventricular filling increases

Why this is the answer

Greater end-diastolic volume stretches the myocardium, which increases the force of contraction and the stroke volume, matching output to venous return.

Answer

C · Stroke volume rises when ventricular filling increases
4.Human physiology

Answer: B · ACTH is suppressed and the adrenal cortex has atrophied

Why this is the answer

Exogenous glucocorticoid suppresses CRH and ACTH, so the adrenal cortex atrophies. Stopping the drug suddenly can cause an adrenal crisis, so it is tapered.

Answer

B · ACTH is suppressed and the adrenal cortex has atrophied
5.Microbiology

Answer: A · Pseudomonas aeruginosa

Why this is the answer

Pseudomonas aeruginosa is an opportunistic pathogen of burns, ventilated patients and cystic fibrosis lungs. It is naturally resistant to many antibiotics.

Answer

A · Pseudomonas aeruginosa
6.Microbiology

Answer: B · Using carbolic acid (phenol) as an antiseptic on wounds and instruments

Why this is the answer

Lister applied carbolic acid to wounds, dressings and instruments, which greatly reduced post-operative infection. This started antiseptic surgery.

Answer

B · Using carbolic acid (phenol) as an antiseptic on wounds and instruments
7.Pharmacology

Answer: D · "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

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

Answer: B · IV hydrocortisone and IV fluids

Why this is the answer

This suggests an adrenal crisis triggered by missed steroids and illness. Treatment is immediate IV or IM hydrocortisone, IV fluids with glucose as needed, and treating the cause.

Answer

B · IV hydrocortisone and IV fluids
9.Arterial blood gas interpretation

Answer: PaCO₂ = 17 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.

Winter’s formula

PaCO₂ = 1.5·6 + 8 = 17 mmHg
range: 15–19 mmHg

Answer

PaCO₂ = 17 mmHg
10.Arterial blood gas interpretation

Answer: added metabolic alkalosis

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 − (90 + 15) = 37

Delta ratio

(37 − 12)/(24 − 15) = 2.778
added metabolic alkalosis

Answer

added metabolic alkalosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.436 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 = 9.5 × 0.04 = 0.38 s
RR = 19 × 0.04 = 0.76 s

Bazett’s formula

QTc = 0.38/√0.76 = 0.38/0.8718 = 0.436 s

Answer

QTc = 0.436 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (436 ms)

12.ECG rhythm strip interpretation

Answer: pulseless electrical activity (PEA)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

1. Rate: R–R = 31 small boxes, 1500 ÷ 31 ≈ 48 per minute.
2. Rhythm: regular, every R–R is 1.24 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.12 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).
sinus bradycardia

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

pulseless electrical activity (PEA)

Answer

pulseless electrical activity (PEA)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: LR− = 0.48

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 = 133/190 = 0.7
Sp = 744/1200 = 0.62

Negative likelihood ratio

LR− = (1 − 0.7)/0.62 = 0.4839 ≈ 0.48

Answer

LR− = 0.48
14.Evidence-based practice statistics

Answer: FN = 192

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.

With and without the disease

10 000·0.08 = 800
10 000 − 800 = 9200

False negatives

FN = 800·0.24 = 192

Answer

FN = 192

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