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 valve lies between the left atrium and the left ventricle?

  1. AAortic valve
  2. BPulmonary valve
  3. CTricuspid valve
  4. DMitral (bicuspid) valve
2.Human anatomyHard

When inserting a chest drain or needle into the pleural space, why is it placed just above the upper border of a rib?

  1. AThe lung does not reach the area above each rib
  2. BThe pleura is thickest just above each rib
  3. CThe intercostal vein, artery and nerve run along the lower border of each rib
  4. DThe intercostal muscles are absent above each rib
3.Human physiologyMedium

What causes the first heart sound (S1)?

  1. AClosure of the mitral and tricuspid valves
  2. BBlood filling the atria
  3. COpening of the aortic valve
  4. DClosure of the aortic and pulmonary valves
4.Human physiologyHard

Why is severe hyperkalaemia dangerous for the heart?

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

How does an mRNA vaccine produce immunity?

  1. AThe mRNA kills the virus directly in the blood
  2. BBody cells use the mRNA to make a viral protein that the immune system learns to recognise
  3. CThe mRNA is inserted permanently into human DNA
  4. DThe mRNA contains weakened live virus
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

  1. AIt lives only inside red blood cells
  2. BIt produces large amounts of beta-lactamase
  3. CIt has a thick waxy mycolic acid layer that blocks entry
  4. DIt has no cell wall for penicillin to act on
7.PharmacologyMedium

A patient takes isoniazid. Which advice is most important?

  1. AAvoid alcohol and report jaundice, dark urine or poor appetite
  2. BStop the drug when the cough improves
  3. CTake it with antacids to protect the stomach from irritation
  4. DExpect the urine to turn orange
8.PharmacologyHard

Why is pyridoxine (vitamin B6) often given together with isoniazid for tuberculosis?

  1. ATo prevent peripheral neuropathy
  2. BTo reduce bacterial resistance
  3. CTo prevent liver damage from isoniazid
  4. DTo increase the absorption of isoniazid
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 144 mmol/L, glucose 24.7 mmol/L and urea 24.4 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 144 mmol/Lglucose 24.7 mmol/Lurea 24.4 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.05PaCO₂mmHg354541HCO₃⁻mmol/L222611appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.05, PaCO₂ 41 mmHg (5.5 kPa), HCO₃⁻ 11 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.05PaCO₂ 41 mmHg (5.5 kPa)HCO₃⁻ 11 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory 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/mVatrial flutter, 2:1 conductionventricular tachycardiasinus tachycardiaventricular fibrillation

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. 1atrial flutter, 2:1 conduction
  2. 2ventricular tachycardia
  3. 3sinus tachycardia
  4. 4ventricular fibrillation
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment64176240abcontrol106174280cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 240 patients received a new treatment and 280 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 64/240control: 106/280
NNT =
14.Evidence-based practice statisticsHard
CER29%EER?RRR 32%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 32% in relative terms (RRR = 32%). In a patient group the risk without treatment (CER) is 29% 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 = 32%CER = 29%
NNT =

3Solutions

1.Human anatomy

Answer: D · Mitral (bicuspid) valve

Why this is the answer

The mitral (bicuspid) valve separates the left atrium and left ventricle; the tricuspid valve does the same on the right side.

Answer

D · Mitral (bicuspid) valve
2.Human anatomy

Answer: C · The intercostal vein, artery and nerve run along the lower border of each rib

Why this is the answer

The intercostal neurovascular bundle (vein, artery, nerve from above down) lies in the costal groove under each rib. Going just above the rib below avoids it.

Answer

C · The intercostal vein, artery and nerve run along the lower border of each rib
3.Human physiology

Answer: A · Closure of the mitral and tricuspid valves

Why this is the answer

S1 ("lub") is caused by closure of the atrioventricular valves at the start of systole. S2 ("dub") is closure of the semilunar valves.

Answer

A · Closure of the mitral and tricuspid valves
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 · Body cells use the mRNA to make a viral protein that the immune system learns to recognise

Why this is the answer

The mRNA is translated by cells into an antigen, such as a coronavirus spike protein. The immune system responds to it. The mRNA is broken down and does not enter the nucleus.

Answer

B · Body cells use the mRNA to make a viral protein that the immune system learns to recognise
6.Microbiology

Answer: D · It has no cell wall for penicillin to act on

Why this is the answer

Mycoplasma lacks a cell wall, so beta-lactams have no target. Macrolides or tetracyclines, which act on the ribosome, are used instead.

Answer

D · It has no cell wall for penicillin to act on
7.Pharmacology

Answer: A · Avoid alcohol and report jaundice, dark urine or poor appetite

Why this is the answer

Isoniazid can cause hepatitis, and alcohol increases the risk. Signs of liver injury are reported at once, and liver tests may be checked.

Answer

A · Avoid alcohol and report jaundice, dark urine or poor appetite
8.Pharmacology

Answer: A · To prevent peripheral neuropathy

Why this is the answer

Isoniazid causes pyridoxine deficiency, which can lead to peripheral neuropathy. The risk is greater in slow acetylators, malnourished patients and people with diabetes or alcohol dependence.

Answer

A · To prevent peripheral neuropathy
9.Arterial blood gas interpretation

Answer: Osm = 337 mOsm/kg

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.

Calculated osmolality

Osm = 2·144 + 24.7 + 24.4 = 337.1 ≈ 337 mOsm/kg

Answer

Osm = 337 mOsm/kg
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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 PaCO₂

1.5·11 + 8 = 24.5 → 22.5–26.5 mmHg

Compare

measured: 41 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.426 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 = 10 × 0.04 = 0.40 s
RR = 22 × 0.04 = 0.88 s

Bazett’s formula

QTc = 0.40/√0.88 = 0.40/0.9381 = 0.426 s

Answer

QTc = 0.426 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (426 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: NNT = 9

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 = 64/240 = 0.2667
CER = 106/280 = 0.3786

Number needed to treat

ARR = 0.3786 − 0.2667 = 0.1119
NNT = 1/0.1119 = 8.936 → 9

Answer

NNT = 9

Treating 9 patients prevents about one event.

14.Evidence-based practice statistics

Answer: NNT = 11

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 = 0.29·0.32 = 0.0928

Number needed to treat

NNT = 1/0.0928 = 10.78 → 11

Answer

NNT = 11

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

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