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. AMitral (bicuspid) valve
  2. BPulmonary valve
  3. CAortic valve
  4. DTricuspid valve
2.Human anatomyHard

A large central disc prolapse at L4–L5 causes saddle anaesthesia, urinary retention and bilateral leg weakness. Which structure is compressed?

  1. ASciatic nerve in the buttock
  2. BCauda equina
  3. CThoracic spinal cord
  4. DFemoral nerve
3.Human physiologyMedium

Which protein forms the mesh that stabilises a blood clot?

  1. AFibrin
  2. BCollagen
  3. CThrombin
  4. DAlbumin
4.Human physiologyHard

In pernicious anaemia, autoimmune destruction of gastric parietal cells leads to anaemia because:

  1. APepsin is lost, so haemoglobin cannot be made
  2. BGastrin is lost, so the bone marrow is no longer stimulated
  3. CIntrinsic factor is lost, so vitamin B12 is not absorbed
  4. DAcid is lost, so iron is never absorbed in any form
5.MicrobiologyMedium

Toxoplasma gondii is a risk in pregnancy. Which advice reduces exposure?

  1. AAvoid swimming pools and all other public bathing areas
  2. BAvoid contact with dogs
  3. CAvoid cleaning cat litter and avoid undercooked meat
  4. DAvoid all fruit and vegetables
6.MicrobiologyHard

Which feature distinguishes most exotoxins from endotoxin?

  1. AExotoxins are only released when bacteria die
  2. BExotoxins are heat-stable lipids
  3. CExotoxins are proteins and can be turned into toxoid vaccines
  4. DExotoxins are lipopolysaccharides of the Gram-negative outer membrane
7.PharmacologyMedium

Which adverse effect of ciprofloxacin should a patient report at once?

  1. APain or swelling in a tendon, such as the Achilles tendon
  2. BDarker stools than usual
  3. CA slightly bitter or metallic taste for a while after each dose
  4. DMild tiredness in the first few days
8.PharmacologyHard

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

  1. ATo prevent liver damage from isoniazid
  2. BTo increase the absorption of isoniazid
  3. CTo prevent peripheral neuropathy
  4. DTo reduce bacterial resistance
9.Arterial blood gas interpretationMedium
pH7.357.457.43PaCO₂mmHg354531HCO₃⁻mmol/L222620uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.43, PaCO₂ 31 mmHg (4.1 kPa) and HCO₃⁻ 20 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.43PaCO₂ 31 mmHg (4.1 kPa)HCO₃⁻ 20 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 35% oxygen shows PaO₂ 57 mmHg (7.6 kPa) and PaCO₂ 49 mmHg (6.5 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 35%PaO₂ 57 mmHg (7.6 kPa)PaCO₂ 49 mmHg (6.5 kPa)
A–a gradient = mmHg
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 Fridericia’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/mVidioventricular rhythmsecond-degree AV block type IIdual-chamber (AV) paced rhythmpaced rhythm, failure to capture

This patient has a pacemaker. Interpret the 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. 1idioventricular rhythm
  2. 2second-degree AV block type II
  3. 3dual-chamber (AV) paced rhythm
  4. 4paced rhythm, failure to capture
13.Evidence-based practice statisticsMedium
Se87%Sp84%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 87% and a specificity of 84%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 87%Sp = 84%
LR− =
14.Evidence-based practice statisticsHard
p (%)NPV (%)0.5%NPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 73% and a specificity of 85%. It is used in a population where the prevalence is 0.5%. Find the negative predictive value NPV as a percentage. Round to one decimal place.

Se = 73%Sp = 85%p = 0.5%
NPV = %

3Solutions

1.Human anatomy

Answer: A · 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

A · Mitral (bicuspid) valve
2.Human anatomy

Answer: B · Cauda equina

Why this is the answer

Below L1–L2 the canal holds the cauda equina. Central compression of these lumbar and sacral roots causes cauda equina syndrome, a surgical emergency.

Answer

B · Cauda equina
3.Human physiology

Answer: A · Fibrin

Why this is the answer

Thrombin converts soluble fibrinogen into insoluble fibrin strands, which bind the platelet plug and trap red cells to form a stable clot.

Answer

A · Fibrin
4.Human physiology

Answer: C · Intrinsic factor is lost, so vitamin B12 is not absorbed

Why this is the answer

Parietal cells secrete intrinsic factor, needed for B12 absorption in the terminal ileum. B12 deficiency impairs DNA synthesis and causes megaloblastic anaemia.

Answer

C · Intrinsic factor is lost, so vitamin B12 is not absorbed
5.Microbiology

Answer: C · Avoid cleaning cat litter and avoid undercooked meat

Why this is the answer

Toxoplasma oocysts are shed in cat faeces and cysts are found in undercooked meat. Infection during pregnancy can damage the fetal brain and eyes.

Answer

C · Avoid cleaning cat litter and avoid undercooked meat
6.Microbiology

Answer: C · Exotoxins are proteins and can be turned into toxoid vaccines

Why this is the answer

Exotoxins are secreted proteins with specific actions and are often very potent; many can be inactivated into toxoids. Endotoxin is lipopolysaccharide, more heat-stable and cannot be made into a toxoid.

Answer

C · Exotoxins are proteins and can be turned into toxoid vaccines
7.Pharmacology

Answer: A · Pain or swelling in a tendon, such as the Achilles tendon

Why this is the answer

Fluoroquinolones can cause tendinitis and tendon rupture. Patients should stop exercise and report tendon pain promptly.

Answer

A · Pain or swelling in a tendon, such as the Achilles tendon
8.Pharmacology

Answer: C · 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

C · To prevent peripheral neuropathy
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 7.43: within 7.35–7.45
PaCO₂ 31 mmHg: low (35–45)
HCO₃⁻ 20 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 131.3 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 = 0.35·713 − 49/0.8 = 249.5 − 61.25 = 188.3 mmHg

Gradient

A–a = 188.3 − 57 = 131.3 mmHg

Answer

A–a gradient = 131.3 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.468 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 = 12 × 0.04 = 0.48 s
RR = 27 × 0.04 = 1.08 s

Fridericia’s formula

QTc = 0.48/∛1.08 = 0.48/1.026 = 0.468 s

Answer

QTc = 0.468 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (468 ms)

12.ECG rhythm strip interpretation

Answer: paced rhythm, failure to capture

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: 6 QRS complexes in 6 s, × 10 = 60 per minute.
2. Rhythm: the pacing spikes are regular (every 0.84 s), but the R–R is not, because a QRS is missing after some spikes.
3. P waves: none visible.
4. PR interval: not measurable.
5. QRS: 0.16 s and wide after the captured spikes; one spike is not followed by a QRS (no capture).

Interpretation

paced rhythm, failure to capture

Answer

paced rhythm, failure to capture

Failure to capture: the pacemaker fires but the heart does not respond. Textbooks treat it as urgent to report, because the patient may depend on the pacemaker.

13.Evidence-based practice statistics

Answer: LR− = 0.15

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.

Negative likelihood ratio

LR− = (1 − 0.87)/0.84 = 0.1548 ≈ 0.15

Answer

LR− = 0.15
14.Evidence-based practice statistics

Answer: NPV = 99.8 %

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 negatives (per person)

Sp·(1 − p) = 0.85·0.995 = 0.8458
(1 − Se)·p = 0.27·0.005 = 0.00135

Negative predictive value

NPV = 0.8458/(0.8458 + 0.00135) = 0.9984 ≈ 99.8%

Answer

NPV = 99.8%

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