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 superficial vein in the front of the elbow is most often used for venepuncture?

  1. AMedian cubital vein
  2. BBrachial vein
  3. CAxillary vein
  4. DGreat saphenous vein
2.Human anatomyHard

A typical posterolateral disc herniation between L4 and L5 most often compresses which nerve root?

  1. AL4
  2. BS1
  3. CL5
  4. DL3
3.Human physiologyMedium

Which cells in the stomach secrete hydrochloric acid?

  1. AChief cells
  2. BG cells
  3. CParietal cells
  4. DGoblet cells
4.Human physiologyHard

A young woman has muscle weakness that gets worse with repeated use and improves with an acetylcholinesterase inhibitor. What is the most likely mechanism?

  1. AA defect in the dystrophin protein of muscle
  2. BDemyelination of central nervous system tracts
  3. CLoss of motor neurons in the spinal cord
  4. DAntibodies against acetylcholine receptors at the neuromuscular junction
5.MicrobiologyMedium

Which antibody class is the first to rise in a new infection?

  1. AIgG
  2. BIgA
  3. CIgE
  4. DIgM
6.MicrobiologyHard

Primary syphilis typically presents with:

  1. ADamage to the heart and brain
  2. BA painless ulcer (chancre) at the site of infection
  3. CA widespread rash on the palms and soles
  4. DA painful cluster of small blisters on the genitals or the mouth
7.PharmacologyMedium

Which technique is correct when giving subcutaneous enoxaparin from a prefilled syringe?

  1. AInject into the abdomen away from the navel and do not rub the site afterwards
  2. BMassage the site well for one minute after the injection
  3. CInject into a vein on the back of the hand
  4. DExpel the air bubble from the syringe first, then inject into the deltoid muscle
8.PharmacologyHard

A patient with severe chronic hyponatraemia receives hypertonic saline. Why is the rate of correction strictly limited?

  1. ARaising sodium too fast causes severe hypokalaemia and cardiac arrest
  2. BFast correction causes immediate kidney failure
  3. CRaising sodium too fast can cause osmotic demyelination in the brain
  4. DHypertonic saline is toxic to the liver at high rates
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 64 mmHg (8.5 kPa). Use the rule that in chronic respiratory acidosis HCO₃⁻ rises by 3.5 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 64 mmHg (8.5 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard
pH7.357.457.28PaCO₂mmHg354524HCO₃⁻mmol/L222611added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.28, PaCO₂ 24 mmHg (3.2 kPa) and HCO₃⁻ 11 mmol/L, with Na⁺ 132 and Cl⁻ 86 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.28PaCO₂ 24 mmHg (3.2 kPa)HCO₃⁻ 11 mmol/LNa⁺ 132 mmol/LCl⁻ 86 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 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/mVsinus rhythm with wide QRSpaced rhythm, failure to captureidioventricular rhythmventricular paced rhythm

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. 1sinus rhythm with wide QRS
  2. 2paced rhythm, failure to capture
  3. 3idioventricular rhythm
  4. 4ventricular paced rhythm
13.Evidence-based practice statisticsMedium
Se88%Sp68%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 88% and a specificity of 68%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 88%Sp = 68%
LR− =
14.Evidence-based practice statisticsHard
p (%)PPV (%)3%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 90% and a specificity of 83%. It is used in a population where the prevalence is 3%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 90%Sp = 83%p = 3%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Median cubital vein

Why this is the answer

The median cubital vein crosses the cubital fossa between the cephalic and basilic veins. It is superficial, large and fairly fixed, so it is easy to puncture.

Answer

A · Median cubital vein
2.Human anatomy

Answer: C · L5

Why this is the answer

A posterolateral L4–L5 herniation usually catches the traversing L5 root, causing weakness of big toe extension and numbness on the top of the foot.

Answer

C · L5
3.Human physiology

Answer: C · Parietal cells

Why this is the answer

Parietal cells secrete HCl and intrinsic factor. Chief cells secrete pepsinogen and G cells secrete gastrin.

Answer

C · Parietal cells
4.Human physiology

Answer: D · Antibodies against acetylcholine receptors at the neuromuscular junction

Why this is the answer

In myasthenia gravis, autoantibodies reduce the number of functional acetylcholine receptors. Blocking acetylcholinesterase leaves more ACh to bind the remaining receptors.

Answer

D · Antibodies against acetylcholine receptors at the neuromuscular junction
5.Microbiology

Answer: D · IgM

Why this is the answer

IgM appears first in a primary response; IgG follows and provides long-term protection. A positive IgM therefore suggests recent infection.

Answer

D · IgM
6.Microbiology

Answer: B · A painless ulcer (chancre) at the site of infection

Why this is the answer

Treponema pallidum causes a painless chancre in the primary stage. The secondary stage brings rash and systemic symptoms, and tertiary syphilis can damage the heart and nervous system. Painful blisters suggest herpes.

Answer

B · A painless ulcer (chancre) at the site of infection
7.Pharmacology

Answer: A · Inject into the abdomen away from the navel and do not rub the site afterwards

Why this is the answer

Enoxaparin is given deep subcutaneously, usually in the abdomen at least 5 cm from the umbilicus. The air bubble in the prefilled syringe is not expelled, and rubbing the site increases bruising.

Answer

A · Inject into the abdomen away from the navel and do not rub the site afterwards
8.Pharmacology

Answer: C · Raising sodium too fast can cause osmotic demyelination in the brain

Why this is the answer

In chronic hyponatraemia the brain adapts to low osmolality. Correcting sodium too rapidly shrinks brain cells and can cause osmotic demyelination (central pontine myelinolysis), so sodium is checked often.

Answer

C · Raising sodium too fast can cause osmotic demyelination in the brain
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 32.4 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

|64 − 40| = 24 mmHg → 2.4 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 3.5·2.4 = 32.4 mmol/L

Answer

HCO₃⁻ = 32.4 mmol/L
10.Arterial blood gas interpretation

Answer: pure high-gap 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.

Anion gap

AG = 132 − (86 + 11) = 35

Delta ratio

(35 − 12)/(24 − 11) = 1.769
pure high-gap acidosis

Answer

pure high-gap acidosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.488 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 = 11.5 × 0.04 = 0.46 s
RR = 21 × 0.04 = 0.84 s

Fridericia’s formula

QTc = 0.46/∛0.84 = 0.46/0.9435 = 0.488 s

Answer

QTc = 0.488 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (488 ms)

12.ECG rhythm strip interpretation

Answer: ventricular paced rhythm

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: R–R = 21 small boxes, 1500 ÷ 21 ≈ 71 per minute.
2. Rhythm: regular, every R–R is 0.84 s.
3. P waves: none visible; a sharp pacing spike comes just before every QRS.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide, and every spike is followed by a QRS (capture).

Interpretation

ventricular paced rhythm

Answer

ventricular paced rhythm

The paced QRS is wide by nature; do not call it a bundle branch block or a ventricular rhythm.

13.Evidence-based practice statistics

Answer: LR− = 0.18

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 − 0.88)/0.68 = 0.1765 ≈ 0.18

Answer

LR− = 0.18
14.Evidence-based practice statistics

Answer: PPV = 14.1 %

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 positives (per person)

Se·p = 0.9·0.03 = 0.027
(1 − Sp)·(1 − p) = 0.17·0.97 = 0.1649

Positive predictive value

PPV = 0.027/(0.027 + 0.1649) = 0.1407 ≈ 14.1%

Answer

PPV = 14.1%

The lower the prevalence, the lower the PPV of the same test.

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