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 structure produces most of the cerebrospinal fluid?

  1. AChoroid plexus
  2. BPia mater
  3. CArachnoid granulations
  4. DPineal gland
2.Human anatomyHard

Which muscle "unlocks" the fully extended knee by rotating the femur laterally on the tibia at the start of flexion?

  1. ASartorius
  2. BPopliteus
  3. CBiceps femoris
  4. DGastrocnemius
3.Human physiologyMedium

How does glucagon raise blood glucose?

  1. AIt blocks insulin receptors on fat cells
  2. BIt stimulates glycogen breakdown and gluconeogenesis in the liver
  3. CIt slows glucose absorption from the gut
  4. DIt stimulates glucose uptake by muscle
4.Human physiologyHard

What is the main reason the ventricles do not contract at the same moment as the atria?

  1. AThe SA node fires twice per beat
  2. BThe Purkinje fibres conduct slowly
  3. CThe ventricles have a longer refractory period only
  4. DConduction is delayed at the atrioventricular node
5.MicrobiologyMedium

Which organism causes typhoid fever?

  1. AVibrio cholerae
  2. BSalmonella Typhi
  3. CShigella dysenteriae
  4. DCampylobacter jejuni
6.MicrobiologyHard

A healthcare worker's blood test is positive for anti-HBs (hepatitis B surface antibody) and negative for HBsAg and anti-HBc. What does this most likely mean?

  1. ACurrent acute hepatitis B infection
  2. BPast natural infection that has cleared
  3. CChronic hepatitis B infection
  4. DImmunity from hepatitis B vaccination
7.PharmacologyMedium

When should a patient take a once-daily proton pump inhibitor such as omeprazole?

  1. AWith a glass of milk at bedtime, when acid output is highest
  2. BOnly when heartburn is severe
  3. CStraight after a large evening meal
  4. DAbout 30–60 minutes before the first meal of the day
8.PharmacologyHard

In aspirin overdose the urine may be made alkaline with sodium bicarbonate. Why does this increase salicylate excretion?

  1. AAlkaline urine increases glomerular filtration
  2. BBicarbonate binds salicylate and makes it inactive
  3. CMore salicylate is ionised in the tubule, so less is reabsorbed
  4. DBicarbonate speeds up the liver metabolism of salicylate to inactive forms
9.Arterial blood gas interpretationMedium
pH7.357.457.42PaCO₂mmHg354549HCO₃⁻mmol/L222631uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.42, PaCO₂ 49 mmHg (6.5 kPa) and HCO₃⁻ 31 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.42PaCO₂ 49 mmHg (6.5 kPa)HCO₃⁻ 31 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.15PaCO₂mmHg354550HCO₃⁻mmol/L222617appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.15, PaCO₂ 50 mmHg (6.7 kPa), HCO₃⁻ 17 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.15PaCO₂ 50 mmHg (6.7 kPa)HCO₃⁻ 17 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/mVthird-degree (complete) AV blockjunctional rhythmdual-chamber (AV) paced rhythmidioventricular 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. 1third-degree (complete) AV block
  2. 2junctional rhythm
  3. 3dual-chamber (AV) paced rhythm
  4. 4idioventricular rhythm
13.Evidence-based practice statisticsMedium
Se90%Sp96%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 90% and a specificity of 96%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 90%Sp = 96%
LR− =
14.Evidence-based practice statisticsHard
p (%)PPV (%)30%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 80% and a specificity of 89%. It is used in a population where the prevalence is 30%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 80%Sp = 89%p = 30%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

A · Choroid plexus
2.Human anatomy

Answer: B · Popliteus

Why this is the answer

At full extension the knee locks by medial rotation of the femur. Popliteus laterally rotates the femur on the fixed tibia to unlock it so flexion can begin.

Answer

B · Popliteus
3.Human physiology

Answer: B · It stimulates glycogen breakdown and gluconeogenesis in the liver

Why this is the answer

Glucagon from alpha cells acts on the liver to break down glycogen and make new glucose from non-carbohydrate sources.

Answer

B · It stimulates glycogen breakdown and gluconeogenesis in the liver
4.Human physiology

Answer: D · Conduction is delayed at the atrioventricular node

Why this is the answer

The AV node conducts slowly (about 0.1 s delay), so atrial contraction completes ventricular filling before ventricular depolarisation begins.

Answer

D · Conduction is delayed at the atrioventricular node
5.Microbiology

Answer: B · Salmonella Typhi

Why this is the answer

Salmonella enterica serotype Typhi causes typhoid fever, a systemic illness with prolonged fever. Some people become chronic carriers, often in the gallbladder.

Answer

B · Salmonella Typhi
6.Microbiology

Answer: D · Immunity from hepatitis B vaccination

Why this is the answer

The vaccine contains HBsAg, so a vaccinated person makes anti-HBs but no anti-HBc. Past natural infection gives both anti-HBs and anti-HBc, and ongoing infection shows HBsAg.

Answer

D · Immunity from hepatitis B vaccination
7.Pharmacology

Answer: D · About 30–60 minutes before the first meal of the day

Why this is the answer

Proton pump inhibitors block pumps that are active, so they work best when taken before breakfast. Food then activates the pumps when the drug level is high.

Answer

D · About 30–60 minutes before the first meal of the day
8.Pharmacology

Answer: C · More salicylate is ionised in the tubule, so less is reabsorbed

Why this is the answer

Salicylate is a weak acid. In alkaline urine more of it is in the ionised form, which is "trapped" in the tubule and excreted. This is called ion trapping.

Answer

C · More salicylate is ionised in the tubule, so less is reabsorbed
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 7.42: within 7.35–7.45
PaCO₂ 49 mmHg: high (35–45)
HCO₃⁻ 31 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 40.7–44.7 mmHg, so the measured 49 mmHg points to an additional respiratory acidosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
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

1.5·17 + 8 = 33.5 → 31.5–35.5 mmHg

Compare

measured: 50 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
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: dual-chamber (AV) 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 = 22 small boxes, 1500 ÷ 22 ≈ 68 per minute.
2. Rhythm: regular, every R–R is 0.88 s.
3. P waves: each P wave follows its own pacing spike (atrial pacing).
4. AV interval: the second spike comes 0.16 s after the first one (the programmed AV delay).
5. QRS: 0.14 s, wide, right after the second spike (ventricular pacing).

Interpretation

dual-chamber (AV) paced rhythm

Answer

dual-chamber (AV) 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− = 0.1

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 − 0.9)/0.96 = 0.1042 ≈ 0.1

Answer

LR− = 0.1
14.Evidence-based practice statistics

Answer: PPV = 75.7 %

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 = 0.8·0.3 = 0.24
(1 − Sp)·(1 − p) = 0.11·0.7 = 0.077

Positive predictive value

PPV = 0.24/(0.24 + 0.077) = 0.7571 ≈ 75.7%

Answer

PPV = 75.7%

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

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