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

Besides lowering glucose, insulin moves which ion into cells, an effect used to treat hyperkalaemia?

  1. ACalcium
  2. BPotassium
  3. CSodium
  4. DChloride
4.Human physiologyHard

A patient with diabetic ketoacidosis breathes deeply and rapidly. What pattern is expected on the blood gas?

  1. ALow pH, low bicarbonate and low PaCO₂
  2. BLow pH, normal bicarbonate and high PaCO₂
  3. CHigh pH, low bicarbonate and low PaCO₂
  4. DLow pH, high bicarbonate and high PaCO₂
5.MicrobiologyMedium

Pneumocystis jirovecii pneumonia in a person with advanced HIV is an example of:

  1. AA vector-borne infection
  2. BA food-borne infection
  3. CA zoonotic infection
  4. DAn opportunistic infection
6.MicrobiologyHard

Why can a person get influenza many times but measles usually only once?

  1. AInfluenza attacks and destroys the memory cells formed after infection
  2. BMeasles is caused by a bacterium
  3. CInfluenza viruses change their surface antigens often
  4. DMeasles virus has no surface antigens
7.PharmacologyMedium

A nurse has a needlestick injury from a patient with HIV. When should post-exposure prophylaxis start?

  1. AOnly if the patient's viral load is above a set level
  2. BAfter one week, when the risk of infection is clearer
  3. COnly after the nurse's HIV test turns positive
  4. DAs soon as possible, and within 72 hours at the latest
8.PharmacologyHard

A nurse gave a patient ten times the prescribed dose of hydromorphone. The patient is currently alert. What is the most appropriate sequence of actions?

  1. AMonitor closely, have naloxone ready, inform the prescriber and report
  2. BChange the chart so that it shows the correct dose, and continue to monitor
  3. CGive another dose later to balance it out
  4. DSay nothing because the patient is alert
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 25 mmHg (3.3 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 25 mmHg (3.3 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard
pH7.357.457.26PaCO₂mmHg354571HCO₃⁻mmol/L222631acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.26, PaCO₂ 71 mmHg (9.5 kPa), HCO₃⁻ 31 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.26PaCO₂ 71 mmHg (9.5 kPa)HCO₃⁻ 31 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
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/mVidioventricular rhythmthird-degree (complete) AV blockpaced rhythm, failure to capturedual-chamber (AV) 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. 1idioventricular rhythm
  2. 2third-degree (complete) AV block
  3. 3paced rhythm, failure to capture
  4. 4dual-chamber (AV) paced rhythm
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive180540720abnegative70880950cdtotal25014201670

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 = 180b = 540c = 70d = 880
LR− =
14.Evidence-based practice statisticsHard
p (%)PPV (%)15%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 94% and a specificity of 81%. It is used in a population where the prevalence is 15%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 94%Sp = 81%p = 15%
PPV = %

3Solutions

1.Human anatomy

Answer: C · 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

C · Median cubital vein
2.Human anatomy

Answer: B · 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

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

Answer: B · Potassium

Why this is the answer

Insulin stimulates the Na⁺/K⁺-ATPase and shifts potassium into cells. Insulin with glucose is therefore used to lower dangerously high plasma potassium.

Answer

B · Potassium
4.Human physiology

Answer: A · Low pH, low bicarbonate and low PaCO₂

Why this is the answer

Ketoacids consume bicarbonate, causing metabolic acidosis. Kussmaul breathing lowers PaCO₂ as respiratory compensation.

Answer

A · Low pH, low bicarbonate and low PaCO₂
5.Microbiology

Answer: D · An opportunistic infection

Why this is the answer

Opportunistic infections take advantage of a weakened immune system. In HIV they become common when the CD4 count falls to low levels.

Answer

D · An opportunistic infection
6.Microbiology

Answer: C · Influenza viruses change their surface antigens often

Why this is the answer

Influenza haemagglutinin and neuraminidase change through drift (small mutations) and shift (reassortment), so old antibodies may not recognise new strains. Measles is antigenically stable.

Answer

C · Influenza viruses change their surface antigens often
7.Pharmacology

Answer: D · As soon as possible, and within 72 hours at the latest

Why this is the answer

Post-exposure prophylaxis aims to stop infection becoming established. It works best when started within hours, is not started after 72 hours, and is usually taken for 28 days.

Answer

D · As soon as possible, and within 72 hours at the latest
8.Pharmacology

Answer: A · Monitor closely, have naloxone ready, inform the prescriber and report

Why this is the answer

The patient may become sedated and develop respiratory depression later, so close monitoring and a ready antidote are needed. The prescriber is informed, the patient is told honestly, and the error is reported to improve the system.

Answer

A · Monitor closely, have naloxone ready, inform the prescriber and report
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 21 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

|25 − 40| = 15 mmHg → 1.5 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·1.5 = 21 mmol/L

Answer

HCO₃⁻ = 21 mmol/L
10.Arterial blood gas interpretation

Answer: acute on chronic

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 HCO₃⁻

acute: 24 + 1·3.1 = 27.1 mmol/L
chronic: 24 + 3.5·3.1 = 34.85 mmol/L

Compare

measured: 31 mmol/L → acute on chronic

Answer

acute on chronic
11.ECG rhythm strip interpretation

Answer: QTc = 0.385 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 = 27 × 0.04 = 1.08 s

Bazett’s formula

QTc = 0.40/√1.08 = 0.40/1.039 = 0.385 s

Answer

QTc = 0.385 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (385 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 = 21 small boxes, 1500 ÷ 21 ≈ 71 per minute.
2. Rhythm: regular, every R–R is 0.84 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: 0.16 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− = 0.45

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 = 180/250 = 0.72
Sp = 880/1420 = 0.6197

Negative likelihood ratio

LR− = (1 − 0.72)/0.6197 = 0.4518 ≈ 0.45

Answer

LR− = 0.45
14.Evidence-based practice statistics

Answer: PPV = 46.6 %

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 = 0.94·0.15 = 0.141
(1 − Sp)·(1 − p) = 0.19·0.85 = 0.1615

Positive predictive value

PPV = 0.141/(0.141 + 0.1615) = 0.4661 ≈ 46.6%

Answer

PPV = 46.6%

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

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