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 nerve is compressed in carpal tunnel syndrome?

  1. AUlnar nerve
  2. BMusculocutaneous nerve
  3. CRadial nerve
  4. DMedian nerve
2.Human anatomyHard

Where does the thoracic duct usually empty its lymph into the blood?

  1. AInferior vena cava at the level of the kidneys
  2. BJunction of the right subclavian and right internal jugular veins
  3. CRight atrium directly
  4. DJunction of the left subclavian and left internal jugular veins
3.Human physiologyMedium

How is the ejection fraction calculated?

  1. AEnd-systolic volume ÷ stroke volume
  2. BCardiac output ÷ heart rate
  3. CEnd-diastolic volume ÷ end-systolic volume
  4. DStroke volume ÷ end-diastolic volume
4.Human physiologyHard

Why does a deep sea diver risk decompression sickness when surfacing quickly?

  1. AThe lungs collapse when the pressure falls
  2. BNitrogen dissolved at high pressure forms bubbles as the pressure falls
  3. COxygen becomes toxic at the surface
  4. DCarbon dioxide cannot leave the lungs fast enough
5.MicrobiologyMedium

Which organism causes typhoid fever?

  1. AVibrio cholerae
  2. BShigella dysenteriae
  3. CCampylobacter jejuni
  4. DSalmonella Typhi
6.MicrobiologyHard

Corynebacterium diphtheriae causes diphtheria only if it produces diphtheria toxin. When does it make this toxin?

  1. AWhenever it is exposed to antibiotics
  2. BOnly when it is grown at high temperature
  3. CWhen it carries a bacteriophage with the toxin gene
  4. DOnly after it has conjugated with E. coli and received a plasmid
7.PharmacologyMedium

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

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

A patient who has taken lorazepam daily for many months stops it suddenly. Which serious complication may follow?

  1. APinpoint pupils and coma
  2. BWithdrawal seizures
  3. CSevere bradycardia
  4. DProfound respiratory depression
9.Arterial blood gas interpretationMedium
pH7.357.457.53PaCO₂mmHg354551HCO₃⁻mmol/L222641uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.53, PaCO₂ 51 mmHg (6.8 kPa) and HCO₃⁻ 41 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.53PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 41 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 30% oxygen shows PaO₂ 67 mmHg (8.9 kPa) and PaCO₂ 40 mmHg (5.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 30%PaO₂ 67 mmHg (8.9 kPa)PaCO₂ 40 mmHg (5.3 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 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 fibrillationventricular tachycardiatorsades de pointessupraventricular tachycardia (SVT)

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 fibrillation
  2. 2ventricular tachycardia
  3. 3torsades de pointes
  4. 4supraventricular tachycardia (SVT)
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment84616700abcontrol117663780cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 700 patients received a new treatment and 780 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: 84/700control: 117/780
NNT =
14.Evidence-based practice statisticsHard
control6%treatment?

Practice exercise (made-up values, not clinical guidance). Without a drug, 6% of patients have a certain side effect during a year. The drug raises this risk with a relative risk of RR = 2.1. Find the number needed to harm NNH: how many patients must take the drug for a year for one extra patient to have the side effect? Round up to a whole number of patients.

control 6%RR = 2.1
NNH =

3Solutions

1.Human anatomy

Answer: D · Median nerve

Why this is the answer

The median nerve passes through the carpal tunnel under the flexor retinaculum; compression causes tingling in the thumb, index and middle fingers.

Answer

D · Median nerve
2.Human anatomy

Answer: D · Junction of the left subclavian and left internal jugular veins

Why this is the answer

The thoracic duct drains lymph from both legs, the abdomen and the left side of the upper body into the left venous angle. The right lymphatic duct drains the rest into the right venous angle.

Answer

D · Junction of the left subclavian and left internal jugular veins
3.Human physiology

Answer: D · Stroke volume ÷ end-diastolic volume

Why this is the answer

Ejection fraction is the proportion of blood in the full ventricle that is ejected per beat. A normal value is about 55–70%.

Answer

D · Stroke volume ÷ end-diastolic volume
4.Human physiology

Answer: B · Nitrogen dissolved at high pressure forms bubbles as the pressure falls

Why this is the answer

At depth more nitrogen dissolves in the tissues. If pressure falls too fast it comes out of solution as bubbles in tissues and blood, causing "the bends".

Answer

B · Nitrogen dissolved at high pressure forms bubbles as the pressure falls
5.Microbiology

Answer: D · 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

D · Salmonella Typhi
6.Microbiology

Answer: C · When it carries a bacteriophage with the toxin gene

Why this is the answer

The tox gene is carried by a bacteriophage. When the phage is integrated as a prophage, the bacterium can produce toxin. Strains without the phage are non-toxigenic.

Answer

C · When it carries a bacteriophage with the toxin gene
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: B · Withdrawal seizures

Why this is the answer

Abrupt withdrawal after long-term benzodiazepine use causes anxiety, insomnia, tremor and sometimes seizures. Long-term users should have the dose tapered gradually.

Answer

B · Withdrawal seizures
9.Arterial blood gas interpretation

Answer: partially 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 7.53: alkalaemia (above 7.45)
PaCO₂ 51 mmHg: high (35–45)
HCO₃⁻ 41 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 96.9 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 = 0.3·713 − 40/0.8 = 213.9 − 50 = 163.9 mmHg

Gradient

A–a = 163.9 − 67 = 96.9 mmHg

Answer

A–a gradient = 96.9 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.481 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 = 12.5 × 0.04 = 0.50 s
RR = 27 × 0.04 = 1.08 s

Bazett’s formula

QTc = 0.50/√1.08 = 0.50/1.039 = 0.481 s

Answer

QTc = 0.481 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (481 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 = 34

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 = 84/700 = 0.12
CER = 117/780 = 0.15

Number needed to treat

ARR = 0.15 − 0.12 = 0.03
NNT = 1/0.03 = 33.33 → 34

Answer

NNT = 34

Treating 34 patients prevents about one event.

14.Evidence-based practice statistics

Answer: NNH = 16

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.

Risk with the drug

0.06·2.1 = 0.126

Absolute risk increase

ARI = 0.126 − 0.06 = 0.066

Number needed to harm

NNH = 1/0.066 = 15.15 → 16

Answer

NNH = 16

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