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. BPineal gland
  3. CArachnoid granulations
  4. DPia mater
2.Human anatomyHard

Injury to the common fibular (peroneal) nerve at the neck of the fibula typically causes:

  1. ALoss of sensation on the sole of the foot
  2. BWeak hip abduction
  3. CInability to flex the knee
  4. DFoot drop
3.Human physiologyMedium

Which ABO blood group has both anti-A and anti-B antibodies in the plasma?

  1. AGroup O
  2. BGroup AB
  3. CGroup A
  4. DGroup B
4.Human physiologyHard

During exercise, blood flow to active skeletal muscle rises greatly. What is the main cause?

  1. AThe heart pumps blood only to the muscles
  2. BSympathetic stimulation constricts the muscle arterioles via alpha receptors
  3. CThe parasympathetic system dilates all arteries
  4. DLocal metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
5.MicrobiologyMedium

Why does high vaccination coverage also protect babies too young to be vaccinated?

  1. ABabies are naturally immune to all vaccine-preventable diseases
  2. BFewer people can pass on the infection, so it spreads less
  3. CVaccinated people pass antibodies to everyone they meet
  4. DVaccines kill the pathogen in the environment
6.MicrobiologyHard

In 1854 John Snow traced a cholera outbreak in London to the Broad Street water pump. Why is this study important?

  1. AIt showed that cholera spreads through contaminated water, founding modern epidemiology
  2. BIt showed that cholera spreads through "bad air" (miasma)
  3. CIt proved that cholera is caused by a virus
  4. DIt led directly to the first cholera vaccine
7.PharmacologyMedium

Why are benzodiazepines used with great caution in older people?

  1. AThey are not absorbed from the gut after age 65
  2. BThey raise the risk of confusion, falls and fractures
  3. CThey cause severe high blood pressure in older people
  4. DThey cause permanent hearing loss in older people
8.PharmacologyHard

A patient on rifampicin, isoniazid, pyrazinamide and ethambutol develops a painful swollen big toe. Which drug is most likely responsible?

  1. APyrazinamide
  2. BEthambutol
  3. CRifampicin
  4. DIsoniazid
9.Arterial blood gas interpretationMedium
pH7.357.457.49PaCO₂mmHg354526HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.49, PaCO₂ 26 mmHg (3.5 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.49PaCO₂ 26 mmHg (3.5 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 64 mmHg (8.5 kPa) and PaCO₂ 31 mmHg (4.1 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 64 mmHg (8.5 kPa)PaCO₂ 31 mmHg (4.1 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus bradycardiajunctional rhythmatrial fibrillationnormal sinus rhythm

Interpret this lead II rhythm strip. Which rhythm is it? 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 bradycardia
  2. 2junctional rhythm
  3. 3atrial fibrillation
  4. 4normal sinus rhythm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsupraventricular tachycardia (SVT)ventricular fibrillationsinus tachycardiaventricular tachycardia

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. 1supraventricular tachycardia (SVT)
  2. 2ventricular fibrillation
  3. 3sinus tachycardia
  4. 4ventricular tachycardia
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment395585980abcontrol4090130cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 980 patients received a new treatment and 130 received the control treatment. The table shows how many in each group had a side effect. Find the number needed to harm NNH: how many patients must be treated for one extra patient to have the side effect? Round up to a whole number of patients.

treatment: 395/980control: 40/130
NNH =
14.Evidence-based practice statisticsHard
CER9%EER?RRR 17%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 17% in relative terms (RRR = 17%). In a patient group the risk without treatment (CER) is 9% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 17%CER = 9%
NNT =

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: D · Foot drop

Why this is the answer

The common fibular nerve supplies the dorsiflexors and evertors. Damage at the fibular neck causes foot drop and a high-stepping gait. The sole is supplied by the tibial nerve.

Answer

D · Foot drop
3.Human physiology

Answer: A · Group O

Why this is the answer

Group O people have no A or B antigens and make both anti-A and anti-B. Group AB has both antigens and neither antibody.

Answer

A · Group O
4.Human physiology

Answer: D · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles

Why this is the answer

Active hyperaemia: metabolites produced by working muscle relax arteriolar smooth muscle locally, overriding sympathetic vasoconstriction in that tissue.

Answer

D · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
5.Microbiology

Answer: B · Fewer people can pass on the infection, so it spreads less

Why this is the answer

When enough people are immune, chains of transmission break and the pathogen rarely reaches susceptible people, such as young babies or immunosuppressed patients.

Answer

B · Fewer people can pass on the infection, so it spreads less
6.Microbiology

Answer: A · It showed that cholera spreads through contaminated water, founding modern epidemiology

Why this is the answer

Snow mapped cases around the pump and linked them to its water. Removing the pump handle is a classic example of using epidemiology to find and stop a source, before the bacterium was identified.

Answer

A · It showed that cholera spreads through contaminated water, founding modern epidemiology
7.Pharmacology

Answer: B · They raise the risk of confusion, falls and fractures

Why this is the answer

Older people are more sensitive to benzodiazepines and often eliminate them more slowly. Sedation, unsteadiness and confusion raise the risk of falls and fractures.

Answer

B · They raise the risk of confusion, falls and fractures
8.Pharmacology

Answer: A · Pyrazinamide

Why this is the answer

Pyrazinamide reduces uric acid excretion and can cause hyperuricaemia and gout. It is also hepatotoxic, like isoniazid and rifampicin.

Answer

A · Pyrazinamide
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 7.49: alkalaemia (above 7.45)
PaCO₂ 26 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 68.37 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 = 0.24·713 − 31/0.8 = 171.1 − 38.75 = 132.4 mmHg

Gradient

A–a = 132.4 − 64 = 68.37 mmHg

Answer

A–a gradient = 68.37 mmHg
11.ECG rhythm strip interpretation

Answer: junctional rhythm

Rhythm criteria (lead II): sinus rhythm has an upright P wave before every QRS, a constant PR of 0.12–0.20 s and a narrow QRS: normal sinus rhythm at 60–100/min, sinus bradycardia below 60, sinus tachycardia above 100. Atrial fibrillation: no P waves, a fibrillatory baseline and an irregularly irregular R–R. Atrial flutter: sawtooth flutter waves at about 250–350/min with a fixed conduction ratio such as 2:1 or 4:1. First-degree AV block: sinus rhythm with a constant PR above 0.20 s. Junctional rhythm: narrow QRS at 40–60/min with absent or inverted P waves (PR below 0.12 s, or P after the QRS). A PVC is an early, wide (0.12 s or more), bizarre QRS without a P wave, with the T wave in the opposite direction and usually a full compensatory pause; in bigeminy every second beat is a PVC.

Five steps

1. Rate: R–R = 33 small boxes, 1500 ÷ 33 ≈ 45 per minute.
2. Rhythm: regular, every R–R is 1.32 s.
3. P waves: inverted, just before each QRS.
4. PR interval: 0.10 s, shorter than 0.12 s.
5. QRS: 0.10 s, narrow (below 0.12 s).

Interpretation

junctional rhythm

Answer

junctional rhythm
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: 0.16 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: NNH = 11

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 = 395/980 = 0.4031
CER = 40/130 = 0.3077

Number needed to harm

ARI = 0.4031 − 0.3077 = 0.09537
NNH = 1/0.09537 = 10.49 → 11

Answer

NNH = 11

About one in every 11 treated patients has the side effect because of the treatment.

14.Evidence-based practice statistics

Answer: NNT = 66

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.

Absolute risk reduction

ARR = 0.09·0.17 = 0.0153

Number needed to treat

NNT = 1/0.0153 = 65.36 → 66

Answer

NNT = 66

The same relative effect gives a smaller NNT when the baseline risk is higher.

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