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 pulse is felt just behind the medial malleolus of the ankle?

  1. AFibular artery
  2. BPosterior tibial artery
  3. CDorsalis pedis artery
  4. DPopliteal artery
2.Human anatomyHard

After a fracture of the midshaft of the humerus, a patient cannot extend the wrist and fingers ("wrist drop"). Which nerve is most likely injured?

  1. AAxillary nerve
  2. BRadial nerve
  3. CMedian nerve
  4. DUlnar nerve
3.Human physiologyMedium

Which ion enters the cell to cause the depolarisation phase of a typical neuronal action potential?

  1. AChloride (Cl⁻)
  2. BCalcium (Ca²⁺)
  3. CSodium (Na⁺)
  4. DPotassium (K⁺)
4.Human physiologyHard

A pulmonary embolus blocks blood flow to a well-ventilated region of lung. How does the ventilation–perfusion (V/Q) ratio of that region change?

  1. AIt becomes zero, acting as a shunt
  2. BIt stays normal because ventilation falls too
  3. CIt becomes low, like in pneumonia
  4. DIt becomes very high, acting as dead space
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. BVaccinated people pass antibodies to everyone they meet
  3. CVaccines kill the pathogen in the environment
  4. DFewer people can pass on the infection, so it spreads less
6.MicrobiologyHard

Joseph Lister reduced infection after surgery in the 1860s. What was his main innovation?

  1. AUsing carbolic acid (phenol) as an antiseptic on wounds and instruments
  2. BVaccinating surgeons against staphylococci
  3. CUsing steam autoclaves to sterilise all surgical instruments before each operation
  4. DGiving sulfonamide antibiotics after every operation
7.PharmacologyMedium

A patient must mix regular (soluble) insulin and NPH (isophane) insulin in one syringe. What is the correct order?

  1. ADraw up the cloudy NPH insulin first, then the clear regular insulin
  2. BDraw them up in separate syringes, then mix them in a cup
  3. CDraw up the clear regular insulin first, then the cloudy NPH insulin
  4. DShake both vials hard, then draw them up in any order
8.PharmacologyHard

Ten days after chemotherapy, a patient has a temperature of 38.5 °C (101.3 °F) but says she feels fine. What should happen?

  1. AUrgent cultures and IV broad-spectrum antibiotics without delay
  2. BWait 48 hours to see whether the fever settles
  3. CStart oral antibiotics only if a rash develops
  4. DParacetamol at home and review at the next routine clinic visit
9.Arterial blood gas interpretationMedium
pH7.357.457.11PaCO₂mmHg354579HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.11, PaCO₂ 79 mmHg (10.5 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.11PaCO₂ 79 mmHg (10.5 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 137, Cl⁻ 112, HCO₃⁻ 14 mmol/L and albumin 31 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 137 mmol/LCl⁻ 112 mmol/LHCO₃⁻ 14 mmol/Lalbumin 31 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVaccelerated junctional rhythmatrial flutter, 2:1 conductionsupraventricular tachycardia (SVT)atrial fibrillation

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. 1accelerated junctional rhythm
  2. 2atrial flutter, 2:1 conduction
  3. 3supraventricular tachycardia (SVT)
  4. 4atrial fibrillation
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVthird-degree (complete) AV blockjunctional rhythmsecond-degree AV block type IIsecond-degree AV block type I (Wenckebach)

This lead II strip shows a conduction problem between the atria and the ventricles. 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. 1third-degree (complete) AV block
  2. 2junctional rhythm
  3. 3second-degree AV block type II
  4. 4second-degree AV block type I (Wenckebach)
13.Evidence-based practice statisticsMedium
peopleyears11301.52805new cases4

Practice exercise (made-up values, not clinical guidance). In a cohort, groups of people were followed for different lengths of time (see the table: number of people and years of follow-up for each). During follow-up, 4 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

130 × 1.5 years80 × 5 years4 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
p (%)PPV (%)5%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 71% and a specificity of 83%. It is used in a population where the prevalence is 5%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 71%Sp = 83%p = 5%
PPV = %

3Solutions

1.Human anatomy

Answer: B · Posterior tibial artery

Why this is the answer

The posterior tibial artery passes behind the medial malleolus into the sole. The dorsalis pedis pulse is felt on the top of the foot.

Answer

B · Posterior tibial artery
2.Human anatomy

Answer: B · Radial nerve

Why this is the answer

The radial nerve runs in the radial (spiral) groove of the humeral shaft. It supplies the wrist and finger extensors, so injury causes wrist drop.

Answer

B · Radial nerve
3.Human physiology

Answer: C · Sodium (Na⁺)

Why this is the answer

Voltage-gated Na⁺ channels open and Na⁺ rushes in, depolarising the membrane. K⁺ outflow then repolarises it.

Answer

C · Sodium (Na⁺)
4.Human physiology

Answer: D · It becomes very high, acting as dead space

Why this is the answer

Ventilation without perfusion gives a very high V/Q ratio (dead space). A shunt, such as in pneumonia, is the opposite: perfusion without ventilation.

Answer

D · It becomes very high, acting as dead space
5.Microbiology

Answer: D · 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

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

Answer: A · Using carbolic acid (phenol) as an antiseptic on wounds and instruments

Why this is the answer

Lister applied carbolic acid to wounds, dressings and instruments, which greatly reduced post-operative infection. This started antiseptic surgery.

Answer

A · Using carbolic acid (phenol) as an antiseptic on wounds and instruments
7.Pharmacology

Answer: C · Draw up the clear regular insulin first, then the cloudy NPH insulin

Why this is the answer

Drawing up regular insulin first prevents NPH from contaminating the regular insulin vial. NPH is gently rolled, not shaken, to mix it.

Answer

C · Draw up the clear regular insulin first, then the cloudy NPH insulin
8.Pharmacology

Answer: A · Urgent cultures and IV broad-spectrum antibiotics without delay

Why this is the answer

Fever during neutropenia is treated as a medical emergency because infection can progress rapidly. Cultures are taken and empirical IV antibiotics are started promptly, ideally within one hour.

Answer

A · Urgent cultures and IV broad-spectrum antibiotics without delay
9.Arterial blood gas interpretation

Answer: uncompensated

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 7.11: acidaemia (below 7.35)
PaCO₂ 79 mmHg: high (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: AGc = 13.25 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.

Anion gap

AG = 137 − (112 + 14) = 11

Correction for albumin

11 + 0.25·(40 − 31) = 13.25 mmol/L

Answer

AGc = 13.25 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: supraventricular tachycardia (SVT)

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. Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

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 visible; at this rate they are hidden in the QRS complexes or the T waves.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s), so the rhythm starts above the ventricles.

Interpretation

supraventricular tachycardia (SVT)

Answer

supraventricular tachycardia (SVT)
12.ECG rhythm strip interpretation

Answer: third-degree (complete) AV block

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: R–R = 44 small boxes, 1500 ÷ 44 ≈ 34 per minute.
2. Rhythm: R–R regular (1.76 s) and P–P regular (0.68 s), but the two are independent.
3. P waves: upright and regular at 88 per minute, but not linked to the QRS complexes; some hide in a QRS or a T wave.
4. PR interval: varies from beat to beat; there is no fixed relation.
5. QRS: 0.16 s, wide (0.12 s or more).

Interpretation

third-degree (complete) AV block

Answer

third-degree (complete) AV block

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: IR = 6.7 per 1000 person-years

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.

Person-years

PY = 130·1.5 + 80·5 = 595

Incidence rate

IR = 4/595·1000 = 6.7 per 1000 person-years

Answer

IR = 6.7 per 1000 person-years
14.Evidence-based practice statistics

Answer: PPV = 18 %

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 = 0.71·0.05 = 0.0355
(1 − Sp)·(1 − p) = 0.17·0.95 = 0.1615

Positive predictive value

PPV = 0.0355/(0.0355 + 0.1615) = 0.1802 ≈ 18%

Answer

PPV = 18%

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

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