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 connects the middle ear to the nasopharynx?

  1. AExternal acoustic meatus
  2. BCochlear duct
  3. CAuditory (Eustachian) tube
  4. DNasolacrimal duct
2.Human anatomyHard

Which coronary artery most often supplies the sinoatrial (SA) node?

  1. ALeft anterior descending artery
  2. BCircumflex artery
  3. CLeft main coronary artery
  4. DRight coronary artery
3.Human physiologyMedium

Where is the heart's natural pacemaker?

  1. APurkinje fibres
  2. BSinoatrial node
  3. CAtrioventricular node
  4. DBundle of His
4.Human physiologyHard

Which spirometry finding is typical of chronic obstructive pulmonary disease (COPD)?

  1. AIncreased peak expiratory flow
  2. BFEV1/FVC ratio above 0.9 with low FVC
  3. CFEV1/FVC ratio below 0.7
  4. DNormal FEV1 with low FVC
5.MicrobiologyMedium

Why are Gram-negative bacteria often harder to treat with antibiotics?

  1. AThey have a thicker peptidoglycan layer
  2. BThey divide much more slowly
  3. CTheir outer membrane blocks many drugs
  4. DThey have no ribosomes
6.MicrobiologyHard

What is the key difference between bactericidal and bacteriostatic antibiotics?

  1. ABactericidal drugs work only on viruses; bacteriostatic drugs work on bacteria
  2. BBactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
  3. CBacteriostatic drugs always work faster than bactericidal drugs
  4. DBactericidal drugs work only outside the body
7.PharmacologyMedium

How are most medication doses for children calculated?

  1. ABy giving half of the adult dose to all children under 12
  2. BBy body weight in kilograms, or sometimes body surface area
  3. CBy the child's height alone
  4. DBy the child's age in years only
8.PharmacologyHard

A patient on digoxin is started on amiodarone. What change should the nurse expect?

  1. ANo interaction is expected
  2. BDigoxin levels fall sharply, so the digoxin dose is doubled
  3. CAmiodarone levels fall to zero
  4. DDigoxin levels rise, so the digoxin dose is often reduced
9.Arterial blood gas interpretationMedium
pH7.357.457.50PaCO₂mmHg354524HCO₃⁻mmol/L222618uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.50, PaCO₂ 24 mmHg (3.2 kPa) and HCO₃⁻ 18 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.50PaCO₂ 24 mmHg (3.2 kPa)HCO₃⁻ 18 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 141, Cl⁻ 112, HCO₃⁻ 12 mmol/L and albumin 28 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 141 mmol/LCl⁻ 112 mmol/LHCO₃⁻ 12 mmol/Lalbumin 28 g/L
AGc = mmol/L
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/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
peopleyears1590522103new cases50

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, 50 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

590 × 5 years210 × 3 years50 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
pre-test30%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 30% for a disease. A test with sensitivity 71% and specificity 69% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 30%Se = 71%Sp = 69%positive
p′ = %

3Solutions

1.Human anatomy

Answer: C · Auditory (Eustachian) tube

Why this is the answer

The auditory tube equalises air pressure on both sides of the eardrum. In children it is shorter and more horizontal, which favours middle ear infections.

Answer

C · Auditory (Eustachian) tube
2.Human anatomy

Answer: D · Right coronary artery

Why this is the answer

The SA nodal artery arises from the right coronary artery in roughly 60% of people and from the circumflex artery in the rest.

Answer

D · Right coronary artery
3.Human physiology

Answer: B · Sinoatrial node

Why this is the answer

The SA node depolarises spontaneously at the fastest rate and sets the heart rhythm. The AV node delays the impulse before it spreads to the ventricles.

Answer

B · Sinoatrial node
4.Human physiology

Answer: C · FEV1/FVC ratio below 0.7

Why this is the answer

Narrowed airways slow expiration, so FEV1 falls more than FVC and the ratio drops below 0.7. In COPD this is not fully reversed by bronchodilators.

Answer

C · FEV1/FVC ratio below 0.7
5.Microbiology

Answer: C · Their outer membrane blocks many drugs

Why this is the answer

The outer membrane of Gram-negative bacteria, with lipopolysaccharide and porins, keeps many antibiotics out and adds efflux and enzyme defences.

Answer

C · Their outer membrane blocks many drugs
6.Microbiology

Answer: B · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them

Why this is the answer

Bacteriostatic drugs halt multiplication so host defences can eliminate the bacteria. Bactericidal drugs are preferred when defences are weak or hard to reach, such as in endocarditis or neutropenia.

Answer

B · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
7.Pharmacology

Answer: B · By body weight in kilograms, or sometimes body surface area

Why this is the answer

Children's doses are usually weight-based, sometimes using body surface area, and must not exceed the adult maximum. Accurate, recent weight in kilograms is essential.

Answer

B · By body weight in kilograms, or sometimes body surface area
8.Pharmacology

Answer: D · Digoxin levels rise, so the digoxin dose is often reduced

Why this is the answer

Amiodarone inhibits P-glycoprotein and reduces digoxin clearance, so digoxin levels rise. The digoxin dose is often reduced, and the patient is monitored for bradycardia and toxicity; amiodarone also raises warfarin levels.

Answer

D · Digoxin levels rise, so the digoxin dose is often reduced
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 7.50: alkalaemia (above 7.45)
PaCO₂ 24 mmHg: low (35–45)
HCO₃⁻ 18 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: AGc = 20 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 = 141 − (112 + 12) = 17

Correction for albumin

17 + 0.25·(40 − 28) = 20 mmol/L

Answer

AGc = 20 mmol/L

Above about 12 after correction: a high anion gap.

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 = 10 × 0.04 = 0.40 s
RR = 25 × 0.04 = 1.00 s

Bazett’s formula

QTc = 0.40/√1.00 = 0.40/1 = 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: rhythm

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: irregularly irregular, R–R from 0.64 to 0.94 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s).

First abnormal step

rhythm → atrial fibrillation

Answer

rhythm
13.Evidence-based practice statistics

Answer: IR = 14 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 = 590·5 + 210·3 = 3580

Incidence rate

IR = 50/3580·1000 = 14 per 1000 person-years

Answer

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

Answer: p′ = 49.5 %

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.

Likelihood ratio

LR+ = 0.71/(1 − 0.69) = 2.29

Pre-test odds

0.3/(1 − 0.3) = 0.4286

Post-test odds

0.4286·2.29 = 0.9816

Post-test probability

p′ = 0.9816/(1 + 0.9816) = 0.4953 ≈ 49.5%

Answer

p′ = 49.5%

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