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 cranial nerve controls movement of the tongue?

  1. AHypoglossal nerve (XII)
  2. BFacial nerve (VII)
  3. CVagus nerve (X)
  4. DGlossopharyngeal nerve (IX)
2.Human anatomyHard

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

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

Which hormonal event triggers ovulation?

  1. AA surge of luteinising hormone (LH)
  2. BA surge of prolactin
  3. CA rise in progesterone from the corpus luteum
  4. DA fall in oestrogen
4.Human physiologyHard

Why is severe hyperkalaemia dangerous for the heart?

  1. AIt depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
  2. BIt blocks the binding of calcium to troponin
  3. CIt hyperpolarises cardiac cells, so they can never fire
  4. DIt speeds up the SA node until tachycardia causes fainting
5.MicrobiologyMedium

What is the incubation period?

  1. AThe time between infection and the first symptoms
  2. BThe time an antibiotic takes to work
  3. CThe time during which a patient remains infectious to others
  4. DThe time a culture needs in the laboratory
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 led directly to the first cholera vaccine
  3. CIt proved that cholera is caused by a virus
  4. DIt showed that cholera spreads through "bad air" (miasma)
7.PharmacologyMedium

A patient with suspected sepsis has blood cultures ordered and a first antibiotic dose due. What should the nurse do?

  1. AGive the antibiotic only if the temperature is above 40 °C (104 °F)
  2. BGive the antibiotic first, then take blood cultures the next day
  3. CWait for the culture results before giving any antibiotic
  4. DTake the blood cultures first, then give the antibiotic at once
8.PharmacologyHard

A drug has a volume of distribution of 40 L and complete bioavailability. Which loading dose gives a target plasma concentration of 2 mg/L?

  1. A80 mg
  2. B160 mg
  3. C42 mg
  4. D20 mg
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 22 mmHg (2.9 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 22 mmHg (2.9 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 39 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 39 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationjunctional rhythmsinus rhythm with PVCsatrial flutter, 4:1 conduction

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. 1atrial fibrillation
  2. 2junctional rhythm
  3. 3sinus rhythm with PVCs
  4. 4atrial flutter, 4:1 conduction
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
eventno eventtotaltreatment27143170abcontrol93197290cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 170 patients received a new treatment and 290 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the absolute risk reduction ARR as a percentage. Round to one decimal place.

treatment: 27/170control: 93/290
ARR = %
14.Evidence-based practice statisticsHard
CER18%EER?RRR 35%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 35% in relative terms (RRR = 35%). In a patient group the risk without treatment (CER) is 18% 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 = 35%CER = 18%
NNT =

3Solutions

1.Human anatomy

Answer: A · Hypoglossal nerve (XII)

Why this is the answer

The hypoglossal nerve supplies the intrinsic and most extrinsic tongue muscles. A lesion makes the protruded tongue deviate towards the affected side.

Answer

A · Hypoglossal nerve (XII)
2.Human anatomy

Answer: C · 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

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

Answer: A · A surge of luteinising hormone (LH)

Why this is the answer

Rising oestrogen from the dominant follicle triggers an LH surge from the anterior pituitary, which causes ovulation about a day later.

Answer

A · A surge of luteinising hormone (LH)
4.Human physiology

Answer: A · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias

Why this is the answer

High extracellular potassium makes the resting potential less negative. Many fast sodium channels then become inactivated, slowing conduction and risking fatal arrhythmias.

Answer

A · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
5.Microbiology

Answer: A · The time between infection and the first symptoms

Why this is the answer

The incubation period runs from exposure to the onset of symptoms. People can sometimes already transmit the infection during it.

Answer

A · The time between infection and the first symptoms
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: D · Take the blood cultures first, then give the antibiotic at once

Why this is the answer

Cultures are taken before antibiotics so the organism can be identified, but antibiotics must not be delayed in sepsis. Taking cultures quickly and then giving the antibiotic meets both aims.

Answer

D · Take the blood cultures first, then give the antibiotic at once
8.Pharmacology

Answer: A · 80 mg

Why this is the answer

Loading dose = 40 L × 2 mg/L = 80 mg. The loading dose depends on Vd, while the maintenance dose depends on clearance.

Answer

A · 80 mg
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 20.4 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

|22 − 40| = 18 mmHg → 1.8 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·1.8 = 20.4 mmol/L

Answer

HCO₃⁻ = 20.4 mmol/L
10.Arterial blood gas interpretation

Answer: PaCO₂ = 48.3 mmHg

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 PaCO₂

0.7·39 + 21 = 48.3 mmHg

Answer

PaCO₂ = 48.3 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: atrial fibrillation

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: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: irregularly irregular, R–R from 0.56 to 0.98 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.10 s, narrow (below 0.12 s).

Interpretation

atrial fibrillation

Answer

atrial fibrillation
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: 7 QRS complexes in 6 s, × 10 = 70 per minute.
2. Rhythm: irregularly irregular, R–R from 0.62 to 0.96 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: ARR = 16.2 %

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 = 27/170 = 0.1588
CER = 93/290 = 0.3207

Absolute risk reduction

ARR = 0.3207 − 0.1588 = 0.1619 ≈ 16.2%

Answer

ARR = 16.2%
14.Evidence-based practice statistics

Answer: NNT = 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.

Absolute risk reduction

ARR = 0.18·0.35 = 0.063

Number needed to treat

NNT = 1/0.063 = 15.87 → 16

Answer

NNT = 16

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

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