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

The sympathetic nervous system leaves the central nervous system from which spinal segments?

  1. ACervical only
  2. BSacral only (S2–S4)
  3. CCranial and sacral
  4. DThoracic and upper lumbar (T1–L2)
2.Human anatomyHard

Which structure passes through the inguinal canal in males?

  1. AGreat saphenous vein
  2. BSpermatic cord
  3. CObturator nerve
  4. DFemoral artery
3.Human physiologyMedium

Which receptors respond mainly to a fall in arterial oxygen levels?

  1. ACentral chemoreceptors in the medulla
  2. BPeripheral chemoreceptors in the carotid and aortic bodies
  3. CStretch receptors in the lungs
  4. DBaroreceptors in the carotid sinus
4.Human physiologyHard

Why can a patient with carbon monoxide poisoning have a normal PaO₂ but severe tissue hypoxia?

  1. ACO lowers the barometric pressure in the alveoli
  2. BCO blocks diffusion across the alveolar wall
  3. CCO stops oxygen from dissolving in plasma
  4. DCO occupies haemoglobin binding sites, so oxygen content falls
5.MicrobiologyMedium

MRSA is resistant to methicillin because it has:

  1. AAn efflux pump for every antibiotic
  2. BNo cell wall at all
  3. CAn altered penicillin-binding protein (PBP2a)
  4. DA polysaccharide capsule that blocks the entry of all beta-lactams
6.MicrobiologyHard

What did Pasteur's swan-neck flask experiment demonstrate?

  1. AMicroorganisms need light to grow
  2. BMicroorganisms come from other microorganisms, not from spontaneous generation
  3. CAir itself produces microorganisms
  4. DBoiling cannot kill microorganisms
7.PharmacologyMedium

A malnourished patient with alcohol dependence needs IV glucose. Which vitamin should be given before or with it?

  1. AThiamine (vitamin B1)
  2. BVitamin C
  3. CVitamin D
  4. DVitamin K (phytomenadione)
8.PharmacologyHard

An older patient who has taken omeprazole for many years has muscle cramps, tremor and an irregular heartbeat. Which lab finding is most likely linked to the drug?

  1. AHigh serum calcium
  2. BLow serum magnesium
  3. CHigh serum sodium
  4. DLow serum glucose
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 18 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 18 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 34 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 34 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval on this lead II strip, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QT = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVatrial flutter, 2:1 conductiontorsades de pointessupraventricular tachycardia (SVT)idioventricular rhythm

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 flutter, 2:1 conduction
  2. 2torsades de pointes
  3. 3supraventricular tachycardia (SVT)
  4. 4idioventricular rhythm
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment101689790abcontrol1892110cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 790 patients received a new treatment and 110 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: 101/790control: 18/110
ARR = %
14.Evidence-based practice statisticsHard
CER38%EER?RRR 33%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 33% in relative terms (RRR = 33%). In a patient group the risk without treatment (CER) is 38% 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 = 33%CER = 38%
NNT =

3Solutions

1.Human anatomy

Answer: D · Thoracic and upper lumbar (T1–L2)

Why this is the answer

Sympathetic preganglionic neurons lie in the lateral horn from T1 to L2. The parasympathetic system has a craniosacral outflow.

Answer

D · Thoracic and upper lumbar (T1–L2)
2.Human anatomy

Answer: B · Spermatic cord

Why this is the answer

The inguinal canal carries the spermatic cord in males and the round ligament in females. The femoral vessels pass below the inguinal ligament instead.

Answer

B · Spermatic cord
3.Human physiology

Answer: B · Peripheral chemoreceptors in the carotid and aortic bodies

Why this is the answer

The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.

Answer

B · Peripheral chemoreceptors in the carotid and aortic bodies
4.Human physiology

Answer: D · CO occupies haemoglobin binding sites, so oxygen content falls

Why this is the answer

CO binds haemoglobin far more strongly than oxygen and shifts the curve left. Dissolved O₂ (PaO₂) is normal, but total oxygen content and release to tissues drop sharply.

Answer

D · CO occupies haemoglobin binding sites, so oxygen content falls
5.Microbiology

Answer: C · An altered penicillin-binding protein (PBP2a)

Why this is the answer

The mecA gene codes for PBP2a, which has low affinity for beta-lactams, so the bacterium can keep building its cell wall despite methicillin.

Answer

C · An altered penicillin-binding protein (PBP2a)
6.Microbiology

Answer: B · Microorganisms come from other microorganisms, not from spontaneous generation

Why this is the answer

Boiled broth in a flask with a curved neck stayed sterile because dust and microbes were trapped in the bend. When the neck was broken, microbes entered and grew, disproving spontaneous generation.

Answer

B · Microorganisms come from other microorganisms, not from spontaneous generation
7.Pharmacology

Answer: A · Thiamine (vitamin B1)

Why this is the answer

Giving glucose without thiamine to a thiamine-deficient patient can trigger or worsen Wernicke's encephalopathy. Thiamine is therefore given before or alongside glucose.

Answer

A · Thiamine (vitamin B1)
8.Pharmacology

Answer: B · Low serum magnesium

Why this is the answer

Long-term PPI use can cause hypomagnesaemia, which leads to cramps, tremor and arrhythmias. Other long-term risks include fractures, vitamin B12 deficiency and C. difficile infection.

Answer

B · Low serum magnesium
9.Arterial blood gas interpretation

Answer: PaCO₂ = 35 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.

Winter’s formula

PaCO₂ = 1.5·18 + 8 = 35 mmHg
range: 33–37 mmHg

Answer

PaCO₂ = 35 mmHg
10.Arterial blood gas interpretation

Answer: PaCO₂ = 44.8 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

0.7·34 + 21 = 44.8 mmHg

Answer

PaCO₂ = 44.8 mmHg

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

11.ECG rhythm strip interpretation

Answer: QT = 0.46 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

11.5 small boxes from the start of the QRS to the end of the T wave

Convert

QT = 11.5 × 0.04 s = 0.46 s

Answer

QT = 0.46 s

A rough rule: at normal rates the QT should be less than half the R–R interval (here R–R = 1.04 s).

12.ECG rhythm strip interpretation

Answer: torsades de pointes

More ventricular rhythms: torsades de pointes is a polymorphic ventricular tachycardia, usually 150–250/min, in which the wide complexes change in height and twist around the baseline, pointing up for a few beats and then down. Textbooks link it to a prolonged QT interval, and magnesium sulfate is the drug resuscitation guidelines name for it. An idioventricular rhythm is a ventricular escape rhythm: regular, wide QRS (0.12 s or more), no P waves, at 20–40/min (an accelerated idioventricular rhythm runs at 40–100/min). Monomorphic VT has identical wide complexes at more than 100/min. VF is chaotic, without any repeating complex.

Five steps

1. Rate: very fast, the complexes are about 6 small boxes apart (about 250 per minute).
2. Rhythm: fast and roughly regular, but the height and direction of the complexes change in a repeating spindle pattern.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: wide and polymorphic; the complexes twist around the baseline, pointing up for a few beats and then down.

Interpretation

torsades de pointes

Answer

torsades de pointes

Torsades de pointes is a polymorphic VT linked to a prolonged QT interval. This is identification practice only.

13.Evidence-based practice statistics

Answer: ARR = 3.6 %

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 = 101/790 = 0.1278
CER = 18/110 = 0.1636

Absolute risk reduction

ARR = 0.1636 − 0.1278 = 0.03579 ≈ 3.6%

Answer

ARR = 3.6%
14.Evidence-based practice statistics

Answer: NNT = 8

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 = 0.38·0.33 = 0.1254

Number needed to treat

NNT = 1/0.1254 = 7.974 → 8

Answer

NNT = 8

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

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