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 nerve supplies the diaphragm?

  1. AAccessory nerve
  2. BPhrenic nerve
  3. CIntercostal nerves
  4. DVagus nerve
2.Human anatomyHard

Which ligament of the knee prevents the tibia from sliding forward relative to the femur?

  1. AAnterior cruciate ligament
  2. BPatellar ligament
  3. CMedial collateral ligament
  4. DPosterior cruciate ligament
3.Human physiologyMedium

Why do myelinated axons conduct action potentials faster than unmyelinated ones?

  1. AMyelin contains more sodium channels
  2. BMyelin makes the axon thinner
  3. CMyelin releases neurotransmitter along the axon
  4. DThe impulse jumps between nodes of Ranvier
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 very high, acting as dead space
  4. DIt becomes low, like in pneumonia
5.MicrobiologyMedium

Which is a function of the complement system?

  1. AMaking new red blood cells
  2. BProducing antibodies against newly encountered antigens
  3. CPresenting antigens to T cells
  4. DForming pores in the membranes of some bacteria
6.MicrobiologyHard

After eating home-canned vegetables, a patient develops double vision, difficulty swallowing and a descending flaccid paralysis. What is the most likely cause?

  1. AA viral infection of the motor neurons
  2. BEndotoxin from Gram-negative bacteria
  3. CBotulinum toxin, which blocks acetylcholine release
  4. DTetanus toxin, which blocks inhibitory neurotransmitters
7.PharmacologyMedium

After instilling eye drops, why should the patient press gently on the inner corner of the eye for a minute or two?

  1. ATo spread the drop evenly over the eyelid
  2. BTo reduce drainage into the nose and absorption into blood
  3. CTo make the pupil dilate faster
  4. DTo stop the eye from producing tears for about an hour
8.PharmacologyHard

Why is intravenous insulin given with glucose in severe hyperkalaemia?

  1. AInsulin moves potassium from the blood into cells
  2. BGlucose binds potassium in the blood
  3. CInsulin protects the heart muscle directly from potassium
  4. DInsulin increases potassium excretion by the kidney
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 22 mmHg (2.9 kPa). Use the rule that in chronic respiratory alkalosis HCO₃⁻ falls by 5 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
pH7.357.457.23PaCO₂mmHg354566HCO₃⁻mmol/L222627acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.23, PaCO₂ 66 mmHg (8.8 kPa), HCO₃⁻ 27 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.23PaCO₂ 66 mmHg (8.8 kPa)HCO₃⁻ 27 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

This lead II strip shows atrial flutter with a fixed conduction ratio. Find the ventricular rate in beats per minute.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
ventricular rate = bpm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVasystolesinus tachycardiapulseless electrical activity (PEA)ventricular fibrillation

A monitored patient is found unresponsive and not breathing normally, and no carotid pulse can be felt. The monitor shows this organised rhythm. What is this situation called? 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. 1asystole
  2. 2sinus tachycardia
  3. 3pulseless electrical activity (PEA)
  4. 4ventricular fibrillation
13.Evidence-based practice statisticsMedium
casescontrolsexposed238103abnot exposed7277cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 310 patients with a disease (cases) and 180 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 238b = 103c = 72d = 77
OR =
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 82%. 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 = 82%p = 5%
PPV = %

3Solutions

1.Human anatomy

Answer: B · Phrenic nerve

Why this is the answer

The phrenic nerve (roots C3–C5) is the motor supply to the diaphragm. High cervical cord injury above C3 therefore stops spontaneous breathing.

Answer

B · Phrenic nerve
2.Human anatomy

Answer: A · Anterior cruciate ligament

Why this is the answer

The anterior cruciate ligament limits anterior translation of the tibia; a positive anterior drawer or Lachman test suggests an ACL tear.

Answer

A · Anterior cruciate ligament
3.Human physiology

Answer: D · The impulse jumps between nodes of Ranvier

Why this is the answer

Myelin insulates the axon, so action potentials are only generated at the nodes of Ranvier. This saltatory conduction is much faster.

Answer

D · The impulse jumps between nodes of Ranvier
4.Human physiology

Answer: C · 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

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

Answer: D · Forming pores in the membranes of some bacteria

Why this is the answer

Complement proteins coat microbes for phagocytosis (opsonisation), attract immune cells and form the membrane attack complex that punches holes in some bacteria.

Answer

D · Forming pores in the membranes of some bacteria
6.Microbiology

Answer: C · Botulinum toxin, which blocks acetylcholine release

Why this is the answer

Clostridium botulinum can grow in poorly canned, low-acid foods and produce botulinum toxin. The toxin blocks acetylcholine release at nerve endings, causing descending flaccid paralysis.

Answer

C · Botulinum toxin, which blocks acetylcholine release
7.Pharmacology

Answer: B · To reduce drainage into the nose and absorption into blood

Why this is the answer

Nasolacrimal occlusion keeps the drop in the eye longer and reduces systemic absorption through the nasal mucosa. This matters for drugs such as timolol, which can cause bradycardia or bronchospasm.

Answer

B · To reduce drainage into the nose and absorption into blood
8.Pharmacology

Answer: A · Insulin moves potassium from the blood into cells

Why this is the answer

Insulin activates the Na⁺/K⁺-ATPase and drives potassium into cells, lowering plasma levels within minutes. Glucose is given to prevent hypoglycaemia. The effect is temporary; potassium must still be removed from the body.

Answer

A · Insulin moves potassium from the blood into cells
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 15 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 − 5·1.8 = 15 mmol/L

Answer

HCO₃⁻ = 15 mmol/L
10.Arterial blood gas interpretation

Answer: acute

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 HCO₃⁻

acute: 24 + 1·2.6 = 26.6 mmol/L
chronic: 24 + 3.5·2.6 = 33.1 mmol/L

Compare

measured: 27 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: ventricular rate = 150 bpm

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.

Flutter waves

F–F = 5 small boxes = 0.20 s → 1500 ÷ 5 = 300 per minute

QRS complexes

R–R = 10 small boxes = 0.40 s → 1500 ÷ 10 = 150 per minute
conduction ratio = 300 ÷ 150 = 2:1

Answer

ventricular rate = 150 bpm
12.ECG rhythm strip interpretation

Answer: pulseless electrical activity (PEA)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

1. Rate: R–R = 12 small boxes, 1500 ÷ 12 ≈ 125 per minute.
2. Rhythm: regular, every R–R is 0.48 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.06 s, narrow (below 0.12 s).
sinus tachycardia

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

pulseless electrical activity (PEA)

Answer

pulseless electrical activity (PEA)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: OR = 2.47

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.

Odds of exposure

cases: 238/72 = 3.306
controls: 103/77 = 1.338

Odds ratio

OR = (238·77)/(103·72) = 2.471 ≈ 2.47

Answer

OR = 2.47

OR above 1: exposure is more common among the cases.

14.Evidence-based practice statistics

Answer: PPV = 17.2 %

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) = 0.18·0.95 = 0.171

Positive predictive value

PPV = 0.0355/(0.0355 + 0.171) = 0.1719 ≈ 17.2%

Answer

PPV = 17.2%

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

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