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 is the main bundle of nerve fibres connecting the left and right cerebral hemispheres?

  1. ACerebral peduncle
  2. BInternal capsule
  3. CCorpus callosum
  4. DFornix
2.Human anatomyHard

A tumour at the apex of the lung causes drooping of the eyelid, a small pupil and loss of sweating on the same side of the face. Which pathway is disrupted?

  1. AParasympathetic fibres of the vagus
  2. BOculomotor nerve
  3. CFacial nerve
  4. DCervical sympathetic chain
3.Human physiologyMedium

Low plasma albumin, as in severe liver disease, causes oedema mainly because:

  1. AThe capillaries become impermeable
  2. BLymphatic drainage increases
  3. CPlasma oncotic pressure falls
  4. DCapillary hydrostatic pressure falls
4.Human physiologyHard

During exercise, blood flow to active skeletal muscle rises greatly. What is the main cause?

  1. ASympathetic stimulation constricts the muscle arterioles via alpha receptors
  2. BThe parasympathetic system dilates all arteries
  3. CLocal metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
  4. DThe heart pumps blood only to the muscles
5.MicrobiologyMedium

What does an ELISA test detect?

  1. AThe shape of bacteria under the microscope
  2. BSpecific antigens or antibodies, using an enzyme that causes a colour change
  3. CThe DNA sequence of the whole bacterial genome
  4. DBacterial growth on solid agar plates
6.MicrobiologyHard

Why can an HIV antibody test be negative in the first weeks after infection?

  1. AThe antibodies are destroyed by the test reagents
  2. BThe virus hides only in red blood cells during the first weeks
  3. CThe body has not yet produced enough antibodies to detect
  4. DHIV does not trigger antibody production at all
7.PharmacologyMedium

Which advice helps reduce the most common side effect of varenicline?

  1. ATake double doses in the first week
  2. BTake it on an empty stomach at bedtime with a little milk
  3. CTake it after food with a full glass of water
  4. DTake it with alcohol to reduce nausea
8.PharmacologyHard

A baby born to a mother on methadone becomes irritable on day 2, with a high-pitched cry, tremors, sneezing and poor feeding. What is the most likely cause?

  1. AVitamin K deficiency bleeding
  2. BNeonatal opioid withdrawal syndrome
  3. CNeonatal hypoglycaemia from maternal diabetes
  4. DNormal newborn behaviour
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 10 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 10 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.16PaCO₂mmHg354581HCO₃⁻mmol/L222628acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.16, PaCO₂ 81 mmHg (10.8 kPa), HCO₃⁻ 28 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 7.16PaCO₂ 81 mmHg (10.8 kPa)HCO₃⁻ 28 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVventricular bigeminysinus rhythm with PVCsnormal sinus rhythmfirst-degree AV block

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. 1ventricular bigeminy
  2. 2sinus rhythm with PVCs
  3. 3normal sinus rhythm
  4. 4first-degree AV block
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVidioventricular rhythmthird-degree (complete) AV blockdual-chamber (AV) paced rhythmpaced rhythm, failure to capture

This patient has a pacemaker. Interpret the 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. 1idioventricular rhythm
  2. 2third-degree (complete) AV block
  3. 3dual-chamber (AV) paced rhythm
  4. 4paced rhythm, failure to capture
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment32448480abcontrol52418470cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 480 patients received a new treatment and 470 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: 32/480control: 52/470
ARR = %
14.Evidence-based practice statisticsHard
pre-test40%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 40% for a disease. A test with sensitivity 72% and specificity 68% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 40%Se = 72%Sp = 68%positive
p′ = %

3Solutions

1.Human anatomy

Answer: C · Corpus callosum

Why this is the answer

The corpus callosum is the largest commissure, linking matching areas of the two hemispheres. The internal capsule carries projection fibres up and down instead.

Answer

C · Corpus callosum
2.Human anatomy

Answer: D · Cervical sympathetic chain

Why this is the answer

This is Horner's syndrome: ptosis, miosis and anhidrosis from interruption of sympathetic fibres, here by an apical (Pancoast) tumour pressing on the sympathetic chain.

Answer

D · Cervical sympathetic chain
3.Human physiology

Answer: C · Plasma oncotic pressure falls

Why this is the answer

Albumin generates most of the plasma oncotic pressure that pulls fluid back into capillaries. When it falls, more fluid stays in the tissues.

Answer

C · Plasma oncotic pressure falls
4.Human physiology

Answer: C · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles

Why this is the answer

Active hyperaemia: metabolites produced by working muscle relax arteriolar smooth muscle locally, overriding sympathetic vasoconstriction in that tissue.

Answer

C · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
5.Microbiology

Answer: B · Specific antigens or antibodies, using an enzyme that causes a colour change

Why this is the answer

In an enzyme-linked immunosorbent assay, antibodies linked to an enzyme bind the target. Adding the substrate produces a colour, showing whether the antigen or antibody is present.

Answer

B · Specific antigens or antibodies, using an enzyme that causes a colour change
6.Microbiology

Answer: C · The body has not yet produced enough antibodies to detect

Why this is the answer

Antibodies take several weeks to appear. Combined tests that also detect the p24 antigen, or tests for viral RNA, shorten this window period.

Answer

C · The body has not yet produced enough antibodies to detect
7.Pharmacology

Answer: C · Take it after food with a full glass of water

Why this is the answer

Nausea is the most common adverse effect of varenicline and is reduced by taking it after food with water. Patients should also report changes in mood or behaviour.

Answer

C · Take it after food with a full glass of water
8.Pharmacology

Answer: B · Neonatal opioid withdrawal syndrome

Why this is the answer

After birth the baby no longer receives opioid from the mother and develops withdrawal. Assessment uses a scoring tool, with non-drug care first and opioid treatment if signs are severe.

Answer

B · Neonatal opioid withdrawal syndrome
9.Arterial blood gas interpretation

Answer: PaCO₂ = 23 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 = 1.5·10 + 8 = 23 mmHg
range: 21–25 mmHg

Answer

PaCO₂ = 23 mmHg
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 + 1·4.1 = 28.1 mmol/L
chronic: 24 + 3.5·4.1 = 38.35 mmol/L

Compare

measured: 28 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: sinus rhythm with PVCs

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: 9 QRS complexes in 6 s, × 10 = 90 per minute.
2. Rhythm: regular (0.68 s) except for the early beats and the pause after each of them.
3. P waves: upright before every narrow QRS; none before the early wide beats.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.06 s in the sinus beats; the early beats are wide (0.16 s) and bizarre, with the T wave pointing the other way.

Interpretation

sinus rhythm with PVCs

Answer

sinus rhythm with PVCs
12.ECG rhythm strip interpretation

Answer: paced rhythm, failure to capture

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: the pacing spikes are regular (every 0.84 s), but the R–R is not, because a QRS is missing after some spikes.
3. P waves: none visible.
4. PR interval: not measurable.
5. QRS: 0.16 s and wide after the captured spikes; 2 spikes are not followed by a QRS (no capture).

Interpretation

paced rhythm, failure to capture

Answer

paced rhythm, failure to capture

Failure to capture: the pacemaker fires but the heart does not respond. Textbooks treat it as urgent to report, because the patient may depend on the pacemaker.

13.Evidence-based practice statistics

Answer: ARR = 4.4 %

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 = 32/480 = 0.06667
CER = 52/470 = 0.1106

Absolute risk reduction

ARR = 0.1106 − 0.06667 = 0.04397 ≈ 4.4%

Answer

ARR = 4.4%
14.Evidence-based practice statistics

Answer: p′ = 60 %

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+ = 0.72/(1 − 0.68) = 2.25

Pre-test odds

0.4/(1 − 0.4) = 0.6667

Post-test odds

0.6667·2.25 = 1.5

Post-test probability

p′ = 1.5/(1 + 1.5) = 0.6 = 60%

Answer

p′ = 60%

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