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. ACorpus callosum
  2. BCerebral peduncle
  3. CInternal capsule
  4. DFornix
2.Human anatomyHard

After an injury at the medial epicondyle of the elbow, a patient has numbness of the little finger and weakness of finger abduction. Which nerve is affected?

  1. AUlnar nerve
  2. BRadial nerve
  3. CMedian nerve
  4. DMusculocutaneous nerve
3.Human physiologyMedium

Which protein forms the mesh that stabilises a blood clot?

  1. AAlbumin
  2. BThrombin
  3. CCollagen
  4. DFibrin
4.Human physiologyHard

Constriction of the efferent arteriole of a glomerulus, with the afferent arteriole unchanged, tends to:

  1. AHave no effect on GFR at all
  2. BStop filtration completely
  3. CLower glomerular capillary pressure and GFR
  4. DRaise glomerular capillary pressure and GFR
5.MicrobiologyMedium

Cholera causes profuse "rice-water" diarrhoea. What is the most important treatment?

  1. AReplacing fluid and salts by oral or intravenous rehydration
  2. BStopping all oral fluid intake so that the bowel can rest and recover
  3. CAntifungal drugs
  4. DAntiviral drugs
6.MicrobiologyHard

Which feature distinguishes most exotoxins from endotoxin?

  1. AExotoxins are proteins and can be turned into toxoid vaccines
  2. BExotoxins are only released when bacteria die
  3. CExotoxins are heat-stable lipids
  4. DExotoxins are lipopolysaccharides of the Gram-negative outer membrane
7.PharmacologyMedium

Warfarin works by:

  1. ABlocking the vitamin K-dependent synthesis of clotting factors
  2. BBlocking platelet aggregation through irreversible inhibition of COX-1
  3. CActivating antithrombin
  4. DDirectly inhibiting thrombin
8.PharmacologyHard

Why is pyridoxine (vitamin B6) often given together with isoniazid for tuberculosis?

  1. ATo prevent liver damage from isoniazid
  2. BTo prevent peripheral neuropathy
  3. CTo increase the absorption of isoniazid
  4. DTo reduce bacterial resistance
9.Arterial blood gas interpretationMedium
pH7.357.457.56PaCO₂mmHg354521HCO₃⁻mmol/L222618uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.56, PaCO₂ 21 mmHg (2.8 kPa) and HCO₃⁻ 18 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.56PaCO₂ 21 mmHg (2.8 kPa)HCO₃⁻ 18 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.05PaCO₂mmHg354530HCO₃⁻mmol/L22268appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.05, PaCO₂ 30 mmHg (4.0 kPa), HCO₃⁻ 8 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.05PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 8 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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/mVsupraventricular tachycardia (SVT)atrial fibrillationventricular tachycardiaventricular fibrillation

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. 1supraventricular tachycardia (SVT)
  2. 2atrial fibrillation
  3. 3ventricular tachycardia
  4. 4ventricular fibrillation
13.Evidence-based practice statisticsMedium
casescontrolsexposed6191abnot exposed199479cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 260 patients with a disease (cases) and 570 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 = 61b = 91c = 199d = 479
OR =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositivenegative?total10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 70% and specificity 95%. The prevalence of the disease is 27%. How many people with the disease are missed by the test (false negatives, FN)?

N = 10 000p = 27%Se = 70%Sp = 95%
FN =

3Solutions

1.Human anatomy

Answer: A · 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

A · Corpus callosum
2.Human anatomy

Answer: A · Ulnar nerve

Why this is the answer

The ulnar nerve passes behind the medial epicondyle. It supplies most intrinsic hand muscles, including the interossei, and the skin of the little finger.

Answer

A · Ulnar nerve
3.Human physiology

Answer: D · Fibrin

Why this is the answer

Thrombin converts soluble fibrinogen into insoluble fibrin strands, which bind the platelet plug and trap red cells to form a stable clot.

Answer

D · Fibrin
4.Human physiology

Answer: D · Raise glomerular capillary pressure and GFR

Why this is the answer

Efferent constriction holds blood in the glomerulus, raising its pressure and GFR. Angiotensin II acts this way, which is why ACE inhibitors can lower GFR.

Answer

D · Raise glomerular capillary pressure and GFR
5.Microbiology

Answer: A · Replacing fluid and salts by oral or intravenous rehydration

Why this is the answer

Cholera toxin makes gut cells secrete large amounts of water and salt. Rapid rehydration saves most lives; antibiotics only shorten the illness.

Answer

A · Replacing fluid and salts by oral or intravenous rehydration
6.Microbiology

Answer: A · Exotoxins are proteins and can be turned into toxoid vaccines

Why this is the answer

Exotoxins are secreted proteins with specific actions and are often very potent; many can be inactivated into toxoids. Endotoxin is lipopolysaccharide, more heat-stable and cannot be made into a toxoid.

Answer

A · Exotoxins are proteins and can be turned into toxoid vaccines
7.Pharmacology

Answer: A · Blocking the vitamin K-dependent synthesis of clotting factors

Why this is the answer

Warfarin inhibits vitamin K epoxide reductase, reducing synthesis of factors II, VII, IX and X. It is monitored with the INR and reversed with vitamin K.

Answer

A · Blocking the vitamin K-dependent synthesis of clotting factors
8.Pharmacology

Answer: B · To prevent peripheral neuropathy

Why this is the answer

Isoniazid causes pyridoxine deficiency, which can lead to peripheral neuropathy. The risk is greater in slow acetylators, malnourished patients and people with diabetes or alcohol dependence.

Answer

B · To prevent peripheral neuropathy
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 7.56: alkalaemia (above 7.45)
PaCO₂ 21 mmHg: low (35–45)
HCO₃⁻ 18 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·8 + 8 = 20 → 18–22 mmHg

Compare

measured: 30 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: ventricular rate = 75 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 = 20 small boxes = 0.80 s → 1500 ÷ 20 = 75 per minute
conduction ratio = 300 ÷ 75 = 4:1

Answer

ventricular rate = 75 bpm
12.ECG rhythm strip interpretation

Answer: ventricular tachycardia

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: R–R = 10 small boxes, 1500 ÷ 10 ≈ 150 per minute.
2. Rhythm: regular, every R–R is 0.40 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide (0.12 s or more).

Interpretation

ventricular tachycardia

Answer

ventricular tachycardia

In resuscitation guidelines VF and pulseless VT are the shockable rhythms. This is identification practice only.

13.Evidence-based practice statistics

Answer: OR = 1.61

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: 61/199 = 0.3065
controls: 91/479 = 0.19

Odds ratio

OR = (61·479)/(91·199) = 1.614 ≈ 1.61

Answer

OR = 1.61

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

14.Evidence-based practice statistics

Answer: FN = 810

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.

With and without the disease

10 000·0.27 = 2700
10 000 − 2700 = 7300

False negatives

FN = 2700·0.3 = 810

Answer

FN = 810

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