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 two regions of the adult spine normally show a lordosis (curve concave towards the back)?

  1. ACervical and thoracic
  2. BThoracic and lumbar
  3. CCervical and lumbar
  4. DThoracic and sacral
2.Human anatomyHard

A blow to the side of the head at the pterion causes an extradural haematoma. Which vessel is usually torn?

  1. AMiddle cerebral artery
  2. BSuperficial temporal artery
  3. CMiddle meningeal artery
  4. DBridging cerebral veins
3.Human physiologyMedium

In which form is most carbon dioxide carried in the blood?

  1. ABound to the haem iron
  2. BAs carbonic acid in platelets
  3. CAs bicarbonate ions in plasma
  4. DDissolved as CO₂ gas
4.Human physiologyHard

A patient hyperventilating during a panic attack has tingling fingers. What would the arterial blood gas most likely show?

  1. ALow pH and low bicarbonate
  2. BHigh pH and low PaCO₂
  3. CLow pH and high PaCO₂
  4. DHigh pH and high bicarbonate
5.MicrobiologyMedium

Which antibody class is the first to rise in a new infection?

  1. AIgA
  2. BIgM
  3. CIgE
  4. DIgG
6.MicrobiologyHard

On MacConkey agar, pink colonies grow from a urine sample. What does this tell you?

  1. AThe organism is a fungus
  2. BThe organism does not ferment lactose, so it is probably Salmonella
  3. CThe organism is probably a Gram-negative rod that ferments lactose
  4. DThe organism is a Gram-positive coccus
7.PharmacologyMedium

A patient with Addison's disease on hydrocortisone develops a fever with flu. What is the usual advice?

  1. AStop the hydrocortisone until the fever settles, to let the body recover
  2. BHalve the hydrocortisone to reduce side effects
  3. CMake no change, as illness does not affect cortisol needs
  4. DIncrease the dose as instructed (sick-day rules) and seek help if vomiting
8.PharmacologyHard

Combining several drugs that prolong the QT interval raises the risk of which life-threatening arrhythmia?

  1. AFirst-degree heart block
  2. BTorsades de pointes
  3. CSinus tachycardia
  4. DAtrial fibrillation
9.Arterial blood gas interpretationMedium
pH7.357.457.56PaCO₂mmHg354539HCO₃⁻mmol/L222634uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.56, PaCO₂ 39 mmHg (5.2 kPa) and HCO₃⁻ 34 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.56PaCO₂ 39 mmHg (5.2 kPa)HCO₃⁻ 34 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 89 mmHg (11.9 kPa) and PaCO₂ 34 mmHg (4.5 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 89 mmHg (11.9 kPa)PaCO₂ 34 mmHg (4.5 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus arrhythmiajunctional rhythmsinus tachycardianormal sinus rhythm

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. 1sinus arrhythmia
  2. 2junctional rhythm
  3. 3sinus tachycardia
  4. 4normal sinus rhythm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsinus bradycardiafirst-degree AV blocksecond-degree AV block type IIsecond-degree AV block type I (Wenckebach)

This lead II strip shows a conduction problem between the atria and the ventricles. 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. 1sinus bradycardia
  2. 2first-degree AV block
  3. 3second-degree AV block type II
  4. 4second-degree AV block type I (Wenckebach)
13.Evidence-based practice statisticsMedium
Se69%Sp77%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 69% and a specificity of 77%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 69%Sp = 77%
LR+ =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 74% and specificity 75%. The prevalence of the disease is 17%. How many true-positive results TP are expected?

N = 10 000p = 17%Se = 74%Sp = 75%
TP =

3Solutions

1.Human anatomy

Answer: C · Cervical and lumbar

Why this is the answer

The cervical and lumbar regions are lordotic (secondary curves). The thoracic and sacral regions are kyphotic (primary curves).

Answer

C · Cervical and lumbar
2.Human anatomy

Answer: C · Middle meningeal artery

Why this is the answer

The middle meningeal artery lies under the pterion, where the skull is thin. Its rupture bleeds between bone and dura. Bridging veins cause subdural haematomas.

Answer

C · Middle meningeal artery
3.Human physiology

Answer: C · As bicarbonate ions in plasma

Why this is the answer

About 70% of CO₂ is carried as bicarbonate. Carbonic anhydrase in red cells converts CO₂ and water to carbonic acid, which dissociates into H⁺ and HCO₃⁻.

Answer

C · As bicarbonate ions in plasma
4.Human physiology

Answer: B · High pH and low PaCO₂

Why this is the answer

Hyperventilation blows off CO₂ and causes acute respiratory alkalosis. Alkalosis increases calcium binding to albumin, lowering ionised calcium and causing tingling.

Answer

B · High pH and low PaCO₂
5.Microbiology

Answer: B · IgM

Why this is the answer

IgM appears first in a primary response; IgG follows and provides long-term protection. A positive IgM therefore suggests recent infection.

Answer

B · IgM
6.Microbiology

Answer: C · The organism is probably a Gram-negative rod that ferments lactose

Why this is the answer

MacConkey agar contains bile salts and crystal violet that inhibit Gram-positive bacteria (selective) and lactose with a pH indicator (differential). Lactose fermenters such as E. coli produce acid and turn pink.

Answer

C · The organism is probably a Gram-negative rod that ferments lactose
7.Pharmacology

Answer: D · Increase the dose as instructed (sick-day rules) and seek help if vomiting

Why this is the answer

During illness, the body needs more cortisol, so patients usually double their glucocorticoid dose as instructed. If they cannot keep tablets down, they need injectable hydrocortisone and urgent care.

Answer

D · Increase the dose as instructed (sick-day rules) and seek help if vomiting
8.Pharmacology

Answer: B · Torsades de pointes

Why this is the answer

A long QT interval delays repolarisation and can trigger torsades de pointes, which may turn into ventricular fibrillation. Drugs such as some macrolides, antipsychotics and antiarrhythmics add to this risk.

Answer

B · Torsades de pointes
9.Arterial blood gas interpretation

Answer: uncompensated

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 39 mmHg: normal (35–45)
HCO₃⁻ 34 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 42.8–46.8 mmHg, so the measured 39 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 39.62 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.24·713 − 34/0.8 = 171.1 − 42.5 = 128.6 mmHg

Gradient

A–a = 128.6 − 89 = 39.62 mmHg

Answer

A–a gradient = 39.62 mmHg
11.ECG rhythm strip interpretation

Answer: normal sinus rhythm

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: R–R = 23 small boxes, 1500 ÷ 23 ≈ 65 per minute.
2. Rhythm: regular, every R–R is 0.92 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.20 s, constant, within 0.12–0.20 s.
5. QRS: 0.06 s, narrow (below 0.12 s).

Interpretation

normal sinus rhythm

Answer

normal sinus rhythm
12.ECG rhythm strip interpretation

Answer: second-degree AV block type II

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: the P waves are regular; R–R is regular except for a long pause where a QRS is missing.
3. P waves: upright and regular (P–P 0.84 s, 71 per minute); one P in every 4 is not followed by a QRS.
4. PR interval: constant at 0.16 s in the conducted beats.
5. QRS: 0.14 s, wide (0.12 s or more).

Interpretation

second-degree AV block type II

Answer

second-degree AV block type II

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: LR+ = 3

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.

Positive likelihood ratio

LR+ = 0.69/(1 − 0.77) = 3

Answer

LR+ = 3
14.Evidence-based practice statistics

Answer: TP = 1258

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

10 000·0.17 = 1700
10 000 − 1700 = 8300

True positives

TP = 1700·0.74 = 1258

Answer

TP = 1258

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