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 rotator cuff consists of supraspinatus, infraspinatus, teres minor and which other muscle?

  1. ASubscapularis
  2. BTeres major
  3. CLatissimus dorsi
  4. DDeltoid
2.Human anatomyHard

An indirect inguinal hernia enters the inguinal canal at which point?

  1. AThrough the posterior wall of the canal, medial to the inferior epigastric vessels
  2. BThrough the superficial ring only, without entering the canal
  3. CBelow the inguinal ligament, through the femoral canal
  4. DThrough the deep inguinal ring, lateral to the inferior epigastric vessels
3.Human physiologyMedium

What is anatomical dead space?

  1. AThe air that stays in the lungs after full exhalation (residual volume)
  2. BThe space between the two pleural layers
  3. CThe volume of the conducting airways where no gas exchange happens
  4. DAlveoli that have collapsed completely
4.Human physiologyHard

Why does breathing 100% oxygen correct hypoxaemia from a true right-to-left shunt only poorly?

  1. AShunted blood is already fully saturated
  2. BPure oxygen damages haemoglobin
  3. CThe extra oxygen is all exhaled as CO₂
  4. DThe shunted blood never comes into contact with alveolar gas
5.MicrobiologyMedium

Which organism is a common cause of infection in burns and in people with cystic fibrosis, and can produce a green pigment?

  1. AStreptococcus pyogenes
  2. BHelicobacter pylori
  3. CClostridium tetani
  4. DPseudomonas aeruginosa
6.MicrobiologyHard

A urinary catheter has become colonised by bacteria in a biofilm. Why is the catheter usually replaced instead of just giving antibiotics?

  1. ABacteria in biofilms are protected and much harder for antibiotics to kill
  2. BAntibiotics damage the catheter material
  3. CBiofilms contain only viruses, so antibiotics do not work
  4. DBiofilm bacteria cannot cause disease
7.PharmacologyMedium

When should a patient take a once-daily proton pump inhibitor such as omeprazole?

  1. AStraight after a large evening meal
  2. BOnly when heartburn is severe
  3. CAbout 30–60 minutes before the first meal of the day
  4. DWith a glass of milk at bedtime, when acid output is highest
8.PharmacologyHard

Before starting long-term bisphosphonate treatment, a patient is advised to have a dental check-up. Why?

  1. ABisphosphonates dissolve tooth enamel within weeks
  2. BThey are linked to osteonecrosis of the jaw after dental surgery
  3. CBisphosphonates cause severe gum overgrowth
  4. DBisphosphonates stain the teeth black if taken for many years
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 26 mmHg (3.5 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 26 mmHg (3.5 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 42 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 42 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial flutter, 2:1 conductionsinus bradycardiasinus tachycardiaatrial fibrillation

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. 1atrial flutter, 2:1 conduction
  2. 2sinus bradycardia
  3. 3sinus tachycardia
  4. 4atrial fibrillation
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV

This lead II strip shows an AV block, so the atria and the ventricles beat at different rates. Measure the P–P interval and find the atrial rate in beats per minute (1500 method, whole number).

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
atrial rate = bpm
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment69911980abcontrol59361420cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 980 patients received a new treatment and 420 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the relative risk RR of the event with treatment. Round to two decimal places.

treatment: 69/980control: 59/420
RR =
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 88% and specificity 87%. The prevalence of the disease is 14%. How many false-positive results FP are expected?

N = 10 000p = 14%Se = 88%Sp = 87%
FP =

3Solutions

1.Human anatomy

Answer: A · Subscapularis

Why this is the answer

SITS: supraspinatus, infraspinatus, teres minor and subscapularis. Teres major is close by but is not part of the cuff.

Answer

A · Subscapularis
2.Human anatomy

Answer: D · Through the deep inguinal ring, lateral to the inferior epigastric vessels

Why this is the answer

An indirect hernia passes through the deep ring, lateral to the inferior epigastric vessels, and runs along the canal. A direct hernia pushes through the posterior wall medial to them.

Answer

D · Through the deep inguinal ring, lateral to the inferior epigastric vessels
3.Human physiology

Answer: C · The volume of the conducting airways where no gas exchange happens

Why this is the answer

Anatomical dead space (about 150 ml) is air in the nose, trachea and bronchi. It is moved with every breath but never reaches the alveoli.

Answer

C · The volume of the conducting airways where no gas exchange happens
4.Human physiology

Answer: D · The shunted blood never comes into contact with alveolar gas

Why this is the answer

Shunted blood bypasses ventilated alveoli and mixes deoxygenated blood into arterial blood. Extra inspired oxygen cannot reach it, unlike in V/Q mismatch or hypoventilation.

Answer

D · The shunted blood never comes into contact with alveolar gas
5.Microbiology

Answer: D · Pseudomonas aeruginosa

Why this is the answer

Pseudomonas aeruginosa is an opportunistic pathogen of burns, ventilated patients and cystic fibrosis lungs. It is naturally resistant to many antibiotics.

Answer

D · Pseudomonas aeruginosa
6.Microbiology

Answer: A · Bacteria in biofilms are protected and much harder for antibiotics to kill

Why this is the answer

In a biofilm, bacteria live in a protective matrix, grow slowly and can tolerate high antibiotic levels. Removing the device removes the source of infection.

Answer

A · Bacteria in biofilms are protected and much harder for antibiotics to kill
7.Pharmacology

Answer: C · About 30–60 minutes before the first meal of the day

Why this is the answer

Proton pump inhibitors block pumps that are active, so they work best when taken before breakfast. Food then activates the pumps when the drug level is high.

Answer

C · About 30–60 minutes before the first meal of the day
8.Pharmacology

Answer: B · They are linked to osteonecrosis of the jaw after dental surgery

Why this is the answer

Osteonecrosis of the jaw is a rare but serious adverse effect, mostly after invasive dental work. Dental problems are treated before starting, and good oral hygiene is maintained.

Answer

B · They are linked to osteonecrosis of the jaw after dental surgery
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 17 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

|26 − 40| = 14 mmHg → 1.4 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 5·1.4 = 17 mmol/L

Answer

HCO₃⁻ = 17 mmol/L
10.Arterial blood gas interpretation

Answer: PaCO₂ = 50.4 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

0.7·42 + 21 = 50.4 mmHg

Answer

PaCO₂ = 50.4 mmHg

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

11.ECG rhythm strip interpretation

Answer: sinus tachycardia

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 = 14 small boxes, 1500 ÷ 14 ≈ 107 per minute.
2. Rhythm: regular, every R–R is 0.56 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).

Interpretation

sinus tachycardia

Answer

sinus tachycardia
12.ECG rhythm strip interpretation

Answer: atrial rate = 83 bpm

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.

Atrial rate

P–P = 18 small boxes = 0.72 s → 1500 ÷ 18 = 83.33 ≈ 83 per minute

Ventricular rate

R–R = 44 small boxes = 1.76 s → 1500 ÷ 44 = 34.09 ≈ 34 per minute

Answer

atrial rate = 83 bpm

Answer

atrial rate = 83 bpm

Third-degree block with a wide-complex ventricular escape (usually 20–40 per minute).

13.Evidence-based practice statistics

Answer: RR = 0.5

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 = 69/980 = 0.07041
CER = 59/420 = 0.1405

Relative risk

RR = 0.07041/0.1405 = 0.5012 ≈ 0.5

Answer

RR = 0.5
14.Evidence-based practice statistics

Answer: FP = 1118

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

10 000·0.14 = 1400
10 000 − 1400 = 8600

False positives

FP = 8600·0.13 = 1118

Answer

FP = 1118

Of the 2350 positives only 1232 have the disease (PPV 52.4%).

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