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 carpal bone is most commonly fractured, typically after a fall on an outstretched hand?

  1. ALunate
  2. BScaphoid
  3. CPisiform
  4. DHamate
2.Human anatomyHard

A patient with a large aneurysm of the aortic arch develops hoarseness. Which nerve is most likely compressed?

  1. ALeft recurrent laryngeal nerve
  2. BRight recurrent laryngeal nerve
  3. CExternal laryngeal nerve
  4. DLeft phrenic nerve
3.Human physiologyMedium

In skeletal muscle, where does most of the calcium for contraction come from?

  1. AThe sarcoplasmic reticulum
  2. BThe mitochondria
  3. CThe nucleus
  4. DThe extracellular fluid
4.Human physiologyHard

Which mechanism mainly creates the concentration gradient in the medulla of the kidney?

  1. AADH acting on the descending limb
  2. BThe countercurrent multiplier of the loop of Henle
  3. CSecretion of urea into the proximal tubule
  4. DGlomerular filtration
5.MicrobiologyMedium

What is the main difference between innate and adaptive immunity?

  1. AInnate immunity uses antibodies and forms memory; adaptive immunity does not
  2. BAdaptive immunity acts within minutes of infection
  3. CInnate immunity develops only after vaccination
  4. DAdaptive immunity is specific and forms memory; innate immunity does not
6.MicrobiologyHard

Why is Chlamydia trachomatis usually diagnosed with nucleic acid amplification tests instead of routine culture on agar?

  1. AIt dies immediately in the presence of oxygen
  2. BIt is an obligate intracellular bacterium that cannot grow on ordinary media
  3. CIt is a virus and has no DNA
  4. DIt is too large to grow on agar plates
7.PharmacologyMedium

Why should doxycycline not be taken at the same time as milk or antacids?

  1. AAntacids turn it into a toxic compound
  2. BCalcium and other metal ions bind it and reduce absorption
  3. CThe combination causes severe constipation
  4. DMilk speeds up its breakdown in the liver by inducing enzymes
8.PharmacologyHard

A patient with Parkinson's disease has nausea. Why should metoclopramide be avoided?

  1. AIt increases dopamine levels in the brain too much and causes psychosis
  2. BIt blocks dopamine receptors in the brain and can worsen the parkinsonism
  3. CIt inhibits the absorption of all oral drugs
  4. DIt causes severe diarrhoea in Parkinson's disease
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 149 mmol/L, glucose 17.2 mmol/L and urea 19.3 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 149 mmol/Lglucose 17.2 mmol/Lurea 19.3 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 88 mmHg (11.7 kPa) and PaCO₂ 54 mmHg (7.2 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 88 mmHg (11.7 kPa)PaCO₂ 54 mmHg (7.2 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Fridericia’s formula QTc = QT/∛RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV2:1 AV block (type undetermined)first-degree AV blocksinus bradycardiasecond-degree AV block type II

Interpret this lead II strip. Which interpretation can you defend from this single 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. 12:1 AV block (type undetermined)
  2. 2first-degree AV block
  3. 3sinus bradycardia
  4. 4second-degree AV block type II
13.Evidence-based practice statisticsMedium
casescontrolsexposed68234abnot exposed32336cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 100 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 = 68b = 234c = 32d = 336
OR =
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 89% and specificity 81%. The prevalence of the disease is 23%. How many positive results n₊ are expected in total?

N = 10 000p = 23%Se = 89%Sp = 81%
n₊ =

3Solutions

1.Human anatomy

Answer: B · Scaphoid

Why this is the answer

The scaphoid is the most often fractured carpal bone. Tenderness in the anatomical snuffbox is a key clinical sign.

Answer

B · Scaphoid
2.Human anatomy

Answer: A · Left recurrent laryngeal nerve

Why this is the answer

The left recurrent laryngeal nerve loops under the aortic arch beside the ligamentum arteriosum. It supplies most laryngeal muscles, so compression causes hoarseness.

Answer

A · Left recurrent laryngeal nerve
3.Human physiology

Answer: A · The sarcoplasmic reticulum

Why this is the answer

Depolarisation of the T-tubules opens ryanodine receptors in the sarcoplasmic reticulum, releasing stored calcium into the cytoplasm.

Answer

A · The sarcoplasmic reticulum
4.Human physiology

Answer: B · The countercurrent multiplier of the loop of Henle

Why this is the answer

The ascending limb actively transports NaCl into the interstitium without letting water follow, and the countercurrent flow multiplies this into a steep gradient that ADH then uses to concentrate urine.

Answer

B · The countercurrent multiplier of the loop of Henle
5.Microbiology

Answer: D · Adaptive immunity is specific and forms memory; innate immunity does not

Why this is the answer

Innate defences (barriers, phagocytes, complement) act fast and in the same way each time. Adaptive immunity (B and T cells) takes days, is specific to each antigen and forms memory.

Answer

D · Adaptive immunity is specific and forms memory; innate immunity does not
6.Microbiology

Answer: B · It is an obligate intracellular bacterium that cannot grow on ordinary media

Why this is the answer

Chlamydia replicates only inside host cells, so it cannot be grown on agar. NAATs such as PCR on urine or swabs are sensitive and are the standard diagnostic test.

Answer

B · It is an obligate intracellular bacterium that cannot grow on ordinary media
7.Pharmacology

Answer: B · Calcium and other metal ions bind it and reduce absorption

Why this is the answer

Tetracyclines form complexes with calcium, magnesium, aluminium and iron in the gut, which reduces absorption. Doses are separated from these products.

Answer

B · Calcium and other metal ions bind it and reduce absorption
8.Pharmacology

Answer: B · It blocks dopamine receptors in the brain and can worsen the parkinsonism

Why this is the answer

Metoclopramide crosses the blood–brain barrier and antagonises D2 receptors. In Parkinson's disease this worsens rigidity and bradykinesia, so antiemetics that do not block central dopamine receptors are preferred.

Answer

B · It blocks dopamine receptors in the brain and can worsen the parkinsonism
9.Arterial blood gas interpretation

Answer: Osm = 335 mOsm/kg

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.

Calculated osmolality

Osm = 2·149 + 17.2 + 19.3 = 334.5 ≈ 335 mOsm/kg

Answer

Osm = 335 mOsm/kg
10.Arterial blood gas interpretation

Answer: A–a gradient = 15.62 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 − 54/0.8 = 171.1 − 67.5 = 103.6 mmHg

Gradient

A–a = 103.6 − 88 = 15.62 mmHg

Answer

A–a gradient = 15.62 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.52 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

QT = 13 × 0.04 = 0.52 s
RR = 25 × 0.04 = 1.00 s

Fridericia’s formula

QTc = 0.52/∛1.00 = 0.52/1 = 0.52 s

Answer

QTc = 0.52 s

Above 0.50 s: markedly prolonged. (520 ms)

12.ECG rhythm strip interpretation

Answer: 2:1 AV block (type undetermined)

2:1 AV block: with two P waves for every QRS, no two conducted P waves follow each other, so you cannot see whether the PR would lengthen (type I) or stay constant (type II) before a non-conducted P wave. From one strip it is called a 2:1 AV block; a longer strip or a change in the conduction ratio decides the type. A narrow QRS makes type I more likely and a wide QRS type II, but neither proves it.

Five steps

1. Rate: R–R = 36 small boxes, 1500 ÷ 36 ≈ 42 per minute.
2. Rhythm: regular, every R–R is 1.44 s.
3. P waves: upright and regular (P–P 0.72 s, 83 per minute), two for every QRS.
4. PR interval: constant at 0.18 s in the conducted beats.
5. QRS: 0.14 s, wide (0.12 s or more).

Why the type stays open

Every second P wave is not conducted, so no two conducted beats follow each other and a lengthening PR could never show.
2:1 AV block (type undetermined)

Answer

2:1 AV block (type undetermined)

A narrow QRS makes type I more likely and a wide QRS type II, but only a longer strip or a change in the conduction ratio decides.

13.Evidence-based practice statistics

Answer: OR = 3.05

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: 68/32 = 2.125
controls: 234/336 = 0.6964

Odds ratio

OR = (68·336)/(234·32) = 3.051 ≈ 3.05

Answer

OR = 3.05

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

14.Evidence-based practice statistics

Answer: n₊ = 3510

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

10 000·0.23 = 2300
10 000 − 2300 = 7700

All positive results

TP = 2300·0.89 = 2047
FP = 7700·0.19 = 1463
n₊ = 2047 + 1463 = 3510

Answer

n₊ = 3510

Of the 3510 positives only 2047 have the disease (PPV 58.3%).

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