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 nerve supplies the diaphragm?

  1. AVagus nerve
  2. BIntercostal nerves
  3. CAccessory nerve
  4. DPhrenic nerve
2.Human anatomyHard

What is the correct order of structures that urine passes through after leaving the collecting ducts?

  1. AMinor calyx, renal pelvis, major calyx, ureter
  2. BRenal pelvis, minor calyx, major calyx, ureter
  3. CMinor calyx, major calyx, renal pelvis, ureter
  4. DMajor calyx, minor calyx, renal pelvis, ureter
3.Human physiologyMedium

Which hormone makes the gallbladder contract after a fatty meal?

  1. ASecretin
  2. BGastrin
  3. CCholecystokinin (CCK)
  4. DInsulin
4.Human physiologyHard

A pulmonary embolus blocks blood flow to a well-ventilated region of lung. How does the ventilation–perfusion (V/Q) ratio of that region change?

  1. AIt stays normal because ventilation falls too
  2. BIt becomes very high, acting as dead space
  3. CIt becomes low, like in pneumonia
  4. DIt becomes zero, acting as a shunt
5.MicrobiologyMedium

What does PCR do in a diagnostic laboratory?

  1. AIt measures the level of specific antibodies in a patient's serum sample
  2. BIt makes many copies of a specific DNA sequence so it can be detected
  3. CIt grows bacteria faster on agar plates
  4. DIt stains bacteria so they can be seen
6.MicrobiologyHard

An older adult develops a painful blistering rash in a band on one side of the chest. What explains this pattern?

  1. AVaricella-zoster virus reactivates from one sensory ganglion and travels along its nerve
  2. BA new chickenpox infection spreads through the blood to one side
  3. CBacteria spread along the lymphatic vessels of the chest
  4. DAn allergic reaction to clothing affects one dermatome
7.PharmacologyMedium

Which receptor do beta blockers such as metoprolol mainly block?

  1. ABeta-1 adrenergic receptors in the heart
  2. BMuscarinic receptors in the heart
  3. CAlpha-1 receptors in blood vessels
  4. DBeta-3 receptors in fat tissue
8.PharmacologyHard

A patient receiving a phenylephrine infusion has a rise in blood pressure and a fall in heart rate. What is the best explanation?

  1. APhenylephrine stimulates muscarinic receptors
  2. BThe fall in heart rate shows phenylephrine toxicity of the AV node
  3. CPhenylephrine directly blocks beta-1 receptors in the heart's conduction system
  4. DAlpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
9.Arterial blood gas interpretationMedium
pH7.357.457.53PaCO₂mmHg354530HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.53, PaCO₂ 30 mmHg (4.0 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.53PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.17PaCO₂mmHg354537HCO₃⁻mmol/L222613appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.17, PaCO₂ 37 mmHg (4.9 kPa), HCO₃⁻ 13 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.17PaCO₂ 37 mmHg (4.9 kPa)HCO₃⁻ 13 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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 Bazett’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/mVfirst-degree AV blocksecond-degree AV block type I (Wenckebach)second-degree AV block type II2:1 AV block (type undetermined)

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. 1first-degree AV block
  2. 2second-degree AV block type I (Wenckebach)
  3. 3second-degree AV block type II
  4. 42:1 AV block (type undetermined)
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive205505710abnegative5512351290cdtotal26017402000

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the positive likelihood ratio LR+. Round to two decimal places.

a = 205b = 505c = 55d = 1235
LR+ =
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 91% and specificity 92%. The prevalence of the disease is 16%. How many people with the disease are missed by the test (false negatives, FN)?

N = 10 000p = 16%Se = 91%Sp = 92%
FN =

3Solutions

1.Human anatomy

Answer: D · Phrenic nerve

Why this is the answer

The phrenic nerve (roots C3–C5) is the motor supply to the diaphragm. High cervical cord injury above C3 therefore stops spontaneous breathing.

Answer

D · Phrenic nerve
2.Human anatomy

Answer: C · Minor calyx, major calyx, renal pelvis, ureter

Why this is the answer

Collecting ducts open at the renal papillae into minor calyces, which join to form major calyces, which empty into the renal pelvis and then the ureter.

Answer

C · Minor calyx, major calyx, renal pelvis, ureter
3.Human physiology

Answer: C · Cholecystokinin (CCK)

Why this is the answer

Fat and protein in the duodenum release CCK, which contracts the gallbladder and stimulates pancreatic enzyme secretion.

Answer

C · Cholecystokinin (CCK)
4.Human physiology

Answer: B · It becomes very high, acting as dead space

Why this is the answer

Ventilation without perfusion gives a very high V/Q ratio (dead space). A shunt, such as in pneumonia, is the opposite: perfusion without ventilation.

Answer

B · It becomes very high, acting as dead space
5.Microbiology

Answer: B · It makes many copies of a specific DNA sequence so it can be detected

Why this is the answer

The polymerase chain reaction amplifies a target sequence millions of times. It can detect pathogens that are hard to culture; RNA viruses are first converted to DNA (RT-PCR).

Answer

B · It makes many copies of a specific DNA sequence so it can be detected
6.Microbiology

Answer: A · Varicella-zoster virus reactivates from one sensory ganglion and travels along its nerve

Why this is the answer

After chickenpox, VZV stays latent in a dorsal root or cranial nerve ganglion. When immunity weakens it can reactivate, travelling down that nerve to cause shingles in its dermatome.

Answer

A · Varicella-zoster virus reactivates from one sensory ganglion and travels along its nerve
7.Pharmacology

Answer: A · Beta-1 adrenergic receptors in the heart

Why this is the answer

Cardioselective beta blockers block beta-1 receptors, lowering heart rate, contractility and renin release.

Answer

A · Beta-1 adrenergic receptors in the heart
8.Pharmacology

Answer: D · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia

Why this is the answer

Phenylephrine is a pure alpha-1 agonist with little direct cardiac action. The higher blood pressure activates baroreceptors, which increase vagal tone and slow the heart.

Answer

D · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
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 7.53: alkalaemia (above 7.45)
PaCO₂ 30 mmHg: low (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
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

1.5·13 + 8 = 27.5 → 25.5–29.5 mmHg

Compare

measured: 37 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.5 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 = 12.5 × 0.04 = 0.50 s
RR = 25 × 0.04 = 1.00 s

Bazett’s formula

QTc = 0.50/√1.00 = 0.50/1 = 0.5 s

Answer

QTc = 0.5 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (500 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 0.20 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: LR+ = 2.72

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.

Sensitivity and specificity

Se = 205/260 = 0.7885
Sp = 1235/1740 = 0.7098

Positive likelihood ratio

LR+ = 0.7885/(1 − 0.7098) = 2.717 ≈ 2.72

Answer

LR+ = 2.72
14.Evidence-based practice statistics

Answer: FN = 144

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

10 000·0.16 = 1600
10 000 − 1600 = 8400

False negatives

FN = 1600·0.09 = 144

Answer

FN = 144

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