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 is the largest nerve in the human body?

  1. AFemoral nerve
  2. BMedian nerve
  3. CSciatic nerve
  4. DVagus nerve
2.Human anatomyHard

A stab wound cuts the left half of the spinal cord at T10. Which pattern of loss is expected below the lesion?

  1. ALeft-sided weakness and loss of proprioception, right-sided loss of pain and temperature
  2. BLoss of all sensation and movement on the left only
  3. CLoss of pain and temperature on both sides only
  4. DRight-sided weakness and loss of proprioception, left-sided loss of pain and temperature
3.Human physiologyMedium

What does the QRS complex on an ECG represent?

  1. AVentricular depolarisation
  2. BVentricular repolarisation
  3. CAtrial depolarisation
  4. DAtrial repolarisation
4.Human physiologyHard

In primary adrenal insufficiency (Addison's disease), which combination is expected?

  1. AHigh sodium, low potassium and low ACTH
  2. BHigh sodium, high potassium and high ACTH
  3. CLow sodium, low potassium and low ACTH
  4. DLow sodium, high potassium and high ACTH
5.MicrobiologyMedium

In which phase of the bacterial growth curve do the cells divide at their fastest constant rate?

  1. ALog (exponential) phase
  2. BLag (adaptation) phase
  3. CStationary (plateau) phase
  4. DDeath phase
6.MicrobiologyHard

What is the key difference between bactericidal and bacteriostatic antibiotics?

  1. ABacteriostatic drugs always work faster than bactericidal drugs
  2. BBactericidal drugs work only outside the body
  3. CBactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
  4. DBactericidal drugs work only on viruses; bacteriostatic drugs work on bacteria
7.PharmacologyMedium

Which adverse effect of ciprofloxacin should a patient report at once?

  1. APain or swelling in a tendon, such as the Achilles tendon
  2. BA slightly bitter or metallic taste for a while after each dose
  3. CMild tiredness in the first few days
  4. DDarker stools than usual
8.PharmacologyHard

A patient taking hydralazine for several months develops joint pain, fever and a rash. Anti-histone antibodies are positive. What is the most likely diagnosis?

  1. ARheumatoid arthritis
  2. BDrug-induced lupus
  3. CGout
  4. DAn acute viral infection
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 129 mmol/L, glucose 6.4 mmol/L and urea 20.5 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 129 mmol/Lglucose 6.4 mmol/Lurea 20.5 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 141, Cl⁻ 109, HCO₃⁻ 19 mmol/L and albumin 18 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 141 mmol/LCl⁻ 109 mmol/LHCO₃⁻ 19 mmol/Lalbumin 18 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsupraventricular tachycardia (SVT)ventricular tachycardiaaccelerated junctional rhythmatrial flutter, 2:1 conduction

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. 1supraventricular tachycardia (SVT)
  2. 2ventricular tachycardia
  3. 3accelerated junctional rhythm
  4. 4atrial flutter, 2:1 conduction
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsecond-degree AV block type I (Wenckebach)first-degree AV blocksecond-degree AV block type IIsinus bradycardia

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. 1second-degree AV block type I (Wenckebach)
  2. 2first-degree AV block
  3. 3second-degree AV block type II
  4. 4sinus bradycardia
13.Evidence-based practice statisticsMedium
casescontrolsexposed97184abnot exposed203616cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 300 patients with a disease (cases) and 800 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 = 97b = 184c = 203d = 616
OR =
14.Evidence-based practice statisticsHard
pre-test5%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 5% for a disease. A test with sensitivity 73% and specificity 60% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 73%Sp = 60%negative
p′ = %

3Solutions

1.Human anatomy

Answer: C · Sciatic nerve

Why this is the answer

The sciatic nerve (L4–S3) leaves the pelvis through the greater sciatic foramen and supplies the hamstrings and all the muscles below the knee. Skin on the inner side of the leg is supplied by the saphenous nerve instead.

Answer

C · Sciatic nerve
2.Human anatomy

Answer: A · Left-sided weakness and loss of proprioception, right-sided loss of pain and temperature

Why this is the answer

In Brown-Séquard syndrome the corticospinal tract and dorsal columns are lost on the same side, while the spinothalamic tract, which crosses near entry, causes contralateral pain and temperature loss.

Answer

A · Left-sided weakness and loss of proprioception, right-sided loss of pain and temperature
3.Human physiology

Answer: A · Ventricular depolarisation

Why this is the answer

The P wave is atrial depolarisation, the QRS complex ventricular depolarisation and the T wave ventricular repolarisation. Atrial repolarisation is hidden in the QRS.

Answer

A · Ventricular depolarisation
4.Human physiology

Answer: D · Low sodium, high potassium and high ACTH

Why this is the answer

Loss of aldosterone causes sodium loss and potassium retention. Low cortisol removes negative feedback, so ACTH rises and can cause skin pigmentation.

Answer

D · Low sodium, high potassium and high ACTH
5.Microbiology

Answer: A · Log (exponential) phase

Why this is the answer

After the lag phase of adjustment, cells enter the log phase and grow exponentially. Growth stops in the stationary phase as nutrients run out and waste builds up.

Answer

A · Log (exponential) phase
6.Microbiology

Answer: C · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them

Why this is the answer

Bacteriostatic drugs halt multiplication so host defences can eliminate the bacteria. Bactericidal drugs are preferred when defences are weak or hard to reach, such as in endocarditis or neutropenia.

Answer

C · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
7.Pharmacology

Answer: A · Pain or swelling in a tendon, such as the Achilles tendon

Why this is the answer

Fluoroquinolones can cause tendinitis and tendon rupture. Patients should stop exercise and report tendon pain promptly.

Answer

A · Pain or swelling in a tendon, such as the Achilles tendon
8.Pharmacology

Answer: B · Drug-induced lupus

Why this is the answer

Hydralazine and procainamide are classic causes of drug-induced lupus, especially in slow acetylators. Symptoms usually resolve after the drug is stopped.

Answer

B · Drug-induced lupus
9.Arterial blood gas interpretation

Answer: Osm = 285 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 = 2·129 + 6.4 + 20.5 = 284.9 ≈ 285 mOsm/kg

Answer

Osm = 285 mOsm/kg
10.Arterial blood gas interpretation

Answer: AGc = 18.5 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.

Anion gap

AG = 141 − (109 + 19) = 13

Correction for albumin

13 + 0.25·(40 − 18) = 18.5 mmol/L

Answer

AGc = 18.5 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: supraventricular tachycardia (SVT)

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. Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

Five steps

1. Rate: R–R = 6 small boxes, 1500 ÷ 6 ≈ 250 per minute.
2. Rhythm: regular, every R–R is 0.24 s.
3. P waves: none visible; at this rate they are hidden in the QRS complexes or the T waves.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s), so the rhythm starts above the ventricles.

Interpretation

supraventricular tachycardia (SVT)

Answer

supraventricular tachycardia (SVT)
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 3 is not followed by a QRS.
4. PR interval: constant at 0.16 s in the conducted beats.
5. QRS: 0.08 s, narrow (below 0.12 s).

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: OR = 1.6

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: 97/203 = 0.4778
controls: 184/616 = 0.2987

Odds ratio

OR = (97·616)/(184·203) = 1.6

Answer

OR = 1.6

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

14.Evidence-based practice statistics

Answer: p′ = 2.3 %

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.

Likelihood ratio

LR− = (1 − 0.73)/0.6 = 0.45

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·0.45 = 0.02368

Post-test probability

p′ = 0.02368/(1 + 0.02368) = 0.02314 ≈ 2.3%

Answer

p′ = 2.3%

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