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 head of the femur articulates with which structure?

  1. AAcetabulum
  2. BGreater trochanter
  3. CGlenoid cavity
  4. DObturator foramen
2.Human anatomyHard

Injury to the common fibular (peroneal) nerve at the neck of the fibula typically causes:

  1. AWeak hip abduction
  2. BLoss of sensation on the sole of the foot
  3. CFoot drop
  4. DInability to flex the knee
3.Human physiologyMedium

Why can cardiac muscle not be tetanised like skeletal muscle?

  1. AIt is not striated
  2. BIt has no calcium in the sarcoplasmic reticulum
  3. CIt is controlled only by hormones
  4. DIts long refractory period lasts almost as long as the contraction
4.Human physiologyHard

A patient with diabetic ketoacidosis breathes deeply and rapidly. What pattern is expected on the blood gas?

  1. AHigh pH, low bicarbonate and low PaCO₂
  2. BLow pH, normal bicarbonate and high PaCO₂
  3. CLow pH, low bicarbonate and low PaCO₂
  4. DLow pH, high bicarbonate and high PaCO₂
5.MicrobiologyMedium

Which bacterium causes whooping cough (pertussis)?

  1. ACorynebacterium diphtheriae
  2. BBordetella pertussis
  3. CHaemophilus influenzae
  4. DMycoplasma pneumoniae
6.MicrobiologyHard

How do retroviruses such as HIV copy their genome into the host DNA?

  1. AReverse transcriptase makes DNA from viral RNA, and integrase inserts it
  2. BThe viral RNA is translated into DNA by ribosomes
  3. CHost DNA polymerase copies the RNA without help
  4. DThe viral DNA is copied directly by host RNA polymerase
7.PharmacologyMedium

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

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

A patient who used heroin a few hours ago is given a first dose of buprenorphine and quickly develops severe withdrawal. Why?

  1. ABuprenorphine is a pure antagonist like naloxone with no agonist effect
  2. BBuprenorphine causes an allergic reaction in heroin users
  3. CBuprenorphine is a high-affinity partial agonist that displaces heroin
  4. DBuprenorphine has no effect at opioid receptors
9.Arterial blood gas interpretationMedium
pH7.357.457.44PaCO₂mmHg354520HCO₃⁻mmol/L222613uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.44, PaCO₂ 20 mmHg (2.7 kPa) and HCO₃⁻ 13 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.44PaCO₂ 20 mmHg (2.7 kPa)HCO₃⁻ 13 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 136, Cl⁻ 113, HCO₃⁻ 15 mmol/L and albumin 17 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 136 mmol/LCl⁻ 113 mmol/LHCO₃⁻ 15 mmol/Lalbumin 17 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval on this lead II strip, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QT = s
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
casescontrolsexposed3798abnot exposed23252cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 60 patients with a disease (cases) and 350 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 = 37b = 98c = 23d = 252
OR =
14.Evidence-based practice statisticsHard
p (%)PPV (%)30%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 89% and a specificity of 84%. It is used in a population where the prevalence is 30%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 89%Sp = 84%p = 30%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Acetabulum

Why this is the answer

The acetabulum is the cup-shaped socket of the hip bone, formed by the ilium, ischium and pubis. The glenoid cavity is the shoulder's socket.

Answer

A · Acetabulum
2.Human anatomy

Answer: C · Foot drop

Why this is the answer

The common fibular nerve supplies the dorsiflexors and evertors. Damage at the fibular neck causes foot drop and a high-stepping gait. The sole is supplied by the tibial nerve.

Answer

C · Foot drop
3.Human physiology

Answer: D · Its long refractory period lasts almost as long as the contraction

Why this is the answer

The plateau of the cardiac action potential gives a long refractory period, so the muscle relaxes before it can be excited again. This allows the heart to refill.

Answer

D · Its long refractory period lasts almost as long as the contraction
4.Human physiology

Answer: C · Low pH, low bicarbonate and low PaCO₂

Why this is the answer

Ketoacids consume bicarbonate, causing metabolic acidosis. Kussmaul breathing lowers PaCO₂ as respiratory compensation.

Answer

C · Low pH, low bicarbonate and low PaCO₂
5.Microbiology

Answer: B · Bordetella pertussis

Why this is the answer

Bordetella pertussis causes long coughing fits with a "whoop". It is most dangerous for young babies, which is why vaccination in pregnancy is offered in many countries.

Answer

B · Bordetella pertussis
6.Microbiology

Answer: A · Reverse transcriptase makes DNA from viral RNA, and integrase inserts it

Why this is the answer

Reverse transcriptase converts the RNA genome into DNA, which integrase inserts into the host genome as a provirus. Both enzymes are drug targets.

Answer

A · Reverse transcriptase makes DNA from viral RNA, and integrase inserts it
7.Pharmacology

Answer: D · 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

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

Answer: C · Buprenorphine is a high-affinity partial agonist that displaces heroin

Why this is the answer

Buprenorphine binds mu receptors more strongly than heroin but activates them less, so it can precipitate withdrawal. Induction is started when the patient already has mild to moderate withdrawal signs.

Answer

C · Buprenorphine is a high-affinity partial agonist that displaces heroin
9.Arterial blood gas interpretation

Answer: fully compensated

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 7.44: within 7.35–7.45
PaCO₂ 20 mmHg: low (35–45)
HCO₃⁻ 13 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: AGc = 13.75 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 = 136 − (113 + 15) = 8

Correction for albumin

8 + 0.25·(40 − 17) = 13.75 mmol/L

Answer

AGc = 13.75 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: QT = 0.3 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

7.5 small boxes from the start of the QRS to the end of the T wave

Convert

QT = 7.5 × 0.04 s = 0.3 s

Answer

QT = 0.3 s

A rough rule: at normal rates the QT should be less than half the R–R interval (here R–R = 0.60 s).

12.ECG rhythm strip interpretation

Answer: atrial rate = 60 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 = 25 small boxes = 1.00 s → 1500 ÷ 25 = 60 ≈ 60 per minute

Ventricular rate

4 QRS complexes in 6 s × 10 = 40 per minute

Answer

atrial rate = 60 bpm

Answer

atrial rate = 60 bpm

Second-degree type I (Wenckebach): 4 P waves for every 3 QRS complexes.

13.Evidence-based practice statistics

Answer: OR = 4.14

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: 37/23 = 1.609
controls: 98/252 = 0.3889

Odds ratio

OR = (37·252)/(98·23) = 4.137 ≈ 4.14

Answer

OR = 4.14

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

14.Evidence-based practice statistics

Answer: PPV = 70.4 %

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.

True and false positives (per person)

Se·p = 0.89·0.3 = 0.267
(1 − Sp)·(1 − p) = 0.16·0.7 = 0.112

Positive predictive value

PPV = 0.267/(0.267 + 0.112) = 0.7045 ≈ 70.4%

Answer

PPV = 70.4%

The lower the prevalence, the lower the PPV of the same test.

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