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 artery is most commonly used to feel the pulse at the wrist?

  1. ARadial artery
  2. BAxillary artery
  3. CUlnar artery
  4. DBrachial artery
2.Human anatomyHard

During a lumbar puncture, which ligament is the last one pierced before the needle enters the epidural space?

  1. APosterior longitudinal ligament
  2. BInterspinous ligament
  3. CSupraspinous ligament
  4. DLigamentum flavum
3.Human physiologyMedium

Which is a classic example of positive feedback in the body?

  1. AOxytocin release during labour
  2. BSweating when body temperature rises
  3. CInsulin release after a meal
  4. DADH release when plasma osmolality rises
4.Human physiologyHard

After a head injury, a patient passes large volumes of very dilute urine and plasma sodium rises. What is the most likely cause?

  1. AUncontrolled diabetes mellitus
  2. BExcess aldosterone
  3. CLack of ADH release (cranial diabetes insipidus)
  4. DExcess ADH release (SIADH)
5.MicrobiologyMedium

Toxoplasma gondii is a risk in pregnancy. Which advice reduces exposure?

  1. AAvoid contact with dogs
  2. BAvoid cleaning cat litter and avoid undercooked meat
  3. CAvoid all fruit and vegetables
  4. DAvoid swimming pools and all other public bathing areas
6.MicrobiologyHard

Several people vomit within a few hours of eating fried rice that was cooked the day before and kept at room temperature. Which organism is the classic cause?

  1. ABacillus cereus
  2. BSalmonella Typhi
  3. CClostridium botulinum
  4. DListeria monocytogenes
7.PharmacologyMedium

Bethanechol may be used for non-obstructive urinary retention. How does it work?

  1. AIt increases urine production in the kidney
  2. BIt blocks muscarinic receptors and relaxes the bladder wall muscle
  3. CIt shrinks the prostate gland
  4. DIt stimulates muscarinic receptors and contracts the bladder muscle
8.PharmacologyHard

A teenager took a large overdose of diphenhydramine. He is agitated, hot, flushed and confused, with dry skin, dilated pupils and a full bladder. What is this pattern?

  1. AAnticholinergic toxidrome
  2. BSerotonin syndrome
  3. CCholinergic toxidrome
  4. DOpioid toxidrome
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 143 mmol/L, glucose 30.1 mmol/L and urea 21.1 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 143 mmol/Lglucose 30.1 mmol/Lurea 21.1 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.34PaCO₂mmHg354531HCO₃⁻mmol/L222616added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.34, PaCO₂ 31 mmHg (4.1 kPa) and HCO₃⁻ 16 mmol/L, with Na⁺ 135 and Cl⁻ 86 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.34PaCO₂ 31 mmHg (4.1 kPa)HCO₃⁻ 16 mmol/LNa⁺ 135 mmol/LCl⁻ 86 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic 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 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/mVsinus rhythm with wide QRSdual-chamber (AV) paced rhythmidioventricular rhythmjunctional rhythm

This patient has a pacemaker. Interpret the lead II 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. 1sinus rhythm with wide QRS
  2. 2dual-chamber (AV) paced rhythm
  3. 3idioventricular rhythm
  4. 4junctional rhythm
13.Evidence-based practice statisticsMedium
Se77%Sp73%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 77% and a specificity of 73%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 77%Sp = 73%
LR− =
14.Evidence-based practice statisticsHard
CER11%EER?RRR 46%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 46% in relative terms (RRR = 46%). In a patient group the risk without treatment (CER) is 11% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 46%CER = 11%
NNT =

3Solutions

1.Human anatomy

Answer: A · Radial artery

Why this is the answer

The radial artery lies superficially on the thumb side of the wrist, against the radius, which makes the pulse easy to feel.

Answer

A · Radial artery
2.Human anatomy

Answer: D · Ligamentum flavum

Why this is the answer

The needle passes skin, supraspinous and interspinous ligaments, then ligamentum flavum into the epidural space, then dura and arachnoid into the subarachnoid space.

Answer

D · Ligamentum flavum
3.Human physiology

Answer: A · Oxytocin release during labour

Why this is the answer

Stretch of the cervix releases oxytocin, which strengthens contractions and causes more stretch. The loop ends with delivery. The other examples are negative feedback.

Answer

A · Oxytocin release during labour
4.Human physiology

Answer: C · Lack of ADH release (cranial diabetes insipidus)

Why this is the answer

Without ADH the collecting ducts stay impermeable to water, so dilute urine is produced and the patient loses free water, raising plasma sodium.

Answer

C · Lack of ADH release (cranial diabetes insipidus)
5.Microbiology

Answer: B · Avoid cleaning cat litter and avoid undercooked meat

Why this is the answer

Toxoplasma oocysts are shed in cat faeces and cysts are found in undercooked meat. Infection during pregnancy can damage the fetal brain and eyes.

Answer

B · Avoid cleaning cat litter and avoid undercooked meat
6.Microbiology

Answer: A · Bacillus cereus

Why this is the answer

Bacillus cereus spores survive boiling. If cooked rice is left warm, the bacteria grow and make a heat-stable emetic toxin, so reheating does not make the rice safe.

Answer

A · Bacillus cereus
7.Pharmacology

Answer: D · It stimulates muscarinic receptors and contracts the bladder muscle

Why this is the answer

Bethanechol mimics acetylcholine at muscarinic receptors, contracting the detrusor muscle. It must not be used if there is mechanical obstruction to outflow.

Answer

D · It stimulates muscarinic receptors and contracts the bladder muscle
8.Pharmacology

Answer: A · Anticholinergic toxidrome

Why this is the answer

Anticholinergic toxicity causes hyperthermia, dry flushed skin, mydriasis, urinary retention, tachycardia and delirium. Dry skin helps distinguish it from serotonin syndrome and sympathomimetic poisoning, which cause sweating.

Answer

A · Anticholinergic toxidrome
9.Arterial blood gas interpretation

Answer: Osm = 337 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 = 2·143 + 30.1 + 21.1 = 337.2 ≈ 337 mOsm/kg

Answer

Osm = 337 mOsm/kg
10.Arterial blood gas interpretation

Answer: added metabolic alkalosis

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 = 135 − (86 + 16) = 33

Delta ratio

(33 − 12)/(24 − 16) = 2.625
added metabolic alkalosis

Answer

added metabolic alkalosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.42 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 = 10.5 × 0.04 = 0.42 s
RR = 25 × 0.04 = 1.00 s

Fridericia’s formula

QTc = 0.42/∛1.00 = 0.42/1 = 0.42 s

Answer

QTc = 0.42 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (420 ms)

12.ECG rhythm strip interpretation

Answer: dual-chamber (AV) paced rhythm

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: R–R = 23 small boxes, 1500 ÷ 23 ≈ 65 per minute.
2. Rhythm: regular, every R–R is 0.92 s.
3. P waves: each P wave follows its own pacing spike (atrial pacing).
4. AV interval: the second spike comes 0.18 s after the first one (the programmed AV delay).
5. QRS: 0.14 s, wide, right after the second spike (ventricular pacing).

Interpretation

dual-chamber (AV) paced rhythm

Answer

dual-chamber (AV) paced rhythm

The paced QRS is wide by nature; do not call it a bundle branch block or a ventricular rhythm.

13.Evidence-based practice statistics

Answer: LR− = 0.32

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.

Negative likelihood ratio

LR− = (1 − 0.77)/0.73 = 0.3151 ≈ 0.32

Answer

LR− = 0.32
14.Evidence-based practice statistics

Answer: NNT = 20

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.

Absolute risk reduction

ARR = 0.11·0.46 = 0.0506

Number needed to treat

NNT = 1/0.0506 = 19.76 → 20

Answer

NNT = 20

The same relative effect gives a smaller NNT when the baseline risk is higher.

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