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 type of epithelium lines the urinary bladder?

  1. ATransitional epithelium (urothelium)
  2. BSimple columnar epithelium
  3. CSimple squamous epithelium
  4. DPseudostratified columnar epithelium
2.Human anatomyHard

In portal hypertension, oesophageal varices form at which portosystemic anastomosis?

  1. ABetween the paraumbilical veins and the epigastric veins
  2. BBetween the left gastric vein and the oesophageal tributaries of the azygos vein
  3. CBetween the splenic vein and the left renal vein
  4. DBetween the superior rectal and middle rectal veins
3.Human physiologyMedium

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

  1. AInsulin release after a meal
  2. BADH release when plasma osmolality rises
  3. CSweating when body temperature rises
  4. DOxytocin release during labour
4.Human physiologyHard

After several days of persistent vomiting of stomach contents, which acid–base disturbance is most likely?

  1. ARespiratory alkalosis
  2. BRespiratory acidosis
  3. CMetabolic acidosis
  4. DMetabolic alkalosis
5.MicrobiologyMedium

Which organism is a common cause of infection in burns and in people with cystic fibrosis, and can produce a green pigment?

  1. APseudomonas aeruginosa
  2. BStreptococcus pyogenes
  3. CClostridium tetani
  4. DHelicobacter pylori
6.MicrobiologyHard

What did Pasteur's swan-neck flask experiment demonstrate?

  1. AMicroorganisms need light to grow
  2. BMicroorganisms come from other microorganisms, not from spontaneous generation
  3. CAir itself produces microorganisms
  4. DBoiling cannot kill microorganisms
7.PharmacologyMedium

A patient starting sulfasalazine should be told about which harmless effect?

  1. AOrange-yellow colouring of the urine
  2. BWhite spots on the nails
  3. CGreen colouring of the sweat
  4. DBlue colouring of the tongue and gums
8.PharmacologyHard

A patient with severe chronic hyponatraemia receives hypertonic saline. Why is the rate of correction strictly limited?

  1. ARaising sodium too fast causes severe hypokalaemia and cardiac arrest
  2. BHypertonic saline is toxic to the liver at high rates
  3. CRaising sodium too fast can cause osmotic demyelination in the brain
  4. DFast correction causes immediate kidney failure
9.Arterial blood gas interpretationMedium
pH7.357.457.57PaCO₂mmHg354543HCO₃⁻mmol/L222638uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.57, PaCO₂ 43 mmHg (5.7 kPa) and HCO₃⁻ 38 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.57PaCO₂ 43 mmHg (5.7 kPa)HCO₃⁻ 38 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 39 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 39 mmol/L
PaCO₂ = 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 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/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
peopleyears117022801.531102.5new cases21

Practice exercise (made-up values, not clinical guidance). In a cohort, groups of people were followed for different lengths of time (see the table: number of people and years of follow-up for each). During follow-up, 21 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

170 × 2 years80 × 1.5 years110 × 2.5 years21 new cases
IR = per 1000 person-years
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 62% and specificity 91% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 62%Sp = 91%positive
p′ = %

3Solutions

1.Human anatomy

Answer: A · Transitional epithelium (urothelium)

Why this is the answer

Transitional epithelium can change shape from rounded to flattened cells as the bladder stretches, while staying watertight.

Answer

A · Transitional epithelium (urothelium)
2.Human anatomy

Answer: B · Between the left gastric vein and the oesophageal tributaries of the azygos vein

Why this is the answer

At the lower oesophagus, portal blood in the left gastric vein meets systemic blood in the oesophageal veins draining to the azygos system. High portal pressure dilates these veins.

Answer

B · Between the left gastric vein and the oesophageal tributaries of the azygos vein
3.Human physiology

Answer: D · 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

D · Oxytocin release during labour
4.Human physiology

Answer: D · Metabolic alkalosis

Why this is the answer

Vomiting removes HCl, and the stomach's acid secretion leaves bicarbonate in the blood. Volume loss and low potassium help keep the alkalosis going.

Answer

D · Metabolic alkalosis
5.Microbiology

Answer: A · Pseudomonas aeruginosa

Why this is the answer

Pseudomonas aeruginosa is an opportunistic pathogen of burns, ventilated patients and cystic fibrosis lungs. It is naturally resistant to many antibiotics.

Answer

A · Pseudomonas aeruginosa
6.Microbiology

Answer: B · Microorganisms come from other microorganisms, not from spontaneous generation

Why this is the answer

Boiled broth in a flask with a curved neck stayed sterile because dust and microbes were trapped in the bend. When the neck was broken, microbes entered and grew, disproving spontaneous generation.

Answer

B · Microorganisms come from other microorganisms, not from spontaneous generation
7.Pharmacology

Answer: A · Orange-yellow colouring of the urine

Why this is the answer

Sulfasalazine can colour urine and sometimes skin and contact lenses orange-yellow. More serious adverse effects include blood disorders and rash, so blood counts are monitored.

Answer

A · Orange-yellow colouring of the urine
8.Pharmacology

Answer: C · Raising sodium too fast can cause osmotic demyelination in the brain

Why this is the answer

In chronic hyponatraemia the brain adapts to low osmolality. Correcting sodium too rapidly shrinks brain cells and can cause osmotic demyelination (central pontine myelinolysis), so sodium is checked often.

Answer

C · Raising sodium too fast can cause osmotic demyelination in the brain
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 7.57: alkalaemia (above 7.45)
PaCO₂ 43 mmHg: normal (35–45)
HCO₃⁻ 38 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 45.6–49.6 mmHg, so the measured 43 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: PaCO₂ = 48.3 mmHg

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

0.7·39 + 21 = 48.3 mmHg

Answer

PaCO₂ = 48.3 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: QTc = 0.449 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 = 11 × 0.04 = 0.44 s
RR = 24 × 0.04 = 0.96 s

Bazett’s formula

QTc = 0.44/√0.96 = 0.44/0.9798 = 0.449 s

Answer

QTc = 0.449 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (449 ms)

12.ECG rhythm strip interpretation

Answer: atrial rate = 63 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 = 24 small boxes = 0.96 s → 1500 ÷ 24 = 62.5 ≈ 63 per minute

Ventricular rate

5 QRS complexes in 6 s × 10 = 50 per minute

Answer

atrial rate = 63 bpm

Answer

atrial rate = 63 bpm

Second-degree type I (Wenckebach): 3 P waves for every 2 QRS complexes.

13.Evidence-based practice statistics

Answer: IR = 28.6 per 1000 person-years

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.

Person-years

PY = 170·2 + 80·1.5 + 110·2.5 = 735

Incidence rate

IR = 21/735·1000 = 28.6 per 1000 person-years

Answer

IR = 28.6 per 1000 person-years
14.Evidence-based practice statistics

Answer: p′ = 26.6 %

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+ = 0.62/(1 − 0.91) = 6.889

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·6.889 = 0.3626

Post-test probability

p′ = 0.3626/(1 + 0.3626) = 0.2661 ≈ 26.6%

Answer

p′ = 26.6%

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