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 hepatic portal vein is formed by the union of which two veins?

  1. ASuperior mesenteric vein and left renal vein
  2. BSuperior mesenteric vein and splenic vein
  3. CInferior vena cava and renal vein
  4. DHepatic vein and splenic vein
2.Human anatomyHard

Which structure passes through the inguinal canal in males?

  1. ASpermatic cord
  2. BFemoral artery
  3. CGreat saphenous vein
  4. DObturator nerve
3.Human physiologyMedium

What is the main stimulus for breathing in a healthy person?

  1. AA fall in blood pH caused by lactate only
  2. BA rise in arterial CO₂
  3. CA fall in arterial O₂
  4. DA rise in blood glucose
4.Human physiologyHard

Why does breathing 100% oxygen correct hypoxaemia from a true right-to-left shunt only poorly?

  1. AThe extra oxygen is all exhaled as CO₂
  2. BThe shunted blood never comes into contact with alveolar gas
  3. CPure oxygen damages haemoglobin
  4. DShunted blood is already fully saturated
5.MicrobiologyMedium

Which cells does HIV mainly infect and destroy?

  1. APlatelets
  2. BNeutrophils
  3. CRed blood cells
  4. DCD4 T helper cells
6.MicrobiologyHard

A young adult with sore throat, fever and swollen lymph nodes is given amoxicillin and develops a widespread rash. Which infection is most likely?

  1. AStreptococcal tonsillitis
  2. BMeasles
  3. CInfectious mononucleosis caused by Epstein–Barr virus
  4. DChickenpox
7.PharmacologyMedium

A patient must mix regular (soluble) insulin and NPH (isophane) insulin in one syringe. What is the correct order?

  1. ADraw up the cloudy NPH insulin first, then the clear regular insulin
  2. BDraw up the clear regular insulin first, then the cloudy NPH insulin
  3. CShake both vials hard, then draw them up in any order
  4. DDraw them up in separate syringes, then mix them in a cup
8.PharmacologyHard

A woman has received a high-dose oxytocin infusion with large volumes of hypotonic fluid for many hours. She now has a headache, confusion and a low serum sodium. What is the most likely cause?

  1. AAn allergic reaction to oxytocin causing brain swelling
  2. BExcessive salt in the infusion fluid
  3. CWater intoxication from the antidiuretic effect of oxytocin
  4. DNormal tiredness after a long labour
9.Arterial blood gas interpretationMedium
pH7.357.457.31PaCO₂mmHg354566HCO₃⁻mmol/L222632uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.31, PaCO₂ 66 mmHg (8.8 kPa) and HCO₃⁻ 32 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.31PaCO₂ 66 mmHg (8.8 kPa)HCO₃⁻ 32 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 28% oxygen shows PaO₂ 79 mmHg (10.5 kPa) and PaCO₂ 46 mmHg (6.1 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 28%PaO₂ 79 mmHg (10.5 kPa)PaCO₂ 46 mmHg (6.1 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

This lead II strip shows atrial flutter with a fixed conduction ratio. Find the ventricular rate in beats per minute.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
ventricular rate = bpm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVjunctional rhythmidioventricular rhythmventricular tachycardiathird-degree (complete) AV block

Identify the rhythm on this 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. 1junctional rhythm
  2. 2idioventricular rhythm
  3. 3ventricular tachycardia
  4. 4third-degree (complete) AV block
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment49311360abcontrol230620850cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 360 patients received a new treatment and 850 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the relative risk reduction RRR as a percentage. Round to one decimal place.

treatment: 49/360control: 230/850
RRR = %
14.Evidence-based practice statisticsHard
p (%)PPV (%)15%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 90% and a specificity of 92%. It is used in a population where the prevalence is 15%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 90%Sp = 92%p = 15%
PPV = %

3Solutions

1.Human anatomy

Answer: B · Superior mesenteric vein and splenic vein

Why this is the answer

The portal vein forms behind the neck of the pancreas from the superior mesenteric and splenic veins. It carries nutrient-rich blood to the liver.

Answer

B · Superior mesenteric vein and splenic vein
2.Human anatomy

Answer: A · Spermatic cord

Why this is the answer

The inguinal canal carries the spermatic cord in males and the round ligament in females. The femoral vessels pass below the inguinal ligament instead.

Answer

A · Spermatic cord
3.Human physiology

Answer: B · A rise in arterial CO₂

Why this is the answer

Central chemoreceptors respond to CO₂ (through the pH of the cerebrospinal fluid). Low O₂ adds strongly to the drive only when PaO₂ falls well below normal, for example at high altitude.

Answer

B · A rise in arterial CO₂
4.Human physiology

Answer: B · The shunted blood never comes into contact with alveolar gas

Why this is the answer

Shunted blood bypasses ventilated alveoli and mixes deoxygenated blood into arterial blood. Extra inspired oxygen cannot reach it, unlike in V/Q mismatch or hypoventilation.

Answer

B · The shunted blood never comes into contact with alveolar gas
5.Microbiology

Answer: D · CD4 T helper cells

Why this is the answer

HIV binds CD4 and a co-receptor on T helper cells. Loss of these cells weakens both antibody and cell-mediated immunity, leading to AIDS.

Answer

D · CD4 T helper cells
6.Microbiology

Answer: C · Infectious mononucleosis caused by Epstein–Barr virus

Why this is the answer

Glandular fever is caused by EBV. Many patients given amoxicillin during the illness develop a rash. Antibiotics do not help because the cause is viral.

Answer

C · Infectious mononucleosis caused by Epstein–Barr virus
7.Pharmacology

Answer: B · Draw up the clear regular insulin first, then the cloudy NPH insulin

Why this is the answer

Drawing up regular insulin first prevents NPH from contaminating the regular insulin vial. NPH is gently rolled, not shaken, to mix it.

Answer

B · Draw up the clear regular insulin first, then the cloudy NPH insulin
8.Pharmacology

Answer: C · Water intoxication from the antidiuretic effect of oxytocin

Why this is the answer

Oxytocin has antidiuretic activity at high doses. With large volumes of fluid this can cause water retention and dilutional hyponatraemia, so fluid balance and sodium are monitored.

Answer

C · Water intoxication from the antidiuretic effect of oxytocin
9.Arterial blood gas interpretation

Answer: partially 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 7.31: acidaemia (below 7.35)
PaCO₂ 66 mmHg: high (35–45)
HCO₃⁻ 32 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 63.14 mmHg

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.

Alveolar oxygen

PAO₂ = 0.28·713 − 46/0.8 = 199.6 − 57.5 = 142.1 mmHg

Gradient

A–a = 142.1 − 79 = 63.14 mmHg

Answer

A–a gradient = 63.14 mmHg
11.ECG rhythm strip interpretation

Answer: ventricular rate = 63 bpm

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.

Flutter waves

F–F = 6 small boxes = 0.24 s → 1500 ÷ 6 = 250 per minute

QRS complexes

R–R = 24 small boxes = 0.96 s → 1500 ÷ 24 = 63 per minute
conduction ratio = 250 ÷ 63 = 4:1

Answer

ventricular rate = 63 bpm
12.ECG rhythm strip interpretation

Answer: idioventricular rhythm

More ventricular rhythms: torsades de pointes is a polymorphic ventricular tachycardia, usually 150–250/min, in which the wide complexes change in height and twist around the baseline, pointing up for a few beats and then down. Textbooks link it to a prolonged QT interval, and magnesium sulfate is the drug resuscitation guidelines name for it. An idioventricular rhythm is a ventricular escape rhythm: regular, wide QRS (0.12 s or more), no P waves, at 20–40/min (an accelerated idioventricular rhythm runs at 40–100/min). Monomorphic VT has identical wide complexes at more than 100/min. VF is chaotic, without any repeating complex.

Five steps

1. Rate: R–R = 51 small boxes, 1500 ÷ 51 ≈ 29 per minute.
2. Rhythm: regular, every R–R is 2.04 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide (0.12 s or more) and bizarre, with the T wave pointing the other way.

Interpretation

idioventricular rhythm

Answer

idioventricular rhythm

An idioventricular rhythm is an escape rhythm: the ventricles take over because the pacemakers above them have failed.

13.Evidence-based practice statistics

Answer: RRR = 49.7 %

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.

Event rates

EER = 49/360 = 0.1361
CER = 230/850 = 0.2706

Relative risk reduction

ARR = 0.2706 − 0.1361 = 0.1345
RRR = 0.1345/0.2706 = 0.497 ≈ 49.7%

Answer

RRR = 49.7%
14.Evidence-based practice statistics

Answer: PPV = 66.5 %

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 = 0.9·0.15 = 0.135
(1 − Sp)·(1 − p) = 0.08·0.85 = 0.068

Positive predictive value

PPV = 0.135/(0.135 + 0.068) = 0.665 ≈ 66.5%

Answer

PPV = 66.5%

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

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