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. AUlnar artery
  2. BAxillary artery
  3. CBrachial artery
  4. DRadial artery
2.Human anatomyHard

Why does a displaced fracture of the femoral neck carry a high risk of avascular necrosis of the femoral head?

  1. AIt damages the sciatic nerve that controls blood flow
  2. BIt cuts the main trunk of the femoral artery
  3. CIt tears the retinacular branches of the medial circumflex femoral artery
  4. DIt blocks the femoral vein and causes congestion
3.Human physiologyMedium

Which protein forms the mesh that stabilises a blood clot?

  1. ACollagen
  2. BFibrin
  3. CThrombin
  4. DAlbumin
4.Human physiologyHard

A patient hyperventilating during a panic attack has tingling fingers. What would the arterial blood gas most likely show?

  1. ALow pH and high PaCO₂
  2. BLow pH and low bicarbonate
  3. CHigh pH and low PaCO₂
  4. DHigh pH and high bicarbonate
5.MicrobiologyMedium

In the chain of infection, what is the "reservoir"?

  1. AThe route by which the pathogen leaves the infected host's body
  2. BThe place where the pathogen normally lives and multiplies
  3. CThe way the pathogen enters a new host
  4. DThe person who is most at risk of infection
6.MicrobiologyHard

Primary syphilis typically presents with:

  1. AA painful cluster of small blisters on the genitals or the mouth
  2. BA widespread rash on the palms and soles
  3. CDamage to the heart and brain
  4. DA painless ulcer (chancre) at the site of infection
7.PharmacologyMedium

Which patient should usually not receive a live vaccine?

  1. AA healthy 1-year-old child
  2. BA patient with mild seasonal allergies
  3. CA healthy adult nurse who works on a children's ward
  4. DA patient receiving chemotherapy for leukaemia
8.PharmacologyHard

A patient receiving frequent salbutamol (albuterol) nebulisers develops a fine tremor and a heart rate of 120 per minute. What is the best explanation?

  1. ASalbutamol blocks muscarinic receptors in the heart
  2. BAt high doses it also stimulates beta receptors in skeletal muscle and the heart
  3. CSalbutamol causes high potassium, which speeds the heart and causes muscle twitching
  4. DThe patient is allergic to salbutamol and needs adrenaline
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 18 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 18 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 53 mmHg (7.1 kPa) and PaCO₂ 47 mmHg (6.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 53 mmHg (7.1 kPa)PaCO₂ 47 mmHg (6.3 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus arrhythmiaventricular bigeminynormal sinus rhythmsinus rhythm with PVCs

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. 1sinus arrhythmia
  2. 2ventricular bigeminy
  3. 3normal sinus rhythm
  4. 4sinus rhythm with PVCs
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
casescontrolsexposed21986abnot exposed171134cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 390 patients with a disease (cases) and 220 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 = 219b = 86c = 171d = 134
OR =
14.Evidence-based practice statisticsHard
pre-test50%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 50% for a disease. A test with sensitivity 89% and specificity 78% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 50%Se = 89%Sp = 78%negative
p′ = %

3Solutions

1.Human anatomy

Answer: D · 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

D · Radial artery
2.Human anatomy

Answer: C · It tears the retinacular branches of the medial circumflex femoral artery

Why this is the answer

The femoral head is supplied mainly by retinacular branches of the medial circumflex femoral artery running along the neck. A displaced neck fracture tears them and the head can die.

Answer

C · It tears the retinacular branches of the medial circumflex femoral artery
3.Human physiology

Answer: B · Fibrin

Why this is the answer

Thrombin converts soluble fibrinogen into insoluble fibrin strands, which bind the platelet plug and trap red cells to form a stable clot.

Answer

B · Fibrin
4.Human physiology

Answer: C · High pH and low PaCO₂

Why this is the answer

Hyperventilation blows off CO₂ and causes acute respiratory alkalosis. Alkalosis increases calcium binding to albumin, lowering ionised calcium and causing tingling.

Answer

C · High pH and low PaCO₂
5.Microbiology

Answer: B · The place where the pathogen normally lives and multiplies

Why this is the answer

The chain of infection links the agent, reservoir, portal of exit, mode of transmission, portal of entry and susceptible host. Breaking any link stops transmission.

Answer

B · The place where the pathogen normally lives and multiplies
6.Microbiology

Answer: D · A painless ulcer (chancre) at the site of infection

Why this is the answer

Treponema pallidum causes a painless chancre in the primary stage. The secondary stage brings rash and systemic symptoms, and tertiary syphilis can damage the heart and nervous system. Painful blisters suggest herpes.

Answer

D · A painless ulcer (chancre) at the site of infection
7.Pharmacology

Answer: D · A patient receiving chemotherapy for leukaemia

Why this is the answer

Live attenuated vaccines can cause serious infection in immunosuppressed people and are generally avoided in pregnancy. Inactivated vaccines are safe but may give a weaker response.

Answer

D · A patient receiving chemotherapy for leukaemia
8.Pharmacology

Answer: B · At high doses it also stimulates beta receptors in skeletal muscle and the heart

Why this is the answer

Tremor comes from beta-2 stimulation of skeletal muscle. Tachycardia comes from some beta-1 (and cardiac beta-2) stimulation and a reflex response to vasodilation. High doses also shift potassium into cells and can cause hypokalaemia.

Answer

B · At high doses it also stimulates beta receptors in skeletal muscle and the heart
9.Arterial blood gas interpretation

Answer: PaCO₂ = 35 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.

Winter’s formula

PaCO₂ = 1.5·18 + 8 = 35 mmHg
range: 33–37 mmHg

Answer

PaCO₂ = 35 mmHg
10.Arterial blood gas interpretation

Answer: A–a gradient = 37.98 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 = 0.21·713 − 47/0.8 = 149.7 − 58.75 = 90.98 mmHg

Gradient

A–a = 90.98 − 53 = 37.98 mmHg

Answer

A–a gradient = 37.98 mmHg
11.ECG rhythm strip interpretation

Answer: ventricular bigeminy

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.

Five steps

1. Rate: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: regularly irregular, a short and a long R–R alternate (0.46 s and 1.14 s).
3. P waves: upright before every narrow QRS; none before the early wide beats.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s in the sinus beats; the early beats are wide (0.16 s) and bizarre, with the T wave pointing the other way.

Interpretation

ventricular bigeminy

Answer

ventricular bigeminy
12.ECG rhythm strip interpretation

Answer: P waves

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: R–R = 17 small boxes, 1500 ÷ 17 ≈ 88 per minute.
2. Rhythm: regular, every R–R is 0.68 s.
3. P waves: none visible.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s).

First abnormal step

P waves → accelerated junctional rhythm

Answer

P waves
13.Evidence-based practice statistics

Answer: OR = 2

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: 219/171 = 1.281
controls: 86/134 = 0.6418

Odds ratio

OR = (219·134)/(86·171) = 1.996 ≈ 2

Answer

OR = 2

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

14.Evidence-based practice statistics

Answer: p′ = 12.4 %

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.

Likelihood ratio

LR− = (1 − 0.89)/0.78 = 0.141

Pre-test odds

0.5/(1 − 0.5) = 1

Post-test odds

1·0.141 = 0.141

Post-test probability

p′ = 0.141/(1 + 0.141) = 0.1236 ≈ 12.4%

Answer

p′ = 12.4%

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