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 part of the brainstem contains the main cardiovascular and respiratory centres?

  1. AMedulla oblongata
  2. BCerebellum
  3. CMidbrain
  4. DPons
2.Human anatomyHard

A footballer takes a blow to the outside of the planted knee. Which combination of injuries is classically called the "unhappy triad"?

  1. AAnterior cruciate ligament, posterior cruciate ligament and patellar ligament
  2. BPosterior cruciate ligament, lateral collateral ligament and lateral meniscus
  3. CAnterior cruciate ligament, medial collateral ligament and medial meniscus
  4. DMedial collateral ligament, lateral collateral ligament and patella
3.Human physiologyMedium

Which receptors respond mainly to a fall in arterial oxygen levels?

  1. ABaroreceptors in the carotid sinus
  2. BStretch receptors in the lungs
  3. CCentral chemoreceptors in the medulla
  4. DPeripheral chemoreceptors in the carotid and aortic bodies
4.Human physiologyHard

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

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

In which phase of the bacterial growth curve do the cells divide at their fastest constant rate?

  1. ALag (adaptation) phase
  2. BStationary (plateau) phase
  3. CDeath phase
  4. DLog (exponential) phase
6.MicrobiologyHard

A healthcare worker's blood test is positive for anti-HBs (hepatitis B surface antibody) and negative for HBsAg and anti-HBc. What does this most likely mean?

  1. APast natural infection that has cleared
  2. BImmunity from hepatitis B vaccination
  3. CCurrent acute hepatitis B infection
  4. DChronic hepatitis B infection
7.PharmacologyMedium

A patient is starting olanzapine. Which monitoring is most important over the following months?

  1. AINR and platelet count
  2. BWeight, blood glucose and blood lipids
  3. CHearing tests and vision tests every month
  4. DPeak expiratory flow
8.PharmacologyHard

Morphine 4 mg IV is ordered. The ampoule contains 10 mg/mL. What volume should be drawn up?

  1. A0.04 mL
  2. B0.4 mL
  3. C4 mL
  4. D2.5 mL
9.Arterial blood gas interpretationMedium
pH7.357.457.38PaCO₂mmHg354551HCO₃⁻mmol/L222629uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.38, PaCO₂ 51 mmHg (6.8 kPa) and HCO₃⁻ 29 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.38PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 29 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 143, Cl⁻ 112 and HCO₃⁻ 11 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 143 mmol/LCl⁻ 112 mmol/LHCO₃⁻ 11 mmol/L
delta ratio =
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/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
eventno eventtotaltreatment3278110abcontrol98152250cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 110 patients received a new treatment and 250 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the absolute risk reduction ARR as a percentage. Round to one decimal place.

treatment: 32/110control: 98/250
ARR = %
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 84% and specificity 89% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 84%Sp = 89%positive
p′ = %

3Solutions

1.Human anatomy

Answer: A · Medulla oblongata

Why this is the answer

The medulla oblongata contains the vital centres that regulate heart rate, blood pressure and breathing rhythm.

Answer

A · Medulla oblongata
2.Human anatomy

Answer: C · Anterior cruciate ligament, medial collateral ligament and medial meniscus

Why this is the answer

A valgus force with rotation tears the MCL, the ACL and the medial meniscus, which is firmly attached to the MCL.

Answer

C · Anterior cruciate ligament, medial collateral ligament and medial meniscus
3.Human physiology

Answer: D · Peripheral chemoreceptors in the carotid and aortic bodies

Why this is the answer

The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.

Answer

D · Peripheral chemoreceptors in the carotid and aortic bodies
4.Human physiology

Answer: A · 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

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

Answer: D · Log (exponential) phase

Why this is the answer

After the lag phase of adjustment, cells enter the log phase and grow exponentially. Growth stops in the stationary phase as nutrients run out and waste builds up.

Answer

D · Log (exponential) phase
6.Microbiology

Answer: B · Immunity from hepatitis B vaccination

Why this is the answer

The vaccine contains HBsAg, so a vaccinated person makes anti-HBs but no anti-HBc. Past natural infection gives both anti-HBs and anti-HBc, and ongoing infection shows HBsAg.

Answer

B · Immunity from hepatitis B vaccination
7.Pharmacology

Answer: B · Weight, blood glucose and blood lipids

Why this is the answer

Olanzapine and several other atypical antipsychotics cause weight gain, insulin resistance and dyslipidaemia. Weight, waist size, glucose and lipids are checked regularly.

Answer

B · Weight, blood glucose and blood lipids
8.Pharmacology

Answer: B · 0.4 mL

Why this is the answer

4 mg ÷ 10 mg/mL = 0.4 mL. The unused remainder of a controlled drug is discarded with a witness.

Answer

B · 0.4 mL
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 7.38: within 7.35–7.45
PaCO₂ 51 mmHg: high (35–45)
HCO₃⁻ 29 mmol/L: high (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: delta ratio = 0.6154

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 = 143 − (112 + 11) = 20

Delta ratio

(20 − 12)/(24 − 11) = 8/13 = 0.6154

Answer

delta ratio = 0.6154

Below 1: an added normal anion gap acidosis.

11.ECG rhythm strip interpretation

Answer: QTc = 0.415 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 = 9.5 × 0.04 = 0.38 s
RR = 21 × 0.04 = 0.84 s

Bazett’s formula

QTc = 0.38/√0.84 = 0.38/0.9165 = 0.415 s

Answer

QTc = 0.415 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (415 ms)

12.ECG rhythm strip interpretation

Answer: PR interval

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 = 20 small boxes, 1500 ÷ 20 ≈ 75 per minute.
2. Rhythm: regular, every R–R is 0.80 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.26 s, constant, longer than 0.20 s.
5. QRS: 0.10 s, narrow (below 0.12 s).

First abnormal step

PR interval → first-degree AV block

Answer

PR interval
13.Evidence-based practice statistics

Answer: ARR = 10.1 %

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 = 32/110 = 0.2909
CER = 98/250 = 0.392

Absolute risk reduction

ARR = 0.392 − 0.2909 = 0.1011 ≈ 10.1%

Answer

ARR = 10.1%
14.Evidence-based practice statistics

Answer: p′ = 28.7 %

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+ = 0.84/(1 − 0.89) = 7.636

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·7.636 = 0.4019

Post-test probability

p′ = 0.4019/(1 + 0.4019) = 0.2867 ≈ 28.7%

Answer

p′ = 28.7%

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