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 vessels carry oxygenated blood from the lungs to the heart?

  1. AVenae cavae
  2. BBronchial arteries
  3. CPulmonary arteries
  4. DPulmonary veins
2.Human anatomyHard

Which ligament of the knee prevents the tibia from sliding forward relative to the femur?

  1. AAnterior cruciate ligament
  2. BPosterior cruciate ligament
  3. CMedial collateral ligament
  4. DPatellar ligament
3.Human physiologyMedium

Why can cardiac muscle not be tetanised like skeletal muscle?

  1. AIt is controlled only by hormones
  2. BIts long refractory period lasts almost as long as the contraction
  3. CIt has no calcium in the sarcoplasmic reticulum
  4. DIt is not striated
4.Human physiologyHard

In long-standing aortic stenosis, how does the left ventricle adapt?

  1. AAtrophy of the muscle due to less work
  2. BConcentric hypertrophy with a thicker wall
  3. CNo change because the valve is not part of the ventricle
  4. DThinning of the wall with dilation
5.MicrobiologyMedium

How does an autoclave sterilise instruments?

  1. AWith ultraviolet light only
  2. BWith alcohol vapour at room temperature
  3. CWith dry heat at about 60 °C
  4. DWith steam under pressure at about 121 °C
6.MicrobiologyHard

Why is Chlamydia trachomatis usually diagnosed with nucleic acid amplification tests instead of routine culture on agar?

  1. AIt is too large to grow on agar plates
  2. BIt dies immediately in the presence of oxygen
  3. CIt is an obligate intracellular bacterium that cannot grow on ordinary media
  4. DIt is a virus and has no DNA
7.PharmacologyMedium

Which drug is used for torsades de pointes?

  1. AOral digoxin
  2. BIntravenous magnesium sulfate
  3. CIntravenous adenosine (rapid push)
  4. DIntravenous verapamil
8.PharmacologyHard

Which antiepileptic drug carries the highest well-known risk of neural tube defects and developmental problems when taken in pregnancy?

  1. ASodium valproate
  2. BLevetiracetam
  3. CGabapentin
  4. DLamotrigine
9.Arterial blood gas interpretationMedium
pH7.357.457.44PaCO₂mmHg354529HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.44, PaCO₂ 29 mmHg (3.9 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.44PaCO₂ 29 mmHg (3.9 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 37 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 37 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 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/mVCPR (non-shockable rhythm)transcutaneous pacingimmediate defibrillationsynchronised cardioversion

A patient without a palpable pulse has this organised rhythm on the monitor (pulseless electrical activity). Which treatment do adult resuscitation guidelines name for 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. 1CPR (non-shockable rhythm)
  2. 2transcutaneous pacing
  3. 3immediate defibrillation
  4. 4synchronised cardioversion
13.Evidence-based practice statisticsMedium
peopleyears1270124402.535301new cases29

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, 29 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

270 × 1 year440 × 2.5 years530 × 1 year29 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
CER12%EER?RRR 16%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 16% in relative terms (RRR = 16%). In a patient group the risk without treatment (CER) is 12% 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 = 16%CER = 12%
NNT =

3Solutions

1.Human anatomy

Answer: D · Pulmonary veins

Why this is the answer

Four pulmonary veins drain oxygenated blood into the left atrium. They are the main exception to the rule that veins carry deoxygenated blood.

Answer

D · Pulmonary veins
2.Human anatomy

Answer: A · Anterior cruciate ligament

Why this is the answer

The anterior cruciate ligament limits anterior translation of the tibia; a positive anterior drawer or Lachman test suggests an ACL tear.

Answer

A · Anterior cruciate ligament
3.Human physiology

Answer: B · Its long refractory period lasts almost as long as the contraction

Why this is the answer

The plateau of the cardiac action potential gives a long refractory period, so the muscle relaxes before it can be excited again. This allows the heart to refill.

Answer

B · Its long refractory period lasts almost as long as the contraction
4.Human physiology

Answer: B · Concentric hypertrophy with a thicker wall

Why this is the answer

Pressure overload makes the ventricular wall thicken (concentric hypertrophy) to keep wall stress normal. Volume overload, as in regurgitation, causes dilation instead.

Answer

B · Concentric hypertrophy with a thicker wall
5.Microbiology

Answer: D · With steam under pressure at about 121 °C

Why this is the answer

Pressurised steam reaches about 121 °C and kills all microorganisms, including spores, typically in about 15 minutes or more depending on the load.

Answer

D · With steam under pressure at about 121 °C
6.Microbiology

Answer: C · It is an obligate intracellular bacterium that cannot grow on ordinary media

Why this is the answer

Chlamydia replicates only inside host cells, so it cannot be grown on agar. NAATs such as PCR on urine or swabs are sensitive and are the standard diagnostic test.

Answer

C · It is an obligate intracellular bacterium that cannot grow on ordinary media
7.Pharmacology

Answer: B · Intravenous magnesium sulfate

Why this is the answer

IV magnesium is first-line for torsades de pointes, even when serum magnesium is normal. QT-prolonging drugs are stopped and potassium is corrected.

Answer

B · Intravenous magnesium sulfate
8.Pharmacology

Answer: A · Sodium valproate

Why this is the answer

Valproate is strongly teratogenic, causing neural tube defects and other malformations, and it affects neurodevelopment. It should be avoided in pregnancy unless no alternative works.

Answer

A · Sodium valproate
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 7.44: within 7.35–7.45
PaCO₂ 29 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: PaCO₂ = 46.9 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

0.7·37 + 21 = 46.9 mmHg

Answer

PaCO₂ = 46.9 mmHg

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

11.ECG rhythm strip interpretation

Answer: QTc = 0.409 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 = 27 × 0.04 = 1.08 s

Fridericia’s formula

QTc = 0.42/∛1.08 = 0.42/1.026 = 0.409 s

Answer

QTc = 0.409 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (409 ms)

12.ECG rhythm strip interpretation

Answer: CPR (non-shockable rhythm)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

1. Rate: R–R = 19 small boxes, 1500 ÷ 19 ≈ 79 per minute.
2. Rhythm: regular, every R–R is 0.76 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.16 s, constant, within 0.12–0.20 s.
5. QRS: 0.06 s, narrow (below 0.12 s).
normal sinus rhythm

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

CPR (non-shockable rhythm)

Answer

CPR (non-shockable rhythm)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: IR = 15.3 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 = 270·1 + 440·2.5 + 530·1 = 1900

Incidence rate

IR = 29/1900·1000 = 15.3 per 1000 person-years

Answer

IR = 15.3 per 1000 person-years
14.Evidence-based practice statistics

Answer: NNT = 53

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 = 0.12·0.16 = 0.0192

Number needed to treat

NNT = 1/0.0192 = 52.08 → 53

Answer

NNT = 53

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

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