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 brain is chiefly responsible for coordination and balance?

  1. ACerebellum
  2. BThalamus
  3. CHypothalamus
  4. DMedulla oblongata
2.Human anatomyHard

After a difficult delivery with traction on the neck, a baby's arm hangs by the side, internally rotated with the forearm pronated ("waiter's tip"). Which part of the brachial plexus is injured?

  1. ALower trunk (C8–T1)
  2. BPosterior cord
  3. CMedial cord
  4. DUpper trunk (C5–C6)
3.Human physiologyMedium

Vital capacity is the sum of which lung volumes?

  1. AInspiratory reserve volume and residual volume
  2. BTidal volume and residual volume
  3. CTidal volume, inspiratory reserve volume and expiratory reserve volume
  4. DResidual volume and expiratory reserve volume
4.Human physiologyHard

In the renin–angiotensin–aldosterone system, where is angiotensin I mainly converted to angiotensin II?

  1. AIn the kidneys' juxtaglomerular cells
  2. BIn the lungs
  3. CIn the liver
  4. DIn the adrenal cortex
5.MicrobiologyMedium

How does an autoclave sterilise instruments?

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

Which bacterial toxin causes the muscle spasms of tetanus?

  1. AEndotoxin from the outer membrane
  2. BTetanospasmin, which blocks inhibitory neurotransmitter release
  3. CBotulinum toxin, which blocks acetylcholine release at the neuromuscular junction
  4. DCholera toxin, which activates adenylate cyclase
7.PharmacologyMedium

When does oseltamivir give the most benefit in influenza?

  1. AAt any time, as the timing makes no difference
  2. BWhen started within 48 hours of the first symptoms
  3. COnly after symptoms have lasted at least one week
  4. DOnly after a bacterial pneumonia has developed
8.PharmacologyHard

Probenecid has been used to raise plasma penicillin levels. How does it do this?

  1. AIt blocks the tubular secretion of penicillin in the kidney
  2. BIt displaces penicillin from plasma proteins
  3. CIt inhibits the liver metabolism of penicillin
  4. DIt increases the absorption of penicillin from the small intestine
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.13PaCO₂mmHg354544HCO₃⁻mmol/L222614appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.13, PaCO₂ 44 mmHg (5.9 kPa), HCO₃⁻ 14 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.13PaCO₂ 44 mmHg (5.9 kPa)HCO₃⁻ 14 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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 eventtotaltreatment98422520abcontrol97263360cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 520 patients received a new treatment and 360 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 98/520control: 97/360
NNT =
14.Evidence-based practice statisticsHard
p (%)PPV (%)10%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 88% and a specificity of 83%. It is used in a population where the prevalence is 10%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 88%Sp = 83%p = 10%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Cerebellum

Why this is the answer

The cerebellum fine-tunes movement, posture and balance. Damage causes ataxia and an unsteady gait.

Answer

A · Cerebellum
2.Human anatomy

Answer: D · Upper trunk (C5–C6)

Why this is the answer

Erb's palsy follows stretching of the upper trunk (C5–C6), paralysing deltoid, the external rotators and biceps. Lower trunk injury (Klumpke's) affects the small hand muscles instead.

Answer

D · Upper trunk (C5–C6)
3.Human physiology

Answer: C · Tidal volume, inspiratory reserve volume and expiratory reserve volume

Why this is the answer

Vital capacity = IRV + TV + ERV. It excludes the residual volume, which always stays in the lungs.

Answer

C · Tidal volume, inspiratory reserve volume and expiratory reserve volume
4.Human physiology

Answer: B · In the lungs

Why this is the answer

Renin (kidney) cleaves angiotensinogen (liver) to angiotensin I, which ACE, mainly on pulmonary capillary endothelium, converts to angiotensin II.

Answer

B · In the lungs
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: B · Tetanospasmin, which blocks inhibitory neurotransmitter release

Why this is the answer

Tetanospasmin from Clostridium tetani blocks the release of GABA and glycine from inhibitory interneurons, causing spastic paralysis. Botulinum toxin, by contrast, causes flaccid paralysis.

Answer

B · Tetanospasmin, which blocks inhibitory neurotransmitter release
7.Pharmacology

Answer: B · When started within 48 hours of the first symptoms

Why this is the answer

Neuraminidase inhibitors work best early, while the virus is multiplying. Started within 48 hours, they shorten illness; in high-risk or hospitalised patients they may still be given later.

Answer

B · When started within 48 hours of the first symptoms
8.Pharmacology

Answer: A · It blocks the tubular secretion of penicillin in the kidney

Why this is the answer

Penicillins are excreted largely by organic anion transporters in the proximal tubule. Probenecid competes for these transporters, so penicillin is excreted more slowly and its level stays higher.

Answer

A · It blocks the tubular secretion of penicillin in the kidney
9.Arterial blood gas interpretation

Answer: PaCO₂ = 26 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 = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg

Answer

PaCO₂ = 26 mmHg
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·14 + 8 = 29 → 27–31 mmHg

Compare

measured: 44 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: QTc = 0.491 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 = 15 × 0.04 = 0.60 s

Bazett’s formula

QTc = 0.38/√0.60 = 0.38/0.7746 = 0.491 s

Answer

QTc = 0.491 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (491 ms)

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 = 20 small boxes, 1500 ÷ 20 ≈ 75 per minute.
2. Rhythm: regular, every R–R is 0.80 s.
3. P waves: inverted, just before each QRS.
4. PR interval: 0.08 s, shorter than 0.12 s.
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: NNT = 13

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 = 98/520 = 0.1885
CER = 97/360 = 0.2694

Number needed to treat

ARR = 0.2694 − 0.1885 = 0.08098
NNT = 1/0.08098 = 12.35 → 13

Answer

NNT = 13

Treating 13 patients prevents about one event.

14.Evidence-based practice statistics

Answer: PPV = 36.5 %

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 = 0.88·0.1 = 0.088
(1 − Sp)·(1 − p) = 0.17·0.9 = 0.153

Positive predictive value

PPV = 0.088/(0.088 + 0.153) = 0.3651 ≈ 36.5%

Answer

PPV = 36.5%

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

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