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 circle of Willis at the base of the brain connects which two arterial supplies?

  1. AExternal carotid and subclavian arterial systems
  2. BLeft and right external carotid arteries
  3. CInternal carotid and vertebrobasilar systems
  4. DJugular and vertebral systems
2.Human anatomyHard

A stroke affecting the left middle cerebral artery in a right-handed person most likely causes:

  1. ALeft-sided weakness and aphasia
  2. BIsolated loss of balance
  3. CRight-sided weakness and left visual neglect
  4. DRight-sided weakness and aphasia
3.Human physiologyMedium

Why is the oxygen–haemoglobin dissociation curve S-shaped?

  1. AOxygen dissolves better in plasma at high partial pressure
  2. BRed cells change size as they take up oxygen
  3. CHaemoglobin can bind only one oxygen molecule
  4. DBinding of one oxygen makes the next bind more easily
4.Human physiologyHard

What is the main reason the ventricles do not contract at the same moment as the atria?

  1. AThe SA node fires twice per beat
  2. BThe ventricles have a longer refractory period only
  3. CThe Purkinje fibres conduct slowly
  4. DConduction is delayed at the atrioventricular node
5.MicrobiologyMedium

Pneumocystis jirovecii pneumonia in a person with advanced HIV is an example of:

  1. AAn opportunistic infection
  2. BA zoonotic infection
  3. CA vector-borne infection
  4. DA food-borne infection
6.MicrobiologyHard

In Griffith's 1928 experiment, mice died after injection of heat-killed smooth (S) pneumococci mixed with live rough (R) pneumococci. What did this show?

  1. ARough pneumococci are always more virulent than smooth ones
  2. BA "transforming principle" from dead bacteria could change harmless bacteria into virulent ones
  3. CHeat does not kill pneumococci
  4. DViruses carry genes between bacteria
7.PharmacologyMedium

An adult patient is due to receive digoxin. The apical pulse, counted for a full minute, is 52 beats per minute. What should the nurse do?

  1. AWithhold the dose and notify the prescriber
  2. BGive half the dose and document the pulse
  3. CGive the dose and recheck the pulse in one hour
  4. DGive the dose with food to slow absorption
8.PharmacologyHard

A patient with Parkinson's disease has nausea. Why should metoclopramide be avoided?

  1. AIt causes severe diarrhoea in Parkinson's disease
  2. BIt blocks dopamine receptors in the brain and can worsen the parkinsonism
  3. CIt increases dopamine levels in the brain too much and causes psychosis
  4. DIt inhibits the absorption of all oral drugs
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 24 mmHg (3.2 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 24 mmHg (3.2 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard
pH7.357.457.30PaCO₂mmHg354575HCO₃⁻mmol/L222636acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.30, PaCO₂ 75 mmHg (10.0 kPa), HCO₃⁻ 36 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.30PaCO₂ 75 mmHg (10.0 kPa)HCO₃⁻ 36 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
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
Se97%Sp74%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 97% and a specificity of 74%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 97%Sp = 74%
LR+ =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 87% and specificity 75%. The prevalence of the disease is 4%. How many false-positive results FP are expected?

N = 10 000p = 4%Se = 87%Sp = 75%
FP =

3Solutions

1.Human anatomy

Answer: C · Internal carotid and vertebrobasilar systems

Why this is the answer

The circle of Willis links the internal carotid arteries with the basilar artery (formed by the vertebral arteries), allowing some collateral flow.

Answer

C · Internal carotid and vertebrobasilar systems
2.Human anatomy

Answer: D · Right-sided weakness and aphasia

Why this is the answer

The left MCA supplies the left motor cortex (face and arm of the right side) and Broca's and Wernicke's areas, so right hemiparesis with aphasia is typical.

Answer

D · Right-sided weakness and aphasia
3.Human physiology

Answer: D · Binding of one oxygen makes the next bind more easily

Why this is the answer

Haemoglobin shows cooperative binding: each bound O₂ increases the affinity of the remaining sites, giving a sigmoid curve.

Answer

D · Binding of one oxygen makes the next bind more easily
4.Human physiology

Answer: D · Conduction is delayed at the atrioventricular node

Why this is the answer

The AV node conducts slowly (about 0.1 s delay), so atrial contraction completes ventricular filling before ventricular depolarisation begins.

Answer

D · Conduction is delayed at the atrioventricular node
5.Microbiology

Answer: A · An opportunistic infection

Why this is the answer

Opportunistic infections take advantage of a weakened immune system. In HIV they become common when the CD4 count falls to low levels.

Answer

A · An opportunistic infection
6.Microbiology

Answer: B · A "transforming principle" from dead bacteria could change harmless bacteria into virulent ones

Why this is the answer

Something from the dead S strain turned live R bacteria into capsule-forming, virulent S bacteria. Avery, MacLeod and McCarty later showed that this transforming principle was DNA.

Answer

B · A "transforming principle" from dead bacteria could change harmless bacteria into virulent ones
7.Pharmacology

Answer: A · Withhold the dose and notify the prescriber

Why this is the answer

Digoxin is usually withheld in adults if the apical pulse is below 60 per minute, and the prescriber is informed. Bradycardia may be an early sign of toxicity.

Answer

A · Withhold the dose and notify the prescriber
8.Pharmacology

Answer: B · It blocks dopamine receptors in the brain and can worsen the parkinsonism

Why this is the answer

Metoclopramide crosses the blood–brain barrier and antagonises D2 receptors. In Parkinson's disease this worsens rigidity and bradykinesia, so antiemetics that do not block central dopamine receptors are preferred.

Answer

B · It blocks dopamine receptors in the brain and can worsen the parkinsonism
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 20.8 mmol/L

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.

Change in PaCO₂

|24 − 40| = 16 mmHg → 1.6 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·1.6 = 20.8 mmol/L

Answer

HCO₃⁻ = 20.8 mmol/L
10.Arterial blood gas interpretation

Answer: chronic

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 HCO₃⁻

acute: 24 + 1·3.5 = 27.5 mmol/L
chronic: 24 + 3.5·3.5 = 36.25 mmol/L

Compare

measured: 36 mmol/L → chronic

Answer

chronic
11.ECG rhythm strip interpretation

Answer: QTc = 0.49 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 = 12 × 0.04 = 0.48 s
RR = 24 × 0.04 = 0.96 s

Bazett’s formula

QTc = 0.48/√0.96 = 0.48/0.9798 = 0.49 s

Answer

QTc = 0.49 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (490 ms)

12.ECG rhythm strip interpretation

Answer: QRS duration

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 = 16 small boxes, 1500 ÷ 16 ≈ 94 per minute.
2. Rhythm: regular, every R–R is 0.64 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: 0.12 s, wide (0.12 s or more).

First abnormal step

QRS duration → sinus rhythm with wide QRS

Answer

QRS duration
13.Evidence-based practice statistics

Answer: LR+ = 3.73

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.

Positive likelihood ratio

LR+ = 0.97/(1 − 0.74) = 3.731 ≈ 3.73

Answer

LR+ = 3.73
14.Evidence-based practice statistics

Answer: FP = 2400

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.

With and without the disease

10 000·0.04 = 400
10 000 − 400 = 9600

False positives

FP = 9600·0.25 = 2400

Answer

FP = 2400

Of the 2748 positives only 348 have the disease (PPV 12.7%).

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