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 bone of the skull contains the foramen magnum?

  1. ATemporal bone
  2. BParietal bone
  3. CSphenoid bone
  4. DOccipital bone
2.Human anatomyHard

A lesion of the left optic tract causes which visual field defect?

  1. ARight homonymous hemianopia
  2. BBlindness in the left eye only
  3. CLeft homonymous hemianopia
  4. DBitemporal hemianopia
3.Human physiologyMedium

According to Poiseuille's law, if the radius of an arteriole halves, its resistance to flow:

  1. AIncreases about 16-fold
  2. BIncreases 4-fold
  3. CHalves
  4. DDoubles
4.Human physiologyHard

After a head injury, a patient passes large volumes of very dilute urine and plasma sodium rises. What is the most likely cause?

  1. ALack of ADH release (cranial diabetes insipidus)
  2. BExcess aldosterone
  3. CExcess ADH release (SIADH)
  4. DUncontrolled diabetes mellitus
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 way the pathogen enters a new host
  3. CThe person who is most at risk of infection
  4. DThe place where the pathogen normally lives and multiplies
6.MicrobiologyHard

How do high-risk HPV types contribute to cervical cancer?

  1. AThe virus kills cells so quickly that they are replaced by cancer cells
  2. BViral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb
  3. CThe virus produces an endotoxin that damages DNA
  4. DThe virus destroys CD4 T cells in the cervix
7.PharmacologyMedium

After naloxone reverses an opioid overdose, why must the patient be watched closely?

  1. ANaloxone makes the opioid stay longer in the body
  2. BNaloxone may wear off before the opioid does, so breathing can slow again
  3. CNaloxone often causes severe low blood glucose a few hours after the dose
  4. DNaloxone itself causes respiratory depression at high doses
8.PharmacologyHard

A teenager took a large overdose of diphenhydramine. He is agitated, hot, flushed and confused, with dry skin, dilated pupils and a full bladder. What is this pattern?

  1. ACholinergic toxidrome
  2. BOpioid toxidrome
  3. CSerotonin syndrome
  4. DAnticholinergic toxidrome
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 149 mmol/L, glucose 21.5 mmol/L and urea 18 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 149 mmol/Lglucose 21.5 mmol/Lurea 18 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 77 mmHg (10.3 kPa) and PaCO₂ 58 mmHg (7.7 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 77 mmHg (10.3 kPa)PaCO₂ 58 mmHg (7.7 kPa)
A–a gradient = 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 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/mVsinus bradycardiajunctional rhythmthird-degree (complete) AV blockasystole

Identify the rhythm on this lead II strip. 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 bradycardia
  2. 2junctional rhythm
  3. 3third-degree (complete) AV block
  4. 4asystole
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive69115184abnegative41245286cdtotal110360470

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the positive likelihood ratio LR+. Round to two decimal places.

a = 69b = 115c = 41d = 245
LR+ =
14.Evidence-based practice statisticsHard
CER37%EER?RRR 27%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 27% in relative terms (RRR = 27%). In a patient group the risk without treatment (CER) is 37% 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 = 27%CER = 37%
NNT =

3Solutions

1.Human anatomy

Answer: D · Occipital bone

Why this is the answer

The foramen magnum is a large opening in the occipital bone through which the medulla oblongata continues as the spinal cord.

Answer

D · Occipital bone
2.Human anatomy

Answer: A · Right homonymous hemianopia

Why this is the answer

The left optic tract carries fibres from the left half of each retina, which see the right visual field. Its lesion causes loss of the right half of the field in both eyes.

Answer

A · Right homonymous hemianopia
3.Human physiology

Answer: A · Increases about 16-fold

Why this is the answer

Resistance is proportional to 1/r⁴, so halving the radius raises resistance by 2⁴ = 16. This is why small changes in arteriole diameter control blood flow so strongly.

Answer

A · Increases about 16-fold
4.Human physiology

Answer: A · Lack of ADH release (cranial diabetes insipidus)

Why this is the answer

Without ADH the collecting ducts stay impermeable to water, so dilute urine is produced and the patient loses free water, raising plasma sodium.

Answer

A · Lack of ADH release (cranial diabetes insipidus)
5.Microbiology

Answer: D · 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

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

Answer: B · Viral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb

Why this is the answer

E6 promotes the breakdown of p53 and E7 binds Rb, removing controls on cell division and DNA repair. Infected cells can then accumulate mutations and become cancerous over years.

Answer

B · Viral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb
7.Pharmacology

Answer: B · Naloxone may wear off before the opioid does, so breathing can slow again

Why this is the answer

Naloxone acts for a shorter time than many opioids, especially long-acting and slow-release ones. Repeated doses or an infusion may be needed.

Answer

B · Naloxone may wear off before the opioid does, so breathing can slow again
8.Pharmacology

Answer: D · Anticholinergic toxidrome

Why this is the answer

Anticholinergic toxicity causes hyperthermia, dry flushed skin, mydriasis, urinary retention, tachycardia and delirium. Dry skin helps distinguish it from serotonin syndrome and sympathomimetic poisoning, which cause sweating.

Answer

D · Anticholinergic toxidrome
9.Arterial blood gas interpretation

Answer: Osm = 338 mOsm/kg

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.

Calculated osmolality

Osm = 2·149 + 21.5 + 18 = 337.5 ≈ 338 mOsm/kg

Answer

Osm = 338 mOsm/kg
10.Arterial blood gas interpretation

Answer: A–a gradient = 21.62 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 = 0.24·713 − 58/0.8 = 171.1 − 72.5 = 98.62 mmHg

Gradient

A–a = 98.62 − 77 = 21.62 mmHg

Answer

A–a gradient = 21.62 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.451 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 = 11.5 × 0.04 = 0.46 s
RR = 26 × 0.04 = 1.04 s

Bazett’s formula

QTc = 0.46/√1.04 = 0.46/1.02 = 0.451 s

Answer

QTc = 0.451 s

Between the usual limits for men (about 0.45 s) and women (about 0.46 s): borderline, depending on the reference used. (451 ms)

12.ECG rhythm strip interpretation

Answer: asystole

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: no countable ventricular rate.
2. Rhythm: none; an almost flat line.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: no QRS complexes.

Interpretation

asystole

Answer

asystole

A flat line is always checked: look at the patient, the leads and the gain, and view a second lead, because a loose electrode or fine VF can look like asystole.

13.Evidence-based practice statistics

Answer: LR+ = 1.96

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.

Sensitivity and specificity

Se = 69/110 = 0.6273
Sp = 245/360 = 0.6806

Positive likelihood ratio

LR+ = 0.6273/(1 − 0.6806) = 1.964 ≈ 1.96

Answer

LR+ = 1.96
14.Evidence-based practice statistics

Answer: NNT = 11

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 = 0.37·0.27 = 0.0999

Number needed to treat

NNT = 1/0.0999 = 10.01 → 11

Answer

NNT = 11

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

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