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

In which structure do sperm mature and get stored after leaving the testis?

  1. AEpididymis
  2. BSeminiferous tubules
  3. CProstate gland
  4. DSeminal vesicle
2.Human anatomyHard

A pituitary tumour grows upwards and causes loss of both outer (temporal) halves of the visual field. Where is the visual pathway compressed?

  1. ALeft optic tract
  2. BRight optic nerve
  3. COccipital cortex
  4. DOptic chiasm
3.Human physiologyMedium

Which hormonal event triggers ovulation?

  1. AA surge of prolactin
  2. BA fall in oestrogen
  3. CA rise in progesterone from the corpus luteum
  4. DA surge of luteinising hormone (LH)
4.Human physiologyHard

At the start of a fever, a patient shivers and feels cold even though body temperature is rising. Why?

  1. AThe thermoreceptors in the skin are destroyed
  2. BPyrogens raise the hypothalamic set point above the current body temperature
  3. CThe body has lost its ability to produce heat
  4. DSweating has already cooled the body too much
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 place where the pathogen normally lives and multiplies
  3. CThe way the pathogen enters a new host
  4. DThe person who is most at risk of infection
6.MicrobiologyHard

What does an R0 (basic reproduction number) of 3 mean?

  1. AThe infection lasts three days
  2. BOn average one case infects three others in a fully susceptible population
  3. CThree percent of infected people die
  4. DThree doses of vaccine are needed
7.PharmacologyMedium

A patient must mix regular (soluble) insulin and NPH (isophane) insulin in one syringe. What is the correct order?

  1. ADraw up the cloudy NPH insulin first, then the clear regular insulin
  2. BShake both vials hard, then draw them up in any order
  3. CDraw them up in separate syringes, then mix them in a cup
  4. DDraw up the clear regular insulin first, then the cloudy NPH insulin
8.PharmacologyHard

A patient who used heroin a few hours ago is given a first dose of buprenorphine and quickly develops severe withdrawal. Why?

  1. ABuprenorphine has no effect at opioid receptors
  2. BBuprenorphine causes an allergic reaction in heroin users
  3. CBuprenorphine is a high-affinity partial agonist that displaces heroin
  4. DBuprenorphine is a pure antagonist like naloxone with no agonist effect
9.Arterial blood gas interpretationMedium
pH7.357.457.36PaCO₂mmHg354529HCO₃⁻mmol/L222616uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.36, PaCO₂ 29 mmHg (3.9 kPa) and HCO₃⁻ 16 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.36PaCO₂ 29 mmHg (3.9 kPa)HCO₃⁻ 16 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 35% oxygen shows PaO₂ 62 mmHg (8.3 kPa) and PaCO₂ 55 mmHg (7.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 35%PaO₂ 62 mmHg (8.3 kPa)PaCO₂ 55 mmHg (7.3 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/mVthird-degree (complete) AV blocksecond-degree AV block type IIsecond-degree AV block type I (Wenckebach)first-degree AV block

This lead II strip shows a conduction problem between the atria and the ventricles. Which rhythm is 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. 1third-degree (complete) AV block
  2. 2second-degree AV block type II
  3. 3second-degree AV block type I (Wenckebach)
  4. 4first-degree AV block
13.Evidence-based practice statisticsMedium
Se68%Sp64%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 68% and a specificity of 64%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 68%Sp = 64%
LR+ =
14.Evidence-based practice statisticsHard
pre-test40%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 40% for a disease. A test with sensitivity 98% and specificity 75% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 40%Se = 98%Sp = 75%negative
p′ = %

3Solutions

1.Human anatomy

Answer: A · Epididymis

Why this is the answer

Sperm are made in the seminiferous tubules and then mature and are stored in the epididymis before passing into the ductus deferens.

Answer

A · Epididymis
2.Human anatomy

Answer: D · Optic chiasm

Why this is the answer

Bitemporal hemianopia results from compression of the crossing nasal fibres at the optic chiasm, which lies directly above the pituitary gland.

Answer

D · Optic chiasm
3.Human physiology

Answer: D · A surge of luteinising hormone (LH)

Why this is the answer

Rising oestrogen from the dominant follicle triggers an LH surge from the anterior pituitary, which causes ovulation about a day later.

Answer

D · A surge of luteinising hormone (LH)
4.Human physiology

Answer: B · Pyrogens raise the hypothalamic set point above the current body temperature

Why this is the answer

Pyrogens trigger prostaglandin E₂ in the hypothalamus, raising the set point. Until body temperature reaches the new set point, heat-gain responses such as shivering occur.

Answer

B · Pyrogens raise the hypothalamic set point above the current body temperature
5.Microbiology

Answer: B · 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

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

Answer: B · On average one case infects three others in a fully susceptible population

Why this is the answer

R0 is the average number of secondary cases from one case when everyone is susceptible. Herd immunity needs roughly 1 − 1/R0 of the population immune: about 67% for R0 = 3.

Answer

B · On average one case infects three others in a fully susceptible population
7.Pharmacology

Answer: D · Draw up the clear regular insulin first, then the cloudy NPH insulin

Why this is the answer

Drawing up regular insulin first prevents NPH from contaminating the regular insulin vial. NPH is gently rolled, not shaken, to mix it.

Answer

D · Draw up the clear regular insulin first, then the cloudy NPH insulin
8.Pharmacology

Answer: C · Buprenorphine is a high-affinity partial agonist that displaces heroin

Why this is the answer

Buprenorphine binds mu receptors more strongly than heroin but activates them less, so it can precipitate withdrawal. Induction is started when the patient already has mild to moderate withdrawal signs.

Answer

C · Buprenorphine is a high-affinity partial agonist that displaces heroin
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 7.36: within 7.35–7.45
PaCO₂ 29 mmHg: low (35–45)
HCO₃⁻ 16 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 30–34 mmHg, so the measured 29 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 118.8 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 = 0.35·713 − 55/0.8 = 249.5 − 68.75 = 180.8 mmHg

Gradient

A–a = 180.8 − 62 = 118.8 mmHg

Answer

A–a gradient = 118.8 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.38 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 = 25 × 0.04 = 1.00 s

Bazett’s formula

QTc = 0.38/√1.00 = 0.38/1 = 0.38 s

Answer

QTc = 0.38 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (380 ms)

12.ECG rhythm strip interpretation

Answer: second-degree AV block type II

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: the P waves are regular; R–R is regular except for a long pause where a QRS is missing.
3. P waves: upright and regular (P–P 0.80 s, 75 per minute); one P in every 4 is not followed by a QRS.
4. PR interval: constant at 0.20 s in the conducted beats.
5. QRS: 0.14 s, wide (0.12 s or more).

Interpretation

second-degree AV block type II

Answer

second-degree AV block type II

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: LR+ = 1.89

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+ = 0.68/(1 − 0.64) = 1.889 ≈ 1.89

Answer

LR+ = 1.89
14.Evidence-based practice statistics

Answer: p′ = 1.7 %

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− = (1 − 0.98)/0.75 = 0.02667

Pre-test odds

0.4/(1 − 0.4) = 0.6667

Post-test odds

0.6667·0.02667 = 0.01778

Post-test probability

p′ = 0.01778/(1 + 0.01778) = 0.01747 ≈ 1.7%

Answer

p′ = 1.7%

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