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 structure produces most of the cerebrospinal fluid?

  1. APineal gland
  2. BPia mater
  3. CChoroid plexus
  4. DArachnoid granulations
2.Human anatomyHard

In which part of the small intestine are vitamin B12 and bile salts mainly absorbed?

  1. ADuodenum
  2. BCaecum
  3. CJejunum
  4. DTerminal ileum
3.Human physiologyMedium

What causes the first heart sound (S1)?

  1. AClosure of the aortic and pulmonary valves
  2. BClosure of the mitral and tricuspid valves
  3. COpening of the aortic valve
  4. DBlood filling the atria
4.Human physiologyHard

Which combination of signs is expected in a patient in early hypovolaemic shock after major bleeding?

  1. ATachycardia, cool pale skin and reduced urine output
  2. BBradycardia, cool pale skin and high urine output
  3. CBradycardia, warm flushed skin and high urine output
  4. DTachycardia, warm flushed skin and high urine output
5.MicrobiologyMedium

Which statement is one of Koch's postulates?

  1. AThe organism must be found in healthy people as well
  2. BThe disease must respond to antibiotics
  3. CThe organism must be visible with the naked eye
  4. DThe organism must cause the same disease when introduced into a healthy susceptible host
6.MicrobiologyHard

Why must a negative-sense RNA virus such as influenza carry its own RNA-dependent RNA polymerase into the host cell?

  1. AHost ribosomes cannot read any viral genes
  2. BThe polymerase is needed to integrate the genome into host DNA
  3. CThe polymerase protects the virus from antibodies
  4. DHost cells cannot make mRNA from an RNA template
7.PharmacologyMedium

Why do patients taking clozapine need regular blood counts?

  1. AIt can cause agranulocytosis
  2. BIt changes the blood group
  3. CIt often causes iron-deficiency anaemia
  4. DIt raises the platelet count dangerously
8.PharmacologyHard

A drug is ordered at 5 micrograms/kg/min for an 80 kg patient. The infusion contains 1,600 micrograms per mL. What rate in mL/h is needed?

  1. A25 mL/h
  2. B150 mL/h
  3. C4 mL/h
  4. D15 mL/h
9.Arterial blood gas interpretationMedium
pH7.357.457.16PaCO₂mmHg354570HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.16, PaCO₂ 70 mmHg (9.3 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.16PaCO₂ 70 mmHg (9.3 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 70 mmHg (9.3 kPa) and PaCO₂ 32 mmHg (4.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 70 mmHg (9.3 kPa)PaCO₂ 32 mmHg (4.3 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 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/mV

This lead II strip shows an AV block, so the atria and the ventricles beat at different rates. Measure the P–P interval and find the atrial rate in beats per minute (1500 method, whole number).

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
atrial rate = bpm
13.Evidence-based practice statisticsMedium
casesperson-yearsexposed1113900not exposed361900

Practice exercise (made-up values, not clinical guidance). In a cohort study, exposed people contributed 3900 person-years with 111 new cases, and unexposed people 1900 person-years with 36 new cases. Find the incidence rate ratio IRR (exposed versus unexposed). Round to two decimal places.

exposed: 111/3900 PYnot exposed: 36/1900 PY
IRR =
14.Evidence-based practice statisticsHard
pre-test5%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 5% for a disease. A test with sensitivity 67% and specificity 83% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 67%Sp = 83%positive
p′ = %

3Solutions

1.Human anatomy

Answer: C · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

C · Choroid plexus
2.Human anatomy

Answer: D · Terminal ileum

Why this is the answer

The terminal ileum absorbs vitamin B12 (bound to intrinsic factor) and reabsorbs bile salts. The duodenum mainly absorbs iron.

Answer

D · Terminal ileum
3.Human physiology

Answer: B · Closure of the mitral and tricuspid valves

Why this is the answer

S1 ("lub") is caused by closure of the atrioventricular valves at the start of systole. S2 ("dub") is closure of the semilunar valves.

Answer

B · Closure of the mitral and tricuspid valves
4.Human physiology

Answer: A · Tachycardia, cool pale skin and reduced urine output

Why this is the answer

Baroreceptor-driven sympathetic activation raises heart rate and constricts skin vessels. Reduced renal perfusion, ADH and aldosterone lower urine output.

Answer

A · Tachycardia, cool pale skin and reduced urine output
5.Microbiology

Answer: D · The organism must cause the same disease when introduced into a healthy susceptible host

Why this is the answer

Koch's postulates say the microbe must be found in every case, grown in pure culture, cause the disease in a healthy host and be recovered again from that host. Some pathogens cannot be cultured, so the postulates have limits.

Answer

D · The organism must cause the same disease when introduced into a healthy susceptible host
6.Microbiology

Answer: D · Host cells cannot make mRNA from an RNA template

Why this is the answer

A negative-sense genome must first be copied into positive-sense mRNA. Human cells have no enzyme that copies RNA from RNA, so the virus brings its own polymerase.

Answer

D · Host cells cannot make mRNA from an RNA template
7.Pharmacology

Answer: A · It can cause agranulocytosis

Why this is the answer

Clozapine can cause severe neutropenia (agranulocytosis). Regular white cell and neutrophil counts allow treatment to be stopped before life-threatening infection occurs.

Answer

A · It can cause agranulocytosis
8.Pharmacology

Answer: D · 15 mL/h

Why this is the answer

5 × 80 = 400 micrograms/min, × 60 = 24,000 micrograms/h, ÷ 1,600 micrograms/mL = 15 mL/h. Weight-based infusions are double-checked because errors are easy to make.

Answer

D · 15 mL/h
9.Arterial blood gas interpretation

Answer: uncompensated

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 7.16: acidaemia (below 7.35)
PaCO₂ 70 mmHg: high (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 61.12 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 − 32/0.8 = 171.1 − 40 = 131.1 mmHg

Gradient

A–a = 131.1 − 70 = 61.12 mmHg

Answer

A–a gradient = 61.12 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

Fridericia’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: atrial rate = 79 bpm

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.

Atrial rate

P–P = 19 small boxes = 0.76 s → 1500 ÷ 19 = 78.95 ≈ 79 per minute

Ventricular rate

R–R = 34 small boxes = 1.36 s → 1500 ÷ 34 = 44.12 ≈ 44 per minute

Answer

atrial rate = 79 bpm

Answer

atrial rate = 79 bpm

Third-degree block with a narrow-complex junctional escape (usually 40–60 per minute).

13.Evidence-based practice statistics

Answer: IRR = 1.5

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.

Incidence rates

exposed: 111/3900 = 28.46 per 1000 person-years
not exposed: 36/1900 = 18.95 per 1000 person-years

Rate ratio

IRR = 28.46/18.95 = 1.502 ≈ 1.5

Answer

IRR = 1.5
14.Evidence-based practice statistics

Answer: p′ = 17.2 %

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+ = 0.67/(1 − 0.83) = 3.941

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·3.941 = 0.2074

Post-test probability

p′ = 0.2074/(1 + 0.2074) = 0.1718 ≈ 17.2%

Answer

p′ = 17.2%

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