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. ASphenoid bone
  2. BOccipital bone
  3. CTemporal bone
  4. DParietal bone
2.Human anatomyHard

A patient cannot abduct the arm beyond about 15° after a fracture of the surgical neck of the humerus, and has numbness over the lateral shoulder. Which nerve is most likely injured?

  1. ASuprascapular nerve
  2. BAxillary nerve
  3. CRadial nerve
  4. DLong thoracic nerve
3.Human physiologyMedium

Cardiac output equals heart rate multiplied by:

  1. APeripheral resistance
  2. BBlood pressure
  3. CStroke volume
  4. DEjection fraction
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

Many antifungal drugs target ergosterol. Why does this work?

  1. AErgosterol is the main structural component of bacterial cell walls
  2. BErgosterol is only found in viruses
  3. CErgosterol is in fungal cell membranes but not in human cells
  4. DHuman cells use ergosterol to make energy
6.MicrobiologyHard

A healthcare worker's blood test is positive for anti-HBs (hepatitis B surface antibody) and negative for HBsAg and anti-HBc. What does this most likely mean?

  1. AChronic hepatitis B infection
  2. BPast natural infection that has cleared
  3. CImmunity from hepatitis B vaccination
  4. DCurrent acute hepatitis B infection
7.PharmacologyMedium

A patient is starting lisinopril. Which rare but serious adverse effect should the nurse teach the patient to report immediately?

  1. ADarker skin after exposure to sunlight
  2. BAn increase in appetite in the evening
  3. CSwelling of the lips, tongue or face
  4. DA harmless rash on the palms of the hands
8.PharmacologyHard

A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?

  1. AA stroke unrelated to the medication
  2. BMyasthenic crisis from too little anticholinesterase drug
  3. CAn allergic reaction to pyridostigmine
  4. DCholinergic crisis from too much anticholinesterase drug
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 59 mmHg (7.9 kPa). Use the rule that in chronic respiratory acidosis HCO₃⁻ rises by 3.5 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 59 mmHg (7.9 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 146, Cl⁻ 108, HCO₃⁻ 21 mmol/L and albumin 32 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 146 mmol/LCl⁻ 108 mmol/LHCO₃⁻ 21 mmol/Lalbumin 32 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVnormal sinus rhythmsinus rhythm with sinus arrestsinus rhythm with PVCssecond-degree AV block type II

Interpret this lead II rhythm strip. 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. 1normal sinus rhythm
  2. 2sinus rhythm with sinus arrest
  3. 3sinus rhythm with PVCs
  4. 4second-degree AV block type II
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVventricular tachycardiajunctional rhythmidioventricular rhythmasystole

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. 1ventricular tachycardia
  2. 2junctional rhythm
  3. 3idioventricular rhythm
  4. 4asystole
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment119811930abcontrol20100120cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 930 patients received a new treatment and 120 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: 119/930control: 20/120
NNT =
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 66% and specificity 93% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 40%Se = 66%Sp = 93%positive
p′ = %

3Solutions

1.Human anatomy

Answer: B · 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

B · Occipital bone
2.Human anatomy

Answer: B · Axillary nerve

Why this is the answer

The axillary nerve wraps around the surgical neck of the humerus. It supplies deltoid and teres minor and the skin over the lateral shoulder ("regimental badge" area).

Answer

B · Axillary nerve
3.Human physiology

Answer: C · Stroke volume

Why this is the answer

CO = HR × SV. At rest about 70 beats/min × 70 mL ≈ 5 L/min.

Answer

C · Stroke volume
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: C · Ergosterol is in fungal cell membranes but not in human cells

Why this is the answer

Fungal membranes contain ergosterol, while human membranes contain cholesterol. Azoles block ergosterol synthesis and amphotericin binds ergosterol, so they target fungi selectively.

Answer

C · Ergosterol is in fungal cell membranes but not in human cells
6.Microbiology

Answer: C · Immunity from hepatitis B vaccination

Why this is the answer

The vaccine contains HBsAg, so a vaccinated person makes anti-HBs but no anti-HBc. Past natural infection gives both anti-HBs and anti-HBc, and ongoing infection shows HBsAg.

Answer

C · Immunity from hepatitis B vaccination
7.Pharmacology

Answer: C · Swelling of the lips, tongue or face

Why this is the answer

ACE inhibitors can cause angioedema, which can obstruct the airway and needs emergency care. It is linked to raised bradykinin levels and can occur even after long use.

Answer

C · Swelling of the lips, tongue or face
8.Pharmacology

Answer: D · Cholinergic crisis from too much anticholinesterase drug

Why this is the answer

Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.

Answer

D · Cholinergic crisis from too much anticholinesterase drug
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 30.65 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

|59 − 40| = 19 mmHg → 1.9 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 3.5·1.9 = 30.65 mmol/L

Answer

HCO₃⁻ = 30.65 mmol/L
10.Arterial blood gas interpretation

Answer: AGc = 19 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.

Anion gap

AG = 146 − (108 + 21) = 17

Correction for albumin

17 + 0.25·(40 − 32) = 19 mmol/L

Answer

AGc = 19 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: sinus rhythm with sinus arrest

Rhythm criteria (lead II): sinus rhythm has an upright P wave before every QRS, a constant PR of 0.12–0.20 s and a narrow QRS: normal sinus rhythm at 60–100/min, sinus bradycardia below 60, sinus tachycardia above 100. Atrial fibrillation: no P waves, a fibrillatory baseline and an irregularly irregular R–R. Atrial flutter: sawtooth flutter waves at about 250–350/min with a fixed conduction ratio such as 2:1 or 4:1. First-degree AV block: sinus rhythm with a constant PR above 0.20 s. Junctional rhythm: narrow QRS at 40–60/min with absent or inverted P waves (PR below 0.12 s, or P after the QRS). A PVC is an early, wide (0.12 s or more), bizarre QRS without a P wave, with the T wave in the opposite direction and usually a full compensatory pause; in bigeminy every second beat is a PVC. Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: regular (R–R 0.96 s) except for one pause of 2.32 s, which is not a whole number of P–P cycles.
3. P waves: upright, one before every QRS; no P wave at all during the pause.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.10 s, narrow (below 0.12 s).

Interpretation

sinus rhythm with sinus arrest

Answer

sinus rhythm with sinus arrest
12.ECG rhythm strip interpretation

Answer: idioventricular rhythm

More ventricular rhythms: torsades de pointes is a polymorphic ventricular tachycardia, usually 150–250/min, in which the wide complexes change in height and twist around the baseline, pointing up for a few beats and then down. Textbooks link it to a prolonged QT interval, and magnesium sulfate is the drug resuscitation guidelines name for it. An idioventricular rhythm is a ventricular escape rhythm: regular, wide QRS (0.12 s or more), no P waves, at 20–40/min (an accelerated idioventricular rhythm runs at 40–100/min). Monomorphic VT has identical wide complexes at more than 100/min. VF is chaotic, without any repeating complex.

Five steps

1. Rate: R–R = 54 small boxes, 1500 ÷ 54 ≈ 28 per minute.
2. Rhythm: regular, every R–R is 2.16 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.18 s, wide (0.12 s or more) and bizarre, with the T wave pointing the other way.

Interpretation

idioventricular rhythm

Answer

idioventricular rhythm

An idioventricular rhythm is an escape rhythm: the ventricles take over because the pacemakers above them have failed.

13.Evidence-based practice statistics

Answer: NNT = 26

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 = 119/930 = 0.128
CER = 20/120 = 0.1667

Number needed to treat

ARR = 0.1667 − 0.128 = 0.03871
NNT = 1/0.03871 = 25.83 → 26

Answer

NNT = 26

Treating 26 patients prevents about one event.

14.Evidence-based practice statistics

Answer: p′ = 86.3 %

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+ = 0.66/(1 − 0.93) = 9.429

Pre-test odds

0.4/(1 − 0.4) = 0.6667

Post-test odds

0.6667·9.429 = 6.286

Post-test probability

p′ = 6.286/(1 + 6.286) = 0.8627 ≈ 86.3%

Answer

p′ = 86.3%

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