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 artery supplies most of the anterior wall of the left ventricle and the front of the interventricular septum?

  1. ACircumflex artery
  2. BLeft anterior descending artery
  3. CRight coronary artery
  4. DPosterior descending artery
2.Human anatomyHard

Which muscle "unlocks" the fully extended knee by rotating the femur laterally on the tibia at the start of flexion?

  1. AGastrocnemius
  2. BSartorius
  3. CPopliteus
  4. DBiceps femoris
3.Human physiologyMedium

What is the normal pH range of arterial blood?

  1. A7.35 to 7.45
  2. B7.50 to 7.65
  3. C7.00 to 7.20
  4. D6.80 to 7.00
4.Human physiologyHard

In pernicious anaemia, autoimmune destruction of gastric parietal cells leads to anaemia because:

  1. APepsin is lost, so haemoglobin cannot be made
  2. BGastrin is lost, so the bone marrow is no longer stimulated
  3. CIntrinsic factor is lost, so vitamin B12 is not absorbed
  4. DAcid is lost, so iron is never absorbed in any form
5.MicrobiologyMedium

What is the incubation period?

  1. AThe time between infection and the first symptoms
  2. BThe time a culture needs in the laboratory
  3. CThe time an antibiotic takes to work
  4. DThe time during which a patient remains infectious to others
6.MicrobiologyHard

A traveller returns from sub-Saharan Africa with fever. Malaria is suspected. Which species is most likely to cause severe and cerebral malaria?

  1. APlasmodium falciparum
  2. BPlasmodium malariae
  3. CPlasmodium vivax
  4. DPlasmodium ovale
7.PharmacologyMedium

Besides lithium levels, which blood tests are monitored in long-term lithium treatment?

  1. ALiver enzymes, serum amylase and lipase
  2. BTroponin and CK-MB
  3. CKidney function and thyroid function
  4. DINR and fibrinogen
8.PharmacologyHard

A patient with asthma starts timolol eye drops for glaucoma and soon becomes wheezy. What is the most likely explanation?

  1. AThe wheeze is unrelated to the eye drops
  2. BTimolol is absorbed and blocks beta-2 receptors in the airways
  3. CThe eye drops contain an allergen that causes hay fever and asthma
  4. DTimolol activates histamine receptors in the lungs
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 6 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 6 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 33 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 33 mmol/L
PaCO₂ = 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/mVventricular fibrillationtorsades de pointesidioventricular rhythmatrial flutter, 2:1 conduction

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 fibrillation
  2. 2torsades de pointes
  3. 3idioventricular rhythm
  4. 4atrial flutter, 2:1 conduction
13.Evidence-based practice statisticsMedium
Se89%Sp66%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 89% and a specificity of 66%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 89%Sp = 66%
LR− =
14.Evidence-based practice statisticsHard
control8%treatment?

Practice exercise (made-up values, not clinical guidance). Without a drug, 8% of patients have a certain side effect during a year. The drug raises this risk with a relative risk of RR = 2.48. Find the number needed to harm NNH: how many patients must take the drug for a year for one extra patient to have the side effect? Round up to a whole number of patients.

control 8%RR = 2.48
NNH =

3Solutions

1.Human anatomy

Answer: B · Left anterior descending artery

Why this is the answer

The left anterior descending (anterior interventricular) artery supplies the anterior left ventricle and the anterior two thirds of the septum. Its blockage causes an anterior infarct.

Answer

B · Left anterior descending artery
2.Human anatomy

Answer: C · Popliteus

Why this is the answer

At full extension the knee locks by medial rotation of the femur. Popliteus laterally rotates the femur on the fixed tibia to unlock it so flexion can begin.

Answer

C · Popliteus
3.Human physiology

Answer: A · 7.35 to 7.45

Why this is the answer

Arterial pH is normally 7.35–7.45. Below 7.35 is acidaemia and above 7.45 alkalaemia.

Answer

A · 7.35 to 7.45
4.Human physiology

Answer: C · Intrinsic factor is lost, so vitamin B12 is not absorbed

Why this is the answer

Parietal cells secrete intrinsic factor, needed for B12 absorption in the terminal ileum. B12 deficiency impairs DNA synthesis and causes megaloblastic anaemia.

Answer

C · Intrinsic factor is lost, so vitamin B12 is not absorbed
5.Microbiology

Answer: A · The time between infection and the first symptoms

Why this is the answer

The incubation period runs from exposure to the onset of symptoms. People can sometimes already transmit the infection during it.

Answer

A · The time between infection and the first symptoms
6.Microbiology

Answer: A · Plasmodium falciparum

Why this is the answer

P. falciparum causes very high parasite levels and makes infected red cells stick in small vessels, including in the brain. It is common in sub-Saharan Africa and is a medical emergency.

Answer

A · Plasmodium falciparum
7.Pharmacology

Answer: C · Kidney function and thyroid function

Why this is the answer

Lithium can impair kidney function and cause hypothyroidism. Kidney function, thyroid function and calcium are checked regularly, along with lithium levels.

Answer

C · Kidney function and thyroid function
8.Pharmacology

Answer: B · Timolol is absorbed and blocks beta-2 receptors in the airways

Why this is the answer

Ophthalmic timolol is a non-selective beta blocker and can reach the circulation in amounts that cause bronchospasm or bradycardia. It is generally avoided in asthma.

Answer

B · Timolol is absorbed and blocks beta-2 receptors in the airways
9.Arterial blood gas interpretation

Answer: PaCO₂ = 17 mmHg

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.

Winter’s formula

PaCO₂ = 1.5·6 + 8 = 17 mmHg
range: 15–19 mmHg

Answer

PaCO₂ = 17 mmHg
10.Arterial blood gas interpretation

Answer: PaCO₂ = 44.1 mmHg

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 PaCO₂

0.7·33 + 21 = 44.1 mmHg

Answer

PaCO₂ = 44.1 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: QTc = 0.405 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 = 22 × 0.04 = 0.88 s

Bazett’s formula

QTc = 0.38/√0.88 = 0.38/0.9381 = 0.405 s

Answer

QTc = 0.405 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (405 ms)

12.ECG rhythm strip interpretation

Answer: torsades de pointes

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: very fast, the complexes are about 6 small boxes apart (about 250 per minute).
2. Rhythm: fast and roughly regular, but the height and direction of the complexes change in a repeating spindle pattern.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: wide and polymorphic; the complexes twist around the baseline, pointing up for a few beats and then down.

Interpretation

torsades de pointes

Answer

torsades de pointes

Torsades de pointes is a polymorphic VT linked to a prolonged QT interval. This is identification practice only.

13.Evidence-based practice statistics

Answer: LR− = 0.17

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.

Negative likelihood ratio

LR− = (1 − 0.89)/0.66 = 0.1667 ≈ 0.17

Answer

LR− = 0.17
14.Evidence-based practice statistics

Answer: NNH = 9

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.

Risk with the drug

0.08·2.48 = 0.1984

Absolute risk increase

ARI = 0.1984 − 0.08 = 0.1184

Number needed to harm

NNH = 1/0.1184 = 8.446 → 9

Answer

NNH = 9

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