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 is the largest nerve in the human body?

  1. AVagus nerve
  2. BSciatic nerve
  3. CMedian nerve
  4. DFemoral nerve
2.Human anatomyHard

A typical posterolateral disc herniation between L4 and L5 most often compresses which nerve root?

  1. AS1
  2. BL5
  3. CL4
  4. DL3
3.Human physiologyMedium

What is anatomical dead space?

  1. AThe air that stays in the lungs after full exhalation (residual volume)
  2. BThe volume of the conducting airways where no gas exchange happens
  3. CThe space between the two pleural layers
  4. DAlveoli that have collapsed completely
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. BSweating has already cooled the body too much
  3. CPyrogens raise the hypothalamic set point above the current body temperature
  4. DThe body has lost its ability to produce heat
5.MicrobiologyMedium

Which type of immunity is given by breast milk antibodies?

  1. ANatural active immunity
  2. BArtificial passive immunity
  3. CNatural passive immunity
  4. DArtificial active immunity
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. AImmunity from hepatitis B vaccination
  2. BChronic hepatitis B infection
  3. CPast natural infection that has cleared
  4. DCurrent acute hepatitis B infection
7.PharmacologyMedium

Which assessment is most important before giving a dose of IV morphine?

  1. ARespiratory rate and level of sedation
  2. BBowel sounds and urine colour
  3. CBlood glucose and temperature, checked before each dose
  4. DPupil size and hearing
8.PharmacologyHard

A patient taking long-term morphine for cancer pain becomes very sedated with slow breathing. Why is naloxone given in small, diluted doses?

  1. ABecause naloxone is toxic to the liver in large doses
  2. BTo restore breathing without causing severe withdrawal and pain
  3. CTo make the effect of naloxone last longer than morphine
  4. DBecause naloxone is much more potent and toxic in patients with cancer
9.Arterial blood gas interpretationMedium
pH7.357.457.27PaCO₂mmHg354554HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.27, PaCO₂ 54 mmHg (7.2 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.27PaCO₂ 54 mmHg (7.2 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.15PaCO₂mmHg354530HCO₃⁻mmol/L222610appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.15, PaCO₂ 30 mmHg (4.0 kPa), HCO₃⁻ 10 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.15PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 10 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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/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
Se90%Sp80%LR− = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 90% and a specificity of 80%. Find the negative likelihood ratio LR−. Round to two decimal places.

Se = 90%Sp = 80%
LR− =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 80% and specificity 90%. The prevalence of the disease is 7%. How many true-positive results TP are expected?

N = 10 000p = 7%Se = 80%Sp = 90%
TP =

3Solutions

1.Human anatomy

Answer: B · Sciatic nerve

Why this is the answer

The sciatic nerve (L4–S3) leaves the pelvis through the greater sciatic foramen and supplies the hamstrings and all the muscles below the knee. Skin on the inner side of the leg is supplied by the saphenous nerve instead.

Answer

B · Sciatic nerve
2.Human anatomy

Answer: B · L5

Why this is the answer

A posterolateral L4–L5 herniation usually catches the traversing L5 root, causing weakness of big toe extension and numbness on the top of the foot.

Answer

B · L5
3.Human physiology

Answer: B · The volume of the conducting airways where no gas exchange happens

Why this is the answer

Anatomical dead space (about 150 ml) is air in the nose, trachea and bronchi. It is moved with every breath but never reaches the alveoli.

Answer

B · The volume of the conducting airways where no gas exchange happens
4.Human physiology

Answer: C · 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

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

Answer: C · Natural passive immunity

Why this is the answer

Antibodies (mainly IgA) passed in breast milk give passive immunity acquired naturally. It is short-lived because no memory cells form.

Answer

C · Natural passive immunity
6.Microbiology

Answer: A · 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

A · Immunity from hepatitis B vaccination
7.Pharmacology

Answer: A · Respiratory rate and level of sedation

Why this is the answer

Opioids can cause respiratory depression, which is usually preceded by increasing sedation. Both are checked before and after each dose.

Answer

A · Respiratory rate and level of sedation
8.Pharmacology

Answer: B · To restore breathing without causing severe withdrawal and pain

Why this is the answer

In opioid-dependent patients, a large dose of naloxone can cause abrupt withdrawal, severe pain and agitation. Small titrated doses aim to restore adequate breathing while keeping some analgesia.

Answer

B · To restore breathing without causing severe withdrawal and pain
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 7.27: acidaemia (below 7.35)
PaCO₂ 54 mmHg: high (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·10 + 8 = 23 → 21–25 mmHg

Compare

measured: 30 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
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: atrial rate = 75 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 = 20 small boxes = 0.80 s → 1500 ÷ 20 = 75 ≈ 75 per minute

Ventricular rate

R–R = 40 small boxes = 1.60 s → 1500 ÷ 40 = 37.5 ≈ 38 per minute

Answer

atrial rate = 75 bpm

Answer

atrial rate = 75 bpm

2:1 AV block: every second P wave is not conducted, so the atrial rate is twice the ventricular rate.

13.Evidence-based practice statistics

Answer: LR− = 0.13

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 − 0.9)/0.8 = 0.125 ≈ 0.13

Answer

LR− = 0.13
14.Evidence-based practice statistics

Answer: TP = 560

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.

With and without the disease

10 000·0.07 = 700
10 000 − 700 = 9300

True positives

TP = 700·0.8 = 560

Answer

TP = 560

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