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

The rotator cuff consists of supraspinatus, infraspinatus, teres minor and which other muscle?

  1. ALatissimus dorsi
  2. BSubscapularis
  3. CDeltoid
  4. DTeres major
2.Human anatomyHard

Injury to the common fibular (peroneal) nerve at the neck of the fibula typically causes:

  1. AWeak hip abduction
  2. BLoss of sensation on the sole of the foot
  3. CInability to flex the knee
  4. DFoot drop
3.Human physiologyMedium

The hormone secretin is released when acid enters the duodenum. What is its main effect?

  1. ABicarbonate secretion from the pancreas
  2. BInsulin release from the endocrine pancreas
  3. CAcid secretion from the stomach
  4. DContraction of the gallbladder
4.Human physiologyHard

Hodgkin and Huxley's classic studies of the ionic basis of the action potential used which preparation?

  1. AThe squid giant axon
  2. BThe cat spinal cord
  3. CThe frog sciatic nerve–muscle preparation
  4. DCultured human cortical neurons
5.MicrobiologyMedium

Which cells does HIV mainly infect and destroy?

  1. ARed blood cells
  2. BPlatelets
  3. CCD4 T helper cells
  4. DNeutrophils
6.MicrobiologyHard

What is the key difference between bactericidal and bacteriostatic antibiotics?

  1. ABactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
  2. BBacteriostatic drugs always work faster than bactericidal drugs
  3. CBactericidal drugs work only outside the body
  4. DBactericidal drugs work only on viruses; bacteriostatic drugs work on bacteria
7.PharmacologyMedium

An IV site is cool, swollen and pale, and the infusion is running slowly. What should the nurse do?

  1. AStop the infusion, remove the cannula and elevate the limb
  2. BApply a tight bandage over the site
  3. CFlush the cannula forcefully with saline
  4. DIncrease the infusion rate to push through and clear the blockage
8.PharmacologyHard

How does levonorgestrel emergency contraception mainly work?

  1. AIt kills sperm in the vagina
  2. BIt ends an established pregnancy
  3. CIt causes an immediate period
  4. DIt delays or prevents ovulation
9.Arterial blood gas interpretationMedium
pH7.357.457.38PaCO₂mmHg354526HCO₃⁻mmol/L222615uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.38, PaCO₂ 26 mmHg (3.5 kPa) and HCO₃⁻ 15 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.38PaCO₂ 26 mmHg (3.5 kPa)HCO₃⁻ 15 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 76 mmHg (10.1 kPa) and PaCO₂ 33 mmHg (4.4 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 76 mmHg (10.1 kPa)PaCO₂ 33 mmHg (4.4 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/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
peopleyears136042470532102new cases173

Practice exercise (made-up values, not clinical guidance). In a cohort, groups of people were followed for different lengths of time (see the table: number of people and years of follow-up for each). During follow-up, 173 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

360 × 4 years470 × 5 years210 × 2 years173 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
p (%)PPV (%)0.5%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 85% and a specificity of 99%. It is used in a population where the prevalence is 0.5%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 85%Sp = 99%p = 0.5%
PPV = %

3Solutions

1.Human anatomy

Answer: B · Subscapularis

Why this is the answer

SITS: supraspinatus, infraspinatus, teres minor and subscapularis. Teres major is close by but is not part of the cuff.

Answer

B · Subscapularis
2.Human anatomy

Answer: D · Foot drop

Why this is the answer

The common fibular nerve supplies the dorsiflexors and evertors. Damage at the fibular neck causes foot drop and a high-stepping gait. The sole is supplied by the tibial nerve.

Answer

D · Foot drop
3.Human physiology

Answer: A · Bicarbonate secretion from the pancreas

Why this is the answer

Secretin stimulates pancreatic duct cells to secrete bicarbonate-rich fluid, which neutralises acidic chyme so intestinal enzymes can work.

Answer

A · Bicarbonate secretion from the pancreas
4.Human physiology

Answer: A · The squid giant axon

Why this is the answer

The squid giant axon is up to about 1 mm wide, so voltage-clamp electrodes could be inserted. This showed that sodium inflow and potassium outflow produce the action potential.

Answer

A · The squid giant axon
5.Microbiology

Answer: C · CD4 T helper cells

Why this is the answer

HIV binds CD4 and a co-receptor on T helper cells. Loss of these cells weakens both antibody and cell-mediated immunity, leading to AIDS.

Answer

C · CD4 T helper cells
6.Microbiology

Answer: A · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them

Why this is the answer

Bacteriostatic drugs halt multiplication so host defences can eliminate the bacteria. Bactericidal drugs are preferred when defences are weak or hard to reach, such as in endocarditis or neutropenia.

Answer

A · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
7.Pharmacology

Answer: A · Stop the infusion, remove the cannula and elevate the limb

Why this is the answer

These signs suggest infiltration. The infusion is stopped and the cannula removed, the limb is elevated, and a new cannula is placed elsewhere; vesicant drugs need the extravasation protocol.

Answer

A · Stop the infusion, remove the cannula and elevate the limb
8.Pharmacology

Answer: D · It delays or prevents ovulation

Why this is the answer

Levonorgestrel emergency contraception mainly prevents or delays ovulation and does not disrupt an implanted pregnancy. Its effectiveness falls the longer it is delayed after unprotected sex.

Answer

D · It delays or prevents ovulation
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 7.38: within 7.35–7.45
PaCO₂ 26 mmHg: low (35–45)
HCO₃⁻ 15 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 28.5–32.5 mmHg, so the measured 26 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 = 32.48 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 = 0.21·713 − 33/0.8 = 149.7 − 41.25 = 108.5 mmHg

Gradient

A–a = 108.5 − 76 = 32.48 mmHg

Answer

A–a gradient = 32.48 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.424 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 × 0.04 = 0.36 s
RR = 18 × 0.04 = 0.72 s

Bazett’s formula

QTc = 0.36/√0.72 = 0.36/0.8485 = 0.424 s

Answer

QTc = 0.424 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (424 ms)

12.ECG rhythm strip interpretation

Answer: rate

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: R–R = 13 small boxes, 1500 ÷ 13 ≈ 115 per minute.
2. Rhythm: regular, every R–R is 0.52 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

First abnormal step

rate → sinus tachycardia

Answer

rate
13.Evidence-based practice statistics

Answer: IR = 41.1 per 1000 person-years

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.

Person-years

PY = 360·4 + 470·5 + 210·2 = 4210

Incidence rate

IR = 173/4210·1000 = 41.1 per 1000 person-years

Answer

IR = 41.1 per 1000 person-years
14.Evidence-based practice statistics

Answer: PPV = 29.9 %

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.

True and false positives (per person)

Se·p = 0.85·0.005 = 0.00425
(1 − Sp)·(1 − p) = 0.01·0.995 = 0.00995

Positive predictive value

PPV = 0.00425/(0.00425 + 0.00995) = 0.2993 ≈ 29.9%

Answer

PPV = 29.9%

The lower the prevalence, the lower the PPV of the same test.

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