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 valve lies between the left atrium and the left ventricle?

  1. APulmonary valve
  2. BAortic valve
  3. CTricuspid valve
  4. DMitral (bicuspid) valve
2.Human anatomyHard

Why can an inflamed gallbladder that irritates the diaphragm cause pain at the tip of the right shoulder?

  1. AThe vagus nerve supplies the skin of the shoulder
  2. BThe phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder
  3. CBile travels up the lymphatics to the shoulder
  4. DThe gallbladder is attached to the right clavicle
3.Human physiologyMedium

Which receptors respond mainly to a fall in arterial oxygen levels?

  1. ABaroreceptors in the carotid sinus
  2. BStretch receptors in the lungs
  3. CPeripheral chemoreceptors in the carotid and aortic bodies
  4. DCentral chemoreceptors in the medulla
4.Human physiologyHard

Constriction of the efferent arteriole of a glomerulus, with the afferent arteriole unchanged, tends to:

  1. AHave no effect on GFR at all
  2. BLower glomerular capillary pressure and GFR
  3. CStop filtration completely
  4. DRaise glomerular capillary pressure and GFR
5.MicrobiologyMedium

Which cells does HIV mainly infect and destroy?

  1. APlatelets
  2. BRed blood cells
  3. CCD4 T helper cells
  4. DNeutrophils
6.MicrobiologyHard

The minimum inhibitory concentration (MIC) of an antibiotic is:

  1. AThe lowest concentration that kills 99.9% of the bacterial inoculum in vitro
  2. BThe plasma level at which side effects begin
  3. CThe highest dose a patient can tolerate
  4. DThe lowest concentration that prevents visible bacterial growth in vitro
7.PharmacologyMedium

Which statement about allopurinol is correct?

  1. AIt increases uric acid production to flush out crystals
  2. BIt lowers uric acid over time and does not relieve the pain of an acute attack
  3. CIt works within an hour to relieve joint pain
  4. DIt is taken only during an acute attack and stopped as soon as the pain settles
8.PharmacologyHard

A patient on methadone is also prescribed diazepam for anxiety. What is the main safety concern?

  1. AMethadone causes diazepam to be excreted very quickly
  2. BSevere hypertension from the combination
  3. CAdditive sedation and respiratory depression
  4. DDiazepam blocks the effect of methadone completely
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 146 mmol/L, glucose 25.5 mmol/L and urea 21.4 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 146 mmol/Lglucose 25.5 mmol/Lurea 21.4 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.10PaCO₂mmHg354533HCO₃⁻mmol/L222610appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.10, PaCO₂ 33 mmHg (4.4 kPa), HCO₃⁻ 10 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.10PaCO₂ 33 mmHg (4.4 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/mVsinus bradycardiasinus tachycardiaatrial flutter, 2:1 conductionnormal sinus rhythm

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. 1sinus bradycardia
  2. 2sinus tachycardia
  3. 3atrial flutter, 2:1 conduction
  4. 4normal sinus rhythm
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsynchronised cardioversionimmediate defibrillationtranscutaneous pacingCPR (non-shockable rhythm)

A patient without a palpable pulse has this organised rhythm on the monitor (pulseless electrical activity). Which treatment do adult resuscitation guidelines name for 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. 1synchronised cardioversion
  2. 2immediate defibrillation
  3. 3transcutaneous pacing
  4. 4CPR (non-shockable rhythm)
13.Evidence-based practice statisticsMedium
casesperson-yearsexposed2783700not exposed1264200

Practice exercise (made-up values, not clinical guidance). In a cohort study, exposed people contributed 3700 person-years with 278 new cases, and unexposed people 4200 person-years with 126 new cases. Find the incidence rate ratio IRR (exposed versus unexposed). Round to two decimal places.

exposed: 278/3700 PYnot exposed: 126/4200 PY
IRR =
14.Evidence-based practice statisticsHard
CER20%EER?RRR 46%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 46% in relative terms (RRR = 46%). In a patient group the risk without treatment (CER) is 20% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 46%CER = 20%
NNT =

3Solutions

1.Human anatomy

Answer: D · Mitral (bicuspid) valve

Why this is the answer

The mitral (bicuspid) valve separates the left atrium and left ventricle; the tricuspid valve does the same on the right side.

Answer

D · Mitral (bicuspid) valve
2.Human anatomy

Answer: B · The phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder

Why this is the answer

Diaphragmatic irritation is carried by the phrenic nerve (C3–C5). The brain refers it to skin supplied by the same segments, via the supraclavicular nerves over the shoulder.

Answer

B · The phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder
3.Human physiology

Answer: C · Peripheral chemoreceptors in the carotid and aortic bodies

Why this is the answer

The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.

Answer

C · Peripheral chemoreceptors in the carotid and aortic bodies
4.Human physiology

Answer: D · Raise glomerular capillary pressure and GFR

Why this is the answer

Efferent constriction holds blood in the glomerulus, raising its pressure and GFR. Angiotensin II acts this way, which is why ACE inhibitors can lower GFR.

Answer

D · Raise glomerular capillary pressure and GFR
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: D · The lowest concentration that prevents visible bacterial growth in vitro

Why this is the answer

The MIC is the lowest concentration that inhibits visible growth. The minimum bactericidal concentration (MBC) is the lowest that kills 99.9% of the bacteria.

Answer

D · The lowest concentration that prevents visible bacterial growth in vitro
7.Pharmacology

Answer: B · It lowers uric acid over time and does not relieve the pain of an acute attack

Why this is the answer

Allopurinol reduces urate production and is taken daily to prevent attacks. Acute attacks are treated with NSAIDs, colchicine or corticosteroids, and a new rash on allopurinol must be reported.

Answer

B · It lowers uric acid over time and does not relieve the pain of an acute attack
8.Pharmacology

Answer: C · Additive sedation and respiratory depression

Why this is the answer

Combining opioids with benzodiazepines greatly increases the risk of sedation, respiratory depression and death. If both are needed, the lowest doses are used and the patient is monitored closely.

Answer

C · Additive sedation and respiratory depression
9.Arterial blood gas interpretation

Answer: Osm = 339 mOsm/kg

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.

Calculated osmolality

Osm = 2·146 + 25.5 + 21.4 = 338.9 ≈ 339 mOsm/kg

Answer

Osm = 339 mOsm/kg
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: 33 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: sinus tachycardia

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.

Five steps

1. Rate: R–R = 14 small boxes, 1500 ÷ 14 ≈ 107 per minute.
2. Rhythm: regular, every R–R is 0.56 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).

Interpretation

sinus tachycardia

Answer

sinus tachycardia
12.ECG rhythm strip interpretation

Answer: CPR (non-shockable rhythm)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

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).
sinus tachycardia

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

CPR (non-shockable rhythm)

Answer

CPR (non-shockable rhythm)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: IRR = 2.5

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: 278/3700 = 75.14 per 1000 person-years
not exposed: 126/4200 = 30 per 1000 person-years

Rate ratio

IRR = 75.14/30 = 2.505 ≈ 2.5

Answer

IRR = 2.5
14.Evidence-based practice statistics

Answer: NNT = 11

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.

Absolute risk reduction

ARR = 0.2·0.46 = 0.092

Number needed to treat

NNT = 1/0.092 = 10.87 → 11

Answer

NNT = 11

The same relative effect gives a smaller NNT when the baseline risk is higher.

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