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

In which part of the nephron does most reabsorption of water and sodium take place?

  1. ALoop of Henle
  2. BProximal convoluted tubule
  3. CDistal convoluted tubule
  4. DCollecting duct
2.Human anatomyHard

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

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

The Frank–Starling mechanism describes that:

  1. AHeart rate rises when arterial blood pressure falls suddenly
  2. BContractility falls when temperature rises
  3. CThe atria contract after the ventricles
  4. DStroke volume rises when ventricular filling increases
4.Human physiologyHard

During exercise, blood flow to active skeletal muscle rises greatly. What is the main cause?

  1. ASympathetic stimulation constricts the muscle arterioles via alpha receptors
  2. BLocal metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
  3. CThe parasympathetic system dilates all arteries
  4. DThe heart pumps blood only to the muscles
5.MicrobiologyMedium

Which is a function of the complement system?

  1. AProducing antibodies against newly encountered antigens
  2. BPresenting antigens to T cells
  3. CForming pores in the membranes of some bacteria
  4. DMaking new red blood cells
6.MicrobiologyHard

Why can a person get influenza many times but measles usually only once?

  1. AInfluenza attacks and destroys the memory cells formed after infection
  2. BMeasles is caused by a bacterium
  3. CInfluenza viruses change their surface antigens often
  4. DMeasles virus has no surface antigens
7.PharmacologyMedium

Patients taking metronidazole are usually advised to avoid:

  1. ASunlight
  2. BAlcohol
  3. CDairy products
  4. DGrapefruit juice
8.PharmacologyHard

A 19-year-old woman is starting isotretinoin for severe acne. Which requirement is most important?

  1. AReliable contraception and pregnancy tests, as it is highly teratogenic
  2. BA high-vitamin A diet to boost the effect
  3. CWeekly hearing tests and monthly eye examinations during treatment
  4. DTaking the drug only at weekends
9.Arterial blood gas interpretationMedium
pH7.357.457.60PaCO₂mmHg354520HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.60, PaCO₂ 20 mmHg (2.7 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.60PaCO₂ 20 mmHg (2.7 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.22PaCO₂mmHg354585HCO₃⁻mmol/L222634acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.22, PaCO₂ 85 mmHg (11.3 kPa), HCO₃⁻ 34 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.22PaCO₂ 85 mmHg (11.3 kPa)HCO₃⁻ 34 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
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 fibrillationthird-degree (complete) AV blocksinus bradycardiaasystole

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. 2third-degree (complete) AV block
  3. 3sinus bradycardia
  4. 4asystole
13.Evidence-based practice statisticsMedium
peopleyears139052190235504new cases99

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, 99 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

390 × 5 years190 × 2 years550 × 4 years99 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
p (%)PPV (%)30%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 87% and a specificity of 92%. It is used in a population where the prevalence is 30%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 87%Sp = 92%p = 30%
PPV = %

3Solutions

1.Human anatomy

Answer: B · Proximal convoluted tubule

Why this is the answer

The proximal convoluted tubule reabsorbs about two thirds of the filtered sodium and water, plus nearly all glucose and amino acids.

Answer

B · Proximal convoluted tubule
2.Human anatomy

Answer: D · 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

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

Answer: D · Stroke volume rises when ventricular filling increases

Why this is the answer

Greater end-diastolic volume stretches the myocardium, which increases the force of contraction and the stroke volume, matching output to venous return.

Answer

D · Stroke volume rises when ventricular filling increases
4.Human physiology

Answer: B · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles

Why this is the answer

Active hyperaemia: metabolites produced by working muscle relax arteriolar smooth muscle locally, overriding sympathetic vasoconstriction in that tissue.

Answer

B · Local metabolites such as CO₂, H⁺, K⁺ and adenosine dilate the arterioles
5.Microbiology

Answer: C · Forming pores in the membranes of some bacteria

Why this is the answer

Complement proteins coat microbes for phagocytosis (opsonisation), attract immune cells and form the membrane attack complex that punches holes in some bacteria.

Answer

C · Forming pores in the membranes of some bacteria
6.Microbiology

Answer: C · Influenza viruses change their surface antigens often

Why this is the answer

Influenza haemagglutinin and neuraminidase change through drift (small mutations) and shift (reassortment), so old antibodies may not recognise new strains. Measles is antigenically stable.

Answer

C · Influenza viruses change their surface antigens often
7.Pharmacology

Answer: B · Alcohol

Why this is the answer

Metronidazole can cause a disulfiram-like reaction with alcohol, with flushing, nausea and palpitations. Alcohol is avoided during treatment and for a short time after.

Answer

B · Alcohol
8.Pharmacology

Answer: A · Reliable contraception and pregnancy tests, as it is highly teratogenic

Why this is the answer

Isotretinoin causes severe birth defects. Pregnancy prevention programmes require effective contraception and regular pregnancy tests before, during and after treatment.

Answer

A · Reliable contraception and pregnancy tests, as it is highly teratogenic
9.Arterial blood gas interpretation

Answer: partially 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 7.60: alkalaemia (above 7.45)
PaCO₂ 20 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: acute on chronic

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 HCO₃⁻

acute: 24 + 1·4.5 = 28.5 mmol/L
chronic: 24 + 3.5·4.5 = 39.75 mmol/L

Compare

measured: 34 mmol/L → acute on chronic

Answer

acute on chronic
11.ECG rhythm strip interpretation

Answer: QTc = 0.458 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 = 10.5 × 0.04 = 0.42 s
RR = 21 × 0.04 = 0.84 s

Bazett’s formula

QTc = 0.42/√0.84 = 0.42/0.9165 = 0.458 s

Answer

QTc = 0.458 s

Between the usual limits for men (about 0.45 s) and women (about 0.46 s): borderline, depending on the reference used. (458 ms)

12.ECG rhythm strip interpretation

Answer: asystole

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: no countable ventricular rate.
2. Rhythm: none; an almost flat line.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: no QRS complexes.

Interpretation

asystole

Answer

asystole

A flat line is always checked: look at the patient, the leads and the gain, and view a second lead, because a loose electrode or fine VF can look like asystole.

13.Evidence-based practice statistics

Answer: IR = 21.9 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 = 390·5 + 190·2 + 550·4 = 4530

Incidence rate

IR = 99/4530·1000 = 21.9 per 1000 person-years

Answer

IR = 21.9 per 1000 person-years
14.Evidence-based practice statistics

Answer: PPV = 82.3 %

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.

True and false positives (per person)

Se·p = 0.87·0.3 = 0.261
(1 − Sp)·(1 − p) = 0.08·0.7 = 0.056

Positive predictive value

PPV = 0.261/(0.261 + 0.056) = 0.8233 ≈ 82.3%

Answer

PPV = 82.3%

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

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