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 type of epithelium lines most of the trachea?

  1. ASimple cuboidal epithelium
  2. BPseudostratified ciliated columnar epithelium
  3. CTransitional epithelium
  4. DStratified squamous epithelium
2.Human anatomyHard

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

  1. ALoss of sensation on the sole of the foot
  2. BFoot drop
  3. CWeak hip abduction
  4. DInability to flex the knee
3.Human physiologyMedium

Which ion enters the cell to cause the depolarisation phase of a typical neuronal action potential?

  1. APotassium (K⁺)
  2. BCalcium (Ca²⁺)
  3. CChloride (Cl⁻)
  4. DSodium (Na⁺)
4.Human physiologyHard

Why does left ventricular failure cause pulmonary oedema?

  1. AThe right ventricle pumps less blood into the lungs
  2. BRaised left atrial pressure increases pulmonary capillary hydrostatic pressure
  3. CPlasma oncotic pressure in the lungs rises sharply
  4. DThe bronchial arteries become blocked
5.MicrobiologyMedium

Tetanus and diphtheria vaccines are toxoids. What does that mean?

  1. AThey contain live bacteria that cannot make toxin
  2. BThey contain an inactivated toxin that still triggers an immune response
  3. CThey contain ready-made antibodies against the toxin, giving passive immunity
  4. DThey contain the bacterial DNA only
6.MicrobiologyHard

Corynebacterium diphtheriae causes diphtheria only if it produces diphtheria toxin. When does it make this toxin?

  1. AOnly after it has conjugated with E. coli and received a plasmid
  2. BOnly when it is grown at high temperature
  3. CWhenever it is exposed to antibiotics
  4. DWhen it carries a bacteriophage with the toxin gene
7.PharmacologyMedium

How can the absorption of oral iron be improved?

  1. ATake it with a glass of milk
  2. BTake it with a cup of strong tea
  3. CTake it at the same time as an antacid to protect the stomach
  4. DTake it with vitamin C, such as orange juice, on an empty stomach
8.PharmacologyHard

A patient who uses insulin is taught sick-day rules. Which statement shows a need for further teaching?

  1. A"If I am ill and not eating, I will stop my insulin completely."
  2. B"I will seek help if I keep vomiting or have ketones."
  3. C"I will keep drinking fluids, even if I cannot eat much."
  4. D"I will check my blood glucose and ketones more often while I am ill."
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 8 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 8 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.32PaCO₂mmHg354536HCO₃⁻mmol/L222618added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.32, PaCO₂ 36 mmHg (4.8 kPa) and HCO₃⁻ 18 mmol/L, with Na⁺ 136 and Cl⁻ 98 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.32PaCO₂ 36 mmHg (4.8 kPa)HCO₃⁻ 18 mmol/LNa⁺ 136 mmol/LCl⁻ 98 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationatrial flutter, 2:1 conductionsinus rhythm with PVCssinus arrhythmia

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. 1atrial fibrillation
  2. 2atrial flutter, 2:1 conduction
  3. 3sinus rhythm with PVCs
  4. 4sinus arrhythmia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsecond-degree AV block type IIidioventricular rhythmpaced rhythm, failure to capturethird-degree (complete) AV block

This patient has a pacemaker. Interpret the 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. 1second-degree AV block type II
  2. 2idioventricular rhythm
  3. 3paced rhythm, failure to capture
  4. 4third-degree (complete) AV block
13.Evidence-based practice statisticsMedium
casesperson-yearsexposed5574800not exposed1314500

Practice exercise (made-up values, not clinical guidance). In a cohort study, exposed people contributed 4800 person-years with 557 new cases, and unexposed people 4500 person-years with 131 new cases. Find the incidence rate ratio IRR (exposed versus unexposed). Round to two decimal places.

exposed: 557/4800 PYnot exposed: 131/4500 PY
IRR =
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 85% and specificity 75%. The prevalence of the disease is 1%. How many false-positive results FP are expected?

N = 10 000p = 1%Se = 85%Sp = 75%
FP =

3Solutions

1.Human anatomy

Answer: B · Pseudostratified ciliated columnar epithelium

Why this is the answer

Respiratory epithelium is pseudostratified ciliated columnar with goblet cells. Mucus traps particles and cilia move it up towards the pharynx.

Answer

B · Pseudostratified ciliated columnar epithelium
2.Human anatomy

Answer: B · 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

B · Foot drop
3.Human physiology

Answer: D · Sodium (Na⁺)

Why this is the answer

Voltage-gated Na⁺ channels open and Na⁺ rushes in, depolarising the membrane. K⁺ outflow then repolarises it.

Answer

D · Sodium (Na⁺)
4.Human physiology

Answer: B · Raised left atrial pressure increases pulmonary capillary hydrostatic pressure

Why this is the answer

A failing left ventricle backs up pressure into the left atrium and pulmonary veins. High capillary hydrostatic pressure pushes fluid into the lung interstitium and alveoli.

Answer

B · Raised left atrial pressure increases pulmonary capillary hydrostatic pressure
5.Microbiology

Answer: B · They contain an inactivated toxin that still triggers an immune response

Why this is the answer

A toxoid is a toxin treated (for example with formaldehyde) so it is harmless but still antigenic. The immune system makes antibodies that neutralise the real toxin.

Answer

B · They contain an inactivated toxin that still triggers an immune response
6.Microbiology

Answer: D · When it carries a bacteriophage with the toxin gene

Why this is the answer

The tox gene is carried by a bacteriophage. When the phage is integrated as a prophage, the bacterium can produce toxin. Strains without the phage are non-toxigenic.

Answer

D · When it carries a bacteriophage with the toxin gene
7.Pharmacology

Answer: D · Take it with vitamin C, such as orange juice, on an empty stomach

Why this is the answer

Vitamin C keeps iron in its more absorbable ferrous form. Milk, antacids, tea and some antibiotics reduce iron absorption. If the stomach becomes upset, it may be taken with food, accepting lower absorption.

Answer

D · Take it with vitamin C, such as orange juice, on an empty stomach
8.Pharmacology

Answer: A · "If I am ill and not eating, I will stop my insulin completely."

Why this is the answer

Stress hormones during illness often raise glucose, so basal insulin is usually continued and doses may need adjusting. Stopping insulin in type 1 diabetes can lead to ketoacidosis.

Answer

A · "If I am ill and not eating, I will stop my insulin completely."
9.Arterial blood gas interpretation

Answer: PaCO₂ = 20 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 = 1.5·8 + 8 = 20 mmHg
range: 18–22 mmHg

Answer

PaCO₂ = 20 mmHg
10.Arterial blood gas interpretation

Answer: pure high-gap 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.

Anion gap

AG = 136 − (98 + 18) = 20

Delta ratio

(20 − 12)/(24 − 18) = 1.333
pure high-gap acidosis

Answer

pure high-gap acidosis
11.ECG rhythm strip interpretation

Answer: atrial fibrillation

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: 10 QRS complexes in 6 s, × 10 = 100 per minute.
2. Rhythm: irregularly irregular, R–R from 0.40 to 0.78 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s).

Interpretation

atrial fibrillation

Answer

atrial fibrillation
12.ECG rhythm strip interpretation

Answer: paced rhythm, failure to capture

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: 6 QRS complexes in 6 s, × 10 = 60 per minute.
2. Rhythm: the pacing spikes are regular (every 0.84 s), but the R–R is not, because a QRS is missing after some spikes.
3. P waves: none visible.
4. PR interval: not measurable.
5. QRS: 0.16 s and wide after the captured spikes; one spike is not followed by a QRS (no capture).

Interpretation

paced rhythm, failure to capture

Answer

paced rhythm, failure to capture

Failure to capture: the pacemaker fires but the heart does not respond. Textbooks treat it as urgent to report, because the patient may depend on the pacemaker.

13.Evidence-based practice statistics

Answer: IRR = 3.99

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: 557/4800 = 116 per 1000 person-years
not exposed: 131/4500 = 29.11 per 1000 person-years

Rate ratio

IRR = 116/29.11 = 3.986 ≈ 3.99

Answer

IRR = 3.99
14.Evidence-based practice statistics

Answer: FP = 2475

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

10 000·0.01 = 100
10 000 − 100 = 9900

False positives

FP = 9900·0.25 = 2475

Answer

FP = 2475

Of the 2560 positives only 85 have the disease (PPV 3.3%).

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