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. BTransitional epithelium
  3. CPseudostratified ciliated columnar epithelium
  4. DStratified squamous epithelium
2.Human anatomyHard

Which structure is found in the posterior mediastinum?

  1. AOesophagus
  2. BHeart
  3. CThymus
  4. DAscending aorta
3.Human physiologyMedium

Which hormone is released by the adrenal cortex in response to ACTH?

  1. AAldosterone, as the main response
  2. BAdrenaline
  3. CCortisol
  4. DThyroxine
4.Human physiologyHard

According to the length–tension relationship, why does a skeletal muscle fibre produce less force when overstretched?

  1. AThe muscle runs out of ATP when stretched
  2. BThe neuromuscular junction stops working
  3. CActin and myosin overlap less, so fewer cross-bridges form
  4. DCalcium is no longer released from the sarcoplasmic reticulum when stretched
5.MicrobiologyMedium

What does an ELISA test detect?

  1. AThe DNA sequence of the whole bacterial genome
  2. BBacterial growth on solid agar plates
  3. CThe shape of bacteria under the microscope
  4. DSpecific antigens or antibodies, using an enzyme that causes a colour change
6.MicrobiologyHard

Primary syphilis typically presents with:

  1. ADamage to the heart and brain
  2. BA painless ulcer (chancre) at the site of infection
  3. CA widespread rash on the palms and soles
  4. DA painful cluster of small blisters on the genitals or the mouth
7.PharmacologyMedium

During an oxytocin infusion, contractions become very frequent and the fetal heart rate shows late decelerations. What is the nurse's first action?

  1. AIncrease the infusion to finish labour quickly
  2. BGive a second oxytocin bolus
  3. CPosition the woman flat on her back
  4. DStop the oxytocin infusion
8.PharmacologyHard

A noradrenaline infusion is running through a peripheral cannula. The skin around the site becomes pale, cold and hard. What should the nurse do?

  1. ALeave the infusion running and recheck in 4 hours
  2. BStop the infusion at that site and follow the extravasation protocol
  3. CIncrease the rate to improve blood flow to the area
  4. DApply heat and massage the area, then continue the infusion
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 75 mmHg (10.0 kPa). Use the rule that in acute respiratory acidosis HCO₃⁻ rises by 1 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 75 mmHg (10.0 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 135, Cl⁻ 89 and HCO₃⁻ 10 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 135 mmol/LCl⁻ 89 mmol/LHCO₃⁻ 10 mmol/L
delta ratio =
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 Fridericia’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/mVidioventricular rhythmpaced rhythm, failure to capturedual-chamber (AV) paced rhythmthird-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. 1idioventricular rhythm
  2. 2paced rhythm, failure to capture
  3. 3dual-chamber (AV) paced rhythm
  4. 4third-degree (complete) AV block
13.Evidence-based practice statisticsMedium
casescontrolsexposed48185abnot exposed162315cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 210 patients with a disease (cases) and 500 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 48b = 185c = 162d = 315
OR =
14.Evidence-based practice statisticsHard
pre-test5%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 5% for a disease. A test with sensitivity 84% and specificity 86% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 84%Sp = 86%positive
p′ = %

3Solutions

1.Human anatomy

Answer: C · 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

C · Pseudostratified ciliated columnar epithelium
2.Human anatomy

Answer: A · Oesophagus

Why this is the answer

The posterior mediastinum contains the oesophagus, descending aorta, azygos veins and thoracic duct. The heart and ascending aorta are in the middle mediastinum; the thymus is in the superior and anterior mediastinum.

Answer

A · Oesophagus
3.Human physiology

Answer: C · Cortisol

Why this is the answer

ACTH from the anterior pituitary stimulates cortisol release from the zona fasciculata. Adrenaline comes from the adrenal medulla.

Answer

C · Cortisol
4.Human physiology

Answer: C · Actin and myosin overlap less, so fewer cross-bridges form

Why this is the answer

Maximum force occurs at an optimal sarcomere length with best filament overlap. Overstretching reduces overlap; too short a length makes filaments collide.

Answer

C · Actin and myosin overlap less, so fewer cross-bridges form
5.Microbiology

Answer: D · Specific antigens or antibodies, using an enzyme that causes a colour change

Why this is the answer

In an enzyme-linked immunosorbent assay, antibodies linked to an enzyme bind the target. Adding the substrate produces a colour, showing whether the antigen or antibody is present.

Answer

D · Specific antigens or antibodies, using an enzyme that causes a colour change
6.Microbiology

Answer: B · A painless ulcer (chancre) at the site of infection

Why this is the answer

Treponema pallidum causes a painless chancre in the primary stage. The secondary stage brings rash and systemic symptoms, and tertiary syphilis can damage the heart and nervous system. Painful blisters suggest herpes.

Answer

B · A painless ulcer (chancre) at the site of infection
7.Pharmacology

Answer: D · Stop the oxytocin infusion

Why this is the answer

Excessive contractions reduce placental blood flow and cause fetal distress. The oxytocin is stopped first, then the woman is turned on her side, IV fluids and oxygen are given as per protocol and the provider is informed.

Answer

D · Stop the oxytocin infusion
8.Pharmacology

Answer: B · Stop the infusion at that site and follow the extravasation protocol

Why this is the answer

Extravasation of a vasopressor can cause tissue necrosis. The infusion is stopped and moved to another site, and phentolamine, an alpha blocker, may be injected into the area to reverse vasoconstriction.

Answer

B · Stop the infusion at that site and follow the extravasation protocol
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 27.5 mmol/L

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.

Change in PaCO₂

|75 − 40| = 35 mmHg → 3.5 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·3.5 = 27.5 mmol/L

Answer

HCO₃⁻ = 27.5 mmol/L
10.Arterial blood gas interpretation

Answer: delta ratio = 1.714

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 = 135 − (89 + 10) = 36

Delta ratio

(36 − 12)/(24 − 10) = 24/14 = 1.714

Answer

delta ratio = 1.714

Between 1 and 2: a pure high anion gap acidosis.

11.ECG rhythm strip interpretation

Answer: QTc = 0.426 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 = 24 × 0.04 = 0.96 s

Fridericia’s formula

QTc = 0.42/∛0.96 = 0.42/0.9865 = 0.426 s

Answer

QTc = 0.426 s

Within the usual limits (about 0.45 s for men, 0.46 s for women). (426 ms)

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: 4 QRS complexes in 6 s, × 10 = 40 per minute.
2. Rhythm: the pacing spikes are regular (every 0.92 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; 2 spikes are 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: OR = 0.5

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.

Odds of exposure

cases: 48/162 = 0.2963
controls: 185/315 = 0.5873

Odds ratio

OR = (48·315)/(185·162) = 0.5045 ≈ 0.5

Answer

OR = 0.5

OR below 1: exposure is less common among the cases, which suggests a protective effect.

14.Evidence-based practice statistics

Answer: p′ = 24 %

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.

Likelihood ratio

LR+ = 0.84/(1 − 0.86) = 6

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·6 = 0.3158

Post-test probability

p′ = 0.3158/(1 + 0.3158) = 0.24 = 24%

Answer

p′ = 24%

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