Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
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.
In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.
Clinical pharmacokinetics
Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
2Practice problems
1.Lab values & electrolytesMedium
Why can a patient with liver failure have a raised INR without taking warfarin?
AThe liver makes most clotting factors, so production falls
BThe kidneys stop clearing the clotting factors from the blood
CBilirubin directly destroys the clotting factors
DAlbumin is a clotting factor, and its level falls
2.Lab values & electrolytesHard
A patient using an insulin pump has a glucose of 300 mg/dL (16.7 mmol/L) that has not fallen 2 hours after a correction bolus through the pump. Blood ketones are 1.8 mmol/L. What is the most likely problem and action?
ARebound after a hypo; give fast-acting carbohydrate and recheck in 15 minutes
BInsulin delivery failure; inject a correction dose by pen and change the set
CInsulin overdose from the pump; suspend the pump and stop all insulin for a day
DNormal pump function; wait for the next mealtime bolus to lower the glucose
3.Arterial blood gas interpretationMedium
A practice gas shows PaCO₂ 49 mmHg (6.5 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⁻.
Practice values: Na⁺ 144, Cl⁻ 101 and HCO₃⁻ 11 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 144 mmol/LCl⁻ 101 mmol/LHCO₃⁻ 11 mmol/L
delta ratio =
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 60 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
60 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4 L/h. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 4 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L
7.Clinical nursingMedium
Which tool is commonly used at the bedside to screen for delirium?
AThe Braden scale
BThe Glasgow-Blatchford score
CThe Malnutrition Universal Screening Tool
DThe Confusion Assessment Method (CAM)
8.Clinical nursingHard
A patient with stress incontinence is taught self-care. Which statement shows a need for further teaching?
A"I'll cut down on caffeine."
B"I'll drink as little as possible so I don't leak."
C"I'll try to lose some weight if I can."
D"I'll do my pelvic floor exercises every day."
3Solutions
1.Lab values & electrolytes
Answer: A · The liver makes most clotting factors, so production falls
Why this is the answer
The liver makes most clotting factors, including the vitamin K–dependent ones. In severe liver disease their production falls, so the INR rises. A raised INR is one of the markers of how severe liver failure is.Checked against:Prothrombin Time Test and INR (PT/INR) · MedlinePlus (NIH) (2024)
Answer
A · The liver makes most clotting factors, so production falls
2.Lab values & electrolytes
Answer: B · Insulin delivery failure; inject a correction dose by pen and change the set
Why this is the answer
A high glucose that does not respond to a pump bolus, with rising ketones, suggests a kinked, blocked or dislodged cannula. Because pumps use only rapid-acting insulin, DKA can develop within hours. The usual advice is to give a correction dose by pen or syringe, change the infusion set, check glucose and ketones often, and seek help if ketones keep rising or vomiting starts.
Answer
B · Insulin delivery failure; inject a correction dose by pen and change the set
3.Arterial blood gas interpretation
Answer: HCO₃⁻ = 24.9 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
|49 − 40| = 9 mmHg → 0.9 × 10 mmHg
Expected HCO₃⁻
HCO₃⁻ = 24 + 1·0.9 = 24.9 mmol/L
Answer
HCO₃⁻ = 24.9 mmol/L
4.Arterial blood gas interpretation
Answer: delta ratio = 1.538
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 = 144 − (101 + 11) = 32
Delta ratio
(32 − 12)/(24 − 11) = 20/13 = 1.538
Answer
delta ratio = 1.538
Between 1 and 2: a pure high anion gap acidosis.
5.Clinical pharmacokinetics
Answer: LD = 562.5 mg
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Volume of distribution
Vd = 0.5·60 = 30 L
Amount of active drug needed
Vd·C = 30·15 = 450 mg
Loading dose
LD = 450/(0.8·1) = 562.5 mg
Answer
LD = 562.5 mg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: Css,avg = 20.83 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
The CAM, and similar tools such as the 4AT, check for an acute onset or fluctuating course, inattention and disorganised thinking or altered consciousness. Early detection allows causes to be treated.
Answer
D · The Confusion Assessment Method (CAM)
8.Clinical nursing
Answer: B · "I'll drink as little as possible so I don't leak."
Why this is the answer
Restricting fluids concentrates urine, irritates the bladder and risks dehydration and infection. Pelvic floor exercises, weight loss and reducing caffeine are recommended measures.
Answer
B · "I'll drink as little as possible so I don't leak."