Critical Care & Titration

Scope: Weight- and time-based continuous infusions (mcg/kg/min, mcg/kg/hr, mg/kg/hr, units/kg/hr), concentration preparation, and protocol-driven titration — solved both directions (ordered dose → pump rate, and pump rate → actual dose delivered). Dimensional analysis is the primary method throughout.

7.1 Concept — Continuous Infusions & Why the Units Matter

Critical-care drugs are given as continuous infusions because their effect must be precisely controlled minute-to-minute. The order is often a rate of drug per kg per time (e.g., 5 mcg/kg/min) or a rate per time (e.g., 8 mcg/min). You convert that order into a pump rate (mL/hr) using the concentration of the mixed bag.

Three moving parts: the dose (what's ordered), the concentration (how the bag is mixed), and the weight (when the dose is weight-based). Master the two directions:

Universal facts: 1 mg = 1000 mcg, 1 g = 1000 mg, 1 hr = 60 min. Convention: 1 kg ≈ 2.2 lb (see §6.2).

7.2 Concentration Preparation (always compute this first)

mg/mL = total mgtotal mL   units/mL = total unitstotal mL

mcg/mL = mg × 1000mL

Standardize units first. If the dose is in mcg and the bag is labeled in mg, convert the bag to mcg/mL before setting up dimensional analysis — mismatched units are the classic titration error.

7.3 Core Formulas — Forward & Reverse

Where the ×60 goes: only mcg/kg/min (and mcg/min) carries the ×60, because the order is per minute but the pump runs in per hour. The "per hour" doses (mcg/kg/hr, mg/kg/hr, units/kg/hr) do not need it.

7.4 Dimensional-Analysis Setup

Forward — mcg/kg/min → mL/hr

5 mcgkg · min × 70 kg × 60 min1 hr × 1 mL1600 mcg = mL/hr

Reverse — mL/hr → mcg/kg/min (flip the same factors)

13.1 mLhr × 1600 mcg1 mL × 170 kg × 1 hr60 min = mcg/kg/min

Read the flow: every factor cancels the unit before it. In the reverse setup the concentration is flipped (mcg on top), and kg and time are divided — the mirror image of forward.

7.5 Worked Examples — Both Directions

Example 1 — Dopamine, mcg/kg/min (forward)

Order: dopamine 5 mcg/kg/min. Patient: 70 kg. Available: 400 mg in 250 mL.

1. Concentration: 400 mg × 1000 = 400,000 mcg ÷ 250 mL = 1600 mcg/mL.
2. 5 × 70 × 601600 = 210001600 = 13.125
3. 13.1 mL/hr (nearest tenth).

Example 2 — Dopamine, reverse (what is actually running?)

Pump at 13.1 mL/hr, same bag (1600 mcg/mL), 70 kg.

13.1 × 160070 × 60 = 209604200 = 4.99 → 5.0 mcg/kg/min

Pearl: the reverse answer is ~5.0, not exactly 5, because we set the pump to a rounded 13.1. That tiny tolerance is normal — and why you report to the ordered precision, not 12 decimals.

Example 3 — mcg/kg/hr (forward)

Order: 2 mcg/kg/hr. Patient: 60 kg. Available: 50 mg in 250 mL.

1. Conc: 50 mg × 1000 = 50,000 mcg ÷ 250 = 200 mcg/mL.
2. No ×60 (order is per hour): 2 × 60200 = 120200 = 0.6
3. 0.6 mL/hr.

Reverse: 0.6 mL/hr × 200 mcg/mL = 120 mcg/hr ÷ 60 kg = 2 mcg/kg/hr. ✓

Example 4 — mg/kg/hr (forward)

Order: 0.5 mg/kg/hr. Patient: 80 kg. Available: 2 g in 500 mL.

1. Conc: 2000 mg ÷ 500 mL = 4 mg/mL.
2. 0.5 × 804 = 404 = 10
3. 10 mL/hr.

Reverse: 10 mL/hr × 4 mg/mL = 40 mg/hr ÷ 80 kg = 0.5 mg/kg/hr. ✓

Example 5 — Norepinephrine, mcg/min (non-weight-based convention)

Order: norepinephrine 8 mcg/min. Available: 4 mg in 250 mL.

1. Conc: 4 mg × 1000 = 4000 mcg ÷ 250 = 16 mcg/mL.
2. Forward: 8 mcgmin × 60 min1 hr × 1 mL16 mcg = 48016 = 30 mL/hr.
3. Reverse: 30 mL/hr × 16 mcg/mL = 480 mcg/hr ÷ 60 = 8 mcg/min. ✓

Convention note: vasopressors are commonly ordered mcg/min (not weight-based) in many adult settings, while mcg/kg/min is also used (common in pediatrics). Use whichever the order states — the setup only differs by whether "kg" appears.

7.6 Protocol-Based Dosing

Titratable drugs are rarely "set and forget." They run on a protocol: a written rule that says start here, measure X, adjust Y. Every titratable question must give you the complete protocol — you never infer missing parameters.

7.6.1 Heparin — complete hypothetical protocol (weight-based)

⚠ Educational example only. Bolus doses, infusion rates, and aPTT targets are institution-specific. This is a complete, self-contained hypothetical protocol for practice — it is not a universal standard.

Hypothetical protocol:

• Concentration: heparin 25,000 units in 250 mL D5W = 100 units/mL.
• Loading bolus: 80 units/kg IV (max 10,000 units — hypothetical cap).
• Initial infusion: 18 units/kg/hr.
• Monitoring: aPTT 6 hr after start, then per protocol until therapeutic, then per policy.
• Titration table (hypothetical):

Worked problem — 70 kg patient:

1. Bolus: 80 × 70 = 5600 units; volume = 5600 × 1 mL100 units = 56 mL IV push.
2. Initial infusion (forward): 18 × 70100 = 1260100 = 12.6 mL/hr.
3. Reverse check: 12.6 mL/hr × 100 units/mL = 1260 units/hr ÷ 70 kg = 18 units/kg/hr. ✓
4. Titration: aPTT comes back 32 sec → per table, bolus 80 units/kg + increase 4 units/kg/hr → new rate = 22 units/kg/hr → 22 × 70100 = 15.4 mL/hr.

7.6.2 Insulin infusion — complete hypothetical protocol

⚠ Educational example only. Start rates, targets, and titration steps are institution-specific.

Hypothetical protocol:

• Concentration: regular insulin 100 units in 100 mL NS = 1 unit/mL.
• Start: 1 unit/hr (hypothetical).
• Monitoring: capillary blood glucose (BG) hourly.
• Titration table (hypothetical):

Worked problem: BG = 205, current rate 2 units/hr.

• Per table: increase 1 unit/hr → new rate 3 units/hr.
• At 1 unit/mL, 3 units/hr = 3 mL/hr. Reverse check: 3 mL/hr × 1 unit/mL = 3 units/hr. ✓

7.6.3 Vasopressor titration (norepinephrine) — complete hypothetical protocol

⚠ Educational example only. Start doses and titration increments are institution-specific.

Hypothetical protocol:

• Concentration: norepinephrine 4 mg in 250 mL = 16 mcg/mL (see §7.5 Ex. 5).
• Start: 2 mcg/min (hypothetical).
• Titrate: by 1–2 mcg/min every 5 min (hypothetical) to target mean arterial pressure (MAP) ≥ 65 mmHg.
• Max: 30 mcg/min (hypothetical); notify provider if approaching max.

Worked problem: start 2 mcg/min → 2 × 6016 = 7.5 mL/hr. MAP still low → increase to 4 mcg/min → 4 × 6016 = 15 mL/hr.

Titration safety: vasopressors are titrated up to effect and down with weaning per protocol — never changed without an order, and always on a pump with a hard upper limit (smart-pump guardrail).

7.7 Rounding Rules (Section 7)

7.8 Common Mistakes

1. Missing the ×60 for per-minute orders (mcg/kg/min) — off by 60×.
2. Adding a ×60 to per-hour orders (mcg/kg/hr, units/kg/hr) — same magnitude, opposite direction.
3. mg/mcg mismatch — using 400 mg instead of 400,000 mcg against a mcg concentration.
4. Forgetting weight in weight-based orders, or adding weight to a non-weight-based order (mcg/min).
5. Wrong direction in reverse calcs — multiplying when you should divide (or vice versa).
6. Rounding the concentration before use — 1.6 mg/mL → "2" wrecks the rate.
7. Using an unlabeled/unknown protocol parameter — if the protocol doesn't state it, you can't compute it.
8. Reporting reverse dose to absurd precision (4.99987 mcg/kg/min) instead of the ordered precision.

7.9 Safety Implications

• Heparin, insulin, and vasopressors are high-alert medications — errors can be fatal. Independent double checks are standard.
• A 60× error kills. "Per minute" vs "per hour" confusion is a sentinel-event class of error.
• Concentration confusion is a top cause of wrong-rate infusions — always verify the exact mix (mg or units per mL) before programming.
• Smart pumps with guardrails (hard limits) are a safety net, not a substitute for correct math.
• Never bolus from or flush through a running vasopressor line — it can deliver a sudden overdose.
• Label every line (high-alert stickers, dedicated lumens) and trace lines to the pump before changes.

7.10 Memory Aids

• "Minute → ×60. Hour → no 60." The only formulas with ×60 are per-minute orders.
• "Conc first, then dose." Always compute mcg/mL (or units/mL, mg/mL) before the main setup.
• "Forward vs reverse is just flipping the fraction." Reverse = flip the concentration and divide by kg (and 60 if per-minute).
• "The bag is labeled mg, the drug is dosed in mcg" → ×1000 the bag first.
• "µg/kg/min = (dose × kg × 60) ÷ conc." — memorize the numerator order: dose, kg, 60.

7.11 Exam Traps

• A question giving two concentrations (or "double strength") — compute with the actual one.
• Reverse calculation asked when only forward is taught — practice both directions.
• Order in mcg/kg/min but weight in lb — convert to kg first, then the titration.
• Bolus + infusion in one heparin question — two separate answers (units/mL for bolus; mL/hr for infusion).
• Titration step requiring you to apply a protocol row, not just a formula — read the table carefully.
• "What is the patient actually receiving?" = reverse; the answer is a dose, not a mL/hr.
• Zero/leading-zero formatting on rates (0.6 mL/hr, never .6; 15 mL/hr, never 15.0).

7.12 Clinical Pearls

• Verify the running rate against the ordered dose at every handoff using the reverse formula.
• Know your concentrations — many institutions standardize (e.g., dopamine "1600 mcg/mL" from 400 mg/250 mL), but never assume; read the bag.
• Titrate by the protocol's smallest increment and re-measure before the next change.
• Document each rate change with the corresponding parameter (e.g., "rate ↑ to 15.4 mL/hr for aPTT 32").
• When a rate feels wrong, reverse-calculate before you touch the pump — a 10-second sanity check.

7.13 Check Yourself

1. Forward (mcg/kg/min): dopamine 5 mcg/kg/min, 80 kg, 800 mg in 500 mL → ? mL/hr
2. Reverse: same bag at 15 mL/hr, 80 kg → ? mcg/kg/min
3. Heparin forward: 18 units/kg/hr, 65 kg, 25,000 units/250 mL → ? mL/hr
4. Heparin reverse: same bag at 11.7 mL/hr, 65 kg → ? units/kg/hr
5. Norepinephrine: 8 mcg/min, 4 mg/250 mL → ? mL/hr (reverse-check your answer)

7.14 Source Note

All concentrations, bolus doses, start rates, titration steps, and "maximum" values in this section are clearly-labeled hypothetical educational examples. Real heparin, insulin, and vasopressor protocols are institution-specific and must be sourced from facility policy and current references. The math (conversions, forward/reverse dimensional analysis) is universal; the numbers are not.