13.3 Injectable Medicines, Dilutions, Percentages & Weight-Based Calculations

Injectable Medicines, Dilutions, Percentages & Weight-Based Calculations

Parenteral administration—encompassing subcutaneous (SC), intramuscular (IM), intravenous (IV), and intraosseous (IO) routes—bypasses the protective barriers of the gastrointestinal tract, delivering rapid bioavailability. In acute intrapartum emergencies, maternal resuscitation, and neonatal care, there is no margin for error. A calculation mistake in an injectable medicine takes effect immediately and cannot be recalled.

Under the NMC Code (Section 18) and national medicines management standards, midwives must master the mathematical foundations of injectable drug volume calculation, dry powder reconstitution, percentage concentrations, ratio strengths, and weight-based neonatal dosing.

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Liquid Injectable Volume Calculations

When a drug is supplied in liquid form in an ampoule or vial, the volume to be withdrawn into the syringe is determined using the core parenteral formula:

$\text{Volume to Administer (mL)} = \frac{\text{Dose Prescribed (What You Want)}}{\text{Stock Concentration on Ampoule (What You Have)}} \times \text{Ampoule Volume}$

Clinical Example 1: Intrapartum Opioid Analgesia (Pethidine)

• Prescription: A woman in established labour requests systemic analgesia. The obstetrician prescribes pethidine 75 mg IM.
• Available Stock: Pethidine ampoules labelled $100\text{ mg in } 2\text{ mL}$ ($50\text{ mg/mL}$).
• Calculation: $\text{Volume (mL)} = \frac{75\text{ mg}}{100\text{ mg}} \times 2\text{ mL} = 0.75 \times 2\text{ mL} = 1.5\text{ mL}$
• Sanity check: $75\text{ mg}$ is midway between $50\text{ mg}$ ($1\text{ mL}$) and $100\text{ mg}$ ($2\text{ mL}$). The answer $1.5\text{ mL}$ is logically sound.

Clinical Example 2: Co-Administered Antiemetic (Cyclizine)

• Prescription: Co-administered with pethidine to prevent opioid-induced nausea: cyclizine 50 mg IM.
• Available Stock: Cyclizine $50\text{ mg in } 1\text{ mL}$.
• Calculation: $\text{Volume (mL)} = \frac{50\text{ mg}}{50\text{ mg}} \times 1\text{ mL} = 1.0\text{ mL}$

Controlled Drugs (CD) Governance in the UK

Pethidine and diamorphine are Schedule 2 Controlled Drugs under the Misuse of Drugs Regulations 2001. In the UK, administration mandates strict governance:

1. Independent Double-Checking: Two registered practitioners (e.g. two registered midwives, or a midwife and a doctor) must independently calculate the dose, inspect the ampoule label, verify expiry dates, confirm patient identity and allergy status, observe drug preparation, and witness administration.
2. Witnessed Destruction: When an ampoule contains more drug than required (e.g. drawing $1.5\text{ mL}$ [75 mg] from a $2\text{ mL}$ [100 mg] pethidine ampoule), the surplus $0.5\text{ mL}$ (25 mg) must be destroyed immediately in the presence of the second checker into an approved denaturing kit or clinical sharps receptacle before administration.
3. Controlled Drugs Register Entry: Both practitioners must immediately sign the statutory CD register, recording date, time, patient name, dose administered, dose discarded, and balance remaining in the ward cupboard.

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Dry Powder Reconstitution & Displacement Volume

Many parenteral medications—including diamorphine, benzylpenicillin, and IV co-amoxiclav—are unstable in solution and manufactured as dry lyophilised powders that must be reconstituted with sterile diluent (Water for Injection or 0.9% Sodium Chloride) immediately prior to use.

Reconstitution Mathematics

• Diamorphine Reconstitution: Diamorphine powder ampoules are supplied as $5\text{ mg}$ or $10\text{ mg}$. The displacement volume of small powder quantities ($<10\text{ mg}$) is clinically negligible ($<0.02\text{ mL}$). Adding $1\text{ mL}$ of sterile water for injection to a $10\text{ mg}$ powder ampoule produces a final solution of $10\text{ mg/mL}$.

  • Example: Prescribed diamorphine $7.5\text{ mg IM}$.
  • Reconstitute $10\text{ mg}$ vial with $1\text{ mL}$ Water for Injection $\rightarrow$ concentration is $10\text{ mg/mL}$. $\text{Volume} = \frac{7.5\text{ mg}}{10\text{ mg}} \times 1\text{ mL} = 0.75\text{ mL}$

• Large Powder Displacement Volumes: When reconstituting large gram-weight powders (e.g. benzylpenicillin $1.2\text{ g}$ or IV ampicillin), the physical mass of the powder occupies significant volume (displacement volume). Midwives must consult the manufacturer summary of product characteristics (SmPC) to calculate total final volume accurately.

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Percentage Concentrations: The "Multiply by 10" Rule

In clinical practice, local anaesthetics, IV electrolytes, and topical antiseptics are expressed as percentage concentrations ($w/v$, weight in volume).

The Mathematical Definition of Percentage Concentration

A percentage concentration ($X\%$) represents the number of grams of solid solute dissolved in 100 mL of liquid solution:

$X\% = X\text{ grams in } 100\text{ mL}$

To convert any percentage concentration into milligrams per millilitre (mg/mL), multiply the percentage number by 10:

$\text{Concentration in mg/mL} = \text{Percentage (\%)} \times 10$

                    THE "MULTIPLY BY 10" PERCENTAGE RULE
                    
      Percentage (%)  ───────× 10───────►  Concentration (mg/mL)
      
      Examples:
      • 0.5% Bupivacaine   ───× 10───►    5 mg/mL
      • 1.0% Lidocaine     ───× 10───►   10 mg/mL
      • 2.0% Lidocaine     ───× 10───►   20 mg/mL
      • 0.9% Normal Saline ───× 10───►    9 mg/mL  (9 g/L)
      • 5.0% Glucose       ───× 10───►   50 mg/mL  (50 g/L)
      • 10% Calcium Gluc.  ───× 10───►  100 mg/mL
      • 50% Magnesium SO4  ───× 10───►  500 mg/mL

Clinical Applications in Midwifery

1. Perineal Infiltration for Episiotomy Repair (Lidocaine)

• Prescription: Prior to suturing a second-degree perineal tear or performing an episiotomy, the midwife infiltrates the perineum with lidocaine 100 mg.
• Available Stock: Lidocaine 1% solution ($20\text{ mL}$ vial).
• Step 1: Convert percentage to $\text{mg/mL}$: $1\% \times 10 = 10\text{ mg/mL}$.
• Step 2: Calculate volume: $\text{Volume (mL)} = \frac{\text{Dose Prescribed}}{\text{Concentration}} = \frac{100\text{ mg}}{10\text{ mg/mL}} = 10\text{ mL}$
• Maximum Safe Dose of Lidocaine: The maximum safe infiltration dose of plain lidocaine is $3\text{ mg/kg}$ (up to a maximum absolute limit of $200\text{ mg}$ in an adult). For a $70\text{ kg}$ woman, $70 \times 3 = 210\text{ mg}$ (capped at $200\text{ mg} = 20\text{ mL}$ of 1% lidocaine).

2. Emergency Antidote: Calcium Gluconate 10%

• Clinical Scenario: Magnesium sulfate toxicity (loss of patellar reflexes, respiratory depression $<12\text{ breaths/min}$). The emergency antidote is calcium gluconate 10% 1 g IV administered over 10 minutes.
• Concentration: $10\% \times 10 = 100\text{ mg/mL}$.
• Volume: $1\text{ g} = 1,000\text{ mg} \rightarrow \frac{1,000\text{ mg}}{100\text{ mg/mL}} = 10\text{ mL}$ (one standard $10\text{ mL}$ ampoule).

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Ratio Strengths: Adrenaline (Epinephrine) Dilutions

Ratio strengths express the relationship between parts of solute and parts of solution. In emergency resuscitation, adrenaline is prepared in two distinct standard ratio strengths:

$\text{Ratio } 1 : Y = 1\text{ gram of drug in } Y\text{ mL of solution}$

Resuscitation Council UK (NLS) Neonatal Adrenaline Calculations

Under the Newborn Life Support (NLS) algorithm, if the neonatal heart rate remains $<60\text{ bpm}$ despite effective positive-pressure lung inflation and 30 seconds of coordinated chest compressions, adrenaline is indicated:

• Recommended IV/IO Dose (RCUK 2025): $20\text{ micrograms/kg}$ of adrenaline $1:10,000$, repeated every 4 minutes if the heart rate stays below 60 bpm.
• Since $1:10,000$ adrenaline contains $100\text{ micrograms/mL}$, this equates directly to: $\text{Volume of } 1:10,000 = 0.2\text{ mL/kg}$
• Worked Example: A term neonate weighing $3.0\text{ kg}$ requires an IV adrenaline dose of $20\text{ micrograms/kg}$:
  • $\text{Total dose} = 3.0\text{ kg} \times 20\text{ micrograms/kg} = 60\text{ micrograms}$.
  • $\text{Volume of } 1:10,000 = \frac{60\text{ micrograms}}{100\text{ micrograms/mL}} = 0.6\text{ mL}$.

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Weight-Based Parenteral Dosing in Neonates

Neonatal antimicrobial therapy and emergency resuscitation require accurate birthweight calculations.

1. Intravenous Gentamicin in Early-Onset Sepsis (NICE NG195)

• Standard Dose: $5\text{ mg/kg}$ IV every 36 hours (extended interval regimen for term infants).
• Clinical Scenario: Term infant weighing $3.4\text{ kg}$.
  • $\text{Dose required} = 3.4\text{ kg} \times 5\text{ mg/kg} = 17\text{ mg}$.
  • Available paediatric stock: Gentamicin $20\text{ mg in } 2\text{ mL}$ ($10\text{ mg/mL}$).
  • $\text{Volume to draw up} = \frac{17\text{ mg}}{10\text{ mg/mL}} = 1.7\text{ mL}$.

2. Intravenous Benzylpenicillin

• Standard Dose: $25\text{ mg/kg}$ IV every 12 hours.
• Clinical Scenario: Infant weighing $2.8\text{ kg}$.
  • $\text{Dose required} = 2.8\text{ kg} \times 25\text{ mg/kg} = 70\text{ mg}$.
  • Reconstituted vial: Benzylpenicillin $600\text{ mg}$ made up to a final volume of $6\text{ mL}$ with Water for Injection, allowing for displacement ($100\text{ mg/mL}$; check the product information for the diluent volume).
  • $\text{Volume to draw up} = \frac{70\text{ mg}}{100\text{ mg/mL}} = 0.7\text{ mL}$.