Displacement Value & Suppository Calculations

Overview

• Subject matter: Accurate formulation of medicated suppositories when ingredients are weighed (g, mg) but dispensed by volume (mL) into fixed‐volume mould cavities.
• Central challenge: Each Active Pharmaceutical Ingredient (API) has its own density; when mixed with a suppository base it displaces a characteristic mass of base. Correct dosing therefore requires density-based corrections.

Key Definitions

• Suppository: Solid dosage form intended for insertion into body cavities (rectal, vaginal …); melts/softens at body temperature to release API.
• Suppository base: Usually cocoa-butter (Theobroma oil) in examples, can also be synthetic fats or water-soluble PEGs. Supplies bulk and melting characteristics.
• Mould calibration value (y): Average weight (g) of blank suppositories produced by a particular mould when filled with molten base under routine conditions. Usually given per cavity; typical capacities: 1 g or 2 g.
• Displacement Value (DV): Volume of drug that displaces 1 g of a specified suppository base. Numerically:
  $DV = \frac{\text{weight of drug that displaces }1\,\text{g base}}{1\,\text{g}}$
  ‑ If drug density = base density ⇒ $DV = 1$ (equal masses exchanged).
  ‑ Drug density > base density ⇒ $DV < 1$ (heavier drug displaces less base by weight). ‑ Drug density < base density ⇒ $DV > 1$ (lighter drug displaces more base by weight).

Conceptual Points About DV

• Fixed mould volume means added drug must push out an equivalent volume of base; otherwise cavities under- or over-fill.
• DV data for many common APIs in cocoa-butter are tabulated in pharmacopeias & compounding references.
• Two categories of calculations:
  1. Type 1 – Single drug with known DV.
  2. Type 2 – Multiple drugs, each with its own DV.
  3. Type 3 – Drug given as % w/w of final suppository; DV not required (density effect inherently included in percentage).

Cocoa-Butter Displacement Values (selected)

• (From Table 9-1; all values relative to cocoa-butter)
  • Aminophylline – 1.5
  • Aspirin – 1.1
  • Bismuth subgallate – 3.0
  • Bismuth subnitrate – 6.0
  • Boric acid – 1.5
  • Chloral hydrate – 1.5
  • Dimenhydrinate – 1.3
  • Hydrocortisone – 0.7
  • Menthol – 2.0
  • Morphine HCl – 1.5
  • Potassium bromide – 2.2
  • Quinidine HCl – 3.0
  • Resorcinol – 1.0
  • Salicylic acid – 1.3
  • Tannic acid – 1.6
  • Zinc oxide – 5.0
  • Zinc sulfate – 2.8
    (Full table in transcript; always verify with latest reference when compounding.)

Core Formulae

• Single-drug base requirement:
  $\text{Amount of base (g)} = (N \times y) - \frac{N \times D}{DV}$
  where
  • $N$ = total suppositories prepared ("order + 2" rule: always compound ⁺2 to cover losses)
  • $y$ = mould calibration value (g)
  • $D$ = individual dose of drug (g)
  • $DV$ = displacement value of that drug.

• Two-drug scenario:
  $\text{Amount of base (g)} = N \times y - \left(\frac{N \times D<em>1}{DV</em>1} + \frac{N \times D<em>2}{DV</em>2}\right)$

• Percentage strength (Type 3):
  • Determine total fill weight $= N \times y$.
  • API mass $= \text{percent} \times \text{total fill weight}$.
  • Base mass $= \text{total fill weight} - \text{API mass}$.
  (DV unnecessary because the percentage already expresses the final w/w proportion.)

Worked Examples – Type 1 (Single Drug)

Example 1: 6 × 250 mg Bismuth Subgallate

• Order: 6 suppositories; add 2 extra ⇒ $N = 8$.
• Data: $D = 0.25\,g$, $DV = 2.7$, $y = 0.94\,g$.
• Base:
  $\text{Base} = (8\times0.94) - \frac{8\times0.25}{2.7} = 7.52 - 0.741 = 6.779 \approx 6.78\,g$
• Final formula:
  • Bismuth subgallate – 2 g (8 doses × 0.25 g)
  • Cocoa-butter base – 6.78 g.

Example 2: 8 × 500 mg Zinc Oxide

• Add 2 extra ⇒ $N = 10$.
• Data: $D = 0.5\,g$, $DV = 4.7$, $y = 1.0\,g$.
• Base:
  $\text{Base} = (10\times1) - \frac{10\times0.5}{4.7} = 10 - 1.0638 = 8.9362\,g$
• Final formula:
  • Zinc oxide – 5 g
  • Base – 8.94 g.

Example 3: 4 × 200 mg Metronidazole

• Add 2 ⇒ $N = 6$.
• Data: $D = 0.2\,g$, $DV = 1.7$, $y = 1.0\,g$.
• Base:
  $\text{Base} = (6\times1) - \frac{6\times0.2}{1.7} = 6 - 0.7058 = 5.2942\,g$
• Final: Drug 1.2 g; Base 5.29 g.

Example 4: 8 × 500 mg Paracetamol (2 g mould)

• Add 2 ⇒ $N = 10$.
• Data: $D = 0.5\,g$, $DV = 1.5$, $y = 2.04\,g$.
• Base:
  $\text{Base} = (10\times2.04) - \frac{10\times0.5}{1.5} = 20.4 - 3.33 = 16.71\,g$
• Final: Paracetamol 5 g; Base 16.71 g.

Suppositories with Two Drugs (Type 2)

• Strategy: Calculate each drug’s displaced base separately, subtract both from total mould fill.

Example 1: 15 × (150 mg Cortisone + 560 mg Zinc Oxide)

• Add 2 ⇒ $N = 17$.
• Doses: $D<em>1 = 0.15\,g$, $D</em>2 = 0.56\,g$.
• DV: $DV<em>1 = 1.5$, $DV</em>2 = 4.7$.
• Calibration $y = 2.04$.
• Drug masses:
  • Cortisone = $17\times0.15 = 2.55\,g$
  • ZnO = $17\times0.56 = 9.52\,g$.
• Base:
  $\text{Base} = 17\times2.04 - \left(\frac{2.55}{1.5} + \frac{9.52}{4.7}\right) = 34.68 - (1.70 + 2.03) = 30.95\,g$
• Final: Cortisone 2.55 g; ZnO 9.52 g; Base 30.95 g.

Example 2: 18 × (200 mg Metronidazole + 250 mg Paracetamol)

• Add 2 ⇒ $N = 20$.
• Doses: 0.2 g & 0.25 g.
• DV: 1.7 & 1.5; mould $y = 2.04$.
• Drug masses: Metronidazole 4 g; Paracetamol 5 g.
• Base:
  $\text{Base} = 20\times2.04 - \left(\frac{4}{1.7} + \frac{5}{1.5}\right) = 40.8 - (2.35 + 3.33) = 35.12\,g$
• Final: Metronidazole 4 g; Paracetamol 5 g; Base 35.12 g.

Percentage-Strength Calculations (Type 3)

• DV not used; base weight derived from desired % w/w.

Example 1: 8 × 18 % w/w Zinc Oxide, 1 g mould

• Add 2 ⇒ $N = 10$. Total fill = 10 g.
• Drug = 18 % of 10 g = 1.8 g.
• Base = 10 – 1.8 = 8.2 g.

Example 2: 18 × 5 % Metronidazole

• Add 2 ⇒ $N = 20$. Fill = 20 g.
• Drug = 5 % of 20 g = 1 g.
• Base = 19 g.

Example 3: 8 × 10 % Aspirin

• Add 2 ⇒ $N = 10$. Fill = 10 g.
• Drug = 1 g; Base = 9 g.

Example 4: 6 × 3 % Paracetamol

• Add 2 ⇒ $N = 8$. Fill = 8 g.
• Drug = 0.24 g; Base = 7.76 g.

Practical & Pharmacological Implications

• Uniformity: Correct base substitution ensures each suppository occupies mould volume without voids ≡ dose accuracy & regulatory compliance.
• Stability: Some drugs alter melting point; large percentages may require base modification or alternative (e.g., PEG) to prevent softening below room temperature.
• Patient comfort: Excessive solids may create gritty texture; guidelines often limit solid content to about 30 % w/w.
• Manufacturing loss: The “+2” rule hedges against wastage during pouring & trimming; number can be adjusted for larger runs.
• Ethics/Regulation:
  • Pharmacist must verify DV values from current compendia; outdated data can lead to sub-therapeutic or toxic doses.
  • Documentation: Batch records should detail calibration runs, DV source, calculations, and actual weights measured.
• Real-world tie-ins: Similar displacement principles apply in capsule packing (tapped density) and parenteral admixtures (e.g., concentrated drug volumes displacing saline in IV bags).

Tips for Exam Preparation

• Memorise the base formula; practise rearranging for unknowns.
• Keep typical DV values of common drugs (ZnO, Bismuth salts, Paracetamol, Metronidazole) at fingertips.
• Double-check units (mg ↔ g) before substitution.
• Always include extra suppositories in calculations; exam questions nearly always require it.