Math - October 23, 2025

Introduction to Parenteral Drug Administration

• Definition of Parenteral Administration:

  • Refers to any drug administration route other than the gastrointestinal tract, primarily involving injections (e.g., subcutaneous, intramuscular, intravenous).

Syringe Measurements

• Use of Syringes:

  • Syringes are necessary for administering medications in liquid form, involving precise measurements.

  • Common syringe measurements include:

  • Half ml (0.5 ml)

  • One ml (1 ml)

  • One and a half ml (1.5 ml)

  • Two ml (2 ml)

  • Two and a half ml (2.5 ml)

  • Three ml (3 ml)

• Additional fractional measurements include:

  • 0.1 ml, 0.2 ml, 0.3 ml up to 1 ml for smaller doses.

• Measuring Specific Volumes:

  • Example: To measure 1.3 ml using a 3 ml syringe:

  • Identify the mark between 1 ml and 1.5 ml (1.5 ml equals 1 and a half ml).

  • Measure carefully between known measurements for accuracy.

  • For example, to measure 0.6 ml:

  • First identify 0.5 ml (half ml), then move to the 0.6 ml mark.

Practical Calculations in Dosage Administration

• Dosage Calculation Formula Using "Desired (D), On Hand (H), and Vehicle (V)":

  • The equation is expressed as:

  • $D/H imes V = Amount$

  • Example Calculation:

  • If a physician orders 0.25 ml (D) and has a stock of 0.5 mg in 2 ml (H):

    • Calculation:

      1. Desired (D) = 0.25 ml

      2. On Hand (H) = 0.5 mg / 2 ml

      3. Volume (V) = 2 ml

      4. Plugging in:

      • $D/H imes V = (0.25/0.5) imes 2$

      • Result: 0.25/0.5 = 0.5 -> 0.5 * 2 = 1 ml

• Additional Examples:

  • Ordering of 60 mg of a medication when stock is 25 mg/ml in 5 ml:

  • Setup as:

    • $60 mg = x ml imes 25 mg/ml$

  • Solve:

    • $x = 60 / 25 = 2.4 ml$

Common Medication Orders and Dosages

• Example Case Adjusting for Different Concentrations:

  • Physician orders:

  • 80 mg of medication, stock available is 100 mg per 2 ml:

    • Setup:

    • $100/2 = 80/x$

    • Resulting calculation gives you:

    • Cross Multiplication to solve for x yields 1.6 ml.

• Example of Volume Calculations for Different Dosages:

  • For order of 50 mg with 100 mg per 2 ml available:

  • Setup:

    • Similar proportion setup leads to 1 ml.

Reconstitution of Medications

• Goals of Reconstitution:

  • To convert powdered medications into liquid form for administration, requiring mixing with diluents (e.g., sterile water).

• Example Scenario:

  • Physician orders 300 mg Dithromax; stock is in powdered form:

    • States

    • Must add 4.8 ml sterile water; single vial has 500 mg:

    • Calculation:

    • Set up proportionality:
      
      

      • For 300 mg required based on the 500 mg available:

      • $100/proportion = 300/x$ => Solve for x = 6 ml.

• Units of Medications:

  • Understanding units is crucial, such as:

  • 1 grain of morphine = 60 mg

  • Confirming quantities (e.g., converting and calculating recommended dosage).

Conclusion

• Importance of Proportions and Calculations:

  • Mastery of setup and understanding of calculations is essential in clinical practice to ensure accurate medication administration.

• Rounding Off and Approximations:

  • Understanding to round off final values to practical volume measurement and confirming the stock value per ml when administering medications is crucial.