Math - October 28, 2025

Introduction to Medical Dosage Calculations

• Discussion of upcoming exams and attendance.

• Reference to mixing medications and calculating volumes of reconstituted medications.

Medication Reconstitution and Calculation

General Process

• Instructions to mix medications and the importance of understanding the correct volume needed for injections.

Zithromax Example

• Physician's order: 250 mg of medication by intramuscular injection.

• Stock vial: 1 gram of medication.

• Directions on the vial: Add 2.5 ml diluent to achieve a concentration of 300 mg/ml.

• Required calculation:

  • Determine the volume to administer:

  • 1 gram = 1000 mg.

  • To find out how much 250 mg corresponds to, use proportions.

  • The relation between mg and ml is established:

    • 1000 mg needs 2.5 ml.

    • To determine how much volume corresponds to 250 mg, calculate:
      $\text{Volume for 250 mg} = \frac{250}{1000} \times 2.5 \text{ ml}$

    • This results in:
      $\text{Volume for 250 mg} = 0.625 \text{ ml}$

Penicillin Example

• Physician's order: 2 million units of Penicillin by intramuscular injection.

• Stock vial: 5 million units of Penicillin.

• Directions specify different diluents and resulting concentrations.

• Concentrations and diluents:

  • 18.2 ml gives 250,000 units/ml.

  • 2.5 ml gives 500,000 units/ml.

  • 3.2 ml gives 1,000,000 units/ml.

• Requirement: Determine which concentration to use, ensuring the total does not exceed 3 ml.

  • Option one gives a volume of 3 ml and satisfies the order of 2 million units.

  • 2,000,000 units requires the use of diluent to calculate how much would be used in this case.

• Make calculations for the preferred diluent.

  • Review the relationship between the unit dose and the volume.

• Set up equations to confirm the desired dosages:

  • $\frac{2,000,000 \text{ units}}{500,000 \text{ units/ml}} = 4 \text{ ml}$

  • For 1 million units/ml, it would require:

  • $\frac{2,000,000 \text{ units}}{1,000,000 \text{ units/ml}} = 2 \text{ ml}$

  • Confirm the total volume needs, ensuring not to exceed 3ml for adult patients.

IV Flow Rates

Terminology

• Rate of Flow (GTT/min): Number of drops delivered to the patient per minute.

• Drop Factor: Number of drops needed to produce a certain volume (cc).

• Solution Amount: Total volume of fluid administered.

• Time: Duration over which the fluid is administered.

Flow Rate Formula

• General formula for calculating flow rates:

  • $\text{Rate of Flow} = \frac{\text{Drop Factor} \times \text{Total Amount of Solution}}{\text{Time}}$

Example Calculation of IV Flow Rate

• Scenario: IV contains 1000 ml of Dextrose insulin solution with a drop factor of 10 GTT/ml and set to run for 5 hours.

• Calculate GTT/min and GTT/hour.

  • 1. Rate of flow per minute:

  • $\text{GTT/min} = \frac{10 \text{ GTT/ml} \times 1000 \text{ ml}}{5 \text{ hours} \times 60 \text{ min/hour}} = \frac{10,000}{300} \approx 33.33 \text{ GTT/min}$

  • 2. Rate of flow per hour:

  • $\text{GTT/hour} = \frac{10 \text{ GTT/ml} \times 1000 \text{ ml}}{5} = 2000 \text{ GTT/hour}$

Review of Calculations and Concepts

Proportions and Dosages

• Emphasize the importance of setting up correct proportions to find the necessary volumes.

• Highlight proportionality in determining volumes based on the required dosage.

Importance in Practice

• Allowance for different syringe sizes based on patient needs and drug concentrations ensures safe and effective administration.

• Acknowledge the parameters of maximum dosage to avoid over-administration of medication in adult patients.

Conclusion

• Summary of principles discussed in medication reconstitution, calculation, and IV flow rates and their applications in clinical settings.