Dosage Calculations Based on Body Surface Area (BSA)

Abstract

In the previous chapter, drug concentration in the blood was correlated to the clearance and drug distribution in the body. In this chapter, I discuss the relation of the body surface area (BSA) to the body weight. Subsequently, a number of complicated BSA equations are derived by applying simple concepts of geometry. Through these derivations you have the opportunity to comprehend and further apply the equations to calculate drug doses. The chapter is focused on the rational use of BSA equations for dosage calculations. Close to the end of the chapter, higher exponential equations are solved, either as they are or after conversion to the more convenient linear form to calculate doses for pediatric populations. In general, not all the drugs can be dosed using the concept of body surface area. Clinicians have to be able to see the connection between drug disposition, organ size, and body size in order to confidently use these equations to calculate doses. This chapter offers a conceptual approach to the use of BSA equations for dosage calculations. It also discusses the advantages and disadvantages of the method.

Exercises

• 14.1. The pediatric recommended dose of an antibiotic drug is 2.5 mg/kg or 32.5 mg/m². How many milligrams are represented in each dose for a 4.2 lb, 17 in. infant? Compare the dose normalized per body weight with the dose adjusted using the DuBois’s formula.

  • (Answer: 4.78 mg as adjusted per kg versus 4.71 mg as the dose adjusted with BSA)

• 14.2. Calculate the daily dose for a 30 lb, 36.6 in. child using the Boyd’s formula if the adult normal dose of a drug is 2.5 mg, q.i.d.

  • (Answer: 3.54 mg/day)

• 14.3. A 136 lb, 1.67 m, 67-year-old male patient is to be infused with 144 (μg/m²)/h of an anticancer drug over 75 min once a day, 5 days per week for 3 weeks.

  • (a) Convert the dose of the drug in μg/kg/day using the Mosteller’s formula.

  • (b) How many milligrams of drug has the patient received by the end of his treatment?

    • (Answer: (a) 4.92 (μg/kg)/day; (b) 4.56 mg)

• 14.4. Given the following information for a female patient receiving chemotherapy:

  • Age: 54  Weight: 163 lb  Height: 5 ft 8 in.

  • Methotrexate recommended dose: 40 mg/m²

  • Drug concentration in IV bag: 450 mg/L

  • Dosage regimen: IV infusion once a day, q.i.w. for 6 weeks

    • (a) Calculate patient’s BSA using the Fujimoto’s formula.

    • (b) What is the daily volume of infusion?

      • (Answer: (a) 1.83 m²; (b) 162.5 mL)

• 14.5. Given the information below:

  • Patient: 3-month old infant  Weight: 4 lb, 15 ounces  Height: 20 in

  • Recommended dose: 75 mg/1.72 m²

    • (a) What is the appropriate dose for the infant (use the DuBois’s formula)?

    • (b) If the baby is to receive the recommended dose in two separate injections of 150 μL each, how much drug should the pharmacist weigh to prepare 0.5 mL of solution?

      • (Answer: (a) 7.61 mg; (b) 12.68 mg)

• 14.6. The recommended “normal” oral dose for an antibiotic in suspension form is 350 mg t.i.d.

  • (a) Use the Boyd’s formula to calculate the dose should a 6-year-old child who weighs 32 lb and is 0.95 m tall receive.

  • (b) Assuming that the antibiotic is supplied as a dry powder, and the dose is to be given in one tsp, how many grams of powder should you weigh out and to what volume should you reconstitute the powder, if the medication is to last 10 days?

  • (c) What is the % w/v of the drug in the suspension?

    • (Answer: (a) 129.1 mg; (b) 3.873 g, 150 mL; (c) 2.6%)

• 14.7. A premature newborn (W = 4.5 lb, H = 18 in.) who has presented a Pseudomonas aeruginosa infection is to be treated with IM injections of polymyxin B sulfate antibiotic. The recommended antibiotic dose is 2.1·10⁶ unit/1.72 m² per day. Polymyxin B sulfate for IM injections is supplied in ampules containing 500,000 units of antibiotic dissolved in 2 mL of sterile isotonic saline. Each milligram of polymyxin B sulfate is equivalent to 10,000 units of antibiotic salt.

  • (a) Use the DuBois’s formula to calculate the milligrams of antibiotic in each injection if the antibiotic is to be given every 6 h.

  • (b) What is the injection volume?

    • (Answer: (a) 4.75 mg; (b) 190 μL)

• 14.8. A student who does not like working with exponential equations derived a linear version of Haycock’s equation and plotted the data as shown in the graph below (Fig. 14.5).

  • (a) Write the linear form of the Haycock’s formula.

  • (b) Do the negative values presented in the y-axis make sense to you?

  • (c) Use the linear form to calculate BSA for a subject whose height and weight is 0.92 m and 14.2 kg, respectively.

    • (Answer: (c) 0.607 m²)

• 14.9. The BSA of a particular patient was found by Fujimoto’s formula and by Mosteller’s formula to be 1.915441 and 1.993523, respectively. Use this information to determine the weight in kilograms and height in meters of the patient.

  • (Answer: W = 83.98 kg, H = 1.703 m)

• 14.10. Pick the correct statement. BSA-based dosage regimens are used _____________,

  • (a) When body weight-based dosing did not provide drug therapeutic levels

  • (b) For clinically obese patients

  • (c) When there are instructions from the manufacturer that the drug must be dosed using BSA methods

  • (d) On patients who have a V_d larger than the population average value

  • (e) To dose premature newborns

Fig. 14.5

The weight and height of males were applied on Haycock’s formula to calculate the ln (BSA). The plotted years of age from left-to-right are 0 (newborn), 0.25 (3 months), 0.5, 0.75, 1, 2, 3, 4, 5, 6, 7, 8, and 9