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b. If the flow rate for the TPN is prescribed at 1 mL/kg/h, how many
total calories will a 187-lb patient receive in 24 hours?
14.D. Compare a 152-lb 5-feet 8-inch patient’s target daily fluid
requirement based on (a) weight, (b) body surface area, and (c) a daily
nutritional requirement of 2000 kcal.
14.E. A high-protein oral nutritional drink has the following label
content based on a 2000-calorie diet. For each item with a question mark
(?), fill in the missing number.
a
Problem courtesy of Flynn Warren, Bishop, GA.
ANSWERS TO “CASE IN POINT” AND
PRACTICE PROBLEMS
Case in Point 14.1
a. The patient weighs 120 lb × 1 kg/2.2 lb = 54.55 kg.
The patient’s height is 5 feet 2 inches = 62 inches × 2.54 cm/inch =
157.48 cm.
Daily fluid requirement:
Based on 30 to 35 mL/kg/day:
54.55 kg × 30 mL/kg/day = 1636.36 mL
54.55 kg × 35 mL/kg/day = 1909.09 mL
Thus, the target is between 1636.36 and 1909.09 mL/day and the
predetermined TPN volume of 2000 mL would suffice.
b. Because this patient is over 60 years old, a target protein
requirement may be based on 1 to 1.5 g/kg/day:
54.55 kg × 1 g/kg/day = 54.55 g/day
54.55 kg × 1.5 g/kg/day = 81.82 g/day
Thus, the acceptable target for protein would be between 54.55 g
and 81.82 g/day
1.
2.
3.
4.
5.
c. The 10% amino acid injection that would be required:
100 mL/10 g × 54.55 g = 545.45 mL, and
100 mL/10 g × 81.82 g = 818.18 mL
Thus, the target for protein would be met by between 545.45 and
818.18 mL of the 10% amino acid injection.
d. The target of the patient’s nonprotein caloric requirements (BEE) is
determined by the Harris-Benedict equation:
655.1 + (9.56 × weight, kg) + (1.85 × height, cm) − (4.68 × age, y)
=
655.1 + (9.56 × 54.55 kg) + (1.85 × 157.48 cm) − (4.68 × 75) =
655.1 + 521.45 + 291.34 − 351 = 1116.89 kcal/day × 1.2 (activity
factor) = 1340.27 kcal/day
e. 1340.27 kcal/day × 1 g/3.4 kcal = 394.2 g/day dextrose required
D50W = 50 g dextrose/100 mL;
100 mL/50 g × 394.2 g dextrose = 788.39 mL D50W
(NOTE: In practice, the quantities may be rounded and
individualized based on clinical factors.)
Case in Point 14.2
a. Protein: 7 g × 4 kcal/g = 28 kcal
Fat: 9 g × 9 kcal/g = 81 kcal
Carbohydrate: 33 g × 4 kcal/g = 132 kcal
Total kcal = 28 + 81 + 132 = 241 kcal
kcal/mL = 241 kcal/237 mL = 1.02 kcal/mL
b. Protein: 7 g/237 mL × 1500 mL = 44.304 g protein
Fat: 9 g/237 mL × 1500 mL = 56.96 g fat
Carbohydrate: 33 g/237 mL × 1500 mL = 208.86 g carbohydrate
c. Daily kcal: Protein, 44.304 g × 4 kcal/g = 177.22 kcal
Fat, 56.96 g × 9 kcal/g = 512.66 kcal
Carbohydrate, 208.86 g × 4 kcal/g = 835.44 kcal
Total daily kcal = 177.22 + 512.64 + 835.44 = 1525.3 kcal
% kcal from protein = 177.22 kcal/1525.31 kcal × 100% = 11.62%
% kcal from fat = 512.64 kcal/1525.31 kcal × 100% = 33.61%
% kcal from carbohydrate = 835.44 kcal/1525.31 kcal × 100% =
54.77%
d. Yes, they compare favorably.
Practice Problems
27 BMI
30.1 BMI
224.28 mg/dose
≥320 lb
IBW = 125 lb
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84.8%, underweight
32.05 g/day
714.29 mL
240 kcal
1200 mL
a. 350 g dextrose
b. 200 g protein
c. 111.11 g lipid
a. 2250 to 2625 mL
b. 2400 mL
c. 1500 mL
a. 3052.21 kcal/day
b. 88.07 g protein/day
c. 101.74 g lipids/day
d. 446.07 g dextrose/day
e. 2254.55 mL fluids/day
411.76 mL amino acid injection
214.29 mL dextrose injection
373.95 mL sterile water for injection
71.43 mL dextrose injection
2193.55 kcal/day
a. 1991.01 kcal/day
b. 479.14 mL amino acid solution/day
c. 298.65 mL lipid emulsion/day
d. 724 mL dextrose solution/day
e. 1991.01 mL fluids/day
261.82 kcal
7.8 mL sodium chloride solution
7.5 mL potassium acetate solutionn
0.1 mL vitamin B12n
0.08 mL insulin
a. 14.89 mL
b. 31.48 mmol
a. 250 mL amino acids injection
b. 400 mL dextrose injection
c. 11.7 mL sodium chloride solution
d. 5.43 mL calcium gluconate solution
e. 0.15 mL insulin
f. 2.5 mL heparin
g. 330.22 mL sterile water
21.
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1560.6 kcal
60 g fat/day
50 g fat
a. 46.43% DV dietary fiber
b. 5.09% DV carbohydrate
c. 23.08% DV calcium
d. 5.11% DV potassium
e. 6.09% DV sodium
References
Dombrowski SR. Pharmacist counseling on nutrition and physical activity—part 1 of 2:
understanding current guidelines. Journal of the American Pharmacists Association
1999;39:479–491.
National Heart Lung and Blood Institute, National Institutes of Health. Management of
overweight and obesity in adults: systematic evidence review from the expert panel. 2013.
Available at: http://www.nhlbi.nih.gov/sites/www.nhlbi.nih.gov/files/obesity-evidence-
review.pdf. Accessed July 16, 2020.
Continuing Education Monograph. Managing Obesity as a Chronic Disease. Washington, DC:
American Pharmacists Association; 2001.
Zagaria MAE. Nutrition in the elderly. U.S. Pharmacist 2000;25:42–44.
Chessman KH, Kumpf VJ. Assessment of nutrition status and nutrition requirements. In:
DiPiro JT, Yee GC, Posey LM, et al., eds. Pharmacotherapy: A Pathophysiologic Approach.
11th Ed. [book online]. New York, NY: McGraw-Hill; 2020.
Mirtallo J, Canada T, Johnson D, et al. Safe practices for parenteral nutrition. Journal of
Parenteral and Enteral Nutrition 2004;28:S39–S70. Available at:
https://onlinelibrary.wiley.com/doi/epdf/10.1177/0148607104028006S39. Accessed July 21,
2020.
Beckwith MC, Feddema SS, Barton RG, et al. A guide to drug therapy in patients with enteral
feeding tubes: dosage form selection and administration methods. Hospital Pharmacy
2004;39:225–237.
Davis A. Indications and techniques for enteral feeds. In: Baker SB, Baker RD Jr, Davis A,
eds. Pediatric Enteral Nutrition. New York, NY: Chapman Hall; 1994:67–94.
Wolf TD. Enteral nutrition. In: Boh LE, ed. Pharmacy Practice Manual: A Guide to the
Clinical Experience. Baltimore, MD: Lippincott Williams & Wilkins; 2001:431–459.
Whitney J. Parenteral nutrition. In: Boh LE, ed. Pharmacy Practice Manual: A Guide to the
Clinical Experience. Baltimore, MD: Lippincott Williams & Wilkins; 2001:460–506.
Wallace JI. Malnutrition and enteral/parenteral alimentation. In: Hazzard WR, Blass JP, Halter
JB, et al., eds. Principles of Geriatric Medicine and Gerontology. New York, NY: McGraw-
Hill; 2003:1179–1192.
Mattox TW, Crill CM. Parenteral nutrition. In: DiPiro JT, Yee GC, Posey LM, et al., eds.
Pharmacotherapy: A Pathophysiologic Approach. 11th Ed. [book online]. New York, NY:
McGraw-Hill; 2020.
Kumpf VJ, Mulherin DW. Enteral nutrition. In: DiPiro JT, Yee GC, Posey LM, et al., eds.
Pharmacotherapy: A Pathophysiologic Approach. 11th Ed. [book online]. New York, NY:
McGraw-Hill; 2020.
Craig SB, Dietz WH. Nutritional requirements. In: Baker SB, Baker RD Jr, Davis A, eds.
Pediatric Enteral Nutrition. New York, NY: Chapman Hall; 1994:67–94.
O’Sullivan TA. Parenteral nutrition calculations. In: Understanding Pharmacy Calculations.
Washington, DC: American Pharmacists’ Association; 2002:143–237.
Данная книга находится в списке для перевода на русский язык сайта https://meduniver.com/
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25.
Lewis JL. Water and sodium balance. In: Porter RS, ed. The Merck Manual Professional
Edition [book online]. Kenilworth, NJ: Merck & Co.; 2020. Available at:
https://www.merckmanuals.com/professional/endocrine-and-metabolic-disorders/fluid-
metabolism/water-and-sodium-balance?query=water%20balance#. Accessed July 22, 2020.
Basal Energy Expenditure: Harris-Benedict Equation. Available at: http://www-
users.med.cornell.edu/~spon/picu/calc/beecalc.htm. Accessed July 22, 2020.
Dlugosz C. Pharmacist’s guide to fiber and digestive health. Pharmacy Today 2008;14.
United States Department of Health and Human Services and United States Department of
Agriculture. Dietary Guidelines for Americans 2015–2020. 8th Ed. Available at:
https://www.dietaryguidelines.gov/sites/default/files/2019-05/2015-
2020_Dietary_Guidelines.pdf. Accessed July 22, 2020.
United States Food and Drug Administration. FDA nutrition innovation strategy. Available at:
https://www.fda.gov/food/food-labeling-nutrition/fda-nutrition-innovation-strategy. Accessed
July 24, 2020.
United States Food and Drug Administration. How to understand and use the nutrition facts
label. Available at: https://www.fda.gov/food/new-nutrition-facts-label/how-understand-and-
use-nutrition-facts-label. Accessed July 24, 2020.
United States Food and Drug Administration. Guidance for industry: food labeling guide.
Available at: https://www.fda.gov/regulatory-information/search-fda-guidance-
documents/guidance-industry-food-labeling-guide. Accessed July 24, 2020.
United States Food and Drug Administration. Daily value on the new nutrition and
supplement facts labels. Available at: https://www.fda.gov/food/new-nutrition-facts-
label/daily-value-new-nutrition-and-supplement-facts-labels. Accessed July 24, 2020.
United States Food and Drug Administration. Added sugars on the new nutrition facts label.
Available at: https://www.fda.gov/food/new-nutrition-facts-label/added-sugars-new-nutrition-
facts-label. Accessed July 24, 2020.
United States Food and Drug Administration. Guidance for industry: a food labeling guide (9.
Appendix A: Definitions of nutrient content claims). Available at:
https://www.fda.gov/regulatory-information/search- fda-guidance-documents/guidance-
industry-food-labeling-guide. Accessed July 24, 2020.
15
Altering Product Strength, Use of
Stock Solutions, and Problem
Solving by Alligation
OBJECTIVES
Upon successful completion of this chapter, the student will be able to:
Perform calculations for altering product strength through dilution or
fortification.
Perform calculations for the preparation and use of stock solutions.
Apply alligation medial and alligation alternate in problem solving.
Introduction
The strength of a pharmaceutical preparation may be increased or decreased
by changing the proportion of active ingredient to the whole. A preparation
may be strengthened, fortified, or made more concentrated by the addition of
active ingredient, by admixture with a like preparation of greater strength, or
through the evaporation of its vehicle, if liquid. The strength of a preparation
may be decreased or diluted by the addition of diluent or by admixture with
a like preparation of lesser strength.
In the course of pharmacy practice, the reduction in the strength of a
commercially available pharmaceutical product may be desired to treat a
particular patient, based on the patient’s age (e.g., pediatric or elderly) or
medical status, or to assess a patient’s initial response to a new medication.
The strengthening of a product may be desired to meet the specific
medication needs of an individual patient.
Various methods of calculation for the alteration of the strength of
pharmaceutical preparations are presented in this chapter.
Relationship between Strength and Total Quantity
The strength of a pharmaceutical preparation is based on its content of active
ingredient relative to the whole.
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Guidance: If the amount of active ingredient remains constant, a change
in the total quantity (volume or weight) of a preparation will alter the
strength inversely; that is, the strength decreases as the total quantity
increases, and vice versa.
For instance, 1 g in 10 mL = 10% w/v, whereas 1 g in 20 mL = 5% w/v.
Thus, by doubling the volume, the strength is halved.
Problems in this section generally may be solved by any of the following
methods:
1. Inverse proportion
2. The equation: (1st quantity) × (1st concentration) = (2nd quantity) × (2nd
concentration), or Q1 × C1 = Q2 × C2
NOTE: Many students prefer this method.
3. Traditional calculations, by determining the quantity of active ingredient
present and relating that amount to the quantity of the total preparation
Dilution and Fortification of Liquids
When altering the strength of a liquid preparation, the final volume of the
liquid preparation must be known. Because volumes may not be additive, the
final volume of the liquid preparation can be determined by diluting to a
final volume rather than adding a liquid diluent. In general, volumes are
additive when water is added to an aqueous solution or when two or more
aqueous solutions are mixed. However, due to volume contraction by
hydrogen bonding, volumes of solutions containing alcohol are usually not
additive.
Example calculations of dilution of liquids
1. If 500 mL of a 15% v/v solution are diluted to 1500 mL, what is the
percent strength (v/v) of the dilution?
Solving by inverse proportion:
Or solving by equation:
Or solving by traditional calculations:
2. How many milliliters of a 1:5000 w/v solution of the preservative
lauralkonium chloride can be made from 125 mL of a 0.2% w/v solution
of the preservative?
NOTE: It is often simpler to convert a given ratio strength to the
corresponding percent strength in solving certain problems.
Solving by inverse proportion:
Or solving by equation:
Or solving by traditional calculations:
3. How many milliliters of water should be added to 80 mL of a 20% w/v
aqueous solution to prepare a 3% w/v solution?
Solving by traditional calculations:
533.3 mL − 80 mL = 453.3 mL of water to add
Or solving by equation:
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4. If 10 mL of an injection containing 50 mg of a medication is diluted to 1
L, calculate the percent strength of the resulting solution.
Solving by traditional calculations:
5. Dopamine HCl injection is available in 5-mL vials each containing 40
mg of dopamine HCl per milliliter. The injection must be diluted before
administration by intravenous infusion. If a pharmacist dilutes the
injection by adding the contents of one vial to 250 mL of 5% dextrose
injection, calculate the percent concentration of dopamine HCl in the
infusion.
Solving by traditional calculations:
Dopamine HCl per vial:
Total infusion volume:
Percent concentration calculation:
Or solving by equation:
6. If a pharmacist reconstitutes a vial to contain 1 g of cefazolin in 3 mL of
injection (see Fig. 15.1), and then dilutes 1.6 mL of the injection with
sodium chloride injection to prepare 200 mL of intravenous infusion,
calculate the concentration of cefazolin in the infusion in percent and in
mg/mL.
Solving by traditional calculations:
Quantity of cefazolin in the infusion:
Percent calculation:
mg/mL calculation:
Or solving by equation:
FIGURE 15.1 Product label for cefazolin for injection. (Source:
https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?
setid=e8f40f72-3cf0-43dc-a797-fb98dd8af228. Courtesy of Sagent
Pharmaceuticals.)
Strengthening of a Liquid Formulation
Strengthening an existing pharmaceutical product may be accomplished by
the addition of active ingredient or by the admixture with a calculated
quantity of a like product of greater concentration. The latter type of
calculation is presented later in this chapter under the discussion of
alligation alternate.
If a cough syrup contains in each teaspoonful 1 mg of chlorpheniramine
maleate and if a pharmacist desired to double the strength, how many
milligrams of that ingredient would need to be added to a 60-mL container
of the syrup? Assume no increase in volume.
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