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c. 10-mg tablets
d. 5-mg tablets
IH is a 42-year-old male patient suffering from chronic back pain due
to a workplace injury. He is currently taking one-half of a 2-mg
levorphanol tartrate tablet every 6 hours to manage his pain but
consults his doctor about switching to BUTRANS weekly
buprenorphine transdermal patches for convenience. BUTRANS
transdermal delivery systems are available in strengths of 5, 7.5, 10,
15, and 20 mcg/h. What strength of patch should be used for this
patient?
NT is taking two PERCOCET tablets each containing 7.5 mg of
oxycodone and 325 mg of acetaminophen every 4 hours to manage his
pain. His physician wants to switch him to oxymorphone extendedrelease tablets for improved pain control. Oxymorphone extendedrelease tablets are available in strengths of 5, 7.5, 10, 15, 20, 30, and
40 mg to be given every 12 hours. What should be the dose and
dosage regimen for this patient?
A patient is receiving morphine sulfate intravenously via a patient
controlled analgesia (PCA) pump. The concentration of the solution is
15 mg/mL and is being infused at a rate of 0.1 mL/h. The patient may
access a 2-mg bolus dose every hour for breakthrough pain and is
currently using an average of 8 doses per day. The patient’s caregiver
requests that the patient be converted to a fentanyl transdermal patch
(DURAGESIC) for a “more safe dosage form.” What strength of
fentanyl patch would be most effective for this patient?
Creatinine Clearance Calculations
Use both the Jelliffe equation and the Cockcroft-Gault equation to
calculate the creatinine clearance rate for a 24-year-old male patient
weighing 70 kg with a serum creatinine of 1 mg/dL.
Use both the Jelliffe equation and the Cockcroft-Gault equation to
calculate the creatinine clearance rate for an 82-year-old female
patient weighing 131 lbs. with a serum creatinine of 3.3 mg/dL.
The usual adult dose of levofloxacin in treating community-acquired
pneumonia is 750 mg every 24 hours for a minimum of 5 days. For
patients with a CrCl of 20 to less than 50 mL/min, the dosing schedule
should be lengthened to every 48 hours, and for patients with a CrCl
of less than 20 mL/min, the 750-mg initial dose should be followed by
500-mg doses every 48 hours. What would be the dosage regimen for
a 75-year-old, 160-lb female patient with a serum creatinine of 1.32
mg/dL? (Use the Cockcroft-Gault equation to determine creatinine
clearance.)
Using Table 10.5, what would be the dose and dosage schedule of
ceftazidime for an 84-year-old male patient weighing 60 kg,
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measuring 66 inches in height, and having a serum creatinine level of
4.22 mg/dL? (Use the Cockcroft-Gault equation to determine
creatinine clearance.)
Ideal Body Weight and Adjusted Body Weight Calculations
Calculate the ideal body weight in pounds and kilograms for an 87year-old female patient who is 5 feet 1 inch tall and weighs 111 lb.
Calculate the 40% adjusted body weight in kilograms for a 50-yearold male patient who is 5 feet 11 inches tall and weighs 288 lb.
The initial dose for atracurium besylate is 0.4 mg/kg and should be
dosed based on IBW for obese patients.12 How much of a 10-mg/mL
injection should be administered to a 42-year-old male patient who is
6 feet 2 inches tall and weighs 262 lb?
DT is a 61-year-old female patient with primary humoral
immunodeficiency. She is 5 feet 6 inches tall and weighs 303 lb. The
dosing range for human immune globulin (BIVIGAM) is 300 to 800
mg/kg given intravenously every 3 to 4 weeks, and the patient’s 25%
adjusted body weight should be used for dosing this drug since she is
obese.12 What would be the dose range for this patient?
Clinical Laboratory Test Calculations
If a serum sample is determined to contain 270 mg/dL of cholesterol,
what is the concentration of cholesterol (m.w. 386) in terms of
millimoles per liter?
The normal blood level of theophylline is 0.055 to 0.11 mmol/L.
Determine the amount range, in micrograms, of theophylline that
would be contained in a 5-mL blood sample to fall within this range.
(m.w. theophylline = 180.17)
Among clinical recommendations to prevent cardiovascular disease in
women is the maintenance of lipid levels as follows: low-density
lipoproteins (LDL) <100 mg/dL; high-density lipoproteins (HDL) >50
mg/dL; and triglycerides (TG) <150 mg/dL.19 Which of the following
meet these criteria?
a. LDL <2.6 mmol/L
b. HDL >1.3 mmol/L
c. TG <1.65 mmol/L
d. All of the above
If a patient is instructed by her physician to reduce her LDL
cholesterol level from 130 mg/dL to 100 mg/dL, calculate the percent
reduction required.
A patient has an HDL of 50 mg/dL, an LDL of 150 mg/dL, and a TG
of 85 mg/dL. Calculate the (a) TC:HDL ratio and (b) LDL percent
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reduction required for a goal of 100 mg/dL.
On the basis of the information in Table 10.6, calculate the mmol/L of
glucose equivalent to a value of 140 mg/dL.
a. 7.7 mmol/L
b. 2.5 mmol/L
c. 5.4 mmol/L
d. 6.2 mmol/L
CALCQUIZ
10.A. When a PTT was performed on the patient described in Case in
Point 10.1, the patient’s value was 40 seconds. Based on the protocol in
Figure 10.1, calculate (a) the needed bolus dose, in units, and (b) the new
infusion rate, in mL/h, using heparin injection, 25,000 units/250 mL.
10.B. A patient has been receiving an intravenous infusion of fentanyl
citrate (SUBLIMAZE) at a rate of 15 mcg/h for pain management during
an extended 4-day hospital stay. His physician wishes to prescribe
oxymorphone ER tablets to be administered every 12 hours to allow the
patient to return home. Should 15-, 20-, 30-, or 40-mg oxymorphone ER
tablets be prescribed for this patient to receive an equivalent dose for his
pain?
10.C. Based on creatinine clearance, the dose of a drug is: CrCl = 8–10
mL/min; dose = 2.43 mg/kg every 24 hours, divided into two doses CrCl
= 11–20 mL/min; dose = 3.58 mg/kg every 24 hours, divided into two
doses CrCl = 21–40 mL/min; dose = 5.87 mg/kg every 24 hours as a
single dose.
For a 52-year-old male patient weighing 155 lb and measuring 69 inches
with a serum creatinine of 2.6 mg/dL, calculate the per-dose volume to
administer of an injection containing drug, 80 mg/mL.
10.D. A hospital order for midazolam for maintenance of sedation at a
rate of 0.05 mg/kg/h is received for a patient. The patient is a 33-year-old
female patient who is 5 feet 4 inches tall and weighs 164 lb. Because she
is obese, the patient should receive a dose based on her ideal body
weight.12 Calculate the infusion rate for an IV solution with a midazolam
concentration of 0.5 mg/mL.
10.E. Calculate the total cholesterol in a patient with a HDL of 87 mg/dL,
LDL of 152 mg/dL, and a TRG of 50 mg/dL. Also, which of the
following are correct?
a. HDL:LDL ratio ≈ 1:1.7
b. TC:HDL ratio ≈ 2.9:1
c. HDL = high risk
d. LDL = low risk
e. TRG = low risk
f. After being placed on a statin drug, the patient’s LDL dropped to
106 mg/dL, equivalent to a 30% reduction.
ANSWERS TO “CASE IN POINT” AND
PRACTICE PROBLEMS
Case in Point 10.1
a. Patient’s weight in kg:
Bolus dose: 80 units heparin/kg
b. Infusion rate: 18 units/kg/h
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d.
Case in Point 10.2
a.
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c. According to Table 10.2, a 2-mg intranasal dose of butorphanol
tartrate is equivalent to 10 mg of parenteral morphine.
According to Table 10.1, a 10-mg parenteral dose of morphine is
equivalent to 30 mg of hydrocodone given orally.
Case in Point 10.3
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b.
c. Dose = 150 mg initially and 150 mg maintenance dose once daily
Practice Problems
0.5 mL heparin injection
0.25 mL/min
a. 1.22 mL heparin injection
b. 27.36 mL/h
c. 24.32 mL/h
a. 4109.12 units
b. 11.3 mL/h
0.2 mL enoxaparin sodium injection
b.One 5-mg hydrocodone/300-mg acetaminophen tablet every 4 to 6
hours
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c.10-mg tablets
10-mcg/h transdermal patch
20-mg tablet every 12 hours
75-mcg/h transdermal patch
94.8 mL/min (Jelliffe)
112.78 mL/min (Cockcroft-Gault)
13.2 mL/min (Jelliffe)
12.36 mL/min (Cockcroft-Gault)
750 mg levofloxacin every 48 hours
500 mg ceftazidime every 24 hours
105 lb
47.8 kg
16. 97.54 kg
3.29 mL atracurium besylate injection
23.67 to 63.13 g human immune globulin
6.99 mmol/L
49.55 to 99.09 mcg
d.All of the above
23.08%
a. 4.34:1 = TC:HDL ratio
b. 33.33%
a.7.7 mmol/L
References
Rx Kinetics. Heparin dosing. Available at: http://www.rxkinetics.com/heparin.html. Accessed
June 22, 2020.
Pfizer. Heparin Sodium Injection, USP. Available at:
http://labeling.pfizer.com/ShowLabeling.aspx?id=665. Accessed June 22, 2020.
Heparin Sodium. Facts & Comparisons eAnswers [book online]. Baltimore, MD: Wolters
Kluwer Clinical Drug Information Inc.; 2020.
Merli GJ, Groce JB. Pharmacological and clinical differences between low-molecular-weight
heparins: implications for prescribing practice and therapeutic interchange. Pharmacy &
Technology 2010;35(2):95–105. Available at:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2827912/. Accessed June 22, 2020.
Stockton SJ. Calculations. International Journal of Pharmaceutical Compounding
2014;18:320.
Stockton SJ. Calculations. International Journal of Pharmaceutical Compounding
2009;13:239.
Jelliffe RW. Estimations of creatinine clearance when urine cannot be collected. Lancet
1971;1:975.
Jelliffe RW. Creatinine clearance bedside estimate. Annals of Internal Medicine 1973;79:604.
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Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron
1976;16:31.
Dowling TC. Evaluation of kidney function. In: DiPiro JT, Yee GC, Posey LM, et al., eds.
Pharmacotherapy: A Pathophysiologic Approach. 11th Ed. [book online]. New York, NY:
McGraw-Hill; 2020.
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.
Drug dosing in obesity reference table. Available at:
https://clincalc.com/kinetics/obesitydosing.aspx. Accessed June 23, 2020.
Ng JK, Schulz LT, Rose WE, et al. Daptomycin dosing based on ideal body weight versus
actual body weight: comparison of clinical outcomes. Antimicrobial Agents in Chemotherapy
2014;58(1):88–93. Available at: https://pubmed.ncbi.nlm.nih.gov/24145531/. Accessed June
23, 2020.
ASCO recommends appropriate weight-based dosing of cytotoxic chemotherapy for obese
patients. Available at: https://connection.asco.org/magazine/society/asco-recommendsappropriate-weight-based-dosing-cytotoxic-chemotherapy-obese. Accessed June 23, 2020.
Drug levels. Facts & Comparisons eAnswers [book online]. Baltimore, MD: Wolters Kluwer
Clinical Drug Information Inc.; 2020.
Grundy SM, Cleeman JI, Merz CNB, et al. Implications of recent clinical trials for the National
Cholesterol Education Program Adult Treatment Panel III guidelines. Circulation
2004;110(2):227–239. Available at:
https://www.ahajournals.org/doi/10.1161/01.CIR.0000133317.49796.0E. Accessed June 26,
2020.
Herrier RN, Apgar DA, Boyce RW, et al. Dyslipidemia. In: Herrier RN, Apgar DA, Boyce
RW, et al., eds. Patient Assessment in Pharmacy [book online]. New York, NY: McGraw-Hill;
2015.
Ansel HC, Prince SJ. The Pharmacist’s Handbook. Baltimore, MD: Lippincott Williams &
Wilkins; 2004: 236–240.
Women’s health: What’s hot. Pharmacy Today 2007;13(9):28.
11
Isotonic and Buffer Solutions
OBJECTIVES
Upon successful completion of this chapter, the student will be able to:
Calculate the dissociation factor (i) of a chemical agent.
Calculate the sodium chloride equivalent (E-value) of a chemical
agent.
Demonstrate by calculation whether a solution is hypotonic, isotonic,
or hypertonic.
Perform calculations required in the preparation of isotonic solutions.
Calculate the pH of a buffer solution.
Determine the amounts of components needed to prepare a buffer at a
specific pH.
Introduction
When a solvent passes through a semipermeable membrane from a dilute
solution into a more concentrated one, the concentrations become equalized
and the phenomenon is known as osmosis. The pressure responsible for this
phenomenon is termed osmotic pressure and varies with the nature of the
solute.
If the solute is a nonelectrolyte, its solution contains only molecules and
the osmotic pressure varies with the concentration of the solute. If the solute
is an electrolyte, its solution contains ions and the osmotic pressure varies
with both the concentration of the solute and its degree of dissociation.
Thus, solutes that dissociate present a greater number of particles in solution
and exert a greater osmotic pressure than do undissociated molecules.
Two solutions that have the same osmotic pressure are termed
isosmotic. Many solutions intended to be mixed with body fluids are
designed to have the same osmotic pressure for greater patient comfort,
efficacy, and safety. A solution having the same osmotic pressure as a
specific body fluid is termed isotonic (meaning of equal tone) with that
specific body fluid.
Solutions of lower osmotic pressure than that of a body fluid are termed
hypotonic, whereas those having a higher osmotic pressure are termed
hypertonic. Pharmaceutical dosage forms intended to be added directly to
the blood or mixed with biological fluids of the eye, nose, and bowel are of
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principal concern to the pharmacist in their preparation and clinical
application.
Special Clinical Considerations of Tonicity
It is generally accepted that for ophthalmic and parenteral administration,
isotonic solutions are better tolerated by the patient than those at the
extremes of hypo- and hypertonicity. With the administration of an isotonic
solution, there is a homeostasis with the body’s intracellular fluids. Thus, in
most instances, preparations that are isotonic, or nearly so, are preferred.
However, there are exceptions, as in instances in which hypertonic solutions
are used to “draw” fluids out of edematous tissues and into the administered
solution.
Most ophthalmic preparations are formulated to be isotonic, or
approximately isotonic, to duplicate ophthalmic tears for the comfort of the
patient. These solutions are also prepared and buffered at an appropriate pH,
both to reduce the likelihood of irritation to the eye’s tissues and to maintain
the stability of the preparations.
Injections that are not isotonic should be administered slowly and in
small quantities to minimize tissue irritation, pain, and cell fluid imbalance.
The tonicity of small-volume injections is generally inconsequential when
added to large-volume parenteral infusions because of the presence of tonic
substances, such as sodium chloride or dextrose in the large-volume
infusion, which serve to adjust the tonicity of the smaller added volume.
1
Intravenous infusions that are hypotonic or hypertonic can have
profound adverse effects because they generally are administered in large
volumes.1 Large volumes of hypertonic infusions containing dextrose, for
example, can result in hyperglycemia, osmotic diuresis, and excessive loss
of electrolytes. Excess infusions of hypotonic fluids can result in the
osmotic hemolysis of red blood cells and surpass the upper limits of the
body’s capacity to safely absorb excessive fluids. Even isotonic fluids, when
infused intravenously in excessive volumes or at excessive rates, can be
deleterious due to an overload of fluids placed into the body’s circulatory
system.
Physical/Chemical Considerations in the
Preparation of Isotonic Solutions
The calculations involved in preparing isotonic solutions may be made in
terms of data relating to the colligative properties of solutions.
Theoretically, any one of these properties may be used as a basis for
determining tonicity. Practically and most conveniently, a comparison of
freezing points is used for this purpose. It is generally accepted that −0.52°C
is the freezing point of both blood serum and lacrimal fluid.
When 1 g molecular weight of any nonelectrolyte—that is, a substance
with negligible dissociation, such as boric acid—is dissolved in 1000 g of
water, the freezing point of the solution is about 1.86°C below the freezing
point of pure water. By simple proportion, therefore, we can calculate the
weight of any nonelectrolyte that should be dissolved in each 1000 g of
water if the solution is to be isotonic with body fluids.
Boric acid, for example, has a molecular weight of 61.8; thus (in
theory), 61.8 g in 1000 g of water should produce a freezing point of
−1.86°C. Therefore:
In short, 17.3 g of boric acid in 1000 g of water, having a weight-in-volume
strength of approximately 1.73%, should make a solution isotonic with
lacrimal fluid.
With electrolytes, the problem is not so simple. Because osmotic
pressure depends more on the number of particles, substances that dissociate
have a tonic effect that increases with the degree of dissociation; the greater
the dissociation, the smaller the quantity required to produce any given
osmotic pressure. If we assume that sodium chloride in weak solutions is
about 80% dissociated, then each 100 molecules yields 180 particles, or 1.8
times as many particles as are yielded by 100 molecules of a nonelectrolyte.
This dissociation factor, commonly symbolized by the letter i, must be
included in the proportion when we seek to determine the strength of an
isotonic solution of sodium chloride (m.w. 58.5):
Hence, 9.09 g of sodium chloride in 1000 g of water should make a solution
isotonic with blood or lacrimal fluid. In practice, a 0.9% w/v sodium
chloride solution is considered isotonic with body fluids.
Simple isotonic solutions may then be calculated by using this formula:
The value of i for many medicinal salts has not been experimentally
determined. Some salts are exceptional (such as zinc sulfate, with only 40%
dissociation and an i value therefore of 1.4), but most medicinal salts
approximate the dissociation of sodium chloride in weak solutions. If the
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