Chapter 29: Parenteral Calculations

Parenteral Calculations

Basic Dimensional Analysis (1 of 3)

Dimensional analysis is a mathematical tool employed in pharmacy for the computation of sterile product preparation and flow rates. This analytical method integrates different units—such as hours, milligrams, liters, or centimeters—allowing the user to solve specific problems efficiently. Notable examples of simple problems addressed through dimensional analysis include calculating the number of seconds in a year and the number of millimeters in a mile.

Basic Dimensional Analysis (2 of 3)

Sample problems illustrate the utility of dimensional analysis. For example, to determine how many hours there are in 6 days, one can use the fact that there are 24 hours in a day. This can be formalized as follows:

1. 24 hours= 1day

2. The equivalency can also be expressed as
   a. 1 day/24hours
   b. 24 hours/1day

Basic Dimensional Analysis (3 of 3)

Continuing from the previous example of calculating hours in 6 days, once the problem is established, one must cancel out like units and/or numbers.

• Mathematically, this can be depicted as:
  $6 \text{ days} = 6 \times 24 \text{ hours} = 144 \text{ hours}$
  Thus, there are 144 hours in 6 days.

Flow Rates (1 of 9)

Flow rates are crucial in pharmacy calculations pertaining to the preparation of intravenous (IV) infusions, which include compounded solutions that deliver fluids, medications, nutrients, electrolytes, and minerals to patients. Accurate calculations are paramount to ensure the infusion occurs at the right speed, strength, and duration.

Flow Rates (2 of 9)

The duration of a flow rate refers to the total length of time that an IV will be administered. It also indicates how long an IV bag will remain effective before replacement is necessary. For instance, if a 1-L IV bag is administered at a rate of 200 mL per hour, one can calculate the duration:

• Using the given rate, one sets up to calculate:

Example: How long will this IV bag last?

Flow Rates (3 of 9)

Clarification of flow rate duration—a practical application involves setting up the problem to cancel out like units and/or numbers when calculating the duration of the IV bag.

Flow Rates (4 of 9)

Flow rate can also be expressed in terms of volume per hour (mL/hr), representing the quantity of fluid or solution administered to a patient intravenously each hour. While duration problems utilize dimensional analysis, volume-per-hour problems often rely on ratios and proportions to derive results through cross-multiplication.

Flow Rates (5 of 9)

Consider a practical scenario where a patient is to receive 750 mL infused over 3 hours. The goal is to find the rate of infusion in mL per hour.

• Setup for ratio and proportion, leading to a solution for the unknown.

Flow Rates (6 of 9)

To solve the previous example, cross-multiplication gives:
$3 \times X = 750 \times 1 \Rightarrow 3X = 750 \Rightarrow X = 250$
Therefore, the infusion rate is 250 mL/hr.

Flow Rates (7 of 9)

Drug per hour (mg/hr) refers to the dosage in milligrams dispensed per hour during an infusion. This calculation follows similar principles as volume-per-hour problems, solved through ratio and proportion:
$\frac{\text{Total mg}}{\text{Total hrs}} = \frac{X}{1 \text{ hr}}$

Flow Rates (8 of 9)

For further illustration, if 100 mg of medication must be administered in 500 mL over 2 hours, the question arises: How much drug is infused per hour? Setting up the necessary ratios and solving follows the prior stated format.

Flow Rates (9 of 9)

Cross-multiplying in the above drug per hour example leads to the following:
$2 \times X = 100 \times 1 \Rightarrow 2X = 100 \Rightarrow X = 50$
Therefore, 50 mg is the amount of drug administered per hour.

Drop Factors (1 of 6)

In the preparation of sterile products, calculating the rate of IV administration becomes vital, often expressed as drops per minute (gtts/minute). This represents the volume of medication administered each minute. Various IV administration sets have specific drop rates that contribute to medication delivery precision.

Drop Factors: Expressed by Drop Factor

A table of typical drop factors identifies the drip rate (gtts/mL) per administration set.

• Drop factor table:

  • 60 gtts/mL

  • 20 gtts/mL

  • 15 gtts/mL

  • 10 gtts/mL

Drop Factors (2 of 6)

The rate of IV administration is typically presented in drops per minute (gtts/min), which holds significance for calibrating IV pumps and determining the volume of medication delivered each minute.

Drop Factors (3 of 6)

Commonly utilized in pharmacy, microdrip sets deliver 60 drops per mL, whereas macrodrip sets offer variability with drop rates of 10, 15, or 20 drops per mL, where increased drop counts signify smaller individual drops (1 mL = 1 mL remains mathematically true).

Drop Factors (4 of 6)

In pharmacy practice, four common IV drip rates are:

1. 10 gtts/mL (drop factor 10)

2. 15 gtts/mL (drop factor 15)

3. 20 gtts/mL (drop factor 20)

4. 60 gtts/mL (drop factor 60)

Drop Factors (5 of 6)

An example illustrates: A 1-L bag of D5W is administered at a drop factor of 60 over 6 hours. The flow rate calculation in gtts/min follows problem setup and cancellation of like units:

Drop Factors (6 of 6)

Solution yields an infusion rate of 167 gtts/min after a set calculation.

TPN and Milliequivalents (1 of 6)

Total parenteral nutrition (TPN) refers to a solution that aims to fulfill the body's fundamental nutritional requirements, including fluids, vitamins, and lipids. The delivery of electrolytes, common in TPN solutions, serves vital roles in maintaining the body's acid-base balance, controlling water volume, and regulating metabolism.

TPN and Milliequivalents (2 of 6)

Electrolytes are typically integrated into TPN solutions per physician's directives, delivered via IV infusion. To express electrolytes' concentration in solution, milliequivalents are utilized. Furthermore, solutions can be classified based on their osmotic pressure relative to human red blood cells.

TPN and Milliequivalents (3 of 6)

Electrolyte solutions are categorized based on their osmotic behavior:

1. Isotonic solutions: exhibit equivalent osmotic pressure to cell contents, with normal saline (sodium chloride 0.9% solution) being isotonic.

2. Hypertonic solutions: carry a higher osmotic pressure than cell contents, prompting cell dehydration and shrinkage.

3. Hypotonic solutions: have lower osmotic pressure, causing cells to absorb water and swell.

TPN and Milliequivalents (4 of 6)

To calculate the necessary volume for electrolyte milliequivalents, three methods can be employed:

1. Establishing a proportion to solve for X (the required volume).

2. Utilizing a basic algebraic equation.

3. Dividing the ordered milliequivalents by the concentration stated in stock vial (as X mEq per 1 mL).

TPN and Milliequivalents (5 of 6)

Example:
Electrolyte: NaCl (4 mEq/mL)
Rx Order: 60 mEq
Volume Required: X
To determine:
$X = \frac{60 \text{ mEq}}{4 \text{ mEq/mL}} = 15 mL$
Thus, 15 mL of the stock NaCl is required for the TPN mixture.

TPN and Milliequivalents (6 of 6)

Similarly, for potassium acetate:

• Electrolyte: K acetate (2 mEq/mL)

• Rx Order: 20 mEq

• Volume Required: X
  To solve:
  $X = \frac{20 \text{ mEq}}{2 \text{ mEq/mL}} = 10 mL$
  Thus, 10 mL of K acetate at 2 mEq/mL is to be added to the TPN.

Final Problem Calculation

Assess the total minutes for an IV infusion: converting 4 hours into minutes yields:

• $4 \text{ hours} \times 60 \text{ minutes/hour} = 240 \text{ minutes}$
  Calculate total drops needed using the drop factor:

• Total drops required = Volume (mL) x Drop factor (gtt/mL)

• Using the numbers, we find:
  Total drops required = $750 \text{ mL} \times 15 \text{ gtt/mL} = 11,250 \text{ drops}$
  Determine the flow rate (gtt/min):

• $\text{Flow rate (gtt/min)} = \frac{\text{Total drops required}}{\text{Total time (min)}}$

• This presents as:
  Flow rate (gtt/min) = $\frac{11,250 \text{ drops}}{240 \text{ minutes}} = 46.875 \text{ gtt/min}$

• Hence, rounding presents a flow rate of approximately 47 gtt/min for accurate IV administration.

Additional Example Problem

An IV infusion of 1,000 mL saline is prescribed over 6 hours using a drop factor of 20 drops/mL. The procedure to find the flow rate in drops per minute involves:

• Total minutes for infusion:
  $6 \text{ hours} \times 60 \text{ minutes/hour} = 360 \text{ minutes}$

• Total drops required:
  $1,000 \text{ mL} \times 20 \text{ gtt/mL} = 20,000 \text{ drops}$

• Flow rate calculation:
  $\text{Flow rate (gtt/min)} = \frac{20,000 \text{ drops}}{360 \text{ minutes}} = 56 \text{ gtt/min}$

Additional Practical Applications

Clinical scenarios include dosing medications per patient weight, expressing flows in mL/hour for IV infusions, and adapting infusion rates based on varying patient health conditions.