Question

A patient receives all her nutrition from fluids given through the vena cava. Every 12 hours, \(500 \mathrm{~mL}\) of a solution that is \(5.0 \%(\mathrm{~m} / \mathrm{v})\) amino acids (protein) and \(20 \%(\mathrm{~m} / \mathrm{v})\) glucose (carbohydrate) is given along with \(500 \mathrm{~mL}\) of a \(10 \%(\mathrm{~m} / \mathrm{v})\) lipid (fat). a. In 1 day, how many grams each of amino acids, glucose, and lipid are given to the patient? b. How many kilocalories does she obtain in 1 day?

Short answer

In 1 day, the patient receives 50 g amino acids, 200 g glucose, and 100 g lipid, totaling 1900 kilocalories.

Step-by-step solution

Calculate the total volume of each component in 12 hours

The patient receives 500 mL of a solution and another 500 mL of a lipid solution every 12 hours. Together, this adds up to 1000 mL every 12 hours.

Determine the mass of amino acids received in 12 hours

The concentration of amino acids in the solution is 5% (m/v). This means there are 5 grams of amino acids per 100 mL. Therefore, in 500 mL, the patient will receive:\[ \frac{5 \text{ g}}{100 \text{ mL}} \times 500 \text{ mL} = 25 \text{ g of amino acids} \].

Determine the mass of glucose received in 12 hours

The concentration of glucose in the solution is 20% (m/v). This means there are 20 grams of glucose per 100 mL. Therefore, in 500 mL, the patient will receive:\[ \frac{20 \text{ g}}{100 \text{ mL}} \times 500 \text{ mL} = 100 \text{ g of glucose} \].

Determine the mass of lipid received in 12 hours

The concentration of lipid in the solution is 10% (m/v). This means there are 10 grams of lipid per 100 mL. Therefore, in 500 mL, the patient will receive:\[ \frac{10 \text{ g}}{100 \text{ mL}} \times 500 \text{ mL} = 50 \text{ g of lipid} \].

Calculate the total mass received in 1 day

Since the patient gets the solutions every 12 hours, we need to double the values calculated in Steps 2, 3, and 4 to find the daily intake.\[ \text{In 1 day:} \]\[ \text{Amino acids} = 25 \text{ g} \times 2 = 50 \text{ g} \]\[ \text{Glucose} = 100 \text{ g} \times 2 = 200 \text{ g} \]\[ \text{Lipid} = 50 \text{ g} \times 2 = 100 \text{ g} \].

Determine the kilocalories from amino acids

Each gram of amino acids provides 4 kcal. Therefore, the kilocalories from amino acids are:\[ 50 \text{ g} \times 4 \text{ kcal/g} = 200 \text{ kcal} \].

Determine the kilocalories from glucose

Each gram of glucose provides 4 kcal. Therefore, the kilocalories from glucose are:\[ 200 \text{ g} \times 4 \text{ kcal/g} = 800 \text{ kcal} \].

Determine the kilocalories from lipid

Each gram of lipid provides 9 kcal. Therefore, the kilocalories from lipid are:\[ 100 \text{ g} \times 9 \text{ kcal/g} = 900 \text{ kcal} \].

Calculate the total kilocalories

Add the kilocalories from amino acids, glucose, and lipid to get the total kilocalories:\[200 \text{ kcal} + 800 \text{ kcal} + 900 \text{ kcal} = 1900 \text{ kcal}\].

Key concepts

Amino Acids

Amino acids are the building blocks of proteins. Proteins are essential nutrients for the body’s growth and repair.
Amino acids come in two types: essential and non-essential. Essential amino acids cannot be synthesized by the body and must be obtained through diet.
In the given problem, the patient receives a solution with a concentration of 5% (mass/volume), meaning there are 5 grams of amino acids per 100 mL of solution. Understanding this concentration helps in calculating the exact amount of amino acids delivered to the patient throughout the day.

Glucose

Glucose is a simple sugar and serves as a primary energy source for the body's cells. It’s vital for brain function and physical activity.
In medical nutrition, ensuring the patient receives adequate glucose is crucial for maintaining energy levels.
In the problem exercise, the solution contains 20% (m/v) glucose, meaning 20 grams of glucose per 100 mL of fluid. This concentration information is used to compute the total glucose intake daily for the patient.

Lipid

Lipids, commonly known as fats, are an essential part of a balanced diet. They play roles in storing energy, supporting cell membrane structure, and aiding in the absorption of fat-soluble vitamins.
The solution in the exercise includes a 10% (m/v) lipid concentration, which translates to 10 grams of lipid per 100 mL. Calculating the total lipid intake helps ensure that the patient gets enough fat for energy and cellular functions.
Lipids have a higher energy content compared to proteins and carbohydrates, providing 9 kcal per gram.

Kilocalories

Kilocalories (kcal) measure the energy provided by food nutrients. It's essential to calculate the caloric content of a patient's nutrition to meet their energy needs.
In the exercise, each nutrient's caloric contribution is calculated as follows: each gram of amino acids and glucose gives 4 kcal, while each gram of lipid provides 9 kcal.
Summing the caloric contributions from amino acids, glucose, and lipids gives the total daily energy intake for the patient, ensuring they get an adequate amount to support their metabolic demands.

Mass-Volume Percentage

Mass-volume percentage (m/v) expresses the concentration of a substance in a solution. It indicates the mass of the solute per 100 mL of solution.
For instance, a 5% (m/v) amino acid solution means there are 5 grams of amino acids in 100 mL of the solution.
This concept is crucial in the exercise to calculate the precise amounts of amino acids, glucose, and lipids being administered to the patient over a given period. Correctly understanding and applying these concentrations ensures accurate and effective nutritional support.