# Dosage Calculation

Doctors routinely prescribe medications and should, therefore, be comfortable with basic calculations used to determine the optimal dosage. A dosing regimen is the manner in which a drug is administered to an individual, and describes the dose and frequency of the medication to be administered. Accuracy in dosing and the frequency of drug administration is necessary to achieve the desired effect while avoiding side effects and toxicity. In a clinical setting, both the prescribing doctor and pharmacist should review the optimal dose. Several medical conditions, including kidney and liver Liver The liver is the largest gland in the human body. The liver is found in the superior right quadrant of the abdomen and weighs approximately 1.5 kilograms. Its main functions are detoxification, metabolism, nutrient storage (e.g., iron and vitamins), synthesis of coagulation factors, formation of bile, filtration, and storage of blood. Liver diseases and hypersensitivity, require dose adjustments to achieve the desired therapeutic effect.

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Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

## Overview

It is important for healthcare professionals including doctors, nurses, pharmacists, and pharmacy technicians to know which medications to prescribe and at what dose to prescribe them.

• Dose calculations should be performed before a medication is prescribed so that it is not wasted.
• A dosage calculator should be used if there is any concern about the correct dose.
• Common means of administering a medication:
• Volume infusion: medication given over a set period of time
• Bolus: medication administered quickly or in a short burst
• Continuous infusion: medication administered continuously over an extended period of time
• Dosage regimen is a plan for the administration of a drug for a given time period to achieve the desired physiological and pharmacological effects.
• Loading dose is a specific dose of the medication given, usually when initiating therapy, to achieve the desired plasma drug concentration rapidly.
• Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma drug concentration over a given time period.

## Therapeutic Window

### Definition

Therapeutic window is the dosage range within which the drug is effective (i.e., the dose at which the drug produces the desired effect) without causing toxicity.

• Minimum effective concentration is the minimum drug level in the blood required to achieve the desired effect.
• Minimum toxic concentration is the minimum drug level in the blood at which toxic side effects occur.

### Therapeutic index

Therapeutic index is a measure similar to therapeutic window and is used for:

• Measurement of the relative safety of a medication
• Comparison between the dose needed for therapeutic effect and the dose that causes toxicity
• Therapeutic index is calculated by dividing the toxic dose for 50% of the population by the minimum effective dose for 50% of the population.
$$Therapeutic~index=\frac{TD_{50}}{ED_{50}}$$
TD50 = toxic dose for 50% of the population
ED50 = effective dose for 50% of the population

### Example

The therapeutic window for digoxin is 0.8–2.0 ng/mL.

• A level lower than this range may not have the desired therapeutic effect.
• A level > 2.4 ng/mL may cause hypokalemia Hypokalemia Hypokalemia is defined as plasma potassium (K+) concentration < 3.5 mEq/L. Homeostatic mechanisms maintain plasma concentration between 3.5-5.2 mEq/L despite marked variation in dietary intake. Hypokalemia can be due to renal losses, GI losses, transcellular shifts, or poor dietary intake. Hypokalemia, hypomagnesemia, and arrhythmia.
• Digoxin is known to have a narrow therapeutic index. Because of its potentially fatal toxicity, digoxin should be administered with caution.
• Elderly individuals are at increased risk for toxicity:
• Impaired renal function
• Decreased muscle mass
• May have comorbidities

## Maintenance Dose

Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma drug concentration over a given time period of time. Typically, a loading dose is administered before administering the maintenance dose.

• The rate of administration is equal to the rate of elimination at the steady state.
• Maintenance dose is a function of the rate of removal of a drug from circulation (clearance) and its calculation depends on the rate of excretion.
• Administration is repeated at specific intervals to maintain the desired steady-state plasma drug concentration. A maintenance dose administered at least 4 times and 1 half-life (time required for the plasma drug concentration to decrease by 50%) apart will result in steady-state levels.
• The formula typically used to calculate the maintenance dose is:
$$Maintenance~dose =\frac{Clearance \times Desired~peak~concentration}{Bioavailability}$$

• A single or few quick doses administered usually at the onset of therapy
• Often used in an emergency:
• An understanding of the pharmacokinetics Pharmacokinetics Pharmacokinetics is the science that analyzes how the human body interacts with a drug. Pharmacokinetics examines how the drug is absorbed, distributed, metabolized, and excreted by the body. Pharmacokinetics and Pharmacodynamics of the drug is important when prescribing a loading dose.
• Some individuals may need to be monitored on telemetry or may require additional laboratory studies.
$$Loading~dose =\frac{Volume~of~distribution^{^{*}} \times Concentration~at~steady~state}{Bioavailability}$$
*Volume of distribution is the dose of the medication given divided by the concentration in the plasma.

### Example

A 12-year-old boy has pneumonia Pneumonia Pneumonia or pulmonary inflammation is an acute or chronic inflammation of lung tissue. Causes include infection with bacteria, viruses, or fungi. In more rare cases, pneumonia can also be caused through toxic triggers through inhalation of toxic substances, immunological processes, or in the course of radiotherapy. Pneumonia. He receives antibiotic X with a volume of distribution of 31 L and oral bioavailability of 55%. The required plasma concentration is 55 µg/mL. Calculate the loading dose.

$$Loading~dose =\frac{Volume~of~distribution \times Concentration~at~steady~state}{Bioavailability}$$
$$= \frac{31\times 55}{0.55}= 31000\times 100= 3100000~µg= 3.1~g$$

## Correction for Renal Disease

In individuals with renal disease, the drug dosage must be modified to account for reduced clearance.

• The kidney is the primary organ of drug excretion for many medications.
• Kidney function must be accounted for when prescribing a drug.
• Drug clearance is affected by:
• GFR
• Kidney disease
• Renal failure
• Drug dose should be adjusted based on renal function in individuals with renal disease. Given the same dose of medication:
• Increased drug clearance can lead to lower drug concentration.
• Decreased drug clearance can lead to higher drug concentration.
• It is more common for the effect of a drug to be amplified in individuals with renal disease due to drug accumulation. Drug doses should be decreased proportionally with a decrease in kidney function.

### Example

A 68-year-old individual has to be prescribed a drug with a narrow therapeutic index. The drug parameters are as follows:

• Bioavailability = 100%
• Renal excretion = 100%
• Clearance = 1.8 L/hour
• Half-life = 27 hours
• Volume of distribution = 51 L
• Minimum effective concentration = 25 mg/L
• Maximum effective concentration = 63 mg/L
• Creatinine clearance = 66 mL/min

$$Loading~dose =\frac{Volume~of~distribution \times Concentration~at~steady~state}{Bioavailability}$$
$$=\frac{51\times 63}{1}= 3213~mg$$

Dosing interval:

$$Dosing~interval =\frac{Peak~concentration~\text{-}~Trough~concentration}{Clearance}$$
$$= \frac{63~\text{-}~25}{1.8}= 21~hours$$

Maintenance dose:

$$Maintenance~dose = Serum~concentration \times Clearance$$
$$=(\frac{63~\text{-}~25}{2}+25)\times 1.8\times 24 = 44\times 1.8\times 24 =\frac{1900.8~mg}{day}$$

Corrected dose:

$$Corrected~dose = \frac{Original~dose \times Creatinine~clearance~of~the~individual}{100}$$
$$=\frac{1.9\times 66}{100} =\frac{1254~mg}{day} =\frac{1~g}{day}$$

## References

1. Trevor, A.J., et al. (2008). Katzung & Trevor’s Pharmacology: Examination & Board Review. McGraw-Hill.
2. Goodman, L.S., et al., (Eds.) (2011). Goodman & Gilman’s Pharmacological Basis of Therapeutics, 12th ed. McGraw-Hill.
3. Rang, H.P., Dale, M.M. (Eds.) (2016). Rang and Dale’s Pharmacology, 8th Ed. Elsevier, Churchill Livingstone.
4. Miniaci, A., Gupta, V. (2021). Loading Dose. StatPearls. Treasure Island (FL): StatPearls Publishing. Retrieved November 25, 2021, from https://www.ncbi.nlm.nih.gov/books/NBK557418/
5. Kyriakopoulos, C., Gupta, V. (2021). Renal Failure Drug Dose Adjustments. StatPearls. Treasure Island (FL): StatPearls Publishing. Retrieved November 25, 2021, from https://www.ncbi.nlm.nih.gov/books/NBK560512/

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