# 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: Anatomy diseases and hypersensitivity, require dose adjustments to achieve the desired therapeutic effect.

Last updated: 14 Mar, 2022

Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

Contents

## 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 Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products drug concentration rapidly.
• Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products 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 Digoxin A cardiotonic glycoside obtained mainly from digitalis lanata; it consists of three sugars and the aglycone digoxigenin. Digoxin has positive inotropic and negative chronotropic activity. It is used to control ventricular rate in atrial fibrillation and in the management of congestive heart failure with atrial fibrillation. Its use in congestive heart failure and sinus rhythm is less certain. The margin between toxic and therapeutic doses is small. Cardiac Glycosides 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 Hypomagnesemia A nutritional condition produced by a deficiency of magnesium in the diet, characterized by anorexia, nausea, vomiting, lethargy, and weakness. Symptoms are paresthesias, muscle cramps, irritability, decreased attention span, and mental confusion, possibly requiring months to appear. Deficiency of body magnesium can exist even when serum values are normal. In addition, magnesium deficiency may be organ-selective, since certain tissues become deficient before others. Electrolytes, and arrhythmia.
• Digoxin Digoxin A cardiotonic glycoside obtained mainly from digitalis lanata; it consists of three sugars and the aglycone digoxigenin. Digoxin has positive inotropic and negative chronotropic activity. It is used to control ventricular rate in atrial fibrillation and in the management of congestive heart failure with atrial fibrillation. Its use in congestive heart failure and sinus rhythm is less certain. The margin between toxic and therapeutic doses is small. Cardiac Glycosides is known to have a narrow therapeutic index. Because of its potentially fatal toxicity, digoxin Digoxin A cardiotonic glycoside obtained mainly from digitalis lanata; it consists of three sugars and the aglycone digoxigenin. Digoxin has positive inotropic and negative chronotropic activity. It is used to control ventricular rate in atrial fibrillation and in the management of congestive heart failure with atrial fibrillation. Its use in congestive heart failure and sinus rhythm is less certain. The margin between toxic and therapeutic doses is small. Cardiac Glycosides should be administered with caution.
• Elderly individuals are at increased risk for toxicity:
• Impaired renal function
• Decreased muscle mass Mass Three-dimensional lesion that occupies a space within the breast Imaging of the Breast
• May have comorbidities Comorbidities The presence of co-existing or additional diseases with reference to an initial diagnosis or with reference to the index condition that is the subject of study. Comorbidity may affect the ability of affected individuals to function and also their survival; it may be used as a prognostic indicator for length of hospital stay, cost factors, and outcome or survival. St. Louis Encephalitis Virus

## Maintenance Dose

Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products 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 Elimination The initial damage and destruction of tumor cells by innate and adaptive immunity. Completion of the phase means no cancer growth. Cancer Immunotherapy at the steady state Steady state Enzyme Kinetics.
• Maintenance dose is a function of the rate of removal of a drug from circulation Circulation The movement of the blood as it is pumped through the cardiovascular system. ABCDE Assessment (clearance) and its calculation depends on the rate of excretion.
• Administration is repeated at specific intervals to maintain the desired steady-state plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products drug concentration. A maintenance dose administered at least 4 times and 1 half-life Half-Life The time it takes for a substance (drug, radioactive nuclide, or other) to lose half of its pharmacologic, physiologic, or radiologic activity. Pharmacokinetics and Pharmacodynamics (time required for the plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products 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 loading dose is a large dose given administered to rapidly increase the plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products drug concentration.

• A single or few quick doses administered usually at the onset of therapy
• Often used in an emergency:
$$Loading\ dose =\frac{Volume\ of\ distribution^{^{*}} \times Concentration\ at\ steady\ state}{Bioavailability}$$
*Volume of distribution is the dose of the medication given divided by the concentration in the plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products.

### 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 Bioavailability Pharmacokinetics and Pharmacodynamics of 55%. The required plasma Plasma The residual portion of blood that is left after removal of blood cells by centrifugation without prior blood coagulation. Transfusion Products concentration is 55 µg/mL. Calculate the loading dose.

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

## 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 GFR The volume of water filtered out of plasma through glomerular capillary walls into Bowman’s capsules per unit of time. It is considered to be equivalent to inulin clearance. Kidney Function Tests
• Kidney disease
• Renal failure Renal failure Conditions in which the kidneys perform below the normal level in the ability to remove wastes, concentrate urine, and maintain electrolyte balance; blood pressure; and calcium metabolism. Renal insufficiency can be classified by the degree of kidney damage (as measured by the level of proteinuria) and reduction in glomerular filtration rate. Crush Syndrome
• 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:

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

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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