Physiology, Zero and First Order Kinetics


Article Author:
Christopher Borowy


Article Editor:
John Ashurst


Editors In Chief:
James Beauchamp
Mark Pellegrini
Nicole Hale-Crutch


Managing Editors:
Avais Raja
Orawan Chaigasame
Carrie Smith
Abdul Waheed
Khalid Alsayouri
Frank Smeeks
Kristina Soman-Faulkner
Trevor Nezwek
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Saad Nazir
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Mark Pellegrini
James Hughes
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Nazia Sadiq
Hajira Basit
Phillip Hynes
Tehmina Warsi


Updated:
2/2/2019 3:02:41 PM

Introduction

As the human body ingests substances and medications, it utilizes a variety of metabolism and elimination processes. The 2 of focus in this article will be zero and first-order kinetic elimination, which are clinically useful in achieving a therapeutic level of medication and prognostically assessing toxicity levels and implementing treatment. For simplicity, the following discussion will be specific to a one-compartment model, which views the human body as a homogeneous unit. Lastly, while the vast majority of drugs are eliminated via first-order kinetics, a firm understanding of both zero and first-order kinetics is crucial in a clinical setting as there can be fluidity between the 2 types of elimination with the same specific substance.[1]

Issues of Concern

Determination and understanding of how a particular substance is eliminated are important when administering medications to achieve a therapeutic level and when assessing a patient who ingested a toxic substance. Specifically in regards to toxicology, if the ingested substance is unknown to the patient and practitioner, routine blood/plasma testing of the substance and analysis of the decline in concentration will aid in the identification of the ingested substance. For example, if the substance follows a zero-order elimination, the amount eliminated will be dependent of time and not the amount ingested, which can be contrasted to first order kinetics, which the amount eliminated will be dependent on the maximum blood/plasma concentration and not of time. Furthermore, once the substance and its properties are understood, proper treatment may be given to a patient that ingested a toxic substance.  

To achieve a desired therapeutic level of a medication, a clinician must understand the elimination order and utilize the information in subsequent dosing to maintain the therapeutic concentration over a set period. Misunderstanding of kinetic elimination may lead to patients experiencing toxic symptoms and could lead to other iatrogenic adverse effects such as death.

Organ Systems Involved

The kidneys are the main excretory system; whereas, the hepatic system is the main site involved in drug metabolism. Other sites of metabolism include the gastrointestinal tract, pulmonary system, kidneys, and skin. An important concept to understand is any impairment of the described systems may alter how a therapeutic level of medication is achieved and can predispose patients to toxicity symptoms with a dose that would otherwise be well-tolerated in a healthy individual. Both metabolism and excretion are combined to form the rate constant of elimination which is useful in determining the order of elimination. This equation can be seen in "Equation  No. 2", where "k" represents the rate constant of elimination, "km" and "ke" represent the rate constant for metabolism and the rate constant for excretion, respectively.

Function

The fundamental difference between zero and first-order kinetics is their elimination rate compared to total plasma concentration. Zero-order kinetics undergo constant elimination regardless of the plasma concentration, following a linear elimination phase as the system becomes saturated. A simple analogy would be an athlete signing an autograph on a picture. Regardless of the total amount of photographs that must be signed, the athlete can only sign one autograph every 15 seconds. The rate-limiting factor of this analogy and zero-order kinetics is time.

First-order kinetics proportionally increases elimination as the plasma concentration increases, following an exponential elimination phase as the system never achieves saturation. Furthermore, when attempting to obtain a therapeutic level of plasma concentration or in regards to drug toxicity, one must utilize their knowledge of a particular drugs elimination kinetic. To utilize the same analogy, now the entire team can sign the photographs. The more photographs to sign, the more athlete's can sign. The rate-limiting factor of this analogy and in first-order kinetics is the initial concentration.

In the case of the autographs, if the amount of needed autographed photos exceeds the number of available athletes, the first-order elimination then becomes zero-order. As described above, the system of first-order kinetic elimination can become saturated, which will force a zero-order kinetic model to be followed. Importantly, once the concentration falls below a certain level, a first-order kinetic elimination will once again be seen as the system is no longer saturation.[2][3][4]

Mechanism

Both zero and first-order kinetics can be derived from the same equation. As seen in "Equation  No. 1 "Kinetic order elimination equation," where delta [drug] represents the change in plasma concentration of the drug divided by time, "n" represents either first or zero order elimination with 1 or 0, respectively, and "-Kc" represents a constant. For example, when n = 1, the change in drug plasma concentration divided by time is proportional to the amount of drug initially given showing the rate limiting factor being the initial concentration. In contrast, when n = 0, [Drug]^0 = equal 1, the change of drug plasma concentration is equal to the constant, -Kc. Thus demonstrating how the rate limiting factor is time.

The same principles with zero and first-order kinetics can be seen in a graph. As seen in "Graph 1: Zero-order kinetics", regardless of the plasma concentration of a substance the same amount is limited over 2 hours. Thus, the graph demonstrates a linear slope. In comparison to "Graph 2: First-order kinetics," the exponential curve of the graph demonstrates how a larger plasma concentration implies a larger amount eliminated in a 2-hour time span.[5][6]

Clinical Significance

When administering medications, one must fully understand the mechanism of action and process of elimination to reduce any unwanted adverse effects. Furthermore, when assessing a patient who either intentionally or accidentally ingested a toxic amount of a substance, knowledge of that substance's properties will aid treatment and the disease course.

For example, in a case of methanol ingestion urgent treatment is desired. Methanol itself causes sedation but is generally nontoxic. The toxicity of methanol stems from the metabolites. As methanol follows a zero-order kinetic elimination, a practitioner can understand that the real danger lies in the time from ingestion, not the total amount. In contrast to methanol, other specific medications that show zero-order elimination are salicylates, fluoxetine, omeprazole, phenytoin, and cisplatin, which when ingested at a toxic level, will be at a higher concentration of the substance within the body over time compared to the same amount of the substance that shows first-order elimination.[7]

A firm understanding of the above-described concepts will help reduced adverse effects of medications on patients and will lead the practitioner to choose better treatments for patients experiencing toxicity symptoms.


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    Contributed by Christopher Borowy
Attributed To: Contributed by Christopher Borowy

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Physiology, Zero and First Order Kinetics - Questions

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Which of the following statements correctly describes rate of excretion of drugs undergoing first-order kinetics?



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Which of the following has a classic type of first order kinetics?



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Which is true about first order drug clearance kinetics?



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Zero-order kinetics:



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Which of the following statements about drug clearance with first order kinetics is true?



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Which of the following is the true statement about zero-order kinetics?



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Which of the following is not true concerning zero and first order kinetics?



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Which is true of zero-order reactions rate?



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Which of the following is equal to a first-order half-life?



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What order reaction is radioactive decay?



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A drug that follows linear pharmacokinetics has a half-life of two hours. How much of the drug will remain in the body after six hours if a 400 mg dose is administered?



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Which is true of a drug's biological half-life if it exhibits first-order kinetics?



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A drug following first-order pharmacokinetics has a half-life of 6 hours. If a patient is administered a 600 mg dose, how much drug will remain after 24 hours?



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If a topical gel has 1,000 units of active ingredient per gram and decomposes at a rate of 50 units weekly, what is the half-life of the medication?



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A homeless 42-year-old male is brought into the emergency department by the local police department for attempting to fight multiple pedestrians. Past medical history is unknown, and the patient is a poor historian. On physical exam, the patient's vital signs are stable, has a wide-based gait, slurred speech, intentional tremor on finger-to-nose testing, and has a distinct odor to his breath. By which order of kinetics is the ingested substance eliminated from this patient?



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Which of the following substances is eliminated following first-order kinetics?



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A 2-year-old female is brought into the emergency department by her mother after being found drinking a clear fluid on the floor in their kitchen. The patient has no significant past medical history. Vital signs are remarkable for a heart rate of 70 bpm, blood pressure of 110/70 mmHg, and respiratory rate of 8/minute. The physical exam is remarkable for a somnolent child that is responsive only to noxious stimuli and a fruity odor to her breath. Which of the following is the most important prognostic fact regarding the substance ingested in this patient?



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What type of graphical curve does first-order kinetic elimination follow?



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Physiology, Zero and First Order Kinetics - References

References

Ф-order kinetics of photoreversible-drug reactions., Maafi M,Maafi W,, International journal of pharmaceutics, 2014 Aug 25     [PubMed]
Kinetics and metabolism of fomepizole in healthy humans., McMartin KE,Sebastian CS,Dies D,Jacobsen D,, Clinical toxicology (Philadelphia, Pa.), 2012 Jun     [PubMed]
Introducing total substrates simplifies theoretical analysis at non-negligible enzyme concentrations: pseudo first-order kinetics and the loss of zero-order ultrasensitivity., Pedersen MG,Bersani AM,, Journal of mathematical biology, 2010 Feb     [PubMed]
Transdermal drug delivery and cutaneous metabolism., Guy RH,Hadgraft J,Bucks DA,, Xenobiotica; the fate of foreign compounds in biological systems, 1987 Mar     [PubMed]
Population Pharmacokinetic Analyses for Rezafungin (CD101) Efficacy Using Phase 1 Data., Lakota EA,Ong V,Flanagan S,Rubino CM,, Antimicrobial agents and chemotherapy, 2018 Mar 19     [PubMed]
Insights into influencing factor, degradation mechanism and potential toxicity involved in aqueous ozonation of oxcarbazepine (CHEM46939R1)., Wang T,Huang ZX,Miao HF,Ruan WQ,Ji XP,Sun FB,Zhao MX,Ren HY,, Chemosphere, 2018 Feb 9     [PubMed]
Severe methanol poisoning with neurological sequelae: implications for diagnosis and management., Holt NR,Nickson CP,, Internal medicine journal, 2018 Mar     [PubMed]

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