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Pharmacokinetics: why do certain drugs follow zero-order kinetics?

Pharmacokinetics: why do certain drugs follow zero-order kinetics?


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I understand that alcohol and phenytoin are two examples of drugs that follow zero-order kinetics. Why do these two particular drugs follow zero-order kinetics as opposed to first-order kinetics?


Basically any compound in concentrations sufficient to saturate its metabolization machinery will show zero-order pharmacokinetics. This reflects the fact that metabolization is taking place at full speed while facing a comparatively enormous amount of substrate (just as @WYSIWYG pointed out). This effect can also be shown in vitro with pure substrate/enzyme solutions.

But the above is a rather simplistic model, valid only in specific situations.

Most of the time in humans, zero-order kinetics stem from the fact that liver enzymes are saturated. However, for most drugs the redistribution phase is much more important than metabolization/elimination in defining the duration of effect. A good example of that would be sodium thiopental. As a single iv bolus dose, it will induce loss of consciousness for a short time due to redistribution. However, continued infusion will allow blood and tissue concentrations to equilibrate, and then the metabolization/elimination rate will become much more prominent in defining the duration of effect. And as sodium thiopental happens to have zero-order metabolization kinetics in continued infusion, it will take you a loooooooooong time to wake up! This is why in human pharmacology, we use context sensitive half-life to better represent drug kinetics.


Alcohol is a drug that is cleared by an enzyme. This interaction is what follows zero-order behavior. However, initially alcohol follows first order behavior because the ability of the enzyme to clear the alcohol exceeds the concentration of alcohol. That means clearance is constant and does not depend on the alcohol concentration.

Now what makes alcohol zero order is that the desired effect of alcohol (the therapeutic effect) occurs when the dose is greater than that enzymes ability to clear the alcohol. Once the alcohol concentration is greater than a certain point the body begins to struggle to clear the alcohol (roughly near the Km of the clearance enzyme) because of a physical limitation on the quantity or quality of the enzyme. So now when you increase the concentration of alcohol, the rate of clearance is not able to account for that increase proportionally because it is saturated. Therefore the alcohol you consume after a certain point (Km of the clearance enzyme) has a greater toxic effect. One drink too many is a very real thing.


As the human body ingests substances and medications, it utilizes a variety of metabolism and elimination processes. The second 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 undergo elimination 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 two types of elimination with the same specific substance.[1]

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 on time and not the amount ingested, in contrast to first-order kinetics, in 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 achieveਊ 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 up to and including death.


Differential Form of the Zeroth Order Rate Law

[Rate = - dfrac

= k[A]^0 = k = constant ag<3>]

where (Rate) is the reaction rate and (k) is the reaction rate coefficient. In this example, the units of (k) are M/s. The units can vary with other types of reactions. For zero-order reactions, the units of the rate constants are always M/s. In higher order reactions, (k) will have different units.

Figure 1: Rate vs. time (A) and Concentration vs. time for a zero order reaction.


Time-Course of Drug Effect

Under certain conditions (first-order kinetics, reversible effect, single compartment kinetics, iv administration), the elimination half-life of a drug and its threshold dose for a particular effect can be estimated by monitoring the effect of the drug as a function of time after drug administration. Data obtained from several doses can then be evaluated by examining the duration of a given level of effect as a function of the logarithm of the dose, as illustrated below. The slope is directly proportional to the elimination half-life the steeper the slope (i.e., increase in duration with an increase in dose), the longer the elimination half-life. The x-intercept indicates the log of the threshold dose the smaller the x-intercept the greater the potency of the drug.

[Duration of Action =< _<1/2>over0.301>(Log Dose - Log Threshold Dose)]


Difference Between First Order and Zero Order Kinetics

Definition

First Order Kinetics: First order kinetics refers to chemical reactions whose rate of reaction depends on the molar concentration of one reactant.

Zero Order Kinetics: Zero order kinetics refers to chemical reactions whose rate of the reaction does not depend on the reactant concentration.

Graph of Reactant Concentration vs. Time

First Order Kinetics: The graph of reactant concentration vs. time for first order kinetics is a curved graph.

Zero Order Kinetics: The graph of reactant concentration vs. time for zero order kinetics is a linear graph.

Reactant Concentration

First Order Kinetics: The first order kinetic reactions depend on the reactant concentration.

Zero Order Kinetics: The zero order kinetic reactions do not depend on the reactant concentration.

Rate Law

First Order Kinetics: The rate law of the first order kinetic reactions includes the rate constant multiplied by the reactant concentration.

Zero Order Kinetics: The rate law of the zero order kinetic reactions includes only the rate constant.

Conclusion

The rate law or the rate equation gives the most important details about the chemical kinetics of systems. It describes the rate of a particular reaction regarding the reactant concentration and the rate constant at a constant temperature. According to the kinetics of chemical reactions, there are three major types of reactions. They are zero order reactions, first order, reactions and second order reactions. These reactions differ from each other according to the order of the reaction with respect to the reactants present in a particular system.

References:

1. “First-Order Reactions.” Chemistry LibreTexts. Libretexts, 04 July 2017. Web. Available here. 14 July 2017.
2. “Zero-Order Reactions.” Chemistry LibreTexts. Libretexts, 21 July 2016. Web. Available here. 14 July 2017.


First Order and Zero Order Kinetics

First order kinetics occur when a constant proportion of the drug is eliminated per unit time.

Rate of elimination is proportional to the amount of drug in the body. The higher the concentration, the greater the amount of drug eliminated per unit time. For every half life that passes the drug concentration is halved. For example a drug concentration of 100 and a half life of one hour will reduce to 50 in the first hour, 25 in the second hour and 12.5 in the 3rd hour and so on. Most drugs are eliminated this way. Elimination mechanisms are NOT saturable

Zero order: a constant amount of drug is eliminated per unit time.

For example 10mg of a drug maybe eliminated per hour, this rate of elimination is constant and is independent of the total drug concentration in the plasma. Zero order kinetics are rare Elimination mechanisms are saturable. Examples of zero order elimination include ethanol, phenytoin and salicylates (at high doses)


METHODS

Medline, PubMed, Embase, Cochrane library and Reference lists were searched for articles published until June 30 2012, using the words �R,” 𠇍rug interactions,” “polytherapy,” 𠇎lderly."

Pharmacokinetic DDI

Pharmacokinetic interactions are often considered on the basis of knowledge of each drug and are identified by controlling the patient's clinical manifestations as well as the changes in serum drug concentrations. As above reported, they involved all the processes from absorption up to excretion that will be now described.

Absorption

Gastro-intestinal absorption

The complexity of the gastro-intestinal tract, and the effects of several drugs with functional activity on the digestive system, represent favourable conditions for the emergence of DDI that may alter the drug bioavailability.[13]

Several factors may influence the absorption of a drug through the gastrointestinal mucosa. The first factor is the change in gastric pH. The majority of drugs orally administered requires, to be dissolved and absorbed, a gastric pH between 2.5 and 3. Therefore, drugs able to increase gastric pH (i.e., antacids, anticholinergics, proton pump inhibitors [PPI] or H2-antagonists) can change the kinetics of other co-administered drugs.

In fact, H2 antagonists (e.g., ranitidine), antacids (e.g., aluminium hydroxide and sodium bicarbonate) and PPI (e.g., omeprazole, esomeprazole, pantoprazole) that increase the gastric pH lead to a decrease in cefpodoxime bioavailability, but on the other hand, facilitate the absorption of beta-blockers and tolbutamide.

Moreover, antifungal agents (e.g., ketoconazole or itraconazole), requires an acidic environment for being properly dissolved, therefore, their co-administration with drugs able to increase gastric pH, may cause a decrease in both dissolution and absorption of antifungal drugs.[14] Therefore, antacid or anticholinergics, or PPI might be administered at least 2 h after the administration of antifungal agents.[15]

Similarly, the administration of drugs able to increase the gastric pH (see above) with ampicillin, atazanavir, clopidogrel, diazepam, methotrexate, vitamin B12, paroxetine and raltegravir are not recommended.

In contrast, the ingestion of drugs that cause a decrease in gastric pH (e.g., pentagastrin), may have an opposite effect. It is worth noting that severity of DDIs caused by alteration of gastric pH mainly depends on pharmacodynamics characteristics of the involved drug, in terms of narrow therapeutic range.

Another factor that modifies the drug absorption is the formation of complexes. In this case, tetracyclines (e.g., doxycycline or minocycline) in the digestive tract can combine with metal ions (e.g., calcium, magnesium, aluminum, iron) to form complexes poorly absorbed. Consequently certain drugs (e.g., antacids, preparations containing magnesium salts, aluminum and calcium preparations containing iron) can significantly reduce the tetracyclines absorption.[16] Analogously, antacids reduce the absorption of fluoroquinolones (e.g., ciprofloxacin), penicillamines and tetracyclines, because the metal ions form complexes with the drug. In agreement, was observed that antacids and fluoroquinolones should be administered at least 2 h apart or more.[17,18]

Cholestyramine and colestipol bind bile acids and prevent their absorption in the digestive tract,[19] but they can also bind other drugs, especially acidic drugs (e.g., warfarin, acetyl salicylic acid, sulfonamides, phenytoin, and furosemide). Therefore, the interval between the administration of cholestyramine or colestipol and other drugs may be as long as possible (preferably 4 h).[20]

Motility disorders represent the third factor involved in absorption DDIs. Drugs able to increase the gastric transit (e.g., metoclopramide, cisapride or cathartic) can reduce the time of contact between drug and mucosal area of absorption inducing a decrease of drug absorption (e.g., controlled-release preparations or entero-protected drugs).[21]

For example, metoclopramide, may accelerate gastric emptying, hence decreasing the absorption of digoxin and theophylline whereas it can accelerate the absorption of alcohol, acetylsalicylic acid, acetaminophen, tetracycline and levo-dopa.[22]

Finally, iron can inhibits the absorption of levodopa and metildopa.

Modulation of P-glycoprotein (P-gp) intestinal

P-gp or gp-120 for its molecular weight, is a transmembrane protein encoded by the human multidrug resistance gene-1 belonging to the adenosine triphosphate-binding cassette (ABC) superfamily, together with other 41 members grouped in 7 families (A to G).[23] Localized in liver, pancreas, kidney, small and large intestine, adrenal cortex, testes and leukocytes, P-gp plays a protective role influencing the trans membrane drugs diffusion thus reducing their absorption or increasing their excretion or limiting their tissues distribution (i.e., central nervous system, foetal and gonadic tissues).[24]

P-gp regulates the intestinal absorption of drugs (it is present on the luminal surface of enterocytes) and promotes their excretion (it is present on the side tubular of epithelium renal and biliary side of hepatocytes). Therefore, the administration of drugs able to stimulate to inhibit the activity of P-gp, can induce the development of DDI.

The P-gp inhibition can significantly increase the bioavailability of drugs poorly absorbed.[25]

Among the interactions studied at the time of this review, it is worth mentioning the effects of terfenadine on the transport of doxorobucin as well as the effects chlorpromazine and progesterone on the transport of cyclosporine.[26] The DDIs on P-gp might induce a clinical effect in presence of drugs with a low therapeutic index (e.g., digoxin, theophylline, anticancer drugs) when co-administered with macrolides (e.g., erythromycin, roxithromycin, clarithromycin), PPIs (e.g., omeprazole or esomeprazole) or anti-arrhythmic drugs (e.g., dronaderon, amiodarone, verapamil or diltiazem).

Many drugs (but not all) that are transported by P-gp are also metabolized by cytochrome P450 (CYP) isoform 3A4 (e.g., cyclosporine, antiepileptic drugs, antidepressant, fluoroquinolones, quinidine and ranitidine), which can confound interpretation of interactions (see later).

Therefore, the co-administration of these drugs with known inhibitors of P-gp above described results in a clinically evident DDI.

Recently, it has been described that aripiprazole and its active metabolite, dehydroaripiprazole, but no risperidone, paliperidone, olanzapine and ziprasidone are strong P-gp inhibitors, in vitro, while in vivo their administration is unlikely to induce DDIs at the blood-brain-barrier, but the possibility of DDIs in the intestine cannot be neglected.

However, it is important to underline that a DDI could be also used in clinical management. In fact, Shi et al.[27] documented that sildenafil inhibits the transporter function of P-gp, suggesting a possible strategy to enhance the distribution and potentially the activity of anticancer drugs.


Contents

When referring to the function of the kidney, clearance is considered to be the amount of liquid filtered out of the blood that gets processed by the kidneys or the amount of blood cleaned per time because it has the units of a volumetric flow rate [ volume per unit time ]. However, it does not refer to a real value "the kidney does not completely remove a substance from the total renal plasma flow." [4] From a mass transfer perspective [5] and physiologically, volumetric blood flow (to the dialysis machine and/or kidney) is only one of several factors that determine blood concentration and removal of a substance from the body. Other factors include the mass transfer coefficient, dialysate flow and dialysate recirculation flow for hemodialysis, and the glomerular filtration rate and the tubular reabsorption rate, for the kidney. A physiologic interpretation of clearance (at steady-state) is that clearance is a ratio of the mass generation and blood (or plasma) concentration.

Its definition follows from the differential equation that describes exponential decay and is used to model kidney function and hemodialysis machine function:

  • m ˙ >> is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time (equal to zero for foreign substances/drugs) [mmol/min] or [mol/s]
  • t is dialysis time or time since injection of the substance/drug [min] or [s]
  • V is the volume of distribution or total body water [L] or [m 3 ]
  • K is the clearance [mL/min] or [m 3 /s]
  • C is the concentration [mmol/L] or [mol/m 3 ] (in the United States often [mg/mL])

From the above definitions it follows that d C d t

>> is the first derivative of concentration with respect to time, i.e. the change in concentration with time.

It is derived from a mass balance.

Clearance of a substance is sometimes expressed as the inverse of the time constant that describes its removal rate from the body divided by its volume of distribution (or total body water).

In steady-state, it is defined as the mass generation rate of a substance (which equals the mass removal rate) divided by its concentration in the blood.

Clearance, half-life and distribution volume

There is an important relationship between clearance, elimination half-life and distribution volume. The elimination rate constant of a drug Κel is equivalent to total clearance divided by the distribution volume (Κel=Cltot/Vd)(note the usage of Cl and not Κ, not to confuse with Κel). But Κel is also equivalent to ln2 divided by elimination rate half-life t1/2 (Κel=ln2t1/2). Thus, Cltot = ln2 Vd/t1/2. This means, for example, that an increase in total clearance results in a decrease in elimination rate half-life, provided distribution volume is constant. Derivation of these equations can be found in e.g. Rang and Dale's Pharmacology [6]

For substances that exhibit substantial plasma protein binding, clearance is generally dependent on the total concentration (free + protein-bound) and not the free concentration. [7]

Most plasma substances have primarily their free concentrations regulated, which thus remains the same, so extensive protein binding increases total plasma concentration (free + protein-bound). This decreases clearance compared to what would have been the case if the substance did not bind to protein. [7] However, the mass removal rate is the same, [7] because it depends only on concentration of free substance, and is independent on plasma protein binding, even with the fact that plasma proteins increase in concentration in the distal renal glomerulus as plasma is filtered into Bowman's capsule, because the relative increases in concentrations of substance-protein and non-occupied protein are equal and therefore give no net binding or dissociation of substances from plasma proteins, thus giving a constant plasma concentration of free substance throughout the glomerulus, which also would have been the case without any plasma protein binding.

In other sites than the kidneys, however, where clearance is made by membrane transport proteins rather than filtration, extensive plasma protein binding may increase clearance by keeping concentration of free substance fairly constant throughout the capillary bed, inhibiting a decrease in clearance caused by decreased concentration of free substance through the capillary.


Facilitated passive diffusion

Certain molecules with low lipid solubility (eg, glucose) penetrate membranes more rapidly than expected. One theory is facilitated passive diffusion: A carrier molecule in the membrane combines reversibly with the substrate molecule outside the cell membrane, and the carrier-substrate complex diffuses rapidly across the membrane, releasing the substrate at the interior surface. In such cases, the membrane transports only substrates with a relatively specific molecular configuration, and the availability of carriers limits the process. The process does not require energy expenditure, and transport against a concentration gradient cannot occur.


Part V: Dosing Strategies for Aminoglycosides – Once Daily Administration (ODA)

ODA is what we use for the vast majority of aminoglycosides today. Just a heads up, you may also see this strategy called "Extended Interval Aminoglycoside Dosing" (EIAD).

The really cool thing about aminoglycosides is that they exhibit what’s called a “post-antibiotic effect (PAE).” In a nutshell, PAE means that the antibiotic's inhibitory action extends beyond the period of exposure. So even AFTER the aminoglycoside concentration falls below the MIC, the bacteria are not able to grow.

Many antibiotics show some degree of PAE. But the aminoglycoside PAE is pretty much near the top of the list in terms of magnitude (along with fluoroquinolones). One might say that aminoglycosides have their very own form of The Force

Even when you don’t think they’re around anymore, they’re still affecting their environment!

The even cooler part of this is that you, the pharmacist, get to be a Jedi!! Yes, YOU, a JEDI! You will USE THE FORCE for your own purposes – and for the greater good, of course!

We heard there was a "pharmacy to dose" order for gentamicin? Image

You are going to exploit PAE in order to maximize efficacy and minimize toxicity of the aminoglycosides.

We do this by using once daily administration (ODA). Once it was recognized that aminoglycosides have PAE, nomograms were developed that would give therapeutic peaks despite longer dosing intervals.

These longer dosing intervals would allow the drug to washout, which then minimizes toxicity. In essence, you get an "aminoglycoside-free period" in the dosing interval.

There are several validated nomograms available, but they generally operate on the same principles.

Using a specified dosing weight, you calculate a mg/kg dose

Give that dose according to a renal function-determined algorithm

Check a level some pre-determined amount of time after the dose

Based on where that level falls on your nomogram, you adjust your interval accordingly.

Seems a lot easier than the calculations in Part IV, right? Almost all of the work is done for you by the chart.

Before we take a closer look at nomograms, it is important to note that ODA is not recommended for all patients!


Watch the video: Παρασκευή ομοιοπαθητικού φαρμάκου (May 2022).


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