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Pharmacodynamics of Gentamicin as they relate to ototoxicity

Timothy C. Hain, MD Gentamicin ototoxicity page. Last revision: February 16, 2014

Level: This material is intended to provide a detailed explanation of how gentamicin affects the inner ear, emphasizing mathematical modeling, without requiring a high level of mathematical knowlege.

Gentamicin and other aminoglycoside antibiotics such as Streptomycin and Tobramycin are handled by the body in a very simple way. Gentamicin is excreted unmodified by the kidneys, and for this reason, follows "first order kinetics". This means that the drug is cleared at a rate from the blood that is proportional to it's concentration. For those of you who are familiar with calculus, if we use G to indicate the gentamicin level, dG/dt = K*G.

After a bolus (dose) of gentamicin, the level in the blood decays exponentially. The way this works is that the kidneys are always removing a fraction of the gentamicin in the blood. As the level goes down with time, there is less gentamicin presented to the kidneys, so less is excreted. This causes the level of gentamicin to decline "exponentially". This pattern is very common for medications that are eliminated by the liver or kidney.

Water tower with a leak. Exponential decay of water or gentamicin in the tank.

You can think of this process as being similar to a water tower that develops a leak at the bottom. When the leak starts, the pressure is high and the water level declines quickly. Later on there is little left in the tank. The pressure is lower and the water just trickles out. Let's assume that the water level starts at 8 gallons, and the rate of the leak is such that half of the water is gone in 2 hours. If you plotted the water level vs. time, you would see an exponential decay. The bigger the leak (K, the rate constant), the faster the water level declines.

Another way of looking at it is to figure out how long it takes for half of the water (or gentamicin) to be eliminated from the tank (blood). The half-life, T 1/2, is the time that it takes for half of something to be eliminated. T1/2 is related to the rate constant, K in that T1/2=Ln(2)/K. (For those of you who were wondering, the ln of 2 is 0.6931).

It is very important to realize that one can't assume that if half is gone in one half-life, then all is gone in two half-lives. You can see from the figure above that at 4 hours, the level is down to 2, not 0. This assumption is incorrect because the half-life just applies to whatever level you start with. After one half life, it takes another half-life for "half of the half" to be eliminated, and so-on. So in two half-lives -- 4 hours, you get down to 1/4 of the initial level. This is the way that exponential decay works.

Switching back to gentamicin now, in persons with normal renal function, T1/2 is 2 hours. In persons with poorly functioning kidneys, T1/2 is greater -- if there is no kidney function, T1/2 is infinite. Another way of looking at it is to compute the time constant of elimination, which is simply 1/K. The time constant tells you how long it takes for the level to decline to 1/e of the initial level. "e", being 2.718, the time constant is a little bit longer than the half-life. Time constants are used mainly by more mathematically oriented people than clinicians, as the same mathematics is used to describe many things - -such as electricity. Because it is so much easier to think in terms of half-lives than time constants, the clinical literature generally uses half lives.

Because Gentamicin's kinetics are so simple, we can produce useful simulations of blood levels using a simple Excel spreadsheet. All one has to do is to set up a time series, and subtract a proportion of the previous value with each step. There are more sophisticated ways to do it, but Excel is good enough, and this method also extends very naturally to questions like - -what if the kidney function was getting worse over time ...

Gentamicin is often given three times per day, with a total dose per day ranging from 2.5 mg/kg to 7.5 mg/kg. The levels in the blood can be predicted closely if the kidney function and the volume of distribution is known. Usually the initial dose of gentamicin is estimated from a combination of patient weight/height and knowledge of kidney function, and subsequent doses are "tuned" by comparing blood levels of gentamicin with target levels, for particular times after the dose. A "peak" level might be drawn 30 minutes after a dose, and a "trough" level just before the next dose. For three times/day dosing, ordinarily a peak level of 5-10 and a trough level of < 2 is aimed for ( Keller et al). The figure below shows a simulation of blood levels in a person with normal renal function, for dosing every 8 hours of 120 mg.

While many assume that gentamicin toxicity is caused by an overdose, and that one is safe if the peaks and troughs remain with the the limits noted above, the situation is actually much more complex. First, toxicity can develop even when blood levels remain within generally accepted limits. Exceptional cases have been reported with toxicity after a single ordinary dose (Halmagyi et al, 1994). It is also possible to develop bilateral vestibular toxicity from gentamicin even when the level of the drug never goes above recommended limits, given that it is given for a long period. The risk may be especially high if there are other drugs being given (see below), and in certain individuals with genetic predisposition (see below).

 

Figure: Simulated blood levels of gentamicin for a typical person with normal kidney function and average size, using a dose of 120 mg of gentamicin every 8 hours. The area under the curve (see text) over 50 hours for this regimen is about 175mg.

Nevertheless, it is very uncommon for gentamicin ototoxicity to develop with with less than 1 week of treatment suggesting that toxicity might be more closely related to the total dose than peak dose. Prazma et al (1976) found ototoxicity due to Tobramycin to be both proportional to total dose and peak level. The same total dose arrived at through two different regimen was more toxic for the regimen with the higher peak levels. Against the idea that toxicity correlates with total dose, Black et al (2001) did not find a correlation between total aminoglycoside dose and ototoxicity. However, their numbers were small and a correlation could have easily been missed. Also, total dose may be the wrong measure as exposure of the ear to gentamicin is presumably correlated to blood level rather than dose. Blood levels are a function of dose, timing, kidney function, and volume of distribution.

Thus a refinement of this idea is that ototoxicity is proportional to the "area under the curve", or AUC, meaning the integral of the gentamicin blood level. This idea is attractive, as it would fit well with the general thought that aminoglycoside ototoxicity is due to diffusion from the blood compartment into an inner ear compartment, which binds gentamicin strongly and for very long periods. Beaubian et al (1989, 1991) has presented strong evidence for this idea using another aminoglycoside, Amikacin, in an animal model. Against this idea is that in humans, Fee did not find that area under the curve (related to total dose, kidney function and volume of distribution) correlated with ototoxicity (Fee, 1980). Fee suggested that there were other, yet unknown factors, operative.

 

Figure: In this simulation of once/day gentamicin dosing, notice that peak levels are much higher than for the every 8 hour dosing simulation in just earlier figure. Nevertheless, this regimen is equally effective and less ototoxic. This suggests that ototoxicity is not directly related to the peak level. The "area under the curve" (see text) for 50 hours of this regimen is similar to the every 8 hour dosing schedule of figure 1, about 225 mg.

Extended Interval Dosing:

It is now well known that a high peak dose is not necessarily harmful. A recent trend is to administer a much larger dose of gentamicin on a once/day or longer schedule (Chuck, Raber et al. 2000). Details about how this is done using a nomogram called the "Hartford Nomogram" is found in in a paper written by Nicolau et al. Other algorithms are discussed by Begg and Barclay (1995). For every 24 hour dosing, peak levels are much higher than the levels expected for three times a day dosing, and targets for three time/day dosing as discussed above are inappropriate for once/day dosing. Instead,  levels drawn at known times from the administration, typically 6-10 hrs after the last dose, are used to adjust the interval of dosing using a nomogram.

Most evidence suggests that ototoxicity is less for once/day dosing than more frequent dosing (Begg and Barclay, 1995). This line of evidence again suggests that high-peak levels are not intrinsically ototoxic, but rather it is the total dose or some other factor that is important. It also possible that toxicity might be related to a combination of peak dose and total dose, or that toxicity is a complex function of peak and total dose, potentiating medications and genetic susceptibility. The few human studies done to date, all necessarily retrospective of course, are not powerful enough to clearly distinguish between these possibilities.

Monitoring extended interval dosing.

Gentamicin kinetics are so simple (well relatively speaking compared to some other drugs), that once you have calibrated your dosing model with a level taken at the proper time, the subseqent levels are easily predicted. As it takes about a week of exposure in most persons for there to be a significant risk of gentamicin toxicity, there is nearly always sufficient time.

Given that the volume of distribution and dosing factors are usually constant, the only thing that might reasonably change over time is kidney function. Kidney function can fluctuate, and as gentamicin sometimes damages the kidneys too, this is a real possibility. There are many ways to infer kidney function-- including mid-level, trough, or kidney function tests. Peak gentamicin levels, especially in persons on extended interval dosing, are not a good measure of kidney function --as they mainly reflect the volume of distribution.

Trough gentamicin levels for extended interval dosing are tricky. Generally, when one goes from three-times/day dosing to once/day dosing (extended interval), one triples the dose. In other words, one uses a linear adjustment of dose. One might think that because the dose is 3X bigger, and the time of measurement is 3X bigger too, then the predicted trough should be the same. However, this is wrong. Gentamicin elimination follows exponential -- not linear -- decay, and because of this, the trough level for once/day dosing should be far less than the trough for 3 times/day. This is the reason that peaks/troughs are not recommended for extended interval dosing -- neither one is very helpful.

Following up on this idea, if the trough of extended interval dosing is high - - kidney function is probably very bad. Get 4-8 hour levels -- not troughs.

Kidney disease

If we accept the reasonable idea, so far unproven in humans, that the AUC predicts ototoxicity more closely than peak and trough levels, then a group that would be expected to have more ototoxicity than the norm are individuals with poor kidney function. Because the blood level of gentamicin decays much more slowly, the AUC is greater.

Figure. This simulation represents blood levels in an individual with renal impairment such that the time constant of gentamicin is increased to 8 hours rather than the usual 2 hours. With every 8 hour dosing, out to about 50 hours, the peak drug level climbs with each dose. The area under the curve for this regimen over 50 hours is 519, roughly twice as much as for simulations shown in figures 3 and 4, of persons with normal renal function.

The figure just above represents this situation in a person with severe renal disease. Here the half-life is 8 hrs rather than the usual 2. In patients on home hemodialysis, Manley and associates indicate that the usual half-life off dialysis and during dialysis is 20.4 and 3.7 hrs. (Manley et al. 2003). This simulation is unrealistic as ordinarily blood levels are monitored and dose reduced. If the dose were halved after the first "loading" dose, the peak levels can be kept below 8, but the trough levels are always above 4, and the AUC at 50 hours is only modestly elevated (303) compared to a similar regimen in persons with normal renal function.

Only a few studies have been done regarding the prevalence of ototoxicity in persons with renal disease (Gendeh 1993; Dayal 1979). While ototoxicity does appear more commonly in this population, other factors such as underlying medical disease as well as previous courses of ototoxic medications are difficult to separate out. Another possibly confounding factor is that when doses are adjusted downward or drug is given less frequently, patients may succumb to their infection more often.

Gentamicin accumulates in the ear

Gentamicin induced inner ear damage can be delayed and progress after blood levels of gentamicin are zero. Present evidence suggests that gentamicin diffuses rapidly into the inner ear (Becvarovski, Michaelides et al. 2002) but animal studies have shown that gentamicin elimination from the inner ear is much slower, occurring over months rather than hours (Dulon, Hiel et al. 1993). Thus gentamicin seems to "stick" to the inner ear, as it can be measured for long periods. Considering the timing of damage, and particularly observations that significant ototoxicity is rare until the drug has been given for at least a week, it seems likely that a toxic metabolite of gentamicin accumulates in the ear. In mathematical terms, gentamicin is "integrated" by the inner ear.

It follows from this line of reasoning that gentamicin given during a previous hospitalization, might increase the risk of gentamicin toxicity in a current hospitalization, even if it was several months in the past.

To make things even more complicated, recently a study of mice being given systemic gentamicin continuously over 4 days, gentamicin can be detected in the inner ear after 4 days, and it plateaus at day 7 (Liu et al, 2014). This would suggest that there are a limited number of binding sites for gentamicin in the inner ear and that they saturate. In other words, a mathematical nonlinearity. If this is also true in humans, it would imply that there might be little difference in outcome between a "lot" of gentamicin, and a "massive" overdose of gentamicin. More is not necessarily worse. This mainly has implications for detective work when one is attempting to determine when did the critical blow fall. More studies are needed as mice and men are often different.

Summary

To summarize, aminoglycoside ototoxicity depends on multiple factors, and because there is little human data, many of these factors remain obscure. The peak level is clearly not as important as was generally thought in the past, because extended interval dose regimens with very high peak doses but the same area under the curve have even less toxicity than dose regimens where gentamicin is given at shorter intervals. The area under the curve combined with other factors of less importance (perhaps peak dose, age, potentiating medications, genetic situation) seems to be the most likely candidate explanation for ototoxicity.

References: See parent document on Gentamicin ototoxicity for some of these references.

Pharmacodynamics of Gentamicin
Copyright March 24, 2014 , Timothy C. Hain, M.D. All rights reserved. Last saved on March 24, 2014