Coming Off Antidepressants: Linear Versus Hyperbolic Tapering

Coming Off Antidepressants: Linear Versus Hyperbolic Tapering

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You’ve probably seen the words hyperbolic tapering all over the Outro website, as it's a foundational part of how we approach antidepressant tapering. But what exactly is it?

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This post will provide you with general information on what hyperbolic tapering is, and why it is highly recommended compared to linear tapering.

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The word hyperbolic describes a relationship between objects that resembles a hyperbola (a “curve”; see figure 2A and 2B for an example of a hyperbola). Hyperbolic tapering, simply put, means making smaller and smaller dose changes as you get closer to zero. Still confused? Keep reading – our graphs might help make sense of this term. 

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Tapering Approaches

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The following graphs provide a great visual representation of the 3 main ways that an individual can discontinue antidepressant medication, and the resulting effect in terms of potential withdrawal effects. The 3 main strategies in tapering include abrupt discontinuation (“cold turkey”), linear tapering, and hyperbolic tapering. Each image below will show the process of “adaptation”, or the body becoming used to the presence of a consistent level of medication, and the changes that occur in the brain as a result. 

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Abrupt Discontinuation

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In the above graph, you can see the body undergoes a process of adaptation (the gradual upward curve on the left), until it reaches the “homeostatic set point”, AKA the “new normal” (the flat straight line). When the drug was abruptly discontinued or stopped cold turkey – you can see in the gray shaded area what would be felt in the body as withdrawal symptoms.

It's important to note that we would NEVER recommend anyone to try stopping abruptly, as it can lead to potentially severe and dangerous withdrawal symptoms.

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Linear Tapering

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In this graph, like the previous one, you can see the process of adaptation: when the homeostatic set point is reached. In this instance – versus abrupt discontinuation – the process of tapering is linear. This is a strategy often used in usual clinical practice, and readers may have first hand experience with this method. The dose was decreased by “linear amounts” such as, using the example of a common medication like escitalopram, 40 mg, 20 mg, 10 mg, 5 mg, 0 mg over a set period of time (often between 2-4 weeks). As the graph shows, the shaded area is smaller than the first example, but still may result in unpleasant and potentially intolerable withdrawal symptoms.

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Hyperbolic Tapering 

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Taking a look at a graph where hyperbolic tapering is applied, you can see the same process of adaptation and reaching homeostasis. The difference here is that when the dose was decreased, it was done in small hyperbolic steps, meaning that each reduction of dose was smaller and smaller as the dose lowered. This is done over a longer period of time and in line with the neurobiology of how the antidepressant medication affects the brain at different doses. This approach helps  minimize the symptoms of antidepressant withdrawal.

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A good analogy to describe these various methods of tapering is that of a staircase. Picture yourself standing at the top of the staircase. In abrupt discontinuation of an antidepressant, imagine someone pushing you from the top of the staircase. You tumble down the stairs and might end up with some nasty bumps and bruises along the way. 

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In linear tapering, imagine you are at the top of the stairs again. This time you are able to take a few steps down, but then you trip and tumble down the stairs – again with some bumps and bruises. 

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In hyperbolic tapering, now you are standing at the top of the staircase and are able to safely walk down the stairs, one step at a time until you reach the bottom. Hopefully without a scratch on you (or at least very minimal ones).   

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Comparing Linear Tapering and Hyperbolic Tapering 

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The two graphs below show the process of linear (2A) and hyperbolic (2B) tapering in a bit more detail. Emerging evidence has shown that the relationship between the dose of medication and effect on the brain is in fact NOT a linear one. Meaning decreasing the dose by 50% does not necessarily mean the effect on the brain/body will be 50% lower. Instead this relationship is hyperbolic. You will see in the below graphs - the relationship between the dose of an antidepressant and its effect on the main target receptor (e.g., for SSRIs it is SERT) follows a dose curve. 

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This is a very important concept to understand. As you can see in figure 2A, starting from the right hand side of the graph, the dose is decreased in a linear fashion (ie. 40 mg, 20 mg, 10 mg, 5 mg, 0 mg). The dotted yellow line shows the receptor occupancy - which can be thought of as “effect on the brain” at each particular dose. When the dose is reduced initially, the change on the effect of the brain is fairly minimal. As the dose continues to be reduced in a linear fashion the change in effect on the brain grows. The dotted yellow line on the left hand side of the graph would be where a linear taper would end - but as you can see there will still be a large amount of receptor occupancy that the brain is expecting but not receiving as the medication has been stopped. This disregard to the residual effect on the brain is what causes withdrawal symptoms in linear tapering. 

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You will see in figure 2B that there are more steps involved towards the base of the curve. This will help to minimize withdrawal symptoms. This process involves using non readily available formulations of medications by compounding, cutting, diluting, and bead counting.  

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Figure 2A

Figure 2B

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The concept of hyperbolic tapering can be applied to a variety of psychotropic medications, including benzodiazepines, Z-drugs and gabapentinoids.

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How To Do A Hyperbolic Taper

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First things first, discontinuing an antidepressant should be done under clinical supervision of a clinician familiar with science-based tapering and antidepressant withdrawal – this is why we created Outro.

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While it may, or may not, seem straightforward, different people have different responses to dose reductions, and tapering plans should be personalized to the individual and their medication history. Moreover, patients should monitor withdrawal symptoms in collaboration with their provider in order to adjust the plan as needed. Lastly comes the problem of dose sizes: often, working with a compounding pharmacy is necessary to achieve the small dose sizes needed to follow a hyperbolic taper as closely as possible.

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It’s about time that a science-based method has been developed to help people safely discontinue their antidepressant medications, while minimizing often severe withdrawal symptoms. There is much work to be done to predict what the best tapering plans are, based on individual needs, and fill this gap in the healthcare system.

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Make sure to follow along for more information on safe and effective methods for sustainable antidepressant discontinuation.

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Resources

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Horowitz, M. A., & Taylor, D. (2019). Tapering of SSRI treatment to mitigate withdrawal symptoms. The Lancet Psychiatry, 6(6), 538–546. https://doi.org/10.1016/s2215-0366(19)30032-x