Hyperbolic Tapering

[[ou...]]

 

I was a member before the forum change but I deleted my account after getting off. I recently found out some stuff regarding withdrawal that I might be of interest to the community. For those of you who don't know, there's a psychiatrist called Mark Horowitz who after having been harmed by antidepressants himself decided to specialize in deprescribing. Besides antidepressants he has also done research on neuroleptics and plans on doing the same with benzos. In his papers he advocates for what he calls "hyperbolic tapering". I'm not sure whether he came up with this idea or not but he definitely popularized it. I presume that many of you will have heard the term by now but if you want to find out exactly how it works including the math involved, keep reading.

The name comes from the fact the relationship between dose and receptor occupancy is not linear but hyperbolic. Receptor occupancy is the percentage of the receptors occupied by a drug. This is why it's a very bad idea to taper by a fixed amount based on a percentage of your initial dose. What you can do however is taper by reducing receptor occupancy at a fixed rate. Based on his research on antidepressants and neuroleptics he suggests reducing receptor occupancy by 10% every 1-4 months. As you will see this corresponds to a very big reduction in dose which might be possible with some other drugs but not with benzos. In order to apply his results to benzos we must divide this rate into smaller steps. If you do the math it's approximately equivalent to 1.25% per week. Finally, we need to know the relationship between dose and receptor occupancy. Luckily I managed to find what I believe is the only thing he's written about benzos[2]. From these data one can find the equation of the specific hyperbola which is Y=1/(1 + 22.25/X) where Y is GABA-A occupancy and X is the dose of Diazepam.

I know this all sounds theoretical and complicated, especially during withdrawal, but please bear with me and it's about to become clearer. For example, if you're taking the equivalent of 22.25mg diazepam, it corresponds to a GABA-A receptor occupancy of 1/(1+1)=1/2=50% which means it occupies 50% of your GABA-A receptors. Now let's say you want to make a 1.4% drop in receptor occupancy. The new Y value would be 48.6%=0.486 and you'd need to solve for X. No worries, I've done that for you and it's X=22.25/(1/Y - 1)=21.038mg which you could round to 21mg. All this is just to understand what's happening under the hood. For those of you who aren't comfortable doing the math, I have done all the necessary calculations and rounded everything in terms of doses you can actually achieve by simple pill splitting. As a result, the reduction in receptor occupancy is not fixed but it's always in the range 0.9-1.7% with a mean of about 1.25%

From 160mg   reductions of 15mg    until reaching 130mg   then
from 130mg   reductions of 10mg    until reaching  90mg   then
from  90mg   reductions of  5mg    until reaching  55mg   then
from  55mg   reductions of  2.5mg  until reaching  40mg   then
from  40mg   reductions of  2mg    until reaching  28mg   then
from  28mg   reductions of  1mg    until reaching  13mg   then
from  13mg   reductions of  0.5mg  until reaching   3.5mg then
from   3.5mg reductions of  0.25mg until completely stopped.

Note that all doses are diazepam equivalents. I haven't been able to find any data regarding the GABA-A occupancy of other benzos. As you can see the above rate of hyperbolic tapering is rather close to Ashton's recommendations at medium to high doses but becomes more conservative at lower doses which addresses the main issue people have with the Ashton manual. Last but not least, I'm not a doctor. I'm just good at math. Hope this helps!

References:
1. https://markhorowitz.org/
2. https://www.rcpsych.ac.uk/docs/default-source/events/congress/2021/speaker-presentations-tuesday/horowi-1.pdf?sfvrsn=bb381fba_2

 

[[Ma...]]

Dear @[ou...],

very interesting, thank you!

Did he recommend how fast to taper? Ashton says reducing each 1-2 weeks, but that is soooo fast and brings unbearable symptoms

Kind regards

[[ou...]]

18 minutes ago, [[M...] said:

Dear @[ou...],

very interesting, thank you!

Did he recommend how fast to taper? Ashton says reducing each 1-2 weeks, but that is soooo fast and brings unbearable symptoms

Kind regards

Like I said these are on average weekly cuts. Some people might need to go slower, say 2 weeks. Other people might be able to go faster like the rate Ashton suggests. Your body will let you know. This is just a general framework.

[[Ma...]]

Thank you @[ou...]!

I will try to find out, how fast I can go.

Edited November 13, 2023 by [Ma...]

[[Gu...]]

Thank you so much for this information and links. Im in withdrawal and can't even function let alone do math. Again, thank you. Very helpful and informative. 

[[Gu...]]

I'm wondering what your thoughts would be about finding the equivalent amount of Klonopin to diazepam and using your equation. Researching now on how to find an accurate equivalent between the two. I know you were just providing the math just thought I'd ask. Maybe have my math double checked. Again, thank you for posting the information and math. I'm not very good at math. 

[[ou...]]

58 minutes ago, [[G...] said:

I'm wondering what your thoughts would be about finding the equivalent amount of Klonopin to diazepam and using your equation. Researching now on how to find an accurate equivalent between the two. I know you were just providing the math just thought I'd ask. Maybe have my math double checked. Again, thank you for posting the information and math. I'm not very good at math. 

According to Ashton 10mg diazepam = 0.5mg clonazepam which implies that 22.25mg diazepam = 1.1125mg clonazepam in the above equations.

[[Ko...]]

I watched a youtube video he did and he had a chart with a proposed slow diazepam taper  of 0.4 mg drops every 1-2 weeks from 10 mg until 4 mg and then 0.2 mg drops from 3 mg to 0 mg. So, very similar to what you outlined...of course you have to use liquid or a scale to do these drops so your suggestion is much easier as you can just break tablets..

I am actually doing even smaller decreases -I'm at 8.5 mg and only do drops of 0.25 mg every 2 weeks- once I am at 5 mg I will likely switch to .1 mg decreases. I am a single parent and sole breadwinner -really need to keep my job.  I got in this situation after being prescribed klonopin 0.5 mg at bedtime for severe insomnia- tried to do standard taper after 3 months and had horrific symptoms so held at 0.5 klonopin and now switched to diazepam. I have made it down to 8.5.  I had no idea how awful this stuff could be to come off of.

Is this hyperbolic taper thought to have better outcomes than the exponential taper?

 

[[Ko...]]

It seems that everyone is so different and its maddening. I don't want to stay on this stuff any longer than I need to and it seems ridiculous to have to taper for much longer than how originally prescribed...but I can't afford to lose my functioning and my job by going fast and that also supposedly increases chances of being protracted as well.

 

[[Gu...]]

Think you @[ou...]. I also checked bioavailability. Klonopin 90% and diazepam 100%. I'm wondering I should plug that into the equation. Which sounds like a nightmare to calculate. Lol. Thank you for posting the equivalent. 

[[ou...]]

1 minute ago, [[K...] said:

I watched a youtube video he did and he had a chart with a proposed slow diazepam taper  of 0.4 mg drops every 1-2 weeks from 10 mg until 4 mg and then 0.2 mg drops from 3 mg to 0 mg. So, very similar to what you outlined...of course you have to use liquid or a scale to do these drops so your suggestion is much easier as you can just break tablets..

I am actually doing even smaller decreases -I'm at 8.5 mg and only do drops of 0.25 mg every 2 weeks- once I am at 5 mg I will likely switch to .1 mg decreases. I am a single parent and sole breadwinner -really need to keep my job.  I got in this situation after being prescribed klonopin 0.5 mg at bedtime for severe insomnia- tried to do standard taper after 3 months and had horrific symptoms so held at 0.5 klonopin and now switched to diazepam. I have made it down to 8.5.  I had no idea how awful this stuff could be to come off of.

Is this hyperbolic taper thought to have better outcomes than the exponential taper?

I was not aware of such a video. Please post a link if you can find it.

An exponential taper is basically approximating a hyperbolic taper until you get to very low doses. In fact you can never reach 0mg with an exponential taper. At some point you have to jump and that's always a 100% reduction of your last dose.

[[Ko...]]

The charts proposed for diazepam taper are near the end.

[[ou...]]

16 minutes ago, [[G...] said:

Think you @[ou...]. I also checked bioavailability. Klonopin 90% and diazepam 100%. I'm wondering I should plug that into the equation. Which sounds like a nightmare to calculate. Lol. Thank you for posting the equivalent. 

Because most commonly prescribed benzos have a bioavailability of at least 90% I think it's not usually factored in for calculation purposes.

[[Li...]]

27 minutes ago, [[K...] said:

Is this hyperbolic taper thought to have better outcomes than the exponential taper?

Excellent question, @[Ko...].  Although I would be delighted to learn otherwise, my current understanding is that research comparing the efficacy of exponential versus hyperbolic tapering regimens for benzodiazepines has not as yet been conducted. The only research of this nature of which I am aware is a small study involving antipsychotics, a larger study currently underway seeking to replicate the results of the small study and two larger studies also currently underway involving antidepressants.

[[Gu...]]

@[ou...]. Thank you. 

[[Li...]]

30 minutes ago, [[G...] said:

I also checked bioavailability. Klonopin 90% and diazepam 100%. I'm wondering I should plug that into the equation. Which sounds like a nightmare to calculate. Lol. Thank you for posting the equivalent. 

Hello @[Gu...].  As far as I know, the bioavailability of a drug is not relevant when calculating hyperbolic reductions, neither are the equivalencies Ashton used for substituting diazepam for other benzodiazepines and z-drugs.

My understanding is that hyperbolic reductions are calculated using values that are drug-specific.  For example, researchers in The Netherlands (see link below), have this to say on the topic of calculating hyperbolic reductions for different antidepressants:

 

“Hyperbolic reductions are calculated based on a desired 10% reduction in serotonin transporter occupancy per step, following the Michaelis–Menten equation: Dose = (Occupancy/Bmax) × (ED50/(1-Occupancy/Bmax), where Bmax is the maximal occupancy possible, ED50 is the dose with 50% occupancy, and both are determined per drug on the basis of PET data.”

 

Link:
Tapering of SSRI treatment to mitigate withdrawal symptoms - The Lancet Psychiatry
https://www.thelancet.com/journals/lanpsy/article/PIIS2215-0366(19)30182-8/fulltext

 

[[Gu...]]

@[Li...] thank you so much for this information. Very grateful for all the helpful people here. 

[[Ko...]]

11 minutes ago, [[L...] said:

Excellent question, @[Ko...].  Although I would be delighted to learn otherwise, my current understanding is that research comparing the efficacy of exponential versus hyperbolic tapering regimens for benzodiazepines has not as yet been conducted. The only research of this nature of which I am aware is a small study involving antipsychotics, a larger study currently underway seeking to replicate the results of the small study and two larger studies also currently underway involving antidepressants.

It is so important for those of us who find ourselves stuck in this mess to know the best way to taper off so as to best preserve our functioning. I don't want to ruin my childrens' lives because I took "a low dose" of klonopin for 2 1/2 months longer than I should have.  

I find the super slow ashtonesque  hyperbolic method referenced above to best suit me at the moment as its relatively simple and I don't have my prescriber on board to do DIY methods.  I just hope my body agrees with it the further down in dosage that I go...as soon as it gets too rough I will either go to every 3 weeks or switch to the liquid and do the .1 mg reduction every 2 weeks. 

@[Li...]how long have you been off and how do you feel? 

[[ou...]]

57 minutes ago, [[K...] said:

The charts proposed for diazepam taper are near the end.

 

You can extract the values from the Lorazepam graphs because the lines fall on nice numbers. Unfortunately I can't make out exact values from the graphs for Alprazolam. The corresponding equation for Lorazepam would be Y=1/(1 + 2.5/X) where Y is GABA-A occupancy and X is the dose in mg or X=2.5/(1/Y - 1) if you want it solved for X.

If we are to trust this numbers it would imply that the conversion ratio between diazepam and lorazepam is 22.25/2.5=8.9 which means that 1mg of lorazepam is actually equivalent to approximately 9mg of diazepam. This is very interesting because I seem to remember having read from Ashton herself that this ratio is in fact a bit lower than 10.

 

[[Li...]]

2 hours ago, [[K...] said:

It is so important for those of us who find ourselves stuck in this mess to know the best way to taper off so as to best preserve our functioning. 

@[Ko...] I have been researching the topic of benzodiazepine withdrawal for 5+ years and have yet to find ‘the best way to taper’. Instead, what I’ve learned is that each of us has to discover via systematic experimentation what works best for us as individuals. Per the Horowitz presentation cited upthread:

“The best pace [to taper] is the pace the patient can tolerate — imposing regimens tends to backfire.”

[[Ma...]]

I have read a lot about this too and think there is a lot of truth to it, but each one of us is a different biological system so kinda hard to apply practically  (I like math too but i am a physician so i probably like biology a little more lol 😂 ). I talked to a gentleman the other day who had a breakthrough around 0.2 of K and was able to speed up his taper because the drug was essentially doing nothing at that dose.  I see others who seem to hit a wall at doses well below this.  I think a general rule of thumb is that you need to slow things down towards the end of the taper but at some point to heal you need to get off.  Some may need to go to very low doses before they can jump and others may be fine speeding up at the end and jumping off earlier.  

Edited November 14, 2023 by [Ma...]

[[Li...]]

16 hours ago, [[G...] said:

I'm wondering what your thoughts would be about finding the equivalent amount of Klonopin to diazepam and using your equation. Researching now on how to find an accurate equivalent between the two. I know you were just providing the math just thought I'd ask. Maybe have my math double checked. Again, thank you for posting the information and math. I'm not very good at math. 

@[Gu...] I swapped from Klonopin to Valium.  I have a dr that works with me and he said that there are general equivalencies but each person can be different on where their own body's equivalent dosage would be. When I got down to 1 mg of Klonopin we switched to 20 mgs of Valium (I think that is where we started).  However, for me the equivalent dosage of V was 30 mgs.  

[[Li...]]

21 hours ago, [[o...] said:

I was a member before the forum change but I deleted my account after getting off. I recently found out some stuff regarding withdrawal that I might be of interest to the community. For those of you who don't know, there's a psychiatrist called Mark Horowitz who after having been harmed by antidepressants himself decided to specialize in deprescribing. Besides antidepressants he has also done research on neuroleptics and plans on doing the same with benzos. In his papers he advocates for what he calls "hyperbolic tapering". I'm not sure whether he came up with this idea or not but he definitely popularized it. I presume that many of you will have heard the term by now but if you want to find out exactly how it works including the math involved, keep reading.

The name comes from the fact the relationship between dose and receptor occupancy is not linear but hyperbolic. Receptor occupancy is the percentage of the receptors occupied by a drug. This is why it's a very bad idea to taper by a fixed amount based on a percentage of your initial dose. What you can do however is taper by reducing receptor occupancy at a fixed rate. Based on his research on antidepressants and neuroleptics he suggests reducing receptor occupancy by 10% every 1-4 months. As you will see this corresponds to a very big reduction in dose which might be possible with some other drugs but not with benzos. In order to apply his results to benzos we must divide this rate into smaller steps. If you do the math it's approximately equivalent to 1.25% per week. Finally, we need to know the relationship between dose and receptor occupancy. Luckily I managed to find what I believe is the only thing he's written about benzos[2]. From these data one can find the equation of the specific hyperbola which is Y=1/(1 + 22.25/X) where Y is GABA-A occupancy and X is the dose of Diazepam.

I know this all sounds theoretical and complicated, especially during withdrawal, but please bear with me and it's about to become clearer. For example, if you're taking the equivalent of 22.25mg diazepam, it corresponds to a GABA-A receptor occupancy of 1/(1+1)=1/2=50% which means it occupies 50% of your GABA-A receptors. Now let's say you want to make a 1.4% drop in receptor occupancy. The new Y value would be 48.6%=0.486 and you'd need to solve for X. No worries, I've done that for you and it's X=22.25/(1/Y - 1)=21.038mg which you could round to 21mg. All this is just to understand what's happening under the hood. For those of you who aren't comfortable doing the math, I have done all the necessary calculations and rounded everything in terms of doses you can actually achieve by simple pill splitting. As a result, the reduction in receptor occupancy is not fixed but it's always in the range 0.9-1.7% with a mean of about 1.25%

From 160mg   reductions of 15mg    until reaching 130mg   then
from 130mg   reductions of 10mg    until reaching  90mg   then
from  90mg   reductions of  5mg    until reaching  55mg   then
from  55mg   reductions of  2.5mg  until reaching  40mg   then
from  40mg   reductions of  2mg    until reaching  28mg   then
from  28mg   reductions of  1mg    until reaching  13mg   then
from  13mg   reductions of  0.5mg  until reaching   3.5mg then
from   3.5mg reductions of  0.25mg until completely stopped.

Note that all doses are diazepam equivalents. I haven't been able to find any data regarding the GABA-A occupancy of other benzos. As you can see the above rate of hyperbolic tapering is rather close to Ashton's recommendations at medium to high doses but becomes more conservative at lower doses which addresses the main issue people have with the Ashton manual. Last but not least, I'm not a doctor. I'm just good at math. Hope this helps!

References:
1. https://markhorowitz.org/
2. https://www.rcpsych.ac.uk/docs/default-source/events/congress/2021/speaker-presentations-tuesday/horowi-1.pdf?sfvrsn=bb381fba_2

@[Gu...] This sounds really good but I guess a little bit scary for me.  I had been on the liquid valium after swapping from klonopin.  I could only dose down 1 drop at a time which was about 0.05 mgs at a time and my body is so sensitive to the decreasing in medication it is ridiculous.  I can't wait to be off......  would love to speed it up but it scares me.  

[[...]]

Thanks for the video post with the taper. I think. My taper just got 100 days longer. 
What is the risk to jumping sooner? Is it protracted withdrawal neuro injury or is it rebound symptoms?

[[ou...]]

Edited November 21, 2023 by [ou...]