I want to know if there is a mathematical equation I could use to predict if I will pass my weekly drug test?

Question

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Background info
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I am in the Suboxone maintenance program at a clinic in Toronto Ontario and I submit it a Urinalysis (pee test) on a weekly basis to test primarily for Opiates. More specifically: A twelve panel test cup with both 300 ng/ml and 2000 ng/ml cutoffs. I believe that if I test positive within the range of 300 to 2000 I will not automatically fail, but the test will be sent to the lab to rule out false positives and, if a true positive is found, to find out which drug it is.

These tests have no bearing on my continuation in the program, they only cause me embarrassment when I fail, and occasionally effects the number of carries (take home doses) that I have. The Doctor will often administer the test, take the bottle out of the room without peeling the label. Then talk to me about the past week, asking if there was any drug use. Obviously if I feel that I will pass I am not going to tell him, as he both lecture me, and potentially take away one of my carries, and at the very least not give me another carry.

Often the reason I use opiate drugs is because I will be sent out of town for work in the middle of the week, and my take home dose days do not always coincide with these days. Since I can not go to the pharmacy those days I will often pick up opiate drugs to avoid getting sick.
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Question
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What I am trying to figure out is if there is a mathematical equation that I could use to determine how many ng of the drug remain in my system based on time elapsed, my weight, the particular drugs halflife and amount (in mg) used.

I can provide:

drug: Hydromorphone

Half-life - 3 hours
Bio-availability (intranasal) - 58%

My weight 184 lbs.

I have a fast metabolism and a high drug tolerance.

Basically I need to figure out how any given amount of the drug (Eg: 30mg @ 58% bio-availability = 17.4mg) is diluted by my body (184lbs) into ng, and at which point I need to factor in half-life (before or after conversion)

Answer 1

Here is a solution which will generally over estimate the time it will take to clear a drug. I will try to find ways to improve the accuracy when I have time but for now this will have to do.



N = No exp^-T(1/2)t where N drug in body and No is the initial amount of drug in your body T(1/2) is the half life and t is the amount of time since administration in the SAME UNITS AS T(1/2). Ie T(1/2) in days, t is days. Same for seconds, minutes, etc.



In simper terms mathematically:



N = No (1/2)^n where n = t / T(1/2)



No = D x f where D is how much drug you took and f is the bio-availability by the route administered.



Using this equation you can calculate how long until the drug reaches a certain concentration. If you know the sensitivity of your test (aka minimum concentration it can detect) then you use this for N. If you don't you can apply standard pharmacological principles and calculate that after 4 T(1/2)s you will have 1/16th of No and after 5 T(1/2)s you have 1/32th No. Most pharmacology texts consider this "no drug" left in your body.



This method will systematically overestimate the amount of time it will take for you test negative due to the fact that drug tests are done with Urinalysis. N is a calculation of total amount of drug left in your body, you can estimate the blood concentration by dividing by your approximate blood volume.



http://easycalculation.com/medical/blood-volume.php



This will overestimate blood concentration because some of the drug in your body will be in your tissue fluid and not in your blood. Once you find the C(blood) of the drug it will be related in some way to the C(urine) of the drug such that:



N / BV = C(blood)



C(urine) = C(blood) x F where F is the relationship between C(blood) and C(urine)... I am unable to find a good estimate of this fraction (F) currently but will look into it further when I have time. It will probably be different for different drugs.



Since the immuno-assays used for most drug tests at methadone clinics test for concentration of a drug in urine we know that increasing urine volume will decrease the concentration of the drug irrespective of your blood concentration. Therefore drinking lots of water prior to a drug test can help minimize C(urine) for a given C(blood).



Conclusion:



Despite our uncertainty about various values we know that:



N > C(blood) > C(urine) so depending on the level of risk you are willing to take you can calculate the amount of time to reach certain risk levels.



ABSOLUTELY NO RISK: 5 half lives (this means there is approximately no drug in your body)



NO RISK: If N = sensitivity of the specific test used on your urine.



PROBABLY NO RISK: If C(blood) = sensitivity of the specific test used on your urine.



GETTING RISKIER: You estimate or determine F and use this to extrapolate the maximum dose you can take given that your test is n number of half lives away:



C(minimum)/F = C(blood) when you will test negative, where C(minimum) is the minimum detectable urine concentration for the SPECIFIC TEST used on your urine at the clinic.



N = C(blood) x BV which would be the amount of drug you can have in your body when you will test negative on your test.



Since N=No (1/2)^n



No = N / [(1/2)^n] where n was calculated by dividing the amount of time until your test by T(1/2).



D = No / f or the maximum dose you can take by an administration route and still test negative on your test n half lives from when you take the dose. The more accurately you calculate n, the more accurate the dose will be.



There are a lot of oversimplifications and error sources in this model but it should give you at least a rough idea of when and how you can use and still test negative on an IMMUNO-ASSAY URINALYSIS. If they use a mass spectrometer... you will not pass! Since mass-spec is expensive it is unlikely that they would but it is always a possibility. Mass-spec would probably only be used in employer drug screenings or criminal cases due to the economic barriers.



Hope this helps. I will research further and adjust my model to be more accurate if I can.

Answer 2

There really is no way to tell as there is no way to no for sure how fast your body metabolizes the drug. I can tell you from personal experience, hydromorphone will clear out of you pretty fast if you are only using occasionally, like every other week or so. I've taken multiple HydromorphContin 30mg (with the time release still in tact) throughout the course of one day and 2 1/2 days later submitted a drug test at the methadone clinic where I tested negative. Prior to that day of using I had not touched any hydro for over a week.



I would be honest with your sub doc and maybe he can arrange something for you with a different pharmacy or something so that you will have access to your subs on those days you go out of town. Many doctors want to see their patients succeed and if you are honest with them they will try their best to make accommodations for you. Good luck.

Answer 3

Yes: x=0 where x is the number of illegal drugs used.



You are kidding, I hope.