2. Acknowledgments
2
Research team:
Dr. Ashlee Ford Versypt,
Minu Pilvankar,
Alexandra McPeak,
Jonathan Ramos, Kody
Harper, Michele Higgins,
Grace Harrell, Anya
Zornes, Ye Nguyen
3. High levels of cannabis are proven to impair
driving ability, implying a public safety risk
3
Drug test results were among drivers tested.
Traffic Safety Facts. 2010
In 2009, 1 in 3
drivers tested
positive for drugs
2X
THC presence in the
blood doubles the
likelihood of a fatal
car accident
Wilson FA, Stimpson JP, Pagán JA. (2014)
Biecheler M-B, Peytavin J-F, Facy F, Martineau H. (2008)
Elvik R. (2013)
12.6%
1.5%
Cannabis Alcohol
US Weekend
Nighttime Drivers
Berning, A., Compton, R., Wochinger, K. 2013-
2014 National Roadside Survey of alcohol and
drug use by drivers. 2015.
4. The main psychoactive ingredient, THC, is fat
soluble, making cannabinoid levels difficult to
quantify
4Ashton, C. H. British Journal of Psychiatry, 2001
5. The main psychoactive ingredient, THC, is fat
soluble, making cannabinoid levels difficult to
quantify
5Ashton, C. H. British Journal of Psychiatry, 2001
6. The main psychoactive ingredient, THC, is fat
soluble, making cannabinoid levels difficult to
quantify
6Ashton, C. H. British Journal of Psychiatry, 2001
Current tests:
• Urine
• Hair follicle
• Blood
concentration
7. Two models are utilized for this study:
a forward model and a reverse model
7
Forward Model:
System of ODEs
Time and
method of
dosage
THC blood
concentration
Reverse Model:
Curve-fitting to
create predictive
function
Time since
last dosage
8. This 4-compartment model is utilized as a
surrogate for experimental studies
8
Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
Forward Model
A1 A2
A3
A4
Ka
K23
K32
K24
K42
K20
Oral(F1)
IV(F=100%)
Inhale(F2)
A1=stomach
A2=blood plasma
A3=fatty tissues
A4=brain
F1=oral bioavailability
F2=inhalation bioavailability
9. Step 1: Utilize the 4-compartment forward
model to get THC blood concentration data
9Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
10. Step 1: Utilize the 4-compartment forward
model to get THC blood concentration data
10Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
11. Step 1: Utilize the 4-compartment forward
model to get THC blood concentration data
11Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
Let’s take a chronic user smoking a single cannabis
cigarette after several days of abstinence for example
12. Step 1: Utilize the 4-compartment forward
model to get THC blood concentration data
12Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
Let’s take a chronic user smoking a single cannabis
cigarette after several days of abstinence for example
Key Assumptions:
• Dose size = 40-60 mg/cigarette
• Bioavailability = 11%
• Time to smoke = 5–10 mins
• Volume of blood = 6 L
13. Using data for a chronic cannabis user smoking
a single cannabis cigarette, we created the
following THC concentration curves
13
14. Using data for a chronic cannabis user smoking
a single cannabis cigarette, we created the
following THC concentration curves
14
Blood plasma
15. Using data for a chronic cannabis user smoking
a single cannabis cigarette, we created the
following THC concentration curves
15
Blood plasma
16. Step 2: Utilize MATLAB lsqcurvefit to find a
mathematical model to fit the concentration data
16
Reverse Model
17. Step 2: Utilize MATLAB lsqcurvefit to find a
mathematical model to fit the concentration data
17
For 10 min to
smoke:
coef(1)=-0.5943
coef(2)=1.3336
Resnorm=34.6
Reverse Model
18. As dose size and time of dosage (time to smoke)
are varied, the modeled coefficients also vary
18
19. As dose size and time of dosage (time to smoke)
are varied, the modeled coefficients also vary
19
Coef(2) affected
more by dose size
Coef(1) affected
more by dose
time
20. As dose size and time of dosage (time to smoke)
are varied, the modeled coefficients also vary
20
Coef(2) affected
more by dose size
Coef(1) affected
more by dose
time
Reverse model is more accurate over longer dosing intervals
21. 21
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
22. Advantages
• Forward model serves as a surrogate for
experimental testing and can take into
account multiple routes of dosage
22
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
23. Advantages
• Forward model serves as a surrogate for
experimental testing and can take into
account multiple routes of dosage
• Reverse model for a single dosage is very
accurate
23
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
24. Advantages
• Forward model serves as a surrogate for
experimental testing and can take into
account multiple routes of dosage
• Reverse model for a single dosage is very
accurate
• More accurately models cannabis
consumption than positive/negative tests
24
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
25. Advantages
• Forward model serves as a surrogate for
experimental testing and can take into
account multiple routes of dosage
• Reverse model for a single dosage is very
accurate
• More accurately models cannabis
consumption than positive/negative tests
Future Work
• Develop a model for each
route of dosage and
combine into a single
framework
• Expand model to include ad
libitum cannabis users
25
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
26. Advantages
• Forward model serves as a surrogate for
experimental testing and can take into
account multiple routes of dosage
• Reverse model for a single dosage is very
accurate
• More accurately models cannabis
consumption than positive/negative tests
Future Work
• Develop a model for each
route of dosage and
combine into a single
framework
• Expand model to include ad
libitum cannabis users
26Questions?
Reverse
model
Forward
model
Conclusion: Developed a model capable of
predicting time of last dosage for inhalation of a
single cannabis cigarette
Series of ODEs to find THC
blood concentration given
route of dosage and time
Mathematical
model to predict
time of last
dosage
27.
28. This 4-compartment model is utilized as a
surrogate for experimental studies
28
Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014
Forward Model
Editor's Notes
Hello everyone. Thank you for your time and attention this morning. My name is Jacquelyn Lane. I’m a chemical engineering senior at Oklahoma State University. I’m an undergraduate researcher in Dr. Ashlee Ford Versypt’s group. Today I will be talking to you about mathematical modeling methods used to study cannabinoid pharmacokinetics.
You can see the research team in this photo. As you might have noticed, we get some wind in Oklahoma. I’d like to thank my research team for their support, especially Dr. Ford Versypt, who has been a great mentor in addition to a great professor and researcher.
I’d like to thank Oklahoma State University for their support of undergraduate research and the many opportunities that the university provides.
My research is generously funded by the Lew Wentz Foundation, so a big thank you to them as well.
Cannabis is the most common illicit drug in the United States with an estimated 19.8 million Americans aged 12 years or older smoking cannabis each month in 2013.
The general perception is that driving after alcohol use is dangerous, but what about after cannabis use? According to the 2014 National Survey on Drug Use and Health (NSDUH), 10 million people aged 12 or older reported driving under the influence of illicit drugs during the year prior to being surveyed, with cannabis being by far the most common.
Wilson FA, Stimpson JP, Pagán JA. Fatal crashes from drivers testing positive for drugs in the U.S., 1993-2010. 2014.
Biecheler M-B, Peytavin J-F, Facy F, Martineau H. SAM survey on "drugs and fatal accidents": search of substances consumed and comparison between drivers involved under the influence of alcohol or cannabis. 2008.
Elvik R. Risk of road accident associated with the use of drugs: a systematic review and meta-analysis of evidence from epidemiological studies. 2013.
In a nationwide study, 12.6% of weekend nighttime drivers tested positive for cannabinoids, while only 1.5% tested positive for alcohol. Three independent studies (Wilson, Biecheler, and Elvik) have shown that a driver with THC in their blood is twice as likely to be responsible for a deadly crash or to be killed in a crash.
Cannabis impairs driving ability by slowing reaction time, impairing time and distance judgment, and decreasing coordination. The combination of cannabis with other drugs and/or alcohol impairs driving ability even more.
The main psychoactive ingredient in cannabis is delta-tetrahydrocannabinol (THC). That “high” feeling comes from THC stimulating brain cells to release dopamine. It is difficult to quantify how “high” someone is or predict how much cannabis has been consumed and/or when it was consumed because THC is fat soluble, not water soluble like alcohol.
As you can see in this figure, as THC moves from the bloodstream to the brain, high and low perfusion tissues, and body fat. As you might have also noted, THC remains present in the body for a very long time. It can be detected within 30 days by urine test or up to one year or longer by hair follicle test. These tests, however, are only positive/ negative tests. In order to quantify the amount of THC in the body, blood sample analysis is by far the easiest method.
The main psychoactive ingredient in cannabis is delta-tetrahydrocannabinol (THC). That “high” feeling comes from THC stimulating brain cells to release dopamine. It is difficult to quantify how “high” someone is or predict how much cannabis has been consumed and/or when it was consumed because THC is fat soluble, not water soluble like alcohol.
As you can see in this figure, as THC moves from the bloodstream to the brain, high and low perfusion tissues, and body fat. As you might have also noted, THC remains present in the body for a very long time. It can be detected within 30 days by urine test or up to one year or longer by hair follicle test. These tests, however, are only positive/ negative tests. In order to quantify the amount of THC in the body, blood sample analysis is by far the easiest method.
The main psychoactive ingredient in cannabis is delta-tetrahydrocannabinol (THC). That “high” feeling comes from THC stimulating brain cells to release dopamine. It is difficult to quantify how “high” someone is or predict how much cannabis has been consumed and/or when it was consumed because THC is fat soluble, not water soluble like alcohol.
As you can see in this figure, as THC moves from the bloodstream to the brain, high and low perfusion tissues, and body fat. As you might have also noted, THC remains present in the body for a very long time. It can be detected within 30 days by urine test or up to one year or longer by hair follicle test. These tests, however, are only positive/ negative tests. In order to quantify the amount of THC in the body, blood sample analysis is by far the easiest method.
There are two models that were utilized from this study. The first, the forward model, allows us to find the THC blood concentration at any point in time given the time and method of dosage. As you might know, marijuana usage is currently illegal in Oklahoma, so this forward model is used to create data points much like would be done if we were taking actual blood samples and measuring for THC. This forward model, which is a system of differential equations, has been proven to give very accurate modeling results when compared with actual data.
The second model is the reverse model. This model is a logarithmic mathematical equation that utilizes MATLAB’s built-in lsqcurvefit function to find the coefficients that result I the line of best fit. Finding these coefficients allows us to interpolate backwards to find the time of last dosage.
This 4-compartment model is used to describe the movement of THC throughout the body with time. It can take into account any combination of oral, inhaled, or intravenous cannabinoid dosing. The central compartment is the blood stream. This is the main area of interest in this study. The “K” values represent the rate of transfer into or out of compartments. It is assumed that inhalation and intravenous dosage result in immediate absorption to the blood stream. The dose depot represents the stomach. It takes some time for the THC to be absorbed into the blood stream in the case of cannabis ingestion. K20 represents the metabolism of THC by the liver an d excretion from the body. The peripheral compartments are the brain and other fatty tissues in the body, respectively.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
This 4-compartment model is used to describe the movement of THC throughout the body with time. It can take into account any combination of oral, inhaled, or intravenous cannabinoid dosing. The central compartment is the blood stream. This is the main area of interest in this study. The “K” values represent the rate of transfer into or out of compartments. It is assumed that inhalation and intravenous dosage result in immediate absorption to the blood stream. The dose depot represents the stomach. It takes some time for the THC to be absorbed into the blood stream in the case of cannabis ingestion. K20 represents the metabolism of THC by the liver an d excretion from the body. The peripheral compartments are the brain and other fatty tissues in the body, respectively.
Some other notable constituents in cannabis include 11-hydroxy-THC and 11-nor-9-carboxy-THC; they have not been the focus of this study, but we hope to expand it to include these components as well.
