Mathematical Modeling of Cannabinoid

Pharmacokinetics

School of Chemical Engineering

Oklahoma State University

Jacquelyn I. Lane

Ashlee N. Ford Versypt, Ph.D.

Acknowledgments

2

Research team:

Dr. Ashlee Ford Versypt,

Minu Pilvankar,

Alexandra McPeak,

Jonathan Ramos, Kody

Harper, Michele Higgins,

Grace Harrell, Anya

Zornes, Ye Nguyen

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

2XTHC 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.

The main psychoactive ingredient, THC, is fat

soluble, making cannabinoid levels difficult to

quantify

4Ashton, C. H. British Journal of Psychiatry, 2001

The main psychoactive ingredient, THC, is fat

soluble, making cannabinoid levels difficult to

quantify

5Ashton, C. H. British Journal of Psychiatry, 2001

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

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

This 4-compartment model is utilized as a

surrogate for experimental studies

8Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014

Forward Model

A1 A2

A3

A4

Ka

K23

K32

K24

K42

K20

Ora

l (F1

)

IV (

F=1

00

%)

Inh

ale

(F2

)A1=stomachA2=blood plasmaA3=fatty tissuesA4=brain

F1=oral bioavailabilityF2=inhalation bioavailability

Step 1: Utilize the 4-compartment forward

model to get THC blood concentration data

9Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014

Step 1: Utilize the 4-compartment forward

model to get THC blood concentration data

10Heuberger, J. A., Guan, Z., Oyetayo, O. Clinical Pharmacokinetics, 2014

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

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

Using data for a chronic cannabis user smoking

a single cannabis cigarette, we created the

following THC concentration curves

13

Using data for a chronic cannabis user smoking

a single cannabis cigarette, we created the

following THC concentration curves

14

Blood plasma

Using data for a chronic cannabis user smoking

a single cannabis cigarette, we created the

following THC concentration curves

15

Blood plasma

Step 2: Utilize MATLAB lsqcurvefit to find a

mathematical model to fit the concentration data

16

Reverse Model

Step 2: Utilize MATLAB lsqcurvefit to find a

mathematical model to fit the concentration data

17

For 10 min to smoke:

coef(1)=-0.5943coef(2)=1.3336

Resnorm=34.6

Reverse Model

As dose size and time of dosage (time to smoke)

are varied, the modeled coefficients also vary

18

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

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

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

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

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

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 tests24

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

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

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

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