1. Pharmacokinetics Part 1: Principles
Abdulfattah Alhazmi, MSc. Pharm.
Faculty of Pharmacy Dept. of Clinical Pharmacy
CIIT Centers for Health Research February 6-10, 2006

2. CIIT Centers for Health Research February 6-10, 2006

3. Pharmacokinetics
Studies of the change in chemical distribution over time in the body
Explores the quantitative relationship between Absorption, Distribution, Metabolism, and Excretion of a given chemical
Classical models
‘Data-based’, empirical compartments
Describes movement of chemicals with fitted rate constants
Physiologically-based models:
Compartments are based on real tissue volumes
Mechanistically based description of chemical movement using tissue blood flow and simulated in vivo transport processes.
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4. Pharmacokinetics Blood Conc - mg/L
The study of the quantitative relationships between the absorption,
distribution, metabolism, and eliminations (A-D-M-E) of chemicals
from the body.
(Chemical)
intravenous
inhalation
time - min
Blood Conc - mg/L
k(abs)
k(elim)
urine,
feces,
air, etc.
C1 V1
k21
k12
C2 V2
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5. Conventional Compartmental PK ModelingX
Tissue Concentration
time
k12
k21
kout KO A1 A2 X
Tissue Concentration
time
Collect
Data
Select
Model
Fit Model to Data
Ct = A e –ka·t + B e-kb·t
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6. Example of Simple Kinetic Model: One-compartment model with bolus dose
Purpose: In a simple (1-compartment) system, determine volume of distribution
Volume?
Dose
Terminology:
Compartment = a theoretical volume for chemical
Steady-state = no net change of concentration
Bolus dose = instantaneous input into compartment
Method: 1. Dose: Add known amount (A) of chemical
2. Experiment: Measure concentration of chemical (C) in compartment
3. Calculate: A ‘compartmental’ Volume (V)
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7. Example of Simple Kinetic Model: One-compartment model with bolus dose
Basic assumption:
Well stirred, instant equal distribution within entire compartment
Volume of distribution = A/C
In this classical model, V is an operational volume
V depends on site of measurement
This simple calculation only works IF:
Compound is rapidly and uniformly distributed
The amount of chemical is known
The concentration of the solution is known.
What happens if the chemical is able to leave the container?
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8. Describing the Rates of Chemical Processes - 1 Chemical in the System
Rate equations:
Describe movement of chemical between compartments
The previous example had instantaneous dosing
Now, we need to describe the rate of loss from the compartment
Zero-order process:
rate is constant, does not depend on chemical concentration
rate = k x C0 = k
First-order process:
rate is proportional to concentration of ONE chemical
rate = k x C1
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9. Describing the Rates of Chemical Processes - 2 Chemical Systems
Second-order process:
rate is proportional to concentration of both chemicals
Rate = k x C1 x C2
Saturable processes*:
Rate is dependent on interaction of two chemicals
One reactant, the enzyme, is constant
Described using Michaelis-Menten* equation
Rate = (Vmaxx C) / ( C + Km)
*Michaelis-Menten kinetics can describe:
Metabolism
Carrier-mediated transport across membranes
Excretion
M-M kinetics
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10. 1-Comp model with bolus dose and 1st order elimination
Purpose: Examine how concentration changes with time
Conc?
Dose
Mass-balance equation (change in C over time):
- dA/dt = -ke x A, or
- dC/dt = -ke x C
where ke = elimination rate constant
Concentration;
- Rearrange and integrate above rate equation
C = C0 x e-ke · t, or
ln C = ln C0 - ke · t
Half-life (t1/2):
-Time to reduce concentration by 50%
-replace C with C0/2 and solve for t
t1/2 = (ln 2)/ke = 0.693/ke
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11. 1-Comp model with bolus dose and 1st order elimination
Clearance: volume cleared per time unit
- if ke = fraction of volume cleared per time unit,
ke = CL/V (CL=ke*V)
Dose
Conc
Calculating Clearance using Area Under the Curve (AUC):
AUC = average concentration
- integral of the concentration
-  C dt
AUC
CL = volume cleared over time (L/min)
dA/dt = - keA = -ke V C
dA/dt = - CL · C
 dA = - CL  C dt
Dose = CL · AUC
CL = Dose / AUC
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12. 1-Comp model with continuous infusion and 1st order elimination
Calculating Clearance at Steady State:
At steady state, there is no net change in concentration:
dC/dt = k0/V – ke · C = 0
Rearrange above equation:
k0/V = ke · Css
Since CL = ke · V ,
CL = k0/Css
Steady State
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13. 2-Comp model with bolus dose and 1st order elimination
Calculating Rate of Change in Chemical:
Central Compartment (C1):
dC1/dt = k21· C2 - k12· C1 - ke· C1
Peripheral (Deep) Compartment (C2):
dC2/dt = k12· C1 - k21· C2 1 2 ke
k12
k21
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14. Linear and Non-linear Kinetics
All elimination and distribution kinetics are 1st order
Double dose double concentration
Non-linear:
At least one process is NOT 1st order
No direct proportionality between dose and compartment concentration 1
100 10
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15. PBPK Modeling
Pharmacokinetic modeling is a valuable tool for evaluating tissue dose under various exposure conditions in different animal species.
To develop a full understanding of the biological responses caused by exposure to toxic chemicals, it is necessary to understand the processes that determine tissue dose and the interactions of chemical with tissues.
Physiological modeling approaches are used to uncover the biological determinants of chemical disposition
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16. Physiologically Based PharmacokineticsQp Ci Cx Qc Qc
Lung Ca
Cvl QL
Liver
Cvf Qf
Fat
Cvr Qr
Rapidly perfused (brain, kidney, etc.)
Slowly perfused (muscle, bone, etc.)
Cvs Qs
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17. PBPK Models Simple model for inhalation Building a PBPK Model:
Define model compartments
Represent tissues
Write differential equation for each compartment
Assign parameter values to compartments
Compartments have defined volumes, blood flows
Solve equations for concentration
Numerical integration software (e.g. Berkeley Madonna, ACSL)
Simple model for inhalation
CIIT Centers for Health Research February 6-10, 2006

18. Parameterizing the Model:
Experimental Determination
Partition Coefficients:
in vitro: vial equilibration (CTissue/Cair) dialysis (CTissue/Cbuffer) ultrafiltration (CTissue/Cbuffer)
in vivo: steady state (CTissue/CBlood)
Metabolism:
in vitro: tissue homogenate cell suspension tissue slice cell gas uptake
in vivo: direct measurement of metabolites
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19. Physiologically Based Pharmacokinetic (PBPK) Modeling
Metabolic Constants
Tissue Solubility
Tissue Volumes
Blood and Air Flows
Experimental System
Model Equations X
Tissue Concentration
Time
You can be wrong!
Liver
Fat
Body
Lung
Air
Define Realistic Model
Collect Needed
Data
Make
Predictions
Refine Model Structure
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20. Approach for Developing a PBPK Model
Problem
Identification
Literature
Evaluation
Biochemical
Constants
Model
Formulation
Simulation
Compare to
Kinetic Data
Design/Conduct
Critical Experiments
Physiological
Mechanisms
of Toxicity
Validate
Extrapolation
to Humans
Refine
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21. Models in Perspective
“…no model can be said to be ‘correct’. The role of any model is to provide a framework for viewing known facts and to suggest experiments.”
-- Suresh Moolgavkar
“All models are wrong and some are useful.”
-- George Box
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22. PBPK Model Compartment Types - Storage compartment
Same as 1-compartment model with continuous infusion QT CA
CVT
Rate in = QT · CA
where QT = tissue blood flow, CA = arterial blood conc
Rate out = QT · CVT = QT · CT/PT
where CVT = conc in tissue blood, CT = conc in tissue, PT = partition coefficient
Assume Well-stirred compartment, so that,
CVT = CT/PT
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23. PBPK Model Compartment Types - Storage compartment
Same as 1-compartment model with continuous infusion QT CA
CVT
Calculating Change in Amount:
Change in amount = rate in – rate out
dA/dt = QT x (CA – CT/PT)
dC/dt = QT x (CA – CT/PT) /V
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24. Description for a Single Tissue Compartment
Terms
Qt = tissue blood flow
Cvt = venous blood
concentration
QtCart
QtCvt
Vt; At; Pt
Pt = tissue blood partition
coefficient
Vt = volume of tissue
Tissue
At = amount of chemical
in tissue
mass-balance equation: dAt = Vt dCt = QtCart - QtCvt dt dt
Cvt = Ct/Pt
(venous equilibration assumption)
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25. Then used in toxicology..... Is any of this really new?
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle Tissue
Group
Richly Perfused
Tissue Group
Liver
Metabolizing ( )
Metabolites
Vmax Km
Cart Ql Qr Qm Qt Qc
Calv (Cart/Pb)
Qalv
Cinh
Cven
Cvt
Cvm
Cvr
Cvl
Ramsey and Andersen (1984)
CIIT Centers for Health Research February 6-10, 2006

26. Styrene & Saturable metabolism
rate of change
of amount
in liver
rate of uptake
in arterial
blood
rate of loss
in venous
blood = - -
rate of loss
by metabolism
dAl = Ql (Ca - Cvl) - Vm Cvl
Km + Cvl dt
Equations solved by numerical integration to simulate kinetic behavior.
With venous equilibration, flow limited assumptions.
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27. Dose Extrapolation – Styrene
How does it work? 25 20 15 10 5
100 1
0.1
0.01
0.001
TIME - hours
Venous Concentration – mg/lier blood
Conc = 80 ppm
Conc = 1200 ppm
Conc = 600 ppm
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28. What do we need to add/change in the models to incorporate another dose route – iv or oral?
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle Tissue
Group
Richly Perfused
Tissue Group
Liver
Metabolizing ( )
Metabolites
Vmax Km
Cart Ql Qr Qm Qt Qc
Calv (Cart/Pb)
Qalv
Cinh
Cven
Cvt
Cvm
Cvr
Cvl IV
Oral
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29. Styrene - Dose Route Extrapolation
What do we need to add/change in the models to incorporate these dose routes?
100 10 IV
Oral 10
1.0
Styrene Concentration (mg/l)
Styrene Concentration (mg/l)
1.0
0.1
0.1
0.01
0.01
0.6
1.2
1.8
2.4
3.0
3.6
0.4
0.8
1.2
1.6
2.0
2.4
2.8
Hours
Hours
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30. What do we need to add/change in the models to describe another animal species?
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle Tissue
Group
Richly Perfused
Tissue Group
Liver
Metabolizing ( )
Metabolites
Vmax Km
Cart Ql Qr Qm Qt Qc
Calv (Cart/Pb)
Qalv
Cinh
Cven
Cvt
Cvm
Cvr
Cvl
Sizes
Flows
Metabolic Constants
CIIT Centers for Health Research February 6-10, 2006

31. Styrene - Interspecies Extrapolation
What do we need to add/change in the models to change animal species? 51
376
216
0.1
0.01
0.001
0.0001
1.5
3.0
4.5
6.0
7.5
9.0
Hours
Styrene Concentration (mg/l)
Blood
80 ppm
Exhaled Air 8 16 24 32 40 48
0.0001
0.001
0.01
0.1
1.0 10
Hours
Styrene Concentration (mg/l)
CIIT Centers for Health Research February 6-10, 2006

32. ADVANTAGES OF SIMULATION MODELING IN PHYSIOLOGY AND ALSO IN PHARMACOKINETICS & RISK ASSESSMENT
Codification of facts and beliefs (organize available information)
Expose contradictions in existing data/beliefs
Explore implications of beliefs about the chemical
Expose serious data gaps limiting use of the model
Predict response under new/inaccessible conditions
Identify essentials of system structure
Provide representation of present state of knowledge
Suggest and prioritize new experiments
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33. A ‘Systems’ Approach for Dose Response
Uptake
Absorption
Distribution
Excretion
DRE
TCDD
Ligand
Ah Receptor
Transcription
Other
Stimulus
MAPK
Adaptor
RTK
Metabolism
Interaction w/ cellular networks
Effects
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34. Biological Interaction
An Alternate View of PK and PD processes – Systems and Perturbations
Inputs
Biological
Function
Impaired
Adaptation
Disease
Morbidity &
Mortality
Exposure
Tissue Dose
Biological Interaction
Perturbation
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35. Physiological Pharmacokinetic Modeling Principles
References
Andersen ME, Clewell HJ, Frederick CB Applying simulation modeling to problems in toxicology and risk assessment -- a short perspective. Toxicol Appl Pharmacol 133:
Brown, R.P., Delp, M.D., Lindstedt, S.L., Rhomberg, L.R., and Beliles, R.P Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Indust Health 13(4):
Clewell, H.J., and Andersen, M.E Risk Assessment Extrapolations and Physiological Modeling. Toxicol Ind Health, 1(4):
Clewell, H.J., Andersen, M.E., Barton, H.A., A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environ. Health Perspect. 110, 85–93.
Dedrick, R.L Animal scale up. J Pharmacokinet Biopharm 1:
Dedrick, R.L., and Bischoff, K.B Species similarities in pharmacokinetics. Fed Proc 39:54 59.
Gerlowski, L.E. and Jain, R. J. (1983). Physiologically based pharmacokinetic modeling: principles and applications. J. Pharm. Sci., 72: 1103.
Ramsey, J.C. and Andersen, M.E. (1984). A physiologically based description of the inhalation pharmacokinetics of styrene in rats and humans. Toxicol. Appl. Pharmacol. 73, 159.
Reddy, M.B. (2005). PBPK modeling approaches for special applications: Dermal exposure models. In: Physiologically Based Pharmacokinetic Modeling: Science and Applications, eds. M.B. Reddy, R.S.H. Yang, H.J. Clewell, III, and M.E. Andersen. John Wiley & Sons, Hoboken, New Jersey, pp
Yates, F.E. (1978). Good manners in good modeling: mathematical models and computer simulation of physiological systems. Amer. J. Physiol., 234, R159-R
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