pharmacokinetics part 1: principles
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Pharmacokinetics Part 1: Principles. Abdulfattah Alhazmi , MSc. Pharm. Faculty of Pharmacy Dept. of Clinical Pharmacy. Pharmacokinetics. Studies of the change in chemical distribution over time in the body - PowerPoint PPT PresentationTRANSCRIPT
Pharmacokinetics
Part 1: Principles
Abdulfattah Alhazmi, MSc. Pharm.Faculty of Pharmacy
Dept. of Clinical Pharmacy
External exposure
Absorbed dose
Target dose
Tissue interaction
Early eff ect
Adverse eff ect
Disease/ injury
Pharmacokinetics
Pharmacodynamics
External exposure
Absorbed dose
Target dose
Tissue interaction
Early eff ect
Adverse eff ect
Disease/ injury
Pharmacokinetics
Pharmacodynamics
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.
PharmacokineticsThe study of the quantitative relationships between the absorption,distribution, metabolism, and eliminations (A-D-M-E) of chemicalsfrom the body.
(Chemical)
k(abs)
C1 V1
C2 V2
k21 k12
k(elim) urine,feces,air, etc.
intravenous
inhalation
time - min
Bloo
d Co
nc -
mg/
L
Conventional Compartmental PK Modeling
CollectData
Select Model
Fit Model to Data
Ct = A e –ka·t + B e-kb·t
X
X
X
X
XX
X X
Tiss
ue C
once
ntra
tion
time
k12k21
koutKO A1
A2
X
X
Tiss
ue C
once
ntra
tion
time
XX X
X
XX
Example of Simple Kinetic Model:One-compartment model with bolus
dose
Terminology:Compartment = a theoretical volume for chemicalSteady-state = no net change of concentrationBolus dose = instantaneous input into compartment
Method:1. Dose: Add known amount (A) of chemical2. Experiment: Measure concentration of chemical (C) in compartment3. Calculate: A ‘compartmental’ Volume (V)
Volume?
DosePurpose: In a simple (1-compartment) system, determine volume of distribution
• 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.
Example of Simple Kinetic Model:One-compartment model with
bolus dose
What happens if the chemical is able to leave the container?
• 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
Describing the Rates of Chemical Processes
- 1 Chemical in the System
Describing the Rates of Chemical Processes
- 2 Chemical Systems• Second-order process:
– rate is proportional to concentration of both chemicalsRate = 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
0
5
10
0 5 10 15 20 25C
Rate
1-Comp model with bolus dose and 1st order elimination
Purpose: Examine how concentration changes with time
Conc?
DoseMass-balance equation (change in C over time): - dA/dt = -ke x A, or - dC/dt = -ke x C
where ke = elimination rate constantConcentration;
- Rearrange and integrate above rate equation C = C0 x e-ke · t, orln 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
1-Comp model with bolus dose and 1st order eliminationClearance: volume cleared per time unit - if ke = fraction of volume cleared per time unit,
ke = CL/V (CL=ke*V)
Conc
Dose
Calculating Clearance using Area Under the Curve (AUC): AUC = average concentration
- integral of the concentration - C dt
CL = volume cleared over time (L/min)dA/dt = - keA = -ke V CdA/dt = - CL · C dA = - CL C dt Dose = CL · AUCCL = Dose / AUC
0
5
10
0 5 10 15 20 25Time
Conc
.
AUC
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
Time
Conc
.
Steady State
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
Time
Conc
.
• Linear:– 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
Linear and Non-linear Kinetics
0
10
20
30
0 5 10 15 20 25Time
Conc
.
1
10
100
0 5 10 15 20 25Time
Conc
.
1
10
100
0 5 10 15 20 25Time
Conc
.
Dose
AUC
Time
Conc
.
1
100
10
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
Physiologically Based Pharmacokinetics
Qc
Cvl
Cvf
Cvr
Cvs
Qc
Ca
QL
Qf
Qr
Qs
Ci Cx
Qp
Lung
Liver
Fat
Rapidly perfused (brain, kidney, etc.)
Slowly perfused (muscle, bone, etc.)
PBPK ModelsBuilding a PBPK Model:1. Define model compartments
– Represent tissues
2. Write differential equation for each compartment
3. Assign parameter values to compartments– Compartments have defined
volumes, blood flows
4. Solve equations for concentration– Numerical integration
software (e.g. Berkeley Madonna, ACSL)
Veno
us s
ide Arterial side
Lungs
Other
Fat tissues
Liver
Chemicalin air
EliminationVe
nous
sid
e Arterial side
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Simple model for inhalation
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
Physiologically Based Pharmacokinetic (PBPK) Modeling
Define Realistic Model
Collect NeededData
Refine Model Structure
Make Predictions
Metabolic ConstantsTissue SolubilityTissue Volumes
Blood and Air FlowsExperimental System
Model EquationsX
X
X
X
XX
X X
Tiss
ue C
once
ntra
tion
Time
You can be wrong!
Liver
Fat
Body
Lung
Air
Approach for Developing a PBPK ModelProblem
Identification
LiteratureEvaluation
BiochemicalConstants
ModelFormulation
Simulation
Compare toKinetic Data
Design/ConductCritical Experiments
PhysiologicalConstants
Mechanismsof Toxicity
ValidateModel
Extrapolationto Humans
RefineModel
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
PBPK Model Compartment Types- Storage compartment
• 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
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Same as 1-compartment model with continuous infusion
QTQTCACVT
PBPK Model Compartment Types- Storage compartment
• 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
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Lungs
Other
Fat tissues
Liver
Chemicalin air
Elimination
Same as 1-compartment model with continuous infusion
QTQTCACVT
Time
Conc
. CA
CVT
Time
Conc
. CA
CVT
Description for a Single Tissue Compartment
(venous equilibration assumption)
Qt = tissue blood flowCvt = venous blood concentrationPt = tissue blood partition coefficientVt = volume of tissueAt = amount of chemical in tissue
QtCart QtCvtVt; At; Pt
Tissue
Cvt = Ct/Pt
mass-balance equation: dAt = Vt dCt = QtCart - QtCvt
dt dt
Terms
Then used in toxicology.....Is any of this really new?
Ramsey and Andersen (1984)
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle TissueGroup
Richly PerfusedTissue Group
LiverMetabolizingTissue Group( )
MetabolitesVmax
Km
Cart
Ql
Cart
Qr
Cart
Qm
Cart
Qt
Cart
Qc
Calv (Cart/Pb)
QalvQalv
Cinh
Qc
Cven
Cvt
Cvm
Cvr
Cvl
• Equations solved by numerical integration to simulate kinetic behavior.
• With venous equilibration, flow limited assumptions.
Styrene & Saturable metabolism
rate of change of amount
in liver
rate of uptake in arterial
blood
rate of loss in venous
bloodrate of loss
by metabolism= - -
dAl = Ql (Ca - Cvl) - Vm Cvl
dt Km + Cvl
2520151050
100
10
1
0.1
0.01
0.001
TIME - hours
Veno
us C
once
ntra
tion
– m
g/lie
r bl
ood
Conc = 80 ppm
Conc = 1200 ppmConc = 600 ppm
Dose Extrapolation – StyreneHow does it work?
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle TissueGroup
Richly PerfusedTissue Group
LiverMetabolizingTissue Group( )
MetabolitesVmax
Km
Cart
Ql
Cart
Qr
Cart
Qm
Cart
Qt
Cart
Qc
Calv (Cart/Pb)
QalvQalv
Cinh
Qc
Cven
Cvt
Cvm
Cvr
Cvl
What do we need to add/change in the models to incorporate another dose
route – iv or oral?
IV
Oral
Styrene - Dose Route Extrapolation
100
10
1.0
0.1
0.010 0.6 1.2 1.8 2.4 3.0 3.6
Hours
IV
Styr
ene
Conc
entr
atio
n (m
g/l) 10
1.0
0.1
0.010 0.4 0.8 1.2 1.6 2.0 2.4
Hours
Oral
Styr
ene
Conc
entr
atio
n (m
g/l)
2.8
What do we need to add/change in the models to incorporate these dose routes?
Alveolar Space
Lung Blood
Fat Tissue Group
Muscle TissueGroup
Richly PerfusedTissue Group
LiverMetabolizingTissue Group( )
MetabolitesVmax
Km
Cart
Ql
Cart
Qr
Cart
Qm
Cart
Qt
Cart
Qc
Calv (Cart/Pb)
QalvQalv
Cinh
Qc
Cven
Cvt
Cvm
Cvr
Cvl
What do we need to add/change in the models to describe another animal
species?
SizesFlowsMetabolic Constants
Styrene - Interspecies Extrapolation
51
376
216
0.1
0.01
0.001
0.00010 1.5 3.0 4.5 6.0 7.5 9.0
Hours
Styr
ene
Conc
entr
atio
n (m
g/l)
Blood80 ppm
Exhaled Air
0 8 16 24 32 40 480.00001
0.0001
0.001
0.01
0.1
1.0
10
Hours
Styr
ene
Conc
entr
atio
n (m
g/l)
What do we need to add/change in the models to change animal species?
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/beliefsExplore implications of beliefs about the chemicalExpose serious data gaps limiting use of the modelPredict response under new/inaccessible conditionsIdentify essentials of system structureProvide representation of present state of knowledgeSuggest and prioritize new experiments
A ‘Systems’ Approach for Dose Response
DRE
TCDD Ligand
Ah Receptor
Transcription
OtherStimulus
MAPK
Adaptor
RTK
Uptake
Absorption
Distribution
Metabolism
Excretion
Interaction w/ cellular networks
Effects
Inputs BiologicalFunction
ImpairedFunction
Adaptation DiseaseMorbidity &
Mortality
Exposure
Tissue Dose
Biological Interaction
Perturbation
An Alternate View of PK and PD processes – Systems and Perturbations
Physiological Pharmacokinetic Modeling Principles
ReferencesAndersen ME, Clewell HJ, Frederick CB. 1995. Applying simulation modeling to problems in toxicology and risk assessment -- a short perspective. Toxicol Appl Pharmacol 133:181-187.Brown, R.P., Delp, M.D., Lindstedt, S.L., Rhomberg, L.R., and Beliles, R.P. 1997. Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Indust Health 13(4):407-484.Clewell, H.J., and Andersen, M.E. 1985. Risk Assessment Extrapolations and Physiological Modeling. Toxicol Ind Health, 1(4):111 131.Clewell, H.J., Andersen, M.E., Barton, H.A., 2002. A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environ. Health Perspect. 110, 85–93.Dedrick, R.L. 1973. Animal scale up. J Pharmacokinet Biopharm 1:435 461.Dedrick, R.L., and Bischoff, K.B. 1980. 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. 375-387.Yates, F.E. (1978). Good manners in good modeling: mathematical models and computer simulation of physiological systems. Amer. J. Physiol., 234, R159-R160. 1978.