Therapeutic window
Rat, 6 mg/kg IV injection of Cyclosporin A
0.0060.002
0.016
0.020
0.031
Adult Rat Regional Blood Flow
(L/min)
0.210.59
0.911.18
0.99
Adult HumanRegional Blood Flow
(L/min)
0.0560.071
0.134
0.050
0.305
Rhesus MonkeyRegional Blood Flow
(L/min)
Parameter Estimation In Global Pharmacokinetic Modelsfor Drug Delivery
A. Mošať , E. Lueshen, C. Hall, and A. LinningerLaboratory for Product and Process Design, Dept. of Bioengineering, University of Illinois at Chicago
2010 AIChE Annual Meeting, Salt Lake City, UT
Rationale Mathematical Model
We propose a pharmacokinetic modeling framework
Create global pharmacokinetic models based onbiochemical, anatomical and physiological data.
Propose efficient drug dosing regimes.
- Accurate drug dosage needed for therapeutic effect- Animal data extrapolation by weight inaccurate- Biochemical drug interactions in vivo are complex
Measures to Optimize Dosage
Allometric:
0
φ φ
QuantifyDrug bioavailability in tissues
Blood and plasma concentrationsTherapeutic/toxic dosage levels
Extrapolation of animal dataInter- and intra-species scaling
Observe Physical PhenomenaDrug administration in animals
Drug concentration in tissuesMRI, organ volumes
Flow Rates
Create a PBPK ModelObtain MRI based parameters
Input parameters into PBPK modelCalculate tissue and organ kinetic rates
Simulate
Process Flow Diagram
0
φ φ
Biochemical & Physiological:
0
a a A φ b
Future Work
- Develop biochemical, anatomical and physiological (BAP) scaling laws
- Create scalable models for different species
AgeWeight
Case Study – Cyclosporin A
Tanaka’s PBPK ModelOur PBPK Model
Reaction Kinetics
Fitted Results
- Conservation of mass- Scalable results- First principle kinetics- Simpler model construction
Benefits of Our Framework:
Step 1: Scaling Laws
,( ( , , ), , ) ( , ) ( , )N
M i E ik
i
min t tF φ x t k t k φ x φ xk
First principle network constraints . . M Ms t A bφ φ
Objective function of location x, time t:
Step 2: Transport and Kinetic Inversion Problem
Therapy Design
Scale-Up of Pharmacokinetic Models
The framework can be used in calculations of:
- Administration route
- Therapeutic dosage amount
- Maximizing drug’s efficacy and bioavailability
- Minimizing toxic effects
- Interactions of several drugs in vivo
LPPDLaboratory for Product
and Process DesignUNIVERSITY OF ILLINOIS
AT CHICAGO
( , )MM
t
φQ φ R k x M
0
P
P QConvection
termsMass transfer
Reactionterms
Results