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