Transport of Pharmocokinetic Agent in the Myocardium

Xianfeng SongSima Setayeshgar

Feb. 16, 2004

Pericardial Delivery: Motivation The pericardial sac is a fluid-filled self-contained space (10ml – 50ml for

human) surrounding the heart. As such, it can be potentially used therapeutically as a “drug reservoir”

Use of pericardial space for delivery of agents (antiarrhythmic, gene therapy) to Coronary vasculature Myocardium

Recently experimental feasibility Verrier VL, Waxman S, Lovett EG, Moreno R. Transatrial access to the

normal pericardial space: a novel approach for diagnostic sampling, pericardiocentesis and therapeutic interventions. Circulation, 1998; 98:2331-2333

Stoll HP, Carlson K, Keefer LK, Hrabie JA, March KL. Pharmacokinetic and consistency of pericardial delivery directed to coronary arteries: direct comparison with endoluminal delivery. Clin Cardiol, 1999; 22(Suppl-I): I-10-I-16

Outline

Experiments on juvenile farm pigs to measure the spatial concentration profile in the myocardium of agents placed in the pericardial space

Mathematical Modeling to investigate the efficacy of agent penetration in myocardial tissue, extract the key physical parameters

Preliminary Results

Conclusions

Experiments Performed by Hans-Peter Stoll, M.D., Keith L. March, M.D., Ph.D.,

Indiana University-Purdue University Indianapolis Medical School

Experimental subjects: juvenile farm pigs

Method: radiotracer method to determine the spatial concentration profile

Radioiodinated test agents Insulin-like Growth Factor (125I-IGF, MW: 7740) Basic Fibroblast Growth Factor (125I-bFGF, MW: 18000)

Brief Introduction of Experimental Procedure

Mathematical ModelGoals

Investigate the efficacy of agent penetration in myocardium

Extract the key physical parametersDetermine appropriate drug quantities and expected

time course of delivery

The key physical processesSubstrate transport across boundary layer between

pericardial sac and myocardium: αSubstrate diffusion in myocardium: DTSubstrate washout through the vascular and lymphatic

capillaries in myocardium: k

Idealized Spherical Geometry

Pericardial sac: R2 – R3

Myocardium: R1 – R2

“Chambers”: 0 – R1

R1 =2.5cmR2 =3.5cmVolume of Pericardial sac:

10ml-40ml

Governing Equations and Boundary conditions

Governing equation in myocardium

CT: concentration of agent in tissue DT: effective diffusion constant in tissue k: washout rate Consider pericardial sac as a drug reservoir (Well mixing and no washout of drug

in pericardial sac)

The drug current flowed through the boundary layer between pericardial sac and myocardium is proportional to the concentration difference between them

Fit to experiments

Fitting Error surface

Fit to experiments (Rough results)

Time-course from simulation

Parameters: DT=7×10-6cm2s-1 k=5×10-4s-1 α=3.2×10-

6cm2s2

D* in tortuous media Fluctuation-dissipation theory D: diffusion constant R: hydrodynamic radius v: T: temperature

In tortuous media

D*: diffusion constant in tortuous media D: diffusion constant in fluid λ: tortuosity

In myocardium, λ=2.11 (M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, Diffusion of sucrose, sodium, and water in ventricular myocardium, American Joural of Physiology, Vol 227, No. 5, Nov. 1974 )

Estimate the diffusion constant IGF bFGF

Our fitted values are in order of 10-6 cm2sec-1

Contradiction?

Speculation on mixing due to viscoelastic motion of heart

The tissue is a porous medium consisting of extracellular space and muscle fibers. The extracellular space consists of an incompressible fluid (mostly water)

Effective stirring: the expansion and contraction of the muscle cells leads to changes in the pore sizes and therefore mixing of the extracellular volume. This effective "stirring" could be responsible for the larger diffusion constants. 

ConclusionModel is consistent with experiments despite its

simplicity

The effective diffusion constants for two drugs (IGF,bFGF) are both in the order of

The wash out rate for both drugs are in the order of

……

Thank you