Transport of Pharmocokinetic Agents in the Myocardium

Xianfeng Song

Sima Setayeshgar

Feb. 16, 2004

Pericardial Delivery: Motivation

The pericardial sac is a fluid-filled self-contained space surrounding the heart. As such, it can be potentially used therapeutically as a “drug reservoir.”

Delivery of anti-arrhythmic, gene therapeutic agents to Coronary vasculature Myocardium

Recent experimental feasibility Verrier VL, et al., “Transatrial access to the normal

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

Stoll HP, et al., “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. Vperi (human) =10ml – 50ml

This work: 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. and Keith L. March, M.D., Ph.D. at Indiana University-Purdue University Indianapolis Medical School

Experimental subjects: juvenile farm pigs

Radiotracer method to determine the spatial concentration profile from gamma radiation rate

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

Experimental Procedure

Mathematical Model

GoalsInvestigate the efficacy of agent penetration in

myocardiumExtract the key physical parameters

Key physical processesSubstrate transport across boundary layer between

pericardial sac and myocardium: Substrate diffusion in myocardium: DT

Substrate washout in myocardium (through the vascular and lymphatic capillaries): k

Idealized Spherical Geometry

Pericardial sac: R2 – R3

Myocardium: R1 – R2

“Chambers”: 0 – R1

R1 = 2.5cm

R2 = 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 Results

Time-course from simulation

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

6cm2s2

Effective Diffusion,D*,in tortuous media

Stokes relation D: diffusion constant R: hydrodynamic radius : viscosity T: temperature

In tortuous media

D*: effective diffusion constant D: diffusion constant in fluid

: tortuosity

For myocardium, = 2.11. (M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, “Diffusion of sucrose, sodium, and water in ventricular

myocardium, American Joural of Physiology,” 227(5), 1974 )

Numerical estimates for diffusion constants IGF : D ~ bFGF: D ~

Our fitted values are in order of 10-6 - 10-5 cm2sec-1 !!

Diffusion in an active viscoelastic medium

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

Expansion and contraction of the fiber sheets leads to changes in the gross pore sizes and therefore mixing of the extracellular volume. This effective "stirring" results in larger diffusion constants. 

Conclusion

Model is consistent with experiments despite its simplicity.

Numerical determination of values for physical parameters Effective diffusion constant IGF: D = , bFGF: D =

Enhanced diffusion due to motion of heart wall.

Washout rate: k = Peri-epicardium boundary permeability: =

Feasibility of computational studies of amount and time course of pericardial drug delivery of drugs to cardiac tissue, using realistic values for physical parameters

Thank you