Download Transport of Pharmocokinetic Agents in the Myocardium

Transport of Pharmocokinetic
Agents in the Myocardium
Xianfeng Song
Sima Setayeshgar
Feb. 16, 2004
Pericardial Delivery: Motivation

The pericardial sac is a fluid-filled selfcontained 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: 7734)
 Basic Fibroblast Growth Factor (125I-bFGF, MW: 18000)
Experimental Procedure
First Step, the delivery of radioiodinated test agents to
pericardial sac was performed using a catheter
designed for controlled penetration through the
myocardium
Second Step, wait 1 hour or 24 hours
Third Step, immediately open pigs’ chest, distill sac
fluid, excise several strips at different locations from
myocardium
Forth Step, submerge strips into liquid nitrogen for 3
seconds
Fifth Step, punch out the cylinder transmyocardial
speciments from the strips using cork bores, sectioned
the speciments into slices
Sixth Step, count the individual slice’s gamma
radiation to determine the concentration
Mathematical Model
 Goals
Investigate the efficacy of agent penetration in
myocardium
Extract the key physical parameters
 Key physical processes
Substrate 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 = 3.5cm
Volume 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
1 Molecule per ml =
1.2808×10-11
Error surface
picograms per ml
Fit Results
•IGF, bFGF: test agents
•200,2000: inject quantities (μg)
•1h, 24h: the time of snapshot
Time-course from simulation
Parameters: DT=7×10-6cm2s-1 k=5×10-4s-1 α=3.2×10-6cm2s2
*
Diffusion,D ,in
Effective
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 ~4×10-7cm2s-1
 bFGF: D ~3×10-7cm2s-1

Our fitted values are in order of 10-6 - 10-5 cm2sec-1 !!
Diffusion Increase due to
vasculature trasportation
Drug permeate into vasculature at high concentration and
permeate out at low concentration can also increase the
effective diffusion constant in the tissue.
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.
Contraction
Expansion
Conclusion
 Model is consistent with experiments despite its simplicity.
 Numerical determination of values for physical parameters
 Effective diffusion constant
IGF: DT = (9±3)×10-6cm2s-1, bFGF: DT = (6±3)×10-6cm2s-1
Enhanced diffusion due to motion of heart wall.
 Washout rate: k = (7±2)×10-4s-1
 Peri-epicardium boundary permeability:  = (3.8±0.8)×10-6cm s-1
 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