Transcript GroupMeeting_5 - Department of Physics

Transport of Pharmocokinetic
Agents in the Myocardium
Xianfeng Song, Department of Physics, IUB
Keith L. March, IUPUI Medical School
Sima Setayeshgar, Department of Physics, IUB
March 22, 2005
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 of
pericardial access
 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
 Experimental subjects: juvenile farm pigs
 Radiotracer method to determine the spatial concentration profile
from gamma radiation rate, using radio-iodinated test agents
 Insulin-like Growth Factor (125I-IGF, MW: 7734)
 Basic Fibroblast Growth Factor (125I-bFGF, MW: 18000)
 Initial concentration delivered to the pericardial sac at t=0
 200 or 2000 mg in 10 ml of injectate
 Harvesting at t=1h or 24h after delivery
Experimental Procedure

At t = T (1h or 24h), sac fluid is distilled,
several strips at different locations from
myocardium are excised.

Strips are submerged in liquid nitrogen to
fix concentration.

Cylindrical transmyocardial specimens are
sectioned into slices.

Gamma radiation CPM is used to
determine the concentration, CiT(x,T), CP(T).
Mathematical Modeling
 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: diffusion + washout
CT: concentration of agent in tissue
DT: effective diffusion constant in tissue
k: washout rate

Pericardial sac as a drug reservoir (well-mixed and no washout): drug number conservation

Boundary condition: drug current through the boundary layer between pericardial sac and
myocardium is proportional to the concentration difference between them
Fit to experiments
Conce
Error surface
1 Molecule per ml = 1.3
x10-11
picograms per ml
Fit Results
Numerical values for DT, k,  consistent for
IGF, bFGF within experimental errors
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-Einstein 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 x 10-7cm2s-1
 bFGF: D ~ 3 x 10-7cm2s-1
Our fitted values are in order of 10-6 - 10-5 cm2sec-1, 10 to 50 times larger !!
Transport via intramural vasculature
Drug permeates into vasculature from interstitium at high
concentration and permeates out at low concentration, thereby
increasing the effective diffusion constant in the tissue.
Epi
Endo
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 pore size
at the tissue level and therefore mixing of the extracellular volume. This
effective "stirring" results in larger diffusion constants.
Conclusion

Model accounting for effective diffusion and washout is consistent with experiments
despite its simplicity.

First quantitative determination of numerical values for physical parameters
 Effective diffusion constant
IGF: DT = (9±3) x 10-6 cm2s-1, bFGF: DT = (6±3) x 10-6 cm2s-1
 Washout rate: k = (7±2) x 10-4 s-1
 Peri-epicardium boundary permeability:  = (3.8±0.8) x 10-6 cm s-1
Enhanced effective diffusion, allowing for improved transport
Feasibility of computational studies of amount and time course
of pericardial delivery of drugs to cardiac tissue, using
experimentally derived values for physical parameters
Thank you