Transcript GroupMeeting_8 - Department of Physics

Transport Through the Myocardium of
Pharmocokinetic Agents Placed in the
Pericardial Sac:
Insights From Physical Modeling
Xianfeng Song, Department of Physics, Indiana University
Keith L. March, IUPUI Medical School
Sima Setayeshgar, Department of Physics, Indiana University
March 22, 2005
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 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
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
This Talk: Outline
Experiments
Mathematical modeling
Comparison with data
Conclusions
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
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 Da)
 Basic Fibroblast Growth Factor (125I-bFGF, MW: 18000 Da)
 Initial concentration delivered to the pericardial sac at t=0
 200 or 2000 g in 10 ml of injectate
 Harvesting at t=1h or 24h after delivery
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Experimental Procedure
 At t = T (1h or 24h), sac fluid is
distilled: CP(T)
 Tissue strips are submerged in
liquid nitrogen to fix concentration.
 Cylindrical transmyocardial
specimens are sectioned into
slices: CiT(x,T) x denotes
i
CT(x,T) = i CiT(x,T)
x: depth in tissue
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Mathematical Modeling
 Goals
 Determine key physical processes, and extract governing
parameters
 Assess the efficacy of drug penetration in the myocardium
using this mode of delivery
 Key physical processes
 Substrate transport across boundary layer between pericardial
sac and myocardium: 
 Substrate diffusion in myocardium: DT
 Substrate washout in myocardium
(through the intramural vascular and lymphatic capillaries): k
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Idealized Spherical Geometry
Pericardial sac: R2 – R3
Myocardium: R1 – R2
Chamber: 0 – R1
R1 = 2.5cm
R2 = 3.5cm
Vperi= 10ml - 40ml
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
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 at peri/epicardial boundary
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Numerical Fits to Experiments
Conce
Drug Concentration
Error surface
1 Molecule per ml = 1.3 x10-11 picograms per ml
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Fit Results
Numerical values for DT, k,  consistent for
IGF, bFGF to within experimental errors
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Time Course from Simulation
Parameters: DT=7×10-6cm2s-1 k=5×10-4s-1 =3.2×10-6cm2s2
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Effective Diffusion,D*, in Tortuous Media

Stokes-Einstein relation
D: diffusion constant
R: hydrodynamic radius
: viscosity
T: temperature

Diffusion in tortuous medium
D*: effective diffusion constant
D: diffusion constant in fluid
: tortuosity
For myocardium, = 2.11.
(from 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 10-7 cm2s-1
 bFGF: D ~ 3 x 10-7 cm2s-1

Our fitted values are in order of 10-6 - 10-5 cm2sec-1, 10 to 50 times larger !!
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Transport via Intramural Vasculature
Drug permeates into vasculature from extracellular space at high
concentration and permeates out of the vasculature into the extracellular
space at low concentration, thereby increasing the effective diffusion
constant in the tissue.
Epi
Endo
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Diffusion in Active Viscoelastic Media
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 bundles and 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.
Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles
Conclusion

Model accounting for effective diffusion and washout is consistent with
experiments despite its simplicity.

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
IGF: k = (8±3) x 10-4 s-1, bFGF: k = (9±3) x 10-4 s-1
 Peri-epicardial boundary permeability
IGF:  = (2.7±0.8) x 10-6 cm s-1, bFGF:  =
(6.0±1.6) x 10-6 cm s-1

Enhanced effective diffusion, allowing for improved transport

Feasibility of computational studies of amount and time course of
pericardial drug delivery to cardiac tissue, using experimentally
derived
values
physical
Xianfeng
Song, for
Indiana
University,parameters.
Bloomington, March APS Meeting 2005, Los Angeles