1. Xianfeng Song[1], Keith L. March[2], Sima Setayeshgar[1]
Transport Through the Myocardium of Pharmocokinetic Agents Placed in the Pericardial Sac: Insights From Physical Modeling
Xianfeng Song[1], Keith L. March[2], Sima Setayeshgar[1]
[1] Department of Physics, Indiana University, Bloomington, [2]Indiana University School of Medicine, Indianapolis
Pericardial Delivery
Mathematical Modeling
Key Biophysical Processes
Substrate transport across boundary layer between pericardial sac and myocardium, described by the parameter a which is the permeability of the peri/epicardium boundary
Substrate diffusion in the myocardium, described by the effective diffusion constant DT
Substrate washout through the vascular and lymphatic capillaries, described by the rate k
Comparison with Experiment
Discussion
Two possible mechanisms can increase the effective diffusion constant:
1) Transport via Intramural Vasculature
2) Diffusion in Active Viscoelastic Media
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” to deliver anti-arrhythmic and gene therapeutic agents to coronary vasculature and myocardium. This has only recently been proven to be experimentally feasible[1,2].
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
Typical volume for the human pericardial sac is 10-15ml.
[1]Verrier VL, et al., Circulation (1998), 98:
[2]Stoll HP, et al., Clin Cardiol (1999), 22(Suppl-I): I-10-I-16.
Idealized Spherical Geometry
Comparison of experimentally measured concentration profiles in tissue with simulation results from the model using the best fitted parameters. Each slice corresponds to 0.4 mm.
Pericardial sac: R2 – R3
Myocardium: R1 – R2
Chamber: 0 – R1
Experiments
The experiments were performed on juvenile farms pigs using the radiotracer method to determine the concentration of radio-iodinated test agents in the tissue from the rate of radioactive decay. These agents, 125I-IGF (MW=7734 Da) and 125bFGF (MW=18000 Da), are relevant therapeutic growth factors. Different initial amounts (200 and 2000 mg in an injectate volume of 10 ml) were delivered to the pericardial space of an anesthetisized animal at t=0. At t=1 hour or t=24 hours, the heart was harvested.
R1 = 2.5cm
R2 = 3.5cm
Vperi= 10ml - 40ml
Typical c2 surfaces showing distinct minima giving the optimal fit parameters (DT, k , a).
Governing Equations / 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
Heart tissue is a porous medium consisting of extracellular space and muscle fibers. The extracellular space is made up 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. 
IGF_2000_24h
Diffusion in Tortuous Media
Stokes-Einstein relation
D: diffusion constant
R: hydrodynamic radius
u: viscosity
T: temperature
Diffusion in tortuous medium
D*: effective diffusion constant
D: diffusion constant in fluid
l: tortuosity
For myocardium, l= 2.11*.
[*] M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, 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 cm2sec-1, 10 to 50 times larger!
CT(x,t) = i CiT(x,t)
x: depth in tissue i
Conclusions
Model accounting for effective diffusion, washout and finite permeability of peri/epi boundary is consistent with experiments despite its simplicity, allowing quantitative determination of numerical values for physical parameters.
We show:
Samples were taken from the pericardial sac fluid, giving CP(t). Tissue strips were excised and fixed in liquid nitrogen. Cylindrical transmyocardial specimens were sectioned into slices as shown, giving CT(x,t), where x is the thickness through the tissue. We focus on the data obtained from the left ventricle only, and average CTi(x,t) obtained at different (i=1, …, 9) spatial locations to obtain a single concentration profile CT(x,t).
Numerical Results
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 for physical parameters.
Goal
Establish a minimal biophysical model for drug penetration in the myocardium using this mode of delivery and extract numerical values for the governing parameters by comparison with experimental data.
Best fit parameters for each group of experiments: Numerical values for (DT, k, a) are consistent for IGF, bFGF to within experimental errors.