Transcript Drug-v3 - Department of Physics

Transport Through the Myocardium of Pharmocokinetic Agents Placed in the Pericardial Sac:
Insights From Physical Modeling
Xianfeng
[1]
Mathematical Modeling
The pericardial sac is a fluid-filled selfcontained 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].
[1]Verrier
VL, et al., Circulation (1998), 98:2331-2333.
[2]Stoll HP, et al., Clin Cardiol (1999), 22(Suppl-I): I-10-I-16.
The experiments were performed on juvenile farms pigs using
the radiotracer method to determine the concentration of radioiodinated 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.
CT(x,t) = i CiT(x,t)
[2]Indiana
University School of Medicine, Indianapolis
Comparison with Experiment
Substrate transport across boundary layer between pericardial sac
and myocardium, described by the parameter a which is the
permeability of the peri/epicardium boundary
1) 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
Endo increasing the effective diffusion
constant in the tissue
Epi
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
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.
2) Diffusion in Active Viscoelastic Media
Ty p i c a l c 2 s u r f a c e s
showing distinct minima
giving the optimal fit
parameters (D T, k , a ).
R1 = 2.5cm
R2 = 3.5cm
Vperi= 10ml - 40ml
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.
Governing Equations / Boundary Conditions
Governing equation in myocardium (diffusion + washout)
IGF_2000_24h
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
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
[*] M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, American Joural of Physiology,” 227(5), 1974.
Numerical Results
Goal
Numerical estimates for diffusion constants
IGF : D* ~ 4 x 10-7 cm2s-1
bFGF: D* ~ 3 x 10-7 cm2s-1
Best fit parameters for each group of experiments: Numerical values for
(DT, k, a) are consistent for IGF, bFGF to within experimental errors.
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.
Diffusion in Tortuous Media
For myocardium, l = 2.11*.
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.
Discussion
Key Biophysical Processes
x: depth in tissue
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).
Sima
[1]
Setayeshgar
Two possible mechanisms can increase the
effective diffusion constant:
Pericardial sac: R2 – R3
Myocardium: R1 – R2
Chamber: 0 – R1
Experiments
i
Keith L.
[2]
March ,
Department of Physics, Indiana University, Bloomington,
Pericardial Delivery
Typical volume for the human
pericardial sac is 10-15ml.
[1]
Song ,
Our fitted values are in order of 10-6 - 10-5 cm2sec-1,
10 to 50 times larger!
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:
 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.