Transcript Drug-v2 - Department of Physics

Transport Through the Myocardium of Pharmocokinetic Agents Placed in the Pericardial Sac:
Insights From Physical Modeling
Xianfeng
[1]
Pericardial Delivery
[1]Verrier
[2]Stoll
Keith L.
VL, et al., Circulation (1998) 98:2331-2333.
[2]
March ,
Sima
Department of Physics, Indiana University,
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 recently been
proved to be experimentally feasible[1,2].
A typical volume for human
pericardial sac is 10-15ml
[1]
Song ,
[1]
Setayeshgar
[2]IUPUI
Medical School
Comparison with experiment
Discussion
Two possible mechanisms can increase the
effective diffusion constant!
The key 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
Transport via Intramural Vasculature
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
Endo
HP, et al., Clin Cardiol (1999) 22(Suppl-I): I-10-I-16
Idealized Spherical Geometry
Pericardial sac: R2 – R3
Myocardium: R1 – R2
Chamber: 0 – R1
Experimental Methods
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
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)
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.
R1 = 2.5cm
R2 = 3.5cm
Vperi= 10ml - 40ml
Typical chi-square surfaces (in
this case, for IGF_2000_24h),
showing distinct minima giving
the optimal fit parameters (D,
k , a).
Governing Equations and Boundary
Conditions
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.
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
Effective Diffusion,D* in
Tortuous Media
Stokes-Einstein relation
Boundary condition: drug current at peri/epicardial
boundary
D: diffusion constant
R: hydrodynamic radius
u: viscosity
T: temperature
Diffusion in tortuous medium
CT(x,T) = i CiT(x,T)
D*: effective diffusion constant
D: diffusion constant in fluid
l: tortuosity
x: depth in tissue
For myocardium, l = 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 )
Result
Our Goal
Our goals are to establish a minimal physical model for drug
penetration in the myocardium using this mode of delivery and
to extract numerical values for the governing parameters by
comparison with experimental data.
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
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
The best fit parameters for each group of experiments. Numerical
values for DT, k, a consistent for IGF, bFGF to within experimental errors
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: a = (2.7±0.8) x 10-6 cm s-1
bFGF: a = (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 for physical
parameters.