Transcript Drug - Department of Physics

Transport Through the Myocardium of Pharmocokinetic Agents Placed in the Pericardial Sac:
Insights From Physical Modeling
Xianfeng
[1]
Pericardial Delivery
[1]
Song ,
Keith L.
[2]
March ,
Sima
Department of Physics, Indiana University,
Mathematical Modeling
[1]
Setayeshgar
[2]IUPUI
Medical School
Comparison with experiment
Discussion (cont.)
Transport via Intramural Vasculature
The key processes
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
A typical volume for human feasible.
pericardial sac is 10-15ml
Epi
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
Idealized Spherical Geometry
Endo
This is an example of the data showing the concentration of IGF
at 24hr through the thickness of the tissue and the resulting fit
for an initial delivery amount of 2000 micrograms. We have
included only 10 slices in the fits since the concentration below
this point was at the background.
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 radioiodinated test agents in the tissue from rate of radioactive decay.
These agents, IGF and bFGF, are relevant therapeutic growth
factors. Different initial amounts (200 and 2000 micrograms 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.
The Chi-square surface as a
function of alpha and k (for
example) clearly showing a
minimum.
R1 = 2.5cm
R2 = 3.5cm
Vperi= 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
CT(x,T) = i CiT(x,T)
x: depth in tissue
Pericardial sac as a drug reservoir (well-mixed and no
washout): drug number conservation
Effective Diffusion,D* in
Tortuous Media
Stokes-Einstein relation
D: diffusion constant
R: hydrodynamic radius
u: viscosity
T: temperature
Diffusion in tortuous medium
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 (total of 9) spatial locations to obtain a
single concentration profile CT(x, T).
D*: effective diffusion constant
D: diffusion constant in fluid
l: tortuosity
Boundary condition: drug current at peri/epicardial boundary
For myocardium, l = 2.11.
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
Our Goal
Result
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.
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.
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
Discussion
Contradiction? NO!
Fit Results: The best parameters for each group of experiment.
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
Two possible mechanisms can increase the effective
diffusion constant!
 Feasibility of computational studies of amount and time
course of pericardial drug delivery to cardiac tissue,
using experimentally derived values for physical
parameters.