Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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.