1. Transport of Pharmocokinetic Agent in the Myocardium Xianfeng Song Sima Setayeshgar Feb. 16, 2004

2. Pericardial Delivery: Motivation  The pericardial sac is a fluid-filled self-contained space (10ml – 50ml for human) surrounding the heart. As such, it can be potentially used therapeutically as a “drug reservoir”  Use of pericardial space for delivery of agents (antiarrhythmic, gene therapy) to  Coronary vasculature  Myocardium  Recently experimental feasibility  Verrier VL, Waxman S, Lovett EG, Moreno R. Transatrial access to the normal pericardial space: a novel approach for diagnostic sampling, pericardiocentesis and therapeutic interventions. Circulation, 1998; 98:2331-2333  Stoll HP, Carlson K, Keefer LK, Hrabie JA, March KL. Pharmacokinetic and consistency of pericardial delivery directed to coronary arteries: direct comparison with endoluminal delivery. Clin Cardiol, 1999; 22(Suppl-I): I-10-I-16

3. Outline  Experiments on juvenile farm pigs to measure the spatial concentration profile in the myocardium of agents placed in the pericardial space  Mathematical Modeling to investigate the efficacy of agent penetration in myocardial tissue, extract the key physical parameters  Preliminary Results  Conclusions

4. Experiments  Performed by Hans-Peter Stoll, M.D., Keith L. March, M.D., Ph.D., Indiana University-Purdue University Indianapolis Medical School  Experimental subjects: juvenile farm pigs  Method: radiotracer method to determine the spatial concentration profile  Radioiodinated test agents  Insulin-like Growth Factor ( 125 I-IGF, MW: 7740)  Basic Fibroblast Growth Factor ( 125 I-bFGF, MW: 18000)

5. Brief Introduction of Experimental Procedure

6. Mathematical Model  Goals  Investigate the efficacy of agent penetration in myocardium  Extract the key physical parameters  Determine appropriate drug quantities and expected time course of delivery  The key physical processes  Substrate transport across boundary layer between pericardial sac and myocardium: α  Substrate diffusion in myocardium: D T  Substrate washout through the vascular and lymphatic capillaries in myocardium: k

7. Idealized Spherical Geometry Pericardial sac: R 2 – R 3 Myocardium: R 1 – R 2 “Chambers”: 0 – R 1 R 1 =2.5cm R 2 =3.5cm Volume of Pericardial sac: 10ml-40ml

8. Governing Equations and Boundary conditions  Governing equation in myocardium C T : concentration of agent in tissue D T : effective diffusion constant in tissue k: washout rate  Consider pericardial sac as a drug reservoir (Well mixing and no washout of drug in pericardial sac)  The drug current flowed through the boundary layer between pericardial sac and myocardium is proportional to the concentration difference between them

9. Fit to experiments Fitting Error surface

10. Fit to experiments (Rough results)

11. Time-course from simulation Parameters: D T =7×10 -6 cm 2 s -1 k=5×10 -4 s -1 α=3.2×10 -6 cm 2 s 2

12. D * in tortuous media  Fluctuation-dissipation theory D: diffusion constant R: hydrodynamic radius v: T: temperature  In tortuous media D * : diffusion constant in tortuous media D: diffusion constant in fluid λ: tortuosity In myocardium, λ=2.11 (M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, Diffusion of sucrose, sodium, and water in ventricular myocardium, American Joural of Physiology, Vol 227, No. 5, Nov. 1974 )  Estimate the diffusion constant  IGF  bFGF  Our fitted values are in order of 10 -6 cm 2 sec -1  Contradiction?

13. Speculation on mixing due to viscoelastic motion of heart  The tissue is a porous medium consisting of extracellular space and muscle fibers. The extracellular space consists of an incompressible fluid (mostly water)  Effective stirring: the expansion and contraction of the muscle cells leads to changes in the pore sizes and therefore mixing of the extracellular volume. This effective "stirring" could be responsible for the larger diffusion constants.

14. Conclusion  Model is consistent with experiments despite its simplicity  The effective diffusion constants for two drugs (IGF,bFGF) are both in the order of  The wash out rate for both drugs are in the order of  ……

15. Thank you