1. Transport of Pharmocokinetic Agents in the Myocardium Xianfeng Song, Department of Physics, IUB Keith L. March, IUPUI Medical School Sima Setayeshgar, Department of Physics, IUB March 22, 2005

2. Pericardial Delivery: Motivation  The pericardial sac is a fluid-filled self- contained space surrounding the heart. As such, it can be potentially used therapeutically as a “drug reservoir.”  Delivery of anti-arrhythmic, gene therapeutic agents to  Coronary vasculature  Myocardium  Recent experimental feasibility of pericardial access  Verrier VL, et al., “Transatrial access to the normal pericardial space: a novel approach for diagnostic sampling, pericardiocentesis and therapeutic interventions,” Circulation (1998) 98:2331-2333.  Stoll HP, et al., “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. V peri (human) =10ml – 50ml

3. This work: 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  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 ( 125 I-IGF, MW: 7734)  Basic Fibroblast Growth Factor ( 125 I-bFGF, MW: 18000)  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

5. Experimental Procedure  At t = T (1h or 24h), sac fluid is distilled, several strips at different locations from myocardium are excised.  Strips are submerged in liquid nitrogen to fix concentration.  Cylindrical transmyocardial specimens are sectioned into slices.  Gamma radiation CPM is used to determine the concentration, C i T (x,T), C P (T).

6. Mathematical Modeling  Goals  Investigate the efficacy of agent penetration in myocardium  Extract the key physical parameters  Key physical processes  Substrate transport across boundary layer between pericardial sac and myocardium:   Substrate diffusion in myocardium: D T  Substrate washout in myocardium (through the vascular and lymphatic capillaries): 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: diffusion + washout C T : concentration of agent in tissue D T : 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 through the boundary layer between pericardial sac and myocardium is proportional to the concentration difference between them

9. Fit to experiments Error surface 1 Molecule per ml = 1.3 x10 -11 picograms per ml Conce

10. Fit Results Numerical values for D T, k,  consistent for IGF, bFGF within experimental errors

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. Effective Diffusion,D *, in tortuous media  Stokes-Einstein relation D: diffusion constant R: hydrodynamic radius : viscosity T: temperature  In tortuous media D * : effective diffusion constant D: diffusion constant in fluid : tortuosity For myocardium,  = 2.11. (M. Suenson, D.R. Richmond, J.B. Bassingthwaighte, “Diffusion of sucrose, sodium, and water in ventricular myocardium, American Joural of Physiology,” 227(5), 1974 )  Numerical estimates for diffusion constants  IGF : D ~ 4 x 10 -7 cm 2 s -1  bFGF: D ~ 3 x 10 -7 cm 2 s -1 Our fitted values are in order of 10 -6 - 10 -5 cm 2 sec -1, 10 to 50 times larger !!

13. Transport via intramural vasculature Drug permeates into vasculature from interstitium at high concentration and permeates out at low concentration, thereby increasing the effective diffusion constant in the tissue. Epi Endo

14. Diffusion in an active viscoelastic medium 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 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.

15. Conclusion  Model accounting for effective diffusion and washout is consistent with experiments despite its simplicity.  First quantitative determination of numerical values for physical parameters  Effective diffusion constant IGF: D T = (9±3) x 10 -6 cm 2 s -1, bFGF: D T = (6±3) x 10 -6 cm 2 s -1  Washout rate: k = (7±2) x 10 -4 s -1  Peri-epicardium boundary permeability:  = (3.8±0.8) x 10 -6 cm s -1 Enhanced effective diffusion, allowing for improved transport Feasibility of computational studies of amount and time course of pericardial delivery of drugs to cardiac tissue, using experimentally derived values for physical parameters

16. Thank you