1. Transport Through the Myocardium of Pharmocokinetic Agents Placed in the Pericardial Sac: Insights From Physical Modeling Xianfeng Song, Department of Physics, Indiana University Keith L. March, IUPUI Medical School Sima Setayeshgar, Department of Physics, Indiana University March 22, 2005

2. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles 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. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles This Talk: Outline  Experiments  Mathematical modeling  Comparison with data  Conclusions

4. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles 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 Da)  Basic Fibroblast Growth Factor ( 125 I-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

5. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Experimental Procedure  At t = T (1h or 24h), sac fluid is distilled: C P (T)  Tissue strips are submerged in liquid nitrogen to fix concentration.  Cylindrical transmyocardial specimens are sectioned into slices: C i T (x,T) x denotes C T (x,T) =  i C i T (x,T) x: depth in tissue i

6. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Mathematical Modeling  Goals  Determine key physical processes, and extract governing parameters  Assess the efficacy of drug penetration in the myocardium using this mode of delivery  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 intramural vascular and lymphatic capillaries): k

7. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Idealized Spherical Geometry Pericardial sac: R 2 – R 3 Myocardium: R 1 – R 2 Chamber: 0 – R 1 R 1 = 2.5cm R 2 = 3.5cm V peri = 10ml - 40ml

8. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles 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 at peri/epicardial boundary

9. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Numerical Fits to Experiments Drug Concentration 1 Molecule per ml = 1.3 x10 -11 picograms per ml Conce Error surface

10. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Fit Results Numerical values for D T, k,  consistent for IGF, bFGF to within experimental errors

11. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Time Course from Simulation Parameters: D T =7×10 -6 cm 2 s -1 k=5×10 -4 s -1  =3.2×10 -6 cm 2 s 2

12. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Effective Diffusion,D *, in Tortuous Media  Stokes-Einstein relation D: diffusion constant R: hydrodynamic radius : viscosity T: temperature  Diffusion in tortuous medium D * : effective diffusion constant D: diffusion constant in fluid : tortuosity For myocardium,  = 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 )  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. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles Transport via Intramural Vasculature 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. Epi Endo

14. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles 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.

15. Xianfeng Song, Indiana University, Bloomington, March APS Meeting 2005, Los Angeles 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: 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 IGF: k = (8±3) x 10 -4 s -1, bFGF: k = (9±3) x 10 -4 s -1  Peri-epicardial boundary permeability  IGF:  = (2.7±0.8) x 10 -6 cm s -1, bFGF :  = (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.