Intravegetation Antimicrobial Distribution in Aortic Endocarditis Analyzed: MATERIALS AND METHODS

Posted by James

Organism

The isolate of P aeruginosa used in this study to induce endocar­ditis has been described in detail elsewhere. The MBC of this strain as determined in cation-supplemented Mueller-Hinton broth for amikacin is 2ug/ml, while that for gentamicin and tobramycin is 1 ug/ml.

Endocarditis

The details of the catheterization and induction of aortic endo­carditis in rabbits have been published previously. Briefly, a transcarotid catheter is passed across the aortic valve to induce sterile endocarditis on the leaflet. Pseudomonal endocarditis is produced 24 hours after catheterization by injecting about 10 cfu of saline-washed cells intravenously. Positive blood cultures for P aeruginosa 24 hours after inoculation serve as presumptive evidence of the induction of bacterial endocarditis. In the present study the model of endocarditis was used to assess densities of infected aortic vegetations.

Model of Diffusion

The general equation characterizing diffusion is as follows.

In this equation, _v² is the Laplacian operator, C, is the concentration of substance A (aminoglycoside in our study), D^ is the diffusion coefficient of substance A (aminoglycosides) through substance В (aortic vegetation), and R, is the rate of intravegetation destruction of substance A. If cardiac vegetations are represented as homoge­neous spheres (ie, C. = C.[r,t]; r = square root of [x² + y² + z²]) and the antibiotic is not appreciably degraded within the vegetation, the equation can be expressed as follows.

This equation, in which the independent variables, rand t, represent the radius of the vegetation and the time following antibiotic doses, respectively, is Ficks second law of diffusion in spherical coordi­nates. Variables were then changed to fit the nondimensional form of a second-order parabolic partial differential equation, in order to simplify the calculations. The initial condition is that the antibiotic concentration in the vegetation is zero at time zero; the model is set to simulate intermittent dosing.
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The following assumptions were made in order to simplify the model for the current study of antibiotic distribution within the vegetation: (1) cardiac vegetations are generally spherical in shape; (2) the antibiotic concentration at the vegetations surface is equal to that of plasma; (3) flow around the vegetation is turbulent, thus continuously exposing the vegetation in a symmetric fashion to the antibiotic-containing plasma; (4) the antibiotic is eliminated through first-order kinetics; and (5) only the unbound fraction of drug (~95 percent for aminoglycosides) diffuses into cardiac vegetations, and this fraction remains constant and independent of drug concentra­tion. The previous equation and conditions were solved analytically using the method of Eigen functions on a computer (Microvax II). A general-purpose interactive mathematical workbench (MATH- LIB; Innosoft International Inc.), consisting of programs built around libraries of numerical analysis routines, was used to support the program.