Mathematical techniques for the estimation of the diffusion coefficient and elimination constant of agents in subcutaneous tissue
Degree Granting Department
Yvonne Moussy, Ph.D.
Mathematical models, Levenberg-Marquardt algorithm, Osmotic pump, Injection, Radiolabeling
The purpose of this work was to develop methods to estimate the diffusion coefficient and elimination constant for dexamethasone in subcutaneous tissue. Solutions to the diffusion equation were found for different conditions relevant to implantation and injection. These solutions were then used as models for measured autoradiography data where the unknown model parameters were the diffusion coefficient and the elimination constant. The diffusion coefficient and elimination constant were then estimated by curve fitting the measured data to these models. Having these estimates would be of practical importance since inflammation surrounding implantable glucose sensors may be controlled through local release of dexamethasone at the site of implantation. Derivation of the appropriate model, how the model was used to estimate D and k, and various specific profile examples were investigated in detail.
Osmotic pumps containing [3H]- dexamethasone were implanted into the subcutaneous tissue of rats. Digital autoradiography was used to measure the distribution of the [3H]-dexamethasone within the subcutaneous tissue at 6, 24, and 60 hours after implantation. Measured concentration profiles, near the catheter tip through which the agent was released, were compared to solutions of the diffusion equation in order to characterize drug diffusion coefficients and elimination constants. There was good agreement between the experimental data and the mathematical model used for estimation. The diffusion coefficient for dexamethasone in subcutaneous tissue was found to be D = 4.11+-1.77x10E-10 m2/s, and the elimination rate constant was found to be k = 3.65+-2.24x10E-5/s. Additionally, [3H]-dexamethasone was injected into the subcutaneous tissue of rats.
Digital autoradiography was again used to measure the distribution of the [3H]- dexamethasone within the subcutaneous tissue at 2.5 and 20 minutes after injection. Measured concentration profiles were again compared to a mathematical model of drug diffusion for injection. There was good agreement between the experimental data and the mathematical model. The diffusion coefficient found using this simple injection method was 4.01+-2.01x10E-10 m2/s. The simple method given here for the determination of the diffusion coefficient is general enough to be applied to other substances and tissues as well.
Scholar Commons Citation
Hersh, Lawrence T., "Mathematical techniques for the estimation of the diffusion coefficient and elimination constant of agents in subcutaneous tissue" (2007). USF Tampa Graduate Theses and Dissertations.