ABSTRACT
The development of effective drug delivery systems remains a focus of extensive research to enhance therapeutic outcomes. Among these, in situ forming gels (ISG) have emerged as a promising avenue for controlled drug release. This research focuses on the mathematical modeling of levofloxacin HCl (Lv) release from zein-based ISG using the cup method, aiming to mimic the environment of a periodontal pocket. The drug release behavior of the ISGs was investigated through experimental observations and numerical simulations employing forward and central difference formula. Notably, the experimental data for drug release from the 20% w/w zein-based ISG formulations closely aligned with the simulations obtained from numerical mechanistic modeling. In summary, 20% w/w zein-based ISG formulations demonstrated nearly complete drug release with the maximum drug concentration at the edge of the matrix phase values consistently around 100-105%, while 25% w/w zein-based ISG formulations exhibited somewhat lower drug release extents, with values ranging from 70-90%. Additionally, the rate of drug transport from the polymer matrix to the external phase influenced initial release rates, resulting in a slower release. The utilization of glycerol formal as a solvent extended drug release further than dimethyl sulfoxide, thanks to denser matrices formed by high-loading polymers that acted as robust barriers to solvent removal and drug diffusion. Furthermore, UV-vis imaging was utilized to visualize the matrix formation process and solvent diffusion within the ISGs. The imaging results offered valuable insights into the matrix formation kinetics, controlled drug release mechanisms, and the influence of solvent properties on drug diffusion. The combination of mathematical modeling and experimental visualization provides a comprehensive understanding of drug release from zein-based ISGs and offers a foundation for tailored drug delivery strategies.
ABSTRACT
We regard the problem of differentiation occurring in the retrieval of aerosol extinction coefficient profiles from inelastic Raman lidar signals by searching for a stable solution of the resulting Volterra integral equation. An algorithm based on a projection method and iterative regularization together with the L-curve method has been performed on synthetic and measured lidar signals. A strategy to choose a suitable range for the integration within the framework of the retrieval of optical properties is proposed here for the first time to our knowledge. The Monte Carlo procedure has been adapted to treat the uncertainty in the retrieval of extinction coefficients.
ABSTRACT
In the analysis of Raman lidar measurements of aerosol extinction, it is necessary to calculate the derivative of the logarithm of the ratio between the atmospheric number density and the range-corrected lidar-received power. The statistical fluctuations of the Raman signal can produce large fluctuations in the derivative and thus in the aerosol extinction profile. To overcome this difficult situation we discuss three methods: Tikhonov regularization, variational, and the sliding best-fit (SBF). Three methods are performed on the profiles taken from the European Aerosol Research Lidar Network lidar database simulated at the Raman shifted wavelengths of 387 and 607 nm associated with the emitted signals at 355 and 532 nm. Our results show that the SBF method does not deliver good results for low fluctuation in the profile. However, Tikhonov regularization and the variational method yield very good aerosol extinction coefficient profiles for our examples. With regard to, e.g., the 532 nm wavelength, the L2 errors of the aerosol extinction coefficient profile by using the SBF, Tikhonov, and variational methods with respect to synthetic noisy data are 0.0015(0.0024), 0.00049(0.00086), and 0.00048(0.00082), respectively. Moreover, the L2 errors by using the Tikhonov and variational methods with respect to a more realistic noisy profile are 0.0014(0.0016) and 0.0012(0.0016), respectively. In both cases the L2 error given in parentheses concerns the second example.
ABSTRACT
The present work develops and analyses a model system of delay-differential equations which describes the core dynamics of the stress-responsive hypothalamus-pituitary-adrenal axis. This neuroendocrine ensemble exhibits prominent pulsatile secretory patterns governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Formulation and subsequent bifurcation analysis of the model provide a qualitative and mathematical frame work for a better understanding of the delayed responsive mechanisms as well as the dynamic variations in different pathological situations.
