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In Vitro Assessment of Dermal Absorption
Published in David W. Hobson, Dermal and Ocular Toxicology, 2020
Diffusion forms the basis of in vitro studies, and the problems of skin absorption are often simplified to a number of diffusion equations and mass transfer coefficients. The justification of such methodology centers upon the generally accepted assumption that the stratum corneum is the principal barrier limiting skin permeability.5,14,21 Since this outermost layer of the skin is composed essentially of nonliving tissue, it is therefore reasoned that biochemical processes cannot influence the diffusional characteristics of the rate limiting membrane, and hence, in vitro diffusion studies will accurately predict in vivo skin penetration and absorption.
Fractional SIR Epidemic Model of Childhood Disease with Mittag-Leffler Memory
Published in Devendra Kumar, Jagdev Singh, Fractional Calculus in Medical and Health Science, 2020
P. Veeresha, D. G. Prakasha, Devendra Kumar
The biological models that are modelled and described with the help of arbitrary order differential equations have been demonstrated in analysing the behaviour of susceptible-infected-recovered (SIR) epidemic models. These models are developed and analysed by many researchers using many techniques with the aid of classical and fractional order derivatives [52–54]. Moreover, many authors have established the arbitrary order models to analyse the diffusion equation to describe the effect of these diseases. In the present framework, we analyse the proposed childhood disease model using the AB derivative and find the solution with the Adams-Bashforth scheme. Further, the considered model is described with the help of a new fractional derivative incorporated in the memory effect, the non-singular as well as non-local kernel, and these properties are very essential while analysing the behaviour of human diseases.
The Electrical Properties of Cells
Published in Richard C. Niemtzow, Transmembrane Potentials and Characteristics of Immune and Tumor Cell, 2020
To deal with this difficulty, we need to formulate our diffusion equation in a somewhat different form. We must consider both the relative permeabilities of different ions as well as their relative concentrations on both sides of the membrane. These considerations led Goldman4 and subsequently Hodgkin and Katz10 to develop the following expression:
Application of HIPEC simulations for optimizing treatment delivery strategies
Published in International Journal of Hyperthermia, 2023
Daan R. Löke, H. Petra Kok, Roxan F. C. P. A Helderman, Bella Bokan, Nicolaas A. P. Franken, Arlene L. Oei, Jurriaan B. Tuynman, Pieter J. Tanis, Johannes Crezee
Chemotherapeutic agents are transported by both diffusion and convection. However, it is impossible to explicitly model microscopic convective flow patterns in a model at this scale. Furthermore, interstitial convection does not have a predetermined direction. Therefore, Equation (6) only features a diffusion term and not a convection term similar to the second term in Equation (4). During the experimental determination of diffusion coefficients in tissues, a solute flux is measured and fitted to a diffusion equation. A major drawback of this approach is that it is impossible to separate the contribution of convection and diffusion to the transport of a solute, resulting in the determination of an apparent or effective diffusion coefficient [23]. In the application presented in this study, using an apparent diffusion coefficient in Equation (6) is an effective way to include both the contribution of convection and diffusion in the diffusion Equation (6). The apparent diffusion coefficient depends on the molecular weight 23,24]
Malignant cell characterization via mathematical analysis of bio impedance and optical properties
Published in Electromagnetic Biology and Medicine, 2021
According to Law of Fresnel, when light particles (or an electromagnetic wave) are incident on a biological cell, they are reflected at boundaries between the heterogeneous media due to its different refractive index. Hence, as iterated, refractive index measurement is a cell characterization procedure. The light particles are scattered and absorbed by the tissue and can be explained by the diffusion equation. It describes propagation of energy particles in the scattering and absorbing tissue medium (Glasstone and Edlund 1952). The diffusion Equation (9) encompasses the following: (1) energy absorbed per m3 per second (2], (2) source term S0, (3) Diffusion constant, D by Eddington approximation it is 2011).
Model-based optimized steering and focusing of local magnetic particle concentrations for targeted drug delivery
Published in Drug Delivery, 2021
Rikkert Van Durme, Guillaume Crevecoeur, Luc Dupré, Annelies Coene
As already mentioned, biomedical targeting applications usually consist of large numbers of particles distributed throughout fluids. The continuity equation describes the mass transport of the particles (Pedlosky, 2013) c is the particle concentration or the amount of particles per unit volume, j is the total flux of particles and S is a volumetric source for c. S = 0 when no particles are added to the system during the considered time interval. The flux consists of a diffusive component D the diffusion coefficient (Fick, 1855). Advection of particles in the fluid is taken into account in 2013). The result is the well-known advection-diffusion equation (Gerber et al., 1983; Takayasu et al., 1983; Grief & Richardson, 2005; Shapiro, 2009)