Filippo de Monte

A two-phase two-layer model for transdermal drug delivery and percutaneous absorption.

One of the promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Drug masses are given and their dependence on the physical parameters is discussed.

Chapter 3 – Drug Release in Biological Tissues

This chapter focuses on the theoretical understanding of the transport of drug in a porous media representation of biological tissues. The derivation of the governing equations using a volume-averaged porous media approach is detailed. This is followed by analytic solution developments that concentrate on the transport of solute in a biological system. The conjugate problem interaction between the fluid and solid phase, known as local mass non-equilibrium, is analyzed in detail and the relative influences of convection and diffusion are investigated. Finally the problem is extended to include the composite nature of biological media. The specific application shown here involves the study of a drug released by a stent within an arterial wall.

Diffusion Penetration Time for Transient Heat Conduction

The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations because the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for six geometries, including one-dimensional cases for Cartesian, cylindrical, and spherical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in cylindrical coordinates. The sixth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise ...

A computational method of temperature distribution in high frequency planar transformers

In high frequency planar transformers and inductors, conventional wires have been replaced by printed circuit boards or laminated copper windings. This technology can outperform traditional wire-wound transformers in terms of cost, dimensions and performance. However, in order to obtain high efficiency and high power/size ratio, their design requires the knowledge of the internal temperature distribution. For such a reason, this paper proposes a two-dimensional numerical method for a combined computation of both the temperature distribution and the electromagnetic behaviour of planar transformers and inductors. After a detailed description of the proposed methodology, this paper reports, compares and analyzes calculated and measured results demonstrating prediction capabilities of the proposed method.

Solar absorptivity of metallic layers subject to a short-flash of concentrated solar energy. Theoretical-experimental calculation

The paper develops a procedure for the theoretical-experimental calculation of the solar absorption coefficient of metallic layers under the action of a short flash of concentrated solar energy. The knowledge of this coefficient is relevant when the solar thermal processing is used to make a quench in a thin superficial layer of metallic slabs. The experimental data of temperature of the sample are obtained using the SURFSOL experimental device at SOLFACE (High Flux Solar Facilities for Europe), France. In particular, the sensors of temperature are located on its back side as the solar radiation impinges the front irradiated one. The theoretical data are obtained solving the nonlinear inverse transient heat conduction problem using the IHCP1D software based on the well-known function specification method (FSM). It gives transient surface heat fluxes as well as temperatures on the irradiated side of the sample using internal temperature histories. Then a transient radial fin model accounts for the heat diffusion in the radial direction and re-calculates the heat fluxes. Once temperatures and heat flows are known, an estimate of the solar absorption coefficient of the metallic layer (during the flash solar heating process) may be obtained as a function of temperature (AISI 316L steel).

Intrinsic Verification of an Exact Analytical Solution in Transient Heat Conduction for Numerical Codes Verification

The concept of intrinsic verification is applied to an exact analytical solution to be used for verification of fully-numerical transient heat conduction solvers, based on finite element and finite difference methods. In particular, the addressed problem concerns a finite onedimensional rectangular body in imperfect thermal contact with a high-conductivity surface layer subject to a jump in heat flux. Once the exact analytical temperature solution is known, it is possible to define a computational analytical solution for short and large times, as well as for a quasi-steady state. The symbolic intrinsic verification of the solution is proven by checking that it satisfies the governing equations, the first law of thermodynamics, and that it reduces to simpler related solutions for special cases. Then, once a computer code is made available, the numerical intrinsic verification is proven by using the concept of penetration time, finite difference schemes, and numerical results from simpler related solutions. Indications of intrinsic verification are obtained, so ensuring a correctness to many significant figures (such as ten or even fifteen), far beyond the accuracy generally practicable from fully numerical solutions.

Transdermal Drug Delivery and Percutaneous Absorption: Mathematical Modeling Perspectives

Abstract Transdermal drug delivery is the systemic or topical release of drugs by percutaneous permeation. It offers several advantages, such as limitation of hepatic first pass metabolism and enhancement of therapeutic efficacy, providing an attractive alternative to oral delivery and hypodermic injections. For the optimization of the effective transdermal release, it is important to understand the mechanism of drug permeation from the vehicle (any delivery device such as a transdermal patch or medicated plaster) across the biological tissues composing the skin. This requires using appropriate mathematical models such as compartment and complex models or slow binding/partitioning kinetics which are reviewed in this chapter. This chapter also reviews novel and efficient solution techniques based on the Laplace transform method, on the finite difference method, the finite element method, and the finite volume method. A one-dimensional, transient, two-phase, two-layer (vehicle/skin) mathematical model of drug delivery and percutaneous absorption is proposed in this chapter. In particular, a system of four partial differential equations describes the diffusion and the reversible binding and unbinding processes in both layers. Additional mass flux continuity at their interface and clearance conditions into systemic circulation are imposed. A semianalytical solution technique based on eigenfunctions and eigenvalues is used in order to provide a novel and efficient methodology for solving such a problem despite the well-established Laplace transform. The solution is given in a closed-form through an infinite series expansion. The typical drug dynamics, the concentration levels, and the optimal delivery rate are shown as results of the resulting simulations and discussed in a case study. The results are used to discuss the roles of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Also, drug masses are given and their dependence on the physical parameters is discussed.

Applications in education for a heat conduction database

Applied computer solutions for conductive heat transfer are a critical component in any modern undergraduate heat transfer course. This need has been addressed in many ways through various textbook exercises and software packages. The present work involves a catalog of analytical solutions organized with a numbering system that describes the boundary conditions and initial conditions for each problem. The solutions are pre-programmed and accessible via a free web site called the Exact Analytical Conduction Toolbox, or EXACT. Students can access these solutions for use in homework and project work. In this paper examples of several types of student exercises are given, including a re-creation of the Heisler charts and a two dimensional steady-state example. Additionally, an account is given of classroom use of these tools in a graduate heat transfer course, outlining the education advantages of the EXACT web page. The concept of intrinsic verification is also discussed, focusing on the applicability of this concept to enhancing insight among undergraduate students. General support is also expressed for the need of analytical solutions to heat transfer and diffusion problems in an undergraduate setting.Copyright