Monte Carlo simulations in drug release.

We present methods based on simple sampling Monte Carlo simulations that are used in the study of controlled drug release from devices of various shapes and characteristics. The manuscript is part of a special tribute issue for Prof. Panos Macheras and we have chosen applications of the Monte Carlo method in the field of drug release that were pioneered by him and his research group.

EEG for Current With Two-Dimensional Support.

Objective: The inverse problem of computing the neuronal current density from scalp EEG is highly ill-posed. In part, this is due to the nonuniqueness of the mapping between current sources and scalp potentials. We develop an explicit formula for the scalp EEG for sources constrained to the cortical surface in terms only of the components of the current that affect the EEG signal.

Functional morphometry for the estimation of the alveolar surface area in prematurely-born infants.

Conventionally, the alveolar surface area (S) has been measured by using post-mortem morphometry. Such studies have highlighted that S in prematurely-born infants is markedly smaller when compared to term-born infants as a result of postnatal impairment or arrest of alveolar development. We herein explore how, non-invasive measurements of the ventilation/perfusion ratio (V/Q) can be used to estimate S in prematurely-born surviving, convalescent infants.

A chemical energy approach of avascular tumor growth: multiscale modeling and qualitative results.

In the present manuscript we propose a lattice free multiscale model for avascular tumor growth that takes into account the biochemical environment, mitosis, necrosis, cellular signaling and cellular mechanics. This model extends analogous approaches by assuming a function that incorporates the biochemical energy level of the tumor cells and a mechanism that simulates the behavior of cancer stem cells. Numerical simulations of the model are used to investigate the morphology of the tumor at the avascular phase.

On the stability of a spherical tumour.

The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour.

Neuronal currents and EEG-MEG fields.

In a recent paper by the author, Fokas and Hadjiloizi proved that a neuronal current within a spherical homogeneous conductor can be split into two orthogonal components in such a way that one component provides the electroencephalography (EEG)-related fields and the other component provides the fields related to magnetoencephalography (MEG). Hence, in spherical geometry, the EEG and MEG measurements contain no overlapping information about the current. In the present work, we utilize a new integral representation for the magnetic potential, introduced recently by Fokas, Kariotou and the author, to prove that this elegant property is not true once the highly symmetric spherical environment is abandoned.

Analytic expansion of the EEG lead field for realistic volume conductors.

EEG forward calculation in realistic volume conductors using the boundary element method suffers from the fact that the solutions become inaccurate for superficial sources. Here we propose to correct an analytical approximation of the respective lead fields with series of spherical harmonics with respect to multiple expansion points. The necessary correction depends very much on the chosen analytical approximation.