Kinetics of protoporphyrin IX formation in rat oral mucosa and skin after application of 5-aminolevulinic acid and its methylester

The kinetics of accumulation of protoporphyrin IX (PpIX) after topical application of 5-aminolevulinic acid (ALA) and its methylester (5-aminolevulinic acid methylester [ALA-Me]) was studied on rat oral mucosa. The accumulation of PpIX in mucosa and skin after intravenous injection of ALA and ALA-Me was also studied. The elimination rate of PpIX was dependent on drug and dose as well as on administration route. Application of ALA on rat oral mucosa and skin caused a systemic effect with PpIX building up in remote skin sites not exposed to the drugs. No such systemic effect was seen after application of ALA-Me either in mucosa or on skin. Intravenous injection of the drugs (0.2 g/kg) leads to more fluorescence in the skin than topical application of the drug (20%). For mucosa, the opposite is true. Maximal PpIX fluorescence appeared later after application of high concentrations of the drugs (around 8 h for 5% and 20% wt/wt) than after application of low concentrations (around 3-5 h for 1% and 2% wt/wt).     

Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region

We present measurements of reflectance spectra from human skin in vivo in the spectral range from 250 to 700 nm. These measurements show that the reflectance from strongly pigmented skin is higher than that from weakly pigmented skin at wavelengths shorter than approximately 300 nm. We simulate the measured results using a new radiative transfer model developed to study light propagation in skin tissue. Our simulations mimic the measured spectra when scattering from melanosomes, and fragmented melanosomes are taken into account. Scattering from microstructures with high relative refractive indices plays a major role in tissue optics. Our results show that scattering from melanosomes and fragmented melanosomes is of particular significance.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

A Monte Carlo Sampling Scheme for the Ising Model

In this paper we describe a Monte Carlo sampling scheme for the Ising model and similar discrete-state models. The scheme does not involve any particular method of state generation but rather focuses on a new way of measuring and using the Monte Carlo data. We show how to reconstruct the entropy S of the model, from which, e.g., the free energy can be obtained. Furthermore we discuss how this scheme allows us to more or less completely remove the effects of critical fluctuations near the critical temperature and likewise how it reduces critical slowing down. This makes it possible to use simple state generation methods like the Metropolis algorithm also for large lattices.     

Posicast control of a class of fractional-order processes

The number of studies on the control of fractional-order processes—processes having dynamics described by differential equations of arbitrary order—has been increasing in the past two decades and it is now ubiquitous. Various methods have emerged and have been proven to effectively control such processes—usually resulting in fractional-order controllers similar to their conventional integer-order counterparts, which include, but are not limited to fractional PID and fractional lead-lag controllers. However, such methods require a lot of computational effort and fractional-order controllers could be challenging when it comes to their synthesis and implementation. In this paper, we propose a simple yet effective delay-based controller with the use of the Posicast control methodology in controlling the overshoot of a fractional-order process of the class $\mathcal{P}:\left\{ {P\left( s \right) = {1 \mathord{\left/ {\vphantom {1 {\left( {as^\alpha + b} \right)}}} \right. \kern-0em} {\left( {as^\alpha + b} \right)}}} \right\}$ having orders 1 < α < 2. Such controllers have proven to be easy to implement because they only require delays and summers. In this paper, the Posicast control methodology introduced in the past few years is modified to minimize the overshoot of the processes step response to a level that is acceptable in control engineering and automation practices. Furthermore, proof of the existence of overshoot for such class of processes, as well as the determination of the peak-time of the open-loop response of a fractional-order process of the class P is presented. Validation through numerical simulations for a class of fractional-order processes are presented in this paper.     

On the tractability of linear tensor product problems in the worst case

It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. The complexity of linear tensor product problems in the worst case depends on the eigenvalues _{λi}i∈N${\left\{{\lambda }_i\right\}}_{i\in \mathbb{N}}$ of a certain operator. It is known that if _λ1=1${\lambda }_1=1$ and _λ2∈(0,1)${\lambda }_2\in (0,1)$ then _λn=o((lnn)⁻²)${\lambda }_n=o\left({(lnn)}^{-2}\right)$, as n→∞$n\to \infty$, is a necessary condition for a problem to be weakly tractable. We show that this is a sufficient condition as well.     

Depth Profile of Protoporphyrin IX Fluorescence in an Amelanotic Mouse Melanoma Model

Protoporphyrin IX (PpIX) fluorescence was measured at different depths in a subcutaneous amelanotic melanoma model (LOX) in mice. PpIX was induced by topical application of 5‐aminolevulinic acid (ALA) and two of its derivatives, the methylester (MAL) and hexylester (HAL) onto the normal skin covering the tumor. The PpIX fluorescence intensity on the surface of the tumors was the highest for HAL, followed by ALA and MAL. Using equimolar concentrations (0.5 mmol g^?1), HAL induced nearly twice as much fluorescence as ALA did. The depth profile of PpIX fluorescence was measured at different layers of the tumor, which was carefully sliced and controlled in situ ex vivo. The PpIX fluorescence was mainly localized within the upper 2 mm of the tissue for ALA and within 1 mm for MAL and HAL. There were no significant differences in the shape of the fluorescence excitation spectra, but the long wavelength excitation peak (633 nm) was so weak that these results are unreliable for depth estimation. When considering the low fluorescence intensity (around 5% of the intensity at the tumor surface), the actual penetration depth of HAL was comparable to that of ALA. The fluorescence after topical application of ALA and HAL was significantly above the background level down to a depth of around 6 mm, and there were traces of PpIX fluorescence even at the tumor base (10 mm). The fluorescence after topical application of MAL was detectable down to 1 mm. In the depth of 2–6 mm, the fluorescence was slightly higher for HAL than for ALA. Using the estimated diffusion coefficients for topically applied ALA (0.16 ± 0.03 mm² h^?1), MAL (0.045 ± 0.005 mm² h^?1) and HAL (0.037 ± 0.003 mm² h^?1), the behavior of the drugs after different application times could be estimated in this tumor model.     

Smolyak cubature of given polynomial degree with few nodes for increasing dimension

Summary. Some recent investigations (see e.g., Gerstner and Griebel [5], Novak and Ritter [9] and [10], Novak, Ritter and Steinbauer [11], Wasilkowski and Woźniakowski [18] or Petras [13]) show that the so-called Smolyak algorithm applied to a cubature problem on the d-dimensional cube seems to be particularly useful for smooth integrands. The problem is still that the numbers of nodes grow (polynomially but) fast for increasing dimensions. We therefore investigate how to obtain Smolyak cubature formulae with a given degree of polynomial exactness and the asymptotically minimal number of nodes for increasing dimension d and obtain their characterization for a subset of Smolyak formulae. Error bounds and numerical examples show their good behaviour for smooth integrands. A modification can be applied successfully to problems of mathematical finance as indicated by a further numerical example. Received September 24, 2001 / Revised version received January 24, 2002 / Published online April 17, 2002 RID="*" ID="*" The author is supported by a Heisenberg scholarship of the Deutsche Forschungsgemeinschaft