A Monte Carlo-based model for steady-state diffuse reflectance spectrometry in human skin: estimation of carbon monoxide concentration in livor mortis.

In terms of physics, the skin can be regarded as an optically turbid medium in which the light is mainly scattered by the collagen fibers, mitochondria and cell nuclei, whereas the absorption is determined by the content of reduced hemoglobin, oxyhemoglobin, bilirubin, and melanin. When the measuring geometry and the illumination spectrum are known, the optical characteristics of the skin can be approximately described by the diffusion and absorption coefficients. These values define the diffusion and absorption probability per unit distance traveled for each wavelength. Based on these parameters, a mathematical skin model was developed with the help of Monte Carlo simulations. By implementing the absorption coefficient of carbon monoxide hemoglobin (CO-Hb) into the skin model, the authors wanted to investigate whether this method is suitable to determine the CO-Hb concentration from spectral reflectance curves of livores. The investigations performed on 28 deaths from CO poisoning so far showed that this is generally possible. In almost all cases, the actual CO-Hb values could be estimated correctly by using the Monte Carlo simulations.

High-throughput evaluation of olefin copolymer composition by means of attenuated total reflection Fourier tranform infrared spectroscopy.

As a consequence of developing fully automated reactors for organic and organometallic synthesis and polymerizations combined with rapid on-line analysis, databases, and data mining, the analysis of polymers with respect to composition and properties has been speeded up. High-throughput evaluation of olefin copolymers requires fast measurements and high accuracy without tedious sample preparation such as pressing KBr pellets. This has been achieved by using attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR spectroscopy) in conjunction with multivariate calibration in order to determine the composition of olefin copolymers such as ethene/propene, ethene/1-hexene and ethene/1-octene copolymers.

Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions.

Dynamic light scattering experiments have become a powerful tool in order to investigate the dynamical properties of complex fluids. In many applications in both soft matter research and industry so-called "real world" systems are subject of great interest. Here, the dilution of the investigated system often cannot be changed without getting measurement artifacts, so that one often has to deal with highly concentrated and turbid media. The investigation of such systems requires techniques that suppress the influence of multiple scattering, e.g., cross correlation techniques. However, measurements at turbid as well as highly diluted media lead to data with low signal-to-noise ratio, which complicates data analysis and leads to unreliable results. In this article a multiangle regularization method is discussed, which copes with the difficulties arising from such samples and enhances enormously the quality of the estimated solution. In order to demonstrate the efficiency of this multiangle regularization method we applied it to cross correlation functions measured at highly turbid samples.

A software for recording and analysis of human tremor.

For many diseases various methods for the diagnosis and treatment monitoring are available. Presently, such methods are not established for an investigation of tremor diseases, although the different forms of tremor are common neurological symptoms and occur frequently in various neurological diseases and also other conditions. We developed an easy-to-use application for tremor-analysis and recording, running under MS-Windows, that allows us to investigate different forms of tremor by advanced mathematical methods of time series analysis. The application is also applicable for users who are not familiar with these kind of advanced data analysis methods. It provides tools for the diagnosis and treatment monitoring under laboratory conditions, based on previously developed and established methods of spectral and cross spectral analysis of tremor and electromyographic time series.

Size Distributions out of Static Light Scattering: Inclusion of Distortions from the Experimental Setup, e.g., a SOFICA-type Goniometer.

In this paper the estimation of sphere size distributions of polymer latex with static light scattering is investigated. For the calculation of the scattering data a model is proposed which describes a SOFICA-type goniometer that was used for the light scattering experiments. From the comparison of this model with a model that is based on Mie's Theory only, conclusions about the reliability of the estimation of size distributions from uni- and bimodal colloidal suspensions with static light scattering could be drawn. Furthermore, the contribution of multiple scattering was investigated, and a method is suggested which further improves the obtained results. Both simulated and experimental data were examined. For data analysis, a method based on Tikhonov regularization was used. Copyright 1999 Academic Press.

Influence of correlated errors on the estimation of the relaxation time spectrum in dynamic light scattering.

An important step in analyzing data from dynamic light scattering is estimating the relaxation time spectrum from the correlation time function. This estimation is frequently done by regularization methods. To obtain good results with this step, the statistical errors of the correlation time function must be taken into account [J. Phys. A 6, 1897 (1973)]. So far error models assuming independent statistical errors have been used in the estimation. We show that results for the relaxation time spectrum are better if correlation between statistical errors is taken into account. There are two possible ways to obtain the error sizes and their correlations. On the one hand, they can be calculated from the correlation time function by use of a model derived by Schätzel. On the other hand, they can be computed directly from the time series of the scattered light. Simulations demonstrate that the best results are obtained with the latter method. This method requires, however, storing the time series of the scattered light during the experiment. Therefore a modified experimental setup is needed. Nevertheless the simulations also show improvement in the resulting relaxation time spectra if the error model of Schätzel is used. This improvement is confirmed when a lattice with a bimodal sphere size distribution is applied to experimental data.

Analysis of multichannel patch clamp recordings by hidden Markov models.

Conventional methods of analysis do not allow the kinetics of patch clamped ion channels to be completely determined if more than one channel is present in the patch. This hinders investigations on small ion channels as well as on channel cooperativity and the homogeneity of channel populations. We present a method to extract the rate constants and current amplitudes for each individual channel from multichannel patches by a one-step procedure. For this purpose, the current record is modeled by the superposed Markov processes of the opening and closing of each channel that is contaminated by noise (Hidden Markov Model). Channel parameters are obtained by maximum likelihood methods. Because the parameters can be calculated directly from the unfiltered record, the dwell time and missed event problems are widely diminished. Confidence bounds for the estimated parameters are given. Statistical tests to decide whether channels switch identically and/or independently are introduced. The application of the method is demonstrated with simulated data.

Stochastic simulation of the transducin GTPase cycle.

On rod disc membranes, single photoactivated rhodopsin (R*) molecules catalytically activate many copies of the G-protein (Gt), which in turn binds and activates the effector (phosphodiesterase). We have performed master equation simulations of the underlying diffusional protein interactions on a rectangular 1-micron2 model membrane, divided into 15 x 15 cells. Mono- and bimolecular reactions occur within cells, and diffusional transitions occur between (neighboring) cells. Reaction and diffusion constants yield the related probabilities for the stochastic transitions. The calculated kinetics of active effector form a response that is essentially determined by the stochastic lifetime distribution of R* (with characteristic time tau R*) and the reaction constants of Gt activation. Only a short tau R* (approximately 0.3 s) and a high catalytic rate (3000-4000 Gt s-1 R*-1) are consistent with electrophysiological data. Although R* shut-off limits the rise of the response, the lifetime distribution of free R* is not translated into a corresponding variability of the response peaks, because 1) the lifetime distribution of catalytically engaged R* is distorted, 2) small responses are enlarged by an overshoot of active effector, and 3) larger responses tend to undergo saturation. Comparison of these results to published photocurrent waveforms may open ways to understand the relative uniformity of the rod response.

Analysing ion channels with hidden Markov models.

Ion channel current amplitudes (mu) and open probabilities (Po) have been analysed so far by defining a 50% threshold to distinguish between open and closed states of the channels. With this standard method (SM) it is very difficult or even impossible to analyse channels of different size in one membrane patch correctly. A stochastical model, named the hidden Markov model (HMM), separates between observation noise and the stochastic process of opening and closing of ion channels. The HMM allows the independent analysis of mu, Po, and mean dwell times (tau) of different channels in one membrane patch, without defining threshold levels. Using this method errors in the analysis are not summarized like in the SM because all different analysing procedures (e.g. filtering, setting of threshold, fitting processes) are done in one step. Two different K+ channels in excised basolateral membranes of the cortical collecting duct of rat (CCD) were analysed by the SM and the HMM. The mu value of the intermediate-conductance K+ channel (i-K+) was 3.9 +/- 0.1 pA (SM) and 3.8 +/- 0.2 pA (HMM) for 11 observations. The Po value of this channel was 10.2 +/- 4.2% (SM) and 10.1 +/- 4.0% (HMM). The mean tau values were 5.4 +/- 0.6 ms for the open state and 9.6 +/- 2.2 ms and 145 +/- 21 ms for the closed states (SM) and 7.8 +/- 1.1 ms, 7.7 +/- 0.9 ms and 148 +/- 24 ms (HMM), respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Pharmacokinetic model identification and parameter estimation as an ill-posed problem.

For model identification and parameter estimation in the framework of linear pharmacokinetics it is most often assumed that the disposition function is a finite sum of exponential functions with time constants lambda i and associated coefficients Ci. Least-square fitting procedures are used to estimate the coefficients Ci and the corresponding discrete locations lambda i on the lambda-axes. This work presents an alternative approach. It does not assume that the non-zero coefficients are located at sharply defined values of lambda, but that they are represented by a continuous function h(lambda), the spectrum of the disposition function. This turns the non-linear least-square problem into a linear problem, which is known to be as so-called "ill-posed". Regularization methods have been developed in recent years as suitable tools for the treatment of such ill-posed problems. Application of Tikhonov regularization to the case of the bolus kinetics of propofol in 8 volunteers is demonstrated. In 7 of the 8 cases a spectrum with 4 to 5 peaks was found, and in one volunteer there were only 2 peaks. All spectra with more than 2 peaks showed negative values of h(lambda). The method used is described and the results are compared with those of conventional compartment analysis.

Characteristics of hand tremor time series.

Tremor is classified into physiological, essential, and parkinsonian tremor by means of clinical criteria. The aim of our work was to extract quantitative features from the measurements of the acceleration of human postural hand tremor. Different mathematical methods were adopted and modified in order to separate these three types of tremor. Best discrimination between physiological and pathological tremors has been achieved by methods distinguishing nonlinear from linear behavior. On the other hand, methods separating different forms of nonlinear behavior have been found to be superior in discriminating parkinsonian and essential tremor. By these methods physiological and pathological tremors can be separated with an error rate below 20% and essential and parkinsonian tremor with an error rate below 10%. This may help to classify tremor time series by objective mathematical criteria and may increase the understanding of the pathophysiological differences underlying these kinds of tremor.

Analyzing the dynamics of hand tremor time series.

We investigate physiological, essential and parkinsonian hand tremor measured by the acceleration of the stretched hand. Methods from the theory of dynamical systems and from stochastics are used. It turns out that the physiological tremor can be described as a linear stochastic process, and that the parkinsonian tremor is nonlinear and deterministic, even chaotic. The essential tremor adopts a middle position, it is nonlinear and stochastic.

Fibrillation of a cardiac region and the tachycardia mode of a two-oscillator system.

The interaction between two nonlinear oscillators is discussed, each one representing a region of the heart and characterized by a specific type of phase transition curve (PTC) which has been derived from human ECG-recordings. Besides the normal conduction a tachycardia mode is studied where the excitation is reflected by each oscillator (reentry). It turns out that under specific physiologically plausible conditions this tachycardia mode cannot be terminated by an external stimulus. Under periodic stimulation the response of the tachycardia mode is chaotic. Within a sheet of nonlinear oscillators the tachycardia mode serves as an ectopic focus or a region of reentry which induces fibrillation of the whole tissue.

The heart as a system of coupled nonlinear oscillators.

In various approximations the heart is considered as a system of coupled nonlinear oscillators which are characterized by their phase transition curve (PTC) only. The system exhibits many phenomena which are known from ECG recordings such as multi-level-Wenckebach periodicity, dissociation, induction or removal of a tachycardia by an extrasystole, pseudo-block and the gap phenomenon. All these can be discussed within the model on a quantitative level.