Effective point of measurement for parallel plate and cylindrical ion chambers in megavoltage electron beams

The presence of an air filled ionization chamber in a surrounding medium introduces several fluence perturbations in high energy photon and electron beams which have to be accounted for. One of these perturbations, the displacement effect, may be corrected in two different ways: by a correction factor p_dis or by the application of the concept of the effective point of measurement (EPOM). The latter means, that the volume averaged ionization within the chamber is not reported to the chambers reference point but to a point within the air filled cavity. Within this study the EPOM was determined for four different parallel plate and two cylindrical chambers in megavoltage electron beams using Monte Carlo simulations. The positioning of the chambers with this EPOM at the depth of measurement results in a largely depth independent residual perturbation correction, which is determined within this study for the first time. For the parallel plate chambers the EPOM is independent of the energy of the primary electrons. Whereas for the Advanced Markus chamber the position of the EPOM coincides with the chambers reference point, it is shifted for the other parallel plate chambers several tenths of millimeters downstream the beam direction into the air filled cavity. For the cylindrical chambers there is an increasing shift of the EPOM with increasing electron energy. This shift is in upstream direction, i.e. away from the chambers reference point toward the focus. For the highest electron energy the position of the calculated EPOM is in fairly good agreement with the recommendation given in common dosimetry protocols, for the smallest energy, the calculated EPOM positions deviate about 30% from this recommendation.     

Nonideal Rayleigh–Taylor mixing

Rayleigh–Taylor mixing is a classical hydrodynamic instability that occurs when a light fluid pushes against a heavy fluid. The two main sources of nonideal behavior in Rayleigh–Taylor (RT) mixing are regularizations (physical and numerical), which produce deviations from a pure Euler equation, scale invariant formulation, and nonideal (i.e., experimental) initial conditions. The Kolmogorov theory of turbulence predicts stirring at all length scales for the Euler fluid equations without regularization. We interpret mathematical theories of existence and nonuniqueness in this context, and we provide numerical evidence for dependence of the RT mixing rate on nonideal regularizations; in other words, indeterminacy when modeled by Euler equations. Operationally, indeterminacy shows up as nonunique solutions for RT mixing, parametrized by Schmidt and Prandtl numbers, in the large Reynolds number (Euler equation) limit. Verification and validation evidence is presented for the large eddy simulation algorithm used here. Mesh convergence depends on breaking the nonuniqueness with explicit use of the laminar Schmidt and Prandtl numbers and their turbulent counterparts, defined in terms of subgrid scale models. The dependence of the mixing rate on the Schmidt and Prandtl numbers and other physical parameters will be illustrated. We demonstrate numerically the influence of initial conditions on the mixing rate. Both the dominant short wavelength initial conditions and long wavelength perturbations are observed to play a role. By examination of two classes of experiments, we observe the absence of a single universal explanation, with long and short wavelength initial conditions, and the various physical and numerical regularizations contributing in different proportions in these two different contexts.     

Detecting the onset of the lateralized readiness potential: a comparison of available methods and procedures

Studies that measure the onset of the lateralized readiness potential (LRP) could well provide researchers with important new data concerning the information-processing locus of experimental effects of interest. However, detecting the onset of the LRP has proved difficult. The present study used computer simulations involving both human and artificial data, and both stimulus- and response-locked effects, to compare a wide variety of techniques for detecting and estimating differences in the onset latency of the LRP. Across the two sets of simulations, different techniques were found to be the most accurate and reliable for the analysis of stimulus- and response-locked data. On the basis of these results, it is recommended that regression-based methods be used to analyze most LRP data.     

A pharmacodynamic analysis method to determine the relative importance of drug concentration and treatment time on effect

Purpose: The pharmacodynamics of most drugs follow the empirical relationship, Cⁿ × T=h, where C is drug concentration, T is exposure time and h is drug exposure constant. The value of n indicates the relative importance of C and T in determining the effect. An n value greater than 1.0 indicates that for two infusions that produce the same C × T, a short infusion that delivers high concentrations over a short duration will produce a greater Cⁿ × T and therefore a greater effect, compared to a long infusion that delivers lower concentrations. The reverse is true for an n value less than 1.0 and would support the use of a slow infusion. Hence, it is important to determine the n values and whether the n value significantly differs from 1.0. This report describes a three-step method for this purpose. Methods: First, we obtained experimental data on the relationship between drug concentration, treatment time and effect, and analyzed the data with a three-dimensional surface response method to obtain the pharmacodynamic model parameters and the magnitude of data variability. The experiments used mitomycin C and two human cancer cell lines, i.e. bladder RT4 and pharynx FaDu cells. The n values obtained from four experiments ranged from 1.04 to 1.16 for FaDu cells and from 1.14 to 1.46 for RT4 cells. The variability in the effect data decreased from 11.9% at 0% effect to 6.14% at 100% effect. Second, these results were used with Monte Carlo simulations to generate 100 concentration-time-effect data sets, which contained randomly and normally distributed data variability comparable to the experimentally observed variability, for each experimentally determined n value. This is analogous to performing 100 experiments under the same experimental conditions. Third, we analyzed the simulated data sets to obtain 100 estimated n values. The frequency with which these estimated n values fell above or below 1.0 indicated the probability that the experimentally determined n value used in the Monte Carlo simulations was truly different from 1.0. We defined this frequency for individual experiments as F_one, and calculated the overall probability for multiple experiments (F_multiple). A probability of greater than 97.5% (i.e. P < 0.05 for a two-tailed test) was considered statistically significant. Results: Analysis of the mitomycin C pharmacodynamic data yielded F_one and F_multiple of 99% to 100% for FaDu and RT4 cells, indicating that the n values for these cells were significantly higher than 1.0. A comparison of the statistical significance of the n value analyzed by the three-step pharmacodynamic analysis method, a conventional statistical method such as the Student's t-test and nonlinear regression analysis, indicated two advantages for the pharmacodynamic method: fewer experiments were required (theoretically only one experiment with three replicates would be sufficient) and a higher statistical significance of the n value was obtained. Conclusions: In summary, the three-step pharmacodynamic study design and analysis method can be used to define the relative importance of drug concentration and treatment time on drug effect. Received: 19 May 1999 / Accepted: 15 September 1999     

Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium

Rapid pacing is an important tool for understanding cardiac arrhythmias. A recent experiment involving rapid pacing of sheep atria indicated that the initiation of atrial arrhythmias may be related to the 1:1/2:1 bistability. To elucidate the mechanism of this relation, this study applied the pacing protocol from the sheep study to an idealized model of the right atrium. The model included all major anatomical features, the sino-atrial node, and the regional differences in the action potential duration (APD). A pacing protocol was applied, in which the basic cycle length (BCL) was decreased in steps of 10 ms until the response switched to 2:1, then BCL was increased. The 1:1-to-2:1 transitions occurred at shorter BCLs than the 2:1-to-1:1 transitions yielding a global bistability window of 60 ms. As in the sheep study, idiopathic waves were observed at BCLs within or near the bistability window. The model was used to quantify the types, prevalence, and persistence of idiopatic waves, study their initiation and termination, and relate them to the model components. The results demonstrate that idiopatic waveforms move with the shift of the bistability window and that they disappear when bistability is eliminated. Thus, this modeling study supports causal relationship between the 1:1/2:1 bistability and the initiation of arrhythmias.     

Pharmacokinetic/pharmacodynamic models for the depletion of Vbeta5.2/5.3 T cells by the monoclonal antibody ATM-027 in patients with multiple sclerosis, as measured by FACS

AIMS: (i) To model the effects of the monoclonal antibody ATM-027 on the number of target cells and on the receptor density on the cell surface as measured by Fluorescence Activated Cell Sorter analysis, (ii) to investigate the effects of categorizing a continuous scale, and (iii) to simulate a phase II trial from phase I data in order to evaluate the predictive performance of the model by comparison with the actual trial results. METHODS: Based on the data from one phase I and one phase II study in multiple sclerosis (MS) patients, models were developed to characterize the pharmacokinetics and pharmacodynamics of the monoclonal antibody ATM-027 and its effects on Vbeta5.2/5.3+ T cells. The pharmacodynamic variables were the number of target T cells and the expression of its receptor. The latter was modelled in both a categorical and continuous way. The modelling was performed with a nonlinear mixed effects approach using the software NONMEM. The joint continuous models were used to simulate the phase II trial from the phase I data. RESULTS: The pharmacokinetics of ATM-027 were characterized by a two-compartment model with a total volume of distribution of 5.9 litres and a terminal half-life of 22.3 days (phase II parameter estimates) in the typical patient. Continuous receptor expression was modelled using an inhibitory sigmoidal Emax-model. Similar results from the phase I and phase II data were obtained, and EC50 was estimated to be 138 and 148 microg litre(-1), respectively. Categorical receptor expression was modelled using a proportional odds model, and the EC50 values obtained were highly correlated with those from the continuous model. The numbers of target T cells were also modelled and treatment with ATM-027 decreased the number of cells to 25.7% and 28.9% of their baseline values in the phase I and II trials, respectively. EC50s for the decrease in the number of T cells were 83 microg litre(-1) and 307 microg litre(-1), respectively. Simulations of the phase II trial from the phase I models gave good predictions of the dosing regimens administered in the phase II study. CONCLUSION: All aspects of effects of the monoclonal antibody ATM-027 on Vbeta5.2/5.3+ T cells were modelled and the phase II trial was simulated from phase I data. The effects of categorizing a continuous scale were also evaluated.     

Remodeled-matrix contraction by fibroblasts: numerical investigations

It is well known that the fibroblast-collagen-matrix contraction model is a unique way to study mechanical interactions that regulate wound contraction of connective tissue cells. This contraction, due to cell traction, plays important roles in wound healing and pathological contractures. A continuum model initially used for the study of mesenchymal morphogenesis is revisited and numerically investigated by assuming that the extracellular matrix has adaptive-elastic properties. The set of non-linear partial differential equations is solved numerically by a finite difference method and the obtained results are discussed.     

A Reappraisal of Drug Release Laws Using Monte Carlo Simulations: The Prevalence of the Weibull Function

Purpose. To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. Methods. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. Results. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Conclusions. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.     

Effect of hydrogen bond cooperativity on the behavior of water

Four scenarios have been proposed for the low-temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism that leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, because there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean-field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model independent. Using estimates from experimental data for H-bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid–liquid critical point at positive pressure.