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Mathematical model of antibody targeting: important parameters defined using clinical data.

Antibody-targeted therapy of cancer has shown benefits in the treatment of some cancers but selective delivery has not been optimized. Many parameters influence antibody targeting; some will have a greater effect than others and their effects will generally be interrelated. They include effects of blood flow and pressure, vascular permeability, venous and lymphatic drainage, permeation through extravascular spaces, antibody clearance, specificity, affinity and resistance to degradation. Quantitative data about the behaviour of targeting systems can be collected, and it is possible to describe the system in terms of compartments interconnected by equations defining the passage of targeting agents between them. A mathematical model of antibody targeting can thus be built. We have collected data on the time course of the distribution of four different antibody molecules of molecular weight 27, 100 and 150 kDa directed against carcinoembryonic antigen in patients with colorectal cancer. Laboratory data were used for parameters which could not be measured in patients. These data have been used to test the validity of the model for man and to develop it so that it is consistent with the diverse clinical data. The model is then used to understand the effects of changes to a parameter on tumour targeting efficiency and to select those parameters which have the greatest effect in therapy. Affinity of antibody, flow of antibody through the tumour and rate of elimination of antibody from the tumour were shown to be the most powerful parameters determining antibody localization. These concepts can be used to determine design parameters for antibody-targeted cancer therapy.

Antigen-Antibody Reactions↗

99Tcm hexamethylpropyleneamineoxime (HMPAO) as a platelet label: evaluation of labelling parameters and first in vivo results.

The lipophilic 99Tcm hexamethylpropyleneamineoxime (HMPAO) complex can be used for labelling platelets as well as granulocytes. For the evaluation of optimal labelling parameters, platelets were isolated according to standard isolation procedures. The labelling efficiency (%) depends on incubation temperature (22 degrees C: 40%; 37 degrees C: 50%), incubation time (3 min: 20%; 25 min: 55%) and the incubation medium (plasma: 40%; saline: 50%). The 60 min 99Tcm elution from the platelets is around 8%. The platelet recovery, used as a quality parameter, is around 25 +/- 4% and is stable for at least 240 min. The high elution rate from the platelets leads to renal excretion of the label and so to significant kidney and bladder activity. Intestinal excretion of the label can also be frequently demonstrated. Fresh thrombotic lesions can usually be detected 4 h after reinjection of the labelled platelets, and in some patients as early as 1 h after reinjection of the platelets. In conclusion, 99Tcm HMPAO seems to be a promising platelet label for imaging thrombotic lesions but not for platelet-survival studies because of the short physical half-life of 99Tcm.

Blood Platelets↗

Evaluation of renal artery stenosis with velocity parameters of Doppler sonography.

OBJECTIVE: The purpose of this study was to evaluate the accuracy of velocity parameters for the diagnosis of renal artery stenosis (RAS) with color Doppler sonography and to determine the optimal threshold values for these parameters. METHODS: The study group was composed of 187 renal arteries, which were examined by color Doppler sonography and angiography. Four Doppler parameters, including the peak systolic velocities (PSVs) in the renal and interlobar arteries, the renal-aortic ratio, and the renal-interlobar ratio (RIR), were measured. Receiver operating characteristic curve analysis was performed to determine the optimal parameter. The sensitivity, specificity, and negative and positive predictive values at various threshold values were calculated. RESULTS: Doppler sonographic examination was technically successful in 96% of renal arteries (180/187). The RIR was determined to be the best parameter. With threshold values of RIR greater than 5, PSV greater than 150 cm/s in the renal artery, renal-aortic ratio greater than 2, and PSV less than 25 cm/s in the interlobar artery, the sensitivity values were 88%, 81%, 70%, and 74%, respectively. An RIR greater than 5 and PSV less than 15 cm/s in the interlobar artery provided the optimal combination of parameters, with sensitivity and specificity of 91% and 87%, respectively. CONCLUSIONS: The RIR is the best velocity parameter in the detection of RAS (> or =50%), and its best cutoff is 5. Valuing influencing factors of PSV in the renal artery will help reduce misdiagnosis. The combination of RIR greater than 5 and PSV less than 15 cm/s in the interlobar artery provides the best diagnostic efficiency of RAS.

Adolescent↗

Tooth enamel EPR dosimetry: optimization of EPR spectra recording parameters and effect of sample mass on spectral sensitivity.

In order to improve the accuracy of the tooth enamel EPR dosimetry method, EPR spectra recording conditions were optimized. The uncertainty of dose determination was obtained as the mean square deviation of doses, determined with the use of a spectra deconvolution program, from the nominal doses for ten enamel samples irradiated in the range from 0 to 500 mGy. The spectra were recorded at different microwave powers and accumulation times. It was shown that minimal uncertainty is achieved at the microwave power of about 2 mW for a used spectrometer JEOL JES-FA100. It was found that a limit of the accumulation time exists beyond which uncertainty reduction is ineffective. At an established total time of measurement, reduced uncertainty is obtained by averaging the experimental doses determined from recorded spectra following intermittent sample shaking and sample tube rotation, rather than from one spectrum recorded at longer accumulation time. The effect of sample mass on the spectrometer's sensitivity was investigated in order to find out how to make appropriate corrections.

Algorithms↗

Optimal control of neuronal activity.

We investigate the optimal control of neuronal spiking activity for neurons receiving a class of random synaptic inputs, characterized by a positive parameter alpha. Optimal control signals and optimal variances are found exactly for the diffusion process approximating an integrate and fire model. When synaptic inputs are "sub-Poisson" (alpha<0.5), we find that the optimal synaptic input is a delta function (corresponding to bang-bang control) and the optimal signal is not unique. Poisson synaptic input is the critical case: The control signal is unique, but the control signal is still a delta function. For "supra-Poisson" (alpha>0.5) inputs, the optimal control is smooth and unique. The optimal variance obtained in the current paper sets the lowest possible bound in controlling the stochasticity of neuronal activity. We also discuss how to implement the optimal control signal for certain model neurons.

Action Potentials↗

18F-FDG PET of gliomas at delayed intervals: improved distinction between tumor and normal gray matter.

UNLABELLED: We hypothesized that delineation of gliomas from gray matter with 18F-FDG PET could be improved by extending the interval between 18F-FDG administration and PET data acquisition. The purposes of this study were, first, to analyze standard and delayed 18F-FDG PET images visually and quantitatively to determine whether definition of tumor improved at later imaging times and, second, to investigate the dynamics of model-derived kinetic rate constants, particularly k4. METHODS: Nineteen adult patients with supratentorial gliomas were imaged from 0 to 90 min and once or twice later at 180-480 min after injection. In 15 patients, arterial sampling provided the early input function. Venous sampling provided the remaining curve to the end of the imaging sequence. Standardized uptake value (SUV) was calculated as tissue concentration of tracer per injected tracer dose per body weight. Ratios of tumor SUV relative to the SUV of gray matter, brain (including gray and white matter), or white matter were calculated at each imaging time point. Dynamic image data from tumor, gray matter, brain, or white matter were analyzed using a 2-compartment, 4-parameter model applied for the entire duration of imaging, in which delay, K1, distribution volume, k3, and k4 were optimized using a nonlinear optimization method. Parameter estimation for each region included both an early subset of data from a conventional dynamic imaging period (0-60 min) and the full, extended dataset for each region. RESULTS: In 12 of the 19 patients, visual analysis showed that the delayed images better distinguished the high uptake in tumors relative to uptake in gray matter. SUV comparisons also showed greater uptake in the tumors than in gray matter, brain, or white matter at the delayed times. The estimated k4 values for tumors were not significantly different from those for gray matter in early imaging analysis but were lower (P < 0.01) using the extended-time data. CONCLUSION: The kinetic parameter results confirm the visual and SUV interpretation that tumor enhancement is greater than enhancement of surrounding brain regions at later imaging times, consistent with a greater effect of FDG-6-phosphate degradation on normal brain relative to glioma.

Adult↗

Systematic tuning of parameters in support vector clustering.

Clustering algorithms divide a set of observations into groups so that members of the same group share common features. In most of the algorithms, tunable parameters are set arbitrarily or by trial and error, resulting in less than optimal clustering. This paper presents a global optimization strategy for the systematic and optimal selection of parameter values associated with a clustering method. In the process, a performance criterion for the optimization model is proposed and benchmarked against popular performance criteria from the literature (namely, the Silhouette coefficient, Dunn's index, and Davies-Bouldin index). The tuning strategy is illustrated using the support vector clustering (SVC) algorithm and simulated annealing. In order to reduce the computational burden, the paper also proposes an alternative to the adjacency matrix method (used for the assignment of cluster labels), namely the contour plotting approach. Datasets tested include the iris and the thyroid datasets from the UCI repository, as well as lymphoma and breast cancer data. The optimal tuning parameters are determined efficiently, while the contour plotting approach leads to significant reductions in computational effort (CPU time) especially for large datasets. The performance criteria comparisons indicate mixed results. Specifically, the Silhouette coefficient and the Davies-Bouldin index perform better, while the Dunn's index is worse on average than the proposed performance index.

Algorithms↗

Accelerated process development for protease production in continuous multi-stage cultures.

A fermentation process was developed and optimized for the production of a specific protease from Bacillus licheniformis PWD-1. Media formulations were constructed and crucial environmental parameters were optimized to enhance growth and product formation. Process dynamics of substrate consumption, biomass-, product-, as well as by-product formation were determined under controlled conditions in a bioreactor. Using kinetic data from batch- and continuous-culture experiments, a fed-batch process was developed producing proteolytic activities 10 times those found during regular batch culture. In one stage continuous stirred tank culture protease formation was completely decoupled from sporulation. Shift experiments in one-stage continuous cultures led to the development of a two-stage continuous stirred tank fermentation process using optimized conditions for growth in the first stage and protease formation in the second stage. Accordingly, the basis for a continuous production of the enzyme on a pilot scale was accomplished.

Bacillus↗

Comparison of solid-phase extraction and solid-phase microextraction for carbofuran in water analyzed by high-performance liquid chromatography-photodiode-array detection.

In this study a direct solid-phase microextraction (SPME) procedure has been developed for the determination of carbofuran in water. Experimental parameters such as selection of SPME coating, effect of temperature, effect of salt addition and solvent desorption were studied and optimized. Analytical parameters such as linearity, precision, detection and quantitation limits, and matrix effects for solid-phase extraction (SPE) and SPME methods were evaluated for comparison purposes with the aim of selecting the most appropriate depending on the detection capabilities required. SPE and SPME were followed by high-performance liquid chromatography with diode-array detection, using a 50 x 4.6 mm I.D. guard column and a 150 x 4.6 mm I.D. analytical column, both packed with C18 silica. Both methods can be applied to real samples and give the same results, but SPE allows the detection of lower carbofuran concentrations (0.06 microg/L) as compared to

Carbofuran↗

Forecasting of life threatening arrhythmias using the compression entropy of heart rate.

OBJECTIVES: Ventricular tachycardia (VT) provoking sudden cardiac death (SCD) are a major cause of mortality in the developed countries. The most efficient therapy for SCD prevention are implantable cardioverter defibrillators (ICD). In this study heart rate variability (HRV) measures were analyzed for short-term forecasting of VT in order to improve VT sensing and to enable a patient warning of forth-coming shocks. METHODS: The last 1000 normal beat-to-beat intervals before 50 VT episodes stored by the ICD were analyzed and compared to individually acquired control time series (CON). HRV analysis was performed with standard parameters of time and frequency domain as suggested by the HRV Task Force and furthermore with a newly developed and optimized nonlinear parameter that assesses the compression entropy of heart rate (Hc). RESULTS: Except of meanNN (p = 0.02) we found no significant differences in standard HRV parameters. In contrast, Hc revealed highly significant (p = 0.007) alterations in VT compared with CON suggesting a decreased complexity before the onset of VT. CONCLUSION: Compression entropy might be a suitable parameter for short-term forecasting of life-threatening tachycardia in ICD.

Arrhythmias, Cardiac↗

Temporal parameters of desensitization to intravesical resiniferatoxin in the rat.

Temporal factors affecting desensitization of bladder sensory afferents to the capsaicin-like irritant resiniferatoxin (RTX) were studied, to determine optimal treatment parameters for clinical application of such substances. Four days after implantation of a chronic cannula into the bladder dome, vehicle or RTX (0.1-10 nmol) was injected into the bladders of awake, freely moving rats four times at 60-min intervals for exposure durations of 5, 15, or 45 min, or at intervals of 15, 60, or 120 min (duration 5 min). The first RTX injection dose-dependently increased time spent engaged in abdominal licking. Regardless of exposure interval and duration, time spent licking increased to a lesser extent with each subsequent injection, indicating desensitization of sensory afferents. Magnitude and duration of desensitization were dose dependent for all exposure regimens, and there were few differences between groups. Desensitization at 24 h was also greater in rats exposed four times compared to rats exposed once. Following four exposures to RTX, nearly complete recovery occurred within 7-14 days, in a dose-dependent manner. Thus, magnitude and duration of desensitization to locally administered RTX depend primarily on dose and number of exposures to RTX; duration of exposure and interval between exposures within the ranges studied were less important determinants.

Administration, Intravesical↗

Optimized Baxter model of protein solutions: electrostatics versus adhesion.

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

Adhesiveness↗

Stochastic optimization of intensity modulated radiotherapy to account for uncertainties in patient sensitivity.

The aim of the present work is to better account for the known uncertainties in radiobiological response parameters when optimizing radiation therapy. The radiation sensitivity of a specific patient is usually unknown beyond the expectation value and possibly the standard deviation that may be derived from studies on groups of patients. Instead of trying to find the treatment with the highest possible probability of a desirable outcome for a patient of average sensitivity, it is more desirable to maximize the expectation value of the probability for the desirable outcome over the possible range of variation of the radiation sensitivity of the patient. Such a stochastic optimization will also have to consider the distribution function of the radiation sensitivity and the larger steepness of the response for the individual patient. The results of stochastic optimization are also compared with simpler methods such as using biological response 'margins' to account for the range of sensitivity variation. By using stochastic optimization, the absolute gain will typically be of the order of a few per cent and the relative improvement compared with non-stochastic optimization is generally less than about 10 per cent. The extent of this gain varies with the level of interpatient variability as well as with the difficulty and complexity of the case studied. Although the dose changes are rather small (<5 Gy) there is a strong desire to make treatment plans more robust, and tolerant of the likely range of variation of the radiation sensitivity of each individual patient. When more accurate predictive assays of the radiation sensitivity for each patient become available, the need to consider the range of variations can be reduced considerably.

Dose-Response Relationship, Radiation↗

Population kinetics and conditional assessment of the optimal dosage regimen using the P-PHARM software package.

The adjustment of individual dosage regimen is an adaptive control process based upon an individual response to a pharmacokinetic model. To attain this objective, it is very helpful to know the characteristics of the population to which the subject belongs, in terms of mean parameters and interindividual variability. Usually the available information consists of incomplete and sparse data. For this reason it is essential to employ a computational methodology based on non-linear mixed-effect procedures in order to obtain a population parameter estimate. A Bayesian methodology can then be applied from the population parameters to the specific data for the individual requiring a dosage adjustment (such data includes drug concentration(s) of the active drug, demographic data, etc). The result of the Bayesian calculation supplies the required individual pharmacokinetic parameters. An optimal dosage regimen can be defined on the basis of therapeutical criteria (concentration ranges) as well as practical constraints such as: the size of available unitary drug dosages, feasible drug intake times, penalties associated with expected concentrations falling outside the therapeutic concentration ranges. In this paper we present the methodology and results obtained using the P-Pharm software tool. P-Pharm implements a non-linear mixed-effect population parameter estimation algorithm based on the EM algorithm. This method allows the inclusion of explicit variables into the calculations, it implements an individual Bayesian parameter estimation procedure and also an algorithm for the conditional assessment of the optimal dosage regimen given a list of practical constraints.

Algorithms↗

Process optimization of continuous gluconic acid fermentation by isolated yeast-like strains of Aureobasidium pullulans.

This study was focused on the optimization of a new fermentation process for continuous gluconic acid production by the isolated yeast-like strain Aureobasidium pullulans DSM 7085 (isolate 70). Operational fermentation parameters were optimized in chemostat cultures, using a defined glucose medium. Different optima were found for growth and gluconic acid production for each set of operation parameters. Highest productivity was recorded at pH values between 6.5 and 7.0 and temperatures between 29 and 31 degrees C. A gluconic acid concentration higher than 230 g/L was continuously produced at residence times of 12 h. A steady state extracellular gluconic acid concentration of 234 g/L was measured at pH 6.5. 122% air saturation yielded the highest volumetric productivity and product concentration. The biomass-specific productivity increased steadily upon raising air saturation. An intracellular gluconic acid concentration of about 159 g/L (0.83 mol) was determined at 31 degrees C. This is to be compared with an extracellular concentration of 223 g/L (1.16 mol), which indicates the possible existence of an active transport system for gluconic acid secretion, or the presence of extracellular glucose oxidizing enzymes. The new process provides significant advantages over the traditional discontinuous fungi operations. The process control becomes easier, thus offering stable product quality and quantity.

Ascomycota↗

Dynamic reaction design of enzymic biotransformations in organic media: equilibrium-controlled synthesis of antibiotics by penicillin G acylase.

Parameters relevant to the thermodynamically controlled synthesis of cephalothin utilizing highly active stabilized penicillin G acylase derivatives were studied. These included solubility/stability of substrates, enzyme derivative activity/stability, reaction course and synthetic yields. These parameters were altered by varying the pH, dimethylformamide concentration and temperature. Simultaneous optimization of the selected parameters could not be achieved with a single set of conditions. However, continuous adjustment of conditions throughout the reaction course allowed each parameter to be optimized (dynamic reaction design). This strategy works by optimizing those parameters that are critical to the overall reaction at a given point, whilst leaving others sub-optimal when their contribution to the total is minimal. This strategy has achieved a 90% transformation of antibiotic nucleus to cephalothin at a final concentration of 20 g/l, high enzyme and reactant stability, with a reaction period of 3 h (using 1 ml of derivative/40 ml of reaction solution).

Anti-Bacterial Agents↗

Selection of measurement frequencies for optimal extraction of tissue impedance model parameters.

The results are presented of a study performed to determine the measurement frequencies that provide optimal extraction of tissue impedance model parameters from in vivo measured electrical impedance spectra. Measurement frequency sets that are logarithmic and quasi-linear, and frequency sets that produce angularly equidistant points on the Nyquist loci are used to test the parametric fitting algorithm that calculates R0, R infinity, alpha and tau tissue parameters from complex impedance spectra. Simulated data, calculated in the presence of < or = 5% measurement noise, and in vivo experiments indicate that the quality of the fitted parameters depends upon the selection of measurement frequencies. The results show that, if measurements are performed with a system that has a realistic measurement bandwidth, then, for the best estimation of: R0, the measurement frequencies should include the decade from 100 Hz-1 kHz; R infinity, the algorithm should not include frequencies under 1 kHz; alpha and tau, the measurement frequencies should be equidistantly spaced on the Nyquist locus.

Algorithms↗

Characterization of a microscale cyclical electrical field flow fractionation system.

A microscale cyclical electrical field flow fractionation (CyElFFF) channel is characterized with regard to the effect of various operating parameters and comparison made to recent theoretical developments. Challenges associated with various operating conditions are reported along with some of the optimized operating parameters. The effect of retention wall choice, an offset voltage, relaxation steps, and flow rates, along with the basic operating parameters of voltage, frequency, and electrophoretic mobility are reported. Retention of polystyrene nanoparticle standards is accomplished and the first separations using this technique in a microscale system are also demonstrated. Relaxation steps and offset voltages are found to be effective in eliminating early peaks and in improving plate heights. Plate heights were also found to decrease with increasing flow rates, which is the opposite of the behavior seen in most existing chromatographic systems. The experimental results are compared to the analytical and empirical models of CyElFFF and found to be compatible. Suggestions are made for improving the separation and analysis methods used with CyElFFF.

Journal Article↗