The reduction of tumour control with increasing overall time: mathematical considerations

The rate of loss of tumour control (dP/dt) with extension of treatment time is analysed to assess the relative contributions of radiobiological parameters (radiosensitivity, clonogen doubling time, clonogen numbers and fractionation schedule) on such loss. Linear quadratic modelling and Poisson statistics are used to study individual tumour responses. A heterogeneous tumour population is constructed by the use of random sampling techniques to allow for variations in intrinsic radiosensitivity and clonogen doubling times. Average tumour control probability is calculated for this population for two different fractionation schedules (60 Gy in 30 fractions and 50 Gy in 15 fractions), each given over 15-60 days. The magnitude of dP/dt will depend upon the tumour cure probability (P): the loss of control will be most significant for tumours which have a cure of 37% when the Poisson survival model is used. The analysis suggests that compensation for short unscheduled treatment gaps (e.g. by increasing the total dose or rescheduling with use of weekend treatment sessions) may only be required for difficult tumours (i.e. radioresistant and/or with short clonogen doubling times). Where pre-treatment clonogen numbers are relatively low as in small volume tumours or after surgical debulking, the model predicts that correction for short treatment gaps is probably not required if the average effective clonogen doubling times are longer than 5 days. Different dose-time-fractionation schedules, even though producing similar overall cure rates in clinical practice, may actually be achieving cures in different subpopulations within a population of tumours, since the value of dP/dt in each individual tumour will depend upon the set of radiobiological parameters given above. For a hypothetical randomly selected heterogeneous tumour population the predicted rates of loss of tumour control produced by an extension in treatment time are 0.9 and 1.1% per day, respectively, for the above fractionation schedules. These values are close to those reported in the clinical literature for the first 2 weeks of treatment prolongation (1-2% per day for squamous cell carcinomas). The Poisson method, when combined with random sampling techniques, consequently provides realistic data. Modelling of this clinical problem provides an insight into how tumour sub-populations, each characterized by its own set of radiobiological parameters, can influence the overall rate of loss of tumour control in a heterogeneous population. Random sampling techniques should be considered as necessary precursors for the assessment of the choices of dose-fractionation in future clinical trials particularly when more precise data regarding the radiobiological parameters and their statistical variations become available.     

Dynamics of Air Flow in Sewer Conduit Headspace

Pressurization in sanitary sewer conduit atmosphere is modeled using computational fluid dynamics techniques. The modeling approach considers both turbulent and laminar flow regimes. The turbulent model takes into consideration the turbulence-driven secondary currents associated with the sewer headspace and hence the Reynolds equations governing the air flow field are closed with an anisotropic closure model which comprises the use of the eddy viscosity concept for the turbulent shear stresses and semiempirical relations for the turbulent normal stresses. The resulting formulations are numerically integrated. The turbulent model outputs are verified with experimental data reported in the literature. Satisfactory agreement is obtained between numerical simulations and experimental data. Mathematical formulas and curves as functions of longitudinal pressure gradient, wastewater velocity, and sewer headspace geometry are developed for the cross-sectional average streamwise velocity.     

Statistical Analysis of Fragility Curves

This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.     

Thermodynamic analysis of the In-Ga-Sb system

The phase diagram and thermodynamic data for the In-Ga-Sb system are fit with a model for the III-V liquid phases, in which the enthalpy and excess entropy of mixing are quartic functions of the atomic fraction and the enthalpy of mixing is a quadratic function of temperature. The Gibbs energy, enthalpy, and entropy of formation of the III-V compounds are obtained as functions of temperature from the heat capacities and the standard enthalpy and entropy of formation at 298 K. The fits are quantitatively satisfactory and better than any hitherto obtained, particularly for the III-V liquidus lines and the ternary liquid. The partial pressures of Sb₂ and Sb₄ are calculated along the three phase curves of In_1-uGa_uJSb(s), and relations given to obtain the relative chemical potentials of In and/or Ga are from these. The enthalpy of mixing of the III-V liquids is calculated for a few hundred degrees above the compound melting points, where presently there are no data. Characteristics of an improved model are postulated.     

Multiple peaks in high-performance liquid chromatography of proteins. beta-Lactoglobulins eluted in a hydrophobic interaction chromatography system

The hypothesis of Geisler (Brain Res. 212 (1981) 198-201), in which the different spontaneous-rate classes of primary auditory neurons were accounted for by the different sizes of uniquantal EPSPs relative to the gap between resting membrane and threshold potentials, was represented with an expanded model which included relative refractory effects. The spike rates generated by the expanded model, when plotted vs. estimated sound level, are qualitatively similar to those of experimentally obtained rate-level curves. The hypothesis is also consistent with recent ultrastructural data which suggest that average quantal-release rates for any particular primary auditory neuron are inversely related to its spontaneous rate. The model's recovery processes following spike generation (hazard functions) are also similar to those observed experimentally.     

马钢H型钢轧机加热炉燃烧控制系统

马钢Ｈ 型钢厂加热炉燃烧控制系统采用二级计算机控制系统。二级监控系统基于先进的最佳加热温度控制曲线数据库,采集并计算炉内坯料的实际温度,进行最佳燃烧控制。一级燃烧控制采用软件控制代替传统的仪表控制系统,实现温度自动控制、煤气／ 空气的交叉限幅控制。其控制水平、高效节能、灵活可靠诸方面均达到国际９０ 年代初的先进水平。     

The problem of inference from curves based on group data.

The use of curves based on averaged data to infer the nature of individual curves or functional relationships is hazardous only when interpretations of the group data, or inferences derived from them, are unwarranted and violate accepted principles of statistical inference. The problems involved in and the procedures appropriate to each of 3 mathematical functions are discussed: Class A, Functions unmodified by averaging; Class B, Functions for which averaging complicates the interpretation of parameters but leaves form unchanged; and Class C, Functions modified in form by averaging. The form of a group mean curve may provide a way to test exact hypotheses about individual curves, although the form of the latter is not determined by the form of the group mean curve. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Quantitative description of the process of radiation inactivation of cells. VIII. Microdosimetry in the analysis of the reproductive death of eukaryotic cells

The microdosimetric approach permits to model the first physical stage of radiation damage developing of multistage model of radiation effect. It describes stochastics of absorbed energy distribution among and inside sensitive cell volumes. The analysis of radiobiological effect becoming more complete and adequate. The limits of application of valuable microdosimetric values to characterizing both the quality and quantity of radiation affecting the cells is considered. The aspects of the theory of dual action of radiation well compare with those of the cytogenetic model linking the reproductive cell death with asymmetrical chromosome exchanges.     

A comparison for use in radiotherapy of neutron beams generated with 16 and 42 MeV deuterons on beryllium

The physical and radiobiological properties of two neutron beams have been compared. The beams were generated by deuterons of 16 MeV at Hammersmith Hospital and 42 MeV at Harwell, in both cases falling on a Be/Cu target. The dose-rate and depth-dose characteristics at the higher energy were found to be superior to those at the lower energy. Collimation and shielding at the higher energy are facilitated by the greater degree of forward-peaking and by the fact that a higher dose-rate allows longer collimators to be used. Attenuation in iron was found to be similar at the two energies. The radiobiological properties of the two neutron beams are very similar. There is a difference of about 20 per cent in RBE for effects on mammalian tissues for doses between 300 and 2,000 rad of neutrons. The OER and the sparing effect of two large fractions are the same for the two beams.     

Radiobiologically based assessments of the net costs of fractionated focal radiotherapy

PURPOSE: To assess the potential changes in the net costs of focal radiotherapy techniques at differing doses per fraction and interfraction intervals. METHODS: Linear quadratic radiobiological modeling is used with appropriate variations in the radiosensitivity and tumor cell proliferation parameters. The notional cost of treatment is calculated from the number of fractions, cost per fraction and the cost of treatment failure, which is itself related to (1-TCP) where TCP is the tumor cure probability. Additional Monte Carlo calculations from ranges of radiobiological parameters have been used to simulate the cost of treatment of tumor populations. RESULTS: The optimum dose per fraction (and optimum overall cost) for conventional (nonfocal) radiotherapy is generally at low doses of around 2 Gy per fraction. The use of hyperfractionated and accelerated radiotherapy in addition to focal radiotherapy techniques appear to be indicated for more radioresistant tumors and if tumor proliferation is extremely rapid, but the need for treatment acceleration is much reduced where effective focal techniques are used. CONCLUSIONS: Radiobiological and economic modeling can be used to guide clinical choices of dose fractionation techniques providing the key radiobiological parameters are known or if the ranges of likely parameters in a tumor population are known. Focal radiotherapy, by the introduction of changes in the physical dose distribution, produces an upward shift in the optimum dose per fraction and a reduced dependency on overall treatment time.     

Kinetic model for the chemical dissolution of multiparticle systems

A kinetic model is designed to interpret fraction reacted/time curves obtained from leaching multiparticle concentrates. The effect of individual particle shape on fraction reacted/time curves was determined by comparing data obtained from leaching a sphere and numerous irregular particles of malachite made by breaking up blocks of ore. All the leaching processes were carried out under the same experimental conditions. Finally, a kinetic model is presented which includes both size and shape of the particles. Experimental results show that fraction reacted/time curves are nearly the same for all particles with the same initial size/shape factor ratio. The importance of the solid's shape in interpreting heterogeneous kinetic data is clearly shown.     

Noninvasive quantification of iodine-123-iomazenil SPECT

The feasibility of a noninvasive method for quantification of [123I]iomazenil binding using a standardized arterial input function and a single venous blood sample was assessed in normal volunteers. METHODS: Serial SPECT images and blood data from six healthy male volunteers after intravenous injection of [123I]iomazenil were used. The standardized input function was derived by averaging the six subjects' arterial curves. Individual input functions were estimated by calibrating the standardized input function with one-point venous blood radioactivity concentration. Ligand transport (K1) and receptor binding were computed from the estimated input functions and two separate SPECT scans using a table look-up procedure based on a three-compartment, two-parameter model. Reference values for K1 and receptor binding were determined from the serial SPECT data and individual arterial curves using a three-compartment, three-parameter model and curve fitting. RESULTS: Analyses of the error caused by the calibration in relation to the time postinjection revealed that the optimal calibration time was 30 min postinjection. Receptor binding obtained by this simplified method correlated well with the reference values (r = 0.941) and was estimated within an error of 10% in the cerebral cortical regions. Although the estimated K1 showed relatively poor correlation (r = 0.699) with the reference value, it was an excellent relative measure in each subject. CONCLUSION: Our method provided an absolute measure of the benzodiazepine receptor binding and a relative measure of ligand transport from two SPECT scans and a venous blood sample. This method would be useful for quantitative assessment of benzodiazepine receptors in clinical settings.     

Selective in vivo stimulation of stress-activated protein kinase in different rat tissues by immobilization stress

The quaternary structure of Lumbricus terrestris hemoglobin was investigated by small-angle x-ray scattering (SAXS). Based on the SAXS data from several independent experiments, a three-dimensional (3D) consensus model was established to simulate the solution structure of this complex protein at low resolution (about 3 nm) and to yield the particle dimensions. The model is built up from a large number of small spheres of different weights, a result of the two-step procedure used to calculate the SAXS model. It accounts for the arrangement of 12 subunits in a hexagonal bilayer structure and for an additional central unit of clylinder-like shape. This model provides an excellent fit of the experimental scattering curve of the protein up to h = 1 nm-1 and a nearly perfect fit of the experimental distance distribution function p(r) in the whole range. Scattering curves and p(r) functions were also calculated for low-resolution models based on 3D reconstructions obtained by cryoelectron microscopy (EM). The calculated functions of these models also provide a very good fit of the experimental scattering curve (even at h > 1 nm-1) and p(r) function, if hydration is taken into account and the original model coordinates are slightly rescaled. The comparison of models reveals that both the SAXS-based and the EM-based model lead to a similar simulation of the protein structure and to similar particle dimensions. The essential differences between the models concern the hexagonal bilayer arrangement (eclipsed in the SAXS model, one layer slightly rotated in the EM model), and the mass distribution, mainly on the surface and in the central part of the protein complex.     

Seepage Modeling Assisted Optimal Design of a Homogeneous Earth Dam: Procedure Evolution

Presented herein is a procedure for arriving at an optimal design of a homogeneous earth dam laid on an impervious foundation and provided with a drain. The procedure, heavily dependent on variably saturated flow modeling, involves optimizing a multiobjective function comprising a weighted summation of four objective functions, viz., the dam section area, seepage discharge, wetted area of the dam section and the drain area. The design variables considered in the optimization are the upstream and downstream slopes and the drain dimensions. The optimization is carried out subject to the constraints ensuring safe upstream and downstream slopes and sufficient distance between the free surface and the downstream face. Two of the objective functions (viz., the seepage discharge and the wetted area) and the constraints are implicit functions of the design variables. Their values are obtained by employing a numerical model of two-dimensional (vertical plane) variably saturated flow in a homogeneous earth dam. Optimization, conducted by the sequential unconstrained minimization technique procedure is preceded by several runs of the model for various combinations of the design variables. The discrete values of the implicit functions so generated are invoked during optimization to compute the implicit objective functions and constraints. The results are presented in the form of nondimensional design tables/curves. The design procedure is illustrated with the help of few examples.     

Moment-Based Calculation of Parameters for the Storage Zone Model for River Dispersion

Theoretical methods have been developed to calculate values of parameters of the storage zone model for river mixing. Analytical solutions of the Laplace-transformed equations of the storage zone model are related to the observed concentration distribution in order to determine model parameters in both the moment matching method and the maximum likelihood method, which were developed in this study. The results obtained by comparison with experimental data show that the parameters calculated by the moment matching method are in good agreement with the observed values of storage zone model parameters, whereas results from the maximum likelihood method and several existing methods are not in good agreement with the experimentally observed values. Dispersion data from natural streams show that the calculated concentration curves from the numerical solutions of the storage zone model with the parameters calculated by the moment matching method fit the observed concentration curves very well. It can be concluded that parameters of the storage zone model calculated using the moment matching method can properly explain the natural dispersion processes in real streams.     

A quantified approach to the analysis of complications in combined external and intracavitary radiotherapy of uterine cervical neoplasms

A method is presented of calculating biological doses in combined external and intracavitary radiotherapy with long-lived radioisotopes. The method utilizes the well-known "nominal standard dose" concept combined with an original correction, based on a radiobiological model, to account for the nonhomogeneity of the external field therapy. Of practical interest are the points of maximal radiation dose sustained by the rectum and bladder in the treatment of carcinoma of the uterine cervix. Forty patients with malignant tumors of the uterine cervix who were treated at the Beilinson Hospital are described. A high degree of correlation was found between the biological dose and long-term regional complications. There appears to be a practical threshold dose, of about 4,000 rets, below which severe gastrointestinal and genitourinary complications are rare. A strategy of optimal treatment leading to limited complications is presented.     

Estimation of growth velocities from individual longitudinal data

Since the construction of growth velocity curves using the simple increment method (i.e., plotting the increments deltaxt vs, time, t) involves a number of methodological problems, when mathematical curves are fit, they are generally fit to the "distance traveled", plot (of xt vs. t) and the corresponding velocity curve is then obtained by differentiation. However, most of the traditional methods for accomplishing this (e.g., fitting the Gompertz or logistic curves) require that the course of growth be studied over a sufficiently long time period to allow accurate determinations of the upper and lower asymptotes of these S-shaped functions. This is not always feasible in practice: a case in point being the mixed-longitudinal Nijmegen Growth Study where each of the cohorts comprising the sample is followed for but a five-year period. In such situations, alternative approaches to the problem of constructing growth velocity curves may be of considerable practical as well as theoretical interest. One such approach is developed in this paper and its use is illustrated on some data collected as part of the Nijmegen Growth Study. These results are then compared with those obtained using the increment method on the same data.     

Effect of radiation on the expression of E-cadherin and alpha-catenin and invasive capacity in human lung cancer cell line in vitro

PURPOSE: To investigate whether electrode measurements of tumor oxygenation obtained under a range of different treatment conditions designed to alter the degree of tumor hypoxia could be correlated with estimates of radiobiological hypoxia measured under the same conditions. METHODS AND MATERIALS: Experiments were performed in restrained, nonanesthetized, female C3H/He mice, which had approximately 0.5 g KHT sarcomas growing intramuscularly in the hind limbs. The treatments used to modify tumor oxygenation status included breathing gas mixtures of varying oxygen content, altering tumor blood flow, and shifting the hemoglobin oxygen dissociation curve. Radiobiological hypoxic fraction was estimated using the paired survival curve assay, while electrode measurements of tumor oxygenation were obtained with an Eppendorf histograph. RESULTS: With the selected manipulations it was possible to vary the radiobiological hypoxic fraction in the tumors from approximately 1 to approximately 100% of the total viable cell population. Furthermore, these changes in radiation response were directly reflected in the changes in tumor oxygenation measurements made with the Eppendorf histograph. CONCLUSION: These findings suggest that in the KHT tumor model the Eppendorf electrode measurements could predict the response of the tumors to radiation as determined by the proportion of hypoxic cells.     

Prediction of Metallic Materials Relaxation at Elevated Temperature

A simple stress relaxation function is presented for metallic materials at elevated temperature. The function is derived from a more general physical‐phenomenological model describing the mechanical behaviour of metallic materials under creep conditions. The physical‐phenomenological model is represented by a simple Theological diagram with the minimum possible number of rheological elements. The creep function has only three fitting parameters whose dependencies on stress are presented by simple functions. The resulting stress relaxation curves agree with the experiments, not only the ones carried out in the laboratory but also the ones taken from literature.     

Short-term effects of early-acting and multilineage hematopoietic growth factors on the repair and proliferation of irradiated pure cord blood (CB) CD34+ hematopoietic progenitor cells

PURPOSE: Hematopoietic growth factor(s) (GF) may exert positive effects in vitro or in vivo on the survival of hematopoietic stem and progenitor cells after accidental or therapeutic total body irradiation. METHODS AND MATERIALS: We studied the clonogenic survival and DNA repair of irradiated (0.36, 0.73, and 1.46 Gy) CD34+ cord blood (CB) cells after short-term incubation (24 h) with GFs. CD34+ cells were stimulated with basic fibroblast growth factor (bFGF), stem cell factor/c-kit ligand (SCF), interleukin-3 (IL-3), IL-6, leukemia inhibitory factor (LIF), and granulocyte-monocyte colony stimulating factor (GM-CSF) alone or in combination in short-term serum-free liquid suspension cultures (LSC) immediately after irradiation and then assayed for clonogenic progenitors. DNA repair was evaluated by analysis of DNA strand breaks using the comet assay. Survival of CFU-GM, BFU-E, and CFU-Mix was determined and dose-response curves were fitted to the data. RESULTS: The radiobiological parameters (D[0] and n) showed significant GF(s) effects. Combination of IL-3 with IL-6, SCF or GM-CSF resulted in best survival for CFU-GM BFU-E and CFU-Mix, respectively. Combinations of three or more GFs did not increase the survival of clonogenic CD34+ cells compared to optimal two-factor combinations. The D[0] values for CFU-GM, BFU-E, and CFU-Mix ranged between 0.56-1.15, 0.41-2.24, and 0.56-1.29 Gy, respectively. As for controls, the curves remained strictly exponential, i.e., all survival curves were strictly exponential without any shoulder (extrapolation numbers n=1 for all tested GF(s). DNA repair capacity of CD34+ cells determined by comet assay, was measured before, immediately after irradiation, as well as 30 and 120 min after irradiation at 1 Gy. Notably, after irradiation the 2-h repair of cytokine-stimulated and unstimulated CD34+ cells was similar. CONCLUSION: Our data indicate that increased survival of irradiated CB CD34+ cells after short-term GF treatment is mediated through proliferative GF effects on the surviving fraction but not through improved DNA repair capacity.