Contributions to the design and statistical analysis of in vivo SCE experiments.

Two issues that arise in the design and statistical analysis of in vivo SCE and similar experiments are considered. First, with regard to analysis, the merits of various methods of data transformation are explored in depth. The conclusion drawn is that common transformations of the type studied here seemingly offer little advantage in the assessment of whether a test agent induces SCE in a dose-related manner. Second, a proposal is made for a method to determine, subject to budgetary constraints, the desired numbers of animals/dose group and cells scored/animal. The approach advocated also lends itself to discussions weighing the gains and losses from possible reductions in the number of animals below the 'desired' levels.     

Field experiments to estimate optimum fertilizer levels

Summary Field experiments provide a basis for fertilizer recommendations. Some defects of an incomplete factorial scheme are discussed and the complete factorial briefly reviewed. Using the general polynomial of the second degree as the equation of a response surface, composite designs provide a more uniform precision for the coefficients. These designs are basically augmented 2^m factorials. One such design and a variation on it are compared. A method is given for calculating the economic optimal rates for the fertilizers.     

Fitting the linear-quadratic model using time of occurrence as the end-point for quantal response multifraction experiments

A statistical technique is given for fitting the linear-quadratic model to experimental quantal response multifraction data using the time of the response as the end-point. The analysis used is based on the Cox Proportional Hazards model. The technique is useful for late effects where the time of occurrence of the response is dose dependent. The technique is compared to logistic regression analysis and the advantages and disadvantages are discussed. Both methods are applied to a lung pneumonitis experiment and a kidney experiment.     

Design of multivariate selection experiments to estimate genetic parameters

Summary The precision of estimates of genetic variances and covariances obtained from multivariate selection experiments of various designs are discussed. The efficiencies of experimental designs are compared using criteria based on a confidence region of the estimated genetic parameters, with estimation using both responses and selection differentials and offspring-parent regression. A good selection criterion is shown to be to select individuals as parents using an index of the sums of squares and crossproducts of the phenotypic measurements. Formulae are given for the optimum selection proportion when the relative numbers of individuals in the parent and progeny generations are fixed or variable. Although the optimum depends on a priori knowledge of the genetic parameters to be estimated, the designs are very robust to poor estimates. For bivariate uncorrelated data, the variance of the estimated genetic parameters can be reduced by approximately 0.4 relative to designs of a more conventional nature when half of the individuals are selected on one trait and half on the other trait. There are larger reductions in variances if the traits are correlated.     

Using interpolation to estimate system uncertainty in gene expression experiments

The widespread use of high-throughput experimental assays designed to measure the entire complement of a cell's genes or gene products has led to vast stores of data that are extremely plentiful in terms of the number of items they can measure in a single sample, yet often sparse in the number of samples per experiment due to their high cost. This often leads to datasets where the number of treatment levels or time points sampled is limited, or where there are very small numbers of technical and/or biological replicates. Here we introduce a novel algorithm to quantify the uncertainty in the unmeasured intervals between biological measurements taken across a set of quantitative treatments. The algorithm provides a probabilistic distribution of possible gene expression values within unmeasured intervals, based on a plausible biological constraint. We show how quantification of this uncertainty can be used to guide researchers in further data collection by identifying which samples would likely add the most information to the system under study. Although the context for developing the algorithm was gene expression measurements taken over a time series, the approach can be readily applied to any set of quantitative systems biology measurements taken following quantitative (i.e. non-categorical) treatments. In principle, the method could also be applied to combinations of treatments, in which case it could greatly simplify the task of exploring the large combinatorial space of future possible measurements.     

Feasibility of incubation experiments to estimate moulting rates in marine copepods

Moulting rate estimates of Temora longicornis and Pseudocalanuselongatus in short incubation experiments in the laboratorywere compared with shipboard experiments in the North Sea. Absenceof food, rotation of bottles and (an extremely small) containersize did not affect the moulting rate in well-fed copepods.A minor bias was found due to gentle handling. High variancewas due to the use of different samples, one before and oneafter incubation, which is part of the so-called ‘Kimmerermethod’. This error can be reduced by monitoring the newproduction of exuviae in a single sample, which makes sortingof individuals unnecessary, while conserving the estimate ofmoulting rate in individual stages.     

Radiosensitization in multifraction schedules. I. Evidence for an extremely low oxygen enhancement ratio

Stable monolayers of contact-inhibited C3H 10T1/2 cells were used in multifraction radiation experiments to measure the oxygen enhancement ratio (OER) at low doses/fraction under conditions where cell cycle effects (repopulation, redistribution) were minimal. Consistent with there being a dose-dependent reduction in the OER at low doses, an extremely low OER of 1.34 was measured after 20 fractions of 1.7 Gy every 12 h. The sparing effects of fractionating radiation doses were not apparent for cells irradiated under hypoxic conditions (i.e., multifraction survivals were lower than acute single-dose values) until doses exceeding 15 Gy were reached. This result suggested a deficiency in the recovery from sublethal and/or potentially lethal damage might exist after hypoxic irradiations, thereby reducing the OER. The capacity to repair potentially lethal damage was found to be nearly the same after hypoxic as compared to aerobic irradiations. However, there was an apparent absence of sublethal damage repair by 10T1/2 cells between two hypoxic irradiations which could be a major contributing factor to the extremely low OER value measured in this multifraction schedule.     

Analysis of reciprocal-transfer experiments to estimate the length of phases having different responses to temperature

Background and Aims: The responsiveness of plant ontogeny to temperature may changewith plant age. These changes may best be identified by experimentsin which individual plants are transferred in a time seriesfrom low temperature (LT) to high temperature (HT), and viceversa. Any change in the value of the slope for a plot of theduration taken to complete a developmental phase against timeof transfer (either LT to HT or HT to LT) will indicate a changein the temperature responsiveness of development, and the timeat which this change occurs. The analysis of this type of reciprocal-transferexperiment is usually performed by regression for each of thevisually identified linear sub-phases, separately for the datafor LT-to-HT and for HT-to-LT transfers. Here, a mathematicalapproach is presented using a single curve-fitting procedure. Methods: Both LT-to-HT and HT-to-LT transfers are combined in a singlecurve-fitting procedure. This new, combined approach is illustratedusing a published data set for three rice (Oryza sativa) cultivars,where the pre-flowering duration is divided into three sub-phases,and temperature responsiveness is generally stronger duringthe second than the first and third sub-phases. Results and Conclusions: This new model approach provides an objective method, relativeto the separate analyses, for assigning data points to a particularsub-phase. Plausible parameter values can be obtained from capturingthe whole data of both sets of transfers, which otherwise couldnot be obtained from the separate-analysis method. Furthermore,the length of sub-phases identified from the LT-to-HT transfersis consistent, in terms of its response to temperature, withthat identified from the HT-to-LT transfers. Re-analysis ofthe published rice data using the new approach reveals thatin addition to temperature sensitivity, the optimum temperatureof pre-flowering development may vary with plant age. The newapproach gives rise to a generalized model for the analysisof reciprocal transfer experiments to quantify age-dependentchanges of response of plants (and potentially insects) to anyenvironmental variables that have a significant impact on theirdevelopment.     

A method to estimate in vivo dynamic articular surface interaction

This paper describes a method to calculate and visualize the proximity of subchondral bone surfaces during dynamic movement. This method combines high-speed biplane radiographic image data and three-dimensional (3D) bone surface information derived from computed tomography to determine subchondral bone motion during dynamic activities. Knowledge of in vivo subchondral bone motion may be useful in the study of osteoarthritis, in biomechanical modeling, and in identifying normal and pathological joint mechanics. This method can be used to identify the regions of close contact during dynamic motion, to calculate the surface area of subchondral bone within close contact, and to determine the changing position of the close contact area during dynamic activities. None of this informations can be obtained using other currently available 3D motion analysis techniques. Example applications showing dynamic in vivo tibio-femoral bone surface motion during canine gait and human one-legged hopping are presented.     

An iterative procedure to estimate muscle lines of action in vivo

A method is described to estimate the line of action of muscles in the three-dimensional space from serial images of parallel muscle sections obtained in vivo by means of CT or MRI scanning. The external shape of a muscle, reconstructed from the series of parallel sections, is mathematically divided into a series of imaginary slices directed arbitrarily in the three-dimensional space. The line of action is estimated initially as a regression line through the centroids of these mathematical slices. A new series of mathematical slices is constructed perpendicular to the regression line and a new estimate of the line of action is obtained from their centroids. This procedure is repeated until the estimated line of action is perpendicular to the mathematical slices; it can then be considered as a reliable estimate of the line of action. The accuracy of the method has been tested for various reconstruction parameters and muscle shapes. The results of these tests show that the accuracy is relatively independent of the direction in which the sectional images have been made and that, except for relatively short and thick muscles, the estimated lines of action deviated less than about 2 degrees from the theoretical one. The presented method is a relatively simple mathematical technique which can be used easily for muscles reconstructed in vivo from routinely obtained sectional MRI or CT images.     

Use of radiolabeled tracers in dilution grazing experiments to estimate bacterial growth and loss rates

Dilution grazing experiments were conducted to determine growth and loss rates of glucose-metabolizing and total bacteria. Bacterial growth rates were low and losses to grazers negligible in samples collected from the Celtic Sea in June 1986. Growth and loss rates of glucose-metabolizing bacteria were higher than growth and loss rates of total bacteria in a sample collected from the North Sea in October 1986.     

The design and interpretation of 'top-up' experiments to investigate the effects of low radiation doses

The experimental design consisting of a partial tolerance dose followed by a top-up dose, is used as a method of comparing the effects of different radiations and irradiation schedules in vivo. It complements the usual approach of giving multiple equal fractions of a single radiation type to obtain an iso-effect, as it enables low doses per fraction to be studied without the need to use a large number of fractions or a long overall time. For normal tissues in animals, the effect of X-ray doses as low as 0.1 Gy per fraction can be detected when given as 20-40 fractions followed by a top-up dose of neutrons. In order to minimize variations in the effect of the top-up dose, neutrons are used as a top-up radiation in preference to X-rays. The methods of implementing this approach are explained in detail. Analysis of the data is described, with emphasis on the Linear Quadratic model of radiation dose-fractionation. However, it is not necessary to adopt this or any particular mathematical model in order to intercompare directly the effects of different radiations or irradiation schedules using the top-up approach. Such models nevertheless simplify the design of top-up experiments. Whilst any type of radiation can in principle be used as the top-up, this is given optimally as a dose of fast neutrons split into two fractions.