Comparing methods to quantify experimental transmission of infectious agents.

Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment to end in final-size (e.g., where no more infections can occur). Because of numerical limitations, the application of the TS algorithm is limited to populations with only a few individuals. We investigated the error of using the easily applicable, time-independent final-size (FS) algorithm knowing that the FS situation was not reached. We conclude that the methods based on the FS algorithm: (i) underestimate R(0), (ii) are liberal when testing H(0):R(0)1 against H(1):R(0)<1, (iii) are conservative when testing H(0):R(0)1 against H(1):R(0)>1, and (iv) are conservative when testing H(0):R(control)=R(treatment) against H(1):R(control)>R(treatment). Furthermore, a new method is presented to find a difference in transmission between two treatment groups (MaxDiff test). The MaxDiff test is compared to tests based on FS and TS algorithms. The TS test and the MaxDiff test were most powerful (approximately equally powerful) in finding a difference, whereas the FS test was less powerful (especially, when both R(control) and R(treatment) are >1).

Dynamics of verotoxin-producing Escherichia coli isolated from German beef cattle between birth and slaughter.

A total of 85 cattle from three German beef farms were followed between birth and slaughter during a period of 2 years and monthly faecal samples were submitted for bacterial culture. Verotoxin-producing Escherichia coli (EC) were detected using a standard diagnostic cascade. Potentially pathogenic VTEC ((p)VTEC) were defined as: positive for (1) verotoxin 1 (vt1) and eae, (2) positive for verotoxin 2 (vt2) and eae, (3) positive for both verotoxins 1 and 2 and eae, while verotoxinogenic EC (EC(vt1,2)) were defined as: (1) positive for vt1, (2) positive for vt2 or (3) positive for both vt1 and vt2. There were 1587 observations (1462 valid) available for the statistical analysis including 6 (0.4%) samples from 6 (7.1%) different animals positive for VTEC O157, 78 (5.3%) pVTEC isolates and 389 (26.6%) EC(vt1,2) isolates. The median day of the study at first detection was 280 days for EC(vt1,2) and 315 days for pVTEC. The median age at first detection was: 121 days for EC(vt1,2) and 215 days for pVTEC. Time series analysis, survival analysis, and stochastic SI models were used to find differences in the population dynamics of EC(vt1,2) and pVTEC. There was a strong farm and age effect for the first detection of EC(vt1,2) and for pVTEC while the seasonal effect was significant for the first EC(vt1,2) detections only. With increasing age at first and all consecutive detections, EC(vt1,2) and pVTEC were detected less frequently. The serotype O157 was found more frequently together with detection of other serotypes of pVTEC in the same sample. The EC(vt1,2) were found more often together with pVTEC. The first EC(vt1,2) were on average found before the first pVTEC's and positive cross-correlations existed between EC(vt1,2) and pVTEC. The critical duration for the shedding period above which the VTEC could propagate themselves on the farms by f.e. transmission between animals was found to be between 8 and 18 sampling intervals of 28 days (224-504 days) for EC(vt1,2), and between 5 and 6 sampling periods of 28 days each (140-168 days) for the pVTEC which is smaller than all critical shedding periods for EC(vt1,2). The reasons for EC(vt1,2) being isolated from faeces earlier than pVTEC are discussed.

Quantification of transmission in one-to-one experiments.

We study the statistical inference from data on transmission obtained from one-to-one experiments, and compare two algorithms by which the reproduction ratio can be quantified. The first algorithm, the transient state (TS) algorithm, takes the time course of the epidemic into account. The second algorithm, the final size (FS) algorithm, does not take time into account but is based on the assumption that the epidemic process has ended before the experiment is stopped. The FS algorithm is a limiting case of the TS algorithm for the situation where time tends to infinity. So far quantification of transmission has relied almost exclusively on the FS algorithm, even if the TS algorithm would have been more appropriate. Its practical use, however, is limited to experiments with only a few animals. Here, we quantify the error made when the FS algorithm is applied to data of one-to-one experiments not having reached the final size. We conclude that given the chosen tests, the FS algorithm underestimates the reproduction ratio R0, is liberal when testing H0: R0 > or = 1 against H1: R0 < 1, is conservative when testing H0: R0 < or = 1 against H1: R0 > 1 and calculates the same probability as the TS algorithm when testing H0: R(0-control) = R(0-treatment) against H1: R(0-control) > R(0-treatment) We show how the power of the test depends on the duration of the experiments and on the number of replicates. The methods are illustrated by an application to porcine reproductive and respiratory syndrome virus (PRRSV).

Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments.

We present a method to estimate basic reproduction ratio R0 from transmission experiments. By using previously published data of experiments with Classical Swine Fever Virus more extensively, we obtained smaller confidence intervals than the martingale method used in the original papers. Moreover, our method allows simultaneous estimation of a reproduction ratio within pens R0w and a modified reproduction ratio between pens R'0b. Resulting estimates of R0w and R'0b for weaner pigs were 100 (95% CI 54.4-186) and 7.77 (4.68-12.9), respectively. For slaughter pigs they were 15.5 (6.20-38.7) and 3.39 (1.54-7.45), respectively. We believe, because of the smaller confidence intervals we were able to obtain, that the method presented here is better suited for use in future experiments.

Clinical thermometry, using the 27 MHz multi-electrode current-source interstitial hyperthermia system in brain tumours.

BACKGROUND AND PURPOSE: In interstitial hyperthermia, temperature measurements are mainly performed inside heating applicators, and therefore, give the maximum temperatures of a rather heterogeneous temperature distribution. The problem of how to estimate lesion temperatures using the multi-electrode current-source interstitial hyperthermia (MECS-IHT) system in the brain was studied. MATERIALS AND METHODS: Temperatures were measured within the electrodes and in an extra catheter at the edge of a 4 x 4 x 4.5 cm(3) glioblastoma multiforme resection cavity. From the temperature decays during a power-off period, information was obtained about local maximum and minimum tissue temperatures. The significance of these data was examined through model calculations. RESULTS: Maximum tissue temperatures could be estimated roughly by switching off all electrodes for about 5 s. Model calculations showed that the minimum tissue temperatures near a certain afterloading catheter correspond well with the temperature of the applicator inside, about 1 min after this applicator was switched off. CONCLUSIONS: Although the electrode temperatures read during heating are not suitable to assess the temperature distribution, it is feasible to heat the brain adequately using the MECS-IHT system with extra sensors outside the electrodes and/or application of decay methods.

Treatment planning of brain implants using vascular information and a new template technique.

A new template technique has been developed for implanting hyperthermia catheters in the treatment of brain tumors. The technique utilizes an imaging template and a drill template which can be rigidly secured to the head with three skull screws. The anatomic and vascular information needed for hyperthermia treatment planning may be assessed with three-dimensional magnetic resonance (MR) imaging and angiography acquisitions which use a surface coil. In the companioning treatment planning system the catheter positions and lengths and the electrodes in the catheter can be interactively manipulated relative to the anatomy and vasculature. The visualization of the blood vessels relative to the template allows the minimization of the risk on intracranial hemorrhages. This template technique is useful for any brain tumor implants, especially when a large number of catheters are involved. A phantom test has shown that this procedure has an accuracy in the order of 1 mm provided that the MR-related geometry distortions are minimized.

Accuracy of geometrical modelling of heat transfer from tissue to blood vessels.

We have developed a thermal model in which blood vessels are described as geometrical objects, 3D curves with associated diameters. Here the behaviour of the model is examined for low resolutions compared with the vessel diameter and for strongly curved vessels. The tests include a single straight vessel and vessels describing the path of a helix embedded in square tissue blocks. The tests show the excellent behaviour of our discrete vessel implementation.

The influence of vasculature on temperature distributions in MECS interstitial hyperthermia: importance of longitudinal control.

The quality of temperature distributions that can be generated with the Multi Electrode Current Source (MECS) interstitial hyperthermia (IHT) system, which allows 3D control of the temperature distribution, has been investigated. For the investigations, computer models of idealised anatomies containing discrete vessels, were used. A 7-catheter hexagonal implant geometry with a nearest neighbour distance of 15 mm was used. In each interstitial catheter with a diameter of 2.1 mm a number of 1 up to 4 electrodes were placed along an 'active section' with a length of 50 mm. The electrode segments had lengths of 50, 20, 12 and 9 mm respectively. Both single vessel and vessel network situations were analysed. This study shows that even in situations with discrete vasculature and perfusion heterogeneity it remains possible to obtain satisfactory temperature distributions with the MECS IHT system. Due to its 3D spatial control the temperature homogeneity in the implant can be made quite satisfactory.

Numerical analysis of capacitively coupled electrodes for interstitial hyperthermia.

Multi electrode current source interstitial hyperthermia (MECS-IHT) employs individually controlled, 27 MHz radiofrequency electrodes inserted into plastic brachytherapy catheters. In order to get a firm understanding of the physical behaviour of the electrodes and to verify the current source approximation in our hyperthermia treatment planning system we have investigated (1) the electrical properties of the electrode-catheter-tissue system, and (2) the impact of inhomogeneity of the electrical properties of the tissue in the vicinity of the electrodes. The results validate the use of the ideal current source approximation in the treatment planning SAR model. The models predict the presence of a significant heat source inside the electrode wall when lossy catheter materials are used, producing a conductive heating component in addition to the SAR in the tissue. For a given catheter spacing this conductive component will produce a more heterogeneous temperature distribution. Thus, low-loss catheter materials like polyethylene and Teflon are recommended. The SAR is highly localized near the catheter. Calculations concerning a fat-muscle interface show that the SAR is higher in the fatty tissue than in the muscle tissue; 3D SAR control by individually controlled electrode segments is essential in such a situation.

A 3-D SAR model for current source interstitial hyperthermia.

A three-dimensional (3-D) model is presented for the calculation of the specific absorption rate (SAR) in human tissue during current source interstitial hyperthermia. The model is capable of millimeter resolution and can cope with irregular implants in heterogeneous tissue. The SAR distribution is calculated from the electrical potential. The potential distribution is determined by the dielectric properties of the tissue and by the electrode configuration. The dielectric properties and the current injection of the electrodes are represented on a 3-D uniform grid. The calculated potential at an electrode current injection point is not the actual electrode potential at that point. To estimate this potential a grid independent representation of an electrode together with an analytical solution in the neighborhood of the electrode are used. The calculated potential on the electrode surface is used to estimate the electrode impedance. The tissue implementation is validated by comparing calculated distributions with analytical solutions. The electrode implementation is verified by comparing different discretizations of an electrode configuration and by comparing numerically calculated electrode impedances with analytically calculated impedances.

A description of discrete vessel segments in thermal modelling of tissues.

In hyperthermia treatment planning vessels with a diameter larger than 0.5 mm must be treated individually. Such vessels can be described as 3D curves with associated diameters. The temperature profile along the vessel is discretized one dimensionally. Separately the tissue is discretized three dimensionally on a regular grid of voxels. The vessel as well as the tissue are positioned in one global space. Methods are supplied to describe the tissue-vessel interaction, the shift of the blood temperature profile describing the flow of blood along the vessel and the calculation of the vessel wall temperature. The calculation of the interaction is based on tissue temperature samples and the blood temperature together with the distance between the centre of the vessel and the tissue temperature sample. An analytical expression for a vessel inside a coaxial tissue cylinder is then used for the calculation of the heat flow rate across the vessel wall. The basic test system is a vessel segment embedded inside a coaxial tissue cylinder. All the tests use this setup while the following simulation parameters are varied: position and orientation of the vessel relative to the tissue grid, vessel radius, sample density of the blood temperature and power deposition inside the tissue cylinder. The blood temperature profile is examined by calculation of the local estimate of the equilibration length. All tests show excellent agreement with the theory.