Marius George Linguraru

Kostas Marias

Ruth English

Michael Brady

A Biologically Inspired Algorithm for Microcalcification Cluster Detection

Keywords: X-ray mammography, microcalcification clusters, image normalization, anisotropic diffusion, human visual system

The early detection of breast cancer greatly improves prognosis. One of the earliest signs of cancer is the formation of clusters of microcalcifications. We introduce a novel method for microcalcification detection based on a biologically inspired adaptive model of contrast detection. This model is used in conjunction with image filtering based on anisotropic diffusion and curvilinear structure removal using local energy and phase congruency. An important practical issue in automatic detection methods is the selection of parameters: we show that the parameter values for our algorithm can be estimated automatically from the image. This way, the method is made robust and essentially free of parameter tuning. We report results on mammograms from two databases and show that the detection performance can be improved by first including a normalisation scheme.

I. INTRODUCTION

Breast screening programs attempt to detect and eradicate cancer at the earliest possible stage to reduce the rate of mortality amongst women. However, detecting the early signs of breast cancer that appear in Xray mammograms presents a significant challenge to radiologists, not least because such signs are often difficult to distinguish against the dense or highly textured breast anatomy. Studies prove that the performance of radiologists is increased when a good segmentation or classification system is used [START_REF] Funovics | Computer-assisted diagnosis in mammography: the R2 ImageChecker system in detection of spiculated lesions[END_REF][START_REF] Giger | Results of an observer study with an intelligent mammographic workstation for CAD[END_REF][START_REF] Petrick | Breast cancer detection: evaluation of a mass-detection algorithm for computer-aided diagnosis[END_REF]. However, such systems must have provably adequate performance and robustness to be used in a clinical setting.

Most ductal and lobular cancers have secretions that may form calcifications [START_REF] Highnam | Mammographic Image Analysis[END_REF]. The smallest of these (under 1 mm in diameter) are called microcalcifications and represent some of the earliest signs of breast cancer. Microcalcification clusters may be the only indication of in-situ tumours. Approximately 80% of microcalcifications are benign [START_REF] Highnam | Mammographic Image Analysis[END_REF]Veldkamp and Kerssemeijer, 1998), their shape and topology differentiating them from the malignant type.

In general, microcalcification detection algorithms consist of three stages: (i) a pre-processing step based on filtering the image, for example, subtracting a signal-enhanced image from a signal-suppressed image [START_REF] Nishikawa | Computer-aided detection of clustered microcalcifications: an improved method for grouping detected signals[END_REF]; (ii) a segmentation step, for example based on global thresholding and morphological erosion [START_REF] Nishikawa | Computer-aided detection of clustered microcalcifications: an improved method for grouping detected signals[END_REF], on region growing [START_REF] Shen | Detection and classification of mammographic calcifications[END_REF] or adaptive thresholding [START_REF] Betal | Segmentation and numerical analysis of microcalcifications on mammograms using mathematical morphology[END_REF]; and (iii) a clustering step, typically using a fixed size kernel to eliminate noise points and isolated calcifications and to identify clusters. A major drawback of such methods is their poor sensitivity to small and faint microcalcifications. Other approaches use neural network classifiers [START_REF] Edwards | Using Bayesian neural network to optimally eliminate false-positive microcalcification detections in a CAD scheme[END_REF][START_REF] Hara | Automated classification method of mammographic microcalcifications by using artificial neural network and ACR BI-RADS criteria for microcalcification distribution[END_REF][START_REF] Kim | Statistical textural features for detection of microcalcifications in digitized mammograms[END_REF][START_REF] Rosen | A Bayesian neural network to detect microcalcifications in digitized mammograms[END_REF], several of which are trained on a single database and give poor results when tested on other databases. Wavelet filters have been used in [START_REF] Aghdasi | Application of neural network adaptive wavelets for signal representation and classification in digital mammography[END_REF][START_REF] Mcleod | Automatic detection of clustered microcalcifications in mammograms[END_REF] to highlight the high frequency signal from the background; unfortunately, noise also has significant power at high frequencies. [START_REF] Yam | Three-dimensional reconstruction of microcalcification clusters from two mammographic views[END_REF] developed a structural approach to microcalcification detection, which exploits the Standard Mammogram Form (SMF) representation (therein called h int ), which is introduced in Section II of the paper. Yam et al.'s technique detects tall thin structures in the h int image and tests with the height of such a structure to its footprint of the same structure in the image to detect possible calcifications. Noise is a major problem and some individual calcifications are overlooked and so statistical analysis of a cluster is compromised. The results appear promising, though it should be noted that they are from a considerably smaller database [START_REF] Yam | Three-dimensional reconstruction of microcalcification clusters from two mammographic views[END_REF].

Perhaps the best-known published statistical method is that of Karssemeijer et al. (1993, Veldkamp andKerssemeijer, 1998). The authors use adaptive noise equalization as part of a Bayesian approach, using Markov Random Fields to detect clusters of microcalcifications. Though it set a new standard for feature detection at the time it was published, the algorithm involves a large number of parameters, and there have been questions raised about its robustness or generalisability to other databases [START_REF] Poissonnier | Noise equalisation' for microcalcification detection?[END_REF]. R2 Technology's commercial product ImageChecker TM [START_REF] Roehrig | The manufacturer's perspective[END_REF]) is a CAD system that is widely acknowledged as the state of the art of microcalcification detection (though, understandably, few details of the detailed operation of ImageChecker TM have been published). Several large studies show the improvements from using ImageChecker TM to detect breast cancer by reducing the false negative rate, while increasing the mean sensitivity of radiologists [START_REF] Roehrig | The manufacturer's perspective[END_REF]. [START_REF] Freer | Screening mammography with computer-aided detection: prospective study of 12860 patients in a community breast center[END_REF] report that radiologists improve the detection of malignant microcalcification clusters from 68% to 100% after the use of CAD. In a more recent study, [START_REF] Birdwell | Computer-aided detection with screening in a university hospital setting[END_REF] notify that the contribution of CAD increased by 7% the number of detected cancers, but without clear benefit of CAD systems in the detection of microcalcifications.

Herein we present a novel "foveal" segmentation algorithm that is based on a biological model of adaptive contrast-detection, complemented with complex pre-processing steps. The rationale for adopting a model inspired from the human visual system derives from the challenge posed by the highly variable mammogram image background that often confounds algorithms or human observers, especially when 'bright' microcalcifications are hidden within 'bright' dense tissue. The paper is structured as follows.

Section II presents the pre-processing of SMF images [START_REF] Highnam | Mammographic Image Analysis[END_REF], in particular the optional, but helpful, normalisation step, the removal of shot-noise, curvilinear structures and image filtering. Α novel statistical approach to derive automatically the parameters of the enhancing diffusion filter is also proposed. Section III introduces the "foveal" segmentation algorithm. In Section IV we perform a Free-Response Operating Characteristic (FROC) curve analysis as a step towards a validation of the microcalcification detection algorithm. Finally, we present a discussion and conclusions.

II. PRE-PROCESSING

Due to the complexity of mammogram image formation, we pre-process images before applying contrastdetection. The aim is to remove structures that may give rise to false positives (e.g. shot noise or curvilinear structures) and to smooth out noise in the image without removing microcalcifications. Note that we also include in this section an image normalisation step SMF, which is optional to the method, but which we have found can improve detection results, since it models the image formation process and removes variability in imaging conditions (e.g. time of exposure, film speed). The pre-processing steps of our method are described in the following paragraphs.

A. The Standard Mammogram Form

A well known normalisation method that results from modelling the process of mammographic image formation is the Standard Mammogram Form (SMF) developed by [START_REF] Highnam | Mammographic Image Analysis[END_REF] and improved in [START_REF] Yam | Denoising h int surfaces: a physics-based approach[END_REF]. The SMF algorithm corrects for scatter and extra-focal radiation, glare and anode heel effect. We have also based our work on previous results by [START_REF] Highnam | Mammographic Image Analysis[END_REF] and [START_REF] Yam | Denoising h int surfaces: a physics-based approach[END_REF], which estimated radiographic mottle, and then used Wiener filtering to subtract its effect and estimate glare and local blur. Our paper started from the observation that sometimes Yam's algorithm gave very poor results, and that led us to use -and analyse -anisotropic diffusion.

Because of the relatively weak control over the image acquisition process, it is difficult to eliminate variability in image characteristics, such as contrast and brightness. It is well known that such differences in imaging conditions lead to a complicated functional relationship between the intensities of temporal pairs of mammograms that varies from patient to patient [START_REF] Marias | A registration framework for the comparison of mammogram sequences[END_REF]0. This is a strong indication that the non-linearities introduced by varying imaging conditions may alter significantly the imageintensity profile and reduce the efficiency of automatic microcalcification detection algorithms. After developing a method for the calculation and correction for the scattered radiation, [START_REF] Highnam | Mammographic Image Analysis[END_REF] discovered a method for mammogram image normalisation that eliminates distracting variations.

This was based on the following assumptions /observations:

-The x-ray attenuation coefficients of normal healthy tissue and cancerous tissue are approximately equal over the range of tube voltages used in mammography; but are significantly different from that of fat; -Fat is clinically uninteresting, therefore normal healthy and cancerous tissues are collectively referred to as "interesting";

Highnam and Brady's method estimates -in millimetres -the amount of interesting tissue in each pixel column, as illustrated in Figure 1. This effectively provides objective quantitative information about the breast anatomy. If, for example, the separation between the Lucite plates is 6.5cm, the amount of interesting tissue at a location (x,y) might be 4.75cm, implying 1.75cm of fat. This way, the interesting tissue representation refers only to (projected) anatomical structures -the SMF algorithm estimates, and then eliminates the effects of, the particular parameters that were used to form the mammographic image. In short, the image can be regarded as standardised (hence the more recent name Standard Mammogram Form or SMF) and quantitative since the 'normalised' pixel values are measurements in millimetres, not in arbitrary units of shading (contrast), and they convey anatomical information. The key point is that without normalisation, for example by the SMF process, there is inevitably the risk of confounding anatomically useful information and imaging parameter effects, whose choice significantly affect contrast, brightness and the level of noise. As we will show in the results section, detection performance is improved if the normalisation step is included. The exception ignored in the generation of an SMF representation of a mammogram is the presence of microcalcifications. The attenuation coefficient of microcalcification is approximately 26 times that of normal/cancer tissue, and so, although microcalcifications are physically small, they appear in the SMF representation as non-fat tissue that is 26 times as high as it actually is, that is as very high, tall thin towers. Thus, although the breast parenchyma is normalised, calcifications remain small areas of higher contrast.

Hence, the contrast of a feature (microcalcification in our case) is largely independent of the film contrast curve. It is its presence in a fat or dense neighbourhood that makes it easy or difficult to detect/visualise. We stress that the inclusion of a normalisation pre-processing step is not essential for our algorithm to work. However, our results indicate that the detection efficiency can be improved by including such a step, probably as a result of removing non-linearities and distracting variations, which in turn improves the contrast.

B. Shot Noise and Curvilinear Structures Removal

An important pre-processing step is the removal of noise, which is a major source of false positives (FP).

In this paper, shot noise refers to an intrinsic noise process during scanning, due to dust and artefacts present on the film or in the scanner. Previous papers report the detection of film-screen artefacts associated with the SMF generation process [START_REF] Ancelin | Automated detection of artifacts on film-screen mammograms using a novel iterative detection and correction scheme[END_REF][START_REF] Highnam | Mammographic Image Analysis[END_REF], for example at the glare removal stage. Although shot noise appears visually similar to microcalcifications, it is introduced at the image digitisation stage, that is, it is introduced to the image after the main blurring stage, and so the boundary shape of shot noise tends to be quite sharp. The point spread function of the intensifying screen (blur function) enables the identification of image locations that are locally bright but the energy imparted becomes negative where shot-noise is present after glare compensation. Using the binary information from the shot noise map, the artefacts can be removed from the SMF image by interpolating between their surrounding backgrounds.

Curvilinear structures (CLS) -ducts, blood vessels, ligaments or tumour spiculations -are locally linear, relatively thin structures, which often produce in a mammogram a characteristically textured appearance.

Removing the CLS turns out to be important for the method specificity [START_REF] Highnam | Mammographic Image Analysis[END_REF], but their identification and removal remains a major challenge [START_REF] Wai | A multi-resolution CLS detection algorithm for mammographic image analysis[END_REF]. The CLS appear relatively bright, though not necessarily with high contrast. They are locally linear, but typically curve at larger scales. Their detection is difficult due to the large variety of widths, contrasts, lengths, and intersections.

Intersections are either genuine bifurcations or may correspond to the overlap of two projected CLS in the compressed breast. The attenuations of the individual CLS add, producing a localized region of higher attenuation. Such points also appear similar to calcifications rather than noise.

The method we propose for CLS removal is based on the local energy model for feature detection of [START_REF] Kovesi | Image features from phase congruency[END_REF] and is presented in [START_REF] Evans | Statistical characterisation of normal curvilinear structures in mammograms[END_REF]. From local energy (LE) we search points with maximum phase congruency (PC) to detect and then remove CLS from mammograms. For the spatial frequency j, if the local Fourier coefficients of a one-dimensional signal are as in equation ( 1), then LE and PC can be calculated according to equations ( 2) and (3). In practice, logGabor filters were used to estimate the local energy and phase, with a spreading function and combination of responses from several discrete directions to extend the analysis to 2D [START_REF] Kovesi | Image features from phase congruency[END_REF].

Several more assumptions are necessary: (i) the intensity profile of a CLS perpendicular to its local orientation is a one-dimensional peak (e.g. cos(φ)), with a phase within -π/2 ≤ φ ≤ π/2; and (ii) the phase congruency PC θ+π/2 > PC θ at a CLS of orientation θ, since CLS are long and thin.

( ) ∑ = + N j j j iB A 1 ;
(1)

2 1 2 1         +         = ∑ ∑ = = N j j N j j B A LE ;
(2)

( ) ∑ = + = N j j j B A LE PC 1 2 2 ;
(3) Our implementation uses a small wavelength, which makes it more sensitive to smaller scales, and a reduced number of scales over which features are detected by phase congruency in order to avoid marking the CLS as calcifications. The limitation is that there are discontinuities that appear in the true CLS and their removal leaves bright areas on the mammogram similar to microcalcifications. We use a smooth interpolation process to remove CLS from mammograms. Figure 2 shows an example of removal of shot noise and CLS.

C. Image Enhancement

We have previously reported our work using anisotropic diffusion to filter and analyse mammographic images [START_REF] Linguraru | Filtering h int images for the detection of microcalcifications[END_REF]. Anisotropic diffusion has the desirable property of smoothing an image, that is reducing noise (hence increasing signal to noise, which is generally poor for mammographic images) while at the same time largely preserving image structure. In this paper we also address the issue of automatically defining the appropriate diffusion parameters. Previous methods used for noise reduction, such as the Wiener filter (originally embedded in the SMF generation), have limitations [START_REF] Linguraru | Feature Detection in Mammographic Image Analysis[END_REF], primarily arising from deconvolution and inevitably simplified models of the complex physical processes involved in mammography. These possible sources of errors leave residual high-frequency noise in mammographic images. Digitiser noise, also of high frequency, adds to it. The anisotropic diffusion filter aims to smooth the remaining high-frequency noise that interferes with our specific application. We base our approach on Weickert's solution [START_REF] Weickert | Anisotropic Diffusion in Image Processing[END_REF] for the diffusion tensor for which we define the corresponding eigenvalues in equation ( 4), where I is the initial image, I σ the Gaussian smoothed image (σ is the standard deviation or scale) and k is a contrast measure. I can be either an intensity or SMF image, depending if SMF normalization has been performed as a pre-processing step.

Shot noise a a b c d

1 0 | | ) / | (| 1 exp 1 , 0 | | 1 2 12 1 =      > ∇         ∇ - - = ∇ = λ λ σ σ σ I k I I ; (4)
The parametric nature of anisotropic diffusion in general makes the process highly dependent on the fine-tuning of its input parameters. In practice, the more complex and variable the images in a dataset, the more problematical it is to choose a single set of values for these parameters that works well for the entire dataset. We address this problem by proposing an automatic scheme that defines the diffusion parameters using image characteristics. The parameters we deal with are: a) a contrast gradient k, b) the standard deviation σ and c) the number of iterations t.

Microcalcifications represent a tiny percentage of the mammogram surface. Typically, they are very small, indeed are only present on average in about a quarter of the total number of screening mammograms [START_REF] Highnam | Mammographic Image Analysis[END_REF]. For these reasons, we generously estimate that at most 5% of the mammogram pixels is sufficient to accommodate the entire population of microcalcification pixels.

Microcalcifications often appear relatively bright in an X-ray image, indeed were it not for surrounding dense tissue they would be the brightest/highest pixels of the mammogram. As illustrated in equation ( 5),

we compute k as a measure of the gradient, where K σ (I) is the Gaussian of image I, M its derivative and N the number of pixels in the neighbourhood δ i . k becomes a value with well-defined physical meaning that discriminates between microcalcifications (the brightest structures after noise removal) and background; more precisely, we chose the 4.4% structures with highest contrast, according to the statistical value in equation ( 5), given that mean(g) is 0. Figure 3 illustrates the estimation and meaning of the value of k.

k= 2*std(g), where

∑ ∈ - = i j j i i M N M g δ 1 and | ) ( ' | I K M σ = ;
(5) The second parameter to be set is σ, the standard deviation of the Gaussian filter used to smooth the image. We need to choose a value for σ so that, on the one hand, it removes high-frequency noise (which is very localized, typically spread over a couple of pixels at, for example, 50µm/pixel), but, on the other hand, preserves microcalcifications (on average 0.5-1 mm in diameter). Digital images are convolved with a Gaussian kernel, whose width is given by σ (n*σ, for example n=10, where n gives the digital finite extent of the Gaussian). σ must be sufficiently small to clean noise and retain microcalcifications and is directly related to the image resolution. For example, the width of the kernel must be 300/50=6 pixels to preserve microcalcifications over 0.3mm (or 300µm) in diameter at an image resolution of 50µm/pixel. [START_REF] Weickert | Anisotropic Diffusion in Image Processing[END_REF] notes that the number of iterations t is related to the spatial width of the Gaussian kernel. To blur features of the kernel order it is required that

( ) 2 / * 2 σ n t =
, which gives excellent noise reduction results in the microcalcification preservation framework.

The reasoning behind the parameter setting in the anisotropic diffusion process has been explained

above. As a concluding remark, we note that our method computes all parameters automatically: k is computed directly from the image and its meaning (it depicts the most outstanding features in the mammogram) and is independent of the data set; σ is strictly related to the size of microcalcifications and the image resolution; and t is set according to the proposed value of σ. We show a typical example of k = 0.47 a b automated image enhancement for microcalcification detection in Figure 4.

With the automatic tuning of parameters that we propose, anisotropic diffusion becomes, for microcalcification detection, a robust process using little, but essential, a-priori knowledge. This is important since anisotropic diffusion has often attracted criticism because of its strong dependency on a number of parameters.

III. FOVEAL SEGMENTATION

An important part in image processing and computer vision is to understand and implement models of the human visual system (HVS), partly because understanding the HVS is an important scientific goal in its own right, and partly because expert radiologists have generally outperformed computer systems, especially for the detection of subtle microcalcifications and/or masses in dense textured backgrounds.

There is over a century of research behind trying to fully understand the way HVS functions, particularly how it responds to intensity transitions and texture variations. A major contribution to this on-going research was made by [START_REF] Holladay | The fundamentals of glare and visibility[END_REF] and later by [START_REF] Moon | The specification of foveal adaptation[END_REF]. They developed several of the fundamentals of the way the human processes visual scenes, at least in the early stages. Nevertheless, the process is very complex and still not fully understood [START_REF] Ashdown | Luminance gradients: photometric analysis and perceptual reproduction[END_REF].

a c b

The adaptation of the eye to light changes is a continuous process in the HVS. We perceive objects differently if they are against a bright surface (for instance a window on a sunny day) or dark area (a dark wooden panel). The adaptation luminance proposed in [START_REF] Moon | The specification of foveal adaptation[END_REF] is the response of the eye in adding an average luminance within the central visual field or fovea (L fov ) and an equivalent veiling luminance caused by surfaces surrounding the peripheral field of view (L seq ) as in equation ( 6).

L a = L fov + L seq ;

(6) However, foveal adaptation stems mainly from the luminance within the foveal field and relates to approximately only ten percent to the luminance of the field of view outside that of the fovea [START_REF] Moon | The specification of foveal adaptation[END_REF]. Furthermore, the visual perception of the eye is dependent on the spatial perception of the object we visualise. This effect is called lightness assimilation. The same object may appear lighter on a dark background and darker over a light surface (see Figure 5).

In mammography, the main advantage of human eye over CAD methods is the detection of microcalcifications in dense areas of the breast, usually the clusters that make the True Positive (TP) ratio inferior to the 100% of the ground truth. At the same time, neither the radiologist nor a computer program must pick FP in the dark areas. This is the result of the adaptation to background, which is equivalent to lowering thresholds in bright areas (to increase the TP ratio by detecting clusters in dense breast areas) and increasing them in dark areas (to decrease the FP number), basically an inverse proportionality to the background. In a mammogram we must consider the neighbouring area of the foveal kernel, as shown in equation ( 6). The adaptive thresholding model that we propose for the detection of microcalcification applies the above-mentioned concepts in the mammographic setting for the improvement of abnormality detection in the breast. The classical contrast (C classic ) is calculated at every pixel as the difference between that pixel value (p 0 ) and a weighted sum of the pixel values in an immediate neighbourhood (N), as in equation ( 7), where n is the number of pixels in N (Gonzalez and Woods, 1993). In mammography, such contrast measures were used in [START_REF] Karssemeijer | Adaptive noise equalisation and recognition of microcalcification clusters in mammograms[END_REF] combined with noise/contrast equalisation and [START_REF] Kegelmeyer | Dense feature maps for the detection of microcalcifications[END_REF] together with local thresholding. In a simpler scenario, C classic is compared with a fixed threshold, C thresh , over the whole image and microcalcifications are marked. The variation in height in an SMF image or intensity in a typical mammogram makes it far easier to detect microcalcifications (or contrast changes) against a fatty (dark) background but more difficult to detect correctly against a denser (bright) background [START_REF] Highnam | Mammographic Image Analysis[END_REF]. The HVS, however, adapts to the local image contrast, and detects faint contrast changes in a manner essentially independent of the background. We adopted a model of contrast detection similar to HVS for mammography with the aim of improving the accuracy of the detection.

∑ ∈ - = N i i classic p n p C 1 0 ; (7)
We initially pre-process the images as described in the previous section (shot-noise and CLS removal, etc.). Then, we compute a set of mean intensity values of the inner area of the object to visualise (i.e.

within the boundary of calcification), its neighbourhood (the local area around the object) and background (the rest of the breast tissue). The histogram of the inner foveal surface provides the mean of the object (µ O ), as the histogram of the whole image will give us the mean of the background (µ B ) and a measure of the density of breast. The mean of the neighbourhood (µ N ) is found from the intensities of pixels within the neighbourhood and excluding the object pixels according to Figure 6. µ N determines whether the visualised object is on a dense (bright) or a fat (dark) area of breast. The size of the kernel of the inner object (O) used to compute µ O is established according to the average size of microcalcifications [START_REF] Highnam | Mammographic Image Analysis[END_REF] and the resolution of the tested images, in a similar manner to the kernel of the Gaussian in Section II. It is desirable to have a slightly smaller kernel than the microcalcification diameter to assure the detection of small calcium salts, which are overlooked by larger kernels. Still, the size of O must not be too small to avoid overlapping O and N for slightly bigger microcalcifications. In our application N is set twice the size of O. Then the perceivable contrast C is calculated in agreement with equation ( 8). Using C min instead of C thresh , the contrast is adapted locally, not just globally, in a manner similar to that of HVS. Figure 7 shows how the variation of perceivable contrast varies with the background in the HVS adaptation method versus classical methods. While C min varies with the local image characteristics, C thresh is constant over the whole image. Microcalcifications can be easily depicted in a fat background for both contrast measures, but C min reduces the number of FP. The main advantage of using C min becomes clear in a dense background, where its adaptability facilitates the detection of microcalcifications.

IV. RESULTS

In this section we present comparative Free-Response Receiver Operating Characteristic (FROC) curves to test the outcome of our method with variations in algorithm and input images. We used a database of 102 samples of digital SMF images from 83 mammograms. 78 of the samples contain between 1 and 3 clusters per image, while 24 are normal mammogram samples. An experienced radiologist annotated a total of 98 microcalcification clusters, which had previously been proven by biopsy. The ground truth for the validation of our detection algorithm was the contour drawn by the radiologist on the film around each detected cluster of microcalcifications. The films were subsequently digitised using the Lumisys scanner at a resolution of 50µm. The cluster positions were then translated into x-y coordinates on the digital images.

The cropped image sizes are of maximum 1500x1500 pixels. Figure 8 shows a schematic of the method flow described in the previous sections. As noted earlier, the normalisation step in the flow is optional and results are reported for both original and normalised (SMF) images. A cluster is detected if it contains at least three microcalcifications, where a distance of maximum 5 mm connects each calcification to the rest of cluster. When a cluster is identified at the position indicated by the radiologist, we count a TP. If a cluster is detected outside the marked areas or more than one cluster are found at the approximate location of a single contour indicated by the radiologist, we count a FP.

Recursively, we noted that the distribution of detected FP/image is equal in samples with microcalcifications and in normal samples. In Figure 9 we note the impact of CLS removal, image smoothing and image normalisation (SMF images) on detecting microcalcification clusters. The results are superior when the proposed algorithm (Figure 8) is employed (the top line in the FROC curve); when the algorithm is applied to intensity (not normalised) images the results are also very satisfactory. In Section III we noted the significance of the value of w in setting the minimal perceivable contrast for obtaining the best detection results when our algorithm is applied. We ran parallel tests to test the consistency of our conclusion to use the value 0.923 for w, by varying the value of w over 5-10%. Figure 10 shows the comparative detection results with the variation of w. A small variation of w around the proposed value of 0.923 does not influence the evolution of our algorithm."

The results used in building the FROC curves in Figure 9 and Figure 10 are based on processing cropped samples of mammograms. To illustrate results on whole mammograms, we used a total number of 83 mammograms in SMF format from the Oxford Screening Database. 59 of them contain between 1 and 5 clusters/image, adding the total number of clusters to 85, while 24 mammograms have no sign of abnormality. The pooled opinions of clinicians at the Oxford Breast Care Unit established ground truth.

The breast margin is detected in SMF, thus a threshold above 0 removes the background. Now we can compute the value of k (see Section II) for the inner area of the breast. The detection results are accurate and similar to those achieved on mammogram samples (see Figure 11). The presence of CLS remains the main source of FP, or more precisely their imperfect removal. A few isolated calcifications were also depicted, but they were not labelled as microcalcification clusters. The method is more robust to detecting microcalcification in samples because the probability of generating FP is increased when applied to the whole image (i.e. the search space for microcalcification detection is larger). All algorithms reach 100% TP fraction with a clear better performance on SMF images, which were denoised and CLS-removed.

The ultimate goal of any CAD algorithm is to perform correctly on any given similar database, no matter where it comes from. As is acknowledged by many authors, without image normalisation this is hard to achieve. The SMF generation algorithm is designed to help in this difficult situation, but excepting the Oxford database, no other image collections have mammograms in SMF format. Our detection algorithm, through its extraction of parameters from image attributes, facilitates the generalization of detection standards.

ο -SMF images ◊ -no diffusion -no CLS removal ∆ -no SMF (intensity) Figure 10. The comparative FROC curve when w is varied over a range of 5 to 10% of its default value of 0.923. The difference in detection results is quite small and all four algorithms converge smoothly to 100% TP ratio. The major difference between these images and the ones from Oxford is the image resolution. To compensate for this difference, we converted the values of σ in the image enhancement step and that of the kernel of fovea in the foveal segmentation change accordingly. These conversions are done automatically in agreement with the user specified image resolution. The FROC curve shown in Figure 12 compares the performance of the microcalcification detection algorithm between the Oxford Screening Database in intensity form and the DDSM database on original images. The algorithm performs better on the Oxford Screening database, but the detection results on the two databases converge at about 0.5 FP/image and they both achieve 100% TP fraction in the vicinity of 2 FP/image. The DDSM database was chosen for its availability; no similarity between databases was considered and no additional tuning of parameters performed. It remains desirable to test the detection algorithm on the DDSM database when images will be available in SMF form, as normalisation would improve the flexibility of the results of the algorithm on other databases.

Finally, this section compares three algorithms to detect microcalcification clusters that operate upon the SMF representation of mammograms from the Oxford Database. The first has been described previously in this paper and is addressed as the "foveal algorithm"; the second one is Yam et al.'s physics based approach that was described in [START_REF] Yam | Three-dimensional reconstruction of microcalcification clusters from two mammographic views[END_REF]. The third is a variation of the statistical analysis introduced in Section II, here addressed as the "statistical approach", and is presented in [START_REF] Linguraru | A non-parametric approach to detecting microcalcifications[END_REF]. Using FROC analysis, we demonstrate the superiority of the foveal algorithm in Figure 13.

In Figure 14 we present examples of microcalcification detection.

V. DISCUSSION AND CONCLUSION

We have presented a novel method for detecting microcalcification clusters based on a biologically inspired contrast detection algorithm in combination with a pre-processing step (shot noise and CLS removal, image enhancement), as well as an optional image normalisation step. Many methods to detect microcalcifications attempt to tune the variety of parameters used in the implementation of the algorithm to best suit the studied cases. The consistency and reproducibility of results becomes highly dependant on the operators and their capability to find the best parametrical configuration for the detection. We proposed a fully automated method to detect microcalcifications and we reported results on both SMF and intensity images.

The first contribution of the presented work is the automatic tuning of the parameters of anisotropic diffusion. The contrast k is found from its direct relation to the image gradient and the percentage of features that we desire to enhance. The second parameter σ reflects the scale of features of interest and must be set according to their size and the given the image resolution (multiscale analysis may be performed). In our application, both σ and k become measures related to the anatomy of breast. The last parameter, the number of iterations t, is derived as a function of σ to remove noise in the context of preserving microcalcifications. In a general application for feature enhancement, the automatic tuning of t may prove to be more difficult than in our particular framework. With the automatic tuning of parameters that we propose, anisotropic diffusion, a method with a solid theoretical basis, but controversial for its parametrical dependency, can be used as a robust process using little, but essential, a-priori knowledge.

However, the main contribution of the paper is the method for adaptively thresholding the filtered results in order to segment microcalcifications. Based on the biologically driven idea that human eye is a better feature detector than a computer algorithm and that both local and global adaptability are necessary for subtle contrast detection, our detection model mimics the human eye's function for improved segmentation results. Therefore, the algorithm combines filters, analysis of image characteristics and adaptive thresholding based on a human visual system paradigm.

The robustness of the algorithm has been demonstrated by the FROC analysis performed over a range of parameters. It is important to note that the parameters are set according to the image attributes and the method is fully automated. The method converged in each case to 100% TP ratio. Similar results were obtained on intensity images, although for the lower scale of FP/image there is a more significant difference in results. We also compared the performance of our algorithm on data from different databases with good detection results. The results indicate that adding adaptive contrast segmentation based on

Figure 1 :

 1 Figure 1: A schematic of h int calculation. In the normalised image each pixel value reflects the

Figure 2 .

 2 Figure 2. Removing artefacts in the pre-processing step; (a) the original image; (b) the shot noise map

Figure 3 :

 3 Figure 3: An example of estimating k. a: From the image shown on the left (after expanded display contrast) the histogram of g is computed from equation (5), b: We note the zero mean value of g, as well as where the value of 0.47 of k (related to the 4.4% structures with highest contrast) falls.

Figure 4 .

 4 Figure 4. Automated image enhancement; (a) the original noisy image with a microcalcification cluster; (b)

Figure 5 .

 5 Figure 5. An illustration of the lightness assimilation. We show three synthetic images with dark (left),

Figure 6 .

 6 Figure 6. The foveal masks used for the computation of µ O , µ N and µ B . The object O is the area of the

Figure 7 .

 7 Figure 7. The simulation of a plot of a mammogram section containing microcalcifications over

Figure 8 .

 8 Figure 8. The diagram of the biologically driven algorithm to detect microcalcifications. The top row

Figure 9 .

 9 Figure 9. The comparative FROC curves for the detection of microcalcifications. ο -represents the detection on SMF images; ◊ -are the results without noise removal by anisotropic diffusion; -are the results without CLS removal; ∇ -shows results on intensity images, when no SMF generation is present.

Figure 11 .

 11 Figure 11. The comparative FROC curve of the detection of microcalcifications when mammogram

Figure 12 .

 12 Figure 12. The comparative FROC curve between the detection results on intensity images from the

Figure 13 .

 13 Figure 13. The FROC curves of the three microcalcification-detection methods on SMF images; the Foveal

ACKNOWLEDGMENTS

This work was supported in part by a Scatcherd European Scholarship from the University of Oxford and an Overseas Research Scholarship from the Committee of Vice-Chancellors and Principals of Universities of United Kingdom. The authors would like to thank Dr. Djamal Boukerroui from Compiegne University of Technology for his assistance.

We then compute C min (9), a measure of contrast sensitivity, where µ A = w µ N + (1-w) µ B and w is a suitable weight between 0 and 1 affecting the amount of background implied in the computation of contrast. C min sets the threshold from which objects in the image are visible for the observer, a measure of the eye's ability to perceive luminance gradients. The literature proposes 7.7% of the adaptive luminance to be due to the background luminance [START_REF] Heucke | A new image segmentation method based on human brightness perception and foveal adaptation[END_REF], which gives a value of 0.923 to our weight w.

In practice, we studied the effect of varying w with 10% more or less than the proposed value. We use w=0.923 as the default value in comparative studies. For parameter b in equation ( 9), we have found that the literature proposed value b=0.0808 [START_REF] Heucke | A new image segmentation method based on human brightness perception and foveal adaptation[END_REF] gives good results. Areas in the image having C>C min are marked as microcalcifications.

( )

The segmentation parameters are established automatically based on the image-adapted value of k, as computed from the statistical analysis, (discussed in Section II). Through the use of the minimal perceivable contrast c w , we include a measure of the image contrast (previously denoted as k) -imagine varying the amount of objects we can distinguish with the naked eye by using a pair of sunglasses. c w is a crucial variable for assessing our method and is consequently used for producing the FROC curves in the results session. From the FROC analysis, we noted that adapting the value of c w to the image characteristics gives a better balance between TP and FP than a constant c w . We performed simple preliminary tests on 13 random cropped mammograms digitised at 50µm resolution and containing 10 prelabelled isolated coarse calcifications. These images originate from Oxford, but are not part of the Oxford database on which the algorithm is evaluated in the next section. We found that 200 / k c w = is appropriate characteristics of the human visual system significantly enhances the detection of microcalcifications.


Osama Felemban

MD Karl Leroux

AAS Guillaume ; Aubertin

MD Fabrice Miandy

Frederic Damagnez

AAS Bruno Amorim

AAS Adriana Ramirez

AAS Brigitte Fauroux
email: brigitte.fauroux@trs.aphp.fr

AAS Frédéric Damagnez

MD Pr Brigitte Fauroux

AAS Frédéric Damagnez

Value of gas exchange recording at home in children receiving noninvasive ventilation

Keywords: noninvasive ventilation, carbon dioxide, pulse oximetry, home, gas exchange carbon dioxide, child, gas exchange, home, noninvasive positive pressure ventilation, pulse oximetry carbon dioxide, child, gas exchange, home, noninvasive positive pressure ventilation, pulse oximetry

come

Introduction

Noninvasive positive pressure ventilation (NPPV) is increasingly used in children presenting various diseases which may cause alveolar hypoventilation such as neuromuscular or lung disease, thoracic deformities, severe upper airway obstruction, or disorders of ventilatory control 1,2 . The main advantage of NPPV is that this technique may be used on demand, preferentially at night, with minimal disruption of normal life. After appropriate training of the family and caregivers, the majority of the children may be discharged home. Regular clinical and physiological follow up is necessary in order to adapt the NPPV modes and settings to the patient's clinical status and growth, and to check any side effect or respiratory or maxillofacial complication.

We have recently demonstrated the importance of a systematic overnight combined pulse oximetry (SpO 2 ) and carbon dioxide (CO 2 ) recording, even in patients in a stable condition without any symptom or sign of alveolar hypoventilation 3 . Indeed, 42% of 50 children who were well acclimatized to NPPV, without evidence of symptoms of sleep disordered breathing, were hypercapnic, defined by a maximal transcutaneous CO 2 (PtcCO 2 ) value > 50 mmHg during sleep. Most importantly, this nocturnal hypercapnia was not associated with nocturnal hypoxemia, defined by a minimal SpO 2 < 92%, or abnormal daytime blood gases in 36% of the patients.

Repeated overnight hospitalizations are associated with disruption of family life and increased health care costs. Because of a general reduction in number of pediatric hospital beds, the transfer of selected, programmed, and well-organized activities or investigations from the hospital to the home is strongly encouraged. However, the feasibility, defined by the ability to obtain technically acceptable overnight recordings as well as the satisfaction of the parents with regard to their preference between hospital and home, and accuracy of these investigations performed in a home environment, should be evaluated before their wide spread use.

The aim of the present study was first to evaluate the feasibility of an overnight gas exchange recording by a combined transcutaneous CO 2 and pulse oximetry (PtcCO 2 /SpO 2 ) monitor at home, and second to compare the results and costs of recordings performed in the hospital and at home in a cohort of stable children, treated at home with long term NPPV.

Material and methods

Patients

Consecutive patients using nocturnal NPPV at home were enrolled during their routine follow up if 1) they were in a stable condition, with no respiratory exacerbation during the previous two months, 2) they were using NPPV for at least one month, and 3) they had no clinical symptoms of nocturnal hypoventilation such as frequent arousals, nocturnal agitation, or daytime fatigue and sleepiness. Exclusion criteria were 1) age less than one year because the ear clip of the PtcCO 2 /SpO 2 monitor is too large for small infants 3 , 2) ear aplasia or hypoplasia for the same technical reasons 3 , 3) dark skin because of inaccurate SpO 2 values, as has been observed with other devices 4 , 4) impossibility to perform the hospital and home recording within one month, and 5) any change in the respiratory and/or clinical status of the patient. This PtcCO 2 /SpO 2 monitor has been validated for adults 5 and for children in our laboratory 3 .

The two overnight SpO 2 and PtcCO 2 recordings were started at the patient's usual bedtime. In the hospital, care was taken to respect the patient's sleep. Prior to the application of the sensor to the patient, the sensor was prepared by the nurse in the hospital and the technician at home and calibrated as per the manufacturer recommendations. The sensor was then applied by the nurse or the technician to the patient's earlobe for 15 minutes, until the stabilization of the PtcCO 2 and SpO 2 values. Monitoring was then performed during at least 6 hours. In the hospital, sleep with NPPV as well as the correct positioning of the nasal mask and the ear clip was regularly checked by the attending nurse during the night. At home, the parents were asked to check these elements before they went to sleep and eventually a second After the two recordings, the parents were asked: "Did your child sleep better in the hospital or at home ?" and "Do you prefer a recording performed in the hospital or at home ?".

Analysis of the nocturnal gas exchange

For each overnight sleep study, the following data were calculated: duration of recording, mean and minimal SpO 2 , percentage of night time spent with a SpO 2 > 95%, between 94 and 95%, between 93 and 92%, and < 92%; mean and maximal PtcCO 2 , % of night time spent with a PtcCO 2 > 50 mm Hg and ≤ 50 mmHg.

Statistical analysis

The patients were separated into two groups; patients with neuromuscular diseases (n=11) and patients with other disorders (n=13). For each group and type of recording (hospital and home), the median value of mean and minimal SpO

Results

Patients

Twenty four consecutive patients were included in the study with 5 patients having 2 series of hospital and home recording more than 3 months apart. Four patients with neuromuscular disease and one patient with another disorder had 2 pairs of recordings. The characteristics of the patients are given in Table 1.

Feasibility of home recording

Of the 29 recordings performed at home, one recording was technically correct but could not be analyzed because of an error on the date. The SpO 2 recording could not be analyzed in another patient in the hospital but the PtcCO 2 recording was exploitable. All the other recordings performed at home and in the hospital were correct and could be analyzed.

Comparison of home and hospital recordings

Despite randomization, only 4 recordings were initially performed at home and 25 in the hospital. The median delay between the hospital and home recordings was 11 (range 3-28) days in patients with neuromuscular disease and 7 (2-30) 2 shows that the SpO 2 and PtcCO 2 values did not differ significantly between the hospital and the home. Moreover, the results were not different between the patients with neuromuscular disease and those with other disorders. Figure 1 shows the correlation of mean and minimal SpO 2 values in the hospital and at home for each patient. The correlation of mean SpO 2 in the hospital and at home was significant for patients with other disorders (r=0.608, p=0.028) but not for patients with neuromuscular diseases (r=0.494, p=0.061). For minimal SpO 2 , no significant correlation was observed for the two groups of patients (r=0.340, p=0.215 and r=0.547, p=0.053 for patients with neuromuscular disease and other diseases, respectively). Interestingly, 4 patients had a minimal SpO 2 below 90% in the hospital but not at home, and conversely, 9 patients had a minimal SpO 2 below 90% at home but not in the hospital. Figure 2 shows the percentage of time spent with the different SpO 2 ranges in the two groups of patients. Again, no significant differences were observed between the recordings performed in the hospital and at home in both groups of patients (t-test, all NS).

Figure 3 shows the correlation of mean and maximal PtcCO 2 values in the hospital and at home for each patient. The correlation of mean PtcCO 2 in the hospital and at home was significant in the two groups of patients (r=0.647, p=0.009, and r=0.562, p=0.037, for patients with neuromuscular disease and patients with other disorders, respectively). The correlation for maximal PtcCO 2 was significant for patients with other diseases (r=0.636, p=0.014) but not for patients with neuromuscular diseases (r=0.417, p=0.122). Figure 4 shows the percentage of time spent with the different PtcCO 2 ranges in the two groups of patients. Again, no significant differences were observed between the recordings performed in the hospital and at home in both groups of patients (t-test, all NS).

According to the parents, they all found that their child slept better at home. With regard to the satisfaction of the parents, they all preferred the recording at home.

The cost of one overnight hospitalization in our pediatric pulmonology unit is 1029,00 euros. This cost should be compared to 2 technician home visits, one in the evening at the child's bedtime and one in the morning (2 x 25,16 = 50,32 euros). The cost of the transport has to be added to this amount; the French health care system reimburses 20,09 euros per visit, which make a total of 90,50 euros per home monitoring. values did not differ significantly between the hospital and the home. However, a better correlation between hospital and home values was observed for mean values as compared to minimal and maximal values, and in patients with other disorders as compared to patients with neuromuscular disease. Of note, parent's preference and cost favored home recording.

Different types of monitoring are routinely performed at home in children such as cardiorespiratory monitoring in children at risk for sudden infant death syndrome 6- 8 , pH monitoring for the diagnosis of gastro-oesophageal reflux 9 , blood pressure monitoring 10 , EEG monitoring 11,12 , polygraphy for the screening of obstructive sleep apnea [13][14][15][16] , and even telemonitoring of exhaled nitric oxide for asthmatic children 17 .

We were initially relatively reluctant to the use of the PtcCO 2 /SpO 2 monitor at home because the device requires a correct calibration, the SignTM Sensor is quite fragile, and the correct positioning of the ear clip with the head gear for the NPPV may not be easy in a young child. Technically acceptable recordings were obtained in 75% to 99% of the cases during the above mentioned studies [6][7][8][9][10][11][12][13][14][15][16][17] . However, no technical problem occurred at home during any of the 29 recordings in the present study. This may be explained by the adequate training of the technicians of the home care organization who installed the PtcCO 2 /SpO 2 monitor on the child at bed time, which requires thus a home visit outside office hours. However, this procedure seemed for us the guarantee of success.

Correlation between hospital and home recordings was better for mean SpO 2 and PtcCO 2 values than for minimal SpO 2 and maximal PtcCO 2 . This is easy understandable because a mean value is calculated over the whole recording period, and it thus less variable than an extreme value. We have no clear explanation for the A limitation of our study is the lack of data on objective sleep quality. Improved nocturnal gas exchange is not obligatory associated with better sleep quality 18 . A parallel improvement in nocturnal gas exchange and sleep architecture during NPPV has been observed in adult patients in two studies 19,20 but not in two others 21,22 . A study establishing home polysomnography norms for children showed better sleep quantity and quality at home 14 . Another study compared 2 sleep studies performed at home and in the hospital in 21 children aged 2-12 years with possible obstructive sleep apnea 13 . Sleep efficiency was significantly greater and the arousal index was significantly lower at home than in the laboratory. Finally, a study that compared blood pressure monitoring at home and in the hospital also observed significant lower diastolic blood pressure at home 10 , which supports a lower stress level when children are in their home environment.

Even if we observed a trend for better results during home recordings, this was not significant (Table 2). We may thus conclude that home recordings are feasible and may show results comparable to those obtained at hospital, justifying their integration in the routine management in children receiving long term NPPV. A regular and systematic check of the ventilator settings and circuit, the interface and its possible side effects, and also the potential problems that may occur during NPPV The aim of the present study was first to evaluate the feasibility of an overnight gas exchange recording by a combined transcutaneous CO 2 and pulse oximetry (PtcCO 2 /SpO 2 ) monitor at home, and second to compare the results and costs of recordings performed in the hospital and at home in a cohort of stable children, treated at home with long term NPPV.

Material and methods

Patients

Consecutive patients using nocturnal NPPV at home were enrolled during their routine follow up if 1) they were in a stable condition, with no respiratory exacerbation during the previous two months, 2) they were using NPPV for at least one month, and 3) they had no clinical symptoms of nocturnal hypoventilation such as frequent arousals, nocturnal agitation, or daytime fatigue and sleepiness. Exclusion criteria were 1) age less than one year because the ear clip of the PtcCO 2 /SpO 2 monitor is too large for small infants 3 , 2) ear aplasia or hypoplasia for the same technical reasons 3 , 3) dark skin because of inaccurate SpO 2 values, as has been observed with other devices 4 , 4) impossibility to perform the hospital and home recording within one month, and 5) any change in the respiratory and/or clinical status of the patient. This PtcCO 2 /SpO 2 monitor has been validated for adults 5 and for children in our laboratory 3 .

The two overnight SpO 2 and PtcCO 2 recordings were started at the patient's usual bedtime. In the hospital, care was taken to respect the patient's sleep. Prior to the application of the sensor to the patient, the sensor was prepared by the nurse in the hospital and the technician at home and calibrated as per the manufacturer recommendations. The sensor was then applied by the nurse or the technician to the patient's earlobe for 15 minutes, until the stabilization of the PtcCO 2 and SpO 2 values. Monitoring was then performed during at least 6 hours. In the hospital, sleep with NPPV as well as the correct positioning of the nasal mask and the ear clip was regularly checked by the attending nurse during the night. At home, the parents were asked to check these elements before they went to sleep and eventually a second After the two recordings, the parents were asked: "Did your child sleep better in the hospital or at home ?" and "Do you prefer a recording performed in the hospital or at home ?".

Analysis of the nocturnal gas exchange

For each overnight sleep study, the following data were calculated: duration of recording, mean and minimal SpO 2 , percentage of night time spent with a SpO 2 > 95%, between 94 and 95%, between 93 and 92%, and < 92%; mean and maximal PtcCO 2 , % of night time spent with a PtcCO 2 > 50 mm Hg and ≤ 50 mmHg.

Statistical analysis

The patients were separated into two groups; patients with neuromuscular diseases (n=11) and patients with other disorders (n=13). For each group and type of recording (hospital and home), the median value of mean and minimal SpO

Results

Patients

Twenty four consecutive patients were included in the study with 5 patients having 2 series of hospital and home recording more than 3 months apart. Four patients with neuromuscular disease and one patient with another disorder had 2 pairs of recordings. The characteristics of the patients are given in Table 1.

Feasibility of home recording

Of the 29 recordings performed at home, one recording was technically correct but could not be analyzed because of an error on the date. The SpO 2 recording could not be analyzed in another patient in the hospital but the PtcCO 2 recording was exploitable. All the other recordings performed at home and in the hospital were correct and could be analyzed. 2 shows that the SpO 2 and PtcCO 2 values did not differ significantly between the hospital and the home. Moreover, the results were not different between the patients with neuromuscular disease and those with other disorders. Figure 1 shows the correlation of mean and minimal SpO 2 values in the hospital and at home for each patient. The correlation of mean SpO 2 in the hospital and at home was significant for patients with other disorders (r=0.608, p=0.028) but not for patients with neuromuscular diseases (r=0.494, p=0.061). For minimal SpO 2 , no significant correlation was observed for the two groups of patients (r=0.340, p=0.215 and r=0.547, p=0.053 for patients with neuromuscular disease and other diseases, respectively). Interestingly, 4 patients had a minimal SpO 2 below 90% in the hospital but not at home, and conversely, 9 patients had a minimal SpO 2 below 90% at home but not in the hospital. Figure 2 shows the percentage of time spent with the different SpO 2 ranges in the two groups of patients. Again, no significant differences were observed between the recordings performed in the hospital and at home in both groups of patients (t-test, all NS).

Comparison of home and hospital recordings

Figure 3 shows the correlation of mean and maximal PtcCO 2 values in the hospital and at home for each patient. The correlation of mean PtcCO 2 in the hospital and at home was significant in the two groups of patients (r=0.647, p=0.009, and r=0.562, p=0.037, for patients with neuromuscular disease and patients with other disorders, respectively). The correlation for maximal PtcCO 2 was significant for patients with other diseases (r=0.636, p=0.014) but not for patients with neuromuscular diseases (r=0.417, p=0.122). Figure 4 shows the percentage of time spent with the different PtcCO 2 ranges in the two groups of patients. Again, no significant differences were observed between the recordings performed in the hospital and at home in both groups of patients (t-test, all NS).

According to the parents, they all found that their child slept better at home. With regard to the satisfaction of the parents, they all preferred the recording at home.

The cost of one overnight hospitalization in our pediatric pulmonology unit is 1029,00 euros. This cost should be compared to 2 technician home visits, one in the evening at the child's bedtime and one in the morning (2 x 25,16 = 50,32 euros). The cost of the transport has to be added to this amount; the French health care system reimburses 20,09 euros per visit, which make a total of 90,50 euros per home monitoring.

The 5 patients who had persistent alveolar hypoventilation during both recordings, as defined by a maximal PtcCO 2 value > 50 mm Hg and/or a minimal SpO 2 value < 90% had one or several interventions in the hospital such as the change of the ventilatory settings or mode, the addition of an abdominal girdle or a chin strap, and/or the change of the interface. An overnight gas exchange control was performed systematically before discharge.

Discussion

This study is the first to show the feasibility of overnight PtcCO 2 /SpO 2 recording in a group of children over the age of 4 years, treated at home with long term NPPV. Twenty eight of the 29 (97%) recordings were analyzable when a trained technician installed the equipment at home and instructed the parents how to values did not differ significantly between the hospital and the home. However, a better correlation between hospital and home values was observed for mean values as compared to minimal and maximal values, and in patients with other disorders as compared to patients with neuromuscular disease. Of note, parent's preference and cost favored home recording.

Different types of monitoring are routinely performed at home in children such as cardiorespiratory monitoring in children at risk for sudden infant death syndrome 6- 8 , pH monitoring for the diagnosis of gastro-oesophageal reflux 9 , blood pressure monitoring 10 , EEG monitoring 11,12 , polygraphy for the screening of obstructive sleep apnea [13][14][15][16] , and even telemonitoring of exhaled nitric oxide for asthmatic children 17 .

We were initially relatively reluctant to the use of the PtcCO 2 /SpO 2 monitor at home because the device requires a correct calibration, the SignTM Sensor is quite fragile, and the correct positioning of the ear clip with the head gear for the NPPV may not be easy in a young child. Technically acceptable recordings were obtained in 75% to 99% of the cases during the above mentioned studies [6][7][8][9][10][11][12][13][14][15][16][17] . However, no technical problem occurred at home during any of the 29 recordings in the present study. This may be explained by the adequate training of the technicians of the home care organization who installed the PtcCO 2 /SpO 2 monitor on the child at bed time, which requires thus a home visit outside office hours. However, this procedure seemed for us the guarantee of success.

Correlation between hospital and home recordings was better for mean SpO 2 and PtcCO 2 values than for minimal SpO 2 and maximal PtcCO 2 . This is easy understandable because a mean value is calculated over the whole recording period, and it thus less variable than an extreme value. We have no clear explanation for the A limitation of our study is the lack of data on objective sleep quality. Improved nocturnal gas exchange is not obligatory associated with better sleep quality 18 . A parallel improvement in nocturnal gas exchange and sleep architecture during NPPV has been observed in adult patients in two studies 19,20 but not in two others 21,22 . A study establishing home polysomnography norms for children showed better sleep quantity and quality at home 14 . Another study compared 2 sleep studies performed at home and in the hospital in 21 children aged 2-12 years with possible obstructive sleep apnea 13 . Sleep efficiency was significantly greater and the arousal index was significantly lower at home than in the laboratory. Finally, a study that compared blood pressure monitoring at home and in the hospital also observed significant lower diastolic blood pressure at home 10 , which supports a lower stress level when children are in their home environment.

Even if we observed a trend for better results during home recordings, this was not significant (Table 2). We may thus conclude that home recordings are feasible and may show results comparable to those obtained at hospital, justifying their integration in the routine management in children receiving long term NPPV. A regular and systematic check of the ventilator settings and circuit, the interface and its possible side effects, and also the potential problems that may occur during NPPV Pediatric Pulmonology

5

 5 All the parents, and if possible the patients, gave informed written consent for the study which was approved by the local ethical committee.Overnight PtcCO 2 /SpO 2 recordingTwo overnight PtcCO 2 /SpO 2 recordings were performed in a random order with the SenTec Digital Monitor (software version SMB SW-V06.10; MPB SW-V04.03) and the V-SignTM Sensor which was applied to the earlobe with a dedicated Ear Clip (SenTec AG, Therwil, Switzerland). This fully digital sensor combines the elements of an electrochemical Severinghaus-type CO 2 tension sensor with the optical elements of conventional SpO 2 sensors, thus providing a noninvasive and continuous PtcCO 2 and SpO 2 monitoring. The sensor is warmed to a constant surface temperature of 42°C to improve local arterialization of the measurement site.

  night. The parents were taught how to remove the ear clip at awakening.

  2 and of mean and maximal PtcCO 2 was calculated because the values were not normally distributed. Comparison between the home and hospital recordings was performed by the Mann Whitney Rank Sum test. Moreover, individual data were analyzed by plotting mean and minimal SpO 2 and mean and maximal PtcCO 2 observed in the hospital against the values obtained at home for each patient. Correlation between the values recorded at home and in the hospital was performed using simple linear regression. Statistical analyses were SigmaStat (Systat Software Inc., San Jose, California). Values of p<0.05 were considered statistically significant.

The 5

 5 patients who had persistent alveolar hypoventilation during both recordings, as defined by a maximal PtcCO 2 value > 50 mm Hg and/or a minimal SpO 2 value < 90% had one or several interventions in the hospital such as the change of the ventilatory settings or mode, the addition of an abdominal girdle or a chin strap, and/or the change of the interface. An overnight gas exchange control was performed systematically before discharge.DiscussionThis study is the first to show the feasibility of overnight PtcCO 2 /SpO 2 recording in a group of children over the age of 4 years, treated at home with long term NPPV. Twenty eight of the 29 (97%) recordings were analyzable when a trained technician installed the equipment at home and instructed the parents how to and remove the ear clip in the morning. SpO 2 and PtcCO 2

  hospital and home SpO 2 and PtcCO 2 values in patients with other diseases as compared to patients with neuromuscular diseases. A possible explanation could be that patients with other diseases, who are predominantly patients with upper airway obstruction, are more stable than patients with neuromuscular disease. In practice, minimal and maximal values should be interpreted with more caution than mean values when comparing hospital and home recordings.

  leaks, are, to our opinion, important to document during an overnight observation in the hospital. As such, we would recommend a combination of home and hospital recordings, nor only for the patient's and parent's comfort but also with regard to the familial and financial burden. Because individual data may be better in the home or in the hospital, we would recommend a change of NPPV settings or additional measures only in case of abnormal values in both conditions. Those patients with an abnormal "in home" gas exchange should be referred for an "in hospital" titration study.In conclusion, overnight PtcCO 2 /SpO 2 monitoring is feasible at home and shows comparable results to hospital recordings. Systematic and regular home monitoring, combined with regular hospital visits, is recommended in children treated at home with NPPV.

1

 1 Figure 1

Figure 2

 2 Figure 2

Figure 3

 3 Figure 3

  For mean PtcCO 2 , regression lines are represented (plain for patients with neuromuscular disease (r=0.647, p=0.009) and dashed for patients with other disorders (r=0.564, p=0.037))For maximal PtcCO 2 , regression lines are represented (plain for patients with neuromuscular disease (r=0.417, p=NS) and dashed for patients with other disorders (r=0.636, p=0.014).Three patients having similar PtcCO 2 values, only 27 of the 29 spots are visible.

Figure 4

 4 Figure 4

Introduction 3 .

 3 Noninvasive positive pressure ventilation (NPPV) is increasingly used in children presenting various diseases which may cause alveolar hypoventilation such as neuromuscular or lung disease, thoracic deformities, severe upper airway obstruction, or disorders of ventilatory control1,2 . The main advantage of NPPV is that this technique may be used on demand, preferentially at night, with minimal disruption of normal life. After appropriate training of the family and caregivers, the majority of the children may be discharged home. Regular clinical and physiological follow up is necessary in order to adapt the NPPV modes and settings to the patient's clinical status and growth, and to check any side effect or respiratory or maxillofacial complication.We have recently demonstrated the importance of a systematic overnight combined pulse oximetry (SpO 2 ) and carbon dioxide (CO 2 ) recording, even in patients in a stable condition without any symptom or sign of alveolar hypoventilation Indeed, 42% of 50 children who were well acclimatized to NPPV, without evidence of symptoms of sleep disordered breathing, were hypercapnic, defined by a maximal transcutaneous CO 2 (PtcCO 2 ) value > 50 mmHg during sleep. Most importantly, this nocturnal hypercapnia was not associated with nocturnal hypoxemia, defined by a minimal SpO 2 < 92%, or abnormal daytime blood gases in 36% of the patients.Repeated overnight hospitalizations are associated with disruption of family life and increased health care costs. Because of a general reduction in number of pediatric hospital beds, the transfer of selected, programmed, and well-organized activities or investigations from the hospital to the home is strongly encouraged. However, the feasibility, defined by the ability to obtain technically acceptable well as the satisfaction of the parents with regard to their preference between hospital and home, and accuracy of these investigations performed in a home environment, should be evaluated before their wide spread use.

5

 5 All the parents, and if possible the patients, gave informed written consent for the study which was approved by the local ethical committee.Overnight PtcCO 2 /SpO 2 recordingTwo overnight PtcCO 2 /SpO 2 recordings were performed in a random order with the SenTec Digital Monitor (software version SMB SW-V06.10; MPB SW-V04.03) and the V-SignTM Sensor which was applied to the earlobe with a dedicated Ear Clip (SenTec AG, Therwil, Switzerland). This fully digital sensor combines the elements of an electrochemical Severinghaus-type CO 2 tension sensor with the optical elements of conventional SpO 2 sensors, thus providing a noninvasive and continuous PtcCO 2 and SpO 2 monitoring. The sensor is warmed to a constant surface temperature of 42°C to improve local arterialization of the measurement site.

  night. The parents were taught how to remove the ear clip at awakening.

  2 and of mean and maximal PtcCO 2 was calculated because the values were not normally distributed. Comparison between the home and hospital recordings was performed by the Mann Whitney Rank Sum test. Moreover, individual data were analyzed by plotting mean and minimal SpO 2 and mean and maximal PtcCO 2 observed in the hospital against the values obtained at home for each patient. Correlation between the values recorded at home and in the hospital was performed using simple linear regression. Statistical analyses were SigmaStat (Systat Software Inc., San Jose, California). Values of p<0.05 were considered statistically significant.

  Despite randomization, only 4 recordings were initially performed at home and 25 in the hospital. The median delay between the hospital and home recordings was 11 (range 3-28) days in patients with neuromuscular disease and 7 (2-30) days in disorders (p not significant (NS)). The median duration of the overnight PtcCO 2 /SpO 2 recording was comparable at home (503 minutes, range 360-609) and in the hospital (560 minutes, range 231-688, p=NS). Table

  and remove the ear clip in the morning. SpO 2 and PtcCO 2

  hospital and home SpO 2 and PtcCO 2 values in patients with other diseases as compared to patients with neuromuscular diseases. A possible explanation could be that patients with other diseases, who are predominantly patients with upper airway obstruction, are more stable than patients with neuromuscular disease. In practice, minimal and maximal values should be interpreted with more caution than mean values when comparing hospital and home recordings.

  leaks, are, to our opinion, important to document during an overnight observation in the hospital. As such, we would recommend a combination of home and hospital recordings, nor only for the patient's and parent's comfort but also with regard to the familial and financial burden. Because individual data may be better in the home or in the hospital, we would recommend a change of NPPV settings or additional measures only in case of abnormal values in both conditions. Those patients with an abnormal "in home" gas exchange should be referred for an "in hospital" titration study.In conclusion, overnight PtcCO 2 /SpO 2 monitoring is feasible at home and shows comparable results to hospital recordings. Systematic and regular home monitoring, combined with regular hospital visits, is recommended in children treated at home with NPPV.

1

 1 Figure 1

Figure 2

 2 Figure 2

Figure 3

 3 Figure 3

  For mean PtcCO 2 , regression lines are represented (plain for patients with neuromuscular disease (r=0.647, p=0.009) and dashed for patients with other disorders (r=0.564, p=0.037))For maximal PtcCO 2 , regression lines are represented (plain for patients with neuromuscular disease (r=0.417, p=NS) and dashed for patients with other disorders (r=0.636, p=0.014).Three patients having similar PtcCO 2 values, only 27 of the 29 spots are visible.

Figure 4

 4 Figure 4

Table 2 :

 2 Abbreviations: NPPV: noninvasive positive pressure ventilation, AC/VT: assist control / volume targeted ventilation, PS: pressure support ventilation.

Table 1 :

 1 Characteristics of the patients.

	patients
	n=24

John Wiley & Sons, Inc.Pediatric Pulmonology

Acknowledgments

All the authors declare that they have no conflict of interest with the data presented in this manuscript.

Acknowledgments

All the authors declare that they have no conflict of interest with the data presented in this manuscript.

Supports and grants

The research of Brigitte Fauroux is supported by the Association Française contre les Myopathies (AFM), Assistance Publique-Hôpitaux de Paris, Inserm, ADEP Assistance, and Université Pierre et Marie Curie-Paris 6.

Supports and grants

The research of Brigitte Fauroux is supported by the Association Française contre les Myopathies (AFM), Assistance Publique-Hôpitaux de Paris, Inserm, ADEP Assistance, and Université Pierre et Marie Curie-Paris 6.


V Colombo

E Ghedini

M Boselli

P Sanibondi

A Concetti

3D static and time-dependent modeling of a dc transferred arc twin torch system

3D static and time-dependent modelling of a dc transferred arc twin torch system

Introduction

The transferred arc plasma torch device, in its more general configuration, consists of two electrodes generating a plasma arc sustained by means of an electric current flowing through the body of the discharge, transferring power from electric field to gas by ohmic heating. A lot of modeling work has been done in order to characterize the behavior of transferred arcs in their typical configurations, like free burning arcs or cutting plasma torches [1], but very little has been done in the investigation of transferred electric arc discharges generated between two suspended metallic electrodes in the twin torch configuration. Twin torch generated arcs differ from the other transferred arcs since the anode is not the workpiece, as shown in figure 1, while the arc may or may not pass through a bath of molten material, depending on the specific application or design. This kind of device has been used mainly in reactors for waste treatment incineration and inertization, or for metallurgical applications [2][START_REF] Salvati | Application of Plasma System for Tundish Heating[END_REF][START_REF] Salvati | Development of Thermal Technologies for Pyrolysis and Combustion of Waste with Vitrification of Ash[END_REF], while on the patent side also some other applications are claimed [START_REF] Johnson | Twin Plasma Torch Apparatus Tetronics[END_REF]. The advantages of such device are: the arc can be elongated and the energy is exerted directly on the process material or on the surface of the component, the powder, gas or dispersed liquid, not in the torch; enhanced convection leading to a more homogeneous temperature in the reactor; electrodes can be protected by inert shrouding gas (e.g. Ar); several free degrees of freedom in the operating conditions (e.g. electrode to bath distance, inlet flows, current) While disadvantages can be:

possibility of instabilities at high current due to the magnetic interaction between the cathodic and anodic arc columns; side arcing can occur at high voltage; increase of design complexity with respect to simple graphite transferred electrode.

The complex shape and fluid dynamics of a twin torch discharge needs a 3D description in order to be predicted. Some research on the subject of DC transferred arc twin torch systems has been done in the past using a 3D steady state modeling of the discharge inside a plasma furnace devoted to combustion/vitrification of radioactive wastes [START_REF] Barthelemy | Modeling a pilotscale combustion vitrification furnace under oxygen plasma arc transferred between twin torches[END_REF] and for asbestos inertization [START_REF] Colombo | 3-D Modelling of DC Transferred arc Twin Torch for Asbestos Inertization[END_REF]. In a recent paper [START_REF] Tang | [END_REF] the same LTE steady state model previously used by the Authors in [START_REF] Colombo | 3-D Modelling of DC Transferred arc Twin Torch for Asbestos Inertization[END_REF] together with the same model validation approach by means of free burning arc simulation comparison with literature experimental data, has been applied to a twin torch system for fine powders production. In [START_REF] Tang | [END_REF] it is experimentally found that the stability of the coupling zone is mainly related to the included angle between the torches, meaning that above a critical angle a steady model can be used to predict the twin torch arcs. However the high speed frame in [START_REF] Tang | [END_REF] shows a very irregular coupling zone with at least two connections between cathodic and anodic arcs that is not consistent with a steady state, and only averaged experimental voltage drop have been included. The extended discharge length that goes from the tungsten pencil cathode to the flat copper anode without any particular confinement wall and the fluid dynamics and magnetic forces acting on the arc may induce an unsteady behavior as shown in [9] for Local Thermodynamic Equilibrium (LTE) conditions. Unfortunately the results shown in [9] predict a higher voltage with respect to the values usually found experimentally, probably to due the LTE model underestimation of electrical conductivity in the cold regions. It is known that also at atmospheric pressure thermal and chemical non equilibrium may occur [10], leading to an overpopulation of electrons in cold regions, where LTE model predicts almost no ionization, and then to an increase of electrical conductivity. In a conventional transferred arc the non equilibrium effects are mainly located in the arc fringes [11] and have almost no influence on the arc voltage, limiting the necessity of 2T calculations. In the twin torch configuration a non equilibrium region between the two torch would facilitate the migration of electrons from cathode to anode reducing the length of the current path and then the voltage drop. For this reasons a 3D time dependent plasma arc model including two temperature (2T) thermal non equilibrium has been developed using a customized commercial code FLUENT.

Model description

An LTE time dependent model previously developed by the Authors [START_REF] Colombo | 3-D Modelling of DC Transferred arc Twin Torch for Asbestos Inertization[END_REF] has been extended to the non thermal equilibrium case. Turbulence effects are taken into account into the model using a RNG model. Anodic and cathodic sheaths have been neglected, while electrodes interfaces are taken into account using a simplified approach, imposing a current density distribution on the cathode surface. Neglecting sheath phenomena allows reducing the computational effort since their influence on the main body of the arcs is negligible as shown in [12]. In all the performed calculations, the required database of equilibrium and non equilibrium thermodynamic and transport properties has been taken from [13].

Geometry

The twin torch configuration is schematically represented in figure 2 and refers to a 1 MW mobile twin torch plant dedicated to asbestos inertization from Centro Sviluppo Materiali (CSM) S.p.A, Rome, Italy [2,[START_REF] Salvati | Application of Plasma System for Tundish Heating[END_REF]. The computational domain does not extend to the whole reactor, since the simulation of the complete 3D configuration would be too computationally expensive. The domain is thus limited to the region between the cathode and anode where the discharge takes place.

The computational mesh has been generated in order to cover the full volume of the discharge and it is shown in figure 3. A 700'000 polyhedral elements mesh has been generated starting from a 2 millions tetrahedrical mesh, in order to lower the computational effort and to improve numerical behavior of the code reducing the effects of badly shaped cells and model stability.

LTE model

The LTE model equations are summarized as follows.

The continuity and Navier-Stokes equations are The energy conservation equation

0 ) ( = ⋅ ∇ + ∂ ∂ u t r ρ ρ g B J p u u t u r r r r r r r r ρ τ ρ ρ + × + ⋅ ∇ + -∇ = ⋅ ∇ + ∂ ∂ ) ( ) (
rad B eff Q E J T J e k T K u h t h - ⋅ + ∇ ⋅ + ∇ ⋅ ∇ = ⋅ ∇ + ∂ ∂ r r r r 2 5 ) ( ) ( ) ( ρ ρ
where h is the enthalpy,

turb lam eff K K K + =
the effective thermal conductivity that includes the contribution of turbulence, E J r r ⋅ the Joule heating and rad Q the radiation losses calculated using a n.e.c. approach [14]. The current density has been calculated using the simplified Ohm's law, neglecting the Hall current E J r r σ = .

2T model

The equations for the 2T thermal non equilibrium model are summarized as follows (see [1,10] for details). Mass conservation and Navier-Stokes equations are the same as LTE model while separate energy equations for the species are needed. The energy equation for the heavy and electron species are

EH h h h h Q T K u h t h + ∇ ⋅ ∇ = ⋅ ∇ + ∂ ∂ ) ( r ρ ρ ( ) EH rad J e B e e e e B e e B Q Q Q T J e k T K u T n k t T n k - - + ∇ ⋅ + ∇ ⋅ ∇ = ⋅ ∇ + ∂ ∂ r r 2
E E ∇ + = ∇ + = ∇ + ≈ r r r r
This expression can be derived from a simplified expression of the generalized Ohm's law as shown in [1].

Electromagnetic model

The electromagnetic field is calculated using the vector and scalar potential form of the Maxwell's equations. The vector and scalar potential equations are solved in this form

0 0 2 = - ∇ E A r r σ µ 0 = ∇ ⋅ ∇ p V σ
while the effective electric field comes from the gradient of the effective scalar potential

p p V E -∇ =
For the LTE case the effective electric potential p V is assumed equal to the electric potentials V .

Boundary conditions

A parabolic profile of the current density on the cathode surface is given as a boundary condition using this relation where is the maximum value of the current density on the cathode, is the distance from the axis of the cathode, is a reference value calculated imposing a given value of the total current ! "# on the cathode surface. On the anode surface the electrical potential is assumed to be zero, while on all the other surfaces of the model the current flux is assumed to be zero.

The boundary condition for the vector potential $ $% & ' has been used on all the wall surfaces, where % & is the unit vector normal to the surface. An alternative condition on the walls has been used to artificially stabilize the discharge in order to define a reference steady configuration for the comparison of discharges at different operating conditions. The condition avoids the fluctuations of the discharge and is to be intended not as a physically realistic condition but as a trick, that makes possible to use a steady code with a considerable saving of computational time. The temperature value given as a boundary condition on the anode and cathode comes from previous calculations developed by CSM S.p.A. and are 600K and 1500K respectively; however, a change in these values does not have a significant influence on the results. On all the other surfaces the temperature is fixed at 500 K. Argon flow rate is 80 slpm for both electrodes.

Results

Time dependent LTE model

The time dependent behaviour of this device has been described in by the Authors in [START_REF] Tang | [END_REF]9] and sketched in figure 4 and will only be briefly discussed here. The dynamic of the twin torch discharge involves the zone of attachment of the two plasma columns and seems to be due to an unbalancing between Lorentz and drag forces that shift downstream the attachment point, until the gradient of the electric potential creates another upstream attachment point by means of a restrike. In this way a periodic oscillation is obtained, limited to the downstream region of the discharge with only a small influence on the fields in the proximity of the electrodes.

The voltage oscillates between 190 to 260V depending on the instantaneous discharge length and it is not in agreement with experimental measurements that predict values around 150V. This means that the LTE model tends to overestimate the discharge power. Moreover, the cathode and anode fall must be added to the model predicted voltage, and can be roughly estimated to be overall around 5-15V for a tungsten cathode [14,15], less then 8% of the total voltage.

Steady state LTE model

Since the time dependent simulation is very computational expensive, an artificial stabilization has been introduced by means of a boundary condition on torch walls that prevents the motion of the zone of attachment of the two plasma columns, as explained in the previous section. Details on the discharge will be presented using the steady model. This assumption also allows easier comparison with the following 2T model results, that predict a steady discharge.

In figure 5 the temperature field is shown using isosurfaces at different temperature values. It is possible to see the repulsion of the two plasma columns due to the self generated magnetic fields. This repulsion can lead to a non symmetric shape of the discharge, as shown in figure 4, that needs a 3D model to be taken into account [9]. This phenomenon is more pronounced with the increasing of the current. The velocity field is shown in figure 6 using a contour on the mid plane; the maximum velocity is about 860 m/s and is located on the cathode tip, where the magnetic constriction is higher. In the main body of the discharge the velocity is in the order of 200 m/s. Figure 7 shows the details of the temperature field on two planes. The maximum plasma temperature is located near the cathode surface and is about 30'000 K, while in the proximity of the anodic surface the plasma temperature reaches a value of about 13'000 K. The main body of the discharge is at a temperature of about 11'000 K. Figure 8 shows the temperature field at different horizontal planes and the detailed shape of the horizontal connecting channel that is quite narrow with respect to the two plasma columns due to the current driven self constriction of the arc.

Steady state 2T model

The time dependent 2T model applied to the twin torch system shows no fluctuations, for both boundary conditions $ $% & ' and . For this reason a steady model approach has been used also in the 2T model.

Figure 9 compares the electrons and heavy particles temperatures while figures 10 and 11 show the region of non equilibrium by means of the non equilibrium parameter ( ) * ) + ' . The highest value of ( is located in the region between the two plasma columns where the electric field is higher. In this region the electric field exchange energy with electrons and the collision term Q EH is not sufficiently high to raise the heavy species particle temperature; also because of the flow convection that pushes cold gas downward that keeps heavy particles cool. Thermal non equilibrium is also located near the walls and in the fringes of the discharge where the temperature gradients are higher.

The strong non equilibrium in the region between the two torches leads to a local increase of the electrical conductivity that facilitates the electrons migration from cathode to anode reducing the total arc length. This has an effect on the electrodes voltage as shown in figure 12 where steady LTE model predicts a voltage of 184 V while the 2T model a voltage of 104 V. A cathode and anode fall overall of about 5-15 V must be added to these values. The total voltage predicted by the 2T model is the 85% of the experimental reference value of 150V. This underestimation could be due to the chemical equilibrium assumption, since the region between the two torches is strongly affected by flow convection that could influence the presence of the ionized species and electrons. Still, even though this underestimation, the agreement of the 2T model is better than the LTE model.

The absence of fluctuations, unlike the LTE model, could be mainly related to the enhanced electrical conductivity non equilibrium region that provides a stable channel for the electrons and that is less affected by the flow drag than the LTE case.

These results show that thermal non equilibrium in arc discharges at atmospheric pressure can have an important influence on the predicted arc properties.

Conclusions

Simulations have been presented for a twin torch system using LTE and 2T approach for the prediction of the discharge properties. A method for artificially stabilize the discharge by changing the magnetic field boundary conditions has been introduced.

While LTE model predicts a fluctuation of the discharge, the 2T model shows no dynamic behavior probably due to the increased electrical conductivity in the cold region between the plasma arc columns. 2T model predicts a substantial lower voltage between electrodes with respect to LTE showing that for this kind of device the LTE approach may fail in the voltage and power prediction of the plasma discharge.

Following these evidences, it is possible that chemical non equilibrium and electron diffusion, which will be introduced as a future development in the model, will have a non negligible effect on the predicted discharge properties. Parameters like electrodes distance or flow rate should be investigated in the future in order to evaluate their influence on the restrike mode and on the voltage.

Figure 1 .

 1 Figure 1. Schematic of a typical free burning transferred arc (left) and of a twin torch system (right).

Figure 3 .

 3 Figure 3. Detail of the mesh and computational domain.

Figure 2 .

 2 Figure 2. Schematic of the twin torch geometry.

  where is the density, u r the fluid velocity, p the pressure, τ r r the viscous stress tensor and B J r r × the contribution of the Lorentz forces.

ν

  e K are the thermal conductivities for heavy particles and electrons, B k the Boltzmann constant, e n the electron number density and e the electron elementary charge. Electron density has been calculated using the Saha equation for 2T systems assuming chemical equilibrium[10]. The energy exchange by collisions between electrons and heavy species EH Q can be expressed using a sum over all species as is the collision frequency between electrons and species s and es δ the inelastic collision factor, that for monoatomic gas is equal to one.

Figure 4 .

 4 Figure 4. Side and bottom view of isotemperature surfaces with computed voltage values in the twin torch system at different time steps for 1500A. Isosurfaces temperature values are: 8000K, 10000K, 11000K, 12000K and 14000K. Cathodic torch is always on the right. (from [9]).

Figure 7 .

 7 Figure 7. Front and side view of the temperature field [K] on the mid planes for the LTE model.

Figure 5 .

 5 Figure 5. Isotemperature surfaces of the twin torch discharge for LTE model.

Figure 6 .

 6 Figure 6. Velocity field [m/s] on the plane passing through the axis of the torches for LTE model.

Figure 8 .

 8 Figure 8. Temperature field [K] on horizontal planes for the LTE model at different vertical distance z from the cathode tip.

Figure 9 .

 9 Figure 9. Front view of the electron (left) and heavy particles (right) temperature field [K] on the mid plane for the 2T model. Electron temperature contour lines are superimposed on the heavy particles field contour.

Figure 10 .

 10 Figure 10. ( isosurfaces over the 9'500 K heavy particles temperature isosurface for the 2T model.

Figure 11 .

 11 Figure 11. ( contour on the mid plane for the 2T model.

Figure 12 .

 12 Figure 12. Electric potential field [V] for the LTE and 2T models.