Mathematical foundations for error estimation in numericalsolutions of integral equations in electromagnetics

The problem of error estimation in the numerical solution of integral equations that arise in electromagnetics is addressed. The direct method (Green's theorem or field approach) and the indirect method (layer ansatz or source approach) lead to well-known integral equations both of the first kind [electric field integral equations (EFIE)] and the second kind [magnetic field integral equations (MFIE)]. These equations are analyzed systematically in terms of the mapping properties of the integral operators. It is shown how the assumption that field quantities have finite energy leads naturally to describing the mapping properties in appropriate Sobolev spaces. These function spaces are demystified through simple examples which also are used to demonstrate the importance of knowing in which space the given data lives and in which space the solution should be sought. It is further shown how the method of moments (or Galerkin method) is formulated in these function spaces and how residual error can be used to estimate actual error in these spaces. The condition number of all of the impedance matrices that result from discretizing the integral equations, including first kind equations, is shown to be bounded when the elements are computed appropriately. Finally, the consequences of carrying out all computations in the space of square integrable functions, a particularly friendly Sobolev space, are explained     

Designing better adaptive sampling algorithms for ECG Holtersystems

Let Ψ be any adaptive sampling algorithm that can run in real time on a tapeless multichannel electrocardiogram (ECG) Holter system. Simple methods which can significantly improve Ψ's fidelity are described and their results are compared in this paper. It is shown that by adding some simple tests to Ψ, the signals reconstructed by Ψ can be improved as much as 5.45 dB. It is also shown that under the same data rate, a good data compressor with slowly sampled input ECG is preferable to a bad data compressor with highly sampled input ECG     

Fullerene Reactivity in an Oxygen Plasma

Fullerene reactivity in an oxygen plasma was measured and compared with those determined under the same conditions for a comprehensive set of 50 carbon materials. The possible reasons for the high plasma reactivity of the fullerene sample in an oxygen plasma are discussed.     

Long-term effect of lisinopril and atenolol on kidney function in hypertensive NIDDM subjects with diabetic nephropathy

The aim of our study was to evaluate whether inhibition of ACE (lisinopril 10-20 mg/day) can reduce the rate of decline in kidney function more than reducing blood pressure with conventional antihypertensive treatment (atenolol 50-100 mg/day), usually in combination with a diuretic. We performed a prospective, randomized, parallel study for 42 months, double blind for the first 12 months and single blind thereafter. Forty-three (21 lisinopril and 22 atenolol) hypertensive NIDDM patients with diabetic nephropathy were enrolled. Data from 36 patients (17 lisinopril and 19 atenolol, 60 +/- 7 years of age, 27 men) who completed at least 12 months of the study period are presented. At baseline, the two groups were comparable: glomerular filtration rate (51Cr-EDTA plasma clearance) was 75 +/- 6 and 74 +/- 8 ml x min(-1) x 1.73 m(-2), mean 24-h ambulatory blood pressure (A&D TM2420) was 110 +/- 3 and 114 +/- 2 mmHg, and 24-h urinary albumin excretion rate was 961 (range 331-5,727) and 1,578 (476-5,806) mg/24 h in the lisinopril and atenolol groups, respectively. The mean follow-up time was similar, 37 and 35 months in the lisinopril and atenolol groups, respectively. Mean ambulatory blood pressure was equally reduced in the two groups, 12 +/- 2 and 10 +/- 2 mmHg in the lisinopril and atenolol groups, respectively. Glomerular filtration rate declined in a biphasic manner with a faster initial (0 to 6 months) change of 1.25 +/- 0.49 and 0.81 +/- 0.29 ml x min(-1) x month(-1) followed by a slower sustained decline (6 to 42 months) of 0.59 +/- 0.10 and 0.54 +/- 0.13 ml x min(-1) x month(-1) in the lisinopril and atenolol groups, respectively. No significant differences were observed in either initial or sustained decline in glomerular filtration rate between the two groups. Urinary albumin excretion was reduced (% reduction of baseline) more in the lisinopril than in the atenolol group, at 55 (95% CI 29-72) and 15% (-13 to 34), respectively (P = 0.01). In conclusion, the relentless decline in kidney function characteristically found in hypertensive NIDDM patients with diabetic nephropathy can be reduced equally effectively by two antihypertensive treatments, the beta-blocker atenolol and the ACE inhibitor lisinopril.     

Stroke in teenagers

Between 3.7% and 8.5% of all strokes occur before the age of 45 years old. In the population under 15 years of age, the annual incidence of strokes is 2.7 per 100,000 children, with ischaemic strokes making up 1.2 and haemorrhagic strokes 1.5 of this total. The main characteristic of ischaemic strokes in childhood is the wide variety of diagnoses involved. Some of these, such as congenital cardiopathy, are rare in adults, as are dissections and arterial dysplasias, arteritis, hereditary connective tissue disorders and disorders of metabolism. Similarly, the aetiology of haemorrhagic stroke is also very varied, with bursting of a vascular malformation or aneurysm being the commonest. Other aetiologies are disorders of haemostasis, arteritis, migraine, retarded post-traumatic phenomena and the use of drugs and sympathomimetic agents. The personal, family and social repercussions are considerable, since both ischaemic and haemorrhagic strokes have an appreciable mortality and morbidity.     

Hypercoagulability and chronic atrial fibrillation: the role of markers of thrombin generation

BACKGROUND: We have studied 64 patients with congestive heart failure, half of them also with chronic nonvalvular atrial fibrillation (AF). Patients were also stratified according to a history of prior stroke. METHODS: The generation of thrombin was investigated by means of the molecular markers prothrombin fragment 1 + 2 (F1 + 2) and thrombin-antithrombin III complex (TAT), because AF patients may have a hypercoagulable state. There was only a trend toward higher values of TAT and F1 + 2 for AF patients, while subjects with previous stroke (irrespective of AF) had increased levels of the markers of thrombin generation (TAT stroke+ 18.95 +/- 5.15 vs TAT stroke- 8.34 +/- 2.41; F1 + 2 stroke+ 2.22 +/- 0.29 vs F1 + 2 stroke- 1.32 +/- 0.12). The presence of spontaneous echo contrast (SEC) within left atrium was also investigated in 32 AF patients by transesophageal echocardiography. RESULTS: TAT were significantly higher in subjects (n = 11) with SEC (TAT sec+ 37.5 +/- 13.41 vs TAT sec- 8.7 +/- 2.51, p = 0.008). CONCLUSIONS: Finally, when we grouped into 1) those with both AF and stroke, 2) AF alone, 3) stroke alone and 4) sinus rhythm without stroke, levels of F1 + 2 were higher (and marginally higher TAT) in patients with AF and stroke than in those without stroke, revealing that there is a true clotting activation state in these subjects.     

Maternal nutrition and socio-economic status as determinants of birthweight in chronically malnourished African women

The birthweight is the most important determinant of mortality and morbidity in the neonatal period and may have an influence on health in adult life. The high rate of low birthweight in developing countries is therefore a major health problem. Maternal malnutrition is usually assumed to be a causal factor but other environmental factors are also involved. In this study we analysed maternal nutritional and socio-economic factors as determinants of birthweight in term infants from a rural African society characterised by a high rate of chronic malnutrition. Relations of maternal weight, gestational weight gain, parity, socio-economic status and infant sex with birthweight were analysed in 1,477 women and child pairs. The selected women were followed from early pregnancy and had an uncomplicated delivery at term of a living singleton child. The gestational weight gain was 5.6 (SD 6.0) kg and the mean birthweight 2.933 kg (SD 408). Maternal weight, representing the maternal long-term nutritional situation, was the most important independent determinant of birthweight, accounting for 13.0% of the variance in birthweight. The weight gain, representing the short-term nutritional situation, explained only 5.6% of the variance. Birthweight increased by 20 g (CI 18-23) for each kg maternal weight and by 15 g (CI 12-18) for each kg gestational weight gained. The socio-economic difference in birth-weight was 153 g (CI 109-196) 88 of which (CI 48-128) remained unexplained after adjustment for differences in maternal weight, parity and gender. Improved long-term nutritional situation and living conditions seems to be the most important prerequisites to counteract low birthweight in developing countries.     

Metastatic parathyroid carcinoma in the MEN2A syndrome

We report a patient with a metastatic parathyroid carcinoma and medullary carcinoma of the thyroid. This patient represents a variation of the multiple endocrine neoplasia syndrome (MEN) type 2A. There was no evidence of a phaeochromocytoma. The case illustrates the difficulties that may be encountered in localising the source of PTH secretion; the patient underwent four unsuccessful exploratory operations of the neck and mediastinum before further investigations revealed a single metastatic deposit of parathyroid carcinoma involving the first thoracic vertebra. PCR amplification and sequencing of the RET oncogene from the metastatic parathyroid carcinoma and genomic DNA revealed a heterozygous mutation (Cys634Tyr) in exon 11, as has previously been described to occur in MEN 2A. In addition, loss of tumour heterozygosity was demonstrated at loci from chromosomes 1, 2, 3p, 13q and 16p. This represents the first report of a parathyroid carcinoma in a MEN2A patient, in which the multiple allelic deletions are consistent with the generalised losses observed in aggressive tumours.     

Prenatal diagnosis of a highly undifferentiated brain tumour--a case report and review of the literature

Intracranial tumours, often presenting with progressive hydrocephalus, are rare congenital diseases accounting for 0.5-1.5 per cent of all cases of brain tumours diagnosed during childhood. The differential diagnosis includes vascular malformations, infarctions, and haemorrhages. Sonographic signs suggestive of glioblastoma, teratoma, and astrocytoma do not establish the histological diagnosis, however. We report a case of an undifferentiated fetal glioma detected at 29 weeks' gestation. The diagnosis of an undifferentiated brain tumour was suspected by sonography because of the lack of normal brain structures in conjunction with a diffuse echogenic central lesion and an external hydrocephalus. Because of the very poor prognosis, we induced labour by intravaginal and intravenous administration of prostaglandin E2 and achieved the vaginal delivery of a stillborn child whose head circumference corresponded to 38 weeks of pregnancy. Histological and immunochemical features of this undifferentiated congenital glioma (glioblastoma) are presented.