Wiskundige Analyse in de Chemische Industrie

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A Mathematical Study of the One-Dimensional Keller and Rubinov Model for Liesegang Bands

Our purpose is to start understanding from a mathematical viewpoint experiments in which regularized structures with spatially distinct bands or rings of precipitated material are exhibited, with clearly visible scaling properties. Such patterns are known as Liesegang bands or rings. In this paper, we study a one-dimensional version of the Keller and Rubinow model and present conditions ensuring the existence of Liesegang bands

Fetal electrocardiography and artificial intelligence for prenatal detection of congenital heart disease

INTRODUCTION: This study aims to investigate non-invasive electrocardiography as a method for the detection of congenital heart disease (CHD) with the help of artificial intelligence.MATERIAL AND METHODS: An artificial neural network was trained for the identification of CHD using non-invasively obtained fetal electrocardiograms. With the help of a Bayesian updating rule, multiple electrocardiographs were used to increase the algorithm's performance.RESULTS: Using 122 measurements containing 65 healthy and 57 CHD cases, the accuracy, sensitivity, and specificity were found to be 71%, 63%, and 77%, respectively. The sensitivity was however 75% and 69% for CHD cases requiring an intervention in the neonatal period and first year of life, respectively. Furthermore, a positive effect of measurement length on the detection performance was observed, reaching optimal performance when using 14 electrocardiography segments (37.5 min) or more. A small negative trend between gestational age and accuracy was found.CONCLUSIONS: The proposed method combining recent advances in obtaining non-invasive fetal electrocardiography with artificial intelligence for the automatic detection of CHD achieved a detection rate of 63% for all CHD and 75% for critical CHD. This feasibility study shows that detection rates of CHD might improve by using electrocardiography-based screening complementary to the standard ultrasound-based screening. More research is required to improve performance and determine the benefits to clinical practice.</p

Burden of illness of Pompe disease in patients only receiving supportive care

Background: Pompe disease is an orphan disease for which enzyme replacement therapy (ERT) recently became available. This study aims to estimate all relevant aspects of burden of illness-societal costs, use of home care and informal care, productivity losses, and losses in health-related quality of life (HRQoL)-for adult Pompe patients only receiving supportive care. Methods: We collected data on all relevant aspects of burden of illness via a questionnaire. We applied a societal perspective in calculating costs. The EQ-5D was used to estimate HRQoL. Results: Eighty adult patients (87% of the total Dutch adult Pompe population) completed a questionnaire. Disease severity ranged from mild to severe. Total annual costs were estimated at €22,475 (range €0-169,539) per adult Pompe patient. Patients on average received 8 h of home care and 19 h of informal care per week. Eighty-five percent of the patients received informal care from one or more caregivers; 40% had stopped working due to their disease; another 20% had reduced their working hours. HRQoL for Pompe patients who only received supportive care was estimated at 0.72, 17% lower than the Dutch population at large. Conclusions: Adult Pompe disease is associated with a considerable burden of illness at both the societal and patient levels. The disease leads to substantial costs and dependency on medical devices, home care, and informal care, and has a high impact on the patient's social network. In addition, patients are limited in their ability to work and have significantly reduced HRQoL

Amplitude saturation of MEMS resonators explained by autoparametric resonance

Abstract This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators

Cardiac outcome in classic infantile Pompe disease after 13\xe2\x80\xafyears of treatment with recombinant human acid alpha-glucosidase

Background: Cardiac failure is the main cause of death in untreated classic infantile Pompe disease, an inheritable metabolic myopathy characterized by progressive hypertrophic cardiomyopathy. Since the introduction of enzyme replacement therapy (ERT), survival has increased significantly due to reduced cardiac hypertrophy and improved cardiac function. However, little is known about ERT\'s long-term effects on the heart. Methods: Fourteen patients were included in this prospective study. Cardiac dimensions, function, conduction and rhythm disturbances were evaluated at baseline and at regular intervals thereafter. Results: Treatment duration ranged from 1.1 to 13.9 years (median 4.8 years). At baseline, all patients had increased left ventricular mass index (LVMI) (median LVMI 226 g/m2, range 98 to 599 g/m2, Z-score median 7, range 2.4\xe2\x80\x9312.4). During the first four weeks, LVMI continued to increase in six patients. Normalization of LVMI was observed in 13 patients (median 30 weeks; range 3 to 660 weeks). After clinical deterioration, LVMI increased again slightly in one patient. At baseline, PR interval was shortened in all patients; it normalized in only three. A delta-wave pattern on ECG was seen in six patients and resulted in documented periods of supraventricular tachycardias (SVTs) in three patients, two of whom required medication and/or ablation. One patient had severe bradycardia (35 beats/min). Conclusion: This study shows that ERT significantly reduced LVMI, and sustained this effect over a period of 13.9 years. The risk for rhythm disturbances remains. Regular cardiac evaluations should be continued, also after initially good response to ERT