Modelling phase transitions via Young measures

We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2]

FHIR-DHP: A standardized clinical data harmonisation pipeline for scalable AI application deployment

Background Increasing digitalisation in the medical domain gives rise to large amounts of healthcare data which has the potential to expand clinical knowledge and transform patient care if leveraged through artificial intelligence (AI). Yet, big data and AI oftentimes cannot unlock their full potential at scale, owing to non-standardised data formats, lack of technical and semantic data interoperability, and limited cooperation between stakeholders in the healthcare system. Despite the existence of standardised data formats for the medical domain, such as Fast Healthcare Interoperability Resources (FHIR), their prevalence and usability for AI remains limited.Objective We developed a data harmonisation pipeline (DHP) for clinical data sets relying on the common FHIR data standard.Methods We validated the performance and usability of our FHIR-DHP with data from the MIMIC IV database including > 40,000 patients admitted to an intensive care unit.Results We present the FHIR-DHP workflow in respect of transformation of “raw” hospital records into a harmonised, AI-friendly data representation. The pipeline consists of five key preprocessing steps: querying of data from hospital database, FHIR mapping, syntactic validation, transfer of harmonised data into the patient-model database and export of data in an AI-friendly format for further medical applications. A detailed example of FHIR-DHP execution was presented for clinical diagnoses records.Conclusions Our approach enables scalable and needs-driven data modelling of large and heterogenous clinical data sets. The FHIR-DHP is a pivotal step towards increasing cooperation, interoperability and quality of patient care in the clinical routine and for medical research

Deriving effective models for multiscale systems via evolutionary GammaGamma-convergence

We discuss possible extensions of the recently established theory of evolutionary Gamma convergence for gradient systems to nonlinear dynamical systems obtained by perturbation of a gradient systems. Thus, it is possible to derive effective equations for pattern forming systems with multiple scales. Our applications include homogenization of reaction-diffusion systems, the justification of amplitude equations for Turing instabilities, and the limit from pure diffusion to reaction-diffusion. This is achieved by generalizing the Gamma-limit approaches based on the energy-dissipation principle or the evolutionary variational estimate

Cross validation of bi-modal health-related stress assessment

This study explores the feasibility of objective and ubiquitous stress assessment. 25 post-traumatic stress disorder patients participated in a controlled storytelling (ST) study and an ecologically valid reliving (RL) study. The two studies were meant to represent an early and a late therapy session, and each consisted of a "happy" and a "stress triggering" part. Two instruments were chosen to assess the stress level of the patients at various point in time during therapy: (i) speech, used as an objective and ubiquitous stress indicator and (ii) the subjective unit of distress (SUD), a clinically validated Likert scale. In total, 13 statistical parameters were derived from each of five speech features: amplitude, zero-crossings, power, high-frequency power, and pitch. To model the emotional state of the patients, 28 parameters were selected from this set by means of a linear regression model and, subsequently, compressed into 11 principal components. The SUD and speech model were cross-validated, using 3 machine learning algorithms. Between 90% (2 SUD levels) and 39% (10 SUD levels) correct classification was achieved. The two sessions could be discriminated in 89% (for ST) and 77% (for RL) of the cases. This report fills a gap between laboratory and clinical studies, and its results emphasize the usefulness of Computer Aided Diagnostics (CAD) for mental health care

Is age an independent determinant of mortality in cardiac surgery as suggested by the EuroSCORE?

BACKGROUND: The proportion of older patients in cardiac surgery is continuously increasing. 37% of patients undergoing heart surgery in Germany in the year 2000 were 70 years of age and older. We have studied the role of age as a determinant of mortality in cardiac surgery in our institutional patient population. METHODS: We have calculated the EuroSCORE and the corresponding age-adjusted EuroSCORE in 8769 patients who underwent heart surgery between January 1996 and January 2002 and collected the information on the occurrence of postoperative complications and 30-days mortality. RESULTS: The multimorbidity increased with ascending age. Both the EuroSCORE and the age-adjusted EuroSCORE values increased significantly with age in the whole group of patients as well as in the group of patients who were alive 30 days after heart surgery. The incidence of postoperative complications and 30-days mortality increased significantly with age. In patients who died within 30 days after surgery, the EuroSCORE increased significantly with age, whereas the age-adjusted EuroSCORE did not. The occurrence of diabetes mellitus, arterial hypertension and atrial fibrillation, i.e., the risk factors not considered by the EuroSCORE, exhibited a significant age dependence in our patients. The univariate analysis identified the significant dependence of 30-days mortality on diabetes and atrial fibrillation. The stepwise logistic regression analysis showed the dependence of mortality on diabetes. CONCLUSIONS: On the background of the well-known age-dependent structural and functional changes of different body organs, our data show that age is a significant risk indicator in cardiac surgery, strongly correlating with morbidity and mortality. Consequently, special preventive and therapeutic measures are required in clinical environment in the case of elderly patients undergoing cardiac surgery

Maßwertige Lösungen für ein Gleichungssystem zur Beschreibung von Phasenübergängen in Kristallen

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Modelling phase transitions via Young measures

We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2]

A general theory for elastic phase transitions in crystals

We derive a general theory for elastic phase transitions in solids subject to diffusion under possibly large deformations. After stating the physical model, we derive an existence result for measure-valued solutions that relies on a new approximation result for cylinder functions in infinite settings

About the limits of regularization and the Ansatz method

The well-known adsorption integral equation (AIE) for calculating pore size and adsorption energy distributions from adsorption isotherms on porous solids is, from the mathematical point of view, a linear Fredholm integral equation of the first kind and therefore an ill-posed problem. What can we realistically expect from the solution of such an ill-posed problem by regularization? Does it make sense to restrict the number of possible solutions by the so-called ansatz method? In this paper, the two methods for solving ill-posed problems are from scratch explained and illuminated by concrete examples. Their relevance and fundamental limitations are discussed