Paul Steinmann

Bio: Paul Steinmann is an academic researcher from University of Erlangen-Nuremberg. The author has contributed to research in topics: Finite element method & Discretization. The author has an hindex of 61, co-authored 638 publications receiving 13535 citations. Previous affiliations of Paul Steinmann include Daimler AG & Schrödinger.

Mechanical properties of gray and white matter brain tissue by indentation.

Abstract: The mammalian brain is composed of an outer layer of gray matter, consisting of cell bodies, dendrites, and unmyelinated axons, and an inner core of white matter, consisting primarily of myelinated axons Recent evidence suggests that microstructural differences between gray and white matter play an important role during neurodevelopment While brain tissue as a whole is rheologically well characterized, the individual features of gray and white matter remain poorly understood Here we quantify the mechanical properties of gray and white matter using a robust, reliable, and repeatable method, flat-punch indentation To systematically characterize gray and white matter moduli for varying indenter diameters, loading rates, holding times, post-mortem times, and locations we performed a series of n = 192 indentation tests We found that indenting thick, intact coronal slices eliminates the common challenges associated with small specimens: it naturally minimizes boundary effects, dehydration, swelling, and structural degradation When kept intact and hydrated, brain slices maintained their mechanical characteristics with standard deviations as low as 5% throughout the entire testing period of five days post mortem White matter, with an average modulus of 1895 kPa±0592 kPa, was on average 39% stiffer than gray matter, p 001 , with an average modulus of 1389 kPa±0289 kPa, and displayed larger regional variations It was also more viscous than gray matter and responded less rapidly to mechanical loading Understanding the rheological differences between gray and white matter may have direct implications on diagnosing and understanding the mechanical environment in neurodevelopment and neurological disorders

Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data

Abstract: Rubber-like materials consist of chain-like macromolecules that are more or less closely connected to each other via entanglements or cross-links As an idealisation, this particular structure can be described as a completely random three-dimensional network To capture the elastic and nearly incompressible mechanical behaviour of this material class, numerous phenomenological and micro-mechanically motivated models have been proposed in the literature This contribution reviews fourteen selected representatives of these models, derives analytical stress–stretch relations for certain homogeneous deformation modes and summarises the details required for stress tensors and consistent tangent operators The latter, although prevalently missing in the literature, are indispensable ingredients in utilising any kind of constitutive model for the numerical solution of boundary value problems by iterative approaches like the Newton–Raphson scheme Furthermore, performance and validity of the models with regard to the classical experimental data on vulcanised rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944) are evaluated These data are here considered as a prototype or worst-case scenario of highly nonlinear elastic behaviour, although inelastic characteristics are clearly observable but have been tacitly ignored by many other authors

A finite element method for the computational modelling of cohesive cracks

Abstract: The present contribution is concerned with the computational modelling of cohesive cracks in quasi-brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage-type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method.

Physical biology of human brain development.

Abstract: Neurodevelopment is a complex, dynamic process that involves a precisely orchestrated sequence of genetic, environmental, biochemical, and physical events. Developmental biology and genetics have shaped our understanding of the molecular and cellular mechanisms during neurodevelopment. Recent studies suggest that physical forces play a central role in translating these cellular mechanisms into the complex surface morphology of the human brain. However, the precise impact of neuronal differentiation, migration, and connection on the physical forces during cortical folding remains unknown. Here we review the cellular mechanisms of neurodevelopment with a view towards surface morphogenesis, pattern selection, and evolution of shape. We revisit cortical folding as the instability problem of constrained differential growth in a multi-layered system. To identify the contributing factors of differential growth, we map out the timeline of neurodevelopment in humans and highlight the cellular events associated with extreme radial and tangential expansion. We demonstrate how computational modeling of differential growth can bridge the scales-from phenomena on the cellular level towards form and function on the organ level-to make quantitative, personalized predictions. Physics-based models can quantify cortical stresses, identify critical folding conditions, rationalize pattern selection, and predict gyral wavelengths and gyrification indices. We illustrate that physical forces can explain cortical malformations as emergent properties of developmental disorders. Combining biology and physics holds promise to advance our understanding of human brain development and enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders including epilepsy, autism spectrum disorders, and schizophrenia.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

Abstract: Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Abstract: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.