There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Background: The American Heart Association, in conjunction with the National Institutes of Health, annually reports on the most up-to-date statistics related to heart disease, stroke, and cardiovas...

Heart Disease and Stroke Statistics—2020 Update: A Report From the American Heart Association

Background: The American Heart Association, in conjunction with the National Institutes of Health, annually reports the most up-to-date statistics related to heart disease, stroke, and cardiovascul...

Heart Disease and Stroke Statistics-2021 Update: A Report From the American Heart Association.

Fiber-based structures are highly desirable for wearable electronics that are expected to be light-weight, long-lasting, flexible, and conformable Many fibrous structures have been manufactured by well-established lost-effective textile processing technologies, normally at ambient conditions The advancement of nanotechnology has made it feasible to build electronic devices directly on the surface or inside of single fibers, which have typical thickness of several to tens microns However, imparting electronic functions to porous, highly deformable and three-dimensional fiber assemblies and maintaining them during wear represent great challenges from both views of fundamental understanding and practical implementation This article attempts to critically review the current state-of-arts with respect to materials, fabrication techniques, and structural design of devices as well as applications of the fiber-based wearable electronic products In addition, this review elaborates the performance requirements of the fiber-based wearable electronic products, especially regarding the correlation among materials, fiber/textile structures and electronic as well as mechanical functionalities of fiber-based electronic devices Finally, discussions will be presented regarding to limitations of current materials, fabrication techniques, devices concerning manufacturability and performance as well as scientific understanding that must be improved prior to their wide adoption

Fiber‐Based Wearable Electronics: A Review of Materials, Fabrication, Devices, and Applications

The American Heart Association, in conjunction with the National Institutes of Health, annually reports the most up-to-date statistics related to heart disease, stroke, and cardiovascular risk factors, including core health behaviors (smoking, physical activity, diet, and weight) and health factors (cholesterol, blood pressure, and glucose control) that contribute to cardiovascular health. The Statistical Update presents the latest data on a range of major clinical heart and circulatory disease conditions (including stroke, congenital heart disease, rhythm disorders, subclinical atherosclerosis, coronary heart disease, heart failure, valvular disease, venous disease, and peripheral artery disease) and the associated outcomes (including quality of care, procedures, and economic costs).The American Heart Association, through its Statistics Committee, continuously monitors and evaluates sources of data on heart disease and stroke in the United States to provide the most current information available in the annual Statistical Update. The 2022 Statistical Update is the product of a full year's worth of effort by dedicated volunteer clinicians and scientists, committed government professionals, and American Heart Association staff members. This year's edition includes data on the monitoring and benefits of cardiovascular health in the population and an enhanced focus on social determinants of health, adverse pregnancy outcomes, vascular contributions to brain health, and the global burden of cardiovascular disease and healthy life expectancy.Each of the chapters in the Statistical Update focuses on a different topic related to heart disease and stroke statistics.The Statistical Update represents a critical resource for the lay public, policymakers, media professionals, clinicians, health care administrators, researchers, health advocates, and others seeking the best available data on these factors and conditions. 

https://www.ahajournals.org/doi/pdf/10.1161/CIR.0000000000001052

Heart Disease and Stroke Statistics—2022 Update: A Report From the American Heart Association

We have studied the three-dimensional arrangement of ventricular muscle cells and the associated extracellular connective tissue matrix in dog hearts. Four hearts were potassium-arrested, excised, and perfusion-fixed at zero transmural pressure. Full-thickness segments were cut from the right and left ventricular walls at a series of precisely located sites. Morphology was visualized macroscopically and with scanning electron microscopy in 1) transmural planes of section and 2) planes tangential to the epicardial surface. The appearance of all specimens was consistent with an ordered laminar arrangement of myocytes with extensive cleavage planes between muscle layers. These planes ran radially from endocardium toward epicardium in transmural section and coincided with the local muscle fiber orientation in tangential section. Stereological techniques were used to quantify aspects of this organization. There was no consistent variation in the cellular organization of muscle layers (48.4 +/- 20.4 microns thick and 4 +/- 2 myocytes across) transmurally or in different ventricular regions (23 sites in 6 segments), but there was significant transmural variation in the coupling between adjacent layers. The number of branches between layers decreased twofold from subepicardium to midwall, whereas the length distribution of perimysial collagen fibers connecting muscle layers was greatest in the midwall. We conclude that ventricular myocardium is not a uniformly branching continuum but a laminar hierarchy in which it is possible to identify three axes of material symmetry at any point.

Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog

We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.

Mathematical model of geometry and fibrous structure of the heart.

We examined the shear properties of passive ventricular myocardium in six pig hearts. Samples (3 × 3 × 3 mm) were cut from adjacent regions of the lateral left ventricular midwall, with sides align...

/pdf/shear-properties-of-passive-ventricular-myocardium-4jbaesgh5h.pdf

Shear properties of passive ventricular myocardium

A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.

Laminar structure of the heart: a mathematical model

Computational models of the electrical and mechanical function of the heart are reviewed. These models attempt to explain the integrated function of the heart in terms of ventricular anatomy, the structure and material properties of myocardial tissue, the membrane ion channels, and calcium handling and myofilament mechanics of cardiac myocytes. The models have established the computational framework for linking the structure and function of cardiac cells and tissue to the integrated behavior of the intact heart, but many more aspects of physiological function, including metabolic and signal transduction pathways, need to be included before significant progress can be made in understanding many disease processes.

Bruce H. Smaill

Papers

Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog

Mathematical model of geometry and fibrous structure of the heart.

Shear properties of passive ventricular myocardium

Laminar structure of the heart: a mathematical model

Modeling total heart function.