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Toshiki Endo

Publications and source records attributed to Toshiki Endo.

4 recordsLinked to original sources

Physiologic Blood Flow is Turbulent: Revisiting the Principles of Vascular Hemodynamics

Contemporary paradigm of vascular hemodynamics considers normal blood flow to be pulsatile laminar flow. Transition to turbulence can cause diseases such as atherosclerosis or brain aneurysms. Recently, we demonstrated the existence of turbulence in experimental models of brain aneurysm; in the aneurysm sac as well as in the main artery. Thus, we were intrigued to explore if such a long-standing assumption of the laminarity of blood flow could be challenged. We have used methods and tools from chaos theory, hydrodynamic stability theory and turbulence physics to explore the existence of turbulence in normal vascular blood flow. We used Womersley exact solution of the Navier-Stokes equation with the HaeMed database of physiologic blood flow measurements, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers. The tools we used to investigate the properties of blood turbulence are well established in the fields of chaos theory, hydrodynamic stability and turbulence dynamics. We show, evidently, that blood flow is inherently chaotic and turbulent and not laminar. We propose a paradigm shift in the theory of vascular hemodynamics which requires rethinking the hemodynamic-biologic links governing physiologic and pathologic processes.

physics.flu-dyn

Vertex unfoldings of tight polyhedra

An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al showed that every triangulated polyhedron has a vertex unfolding. We extend this result to a tight polyhedron, where a polyhedron is tight if all non-triangular faces are mutually non-adjacent parallelograms.

math.CO

A Graph-Theoretic Approach to a Partial Order of Knots and Links

We say that a link $L_1$ is an s-major of a link $L_2$ if any diagram of $L_1$ can be transformed into a diagram of $L_2$ by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by graph-theoretic methods.

math.GT