Biomaterial Database

Cross-sectional shape of collapsible tubes. 1972

E Kresch, and A Noordergraaf

In order to quantify the collapse phenomenon in veins, this paper presents a mathematical analysis of the cross-sectional shape of a flexible tube as its internal pressure varies. Quantitative results are presented in terms of the physical parameters of the tube, such as wall thickness and Young's modulus. It is assumed that the tube is thin walled, that no stretching occurs, that the cross-sectional shape is elliptical when the transmural pressure is zero, and that the longitudinal prestress is zero. The equations were solved on a digital computer which displayed the cross-sectional shapes on an oscilloscope, which were then photographed. A selection of these photographs is presented. Curves are shown which give the cross-sectional area and compliance as functions of transmural pressure. Other curves are shown which are useful for interpolation, and for use in the experimental determination of the physical parameters which may otherwise be difficult or impossible to measure accurately.

UI	MeSH Term	Description	Entries
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D010825	Physics	The study of those aspects of energy and matter in terms of elementary principles and laws. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Physic
D011312	Pressure	A type of stress exerted uniformly in all directions. Its measure is the force exerted per unit area. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Pressures
D003201	Computers	Programmable electronic devices designed to accept data, perform prescribed mathematical and logical operations at high speed, and display the results of these operations.	Calculators, Programmable,Computer Hardware,Computers, Digital,Hardware, Computer,Calculator, Programmable,Computer,Computer, Digital,Digital Computer,Digital Computers,Programmable Calculator,Programmable Calculators
D001696	Biomechanical Phenomena	The properties, processes, and behavior of biological systems under the action of mechanical forces.	Biomechanics,Kinematics,Biomechanic Phenomena,Mechanobiological Phenomena,Biomechanic,Biomechanic Phenomenas,Phenomena, Biomechanic,Phenomena, Biomechanical,Phenomena, Mechanobiological,Phenomenas, Biomechanic
D014680	Veins	The vessels carrying blood away from the CAPILLARY BEDS.	Vein
D055585	Physical Phenomena	The entities of matter and energy, and the processes, principles, properties, and relationships describing their nature and interactions.	Physical Concepts,Physical Processes,Physical Phenomenon,Physical Process,Concept, Physical,Concepts, Physical,Phenomena, Physical,Phenomenon, Physical,Physical Concept,Process, Physical,Processes, Physical