Blood vessels are a unique topic in fluid mechanics as their elastic structure affects flow, while flow also affects structure Purdue University researchers were able to translate this complex relationship into a single mathematical expression (image provided)

WEST LAFAYETTE, Ind – A blood vessel is an elastic tube, the changing shape of which affects the properties of the fluid flowing in it. Conversely, the fluid flow itself also affects the shape of the blood vessel

This complex relationship has been modeled in biomechanics textbooks for years, but Purdue University researchers recently challenged these models Using a combination of advanced fluid mechanics and solid-state mechanics, they established a new general law of flow for elastic microtubes like blood vessels

“When we teach students about fluid mechanics for the first time, the first thing we do is study the flow of fluid in a pipe that has a rigid shape and a fixed length,” said Ivan Christov, Assistant Professor of Mechanical Engineering at Purdue. there is a complex interaction between the flow and the confinement of the vessel walls. Pressure drives flow, but pressure also deforms the tube, and when the tube deforms, the pressure changes “

Christov had observed these principles in his microfluidics research, which focused on flexible, microscale man-made conduits that are often used in technological contexts such as microchips and biomedical devices.He studied the effects of various channel cross-sections – circular, elliptical, rectangular – and consulted the available literature to see if there were any existing theoretical models that he could use

“We assumed that biomechanics have already solved this because this deformation occurs all the time in blood vessels,” said Christov. “We looked at some textbooks on biomechanics and they already had calculations on how pressure and flow rate are related when the pipe deforms However, since we got different results from what the book gave us, we decided to investigate ”

Christov’s PhD Student Vishal Anand, now a postdoctoral fellow at the Davidson School of Chemical Engineering at Purdue, performed the analysis

“We already understand how our elastic microchannels behave,” said Anand. “If we could apply the same principles to blood vessels, we would establish new basic research”

Your research results were published in the ZAMM, the Journal of Applied Mathematics and Mechanics, as “Editor’s Choice”, which was rated as “Particularly valuable or interesting” by the editor-in-chief of the journal “

Anand discovered some discrepancies when considering the elasticity of the structures “When blood vessels expand in one direction, they contract in a perpendicular direction. This is known as the Poisson effect,” Anand said. “Existing equations only accounted for one of these aspects ”

Anand also took into account the attachments of the tube at its ends In contrast to theoretical standalone tubes, blood vessels are always attached to other structures in the body, which affects their deformation

Anand was able to translate the relationship between strain and flow rate into a mathematical expression called the “generalized Hagen-Poiseuille law for soft microtubes”

“I showed Professor Christov this differential equation, and he has an uncanny ability to predict how these equations will behave,” said Anand. “We used Prandtl’s boundary layer theory, which normally applies to aerodynamics, to solve this differential equation and get a single math expression that no one has ever done for this problem ”

Anand confirmed the theory by doing a direct numerical simulation on the ANSYS platform for computational engineering.He included non-Newtonian fluid dynamics because biofluids tend to be non-Newtonian and the simulations confirmed that their math was correct

“Biomechanics is a very mature science and we are certainly not the first to look at the deformation of blood vessels,” said Christov. “Using a combination of fluid mechanics and solid-state mechanics, it’s pretty amazing that we can do this Could define phenomenon with a single mathematical expression ”

Christov sees several practical uses for their equations in addition to its use in microfluids and biomechanics. “Imagine you had a soft robot,” he said. “You could use fluid-filled elastic tubing to operate a manipulator arm, yourself for sizes on the microscale ”

Anand’s journey included discoveries in several ways “When I came to Purdue for my PhDI only knew fluid mechanics. I didn’t know solid mechanics or biomechanics at all, ”he said.“ Because of this project, I spent hours in the library learning the theories behind structural mechanics and was intrigued. Professor Christov gave me all the resources I needed to and I am honored that we were able to validate these theories ”

### Blood vessel, fluid dynamics, fluid mechanics, research, mechanical engineering

News – AU – Description book for the fluid mechanics of blood vessels

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– Rewriting the book on the fluid mechanics of blood vessels

Source: https://www.miragenews.com/rewriting-book-on-fluid-mechanics-of-blood-523410/