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SUMMARY:Optimal flow patterns in branching lymphatic vessels
DTSTART;VALUE=DATE-TIME:20180712T013000Z
DTEND;VALUE=DATE-TIME:20180712T020000Z
DTSTAMP;VALUE=DATE-TIME:20241109T194017Z
UID:indico-contribution-31@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Anne Talkington (University of North Carolina at Cha
pel Hill)\nUnderstanding lymphatic development is clinically relevant in a
pplications from the viability of embryos\, to chronic inflammation\, to c
ancer metastasis. I specifically quantify the branching structure of devel
oping lymphatic vessels and numerically solve for the flow through these v
essels. Branching in arterial development is understood to consistently fo
llow Murray’s Law\, which states that the cube of the radius of a parent
vessel is equal to the sum of the cubes of the radii of the daughter vess
els\, thus minimizing the cost and maintenance of fluid transport. I have
found that an optimization law for lymphatic vessels is less straightforw
ard. The derivation of Murray’s Law includes several assumptions\, such
as vessels of constant diameter filled with a Newtonian fluid\, fully dev
eloped and unidirectional flow\, and long segments between junctions. Sev
eral of these necessary assumptions do not hold for lymphatic capillaries.
The relationship between the parent and daughter vessels is upheld throu
gh a strictly additive rule\, and the daughter vessels are smaller than wo
uld be predicted by the hypothesized radius-cubed law. The variability in
vessel diameter and potential for bidirectional flow suggest a different o
ptimization strategy based on the geometry and function of the system. In
this presentation\, the immersed boundary method is used to numerically s
olve the equations of fluid flow through branching vessels. The results ar
e then used to test the assumptions of Murray’s Law as well as several h
ypotheses regarding branching geometry.\n\nhttps://conferences.maths.unsw.
edu.au/event/2/contributions/31/
LOCATION:University of Sydney New Law School/--102
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/31/
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