Professor Marcus Roper’s new paper uses mathematical modeling to understand blood flow to the brain

A paper, published in last week’s Proceedings of the National Academy of Sciences (PNAS), by mathematics professor, Marcus Roper (pictured above left), and graduate student, Yujia Qi (pictured above right), reveals the surprising challenges of maintaining blood flows within the brain. 

The brain demands a constant supply of glucose and oxygen, which is fed to it by a system of arterioles and venules, linked together by a spaghetti-tangle of very fine vessels called capillaries. Understanding how this network of vessels functions has previously required that the position of every vessel be known. Qi and Roper develop a new method for modeling the blood flow, even when capillaries are too small or too numerous to be medically mapped out. Their model shows that the neuron rich layer of tissue on the surface of the brain is filled with low-flow spots, and that there is no possible arrangement of arterioles and venules that could eliminate these spots. Instead, minimizing the influence of low-flow spots creates an optimal ratio of arterioles to venules that is remarkably close to that seen in real brains. The work shows that the hydraulics of brain blood flow are both exquisitely complex, surprisingly robust to some forms of damage, and surprisingly vulnerable to other types of damage. Lead author Yujia Qi said: “When people suffer brain injuries, sometimes they bounce right back. Other times, they may never recover. We hope that our work will explain some of the physical reasons why brain blood flow is barely affected in some injuries, but experiences life-limiting changes in other injuries.

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