大腦血流和代謝模型分析

Abstract

腦部是一個代謝活躍的器官，需要持續供應氧氣和營養物質才能正常運作。腦血流包括動脈、小動脈、毛細血管和靜脈在內的複雜血管網路組成。腦血流還受到多種因素的影響，包括血液中二氧化碳和氧氣水準、血壓以及腦細胞活動。由於大腦代謝率高，消耗大量氧氣，因此氧氣水準的變化對腦血流有重要影響。

過去中風是與腦血流和代謝相關的主要臨床病症。然而，如今最常見的腦部疾病是失憶症，其中阿爾茨海默病最為普遍。癡呆已逐漸成為臺灣最主要的腦部疾病。這可能由於心臟疾病率的降低、對失憶症的診斷以及人口老齡化。2015年，臺灣患有癡呆症的人數約為244,000人。根據估計[1]，到2033年，臺灣患有失憶症的人數預計將增加一倍，超過460,000人。這意味著到那時，每100個臺灣公民中就有2人受到失憶症的影響。儘管男性和女性的趨勢相似，但由於人口統計因素，絕對發病率仍存在顯著差異。

本研究旨在探索腦血流和代謝的數學模型。首先，將分析單個血管中的血流分支，然後將其擴展到網路模型。最後，研究將探討完整腦血管和氧氣輸送模型。對於這個主題現已有很多的文獻供參考，並且有大量數據可用於開發這個模型。然而大腦血流的建模需要龐大的算力和資源，爲了容易進行計算，我們的研究專注於模型簡化技術和特徵描述，以減少其複雜度，並具有縮放和可應用性。

The brain is a highly metabolically active organ that requires a constant supply of oxygen and nutrients to function properly. Blood flow to the brain is regulated by a complex network of blood vessels, including arteries, arterioles, capillaries, and veins. Cerebral blood flow is also influenced by several factors, including carbon dioxide and oxygen levels in the blood, blood pressure, and the activity of the brain cells themselves. The brain has a high metabolic rate and consumes a large amount of oxygen, so changes in oxygen levels can have a significant impact on cerebral blood flow.

In the past, stroke was the primary clinical context associated with cerebral blood flow and metabolism. However, the most common form of cerebral disease today is dementia, with Alzheimer’s diseases being the most prevalent. Dementia has gradually become the leading brain disease in Taiwan. This can be attributed to a reduction in cardiac disease rates and improved diagnosis of dementia, as well as the aging population. In 2015, the total number of people with dementia in Taiwan was roughly 244,000. According to the estimates [1], the number of individuals living with dementia in Taiwan is projected to double to over 460,000 by the year 2033. This implies that by that time, 2 out of every 100 Taiwanese citizens will be affected by dementia. While the trends remain similar for men and women, there are significant differences in absolute rates due to demographic factors.

The aim of this project is to explore the mathematical models of cerebral blood flow and metabolism. It will begin by investigating the blood flow models in a single vessel and then scaling them up to network models. Finally, the study will examine models of the complete cerebral vasculature and oxygen transport. There is a significant amount of existing research on this topic, and extensive data are available to develop these models. However, modeling across a very large number of blood vessel generations requires either significant computational resources or extensive simplifications to be made. Therefore, recent research has focused on model reduction techniques and characterization to reduce the complexity of the models along with scaling relationships. In this research, we are going to discuss the biology, cerebral autoregulation, development of the network model and how these influence the brain. Hopefully, it will help to provide more understanding into their behaviour in both normal and abnormal physiological conditions.