# Math HL IA (7/7)

본 문서는 IB May 2020에 제출했던 수학 HL IA이며, 7점 (만점)을 받은 IA입니다.
주제는 Mathematics of Blood Vessel Flow입니다.

[본문내용]

#### Introduction

Watching my relatives suffer from hypertension made me sad and anxious every time. Hypertension is a common disease that refers to high blood pressure. Many people say that hypertension seems like a minor symptom, but it can actually lead to severe complications and increase the risk of stroke and heart attack. As a genetic carrier1 of hypertension, I have been concerned if this would apply to myself and my future generation. Since I am interested in studying the relationship between biology and mathematics, I wondered about how the speed of blood flow differs with respect to the shape and conditions of the blood vessel. This prompted me to think about how mathematical conditions and factors can be applied to analyze systemic circulation and further make early diagnosis of hypertension. Although there are underlying factors that affect the blood flow and human circulatory system, this paper will explore specifically on the mathematical grounds of blood vessel’s shape that affect the rate of change of blood flow. Hence, this exploration is based on my hypothesis about how the speed of blood flow will be different depending on the position of the blood flowing at its blood vessel. By evaluating both the strengths and limitations of existing function models, it will help me to understand the relationship between the speed of the blood flow and shape of the blood vessel. Furthermore, people who read this paper would be more aware of the mathematical reason and mechanism of hypertension and understand how hypertension is affected by several factors, including the shape of the blood vessel. This topic is also significant for those who are pursuing medical professions as heart specialists, therapists, and clinical researchers by investigating potential treatments and medications for hypertension patients.

#### Background Information

Hypertension is caused by narrowed vessel walls induced by the accumulation of cholesterol, neutral fats, or blood clots; it is also caused by a high blood viscosity2 due to an increased concentration of lipids or plasma protein. In response, the heart increases blood pressure in order to overcome the increased resistance. As the heart relaxes and contracts, the blood pressure in arteries change periodically. This abnormal fluctuation of blood pressure is the primary cause of hypertension.

Mathematic Exploration of Law of Laminar Flow

While researching about the blood flow vessel, I realized that we can model the blood vessel by ourselves using a geometrical representation. As I magnified the human blood vessel, it looked alike with a circular cylinder. The diagram below represents a section of a cylindrical tube model for a blood vessel…

• 총 페이지수: 14 pages
• 과목명: Mathematics
• 주제: Mathematics of Blood Vessel Flow
• The file is in PDF format.