Exploration of the optimal design of blood vessels that minimizes the cost function

소개글

본 문서는 2018 May IBDP 에 제출된 HL math IA 에세이이며 7점을 받았습니다.
주제는 Exploration of the optimal design of blood vessels that minimizes the cost function. 입니다.
혈관 분기의 최적의 각도를 물리의 개념을 응용하여 미적분 개념을 사용해 찾아내는 과정입니다. 과학적인 부분이 포함되어 수학적인 부분에만 조금 더 집중하기 위해서 assumption을 앞에서 먼저 제기한 후에 분석했습니다.
미적분 개념을 본인 IA에 사용하고 싶으신 분이라면 참고하면 좋을 것 같습니다.

목차

1. Introduction

2. Branching versus bifurcation

3. Assumption

4. Theory

5. Optimal branching angle in relation to the radii of vessels

6. Optimal bifurcation angle in relation to the radii of vessels
1) Shifts along AO
2) Shifts along BO
3) Shifts along CO

7. Conclusion

8. Bibliography

본문내용

1. Introduction
The vascular system, or the circulatory system, is an organ system that allows blood to circulate and transport nutrients, oxygen, and blood cells in the body to provide nourishment. The system is made up of vessels that carry blood through the body: arteries, veins, and capillaries.

It was not until I first had a peripheral intravenous, or IV, placed on my hand that I had more than just a passing interest in the human body’s vascular system. When I went to a hospital to get an IV therapy, I saw a nurse who seemed to be less experienced, observing the back of my hand for a few seconds. Then, she cautiously gave me an injection, penetrating one of my ‘pale blue’ vessel branches.

참고 자료

En.wikipedia.org. (2017). Cost function. [online] Available at: https://en.wikipedia.org/wiki/Cost_function [Accessed 19 Aug. 2017].
Fluid Flow Viscosity Poiseuille's Law. (2017). [ebook] pp.5-6. Available at: http://www.physics.usyd.edu.au/teach_res/jp/fluids/viscosity.pdf [Accessed 19 Aug. 2017].
Chemistry. (2017). Coefficient of Viscosity | Formula | Examples. [online] Available at: http://byjus.com/chemistry/coefficient-of-viscosity/ [Accessed 19 Aug. 2017].
Fluid Flow Viscosity Poiseuille's Law. (2017). [ebook] pp.5-6. Available at: http://www.physics.usyd.edu.au/teach_res/jp/fluids/viscosity.pdf [Accessed 19 Aug. 2017].
dummies. (2017). How to Calculate Force Based on Pressure - dummies. [online] Available at: http://www.dummies.com/education/science/physics/how-to-calculate-force-based-on-pressure/ [Accessed 20 Aug. 2017].
Oilfieldwiki.com. (2017). Hagen–Poiseuille equation - OilfieldWiki. [online] Available at: http://www.oilfieldwiki.com/wiki/Hagen–Poiseuille_equation [Accessed 19 Aug. 2017].
Byjus Formulas. (2017). Poiseuille formula derivation | Hagen poiseuille equation derivation pdf. [online] Available at: http://byjus.com/poiseuilles-law-formula [Accessed 20 Aug. 2017].
Blood Flow, Blood Pressure, And Resistance | Anatomy And Physiology II. Courses.Lumenlearning.Com, 2017, https://courses.lumenlearning.com/ap2/chapter/blood-flow-blood-pressure-and-resistance-no-content/.
Laminar flow. (2017). [image] Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html [Accessed 20 Aug. 2017].