Incorporating HDL interaction in an ODE model of Atherosclerosis

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1 Incorporating HDL interaction in an ODE model of Atherosclerosis Diego Lopez Texas A&M University July 29, 2015 Diego Lopez (TAMU) July 29, / 10

2 Introduction Atherosclerosis A disease of the arteries characterized by the inflammation of arterial walls leading to the deposition of plaques of fatty material on their inner walls. Diego Lopez (TAMU) July 29, / 10

3 Introduction Atherosclerosis A disease of the arteries characterized by the inflammation of arterial walls leading to the deposition of plaques of fatty material on their inner walls. The medical community has long recognized the levels of different types of cholesterol in the blood plasma are directly correlated to the risk of CVDs (cardiovascular diseases) like atherosclerosis (Hao 2014). The goal of this project is to create a model that incorporates components like HDL, and to analyze the dynamics of that model to give insight into the progression of the disease. Diego Lopez (TAMU) July 29, / 10

4 Atherosclerotic Artery Diego Lopez (TAMU) July 29, / 10

5 Types of Cholesterol Carriers There are five types of molecular carriers in the body. Diego Lopez (TAMU) July 29, / 10

6 Types of Cholesterol Carriers There are five types of molecular carriers in the body. LDL A molecule that is a combination of lipid (fat) and protein. Lipoproteins are the form in which lipids are transported in the blood. Low-density lipoprotein LDL transports cholesterol from the liver to the tissues of the body. HDL HDL transports cholesterol from the tissues of the body to the liver, so the cholesterol can be eliminated in the bile. Diego Lopez (TAMU) July 29, / 10

7 Types of Cholesterol Carriers There are five types of molecular carriers in the body. LDL A molecule that is a combination of lipid (fat) and protein. Lipoproteins are the form in which lipids are transported in the blood. Low-density lipoprotein LDL transports cholesterol from the liver to the tissues of the body. HDL HDL transports cholesterol from the tissues of the body to the liver, so the cholesterol can be eliminated in the bile. VLDL, IDL, Chylomicron Other lipoproteins. Diego Lopez (TAMU) July 29, / 10

9 New Model Development Reverse Cholesterol Transport Reverse cholesterol transport is a multi-step process resulting in the net movement of cholesterol from peripheral tissues back to the liver via the plasma. (Tall 1998) Diego Lopez (TAMU) July 29, / 10

10 New Model Development Reverse Cholesterol Transport Reverse cholesterol transport is a multi-step process resulting in the net movement of cholesterol from peripheral tissues back to the liver via the plasma. (Tall 1998) HDL plays a crucial role in RCT (Reverse Cholesterol Trasnport) (McAuley 2012). Studies by Annema (2012) have suggested that HDL picks up free cholesterol from foam cells and debris from inside the intima. Diego Lopez (TAMU) July 29, / 10

11 Model Assumptions 1 Mass Action Kinetics. Diego Lopez (TAMU) July 29, / 10

12 Model Assumptions 1 Mass Action Kinetics. 2 All concentrations are positive. Diego Lopez (TAMU) July 29, / 10

13 Model Assumptions 1 Mass Action Kinetics. 2 All concentrations are positive. 3 All coefficients are positive, constant rate coefficients. Diego Lopez (TAMU) July 29, / 10

14 HDL Model System of ODEs L = l(l B L) r 4 LM d L L (1) I = r 20 F r 18 IL ox (2) F = r 18 IL ox r 10 FH d F F (3) Ḋ = d F F r 17 DH (4) L ox = r 4 LM r 6 IL ox (5) M = mm + r 21 F r 4 LM (6) H = h(h B H) r 10 HF r 17 HD d H H (7) Diego Lopez (TAMU) July 29, / 10

15 Compartment Model Diego Lopez (TAMU) July 29, / 10

16 Future Directions Using the system of ODEs and setting the concentration of the groups I, D, and F to zero, we can reduce the system of equations to two rational functions in terms of LDL concentration and HDL concentration. Plotting these functions and finding their intersection will prove that a healthy state equilibrium exists in terms of LDL and HDL concentration. If the healthy state equilibrium (if it exists) is linearly stable, then it proves that, for this model, the ratio of LDL and HDL in the blood is a controlling factor for the development of atherosclerosis. Diego Lopez (TAMU) July 29, / 10

Nutrition & Wellness for Life 2012 Chapter 6: Fats: A Concentrated Energy Source

Nutrition & Wellness for Life 2012 Chapter 6: Fats: A Concentrated Energy Source Tools: Printer 8.5 x 11 paper Scissors Directions: 1. Print 2. Fold paper in half vertically 3. Cut along dashed lines Copyright Goodheart-Willcox Co., Inc. All rights reserved. Tissue in which the body