Difference between revisions of "Team:Toronto/Model"

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<div style="position:absolute;left:149.74px;top:120.99px" class="cls_002"><span class="cls_002">iGEM Toronto 2018 Mathematical Modelling</span></div>
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<div style="position:relative;left:149.74px;top:120.99px" class="cls_002"><span class="cls_002">iGEM Toronto 2018 Mathematical Modelling</span></div>
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<div style="position:absolute;left:199.60px;top:155.14px" class="cls_003"><span class="cls_003">B. Kell, F. Vermehr, Q. Vilchez, P. Malik</span></div>
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<div style="position:relative;left:199.60px;top:155.14px" class="cls_003"><span class="cls_003">B. Kell, F. Vermehr, Q. Vilchez, P. Malik</span></div>
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<div style="position:absolute;left:271.70px;top:178.59px" class="cls_003"><span class="cls_003">October 2018</span></div>
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<div style="position:relative;left:271.70px;top:178.59px" class="cls_003"><span class="cls_003">October 2018</span></div>
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</div>
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<div style="position:relative;left:86.40px;top:219.10px" class="cls_004"><span class="cls_004">Contents</span></div>
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<div style="position:relative;left:86.40px;top:245.41px" class="cls_005"><span class="cls_005">1</span></div>
 +
<div style="position:relative;left:101.34px;top:245.41px" class="cls_005"><span class="cls_005">Introduction</span></div>
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<div style="position:relative;left:519.87px;top:245.41px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:86.40px;top:267.32px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:101.34px;top:267.32px" class="cls_005"><span class="cls_005">A Differential Bioreactor Model</span></div>
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<div style="position:relative;left:519.87px;top:267.32px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:101.34px;top:279.28px" class="cls_005"><span class="cls_005">2.1</span></div>
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<div style="position:relative;left:124.26px;top:279.28px" class="cls_005"><span class="cls_005">Goals</span></div>
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<div style="position:relative;left:520.62px;top:279.28px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:101.34px;top:291.23px" class="cls_005"><span class="cls_005">2.2</span></div>
 +
<div style="position:relative;left:124.26px;top:291.23px" class="cls_005"><span class="cls_005">Mathematical Formulation</span></div>
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<div style="position:relative;left:520.62px;top:291.23px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:124.26px;top:303.19px" class="cls_005"><span class="cls_005">2.2.1</span></div>
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<div style="position:relative;left:156.13px;top:303.19px" class="cls_005"><span class="cls_005">Concepts</span></div>
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<div style="position:relative;left:520.62px;top:303.19px" class="cls_005"><span class="cls_005">2</span></div>
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<div style="position:relative;left:124.26px;top:315.15px" class="cls_005"><span class="cls_005">2.2.2</span></div>
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<div style="position:relative;left:156.13px;top:315.15px" class="cls_005"><span class="cls_005">The Model</span></div>
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<div style="position:relative;left:520.62px;top:315.15px" class="cls_005"><span class="cls_005">3</span></div>
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<div style="position:relative;left:124.26px;top:327.10px" class="cls_005"><span class="cls_005">2.2.3</span></div>
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<div style="position:relative;left:156.13px;top:327.10px" class="cls_005"><span class="cls_005">Bioreactor Assumptions</span></div>
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<div style="position:relative;left:520.62px;top:327.10px" class="cls_005"><span class="cls_005">4</span></div>
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<div style="position:relative;left:101.34px;top:339.06px" class="cls_005"><span class="cls_005">2.3</span></div>
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<div style="position:relative;left:124.26px;top:339.06px" class="cls_005"><span class="cls_005">Equations</span></div>
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<div style="position:relative;left:520.62px;top:339.06px" class="cls_005"><span class="cls_005">4</span></div>
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<div style="position:relative;left:101.34px;top:351.01px" class="cls_005"><span class="cls_005">2.4</span></div>
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<div style="position:relative;left:124.26px;top:351.01px" class="cls_005"><span class="cls_005">Numerical Solution</span></div>
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<div style="position:relative;left:520.62px;top:351.01px" class="cls_005"><span class="cls_005">5</span></div>
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<div style="position:relative;left:101.34px;top:362.97px" class="cls_005"><span class="cls_005">2.5</span></div>
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<div style="position:relative;left:124.26px;top:362.97px" class="cls_005"><span class="cls_005">Sensitivity Analysis</span></div>
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<div style="position:relative;left:520.62px;top:362.97px" class="cls_005"><span class="cls_005">5</span></div>
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<div style="position:relative;left:124.26px;top:374.92px" class="cls_005"><span class="cls_005">2.5.1</span></div>
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<div style="position:relative;left:156.13px;top:374.92px" class="cls_005"><span class="cls_005">The Effect of Dilution Rate on Bioreactor Performance</span></div>
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<div style="position:relative;left:520.62px;top:374.92px" class="cls_005"><span class="cls_005">6</span></div>
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<div style="position:relative;left:124.26px;top:386.88px" class="cls_005"><span class="cls_005">2.5.2</span></div>
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<div style="position:relative;left:156.13px;top:386.88px" class="cls_005"><span class="cls_005">The Effect of Initial Metal Concentration on Bioreactor Performance</span></div>
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<div style="position:relative;left:520.62px;top:386.88px" class="cls_005"><span class="cls_005">7</span></div>
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<div style="position:relative;left:124.26px;top:398.83px" class="cls_005"><span class="cls_005">2.5.3</span></div>
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<div style="position:relative;left:156.13px;top:398.83px" class="cls_005"><span class="cls_005">The Effect of Attachment Rate on Bioreactor Performance</span></div>
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<div style="position:relative;left:520.62px;top:398.83px" class="cls_005"><span class="cls_005">7</span></div>
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<div style="position:relative;left:124.26px;top:410.79px" class="cls_005"><span class="cls_005">2.5.4</span></div>
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<div style="position:relative;left:156.13px;top:410.79px" class="cls_005"><span class="cls_005">The Effect of Detachment Rate on Bioreactor Performance</span></div>
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<div style="position:relative;left:520.62px;top:410.79px" class="cls_005"><span class="cls_005">8</span></div>
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<div style="position:relative;left:124.26px;top:422.74px" class="cls_005"><span class="cls_005">2.5.5</span></div>
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<div style="position:relative;left:156.13px;top:422.74px" class="cls_005"><span class="cls_005">The Effect of Initial Cellular Population on Bioreactor Performance</span></div>
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<div style="position:relative;left:520.62px;top:422.74px" class="cls_005"><span class="cls_005">8</span></div>
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<div style="position:relative;left:124.26px;top:434.70px" class="cls_005"><span class="cls_005">2.5.6</span></div>
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<div style="position:relative;left:156.13px;top:434.70px" class="cls_005"><span class="cls_005">The Effect of Maximum Specific Growth Rate on Bioreactor Performance  . .</span></div>
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<div style="position:relative;left:520.62px;top:434.70px" class="cls_005"><span class="cls_005">9</span></div>
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<div style="position:relative;left:101.34px;top:446.65px" class="cls_005"><span class="cls_005">2.6</span></div>
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<div style="position:relative;left:124.26px;top:446.65px" class="cls_005"><span class="cls_005">Hypothetical Applications</span></div>
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<div style="position:relative;left:520.62px;top:446.65px" class="cls_005"><span class="cls_005">9</span></div>
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<div style="position:relative;left:86.40px;top:468.57px" class="cls_005"><span class="cls_005">3</span></div>
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<div style="position:relative;left:101.34px;top:468.57px" class="cls_005"><span class="cls_005">A Mechanistic Buoyancy Model: Maximum Carrying Capacity Determination</span></div>
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<div style="position:relative;left:514.14px;top:468.57px" class="cls_005"><span class="cls_005">10</span></div>
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<div style="position:relative;left:101.34px;top:480.52px" class="cls_005"><span class="cls_005">3.1</span></div>
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<div style="position:relative;left:124.26px;top:480.52px" class="cls_005"><span class="cls_005">Goal</span></div>
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<div style="position:relative;left:515.64px;top:480.52px" class="cls_005"><span class="cls_005">10</span></div>
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<div style="position:relative;left:101.34px;top:492.48px" class="cls_005"><span class="cls_005">3.2</span></div>
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<div style="position:relative;left:124.26px;top:492.48px" class="cls_005"><span class="cls_005">Mathematical Formulation</span></div>
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<div style="position:relative;left:515.64px;top:492.48px" class="cls_005"><span class="cls_005">10</span></div>
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<div style="position:relative;left:124.26px;top:504.44px" class="cls_005"><span class="cls_005">3.2.1</span></div>
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<div style="position:relative;left:156.13px;top:504.44px" class="cls_005"><span class="cls_005">Concepts</span></div>
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<div style="position:relative;left:515.64px;top:504.44px" class="cls_005"><span class="cls_005">10</span></div>
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<div style="position:relative;left:124.26px;top:516.39px" class="cls_005"><span class="cls_005">3.2.2</span></div>
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<div style="position:relative;left:156.13px;top:516.39px" class="cls_005"><span class="cls_005">Assumptions</span></div>
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<div style="position:relative;left:515.64px;top:516.39px" class="cls_005"><span class="cls_005">11</span></div>
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<div style="position:relative;left:124.26px;top:528.35px" class="cls_005"><span class="cls_005">3.2.3</span></div>
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<div style="position:relative;left:156.13px;top:528.35px" class="cls_005"><span class="cls_005">The Model</span></div>
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<div style="position:relative;left:515.64px;top:528.35px" class="cls_005"><span class="cls_005">11</span></div>
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<div style="position:relative;left:101.34px;top:540.30px" class="cls_005"><span class="cls_005">3.3</span></div>
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<div style="position:relative;left:124.26px;top:540.30px" class="cls_005"><span class="cls_005">Analytic Solution</span></div>
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<div style="position:relative;left:515.63px;top:540.30px" class="cls_005"><span class="cls_005">11</span></div>
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<div style="position:relative;left:101.34px;top:552.26px" class="cls_005"><span class="cls_005">3.4</span></div>
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<div style="position:relative;left:124.26px;top:552.26px" class="cls_005"><span class="cls_005">Determining Buoyant Force: Temporal Tracking Algorithm</span></div>
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<div style="position:relative;left:515.64px;top:552.26px" class="cls_005"><span class="cls_005">12</span></div>
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<div style="position:relative;left:101.34px;top:564.21px" class="cls_005"><span class="cls_005">3.5</span></div>
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<div style="position:relative;left:124.26px;top:564.21px" class="cls_005"><span class="cls_005">Discussion On Maximum Carrying Capacity</span></div>
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<div style="position:relative;left:515.64px;top:564.21px" class="cls_005"><span class="cls_005">14</span></div>
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<div style="position:relative;left:86.40px;top:586.13px" class="cls_005"><span class="cls_005">4</span></div>
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<div style="position:relative;left:101.34px;top:586.13px" class="cls_005"><span class="cls_005">Growth Dynamics</span></div>
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<div style="position:relative;left:514.14px;top:586.13px" class="cls_005"><span class="cls_005">15</span></div>
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<div style="position:relative;left:101.34px;top:598.08px" class="cls_005"><span class="cls_005">4.1</span></div>
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<div style="position:relative;left:124.26px;top:598.08px" class="cls_005"><span class="cls_005">Objective</span></div>
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<div style="position:relative;left:515.64px;top:598.08px" class="cls_005"><span class="cls_005">15</span></div>
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<div style="position:relative;left:101.34px;top:610.04px" class="cls_005"><span class="cls_005">4.2</span></div>
 +
<div style="position:relative;left:124.26px;top:610.04px" class="cls_005"><span class="cls_005">Approach</span></div>
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<div style="position:relative;left:515.64px;top:610.04px" class="cls_005"><span class="cls_005">15</span></div>
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<div style="position:relative;left:101.34px;top:621.99px" class="cls_005"><span class="cls_005">4.3</span></div>
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<div style="position:relative;left:124.26px;top:621.99px" class="cls_005"><span class="cls_005">Results</span></div>
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<div style="position:relative;left:515.63px;top:621.99px" class="cls_005"><span class="cls_005">15</span></div>
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<div style="position:relative;left:86.40px;top:643.91px" class="cls_005"><span class="cls_005">5</span></div>
 +
<div style="position:relative;left:101.34px;top:643.91px" class="cls_005"><span class="cls_005">Discussion and Future Directions</span></div>
 +
<div style="position:relative;left:514.14px;top:643.91px" class="cls_005"><span class="cls_005">17</span></div>
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<div style="position:relative;left:86.40px;top:665.83px" class="cls_005"><span class="cls_005">6</span></div>
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<div style="position:relative;left:101.34px;top:665.83px" class="cls_005"><span class="cls_005">Appendix</span></div>
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<div style="position:relative;left:514.14px;top:665.83px" class="cls_005"><span class="cls_005">19</span></div>
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<div style="position:relative;left:86.40px;top:687.75px" class="cls_005"><span class="cls_005">7</span></div>
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<div style="position:relative;left:101.34px;top:687.75px" class="cls_005"><span class="cls_005">References</span></div>
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<div style="position:relative;left:514.14px;top:687.75px" class="cls_005"><span class="cls_005">19</span></div>
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<div style="position:relative;left:303.51px;top:725.53px" class="cls_005"><span class="cls_005">1</span></div>
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Revision as of 16:22, 15 October 2018

iGEM Toronto 2018 Mathematical Modelling
B. Kell, F. Vermehr, Q. Vilchez, P. Malik
October 2018
Contents
1
Introduction
2
2
A Differential Bioreactor Model
2
2.1
Goals
2
2.2
Mathematical Formulation
2
2.2.1
Concepts
2
2.2.2
The Model
3
2.2.3
Bioreactor Assumptions
4
2.3
Equations
4
2.4
Numerical Solution
5
2.5
Sensitivity Analysis
5
2.5.1
The Effect of Dilution Rate on Bioreactor Performance
6
2.5.2
The Effect of Initial Metal Concentration on Bioreactor Performance
7
2.5.3
The Effect of Attachment Rate on Bioreactor Performance
7
2.5.4
The Effect of Detachment Rate on Bioreactor Performance
8
2.5.5
The Effect of Initial Cellular Population on Bioreactor Performance
8
2.5.6
The Effect of Maximum Specific Growth Rate on Bioreactor Performance . .
9
2.6
Hypothetical Applications
9
3
A Mechanistic Buoyancy Model: Maximum Carrying Capacity Determination
10
3.1
Goal
10
3.2
Mathematical Formulation
10
3.2.1
Concepts
10
3.2.2
Assumptions
11
3.2.3
The Model
11
3.3
Analytic Solution
11
3.4
Determining Buoyant Force: Temporal Tracking Algorithm
12
3.5
Discussion On Maximum Carrying Capacity
14
4
Growth Dynamics
15
4.1
Objective
15
4.2
Approach
15
4.3
Results
15
5
Discussion and Future Directions
17
6
Appendix
19
7
References
19
1

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