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--- a/wiki/pages/model.html
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@@ -67,7 +67,7 @@
<li><a href="#topic1">Compartment Model for Muscone Inhalation</a></li>
<li><a href="#topic2">Topic2</a></li>
<li><a href="#topic3">ODE of MAPK pathway</a></li>
- <li><a href="#topic4">Topic4</a></li>
+ <li><a href="#topic4">Lactic Acid Absorption Model</a></li>
</ul>
</div>
@@ -455,7 +455,7 @@
<div class="col-lg-12">
<h2 id="topic3">
<h2>Ordinary Differential Equation of the signal transduction of the yeast MAPK pathway</h2>
-
+ <hr>
<h3>Model Description</h3>
<p>In our project, we express the muscone receptor (GPCR) on the yeast cell membrane. After a
certain concentration of muscone diffuses into the intestine and binds to the receptor, it
@@ -971,28 +971,82 @@
<div class="row mt-4">
<div class="col-lg-12">
<h2 id="topic4">
- <h2>Topic4</h2>
+ <h2>Lactic Acid Absorption Model</h2>
<hr>
- <p>Tsinghua University is consistently ranked among the top universities in the Asia-Pacific according
- to major international university rankings. Tsinghua University ranked No. 1 in China, the whole of
- Asia-Oceania region and emerging countries according to the Times Higher Education, with its
- industry income, research, and teaching performance indicator placed at 1st, 4th and 9th
- respectively in the world. Internationally, Tsinghua was regarded as the most reputable Chinese
- university by the Times Higher Education World Reputation Rankings where, it has ranked 8th globally
- and 1st in the Asia-Pacific.</p>
- <p>The Engineering Research Center for Navigation Technology is a relatively young institute in the
- Department of Precision Instrument which was established in 2000, with the intention to "[pursue]
- excellence in the research and development in the field of high-accuracy inertial instruments and
- navigation technology, as well as in MEMS inertial sensor fields, and to provide advanced training
- for future scientists and engineers in the field of inertial technology." Its research interests
- cover high-accuracy inertial instruments and navigation technology, MEMS inertial sensors and
- systems, and precise electro-mechanical control systems and their application. As of 2012, the area
- of the center is 2900 square meters, including approximately 550 square meters of clean rooms.
- Equipment and instruments in this center are worth over 50 million RMB (US$7.56 million).</p>
- </div>
- <div class="image-container">
- <img src="https://static.igem.wiki/teams/5187/figure/ibd-figure.jpg" alt="ibd_figure"
- class="shadowed-image">
+ <h3>Model Description</h3>
+ <p>
+ Our project alleviates IBD symptoms by secreting lactic acid in the intestine to weaken
+ autoimmunity, but it may face two aspects of doubt: first, why can't lactic acid or lactic acid
+ bacteria probiotics be taken directly; second, will the considerable secretion of lactic acid cause
+ acidosis in the human body? We hope to model our project to describe how it has a better sustained
+ release effect compared to direct lactic acid consumption, more precise control compared to
+ probiotic intake, and to avoid adaptation of the immune system and gut microbiota. Additionally, we
+ need to develop a computational method to achieve precise control over lactic acid secretion to
+ regulate treatment time and prevent acidosis.
+ </p>
+
+ <h3>Basic Assumptions</h3>
+ <ol>
+ <li>Only the absorption process of lactic acid is described, without considering other effects of
+ lactic acid on the human body.</li>
+ <li>It is assumed that the location where lactic acid acts on immune cells is separated from the
+ intestinal environment.</li>
+ <li>It is assumed that the secretion rate of lactic acid is uniform, and activated yeast cells
+ secrete a total amount of lactic acid \(a\) within time \(t_0\), secreting \(\frac{a}{n}\) of
+ lactic acid in the time interval \(\frac{t_0}{n}\).</li>
+ </ol>
+ <h3>Model Equation</h3>
+
+ <h4>Direct Administration</h4>
+ <p>
+ In the case of direct lactic acid intake, the content of lactic acid in the intestine can be
+ described by the following equation:
+ </p>
+ <pre>
+ Qd=(Qd_0+a)e^{-(k_1+k_2)t}
+ </pre>
+ <strong>Explanation</strong>: The absorption rate is proportional to the concentration of lactic acid,
+ and the concentration of lactic acid declines in an exponential form.
+
+ <strong>Parameters</strong>:
+ <ul>
+ <li><em>Qd</em>: Remaining lactic acid content in the intestinal environment</li>
+ <li><em>Qd_0</em>: Initial lactic acid content in the intestinal environment</li>
+ <li><em>a</em>: Total amount of lactic acid ingested</li>
+ <li><em>k_1</em>: Absorption rate of lactic acid</li>
+ <li><em>k_2</em>: Rate at which lactic acid is eliminated due to metabolism and excretion</li>
+ <li><em>t</em>: Time</li>
+ </ul>
+
+ <h4>Induced Secretion</h4>
+ <p>
+ According to Fick's Law
+ </p>
+ <pre>
+ %
+ </pre>
+ <p>
+ The remaining lactic acid content in the intestinal environment has a recursive relationship over
+ time:
+ </p>
+ <pre>
+ Qd_i=(Qd_{i-1}+\frac{a}{n})e^{-(k_1+k_2)(t-(i-1)\frac{t_0}{n})}
+ </pre>
+ <p>
+ We can obtain the expression:
+ </p>
+ <pre>
+ Qd_i=\frac{a}{n}\sum_{m=1}^{i-1}e^{-(k_1+k_2)(mt-(j\frac{(m+2)(m+1)}{2}\frac{t_0}{n}))}
+ </pre>
+ <p>
+ TODO: Insert result graph
+ </p>
+ <p>
+ By simulating the absorption process of lactic acid, we can conclude that in the case of direct
+ administration, the concentration of lactic acid decreases exponentially over time, while in the
+ case of induced secretion, the concentration of lactic acid slowly increases over time and reaches
+ equilibrium after a certain period.
+ </p>
</div>
</div>