From 8fae80c6e01bd9468f8eeea3b8d01da88b15a19b Mon Sep 17 00:00:00 2001
From: Zhefu Li <zf-li23@mails.tsinghua.edu.cn>
Date: Tue, 1 Oct 2024 02:09:32 +0000
Subject: [PATCH] Update model.html
---
wiki/pages/model.html | 61 +++++++++++++++++--------------------------
1 file changed, 24 insertions(+), 37 deletions(-)
diff --git a/wiki/pages/model.html b/wiki/pages/model.html
index c450d9f0..642d2bd6 100644
--- a/wiki/pages/model.html
+++ b/wiki/pages/model.html
@@ -146,6 +146,7 @@
muscone in the systemic circulation(\(\text{mg}\)).</li>
<li><strong>Compartment 4</strong> (Target Intestine, \(I\)): \(Q_I(t)\) represents the amount of
muscone in the intestine(\(\text{mg}\)).</li>
+ <p></p>
<h3>Initial Settings and Assumptions</h3>
<p>At \(t=0\), the amount of muscone in all compartments is \(0\).</p>
<p>Assuming that the total amount of inhaled muscone is \(Q_{\text{inhale}}\) (\(\text{mg}\)), which is
@@ -170,8 +171,8 @@
<h4>Compartment 0: \( Q_A(t) \)</h4>
<p>
- \( \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) - \left( k_{\text{exhale}} + k_{\text{perm}} \right)
- Q_A(t) \)
+ \[ \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) - \left( k_{\text{exhale}} + k_{\text{perm}} \right)
+ Q_A(t) \]
</p>
<p><strong>Explanation</strong>: The amount of muscone in the alveoli increases through inhalation and
@@ -182,7 +183,7 @@
<ul>
<li>
- \( k_{\text{exhale}} \): Since most of the muscone is rapidly exhaled, this value is relatively
+ \ k_{\text{exhale}} \): Since most of the muscone is rapidly exhaled, this value is relatively
large, taken as \( 10 \ \text{min}^{-1} \)
</li>
<li>
@@ -194,8 +195,8 @@
<h4>Compartment 1: \( Q_M(t) \)</h4>
<p>
- \( \frac{dQ_M(t)}{dt} = 0.0005 \cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t)
- \)
+ \[ \frac{dQ_M(t)}{dt} = 0.0005 \cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t)
+ \]
</p>
<p><strong>Explanation</strong>: The increase in muscone on the mucosa comes from adhesion in the
@@ -216,7 +217,7 @@
<h4>Compartment 2: \( Q_L(t) \)</h4>
<p>
- \( \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \)
+ \[ \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the alveolar capillaries comes from
@@ -237,8 +238,8 @@
<h4>Compartment 3: \( Q_C(t) \)</h4>
<p>
- \( \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}}
- Q_C(t) - k_{\text{excrete}} Q_C(t) \)
+ \[ \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}}
+ Q_C(t) - k_{\text{excrete}} Q_C(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the systemic circulation comes from the
@@ -267,7 +268,7 @@
<h4>Compartment 4: \( Q_I(t) \)</h4>
<p>
- \( \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t) - k_{move}Q_I(t) \)
+ \[ \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t) - k_{move}Q_I(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the intestine comes from the distribution of
@@ -285,34 +286,20 @@
<p>In summary, we can write a system of ordinary differential equations and import it into MATLAB for
simulation:</p>
<p>
- \( Q_{\text{inhale}}(t)=100(mg)(Assumption) \)
- </p>
-
- <p>
- \( V_{\text{inhale}}(t) =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \)
- </p>
-
- <p>
- \( \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) -\left( k_{\text{exhale}} + k_{\text{perm}} \right)
- Q_A(t) \)
- </p>
-
- <p>
- \( \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \)
- </p>
-
- <p>
- \( \frac{dQ_M(t)}{dt} = 0.0005\cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t)
- \)
- </p>
-
- <p>
- \( \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}}
- Q_C(t) - k_{\text{excrete}} Q_C(t) \)
- </p>
-
- <p>
- \( \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t)-k_{move}Q_I(t) \)
+ \[
+ \begin{align*}
+ Q_{\text{inhale}}(t) & = 100(mg)(Assumption) \\
+ V_{\text{inhale}}(t) & =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \\
+ \frac{dQ_A(t)}{dt} & = V_{\text{inhale}}(t) -\left( k_{\text{exhale}} + k_{\text{perm}} \right)
+ Q_A(t) \\
+ \frac{dQ_L(t)}{dt} & = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \\
+ \frac{dQ_M(t)}{dt} & = 0.0005\cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t) \\
+ \frac{dQ_C(t)}{dt} & = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}} Q_C(t)
+ -
+ k_{\text{excrete}} Q_C(t) \\
+ \frac{dQ_I(t)}{dt} & = k_{\text{dist}} Q_C(t)-k_{move}Q_I(t) \\
+ \end{align*}
+ \]
</p>
<p>TODO：æ’入结果图</p>
--
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