diff --git a/wiki/pages/model.html b/wiki/pages/model.html index 642d2bd6c949bde4940b670b7683e85d0a5ab0a5..54d32a708fd4467955e3d863954feb215df93c2d 100644 --- a/wiki/pages/model.html +++ b/wiki/pages/model.html @@ -7,9 +7,7 @@ <link rel="icon" type="image/png" href="https://static.igem.wiki/teams/5187/art/icon1.png" sizes="364x370"> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/styles/default.min.css"> <script src="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min.js"></script> - <script> - hljs.highlightAll(); - </script> + <script>hljs.highlightAll();</script> <title>Tsinghua - IGEM 2024</title> <script type="text/javascript" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> <style> @@ -163,7 +161,8 @@ \[ V_{\text{inhale}}(t) =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \] </p> - <p><strong>Explanation</strong>:This describes the rate equation for inhaling muscone over five seconds, + <p><strong>Explanation</strong>: This describes the rate equation for inhaling muscone over five + seconds, where the total amount \( Q \) remains constant. The function \( u(t) \) is a step function, which takes the value of \( \frac{Q_{\text{inhale}}}{5} \) from \( t=0s \) to \( t=5s \), and is \( 0 \) otherwise, simulating the scenario of resting human respiration.</p> @@ -183,7 +182,7 @@ <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> @@ -987,6 +986,24 @@ lactic acid in the time interval \(\frac{t_0}{n}\).</li> </ol> <h3>Model Equation</h3> + <p> + According to Fick's law : + </p> + <p> + \[ + \frac{dQd}{dt} = -D \frac{dC}{dx} + \] + </p> + <p> + </p> + Because the distance between diffusion is very small, the concentration difference between the two sides + of the system replaces the concentration gradient, so this formula can be simplified to: + </p> + <p> + \[ + \frac{dQd}{dt} = K\times Qd + \] + </p> <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> @@ -1007,7 +1024,6 @@ </ul> <h4>Induced Secretion</h4> - <p>According to Fick's Law</p> <p>The remaining lactic acid content in the intestinal environment has a recursive relationship over time:</p> <p>