{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "2bXhwsreMfAn"
},
"source": [
"# Cell Lysis modelling"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Code implemented by Mariana Albino, marial@kt.dtu.dk"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "_U_AbENA8F7L"
},
"outputs": [],
"source": [
"# import libraries\n",
"import numpy as np\n",
"import scipy\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"from scipy.integrate import solve_ivp\n",
"from plotly.subplots import make_subplots"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "0N_uSEPwwc_R"
},
"source": [
"## Bead mill"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "I_4IjOk9wV9v"
},
"outputs": [],
"source": [
"def ode_fcn(t, y, k, Rm):\n",
" # define parameters\n",
" R = y[0]\n",
"\n",
" # ODE\n",
" dR_dt = k*(Rm-R)\n",
" dy = [dR_dt]\n",
"\n",
" return dy\n",
"\n",
"def solver(R_0, k ,Rm ,t_end):\n",
" #define the function to solve\n",
" fun = lambda t, y: ode_fcn(t,y,k,Rm)\n",
"\n",
" #set initial value for parameters\n",
" y0 = [R_0]\n",
"\n",
" #set time span\n",
" t_span = np.arange(0, t_end, 0.1) #(t_start, t_end, t_step)\n",
"\n",
" #solve the differential equation\n",
" sol = solve_ivp(fun, [t_span[0], t_span[-1]], y0, method='LSODA', t_eval=t_span, rtol=1e-6, atol=1e-6)\n",
"\n",
" #extract the solution\n",
" t = sol.t.tolist()\n",
" y = sol.y.T\n",
"\n",
" #asign the solution to variables\n",
" R = y[:, 0]\n",
" Y = y[:,0]/Rm*100\n",
"\n",
" return t, R, Y"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "KtOgJ4hp7B-b"
},
"outputs": [],
"source": [
"\"\"\" Set Process Parameters for run generation \"\"\"\n",
"R_0 = 0 #R at time 0\n",
"R_m = 10 #Rm\n",
"K = 0.5\n",
"\n",
"TIME_END = 5 #how much time should be simulated\n",
"\n",
"t, R , Y = solver(R_0, K, R_m, TIME_END) #run the solver function"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "YryhIgGB7-d3",
"outputId": "905efe0d-49be-4b9e-c475-295f4051b600"
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"source": [
"#create the result plots\n",
"fig = px.line(x=t, y=R) #plot time vs. R\n",
"fig2=px.line(x=t, y=Y) #plot time vs. Y\n",
"\n",
"#Define the settings for the figures\n",
"fig.update_layout(title=\"Evolution of R\",xaxis_title=\"t\",yaxis_title=\"R\",width=1000)\n",
"fig2.update_layout(title=\"Evolution of Yield\",xaxis_title=\"t\",yaxis_title=\"Y (%)\", width=1000)\n",
"\n",
"#Display the figures\n",
"fig.show()\n",
"fig2.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "V7lbKvna_JZ6"
},
"source": [
"## **High pressure homogeniser**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "B-GL13YXEu9g"
},
"outputs": [],
"source": [
"def ode_fcn_hph(n, y, k, Rm, P, a):\n",
" # define parameters\n",
" R = y[0]\n",
"\n",
" # mass balances\n",
" dR_dt = k*(P**a)*(Rm-R)\n",
" dy = [dR_dt]\n",
" return dy\n",
"\n",
"def solver_hph(R_0, k ,Rm , P, a ,N):\n",
" fun = lambda n, y: ode_fcn_hph(n,y,k,Rm, P, a)\n",
" y0 = [R_0]\n",
" N_span = np.arange(0, N+1, 1)\n",
" sol = solve_ivp(fun, [N_span[0], N_span[-1]], y0, method='LSODA', t_eval=N_span, rtol=1e-6, atol=1e-6)\n",
" n = sol.t.tolist()\n",
" y = sol.y.T\n",
" R = y[:, 0]\n",
" Y = y[:,0]/Rm*100\n",
"\n",
" return n, R, Y\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "OlXbmCHAF1CH",
"outputId": "97bdcf02-30aa-4da2-c3c6-6501cc1688fa"
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"outputs": [
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"source": [
"\"\"\" Set Process Parameters for run generation \"\"\"\n",
"R_0_hph = 0\n",
"R_m_hph = 100\n",
"K_hph = 5.9e-4\n",
"a = 1.77 #alpha=0.9-2.9 (2.2 E. coli; 2.9 S. cerevisiae)\n",
"N=10\n",
"\n",
"#range of P to test\n",
"P = [50, 75, 100, 125]\n",
"\n",
"\n",
"#list to store the results of the iteration\n",
"all_results = []\n",
"#open two figures\n",
"fig_hph = make_subplots()\n",
"fig2_hph = make_subplots()\n",
"\n",
"#iterate the solver function for all p values\n",
"for p in P:\n",
" n, R_hph, Y_hph = solver_hph(R_0_hph, K_hph, R_m_hph, p, a, N)\n",
" all_results.append((n, R_hph, Y_hph))\n",
"\n",
" #add result for current P to the figures\n",
" fig_hph.add_trace(go.Scatter(x=n,y=R_hph, mode='markers+lines',name=p))\n",
" fig2_hph.add_trace(go.Scatter(x=n,y=Y_hph, mode='markers+lines',name=p))\n",
"\n",
"#Define the settings for the figures\n",
"fig_hph.update_layout(showlegend=True,legend_title='Pressure', title=\"Evolution of R\",xaxis_title=\"N\",yaxis_title=\"R\",width=1000)\n",
"fig2_hph.update_layout(showlegend=True,legend_title='Pressure', title=\"Evolution of Yield\",xaxis_title=\"N\",yaxis_title=\"Y (%)\",width=1000)\n",
"\n",
"#Display the figures\n",
"fig_hph.show()\n",
"fig2_hph.show()\n",
"\n"
]
},
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"execution_count": null,
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