{ "cells": [ { "cell_type": "markdown", "id": "0f275950", "metadata": {}, "source": [ "# Estimation du temps de dialyse et du volume de dialysat\n", "\n", "Sur un fonctionnement à une passe, pour un débit de sang de 300 mL/min, un rein artificiel permet de réduire la concentration en urée de 4g/L à 1,1 g/L.\n", "\n", "Calculer la clairance\n", "\n", "Un patient de 80 kg arrive avec une teneur en urée de 3 g/L. La dialyse doit lui permettre de repartir avec une concentration en urée de 0,8 g/L.\n", "\n", "Calculer la masse d’urée à éliminer\n", "Calculer le temps de dialyse nécessaire\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "8bc7095f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.6249999999999996e-06 m3/s\n", "La clairance peut être estimée à 217.49999999999997 ml/min\n", "La masse en urée à éliminer est : 0.10207999999999999 kg\n", "1.664452642047285\n", "16918.474751773687\n", "Le temps de dialyse estimé est : 4.699576319937135 h\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "Qc=300*1e-6/60\n", "Cse=4 \n", "Css=1.1\n", "\n", "K=Qc*(Cse-Css)/Cse\n", "print(K, 'm3/s')\n", "print('La clairance peut être estimée à', K*1e+6*60, 'ml/min')\n", "\n", "C0=3\n", "Cf=0.8\n", "P=80\n", "ECTF=0.58*P*0.001\n", "VDPoids=0\n", "M=C0*(ECTF+VDPoids)-Cf*ECTF\n", "print ('La masse en urée à éliminer est :', M, 'kg')\n", "cmoy=(Cf-C0)/np.log(Cf/C0)\n", "print (cmoy)\n", "td=M/(K*cmoy)\n", "print (td)\n", "print ('Le temps de dialyse estimé est :', td/3600, 'h')\n", "t=np.linspace(0,5,100)\n", "plt.plot(t,C0*np.exp(-K*t*3600/ECTF))\n", "plt.plot([0,td/3600],[Cf,Cf],'r--')\n", "plt.plot([td/3600,td/3600],[0,Cf],'r--')\n", "plt.xlabel('t (h)')\n", "plt.ylabel('c en urée (g/L)')\n", "plt.ylim(0,C0)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "94e3111e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }