CancerModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling Drug Delivery in Solid Tumors\n",
    "In this notebook, we will provide a simple walkthrough of how to use the cancer model code in order to model drug delivery within tumors. We will highlight the two main models provided within the model and the prebuilt tools to provide comparisons between them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import model files:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pressureplot (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"isolatedvelocity.jl\")\n",
    "include(\"isolatedpressure.jl\")\n",
    "include(\"soluteperm.jl\")\n",
    "include(\"isolatedmodel.jl\")\n",
    "include(\"makeplots.jl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specify the number of time and spatial nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_time = 2000\n",
    "n_spatial = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specify the known metabolic parameters:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will use the parameters available for the 4T1 cell line of metastatic murine breast cancer using a 32nm diameter dexamethasone nanoparticle treatment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100-element Array{Float64,1}:\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
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       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       "  ⋮\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Kt = 2.9712e-7  ##hydraulic conductivity control value taken from ACS Nano paper\n",
    "Lpt = 8.6717e-7 #vascular hydraulic conductivity control value taken from ACS nano paper\n",
    "Svt = 200      #tumor vascular density\n",
    "D = 1.375e-07  #solute diffusion coefficient\n",
    "rs = 16      #partical radius (nm)\n",
    "R=1. # Tumor Radius\n",
    "Pv=25. # Vascular Pressure mm Hg\n",
    "Pvv=1. #Vascular pressure dimensionless\n",
    "kd=1278*60 # Blood circulation time of drug in hours;\n",
    "att=R*sqrt(Lpt*Svt/Kt) #Parameter alpha for tumor, ignoring lymphatics\n",
    "at = [att for i=1:n_spatial]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate additional biological parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100-element Array{Float64,1}:\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
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       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       "  ⋮\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975\n",
       " 24.160236271476975"
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Perm,sigma=soluteperm(Lpt,rs) #Vascular permeability and solute reflection coefficient respectively\n",
    "att=R*sqrt(Lpt*Svt/Kt) #Parameter alpha for tumor, ignoring lymphatics\n",
    "at = [att for i=1:n_spatial]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this model, we assume 1D transport in spherical coordinates. Here we will discretize the spatial domain with respect to R:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "0.0:0.010101010101010102:0.9999999999999999"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dr = 1/(n_spatial-1)\n",
    "r= (range(0,stop=R,length=n_spatial))./R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the previously defined parameters, we can now model the pressure and velocity profiles for this system. We will then use our pre-defined functions to plot these profiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P= Isolated_Pressure(n_spatial,R,Lpt,Svt,Kt,Pvv,at)\n",
    "v =Isolated_Velocity(n_spatial,P,r, dr)\n",
    "pplot = pressureplot(r,P)\n",
    "display(pplot)\n",
    "vplot = velocityplot(r,v)\n",
    "display(vplot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to model the concentration profile of the drug particles within the tumor. We have two types of models avaialble for this purpose. The first is the low peclet regime which assumes that in the tumor enviornment, mass transport is taking place via both convection and diffusion. In the second type of model, we assume a high peclet regime in which convective mass transport dominates so much that we can neglect the effect of diffusive mass transport. This is important because for high peclet numbers, we encounter numerical erros when trying to model the system using a low peclet model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we will model the concentration profile using a low peclet and high peclet model using the integrator provided by DifferentialEquations.jl. We also have available an Explicit Euler integration method for the high peclet regime, which is useful for optimization routines where the integration function needs to be provided by the user."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: 1st order linear\n",
       "t: 2001-element Array{Float64,1}:\n",
       " 0.0\n",
       " 0.0005\n",
       " 0.001\n",
       " 0.0015\n",
       " 0.002\n",
       " 0.0025\n",
       " 0.003\n",
       " 0.0035\n",
       " 0.004\n",
       " 0.0045\n",
       " 0.005\n",
       " 0.0055\n",
       " 0.006\n",
       " ⋮\n",
       " 0.9945\n",
       " 0.995\n",
       " 0.9955\n",
       " 0.996\n",
       " 0.9965\n",
       " 0.997\n",
       " 0.9975\n",
       " 0.998\n",
       " 0.9985\n",
       " 0.999\n",
       " 0.9995\n",
       " 1.0\n",
       "u: 2001-element Array{Array{Float64,2},1}:\n",
       " [0.0; 0.0; … ; 0.0; 0.0]\n",
       " [1.1351346108399447e-11; 1.168938354542749e-11; … ; 0.0055649494465799506; 0.0]\n",
       " [2.270406598171392e-11; 2.3380208267539664e-11; … ; 0.011118662175751347; 0.0]\n",
       " [3.4058159765709836e-11; 3.507247515469785e-11; … ; 0.016661158223511854; 0.0]\n",
       " [4.541362824793251e-11; 4.6766188805597564e-11; … ; 0.02219253282677109; 0.0]\n",
       " [5.677047155632446e-11; 5.84613499484484e-11; … ; 0.02771280110256685; 0.0]\n",
       " [6.812868925763086e-11; 7.015795658019873e-11; … ; 0.0332219196804277; 0.0]\n",
       " [7.9488282566799e-11; 8.185601503984081e-11; … ; 0.038720023205974514; 0.0]\n",
       " [9.084925268370925e-11; 9.355553117517702e-11; … ; 0.04420723721190768; 0.0]\n",
       " [1.0221159960836156e-10; 1.0525650498620736e-10; … ; 0.04968356169822719; 0.0]\n",
       " [1.1357532334075599e-10; 1.169589364729318e-10; … ; 0.05514899666493306; 0.0]\n",
       " [1.249404238808925e-10; 1.286628256353504e-10; … ; 0.06060354211202528; 0.0]\n",
       " [1.363069012287711e-10; 1.4036817247346312e-10; … ; 0.06604719803950386; 0.0]\n",
       " ⋮\n",
       " [2.587123536632077e-8; 2.6703922378705602e-8; … ; 4.597895810388984; 0.0]\n",
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       " [2.5960508646678234e-8; 2.6796067900757096e-8; … ; 4.605275330203315; 0.0]\n",
       " [2.5975394759326877e-8; 2.681143293187364e-8; … ; 4.606503678745786; 0.0]\n",
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       " [2.6005173183986226e-8; 2.6842169374770698e-8; … ; 4.608959028893655; 0.0]\n",
       " [2.602006549599693e-8; 2.6857540786551215e-8; … ; 4.610186030499053; 0.0]\n",
       " [2.6034959874461652e-8; 2.6872914325219717e-8; … ; 4.611412583125427; 0.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lp =Isolated_Model(n_spatial,Kt,Lpt,Svt,D,sigma,Perm,R,Pv,Pvv,kd,n_time,at)\n",
    "sol_hp = Isolated_Model_HP(n_spatial,Kt,Lpt,Svt,D,sigma,Perm,R,Pv,Pvv,kd,n_time,at)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the concentration profile over the spatial domain at several times. This can be individually as well as combined on the same plot. Additionally, we can plot the percent error between the two models with respect to the spatial domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cplot_single = singleconcplot(r,sol_lp)\n",
    "display(cplot_single)\n",
    "\n",
    "cplot_double = doubleconcplot(r,sol_lp,sol_hp,[\"Low Peclet\" \"High Peclet\"])\n",
    "display(cplot_double)\n",
    "\n",
    "cplot_error= errorconcplot(r,sol_lp,sol_hp)\n",
    "display(cplot_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can integrate over the spatial domain to get data for the spatially averaged drug accumulation over time. Once again, we can do this for both models and make individual and combined plots. Furthermore, we can also plot the percent error between the models over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "  180.492,312.64 185.466,312.947 190.44,298.885 195.413,294.851 200.387,300.556 205.361,305.248 210.334,299.155 215.308,283.519 220.282,279.727 225.256,281.891 \n",
       "  230.229,282.097 235.203,273.351 240.177,262.029 245.151,260.709 250.124,263.95 255.098,266.361 260.072,264.174 265.046,254.131 270.019,242.73 274.993,239.574 \n",
       "  279.967,240.454 284.94,241.465 289.914,239.037 294.888,229.895 299.862,219.694 304.835,216.067 309.809,216.248 314.783,217.19 319.757,217.67 324.73,215.576 \n",
       "  329.704,208.811 334.678,197.724 339.652,191.528 344.625,189.522 349.599,189.63 354.573,189.912 359.546,188.549 364.52,183.836 369.494,174.324 374.468,166.239 \n",
       "  379.441,162.385 384.415,160.899 389.389,161.082 394.363,161.813 399.336,161.82 404.31,159.899 409.284,154.909 414.258,145.994 419.231,138.73 424.205,135.014 \n",
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       "  478.916,101.858 483.89,101.978 488.864,102.194 493.837,101.803 498.811,100.129 503.785,96.5252 508.758,90.37 513.732,82.6277 518.706,77.4168 523.68,74.3869 \n",
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "accum_lp= Accumulation_Model(sol_lp,n_spatial,n_time)\n",
    "accum_hp= Accumulation_Model(sol_hp,n_spatial,n_time)\n",
    "aplot_double= doubleaccumplot(sol_lp,sol_hp,[\"Low Peclet\" \"High Peclet\"])\n",
    "display(aplot_double)\n",
    "aplot_error = Accumerrorplot(sol_lp,sol_hp)\n",
    "display(aplot_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This concludes our tutorial of using the cancer model research files. For more information, please consult the documentation available on the [github page](https://github.com/stmorgenstern/CancerResearch/blob/gh-pages/docslatest.md)."
   ]
  }
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