{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Special case: evaporation of water\n",
    "**TL;DR:** Estimation of rates and yields is an important step in characterization and selection of cell factories and bioprocess. Evaporation of water from the bioreactor will bias the estimated yields and rates. Using the Pseudo batch transformation one can estimate the correct values when evaporation is significant.\n",
    "\n",
    "## Why care about evaporation?\n",
    "Evaporation of water from a bioreactor will bias the estimated titer, rates and yields if it is not properly accounted for. As a motivating example, imagine a batch bioreactor with an initial volume of 100 ml. When analysing batch processes it is common to assume that any change in concentration is caused by the metabolic activity of the organism in the reactor. However, if 10 ml water evaporated during the process this would cause a significant increase in concentration which is unrelated to the metabolic activity. As result the production rates will appear larger causing the strains to look more attractive, than reality.\n",
    "\n",
    "Evaporation can vary a lot between different bioreactor equipment and scales, thus evaporation could very well take a part of the blame for the performance variation of cell factories at different scales. The cause of the varying evaporation is multifaceted and can originate from dryness of process air, presence of condensers, differences in agitation method, etc [1]. Thus, the same strain can appear to perform differently in between cultivation setups if evaporation is not accounted for in the bioreactor volume.\n",
    "\n",
    "For fed-batch fermentations, evaporation adds an additional source of volume change. The Pseudo batch transformation can handle scenarios where evaporation is significant, however to get accurate estimates of rates and yields the transformation method needs the true volume of the bioreactor. The true volume data may not always be accessible. This tutorial have two objectives\n",
    "1. Show that the Pseudo batch transformation method works when water evaporation is significant \n",
    "2. Illustrate a common scenario where the evaporation is not accounted for in the volume data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start we will first load the necessary Python packages and functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from pseudobatch import pseudobatch_transform_pandas\n",
    "from pseudobatch.datasets import load_evaporation_fedbatch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pseudo batch transformation works when evaporation is significant\n",
    "The `pseudobatch` package holds an example dataset which is produced to mimic a fed-batch process with an exponential feeding profile where water evaporates from the bioreactor at a constant rate (The simulation script are found in https://github.com/biosustain/pseudobatch/article/simulation_scripts/fed-batch_evaporation.jl). This data is loaded in the code block below. We also show some of the data columns to give an overview of the structure of this data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>timestamp</th>\n",
       "      <th>sample_volume</th>\n",
       "      <th>c_Glucose</th>\n",
       "      <th>c_Biomass</th>\n",
       "      <th>c_Product</th>\n",
       "      <th>c_CO2</th>\n",
       "      <th>v_Volume</th>\n",
       "      <th>v_Feed_accum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.075000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.06006</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.075004</td>\n",
       "      <td>0.503014</td>\n",
       "      <td>0.002474</td>\n",
       "      <td>0.0</td>\n",
       "      <td>999.995704</td>\n",
       "      <td>0.055765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.12012</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.075009</td>\n",
       "      <td>0.506047</td>\n",
       "      <td>0.004964</td>\n",
       "      <td>0.0</td>\n",
       "      <td>999.991745</td>\n",
       "      <td>0.111865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.18018</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.075013</td>\n",
       "      <td>0.509097</td>\n",
       "      <td>0.007469</td>\n",
       "      <td>0.0</td>\n",
       "      <td>999.988123</td>\n",
       "      <td>0.168303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.24024</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.075016</td>\n",
       "      <td>0.512166</td>\n",
       "      <td>0.009988</td>\n",
       "      <td>0.0</td>\n",
       "      <td>999.984842</td>\n",
       "      <td>0.225082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   timestamp  sample_volume  c_Glucose  c_Biomass  c_Product  c_CO2   \n",
       "0    0.00000            0.0   0.075000   0.500000   0.000000    0.0  \\\n",
       "1    0.06006            0.0   0.075004   0.503014   0.002474    0.0   \n",
       "2    0.12012            0.0   0.075009   0.506047   0.004964    0.0   \n",
       "3    0.18018            0.0   0.075013   0.509097   0.007469    0.0   \n",
       "4    0.24024            0.0   0.075016   0.512166   0.009988    0.0   \n",
       "\n",
       "      v_Volume  v_Feed_accum  \n",
       "0  1000.000000      0.000000  \n",
       "1   999.995704      0.055765  \n",
       "2   999.991745      0.111865  \n",
       "3   999.988123      0.168303  \n",
       "4   999.984842      0.225082  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fedbatch_df = load_evaporation_fedbatch()\n",
    "fedbatch_df[['timestamp','sample_volume', 'c_Glucose', 'c_Biomass','c_Product', 'c_CO2', 'v_Volume', 'v_Feed_accum']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To show the effect of the evaporation, we will calculate the expected volume if no volume evaporated. This is simply done by starting with the initial reactor volume, then adding the volume of feed and subtracting the sample volume. Below we calculate the expected volume and store it in a column of the dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='timestamp'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_volume = fedbatch_df['v_Volume'].iloc[0]\n",
    "\n",
    "# Calculated the expected volume by tracking known volume changing \n",
    "# events. For the Pseudo batch transform the volume has to be the \n",
    "# volume BEFORE sampling. Therefore the sampling volume data is \n",
    "# shifted one position before the cumsum.\n",
    "fedbatch_df['expected_volume'] = (\n",
    "    initial_volume \n",
    "    + fedbatch_df['v_Feed_accum']\n",
    "    - fedbatch_df['sample_volume'].shift(1, fill_value=0).cumsum()\n",
    ")\n",
    "\n",
    "fedbatch_df.plot(\n",
    "    x='timestamp',\n",
    "    y=['v_Volume', 'expected_volume'],\n",
    "    label=['True volume', \"Expected volume\"],\n",
    "    color=['C0', 'C2']\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot clearly shows that the expected volume (orange line) diverges from the true volume (blue line) of the bioreactor. This divergence is caused by volume evaporation. To estimate the correct rates and yields using the Pseudo batch transformation the true bioreactor volume is required. In real world scenarios the true volume may not be known, this is discussed further in the next section. For now we will use the simulated true volume to validate the Pseudo batch transformation method.\n",
    "\n",
    "In the following code block the Pseudo batch transformed biomass and glucose concentrations are calculated.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "substrate_in_feed = fedbatch_df['s_f'].iloc[0]\n",
    "fedbatch_df[['pseudo_Biomass', 'pseudo_Glucose']] = pseudobatch_transform_pandas(\n",
    "    df=fedbatch_df,\n",
    "    measured_concentration_colnames=[\"c_Biomass\", \"c_Glucose\"],\n",
    "    reactor_volume_colname='v_Volume',\n",
    "    accumulated_feed_colname='v_Feed_accum',\n",
    "    concentration_in_feed=[0,substrate_in_feed],\n",
    "    sample_volume_colname='sample_volume'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the standard linear modelling procedures to estimate the specific growth rate and the substrate yield coefficient from the Pseudo batch transformed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu0_hat = 0.1\n",
      "true mu0 = 0.1\n"
     ]
    }
   ],
   "source": [
    "mu0_hat, intercept = np.polyfit(fedbatch_df['timestamp'], fedbatch_df['pseudo_Biomass'].transform(np.log), 1)\n",
    "print(f\"mu0_hat = {round(mu0_hat, 5)}\")\n",
    "print(f\"true mu0 = {fedbatch_df['mu0'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Yxs_hat = 1.8500000000000008\n",
      "true Yxs = 1.85\n"
     ]
    }
   ],
   "source": [
    "Yxs_hat, intercept = np.polyfit(fedbatch_df['pseudo_Biomass'], fedbatch_df['pseudo_Glucose'], 1)\n",
    "print(f\"Yxs_hat = {abs(Yxs_hat)}\")\n",
    "print(f\"true Yxs = {fedbatch_df['Yxs'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that both of the estimated parameters match the true simulated parameters, thus showing that the Pseudo batch transformation can be used in situations where the evaporation is present."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What happens when volume data does not account for evaporation\n",
    "In some cultivation systems the volume is not actually measured. This is the case for the M2labs Biolector and Robolector cultivation systems and the Sartorius Ambr® 15 and Ambr® 250 systems. Instead the reactor volume is inferred by keeping track of the liquid going in and out of the reactor. This method does not account for the evaporation of water from the system and will overestimate the actual volume of the reactor. In the simulated example used above, this would mean that the volume time series data outputted from the instrument would be the \"Expected volume\" and NOT the \"True volume\" (See plot above).\n",
    "\n",
    "Let's investigate what happens if we estimate the specific growth rate and substrate yield using the biassed volume data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "fedbatch_df[['pseudo_Biomass_wrong_volume', 'pseudo_Glucose_wrong_volume']] = pseudobatch_transform_pandas(\n",
    "    df=fedbatch_df,\n",
    "    measured_concentration_colnames=[\"c_Biomass\", \"c_Glucose\"],\n",
    "    reactor_volume_colname='expected_volume',\n",
    "    accumulated_feed_colname='v_Feed_accum',\n",
    "    concentration_in_feed=[0,substrate_in_feed],\n",
    "    sample_volume_colname='sample_volume'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the regular linear model, we can estimate the rate and yield from the Pseudo batch concentration based on the wrong volume."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu0_hat = 0.09959\n",
      "true mu0 = 0.1\n"
     ]
    }
   ],
   "source": [
    "mu0_hat, intercept = np.polyfit(fedbatch_df['timestamp'], fedbatch_df['pseudo_Biomass_wrong_volume'].transform(np.log), 1)\n",
    "print(f\"mu0_hat = {round(mu0_hat, 5)}\")\n",
    "print(f\"true mu0 = {fedbatch_df['mu0'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Yxs_hat = 1.6852002355943905\n",
      "true Yxs = 1.85\n"
     ]
    }
   ],
   "source": [
    "Yxs_hat, intercept = np.polyfit(fedbatch_df['pseudo_Biomass_wrong_volume'], fedbatch_df['pseudo_Glucose_wrong_volume'], 1)\n",
    "print(f\"Yxs_hat = {abs(Yxs_hat)}\")\n",
    "print(f\"true Yxs = {fedbatch_df['Yxs'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that both the specific growth rate and the substrate yield estimates are biased. However, the bias of the growth rate is very small. It is important to note that the size of these biases are dependent on the specific evaporation rate, bioprocess, strain, etc. but the bottom line is that there will be a bias."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To improve the estimated rates and yields, we need to estimate the true bioreactor volume. To estimate the true bioreactor volume we need a function which can calculate/estimate how much water has evaporated from the bioreactor at each time point. Below we will implement a Python function to calculate the amount of volume evaporated. For this illustration case, we will assume that the water evaporates at a constant rate. Therefore the accumulated evaporation over a given time period is calculated as\n",
    "\n",
    "$$\n",
    "V_{evaporated} = (t_1 - t_0) * evaporation\\_rate\n",
    "$$\n",
    "\n",
    "\n",
    "Here the evaporated volume of water ($V_{evaporated}$) is a function of three parameters: the initial timepoint ($t_0$), the final time point ($t_1$) and the evaporation rate ($evaporation\\_rate$). One could easily imagine modelling the evaporation rate as a function of other factors such as temperature, stirring speed, etc. We leave it up to the user to decide how they will model evaporation in their setup.\n",
    "\n",
    "**IMPORTANT NOTE:** I, the authors of this tutorial, am not an expert in evaporation, and thus this evaporation function is purely for the sake of the example. We do not recommend using this function for volume correction, instead please refer to the literature on this topic.\n",
    "\n",
    "Now we implement the evaporation function described above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaporated_volume(t1, t0, evaporation_rate):\n",
    "    \"\"\"Calculates the liquid phase volume of evaporated water during a \n",
    "    timespan t0 to t1, assuming that the water evaporates at a known \n",
    "    fixed rate.\"\"\"\n",
    "    return (t1 - t0) * evaporation_rate "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As this is a simulated data set we know the true evaporation rate, which is stored in the `evap_rate` column of the data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated evaporation rate 1.0 µL/h\n"
     ]
    }
   ],
   "source": [
    "simulated_evaporation_rate = fedbatch_df.evap_rate.iloc[0]\n",
    "print(f\"Simulated evaporation rate {simulated_evaporation_rate} µL/h\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will estimate the volume of evaporated water for each time step using the function we defined above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "fedbatch_df['estimated_evaporated_volume'] = fedbatch_df['timestamp'].apply(evaporated_volume, t0=0, evaporation_rate=simulated_evaporation_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can estimate the true volume of the bioreactor by subtracting the evaporated volume from the \"measured\" volume."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "fedbatch_df['estimated_true_volume'] = fedbatch_df['expected_volume'] - fedbatch_df['estimated_evaporated_volume']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can visualize the \"measured\", estimated and the true volume to see that the estimated true volume is similar to the true volume."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='timestamp'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fedbatch_df.plot(\n",
    "    x='timestamp',\n",
    "    y=['expected_volume','v_Volume', 'estimated_true_volume'],\n",
    "    label=[\"Expected volume\", 'True volume', \"Estimated true volume\"],\n",
    "    style=['-', '-', '--'],\n",
    "    color=['C2', 'C0', 'C1']\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the estimated true volume (green dashed line) follows the true volume (blue solid line) showing that we successfully estimated the true volume. In a real world scenario the true volume will rarely be known and one will have to live with the uncertainty that this introduces into the rate and yield estimates.\n",
    "\n",
    "To make the example complete we will estimate the specific growth rate and substrate yield using the estimated true volume for the Pseudo batch transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "fedbatch_df[['pseudo_Biomass_estimated_volume', 'pseudo_Glucose_estimated_volume']] = pseudobatch_transform_pandas(\n",
    "    df=fedbatch_df,\n",
    "    measured_concentration_colnames=[\"c_Biomass\", \"c_Glucose\"],\n",
    "    reactor_volume_colname='estimated_true_volume',\n",
    "    accumulated_feed_colname='v_Feed_accum',\n",
    "    concentration_in_feed=[0,substrate_in_feed],\n",
    "    sample_volume_colname='sample_volume'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu0_hat = 0.1\n",
      "true mu0 = 0.1\n"
     ]
    }
   ],
   "source": [
    "mu0_hat, intercept = np.polyfit(fedbatch_df['timestamp'], fedbatch_df['pseudo_Biomass_estimated_volume'].transform(np.log), 1)\n",
    "print(f\"mu0_hat = {round(mu0_hat, 5)}\")\n",
    "print(f\"true mu0 = {fedbatch_df['mu0'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Yxs_hat = 1.850000000000001\n",
      "true Yxs = 1.85\n"
     ]
    }
   ],
   "source": [
    "Yxs_hat, intercept = np.polyfit(fedbatch_df['pseudo_Biomass_estimated_volume'], fedbatch_df['pseudo_Glucose_estimated_volume'], 1)\n",
    "print(f\"Yxs_hat = {abs(Yxs_hat)}\")\n",
    "print(f\"true Yxs = {fedbatch_df['Yxs'].iloc[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected the calculated rate and yield match the simulated parameters. This high accuracy is of course only possible because we here work with simulated data and know the true evaporation rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "During this tutorial, we have shown that the Pseudo batch transformation is applicable, when significant amounts of water evaporate from the bioreactor. Furthermore, the tutorial highlighted some of the considerations concerning evaporation from bioreactors and illustrated an overall approach to account for water evaporation when applying the Pseudo batch transformation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "[1] M. Ask and S. M. Stocks, “Aerobic bioreactors: condensers, evaporation rates, scale-up and scale-down,” Biotechnol Lett, vol. 44, no. 7, pp. 813–822, Jul. 2022, doi: 10.1007/s10529-022-03258-7."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
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