Lesson 3 Expiratory Waveforms.ipynb

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    "from VentSimulator.VolumeVentilator import VolumeVentilator\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (20.0, 5.0)\n",
    "vent = VolumeVentilator()\n",
    "vent.simulate(3)"
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    "from VentSimulator.PressureVentilator import PressureVentilator\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (20.0, 5.0)\n",
    "vent = PressureVentilator()\n",
    "vent.patient.resistance = 5\n",
    "vent['inspiratory_time'] = 1.0\n",
    "vent['respiratory_rate'] = 15\n",
    "vent['peep'] = 5\n",
    "vent['pressure_target'] = 10\n",
    "vent.simulate(3)"
   ]
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    "# Lesson 3: Expiratory Waveforms\n",
    "### During expiration which wave form is determined by the ventilator?\n",
    "<details><summary>Answer</summary>                    \n",
    "PEEP is the only thing set during expiration -- Expiratory flow is determined by alveolar pressure, airway resistance, elapsed time and tau\n",
    "</details>\n",
    "\n",
    "### Draw the volume-time curve during passive expiration.\n",
    "<img src=\"img/volume_time.png\">\n",
    "    \n",
    "### What determines the shape of the volume-time curve for passive exhalation?\n",
    "<details><summary>Answer</summary>\n",
    "The shape of the volume-time curve (i.e the flow waveform) in passive exhalation is determined by the resistance and compliance of the patient. We commonly refer to the resistance-compliance product as $\\tau$ or the time constant.\n",
    "    \n",
    "**Bonus Question**: What are the units of $\\tau$?\n",
    "</details>\n",
    "\n",
    "\n",
    "### What equation describes the volume-time curve during passive exhalation?\n",
    "<details><summary>Answer</summary>\n",
    "This is determined by the natural decay equation. You'll see a couple different forms of this equation but they are all equivalent:\n",
    "    \n",
    "$ V_t = \\frac{V_0}{e^\\frac{t}{\\tau}} $ or $ \\frac{V_t}{V_0} = e^{-t\\tau}$\n",
    "\n",
    "$t$ = Time \n",
    "    \n",
    "$V_t$ = Volume at time $t$\n",
    "    \n",
    "$V_0$ = Volume at time 0\n",
    "    \n",
    "$\\tau$ = Time constant\n",
    "\n",
    "</details>\n",
    "\n",
    "### What determines $\\tau$?\n",
    "<details><summary>Answer</summary>\n",
    "The resistance and compliance\n",
    "</details>\n",
    "\n",
    "### How can you measure $\\tau$?\n",
    "<details><summary>Answer</summary>\n",
    "There are two approaches:\n",
    "    \n",
    "Measure the exhaled volume at a specific time (i.e. 1 second). We now know $V_t$, $V_0$, and $t$ and can solve for $\\tau$:\n",
    "    \n",
    "$$ \\tau = -t\\ln(\\frac{V_t}{V_0}) $$\n",
    "    \n",
    "Alternatively, you can measure the exhaled $V_t$ and the peak expiratory flow. Then you can use the somewhat less intuitive:\n",
    "    \n",
    "$$ \\tau = \\frac{V_t}{\\dot{V}_\\text{peak}} $$\n",
    "</details>\n",
    "\n",
    "### What percentage of TV will be left in the lung after 2 $\\tau$? 3 $\\tau$?\n",
    "| Time Constant |  0  |  1  |  2  |  3  |  4  |  5  |  6  |  7  | \n",
    "| ------------- | --- | --- | --- | --- | --- | --- | --- | --- | \n",
    "| Precentage Remaining | 100.00% | 36.79% |13.53% |4.98% | 1.83% |0.67% |0.25% |0.09% | 0.03% |\n",
    "\n",
    "Use the Simulator to answer the next two questions. Convince yourself that it doesn't matter which one you use.\n",
    "<a href=\"PressureSimulator.ipynb\">Pressure Control Simulator</a> \n",
    "<a href=\"VolumeSimulator.ipynb\">Volume Control Simulator</a> \n",
    "### What will happen to the wave forms during expiration if compliance changes?\n",
    "\n",
    "### What will happen to the wave forms during expiration if resistance changes?\n",
    "\n",
    "### What is auto-peep and why is it important?\n",
    "<details><summary>Answer</summary>\n",
    "a.\tThe buildup of additional positive pressure due to breath stacking. Important because it represents a risk of lung injury (micro/macro barotrauma), dead space, gas trapping and may result in ineffective triggering (patient has to work harder to trigger a breath so increase risk of fatigue). May also result in hemodynamic compromise or pneumothorax.\n",
    "</details>\n",
    "\n",
    "### What are the risk factors for developing auto-peep?\n",
    "<details><summary>Answer</summary>\n",
    "* Long time constant\n",
    "* High compliance\n",
    "* High respiratory rate\n",
    "* Obstructive lung disease (This implies high compliance or high resistance)\n",
    "</details>\n",
    "\n",
    "### What can be done to minimize auto-peep?\n",
    "<details><summary>Answer</summary>\n",
    "In short, you need to decrease the amount of air remaining at the end of the expiratory cycle. This can be either by decreasing the tidal volume or by increasing the expiratory time. \n",
    "</details>\n",
    "\n",
    "\n",
    "### How can you tell if someone has auto-peep?\n",
    "<details><summary>Answer</summary>\n",
    "By examining the flow-time curve:\n",
    "    \n",
    "1. Look for end expiratory flow. If there is no end expiratory flow, that suggests the alveolar pressure and the ventilator pressure have equalized (at PEEP). If end expiratory flow is present, that means there is still a pressure gradient between the alveoli and the ventilator (Palv > Pvent), the patient is still exhaling and the alveolar pressure is higher than the set PEEP (indicating the presence of auto-peep). The servo-i will measure this for you ($\\dot{V}_\\text{ee}$) or you can use the flow-volume loops.\n",
    "    \n",
    "1.\tLook at the area under the inspiratory and expiratory limbs of the flow-time curve. The area under the inspiratory and expiratory limbs should be equal (the TV that goes in should be the same as what comes out). If the area under the expiratory limb is smaller than the area under the inspiratory limb, this suggests that some air is being trapped and acts as evidence of auto-peep.\n",
    "    \n",
    "1. Measure it directly with an expiratory hold. The ventilator will read out total peep(total peep - set peep = auto peep). \n",
    "    \n",
    "1. Look for ineffective triggering. To Trigger the ventilator, a patient must decrease the alveolar pressure to a pressure below PEEP (to create a gradient of Pvent > Palv). If there is auto-peep, a patient has to have an inspiratory effort great enough to overcome the PEEP + auto-PEEP in order to trigger the ventilator. You can also measure this directly with an esophageal balloon which measures the inspiratory muscule pressure required to counter auto-peep.\n",
    "</details>\n",
    "\n",
    "### A mechanically ventilated patient with COPD has severe autopeep. What can be done to fix this?\n",
    "<details><summary>Answer</summary>\n",
    "1. Decrease the TV \n",
    "1.\tDecrease the RR (i.e. lengthen the e-time)\n",
    "1.\tBronchodilators, steroids (i.e. decrease resistance)\n",
    "1.\tUpsize the ETT (i.e. decrease resistance)\n",
    "1.\tSedate the patient \n",
    "1.\tIncrease inspiratory flow rate or shorten the IT (lengthen the e-time)\n",
    "</details>\n",
    "\n",
    "### The inspiratory flow is increased to shorten the inspiratory time. What will likely happen to the auto-peep?\n",
    "<details><summary>Answer</summary>\n",
    "It should decrease as e-time will lengthen. \n",
    "</details>\n",
    "\n",
    "### The set TV is reduced. What will happen to the auto-peep?\n",
    "<details><summary>Answer</summary>\n",
    "It should decrease.\n",
    "</details>\n",
    "\n",
    "### How might you counteract ineffective triggering?\n",
    "<details><summary>Answer</summary>\n",
    "Set the machine PEEP to 75% of the auto-peep.\n",
    "</details>\n",
    "\n",
    "### What is the stress index?\n",
    "<details><summary>Answer</summary>\n",
    "The strees index can help decide if you have adequate alveolar recruitment without overdistension -- essentially you are evaluating if the compliance ($\\frac{\\delta P}{\\delta V}$) is constant throughout the breath. If it is increasing (i.e. additional volume is increasing the pressure more than the initial volume) this suggests overdistention. If it is decreasing (i.e. additional volume increases the pressure less than the initial volume) this suggests that there is recruitable lung units. \n",
    "    \n",
    "You can evaluate the stress index by looking at the shape of the pressure-time curve during **CONSTANT** flow volume control ventilation. Typically a very slow flow rate is used. A linear increase in pressure reflects constant compliance and a stress index of 1, which suggests adequate alveolar recruitment without overdistension. If compliance worsens as the lung inflates (indicated by an upward concavity), the stress index is > 1 and the recommendation is to decrease the PEEP or TV or both.  If compliance improves as the lung inflates (indicated by a downward concavity), the stress index is < 1 and the recommendation is to increase the PEEP or TV or both.\n",
    "\n",
    "</details>"
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