Pharmacokinetics-Intravenous bolus and infusion calculation

00:22:02
https://www.youtube.com/watch?v=56KlyCBVf6k

Summary

TLDRThis tutorial provides a comprehensive overview of intravenous bolus and infusion administration calculations. It guides viewers through various questions related to determining elimination rate constants, half-lives, initial concentrations, volumes, and clearance. The tutorial emphasizes the use of graphs and equations, including the trapezoidal rule for calculating the area under the curve. Step-by-step solutions are provided for each question, enhancing understanding of pharmacokinetic principles essential for effective drug administration and monitoring.

Takeaways

  • 📊 Understand the importance of graphs in pharmacokinetics.
  • 🧮 Learn to calculate elimination rate constants (ke).
  • ⏳ Master the half-life calculation using T1/2 = ln(2) / ke.
  • 📏 Use the trapezoidal rule for area under the curve calculations.
  • 💡 Identify initial concentrations from graph extrapolation.
  • 📦 Calculate volume using C = Dose / Volume.
  • 🔄 Determine infusion rates for target concentrations.
  • ⚖️ Recognize the impact of the salt factor in dosing.
  • 📈 Calculate concentration at specific time points effectively.
  • 📚 Review clearance calculations for accurate drug monitoring.

Timeline

  • 00:00:00 - 00:05:00

    In this tutorial, the focus is on understanding intravenous bolus and infusion calculations. The initial questions involve plotting a graph to determine the elimination rate constant (ke) and half-life (t1/2) from the graph's gradient and y-intercept, leading to calculations of initial concentration and volume based on given data.

  • 00:05:00 - 00:10:00

    The second part continues with similar calculations, emphasizing the trapezoidal rule to find the area under the curve. This involves calculating gradients, half-lives, and using the trapezoidal rule to sum areas for different time intervals, ultimately leading to the total area under the curve and understanding the implications for drug concentration over time.

  • 00:10:00 - 00:15:00

    The tutorial then shifts to intravenous bolus administration, where the bolus loading dose is calculated based on target concentration and volume. Subsequent questions involve determining how long the concentration remains above a certain level and calculating concentrations at later time points using elimination rate constants derived from previous data.

  • 00:15:00 - 00:22:02

    Finally, the focus transitions to intravenous infusion administration, where calculations for clearance, volume, and infusion rates are performed to maintain target drug concentrations. The tutorial concludes with practice questions that reinforce the concepts of bolus and continuous infusion calculations, ensuring a comprehensive understanding of pharmacokinetic principles.

Show more

Mind Map

Video Q&A

  • What is the elimination rate constant (ke)?

    The elimination rate constant (ke) can be calculated from the gradient of the graph.

  • How do you calculate the half-life (T1/2)?

    Half-life is calculated using the formula T1/2 = ln(2) / ke.

  • What is the trapezoidal rule used for?

    The trapezoidal rule is used to calculate the area under the curve for concentration vs. time graphs.

  • How do you find the initial concentration from a graph?

    The initial concentration can be found by extrapolating the graph to the y-intercept.

  • What is the formula for calculating volume from concentration and dose?

    Volume can be calculated using the formula C = Dose / Volume.

  • How do you determine the infusion rate for a target concentration?

    The infusion rate can be determined using the formula Css = IR / Clearance.

  • What factors affect the clearance calculation?

    Clearance is affected by the elimination rate constant and volume of distribution.

  • How do you calculate the concentration at a specific time?

    Concentration at a specific time can be calculated using the formula C_t = C_0 * e^(-kt).

  • What is the significance of the salt factor in calculations?

    The salt factor accounts for the difference between the drug's molecular weight and its active ingredient.

  • How do you calculate the area under the curve (AUC)?

    AUC can be calculated by summing the areas of trapezoids formed between concentration points.

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  • 00:00:00
    hello everyone in this tutorial we will
  • 00:00:03
    look at some questions to help you to
  • 00:00:05
    understand the calculation for
  • 00:00:06
    intravenous bolus and infusion
  • 00:00:09
    administration first pause the video and
  • 00:00:12
    try to solve the questions and then play
  • 00:00:14
    the video for my explanations let's
  • 00:00:17
    begin this question is related to
  • 00:00:20
    intravenous bolus dose you will need to
  • 00:00:23
    plot the graph using semi-log paper to
  • 00:00:25
    sort the questions so let's pause the
  • 00:00:27
    video and try the questions this is the
  • 00:00:31
    graph
  • 00:00:32
    you should get so let's look at the
  • 00:00:34
    hidden information in this graph so
  • 00:00:37
    first of all if you remember when we
  • 00:00:39
    calculate the gradient for this straight
  • 00:00:41
    line you should able to find rke so this
  • 00:00:45
    is the elimination rate constant once
  • 00:00:47
    you can find this answer you managed to
  • 00:00:50
    convert this to t 1/2 remember this
  • 00:00:53
    equation T 1/2 is equal to lon 2 divided
  • 00:00:57
    by ke so that is a half-life for
  • 00:01:00
    elimination the next information we can
  • 00:01:03
    find from the graph is by extrapolating
  • 00:01:05
    the graph over here into the y-intercept
  • 00:01:08
    so once you find this y-intercept over
  • 00:01:11
    here you can find the initial
  • 00:01:14
    concentration so that is the information
  • 00:01:17
    we can identify from the graph so let's
  • 00:01:20
    move on to the calculation steps I will
  • 00:01:22
    show you how to solve all the questions
  • 00:01:26
    for question number one we need to
  • 00:01:29
    calculate the gradient so I'm going to
  • 00:01:31
    use this equation 1 C 2 minus 1 C 1 T 2
  • 00:01:36
    minus T 1 you can pick any concentration
  • 00:01:40
    or anytime point from the table in this
  • 00:01:43
    case I'm going to use the example 1 2.6
  • 00:01:46
    minus 161 over 8 minus 0.5 so the value
  • 00:01:53
    I obtained will be zero point nine six
  • 00:01:56
    minus four point one one divided by
  • 00:01:58
    seven point five your answer for ke
  • 00:02:02
    should be 0.42 so we soft question one
  • 00:02:07
    the second question is about half-life
  • 00:02:11
    for elimination
  • 00:02:13
    we have is equal to lon 2 divided by ke
  • 00:02:15
    that would be 0.693 divided by 0.4 2 so
  • 00:02:21
    the half-life of elimination should be
  • 00:02:24
    one point six five hour okay for
  • 00:02:28
    question number three you need to
  • 00:02:30
    extrapolate the graph just use your
  • 00:02:33
    ruler placed on the straight line and
  • 00:02:35
    look at the y-intercept you should get a
  • 00:02:37
    value approximately seventy six depend
  • 00:02:41
    on how you read the graph so this is my
  • 00:02:43
    estimation if your answer is slightly
  • 00:02:45
    deviate from my that will be also
  • 00:02:48
    acceptable now proceed to question
  • 00:02:50
    number four you need to identify the
  • 00:02:52
    volume to make it simple since I have
  • 00:02:56
    the initial concentration I'm going to
  • 00:02:58
    use C equal to dose divided by volume
  • 00:03:01
    from the question number three the
  • 00:03:04
    initial concentration is 76 divided
  • 00:03:07
    those three hundred from here you can
  • 00:03:09
    find the volume the volume you should
  • 00:03:12
    get is around three point ninety four
  • 00:03:15
    liter okay for question number five you
  • 00:03:20
    need to identify the concentration a
  • 00:03:22
    chav hour later so T is equal to twelve
  • 00:03:26
    using this equation for IV bolus EK t
  • 00:03:32
    the concentration you need to identify
  • 00:03:35
    the dose is 300 volume is three point
  • 00:03:38
    nine four e- k k is 0.42 x twelve
  • 00:03:45
    solving this equation the concentration
  • 00:03:49
    at T equal to 12 will be 0.49 so that's
  • 00:03:55
    it for question one you can proceed to
  • 00:03:58
    the next question
  • 00:04:00
    this question is very similar to the
  • 00:04:02
    previous questions except you have to
  • 00:04:05
    calculate the area under the curve using
  • 00:04:08
    the trapezoidal rule now you can pause
  • 00:04:11
    the video try the question and I will
  • 00:04:13
    explain to you later this is a graph you
  • 00:04:17
    should get and again by calculating the
  • 00:04:20
    gradient of the straight line you're
  • 00:04:22
    able to find the elimination rate
  • 00:04:24
    constant
  • 00:04:26
    and the next thing is by extrapolating
  • 00:04:28
    the graph the straight line to touch the
  • 00:04:32
    y-intercept you were able to find the
  • 00:04:34
    initial drug concentration the next
  • 00:04:37
    thing I want to remind you is about the
  • 00:04:39
    trapezoidal rule we are going to
  • 00:04:42
    calculate the area under the curve so
  • 00:04:44
    basically the concept is by cutting all
  • 00:04:47
    this time point into tiny little pieces
  • 00:04:51
    and add all the area together so I'm
  • 00:04:55
    going to use this example let's say I'm
  • 00:04:57
    going to calculate the area for time
  • 00:05:01
    point 3 to 4 hour and then the equation
  • 00:05:05
    will be 1/2 C 1 C 2 so what is C 1 and C
  • 00:05:11
    2 that will be the concentration over
  • 00:05:14
    here C 1 and C 2 and then multiplied by
  • 00:05:18
    the height the height will be the time
  • 00:05:21
    so in this case there will be 1 so by
  • 00:05:25
    adding all these tiny pieces together
  • 00:05:27
    you were able to find a you see I will
  • 00:05:30
    show you the calculation in the next
  • 00:05:33
    slide the first part is you have to
  • 00:05:36
    calculate the gradient that would be
  • 00:05:39
    negative ke equal to 1 C 2 minus 1 C 1
  • 00:05:45
    over T 2 T 1 over here I'm going to use
  • 00:05:49
    lon 0.2 minus lon
  • 00:05:53
    7 point 7 divided by 8 minus 0.5 so my
  • 00:05:58
    answer will be 0.49 for the second part
  • 00:06:03
    you need to find the half-life or
  • 00:06:05
    elimination this is simple 0.693 divided
  • 00:06:10
    by 0.49 your answer will be 1 point 4 1
  • 00:06:16
    ok for part 3 is about the y-intercept
  • 00:06:21
    so my one intercept over here 9.2 your
  • 00:06:26
    answer may be slightly different from my
  • 00:06:30
    depends on how you read the graph so now
  • 00:06:32
    we move on to part 4 you need to
  • 00:06:35
    identify the volume using this simple
  • 00:06:37
    equation
  • 00:06:39
    you have to concentration which is 9
  • 00:06:42
    point to those is 500 mg divided by
  • 00:06:45
    volume your volume will be 50 4.3 liter
  • 00:06:50
    and then the next one to identify the
  • 00:06:54
    clearance you use this equation k equal
  • 00:06:57
    to Clarisse divided by volume your ke is
  • 00:07:01
    0.49 equal to clearance divided by
  • 00:07:04
    volume 54.3 your clearance will be 20
  • 00:07:10
    6.6 liter per hour so we solve the five
  • 00:07:15
    question and we will move on to the
  • 00:07:16
    trapezoidal rule to make your
  • 00:07:20
    calculation easier you can generate a
  • 00:07:22
    table like this so I'm going to use the
  • 00:07:25
    time point 0 and 0.5 as example to
  • 00:07:29
    explain to you what is trapezoidal rule
  • 00:07:31
    let's say I have zero zero point five
  • 00:07:35
    the concentration will be nine point two
  • 00:07:37
    and seven point seven I'm going to
  • 00:07:40
    calculate the area for this area under
  • 00:07:43
    the curve the equation will be half C 1
  • 00:07:46
    plus C 2 multiplied by a high-cut in the
  • 00:07:50
    value I will have nine point two plus
  • 00:07:53
    seven point seven multiplied by 0.5 when
  • 00:07:57
    I calculate the answer it should be it
  • 00:07:59
    should be four point two two over here
  • 00:08:02
    you have to do this for all the interval
  • 00:08:06
    and you will get all the area if you sum
  • 00:08:10
    this up you should get nineteen point
  • 00:08:13
    one five
  • 00:08:16
    for the last concentration is going to
  • 00:08:19
    move until infinity how do we calculate
  • 00:08:22
    the area for the last concentration
  • 00:08:24
    point there will be zero point two
  • 00:08:27
    divided by ke remember your ke is 0.49
  • 00:08:32
    so the last piece over here is 0.41 now
  • 00:08:39
    add these two together and you should
  • 00:08:42
    get your answer nineteen point five six
  • 00:08:48
    okay so that is how we calculate a you
  • 00:08:51
    see this question is about intravenous
  • 00:08:55
    bolus administration you can now post
  • 00:08:57
    the video to attempt the questions the
  • 00:09:01
    first part you need to recommend the
  • 00:09:04
    bolus loading dose for this patient and
  • 00:09:06
    the equation I will use is concentration
  • 00:09:09
    equal to those divided by volume the
  • 00:09:12
    concentration will be 80 the dose
  • 00:09:15
    divided by volume so volume is 0.5 x 70
  • 00:09:20
    and you work out the D it should be 2800
  • 00:09:25
    M G so this is question number one for
  • 00:09:29
    question number two you need to
  • 00:09:31
    calculate for how long you can sustain
  • 00:09:35
    above 50 mg bolita so the target level
  • 00:09:41
    previously was 80 so how long will it
  • 00:09:44
    takes to drop from 80 to 50 so first of
  • 00:09:48
    all you need to construct the equation
  • 00:09:51
    that will be 50 equal to 80 multiplied
  • 00:09:55
    by e KP over here you need to solve the
  • 00:10:01
    K before you can solve the t 4k from the
  • 00:10:06
    question we know that the half-life is
  • 00:10:08
    16 hour so over here you can calculate
  • 00:10:12
    the K the K you will find it is zero
  • 00:10:20
    point zero four three so once you
  • 00:10:23
    identify the K you are going to
  • 00:10:25
    substitute back to the equation and then
  • 00:10:27
    you can solve the T now with that I'm
  • 00:10:31
    sure you're able to solve the question
  • 00:10:33
    that he will be 10.9 hour so it will
  • 00:10:38
    sustain for another ten point nine hour
  • 00:10:40
    before it go below the 50 mg per liter
  • 00:10:44
    level in question number three we have
  • 00:10:49
    two different concentration so one is to
  • 00:10:52
    our one is for our and this is 82 that
  • 00:10:59
    is 64
  • 00:11:01
    so over here we need to identify what is
  • 00:11:06
    the concentration at 12 hour later so
  • 00:11:11
    first of all I'm going to calculate the
  • 00:11:13
    ke using these two information over here
  • 00:11:16
    so lon
  • 00:11:18
    64 minus lon 82 that will be 4 minus 2
  • 00:11:26
    calculating the ke that will be 0.125 so
  • 00:11:32
    that is my first information to
  • 00:11:35
    calculate the concentration here I will
  • 00:11:37
    use C 12 is equal to C 4 x EK y it is a
  • 00:11:46
    tower over here because of the interval
  • 00:11:48
    that will be c 12 equal to 64 multiplied
  • 00:11:54
    by e 0.125 multiplied by 8 if that my
  • 00:12:00
    answer to be 23.7 that's it for question
  • 00:12:07
    3 I hope you are familiar with
  • 00:12:11
    intravenous bolus administration from
  • 00:12:13
    this question onwards we will practice
  • 00:12:15
    the calculation for intravenous infusion
  • 00:12:19
    administration now you can post a video
  • 00:12:21
    to attempt the questions to solve this
  • 00:12:25
    question you need to sketch out the
  • 00:12:27
    graph to get a better picture what is
  • 00:12:30
    happening this is to our you have a
  • 00:12:33
    concentration equal to 3 and a
  • 00:12:36
    concentration equal to 6 that will be 16
  • 00:12:40
    and 5 first of all I will need two
  • 00:12:43
    softer ke you can use the lon C 2 minus
  • 00:12:47
    1 C 1 equation divided by T 2 minus T 1
  • 00:12:50
    over here I'm going to use a different
  • 00:12:52
    method there will be 5 equal to 16 x EK
  • 00:12:58
    3 so this is actually C 6 equal to C 3
  • 00:13:04
    multiplied by e k3 so over here
  • 00:13:08
    we need to find a K the 3 is the
  • 00:13:12
    interval between the two concentration
  • 00:13:15
    so over here you should able to find out
  • 00:13:18
    the K E is 0.39 so this is the first
  • 00:13:23
    answer and for the part two you need to
  • 00:13:27
    find volume in order for you to find the
  • 00:13:31
    volume you must remember this equation k
  • 00:13:34
    equal to current divided by volume over
  • 00:13:37
    here you have K but you can find
  • 00:13:42
    clearance from the information over here
  • 00:13:46
    so the equation for me to identify the
  • 00:13:50
    clearance is C equal to sort factor in
  • 00:13:54
    fusion rate 1 minus K time of infusion a
  • 00:13:59
    minus K time - time of infusion over
  • 00:14:03
    here I need to identify the infusion
  • 00:14:07
    rate it is given in the question 10 mg
  • 00:14:11
    per minute that will be equivalent to
  • 00:14:14
    600 mg per hour
  • 00:14:17
    always remember infusion rate is always
  • 00:14:20
    in our so soft factor is not given we
  • 00:14:23
    assume is 1 and over here I'm going to
  • 00:14:26
    use 16 as my example 16 is equal to 600
  • 00:14:33
    and the clearance I need to identify a -
  • 00:14:37
    0.39 x - the infusion time is 2 Alba a -
  • 00:14:43
    3 0.39 time point number 3 - 2 our
  • 00:14:48
    infusion so soft the clearance you will
  • 00:14:51
    get thirteen point seven five liter per
  • 00:14:55
    hour now we have both K and CL you can
  • 00:15:01
    calculate the volume easily using K CL
  • 00:15:05
    volume zero point three nine is equal to
  • 00:15:10
    thirteen point seven five divided by V V
  • 00:15:14
    will be thirty five point three liter so
  • 00:15:20
    that is volume okay part three part
  • 00:15:25
    three you need to identify
  • 00:15:28
    inclusion rate for you to achieve 20 mg
  • 00:15:31
    per liter so this is a steady state you
  • 00:15:34
    need to use CSS equal to as IR /
  • 00:15:39
    clearance the target is 20 soft factor
  • 00:15:43
    is 1 inclusionary unknown the clearance
  • 00:15:46
    thirteen point seven five so easily you
  • 00:15:51
    can identify the infusion rate should be
  • 00:15:53
    275 mg per hour so that's it for this
  • 00:15:58
    question this question is a bit longer
  • 00:16:01
    we have five questions in total I will
  • 00:16:05
    first explain the three questions and
  • 00:16:06
    then follow up by the other two
  • 00:16:09
    questions later
  • 00:16:10
    you can now post a video to attempt the
  • 00:16:12
    questions for part one you need to
  • 00:16:16
    identify the profile using population
  • 00:16:19
    kinetic equation for clearance it is 80
  • 00:16:23
    kg multiplied by 0.04 and there is also
  • 00:16:28
    a factor of 0.8 you should include
  • 00:16:30
    because the patient is suffering from
  • 00:16:33
    Coad the answer for this will be 2 point
  • 00:16:37
    5 6 liter per hour now for volume of
  • 00:16:42
    distribution is zero point four eight
  • 00:16:44
    multiplied by 80 that is 38.4 meter the
  • 00:16:51
    last one the KE you can calculate using
  • 00:16:55
    clearance divided by volume that will be
  • 00:16:58
    zero two point five six two point five
  • 00:17:02
    six divided by thirty eight point four
  • 00:17:05
    the ke will be zero point zero six seven
  • 00:17:10
    so easily you can identify Audis and
  • 00:17:13
    question number two you need to
  • 00:17:17
    recommend the bolus loading dose as well
  • 00:17:20
    as infusion to maintain the level at
  • 00:17:23
    hand mg per litre so for bolus that will
  • 00:17:28
    be concentration shot factor dose
  • 00:17:31
    divided by volume for aminophylline to
  • 00:17:35
    toe for analysis factor of zero point
  • 00:17:37
    seven nine so remember you have to
  • 00:17:39
    include the salt
  • 00:17:40
    factor the target is ten 0.79 x d the
  • 00:17:46
    volume estimate that he study it by for
  • 00:17:49
    the the recommended amount will be 486
  • 00:17:55
    mg for the bolus loading dose to
  • 00:17:58
    maintain the level at 10 mg per liter
  • 00:18:02
    there will be CSS SI r / clearance the
  • 00:18:08
    target is 10 shot factor 0.79 infusion
  • 00:18:13
    rate clearance is two point five six the
  • 00:18:17
    infusion rate should be 32 point 1 mg
  • 00:18:23
    per hour okay so move on to question
  • 00:18:28
    number three for question number three
  • 00:18:31
    it is a bit longer because we are
  • 00:18:33
    combining two different dose we have a
  • 00:18:36
    bolus followed by a continuous infusion
  • 00:18:41
    the graph you should see will be
  • 00:18:45
    something like this this is from the
  • 00:18:47
    bolus and you have a continuous infusion
  • 00:18:52
    and then combined is to you need to find
  • 00:18:56
    what is the concentration at six hour
  • 00:18:59
    later so let us try to solve this
  • 00:19:02
    question the equation is a bit longer
  • 00:19:05
    the concentration at six hour you'll be
  • 00:19:09
    the bolus ekp plus the infusion ir our
  • 00:19:18
    clearance one - EK time of infusion over
  • 00:19:25
    here soft factor zero point seven nine
  • 00:19:28
    multiply the dose four hundred divided
  • 00:19:32
    by the volume 38.4 multiplied by e k
  • 00:19:38
    zero point zero six seven x 6 plus zero
  • 00:19:44
    point seven nine and infusion rate of 40
  • 00:19:49
    divided by clearance the clearance
  • 00:19:53
    2.5 6 y- 0.067 x 6 so over here you
  • 00:20:01
    should get 5.5 1 plus 4 point 0 7 the
  • 00:20:08
    final answer the concentration is five
  • 00:20:11
    nine point five eight okay I hope you
  • 00:20:16
    can understand up to this path question
  • 00:20:20
    four and five to test your understanding
  • 00:20:23
    for continuous steady state infusion you
  • 00:20:27
    can pause the video to attempt the
  • 00:20:30
    questions for question number four your
  • 00:20:34
    patient is given the infusion of 40 mg
  • 00:20:38
    per hour
  • 00:20:40
    after some time you will reach the
  • 00:20:42
    steady state and the measurement for the
  • 00:20:46
    level will be 15 mg per liter so over
  • 00:20:50
    here we need to identify what is the
  • 00:20:53
    actual clearance in order to calculate
  • 00:20:57
    that we use CSS as AI R divided by
  • 00:21:02
    clearance the measured concentration is
  • 00:21:05
    15 sought factor zero point seven nine
  • 00:21:08
    multiplied by infusion rate and the
  • 00:21:12
    clearance over here we can find a
  • 00:21:15
    clearance is two point one ETA power for
  • 00:21:21
    question number five you need to target
  • 00:21:23
    the concentration at 10 mg per liter so
  • 00:21:26
    using the actual clearance in this case
  • 00:21:29
    same equation over here the target is 10
  • 00:21:34
    shot factor zero point seven nine
  • 00:21:37
    infusion rate unknown and the actual
  • 00:21:41
    clearance is two point one solving this
  • 00:21:43
    your answer will be twenty six point six
  • 00:21:47
    mg per hour so that's all for our
  • 00:21:53
    practice question I hope you have
  • 00:21:55
    learned and improve your understanding
  • 00:21:57
    for the calculation thank you very much
Tags
  • intravenous
  • bolus
  • infusion
  • elimination rate
  • half-life
  • concentration
  • volume
  • clearance
  • trapezoidal rule
  • pharmacokinetics