intravenous infusion previous rates of administration were instantaneous iv bolus and first order...
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Intravenous InfusionIntravenous Infusion
Previous rates of administration were
instantaneous IV bolusinstantaneous IV bolus and
first order absorption.first order absorption.
As a rate (mg/hr) a first order rate
constantly declineseven though a
constant percentage of
what remains is handled.
Intravenous InfusionIntravenous Infusion
A first order rate (ka) such as 0.693 hr-1, will peak at about 2.6 hours when the
T½ = 4 hours.
If we deal with ka as we would K, since
ka = 0.693, then T½ka = 1 hour.
This means that followinga 400 mg dose:
Time Am’t Unabs 1 200 2 100 3 50 4 25 5 12.5 6 6.25
25 mg/hr
100 mg/hr
6.25 mg/hr
Intravenous InfusionIntravenous Infusion
A zero order rate is constant (mg/hr).
With a 400 mg dose, a rate of 200mg/hr results in all drug
being delivered in 2 hours
Time Am’t Delivered
hr (mg) 1 200 2 200 3 0
25 mg/hr
100 mg/hr
6.25 mg/hr
Zero-Order Rate200 mg/hr
Tmax = 2 hours
The infusion rate is identified as k0
with units of am’t/time.
Intravenous Infusion-continuousIntravenous Infusion-continuous
If a drug is infused at a constant rate (4 mg/hr)
for a long period of time, concentrations will rise
and approach a constant concentration (CSS).
At that concentration (CSS), the rate of elimination of the drug equals the
infusion rate.
IN = OUT
CSS = k0/VK
Zero-Order Rate4 mg/hr
Approaching maximum concentration of 7.3 mg/L
Intravenous Infusion-continuousIntravenous Infusion-continuous
Number Percent Of of CSS
T½
1 50.0 2 75.0 3 87.5 4 93.75 5 96.875 6 98.438 7 99.219
Zero-Order Rate4 mg/hr
Approaching maximum concentration of 7.3 mg/L
The rate at which the steady-state concentration
is approached is proportional
to the half-life.
Intravenous InfusionIntravenous Infusion
Many drugs are administered by
intermittent intravenous infusions, where the time of the infusion is short and SS is not achieved.
15 min - -lactams30 min – aminoglycosides
1 hr vancomycin 4 hour amphotericin.
For these drugs the infusion rate (mg/hr) is:
k0 = dose / infusion time
IV Intermittent InfusionDose = 400 mg
Infusion Time = 2 hoursInfusion Rate (k0) = 200 mg/hr
Intravenous InfusionIntravenous Infusion
During the infusion period the concentrations increase.
The equation predicting these concentrations is:CSS = (k0/KV) *(1-e-kt)
This has rough similarity to the oral dosing equation
IV Intermittent InfusionDose = 160 mg
Infusion Time = 4 hoursInfusion Rate (k0) = 40 mg/hr
Vol = 10 L; T½ = 2hrCSS = 8.66 mg/L
Dose Clearance
Intravenous InfusionIntravenous Infusion
During the infusion period the concentrations increase.
The equation predicting these concentrations is:CSS = (k0/KV) *(1-e-kt)
Here 160 mg is infused over 4 hours to a patient with a V of 10 L and a
half-life of 2 hours
IV Intermittent InfusionDose = 160 mg
Infusion Time = 4 hoursInfusion Rate (k0) = 40 mg/hr
Vol = 10 L; T½ = 2hrCSS = 8.66 mg/L
The concentration at the end of the infusion (4 hr) is: CSS = (k0/KV) *(1-e-kt) = (40/(0.3465 * 10))*(1--0.3465*4) = (11.54)(1-0.25) = 8.66 mg/L
Intravenous InfusionIntravenous Infusion
During the infusion period the concentrations increase.
The equation predicting these concentrations is:CSS = (k0/KV) *(1-e-kt)
Here 160 mg is infused over 4 hours to a patient with a V of 10 L and a
half-life of 2 hours
IV Intermittent InfusionDose = 160 mg
Infusion Time = 4 hoursInfusion Rate (k0) = 40 mg/hr
Vol = 10 L; T½ = 2hrCSS = 8.66 mg/L
What is the Cl in this patient? Cl = KV
= 0.3465 * 10= 3.465 L/hr
If the infusion is continuous CSS = (k0/KV) *(1-e-kt) = (k0/KV) Cl can be obtained from k0 & CSS
Intravenous InfusionIntravenous Infusion
As soon as the infusion is complete, the concentrations will begin to decline. If distribution is instantaneousThis equation calculates the concentration from the start of the infusion to the end of the infusion at time t
CSS = (k0/KV) *(1-e-kt)
This equation calculates the concentration from the END of the infusion on and so t is the duration of infusion and t’ is the time from the end of the infusion
CSS = [(k0/KV) *(1-e-kt)]e-Kt’
Intravenous InfusionIntravenous Infusion
This equation calculates the concentration from the END of the infusion on and so t is the duration of infusion and t’ is the time from the end of the infusion
CSS = [(k0/KV) *(1-e-Kt)]e-Kt’
To calculate the concentration at 6 hours from the Start of a 4 hour infusion, t will be 4 hours and t’ is the time from the end of the infusion to the time ofinterest – 2 hours.
CSS= [(k0/KV) *(1-e-kt)]e-Kt’
= [(11.54)(1-0.25)]e-0.3465*2
= [8.66]*0.500 = 4.33 mg/L
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Intravenous InfusionIntravenous Infusion
This equation will calculate the concentrations during the infusion but requires that the time t’ is zero.
Example:Calculate the concentration @ 2 hours
CSS = [(k0/KV) *(1-e-Kt)] e-Kt’
= (11.54)*(1-e-0.3465*2) e-0.3465*0
= [(11.54)(1-0.50)] x 1 = [11.54*0.500] x 1 = 5.77 mg/L
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Time Conc(hr) (mg/L) 6 3.333 8 1.667
1. What loading dose would achieve the end of infusion concentration immediately?2. Would a loading dose be considered necessary for this drug in this patient?
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Time Conc(hr) (mg/L) 6 3.333 8 1.667
[ ] end of infusion requires K.
T½ = 2 hours; K = 0.3465 hr-1
C4 = 3.333 eKt
= 3.333 e(0.3465 * 2)
= 6.667 mg/L
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Time Conc(hr) (mg/L) 6 3.333 8 1.667
Calculate Volume:C4 = [(k0/KV) *(1-e-Kt)]e-Kt’
V = [(k0/KC4) *(1-e-Kt)]e-Kt’
t’= 0; t=4; C4 = 6.667; k0=50 mg/hr
V = [(50/(0.3465*6.667) *(1-e-0.3465*4]= 16.23 L
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Volume based on this concentration8
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Time Conc(hr) (mg/L) 6 3.333 8 1.667
1. What loading dose would achieve the end of infusion concentration immediately?
Load = V * CSS
= 16.23 L * 6.667 mg/L= 108.21 mg
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Time Conc(hr) (mg/L) 6 3.333 8 1.667
1. What loading dose would achieve the end of infusion concentration immediately?2. Would a loading dose be considered necessary for this drug in this patient?
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Intravenous InfusionIntravenous Infusion
QuestionA patient is given an intravenousinfusion of 200 mg over 4 hours. Six and 8 hrs after the infusion began samples were taken and the concentrations measured.
Would a loading dose be considered necessary for this drug in this patient?
How long does it take to get to steady state?
3.3 (90%) – 5 (96.8) T½With a T½ of 2 hours
…between 6.6 and 10 hours.
Bolus?? How rapid is response required?Does a 108.2 mg bolus achieve CSS?
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Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a continuous infusion (> 24 hr) what is the steady-state concentration?
Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a continuous infusion (> 24 hr) what is the steady-state concentration?
CSS = [(k0/KV) *(1-e-Kt)]When t is large e-Kt becomes Small and equation becomesCSS = [(k0/KV)]
= 50 (0.3465 x 16.23)= 8.89 mg/L
What bolus loading dose would achieve this true
steady-state?
Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a continuous infusion (> 24 hr) what is the steady-state concentration?
CSS = [(k0/KV) *(1-e-Kt)]When t is large e-Kt becomes Small and equation becomesCSS = [(k0/KV)]
= 50 (0.3465 x 16.23)= 8.89 mg/L
Load = Css V= (8.89 mg/L)(16.23 L)= 144.3 mg
Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a bolus of 144.3 mg and simultaneously receives an intravenous infusion of 50 mg/hr, what will the concentration-time profile look like? … what concentrations are attained?
Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a bolus of 144.3 mg and simultaneously receives an intravenous infusion of 50 mg/hr, what will the concentration-time profile look like? … what concentrations are attained?
What would the initial concentration of the bolus be?
C0 = Dose / V= 144.3 mg / 16.23 L= 8.89 mg/L
Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a bolus of 144.3 mg and simultaneously receives an intravenous infusion of 50 mg/hr, what will the concentration-time profile look like? … what concentrations are attained?
What would the concentration-time profile for the bolus look like?
T½ =
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Intravenous InfusionIntravenous Infusion
QuestionIf this patient receives a bolus of 144.3 mg and simultaneously receives an intravenous infusion of 50 mg/hr, what will the concentration-time profile look like? … what concentrations are attained?
What would the concentration-time profile for the bolus look like?
T½ = 2 hours
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Should the conc.–time profilefrom the bolus and the simultaneous
infusion just be the sum of both profiles?
Intravenous InfusionIntravenous Infusion
QuestionTime Bolus Infusion Total (hr) (mg/L) (mg/L) (mg/L) 0.0 8.891 0.00 8.891 0.5 7.477 1.414 8.891 1.0 6.287 2.604 8.891 1.5 5.287 3.604 8.891 2.0 4.446 4.445 8.891 3.0 3.144 5.747 8.891 4.0 2.223 6.668 8.891 6.0 1.112 7.779 8.891 8.0 0.556 8.335 8.89112.0 0.139 8.752 8.89116.0 0.035 8.856 8.89124.0 0.002 8.889 8.891
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Intravenous InfusionIntravenous Infusion
QuestionTime Bolus Infusion Total (hr) (mg/L) (mg/L) (mg/L) 0.0 8.891 0.00 8.891 0.5 7.477 1.414 8.891 1.0 6.287 2.604 8.891 1.5 5.287 3.604 8.891 2.0 4.446 4.445 8.891 3.0 3.144 5.747 8.891 4.0 2.223 6.668 8.891 6.0 1.112 7.779 8.891 8.0 0.556 8.335 8.89112.0 0.139 8.752 8.89116.0 0.035 8.856 8.89124.0 0.002 8.889 8.891
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2When bolus and infusion
are exactly matched concentration starts at true steady state
and remains unchanged
Intravenous InfusionIntravenous Infusion
Question
What happens if the bolusis larger or smaller?
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