4 pages due by 20 hrs

1_PK-PDExcelfileforPrimerHomework.xlsx

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Intravenous

					These equations are for reference only. You do not have to use them to complete your homework. But they help to understand the results!
					Plasma concentration (Cp) for one compartment model with iv bolus dosing and first order elimination
							Cp= (D/Vd)exp(-ket)
					Equation for extension of duration of action
Using the model in this worksheet, please answer the questions in the handout					Ci is the plasma concentration at a given time, assumed to be Ci>Ceff
Please do not change any of the calculations					Delta teff is for how much longer the drug will be active (above Ceff) for a given half-life
You only have to change some of the values of some of the parameters in bold red					This equation can be derived from the Cp(t) equation above
This plot describes the plasma concentration (Cp) of an ideal drug after administration of an intravenous bolus
(There are no drugs with this simple pharmacokinetic behavior, but it is a simple illustrative example)
The drug is considered active in the patient if its plasma concentration is superior to a threshold value "Ceff" determined from previous clinical experience
Parameter		Abbreviation	Units	Your Values
Elimination half-life		t1/2 (elim)	h	10.0		Same plot, with Y axis set to maximum Cp 10 ug/ml
Dose		D	mg/person	45
Active plasma concentration threshold		Ceff	ug/ml	3.0
	Don't touch these cells
	Elimination rate	ke	1/h	0.069
	Apparent volume of distribution	Vd	L/person	14
		Threshold plot	Time (h)	Ceff (ug/ml)
			0	3.0
			25	3.0
			Don't touch these cells
				Plot
			Time (h)	Cp (ug/ml)
			0	3.2
			0.1	3.2
			0.25	3.2
			0.5	3.1
			1	3.0
			1.5	2.9
			2	2.8
			3	2.6
			4	2.4
			5	2.3
			6	2.1
			8	1.8
			10	1.6
			12	1.4
			14	1.2
			16	1.1
			18	0.9
			20	0.8
			22	0.7
			24	0.609
			26	0.5
			28	0.5
			30	0.4

PK Intravenous Administration

Cp (ug/ml) 0 0.1 0.25 0.5 1 1.5 2 3 4 5 6 8 10 12 14 16 18 20 22 24 26 28 30 3.2142857142857144 3.1920830210476154 3.1590662096097355 3.104795342972718 2.9990346156540237 2.8968764869633832 2.7981982391661133 2.6108112740021858 2.435973053320283 2.2728432252424744 2.1206377137421519 1.8461223562452351 1.6071428571428572 1.3990991195830569 1.2179865266601415 1.060318856871076 0.92306117812261756 0.8035714285714286 0.69954955979152833 0.60899326333007087 0.53015942843553809 0.46153058906130884 0.40178571428571441 Ceff (ug/ml) 0 25 3 3

Time (h)

Cp (ug/ml)

PK Intravenous Administration

Time (h)

Cp (ug/ml)

Subcutaneous

CLRE-238	Applied Translational Research					These equations are for reference only. You do not have to use them to complete your homework. But they help to understand the results!
Spring 2021
PK-PD Primer Homework						Plasma concentration (Cp) for one compartment model with sc bolus dosing and first order elimination
Date	3/30/21
Claudio D. Schteingart Ph.D.
						C(t) is Cp the plasma concentration as a function of time
						f is the bioavailability (scale 0 to 1) of the drug in the sc space
Using the model in this worksheet, please answer the questions in the handout						ka is the absorption rate, ke is the elimination rate
Please do not change any of the calculations						D is the dose, Vd is the apparent volume of distribution
You only have to change some of the values of some of the parameters in bold red
						Equation for extension of duration of action
						Ci is the plasma concentration at a given time, assumed to be Ci>Ceff
						Delta teff is for how much longer the drug will be active (above Ceff) for a given half-life
						This equation can be used during the elimination phase of the above curve
This plot describes the plasma concentration (Cp) of an ideal drug after administration of a subcutaneous bolus
The drug is considered active in the patient if its plasma concentration is superior to a threshold value "Ceff" determined from previous clinical experience
If the absorption half-life equals the elimination half-life the math fails (division by zero). If needed, enter a slightly different value, e.g. 3.99 or 4.01 instead of 4.00
							Same plot, with Y axis set to maximum Cp 10 ug/ml
Parameter			Abbreviation	Units	Your Values
Absorption half-life			t1/2 (abs)	h	9.00
Elimination half-life			t1/2 (elim)	h	7.8
Dose			D	mg/person	300
Active plasma concentration threshold			Ceff	ug/ml	3.0
Don't touch these cells
		Subcutaneous bioavailability 0 to 1	f		1
		Apparent volume of distribution	Vd	L/person	14
		Absorption rate	ka	1/h	0.077
		Elimination rate	ke	1/h	0.089
		Multiplication factor	fDka/(Vd(Ka-ke))	ug/ml	-139
			Threshold plot	Time (h)	Ceff (ug/ml)
				0	3.0
				26	3.0
				Don't touch these cells
					Plot
				Time (h)	Cp (ug/ml)
				0	0.00
				0.1	0.16
				0.25	0.40
				0.5	0.79
				1	1.52
				1.5	2.19
				2	2.80
				2.5	3.35
				3	3.86
				3.5	4.32
				4	4.74
				5	5.45
				6	6.02
				7	6.47
				9	7.04
				11	7.30
				13	7.31
				15	7.14
				17	6.86
				19	6.50
				21	6.09
				23	5.65
				24	5.43
				25	5.21
				26	4.99
				27	4.77

PK Subcutaneous Administration

Cp (ug/ml) 0 0.1 0.25 0.5 1 1.5 2 2.5 3 3.5 4 5 6 7 9 11 13 15 17 19 21 23 24 25 26 27 0 0.16367190140838342 0.40412076579165146 0.79165592858399969 1.5190008883941082 2.1859595477621125 2.7962433329170779 3.3533613076132611 3.860630519029991 4.3211858354398114 4.7379892999460402 5.4513776389343889 6.0213625102136206 6.4662710223426938 7.0443072238819076 7.2953930015832285 7.3060037971859826 7.1437892527819962 6.8613160040050376 6.4991043312597387 6.0880874552893225 5.6515993222877396 5.4294186994073046 5.2069777995194295 4.9857184390268072 4.7668546007904764 Ceff (ug/ml) 0 26 3 3

Time (h)

Cp (ug/ml)

PK Subcutaneous Administration

Time (h)

Cp (ug/ml)