Additional Information - Maple worksheets used in "Physiologically based
pharmacokinetic modeling of arteriovenous concentration differences" by David
G. Levitt; Department of Physiology; University of Minnesota.
I. Ethanol arterial and antecubital vein data and worksheet.
> with(gensolve):
> ethanol_jones:=proc()
Data from Jones et. al. J of Forensic sciences 42: 1088, 1997
Measure arterial, antecubital vein and breath and also arterail data for one individal
ethanol average data for 13 healthy men - average age 31, weight 77 Kg, dose of 0.4 gm/kg
infused at constant rate for 30 minutes
Blood ethanol in unit of mg/dl
> local i,datafile,tdata,xscale;
> defaultpar():
> Wtot:= 70.0; #Arbitray since ethanol dose is per Kg
> standardhuman2(Wtot);
> Fat := 0.2;# averge value for men
> cunit:= "millimoles";
> concunit[vein] :=2;#whole blood conc
> Vm[liver]:= 2.45331; Km[liver]:= .09569;#best vallue
for this data
Kfwat:=0.074;
ninput:=1;findabs:=0;
> finput[1]:=
table([organ=vein,type=1,rate=608/30,tbeg=0,tend=30,csteady
=0,padjust=0]);#Iv infusion of .4 gm/Kg for 30 minutes
> pdata:=2;
> xscale:=0.217; #convert from mg/dl to mm/liter
Arterial data for control subjects
> data[1]:= [[0., 0.], [10., 11.39350688], [20.,
16.62727129], [30., 20.57272623], [35., 14.65454599], [40.,
12.96363642], [45., 11.83636482], [50., 10.95064894], [55.,
10.26623311], [60., 9.70259731], [75., 8.33376565], [90.,
7.44805194], [120., 5.39480445], [150., 3.77797], [180.,
2.25454537], [210., 1.207792271]];
Antecubital vein data for control subjects.
data[2]:=[[0., 0.], [10., 7.56896651], [20., 14.03370248],
[30., 17.86119188], [35., 13.76079286], [40., 12.18686496],
[45., 11.21175484], [50., 10.61896639], [55., 9.887297077],
[60., 9.475822762], [75., 8.270241612], [90., 7.547778478],
[120., 5.656797013], [150., 4.120110862], [180.,
2.794112615]];
> end proc:
II. Thiopental Worksheets:
thiopental_barratt:=proc()
Data from Barratt et. al Brit. J. Anesth. 1984, 56: 1385 Administered 5mg/Kg thiopental at constant rate over 30 second period - sampled
arterial, antecubital, central and jujular vein simultaneously.
> local i,datafile;
> defaultpar():
> Wtot:= 70; #Arbitrary - since dose/kg
standardhuman2(Wtot);
> Fat:=0.26;#No information
> cunit:="milligrams";
> concunit[vein] :=4;#plasma concentration of vein
findabs:=0;
rblpl:=0.94;# required if use freepl
freepl:= 0.15; #fraction free in plasma - this turns on use
of ktiss[i]
X:=0.5; #30 second injection
ninput :=1;
finput[1]:=table([organ=vein,type=1,rate=5*70/X,tbeg=0,
tend=X,csteady=0,padjust=0]);#bolus input
for i from 2 to N do ktiss[i]:=1.0;end do;
ktiss[liver]:=3;ktiss[kidney]:=3;
ktiss[muscle]:=0.8;
ktiss[lipid]:=6;
Tclr[liver]:=3.5;
> De[liver]:=0.3;
> pdata:=2;
data[1]:=[[0,0],[1.0,51.5],[1.5,35.8],[2,22.5],[2.5,13.9],[
3,11],[3.5,10],[4.5,9],[5.5,8.1],[7.5,6.9],[9.5,5.7],[12.5,
4.7]];# Arterial concentration
data[2]:=[[0,0],[1.0,11.7],[1.5,17.4],[2,15.1],[2.5,12.8],[
3,9.8],[3.5,8.6],[4.5,7.4],[5.5,7],[7.5,5.9],[9.5,5.3],[12.
5,4.6]];# Antecubital concentration
>data[3]:=[[0,0],[1.0,11.7],[1.5,17.4],[2,15.1],[2.5,12.8],[
3,9.8],[3.5,8.6],[4.5,7.4],[5.5,7],[7.5,5.9],[9.5,5.3],[12.
5,4.6]];#
> end proc:
> thiopental_stanski:=proc()
Data from Stanski et. al. J. of Pharmacokin. and Biopharm. 12: 223, 1984
Arterial and antecubital veins samples from 1 subject
6 min constant infusion at rate of 150 mg/min in healthy male patients (no body wt
given)
Times are not given - must be read off graph
> local i,datafile;
> defaultpar():
> Wtot:= 65; #Not Known - adjusted to fit data
standardhuman2(Wtot);
> Fat := 0.2;#Guess for normal male patients
> cunit:="milligrams";
> concunit[vein] :=4;#plasma concentration of vein
concunit[muscle]:=2;concunit[lipid]:=2;#mg/liter of tissue
findabs:=0;
rblpl:=0.94;# required if use freepl
freepl:= 0.15; #fraction free in plasma - this turns on use
of ktiss[i]
ninput :=1;
finput[1]:=table([organ=vein,type=1,rate=150,tbeg=0,
tend=6,csteady=0,padjust=0]);#bolus input
for i from 2 to N do ktiss[i]:=1.0;end do;
ktiss[liver]:=3;ktiss[kidney]:=3;
ktiss[muscle]:=0.8;
ktiss[lipid]:=6;
Tclr[liver]:=1.5;
De[liver]:=0.3;
> pdata:=2;
data[1]:=[[2., 22.86466], [3., 42.6147], [4., 46.20732],
[5., 51.04743], [6., 56.39452], [6.3, 51.68705], [8.,
33.42763], [10., 27.56026], [12.5, 22.02628], [15.,
18.85135], [18., 17.17052]];
print("data[1]=",data[1]);
data[2]:=[[2.0, 7.317163], [3., 16.03393], [4., 23.00747],
[5., 33.22015], [6., 44.23674], [6.3, 46.7863], [8.,
30.44713], [10., 24.9471], [12.5, 19.93784], [15.,
17.06394], [18., 15.44601]];
print("data[2]=",data[2]);
> end proc:
III. DPTA worksheet
> with(gensolve):
> dtpa_cousins_2:=proc()
Data from Cousins .. Peters et. al. Nuclear Medicine Communications, 1999, 20 1047
IV Injected (about 15 second) in labeled DTPA (about 200 MBq, but obiously much
variability) and about 5 grams of inulin
Sampled arterial and antecubital venous (with a delay of 30 seconds)This data is from fig. 2 which shows arterial and A-V difference for 3 sugjects: - Subject
2
Since do not know dose or body weight, adjust dose to fit initial points
> local i,datafile1,datafile2,tdata,xscale;
> defaultpar():
> Wtot:= 70.0; #Arbitray since ethanol dose is unknown and
is adjusted
> standardhuman2(Wtot);
> Fat := 0.2;# averge value for men
> cunit:= "cpm";
> concunit[vein] :=4;#plasma conc
> rclr:=0.096;
> mecf:=1;
> pdata:=1;
> ninput:=1;findabs:=0;
X:=0.25;#Inject in 15 seconds (= .25 minutes)
> finput[1]:=
table([organ=vein,type=1,rate=6600000*0.25/X,tbeg=0,tend=X,
csteady=0,padjust=0]);
> pdata:=2;
> data[1]:=[[0., 0.], [2.5, 238759.7], [3.5, 191279.1],
[4.5, 167538.8], [6.5, 139050.4], [8.5, 126162.8], [10.5,
118023.3], [15.5, 99709.3], [20.5, 94282.95], [30.5,
80717.05], [40.5, 73255.81], [50.5, 67151.16], [60.5,
61724.8]];
print("data[1]=",data[1]);
>
data[2]:=[[0., 0.], [3., 153973.], [4., 146512.], [5.,
138372.], [7., 122780.], [9., 118023.], [11., 112597.],
[16., 96996.], [21., 90282.], [31., 80717.05], [41.,
73255.81], [51., 67151.16], [61., 61724.8]];
print("data[2]=",data[2]);
> end proc:
IV. Ketamine
ketamine_R:=proc()
Data from Persson et. al. Eur. J. Clin. Pharm. 2002 57:869
Arterial and arm vein R-ketakine after 30 minute IV infusion
Ave for 10 young Male subjects - (one old = 62) average wt = 76 Kg
Plasma Concentraton normalizied for dose: (nanograms/ml/mg dose)
> local i,datafile;
> defaultpar():
> Wtot:= 76;
standardhuman2(Wtot);
> Fat := 0.2;#Males
> cunit:="micrograms";
> concunit[lipid]:=2;
> concunit[vein] :=4;#plasma concentration of vein
findabs:=0;
rblpl:=0.83;# required if use freepl
freepl:= 0.4; #fraction free in plasma - Hijazi et. al.
Eur. J. clin. Phar. 2002 58:37
X:=30; #30 minute IV constant infusion
ninput :=1;
finput[1]:=table([organ=vein,type=1,rate=1000*237/(237+36)/
X,tbeg=0, tend=X,csteady=0,padjust=0]);#Plasma values
normalized to 1 mg dose of ketamine HCL
for i from 2 to N do ktiss[i]:=4;end do;
ktiss[kidney]:=20;
ktiss[lipid]:=10;
Tclr[liver]:=3;
ktiss[muscle]:=2;
pdata:=2;
De[liver]:=0.3;
> data[1]:=[[0., 0.], [5., 6.122353], [10., 7.786362], [15.,
10.01598], [20., 10.84832], [25., 11.48111], [30.,
11.5157], [40., 4.665677], [50., 3.203885], [60.,
2.473545], [180., .934]];
data[2]:=[[0., 0.], [5., 2.261435], [10., 4.155747], [15.,
5.884456], [20., 6.283622], [25., 7.115176], [30.,
8.178945], [40., 4.891003], [50., 3.596365], [60., 2.767],
[180., 1.06]];
> print("data[1]=",data[1]);
print("data[2]=",data[2]);
> end proc:
V. D2O Worksheet.
> with(gensolve);
> D20_schloerb:=proc()
Data from fig. 7, Schloerb et. al. J. C. I. 29: 1296. 1950. Arterial blood D20
concentration.
Subject JO -Body weight 81.9 gms, Total body water = 48 liters.
Since equilibrium D2O conc. is 0.144 vol %, this indicates that 69.05 ml was injected,
or 276 ml/min for 15 seconds.
Use cunit = 10 ml so that unit of vol% corresponds to 10 ml/liter. In this unit, 276
ml/sec = 27.6 (10 ml)/sec.
Adjusted wrfract[i] so that using standard fat of 20% give the correct water volume.
> local i,datafile,tdata;
> defaultpar():
> Wtot:= 81.9;
> standardhuman2(Wtot);
> cunit:= " 10 ml D20";
> rclr:= 0.0022*Wtot/70; # water loss of 7.7% of total
body water/day
> concunit[artery] :=3;#water conc
> ninput:=1;findabs:=0;
> finput[1]:=
table([organ=vein,type=1,rate=27.6,tbeg=0,tend=.25,csteady=
0,padjust=0]);#15 second IV infusion of 69 ml of 100% D20
> pdata:=2;
> data[1]:=[[.6, 1.030014], [1.617467, .515404], [2.040738,
.4632552], [2.629491, .4324928], [3.29232, .3986502],
[3.654996, .3710066], [5.20962, .3047937], [10.71824,
.2406334], [14.88098, .2120204], [39.47748, .161358], [60.,
.144]];
If want to plot arterial/venous ratio - data[1] and data[2] must have identical time points
data[2]:=[[1.617467,
0.1614964],[3.654996,
0.1700552],[10.71824,
0.155446],[24.9747,
0.1539505],[39.47748,
0.161358],[60,
0.144]];#antecubital vein data
> end proc:
VI. Acetone Worksheet:
> acetone:=proc()
Data from Wigaeus et. al. Scand. J. work env. and Health 7 (1981) 84
Data for arterial, venous and end alveolar from Series1 (mg/Kg blood)
Ave. of 8 subjects - at rest
Insired conc. - 1309 mg/M^3 - Expired conc. (end alveolar) is constant at about 500
mg/M^3
This corresponds to a constant input of alveolar vent(liters) * (0.809 mg/liter) to the
lung TISSUE (not to alveolar space)
Set avent = -1 - this shuts off alveolar lung exchange and simply inputs to lung
tissue
There is an endogenous acetone level at t=0 of 1.3 mg/Kg that has been subtracted.
> local i,datafile,Kfair;
> defaultpar():
> Wtot:= 70; #Arbitrary - Input normalized by alveolar
respiraton
standardhuman2(Wtot);
> Fat:=0.16;
> klip[vein]:=0.01;
> cunit:="mg";
> concunit[1] :=2;# experimental output = blood conc
ninput :=1;
inprate:=6.0*(0.809);#constant input = alvent *(inhaled end alveolar)
finput[1]:=table([organ=lung,type=1,rate=inprate,tbeg=0,
tend=120,csteady=0,padjust=0]);#30 min hour input of 870
mg/M^3
Tclr[liver]:=0.0;
Kfair:=80;
Kbair:= 300;
alvent:= -1;
Kfwat:=Kfair/Kwair;
Kfbld:=Kfair/Kbair;
> fr_arm[muscle]:=0.5;
> pdata:=2;
data[1]:=[[0., 0.], [3.2714, 1.322324], [5.138337,
2.00705], [10.43489, 2.845844], [14.97688, 3.532263],
[20.2783, 4.295113], [24.82759, 4.867612], [30.15335,
5.25073], [35.46694, 5.823713], [39.63165, 6.433944],
[45.35173, 6.627437], [50.27586, 7.314099], [55.21947,
7.696974], [59.76146, 8.383393], [64.69534, 8.91816],
[70.00893, 9.49114], [74.97444, 9.53226], [79.90345,
10.14298], [84.82028, 10.94356], [89.77119, 11.21251],
[95.09209, 11.67158], [100.0552, 11.75067], [104.6337,
11.86749], [109.5505, 12.66807], [114.8957, 12.7474],
[119.3939, 14.11734]];
data[2]:=[[0., 0.], [2.96714, .106941], [5.627586,
.336473], [10.55659, .947188], [14.34888, 1.405284],
[19.66491, 1.940294], [25.36308, 2.475546], [29.91968,
2.934126], [34.47627, 3.392706], [40.18661, 3.738093],
[44.75294, 4.04478], [50.46085, 4.428139], [54.63286,
4.924451], [59.95132, 5.421488], [65.30386, 5.386901],
[69.85314, 5.9594], [74.78458, 6.532142], [80.12495,
6.687421], [85.07343, 6.99435], [89.6714, 6.807387],
[94.98256, 7.418343], [99.97485, 7.041756], [105.2884,
7.614739], [109.8548, 7.921427], [114.8008, 8.266329],
[119.7371, 8.76312]];
print("data[1]=",data[1]);
print("data[2]=",data[2]);
> end proc:
VII. Methylene Chloride Worksheet.
> methylene:=proc()
Data from Astrand et. al. Scand. J. work env. and Health 1 (1975) 78
NOTE - methylene chloride =
Data shown for 1 subject - for arterial, venous and end alveolar for one subject - at rest,
exercise, rest
The is venous and arterial data for for first 60 minutes at rest:
0-30 min Inspired air conc = 870 mg/M^3, 30-60 = 1740 mg/M^3 (1 meter^3 = 1000
liters)
USED -Partition coefficients from Johanson et. al. Toxicology letters 41: 115 (1988) Kbair = 11 - this is referencec in several articles
Not USED -Instead used 2 year old rat data (Thomas et. al. Env. Health Perspectives
104: 858 1996. Kbair = 27
Alveolar ventilation for this subject= 4.8 l/min 0-30, and 5.1 lit/min 30-60
> local i,datafile,Kfair;
> defaultpar():
> Wtot:= 70; #Arbitrary - Input normalized by alveolar
respiraton
standardhuman2(Wtot);
> Fat:=0.2;#Young swedish men
> cunit:="mg";
> concunit[1] :=2;# experimental output = blood conc
ninput :=2;
finput[1]:=table([organ=lung,type=1,rate=0.87,tbeg=0,
tend=30,csteady=0,padjust=0]);#30 min hour input of 870
mg/M^3
finput[2]:=table([organ=lung,type=1,rate=1.74,tbeg=30,
tend=60,csteady=0,padjust=0]);#30 min hour input of 870
mg/M^3
Km[liver]:=1.5;
Vm[liver]:=2.8;#determinse clearance at high concentration
Kfair:=130;#Olive oil partition - Gargas et. al.
Toxicology and App. Pharm. 98:87 (1989)
Kbair:= 11;#Emperical value = experimental arterial/end
alveolar
Kwair:=6;
alvent:=5.1;
> kbair_physical:=11;#True blood air value
Kfbld:=Kfair/kbair_physical;# fat/blood partition coef.
Kfwat:=Kfair/Kwair;
> fr_arm[muscle]:=0.5;
> pdata:=2;
> data[1]:=[[0., 0.], [3.16, .8879057], [5.3, 1.31314],
[10.4, 1.700477], [15.3, 2.106332], [20.0, 2.104784],
[25.2, 2.307053], [30., 2.675872], [32., 3.045894], [33.5,
3.989527], [35.3, 4.637268], [40.2, 4.987568], [45.4,
5.930456], [50.6, 6.002866], [55.6, 6.112429], [60.,
6.44444]];
> data[2]:=[[0., 0.], [3.16, .5458038e-1], [5.3, .1465414],
[10.4, .7190047], [15.3, 1.013808], [20.4, 1.23448], [25.2,
1.195895], [30., 1.176001], [32., 1.304884], [33.5,
1.545278], [35.3, 2.137234], [40.2, 2.209874], [45.4,
3.282276], [50.6, 3.725168], [55.6, 3.649547], [60.,
3.79626]];
print("data[1]=",data[1]);
print("data[2]=",data[2]);
> end proc:
VIII. Toluene Worksheet.
> toluene_carlsson:=proc()
Toluene data of Carlsson (Scand. J Work Env. Health B. 8 43 (1962)
Measured arterial, venous ("brachial") and alveolar
Kbair is the arterial/end tidal ratio during uptake, thys corrects for washin-washout effect
> local i,datafile,Kfair;
> defaultpar():
> Wtot:= 75; #Body weight - Not reported - assumed value to
go with reported alvent
standardhuman2(Wtot);
> Fat:=0.26;#guess men age 22-43 - only one overweight
> cunit:="mg";
> concunit[1] :=2;# experimental output = blood conc
ninput :=1;
finput[1]:=table([organ=lung,type=1,rate=0.3,tbeg=0,
tend=120,csteady=0,padjust=0]);#30 min hour input of 300
mg/M^3
Tclr[liver]:=80.0;
Tclr[kidney]:=8;
klip[vein]:=0.006;
Kfair:=1470;#Value of oil/air from Sato et. al. 1979;
36:231
Kbair:= 9;#The blood/air ratio near steady state corrects
for washin-washout during uptake
Kwair:=2.2;
Kwair:=1.75;#Gargas
kbair_physical:=15.6;#True blood air value
Kfbld:=Kfair/kbair_physical;# fat/blood partition coef.
Kfwat:=Kfair/Kwair;
alvent:=6.8;#Average value
> pdata:=2;
> fr_arm[muscle]:=0.5;
> print("data[1]=",data[1]);print("data[2]=",data[2]);
> data[1]:=[[0., 0.], [1., .3107034], [3.110934, .3237988],
[4.7905, .43838], [10.03027, .518576], [14.69258,
.4975182], [19.89842, .4560983], [24.8881, .6241743],
[29.81558, .5692879], [34.76945, .6089917], [39.71389,
.6149132], [44.92727, .6005191], [49.59524, .5997306],
[54.53969, .6056521], [59.48036, .5980608], [64.68243,
.543128], [69.89203, .5152209], [74.85532, .5887069],
[79.52707, .6014313], [84.72913, .5464985], [89.66981,
.5389071], [94.63687, .6259059], [99.31239, .6521432],
[104.8267, .7322928], [109.4627, .6166449], [114.4184,
.663105], [119.3516, .6284879]];
data[2]:=[[0., 0.], [1.3, .2679384e-1], [3.1, .1211057],
[5.268042, .1815426], [10.23699, .2752978], [14.9125,
.3015351], [19.86072, .3209695], [24.81082, .3471603],
[30.04304, .4003306], [35.28658, .4940394], [39.94324,
.4527123], [45.15662, .4383182], [50.07467, .3496495],
[54.76715, .4366947], [59.97487, .4020313], [64.91554,
.39444], [69.85999, .4003615], [75.08844, .4400189],
[79.7583, .4459868], [84.70086, .4451519], [89.6453,
.4510734], [94.86999, .4772179], [99.81255, .476383],
[104.4805, .4755945], [109.692, .4544439], [114.6365,
.4603655], [119.5771, .4527741]];
> end proc: