A SAAM31   033MG01.S                           8/23/96  
2        2  
C Magnesium kinetics in adolescent girls
C Ref: Sojka et al., Am J Physiol. August 1997  
C (Based on model of Avioli and Berman, J. Appl Physiol 15:503-507, 1960)   
C This file contains data from one subject  
C who was given 25Mg intavenously and 26Mg orally.  
C Data were obtained for 14 days from serum, urine and feces
C The subject was studies twice; first while on 800 mg calcium/d
C  and then 5 weeks later while on 1800 mg calcium/d.   
C   
C The model is set up to fit the IV and oral tracer data simultaneously 
C using duplicate models. A second set of models fit data from the second study;
C COMPARTMENTS 1 T0 9 ARE IV TRACER while on 800 mg Ca/d
C COMPARTMENTS 11 TO 19 are oral tracer while on 800 mg Ca/d
C COMPARTMENTS 21 TO 29 ARE IV TRACER WHILE ON 1800 mg Ca   
C COMPARTMENTS 31 TO 39 ARE ORAL TRACER WHILE ON 1800 mg Ca 
C   
C Compartments 1, 11, 21 and 31 are serum   
C Compartments 4,14,24,34 are urine 
C Compartments 9,19,29,39 are feces 
C   
C ****************STUDY 1 800 mg Ca/D   
H DAT   
C DOSE (100%) INFUSED AFTER 1 HR, OVER 4 MIN (25%/MIN OR 1500/HR)   
XUF(1)=1500*F(6)*(1-P(4))   
C P(4) IS FRACTION OF IV DOSE THAT GOES RAPIDLY TO URINE
XUF(4)=1500*F(6)*P(4)   
XUF(70)=UF(1)   
106QO   
            0.  
            1.            1.
            1.0667        0.
C C70 IS A CHECK OF THE AMOUNT OF DOSE INFUSED INTO SERUM   
170 
            0.  
2           1                            3  
H PAR   
C the dose is given IV, but is simulated using an infusion, UF(1)   
   IC(1)    0.0 
C The urine data indicate that a small % of the dose is 
C excreted rapidly in urine. This is simulated using P(4)   
   P(4)      4.823395E-02  1.590000E-02   1.431000E-01  
   L(2,1)    4.167476E-01  2.233333E-01   2.010000E+00  
   L(1,2)    5.634827E-02  1.000000E-02   1.593000E+00  
   L(3,1)    1.251707E-01  1.083333E-01   9.750000E-01  
   L(1,3)    6.410942E-03  9.999998E-04   9.029998E-02  
   L(5,3)    3.440066E-03  9.999998E-05   1.668000E-02  
C N.B. L(3,5) VALUE in AVIOLI & BERMAN was 6.4E-4/HR
   L(3,5)    0.000000E+00   
   L(4,1)    9.687606E-03  5.500000E-03   1.000000E-01  
   L(9,1)    2.875211E-03  2.134452E-03   1.921007E-02  
   L(1,8)    4.346740E-02  1.000000E-02   2.812500E-01  
   L(10,8)  7.300000E-02
   L(9,10)   1.000000E+00   
C P1 is volume of distribution of compartment 1 in liters   
   P(1)      1.267997E+01  1.000000E+00   3.000000E+01  
   P(21)=P(1)   
C P2 is average serum Mg in mg/dL.  
   P(2)     2.11
   P(12)    2.13
C P3 is volume of distribution of C3 from Avioli and Berman 
   P(3)     126 
C   
C COMPARTMENTS 11 THROUGH 19 ARE 26MG (oral tracer) 
H DAT   
C ORAL DOSE APPEARS AFTER A DELAY of about 1 hour   
C this is simulated using compartment 17
117QO   
            0.  
            1.            100   
H PAR   
   IC(17)   0.0 
   L(11,18)=L(1,8)  
   L(20,18)=L(10,8) 
   L(19,20)=L(9,10) 
   L(18,17)  1.000000E+03   
C   L(14,11)=L(4,1) 
   L(12,11)=L(2,1)  
   L(11,12)=L(1,2)  
   L(13,11)=L(3,1)  
   L(15,13)=L(5,3)  
   L(13,15)=L(3,5)  
   L(11,13)=L(1,3)  
   L(19,11)=L(9,1)  
C +++++++++++++++++++++++++++++ Study 2  1800 mg Ca +++++++++++++++++++ 
C COMPARTMENTS 21 THROUGH 29 ARE 25MG (IV tracer)   
C 35 DAYS AFTER CAMP A (OR +840 HR) 
C IC VALUES ARE RESIDUALS FROM Study 1 are calculated using Compartments 51-55  
C    (SEE BELOW)
   IC(21)    1.430000E-01   
   IC(22)    1.110000E+00   
   IC(23)    1.000000E+00   
C   IC(24)=P(24)
   P(24)     1.216208E-02  0.000000E+00   1.200000E-01  
   IC(25)    4.210000E+01   
H DAT   
C UF(21) is the infusion of IV tracer, as in study 1
XUF(21)=1500*F(26)*(1-P(24))
XUF(24)=1500*F(26)*P(24)
C CHECK 
XUF(71)=UF(21)  
171 
            0.  
2           1                            2  
H PAR   
C  L(21,28)=L(1,8)  
   L(30,28)=L(10,8) 
   L(29,30)=L(9,10) 
C   L(24,21)=L(4,1) 
C   L(22,21)=L(2,1) 
   L(21,22)=L(1,2)  
C   L(23,21)=L(3,1) 
   L(25,23)=L(5,3)  
   L(23,25)=L(3,5)  
   L(21,23)  1.100000E-02   
   L(29,21)=L(9,1)  
C   
C COMPARTMENTS 31 THROUGH 39 ARE 26MG (oral tracer) 
H PAR   
C IC'S ARE RESIDUALS FROM Study 1 calculated using Compartments 61-65   
   IC(31)    5.000000E-02   
   IC(32)    3.960000E-01   
   IC(33)    9.100000E-01   
   IC(34)=P(34) 
   IC(35)    1.179000E+01   
   P(34)    0   
H DAT   
126QO   
            0.  
            1             1.
            1.0667        0.
H DAT   
137QO   
            0   
            1             100   
H PAR   
   L(38,37) 1E3 
   IC(38)   0.0 
   L(31,38)=L(21,28)
   L(40,38)=L(30,28)
   L(39,40)=L(29,30)
C   L(34,31)=L(24,21)   
   L(32,31)=L(22,21)
   L(31,32)=L(21,22)
   L(33,31)=L(23,21)
   L(35,33)=L(25,23)
   L(33,35)=L(23,25)
   L(31,33)=L(21,23)
   L(39,31)=L(29,21)
C +++++++++++++++++++++++   
H STE   
C Study 1   
C P(2) IS SERUM MG (MG/DL), AND THE MASS IS IN MILLIGRAMS   
   M(1) = P(2) * 10 * P(1)  
   U(1)      1.095049E+01                1E2
C Study 1 DIETARY MG INTAKE IS 264 MG/DAY, OR 10 MG/HR  
   U(8)     11. 
C   
C Study 2   
   M(21) = P(2) * 10 * P(1) 
   U(21)     6.722377E+00                1E2
C DIETARY MG INTAKE IS 272 MG/DAY   
   U(28)    11.3
C   
C   
H DAT   
C P(1) IS INITIAL VOLUME OF DISTRIBUTION IN LITERS  
C G(1) TO G(31) converts serum tracer to % of dose/L
XG(1) = F(1)/P(1)   
XG(11) = F(11)/P(1) 
XG(21) = F(21)/P(21)
XG(31) = F(31)/P(21)
C G(3) IS THE TRACER MEASURED IN SERUM IN AVIOLI AND BERMAN (1960) STUDY
XG(3) =(F(1)/p(1)) + F(3)/P(3)  
C G(32) IS FRACTION ABSORBED IN STUDY 1, G(42)IS ABSORPTION IN STUDY 2  
XG(32)= L(1,8)/(L(1,8)+L(10,8)) 
XG(42)=L(21,28)/(L(21,28)+L(30,28)) 
C  G(33) AND G(34) ARE BALANCE IN STUDY 1, G(43) AND G(44) IN STUDY 2   
XG(33)=U(8)-R(10,8)-R(9,1)-R(4,1)   
XG(34)=R(5,3)-U(1)  
XG(43)=U(28)-R(30,28)-R(29,21)-R(24,21) 
XG(44)=R(25,23)-U(21)   
C G(35) IS RATE OF ABSORPTION (MG/D) IN STUDY 1, G(45) IN STUDY 2   
XG(35)=G(32)*U(8)*24
XG(45)=G(42)*U(28)*24   
C G(36) IS ENDOGENOUS EXCRETION (MG/D) IN STUDY 1, G(46) IN STUDY 2 
XG(36)=R(9,1)*24
XG(46)=R(29,21)*24  
C G(37) IS URINE EXCRETION (MG/D)IN STUDY 1, G(47) IN STUDY 2   
XG(37)=R(4,1)*24
XG(47)=R(24,21)*24  
C G(38) IS FECAL (MG/D) IN STUDY 1, G(48) IN STUDY 2
XG(38)=(R(9,10)+R(9,1))*24  
XG(48)=(R(29,30)+R(29,21))*24   
C G(39) IS BALANCE (MG/D)IN STUDY 1, G(49) IN STUDY 2   
XG(39)=G(33)*24 
XG(49)=G(43)*24 
C SIMULATIONS   
101G(1) 
            2.  
2           .5                           20 
111G(11)
            2.  
2           .5                           20 
121G(21)
            2.  
2           .5                           20 
131G(31)
            2.  
2           .5                           20 
C   
103G(3) 
            0.0 
2           1.                           24 
2           12.                          24 
119F(19)
            0.  
2           12                           16 
C ################################################################  
C SIMULATING RESIDUAL TRACER AT END OF STUDY 1 (336 HR) AND AT START
C OF STUDY 2  (I.E AFTER 35 D, OR 840 HR)   
C FOLLOWING IV DOSE 
151F(1) 
            336.
2           840.                         1  
152F(2) 
            336.
2           840.                         1  
153F(3) 
            336.
2           1176.                         1 
154F(4) 
            336.
2           840.                         1  
155F(5) 
            336.
2           840.                         1  
159F(9) 
            336.
2           840.                         1  
C FOLLOWING ORAL DOSE   
161F(11)
            336.
2           840.                         1  
162F(12)
            336.
2           840.                         1  
163F(13)
            336.
2           840.                         1  
164F(14)
            336.
2           840.                         1  
165F(15)
            336.
2           840.                         1  
169F(19)
            336.
2           840.                         1  
C   
100 
   G(32)
   G(42)
   G(33)
   G(34)
   G(43)
   G(44)
   G(35)
   G(45)
   G(36)
   G(46)
   G(37)
   G(47)
   G(38)
   G(48)
   G(39)
   G(49)
110 
   U(1) 
   U(8) 
   U(21)
   U(28)
   M(1) 
   M(2) 
   M(3) 
   M(5) 
   M(8) 
   M(10)
   R(1,8)   
   R(2,1)   
   R(3,1)   
   R(5,3)   
   R(4,1)   
   R(10,8)  
   R(9,1)   
   M(21)
   M(22)
   M(23)
   M(25)
   M(28)
   M(30)
   R(21,28) 
   R(22,21) 
   R(23,21) 
   R(25,23) 
   R(24,21) 
   R(30,28) 
   R(29,21) 
C ***** PARAMETERS THAT DIFFER BETWEEN STUDIES FOR MG01 
H PAR   
   L(14,11)  1.200936E-02  1.000000E-02   1.350000E-01  
C   P(21)     7.076197E+00  1.000000E+00   3.000000E+01 
   L(21,28)  2.248401E-02  1.166667E-02   1.050000E-01  
   L(24,21)  1.432043E-02  1.000000E-02   1.000000E-01  
   L(22,21)  1.995405E-01  1.000000E-01   2.010000E+00  
   L(23,21)  7.503509E-02  7.000000E-02   6.300000E-01  
   L(34,31)  1.109926E-02  7.999999E-03   1.000000E-01  
H DAT   
120                       /24            FSD=1  
   U(8)                   264.  
   U(28)                  272.  
120                                      FSD=1  
   G(37)                  75.   
   G(47)                  82.   
   G(38)                  222.  
   G(48)                  196.  
C *******END OF MODEL ****************************************  
C SUBJECT MG01  
C MG  INTAKE 264 AND 272 MG/D   
C Urine Mg/day for camp A was 75, camp B was 82 
C Fecal Mg/day for camp A was 222, camp was 196 
C Urine and feces Mg is in mg/day converted to mg/h 
H PAR   
   P(2)       2.11  
   P(12)      2.13  
H DAT   
C UNITS: TIME(HOURS) Q0(% OF DOSE/  
C  CUMULATIVE % DOSE URINE, FECES)  
C 26 Mg data /.87 because the dose was 87% enriched with 26Mg   
C BLOOD 25 MG STUDY 1   
101G(1)              +1                  FSD=0.2
                   0.083   7.491
                   0.167   7.028
                    0.36   5.841
                    0.52   4.934
                       1   4.142
                     1.5   2.061
                       3   2.570
                       4   1.571
                   20.77   0.504
                   32.77   0.525
                   44.42   0.357
                   67.67   0.391
                  115.92   0.217
                  164.17   0.249
                  212.14   0.252
                  259.11   0.202
                  307.54   0.186
C URINE01 25 MG STUDY 1 
104                  +1                  FSD=.2 
                      -1
                       0
                      16   6.425
                      24   7.102
                      48   8.652
                      72   10.361   
                      96   10.835   
                     120   11.938   
                     144   12.922   
                     168   14.032   
                     192   15.277   
                     216   16.107   
                     240   16.517   
                     264
C FECALO1 25 MG STUDY 1 
109                   +1
                      -1
                       0
            2.32          0.0000
109                   +1                 FSD=.05
                      22   0.679
                   40.75   1.187
                      71   1.821
                    99.15  1.971
C BLOOD 26MG STUDY 1
111G(11)             +1     /0.87   
                   0.083   0.119
                   0.167   0.074
                    0.36   0.039
                    0.52   0.091
111G(11)             +1     /0.87        FSD=.2 
                       1   0.133
                     1.5   0.169
111G(11)             +1     /0.87        FSD=.02
                       3   0.380
                       4   0.375
111G(11)             +1     /0.87        FSD=.2 
                   20.77   0.174
                   32.77   0.149
                   44.42   0.090
                   67.67   0.096
                  115.92   0.068
                  164.17   0.059
                  212.14   0.062
                  259.11   0.040
                  307.54   0.035
C URINE01 26 MG STUDY 1 
114                  +1     /0.87        FSD=.2 
                      -1
                       0
                      16   0.785
                      24   1.060
                      48   1.582
                      72   2.114
                      96   2.252
                     120   2.534
                     144   2.770
                     168   3.033
                     192   3.324
                     216   3.520
                     240   3.620
                     264
C FECAL01 26MG STUDY 1  
119                  +1     /0.87   
                      -1
                       0
            2.32          0.0001
119                  +1     /0.87        FSD=.2 
                   22     49.9  
                   40.75  51.1  
                      71  51.2  
            99.15         51.2  
C BLOOD 25MG STUDY 2
121G(21)              +1                 FSD=.2 
                   0.083  16.859
                   0.166  14.509
                    0.33   7.41 
                       1   5.872
                     1.5   4.724
                       3   4.015
                       6   1.812
                    7.87   1.243
                   19.85   1.062
                   31.98   0.814
                   67.93   0.638
                  116.11   0.422
                  164.26   0.405
                  212.06   0.362
                  259.81   0.400
C URINE 25 MG STUDY 2   
124                  +1                  FSD=.2 
                      -1
                       0
                       8   5.508
                      16   8.676
                      24   10.163   
                      48   12.802   
                      72   15.109   
                      96   16.821   
                     120   18.757   
                     144   20.638   
                     168   21.484   
                     192   25.051   
                     216   26.655   
                     240   28.113   
                     264   29.646   
                     288   31.486   
                     312   32.591   
                     336   33.018   
C FECAL01 25MG STUDY 2  
C AN EARLY FECAL SAMPLE MAY HAVE BEEN LOST IN THIS STUDY
C THEREFORE, FECAL DATA IN C29 AND C39 ARE NOT FITTED   
128F(29)             +1 
                      -1
                       0
            46            0.0001
                      72   0.228
                   102.2   0.228
                   123.5   0.228
                  142.25   0.228
                     166   0.538
                     192   0.903
                     203   0.903
                     232   0.903
                   245.5   1.287
                   285.5   1.287
            317.75        1.287 
C FECAL01 25MG STUDY 2  
C AN EARLY FECAL SAMPLE MAY HAVE BEEN LOST IN THIS STUDY
C THEREFORE, FECAL DATA IN C29 AND C39 ARE NOT FITTED   
128F(29)             +1 
                      -1
                       0
            46            0.0001
                      72   0.228
                   102.2   0.228
                   123.5   0.228
                  142.25   0.228
                     166   0.538
                     192   0.903
                     203   0.903
                     232   0.903
                   245.5   1.287
                   285.5   1.287
            317.75        1.287 
C BLOOD 26MG01 STUDY 2  
131G(31)            +1      /0.87        FSD=.2 
                   0.083   0.339
                   0.166   0.288
                    0.33   0.163
                       1   0.219
                     1.5   0.216
                       3   0.247
                       6   0.439
                    7.87   0.295
                   19.85   0.262
                   31.98   0.254
                   67.93   0.137
                  116.11   0.094
                  164.26   0.079
                  212.06   0.065
                  259.81   0.068
C URINE01 26 MG STUDY 2 
134                   +1    /0.87        FSD=.2 
                      -1
                       0
                       8   0.199
                      16   0.915
                      24   1.324
                      48   1.964
                      72   2.242
                      96   2.737
                     120   3.123
                     144   3.469
                     168   3.602
C 26MG ENRICHMENT 4 TIMES OTHER SAMPLES, THEREFORE USED AVERAGE 
C OF SAMPLE BEFORE AND AFTER AT 192 HOURS   
C                     192   5.105   
C                     216   5.345   
C                     240   5.614   
C                     264   5.804   
C                     288   6.143   
C                     312   6.472   
C                     336   6.56
                      192   3.77
                      216   4.015   
                      240   4.284   
                      264   4.474   
                     288    4.813   
                     312    5.142   
                     336    5.23
C FECAL01 26MG STUDY 2  
138F(39)              +1   /0.87
                      -1
                       0
            46            0.0001
                      72   0.0001   
                     102   0.0001   
                   123.5   0.0001   
                  142.25   0.0001   
                     166   0.0090   
                     192   0.0090   
                     203   0.0090   
                  231.67   0.0090   
                   245.5   0.09 
                   285.5   0.09 
                  317.75   0.09 
C ****End of data*******