TABLE XXXVI
COEFFICIENTS FOR CALCIUM MODEL AS FUNCTION OF AGE
Flux (my/da)
Gross Endog-.lbsorp- enous
lion Feral
Amount (gm) TolaI.i
Age Weight
(da) (leg) In- Total
take Feces
0-8 3.4 (467)’ (305)
16 (3.7) 467) (309) 40 4.9 467 313
76 5.6 484 69
106 6.5 456 136 7.1 491 589 166 7.6 500 305 196 8.1 506 586
556 8.5 547 348
556 8.9 538 335
586 9.0 .517 313
Acere- Resorp-lion lion Urine (55) (55) 55 35 35 35 57 34 35 54 56 Reten-lion, Ex- change-able Pool ( 5) (30) 15 15 7 6 (195) (188) 184 545 254 535 555 548 559 536 534 Sweat and Saliva (13) (13) 13 13 l3 13 13 13 13 IS 13 (30) (30) So 30 30 30 30 30 30 30 30 lion, Non-ex-change. able l3oie (1l5) ( 93) III 155 134 ISO 148 164 148 165 164 , Non- lz-change- cx-able change-Pool able Ilone 1.31) 56.7 (1.63) (57.6) 5.16 30.6 5.47 34.6 5.87 38.9 3.13 43.5 3.36 47.6 3.58 55.3 3.76 37.0 3.93 61.7 3.97 66.6 (337) (366) 485 554 644 703 753 805 843 885 891 515) (573) 374 405 310 333 603 638 693 717 757 Rele,i-lion (mgi do) )157 (153) I19 167 I46 157 155 171 154 169 165 Body (got) 58.5 (59.5) 35.8 37.1 41.8 46.3 51.0 35.9 60.8 65.6 70.6 .4verage APPENDIX E
CALCIUM
AND
STRONTIUM
MODEL
AS
FUNCTION
OF AGE
C
O1FFICIENTS at the midpoints of 30-dayintervals are summarized in Tables
XXXVI-XXXVIII. Calcium intake and retention as a function of age were taken from Tables VI and XII, respectively, and
corrected according to Appendix C. Stron-tiurn intake was derived similarly from Table XV. The procedures by which the
other values in Tables XXXVI and XXXVII
were computed are summarized in Table
XXXIX. The growth of the infant was
assumed to begin 8 days after birth.
Cal-cium fluxes at age 8 and 16 days were
esti-mated to be the same as those in the
follow-ing 30-day interval (see Table XXXVI),
cx-cept for the total retention value taken from Table XII. Strontium intakes were taken to be 420 i.ig PtI’ day at these ages, based on
an estimated strontium/calcium ratio of 0.9 rng per gram for a diet consisting mostly of formula. These estimates enable one to compute the accumulation of calcium and
strontium between birth and the ages at
which data were collected. Although several
sets of values are given to three (ligits, these are presented only for internal consistency when computing fluxes; the accuracy of the
values is represented better in Figures 15
and 21. Note, for example, that values of calcium in feces in Table XXXVI differ by several milligrams jer day from directly
measured values in Table VIII.
All values in Table XXXVIII, except the
strontium intake (which is identical to
values in Table XXXVII), were obtained
by trial-and-error fitting of strontium-90
values in urine and feces to the measured
values for 30-day intervals (see Figure 9).
A digital computer prograni was written
with several iterations er day to describe the compartment niodel (in the )rogranI,
the gastrointestinal tract was considered to be a compartment with a constant strontium content of 0.6 mg).
.4g. Weight (da) (kg) Flux (pg/da) Total intake Feces Gross Endog-Absorp- enous-lion Fecal Urine Amount(mg) Totals Sweat and Saliva Ref en-lion, Es- change-able Pool Accre- Resorp-lion lion Re’en-lion. Non-es- change-able Bone Es- change-able Pool 8f lOt 46 76 106 136 166 196 556 556 586 3.4 3.7 4.9 5.6 6.5 7.1 7.6 8.1 8.5 8.9 9.0 450 (450) 450 (450) 495 (538) 561 (555) 576 (616) 605 (645) 604 (658) 618 (639) 631 (673) 659 (671) 754 (765) 584 (584)) 595 (595) 368 (415) 377 (371) 415 (455) 459 (469) 440 (464) 430 (431) 456 (498) 483 (495) 330 (591) 145 137 133 195 175 184 176 500 187 188 187 9 9 9 ii 11 Ii l5 IS 15 15 13 71 71 71 91 88 88 81 95 95 80 81 .5 3 3 6 6 6 8 6 6 7 7 56 4 6 7 3 4 4 4 4 3 0 Non- Cx- change-able Bone 7.8 8.0 9-4 ‘1-S 13.4 15.3 17.8 SO. I 55 3 54 9 7.3 96 157 136 2” 241 274 299 331 347 376 386 62 79 I 13 130 176 199 526 245 574 290 300 Ret en-lion (pa’ do) 60 55 48 87 70 79 77 90 77 89 86 34 48 42 80 63 75 73 86 73 86 86 Body (mg) 8.2 8.6 10.1 15.1 14.3 16.7 19. 1 21.6 24.1 26.6 29.2 0.43 0.36 0.70 0.93 I .07 1 .25 1.33 1.48 I .36 I .67 I.75 Average SUPPLEMENT TABLE XXXVII
COEFFICIENTS FOR STRONTIUM MODEL AS FUNCTION OF AGE’
751
164
I
604(643) 431(470) 184I
ii 87 6I
5171
76I
I
17.6I
80 18.9S Values based on calcium coefficients and equations inTable XX. t‘nJuet, were estimated for entire period.
Values in parentheses are for periods in which urine and feces werecollected separately. Other3 apply to au periods.
TABLE XXXVIII
COEFFICIENTS FOR STRONTIUM MODEL AS FUNCTION OF AGE’
Age (da)
Weight
(kg)
Flux (jig/da) Amount (nig) Totals
intake FecesTotal Gross Absorp-Lion Endou-enous Feral Urine Sweat and Saliva Eden- Eden-lion lion
Ex- Accre- Resorp-
Non-ex-change- lion lion
change-able able
I00 none Ex- change-able Pool , ‘ on-CX change-able Bone Reten-lion d(I) Body (mg)
8f 3.4 450(450) 585(585) 147 9 48 5 51 96 65 34 0.43 7.8 85 8.5
let 3.7 450(450) 589(589) 143 15 48 6 7 150 80 70 0.67 8.1 77 8.8
46 4.9 495(536) 361(405) 143 15 48 6 7 195 155 70 0.87 10.5 77 11.1
76 5.6 361(555) 367(361) 508 14 68 7 10 560 151 109 1.13 15.9 119 14.0 106 6.5 576(616) 393(433) 197 14 76 7 5 304 509 95 1.36 15.9 100 17.3 136 7.1 605 (645) 459 (499) 156 IS 75 7 0 301 537 64 1.34 18.S 64 19.8
186 7.6 604(658) 434(478) 163 13 65 7 5 337 560 77 1.51 50.5 85 55.0
196 8. 1 618 (639) 445 (463) 190 14 68 7 5 376 580 96 1.68 23.0 101 54.7 556 8.S 631 (673) 486 (358) 159 14 67 7 0 383 315 71 1.7 1 55.6 7 1 27.3
536 8.9 639(671) 303(315) 171 15 36 8 3 437 358 109 1.94 58.5 115 30.1
586 9.0 754 (765) 577 (618) 161 14 70 7 0 409 339 70 1 .85 31 .0 70 35.8
752 STRONTIUM, CALCIUM, AND PHOSPHORUS RETENTION
+ k21y2 + h31, amid
The following coefficients describe the movement of strontium to and from
corn-partments : Yo radiostrontiun1 in Compart-inent 0 (gastrointestinal tract), in picocuries;
Yi radiostrontiutn in Compartment I
(ex-changeable l)001)
,
in picocuries ; Y2 =radio-strontium in Compartment 2 (non-exchange-able bone), in picocuries; K,0= ingestion of radiostrontium in picocuries per day ; K31
- absorption of radiostrontium through
lung from air in picocuries per day ;k03 = frac-tional loss of radiostrontiun1 from
Compart-ment 0 to the environment (feces) ; k13 =
frac-tional loss of radiostrontium from Compart-n1ent I to the environment (urine, sweat,
and saliva). Coefficients for movement
among colnpartrnents are k01 (absorption),
k10 (endogenous fecal excretion), ku (acere-tion), and k21 (resorption). All coefficients
may be a function of time. The fractional
losses are based on stable strontium values.
The model (Figure 30, for example) is (lescribed mathematically by a set of
simul-taneous linear differential equations.
(Equatioii E-l)
dyo
-.-- en - (k03 + k01)yo + k10y1 + 1\.30,
(Equation E-2)
dy1
-.i--
= +ko1yo- (k13+k10+k,2)yi(Equation E-3)
dy2
k,2y1 - k21y2.
To find Yo, Yi, and V2 as a function of time,
these rate equations are solved by using esti-mated initial activities y(0), yi(0), y2(O).
These equations were solved using a
Taylor’s Series first order approximation to the function. This approximation is equiva-lent to assuming that the rate of change of the activity, dy/ilt in each compartment is
constant for a small increment of time, t. The change in activity (luring time t is
thus equal to t (ly/dt, and
(Equatioii E-4)
y1(t) = Lt (dXL) + YI(O)
Ion = 1, . . .3
where (lVi/(It is given by Equations E-1 to
E-3. Equation E-4 gives values of activity
yj at time zt. A new set of y is then evalu-ated from the last set of calculated values by the same procedure. This method was used
with the value of zt at 1/25 day for the
first 30 days, and 1/5 day for the rest of the
periods.
The method was evaluated by comparing
