Loading…
Four-urn catenary model for excretion
A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomac...
Saved in:
| Published in: | Bulletin of mathematical biology 1984, Vol.46 (2), p.219-227 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placed
w
0 white balls and
r black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, only
r blacks are put in, with no whites. A sample of size
r is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is, where
w
0
2
P
(
t
Δ
t
)
[
1
−
P
(
t
Δ
t
)
]
,
where
P
(
t
Δ
t
)
=
e
−
(
t
/
Δ
t
)
[
1
+
(
t
Δ
t
)
+
1
2
(
t
Δ
t
)
2
]
.
.
In the equation
t is the time after a single intake of
W
0 radio atoms into the stomach and Δ
t is the mean residence time in the stomach. The model is tested with experimental data and a higher variance than the data is obtained. |
|---|---|
| ISSN: | 0092-8240 1522-9602 |
| DOI: | 10.1016/S0092-8240(84)80020-8 |