Computer Analysis of Oscillatory Features of the Red Cell System 229
Comparison of the Formulation with Experiment
The behaviour of the mathematical formulation, with the interacting
loops and the single loops alone, has been compared with the three sets of
experimental data listed above.
In the paper by PORTEOUS and LAJTHA [3], experiments are described in
which mice were first hypertransfused to halt erythropoietin production,
so that the red cell differentiation channel is cut off. Under these conditions,
the stem cell mitotic loop is essentially operating alone, with negligible
interaction from the red cell loop. With the mice in this hypertransfused
condition, they were irradiated, reducing the stem cell population to 10 %
of the norm. The recovery of the stem cell population with time was recorded. After an initial dip of variable length, the stem cell population rises
rapidly to reach the norm in 7 days and continues to reach a maximum of
about 220 % at about 13 days and then falls to cross its steady state value
again. The behaviour of the formulation has been compared with this
experimental situation, and the general features of the experimental data are
found to be well reproduced.
The second set of experimental data is found in the paper by HULSE [1].
In this case, rats under normal steady state conditions were given various
doses of radiation and the recovery of the reticulocytes with time was
studied. A typical set of data shows a marked drop in the reticulocyte population, followed by a rapid rise to overshoot the norm and then an approach
to the steady state level with a damped oscillatory motion. The effect of
the radiation is a reduction of the stem cell pool, and the response of the
mathematical formulation with both interacting loops to this initial
perturbation is found to be in good agreement with the observed experimental data.
The third set of experimental data is furnished in the paper by ORR et
al. [2], which describes the oscillations set up in the red cell system when
rabbits were given a course of red cell iso-antibody. Under these conditions,
the red cell lifetime is reduced due to the premature death of red cells under
the action of the iso-antibody. This drop in the mean red cell level causes an
increase in the production of erythropoietin, stimulating an increase in the
number of stem cells differentiated per day into the red cell channel. This,
in turn, gives rise to an increased production of reticulocytes and so to an
increase in the mean reticulocyte level. The experimental results, two sets
of which are shown in figures 2(a) and 2(b), are presented as the variation
of red cells and reticulocytes with time, and the corresponding behaviour
of the mathematical formulation is shown in figure 2(c). A dominant factor
in satisfactorily reproducing the oscillations of the system under the above
conditions is the choice of the value of the stem cell population, S, and
this is found to be -6 X 10 6 stem cells per gram of body weight.
Comparison of the Formulation with Experiment
The behaviour of the mathematical formulation, with the interacting
loops and the single loops alone, has been compared with the three sets of
experimental data listed above.
In the paper by PORTEOUS and LAJTHA [3], experiments are described in
which mice were first hypertransfused to halt erythropoietin production,
so that the red cell differentiation channel is cut off. Under these conditions,
the stem cell mitotic loop is essentially operating alone, with negligible
interaction from the red cell loop. With the mice in this hypertransfused
condition, they were irradiated, reducing the stem cell population to 10 %
of the norm. The recovery of the stem cell population with time was recorded. After an initial dip of variable length, the stem cell population rises
rapidly to reach the norm in 7 days and continues to reach a maximum of
about 220 % at about 13 days and then falls to cross its steady state value
again. The behaviour of the formulation has been compared with this
experimental situation, and the general features of the experimental data are
found to be well reproduced.
The second set of experimental data is found in the paper by HULSE [1].
In this case, rats under normal steady state conditions were given various
doses of radiation and the recovery of the reticulocytes with time was
studied. A typical set of data shows a marked drop in the reticulocyte population, followed by a rapid rise to overshoot the norm and then an approach
to the steady state level with a damped oscillatory motion. The effect of
the radiation is a reduction of the stem cell pool, and the response of the
mathematical formulation with both interacting loops to this initial
perturbation is found to be in good agreement with the observed experimental data.
The third set of experimental data is furnished in the paper by ORR et
al. [2], which describes the oscillations set up in the red cell system when
rabbits were given a course of red cell iso-antibody. Under these conditions,
the red cell lifetime is reduced due to the premature death of red cells under
the action of the iso-antibody. This drop in the mean red cell level causes an
increase in the production of erythropoietin, stimulating an increase in the
number of stem cells differentiated per day into the red cell channel. This,
in turn, gives rise to an increased production of reticulocytes and so to an
increase in the mean reticulocyte level. The experimental results, two sets
of which are shown in figures 2(a) and 2(b), are presented as the variation
of red cells and reticulocytes with time, and the corresponding behaviour
of the mathematical formulation is shown in figure 2(c). A dominant factor
in satisfactorily reproducing the oscillations of the system under the above
conditions is the choice of the value of the stem cell population, S, and
this is found to be -6 X 10 6 stem cells per gram of body weight.