Previous models of the CO2-H(+) control of ventilation have been concerned either with the response to CO2 inhalation, or the response to perfusion of the surface of the medulla with mock cerebrospinal fluid having a high P sub CO2. Simulation of both responses with the same model has not been attempted. The purpose of the present study was two fold; first to develop such a model and, second, to obtain experimental data from human subjects for both developing this model and for evaluating this and future models

Milhorn, H. T., Jr.

Reynolds, W. J.

English

NASA Technical Reports Server

72 30056,
C
CQ
FINAL TECHNICAL REPORT
Conceptual Idea of Digital Computer Model
of Human Respiratory System
NCR 25-002-015
University of Mississippi Medical Center
June 28, 1972
Howard T. Milhorn, Jr.
https://ntrs.nasa.gov/search.jsp?R=19720022406 2020-03-11T19:34:57+00:00Z
DIGITAL SIMULATION AND EXPERIMENTAL EVALUATION OF THE O>2-H+ CONTROL OF PULMONARY VENTILATION
H. T. Mllhorn, Jr. and W. J. Reynolds
Department of Physiology and Biophysics
University of Mississippi Medical Center
' Jackson, Mississippi I
Previous models of the C02-H+ control of ven-
tilation have been concerned either with the re-
sponse to C02 inhalatlon3>8 or the response to
perfusion of the surface of the medulla with mock
cerebrosplnal fluid having a high Pco2 . Simula-
tion of both responses with the same model has
not been attempted. The purpose of the present
study vas two fold; first to develop such a model
and, second, to obtain experimental data from
human subjects for both developing this model and
for evaluating this and future models.
Experimental Data
By use of the black box approach to the human
respiratory system, one can obtain a considerable
amount of useful Information. One possible view
of the respiratory system as a black box is Illus-
trated In Figure 1. The system inputs are the
Inspired concentrations of oxygen and carbon
dioxide (Fio2i FIco2> and tne outputs are respira-
tory frequency (f), tidal volume (Vf), and alve-
olar oxygen and carbon dioxide partial pressures
(pAo2» FAco2)' Minute ventilation (V) is computed
secondarily from tidal volume and respiratory
frequency. We will be concerned with the step
responses to Fic02 only. Responses to sudden
changes in FIO- with and without end-tidal PCo2
controlled at normal levels have also been ob-
tained by the authors, but since they do not
directly pertain to the portion of the system
described in this paper they will be omitted1*.
Subjects used were healthy males in their third
decade of life. The Instrumentation used is de-
scribed in detail elsewhere by Holldman and
Mllhorn and is shown schematically in Figure 2.
The input side of the apparatus consisted of a
five-way valve through which the operator selected
either room air or the stimulus mixture supplied
from a 60-liter meteorological balloon, which was
in turn supplied from a commercial compressed gas
cylinder. The subject breathed through a mouth-
piece connected to a respiratory valve system con*
dating of two Rudolph valves arranged in parallel.
This arrangement was found to be the best compro- '
mi»e between low resistance and the desired low
dead space. Expiratory flow was measured by a
heated Flcisch pneumotachograph and Statham pres-
sure transducer. The flow signal was detected by
• trigger circuit which produced a short-duration
pulse output at the end of each expiration. Gas
MS continuously sampled through needles inserted
Into the mouthpiece and was analyzed by a Beckman
LB-1 Infrared C02 analyzer and a Thermox fuel cell
oxygen analyzer. The flow signal, the trigger
pulses, and the continuous outputs of the oxygen
and carbon dioxide analyzers were recorded on four
channels of a magnetic tape using a Sanborn 3907
FM magnetic tape system. After an experimental
session, the recorded data was played back, demod-
ulated, digitized, and calculations performed by
• Dltigal Equipment Corporation PDP-9 digital
computer. For each breath, the computing routine
calculated the tidal volume by intcrgration of the
flow signal and the respiratory period by measur-
ing the elapsed time between trigger pulses. From
this, the respiratory frequency and minute venti-
lation associated with that breath were calculated.
The highest carbon dioxide and lowest oxygen val-
ues occurring during the breath were also deter-
.mined and stored as approximations of their alve-
olar concentrations. The occurrence of the pulse
on the trigger channel was used by the program to
initiate and terminate processing of input data
for each breath.
After the calculations for the entire experi-
mental run had been performed, the breath-by-
breath values for tidal volume, respiratory fre-
quency, minute ventilation, and alveolar oxygen
and carbon dioxide were printed out and also
stored as a data file on magnetic tape. The
stored data could then be averaged into 10-sec
intervals and displayed on a storage oscilloscope
or plotted out by an on-line Incremental drum
plotter. All data files for a given stimulus
concentration could also be accessed by another
program and processed to give mean values and
standard errors for each of the five variables.
• Each experiment consisted of a 20-min prestim-
ulus period breathing room air, a 25-mln period
breathing the stimulus mixture, and another 20-
min off-transient period breathing room air. The
stimulus mixtures were either 3, 5, 6, or 7 per
cent carbon dioxide in air provided by commercial
sources. The subjects were placed in a semire-
cuiabent position in a comfortable recliner chair
and listened to a stereophonic music through head-
phones. The music was provided both to relieve
boredom and to mask out any ambient sounds occur-
ring in the room during the course of the experi-
ment. If necessary, instructions could be trans-
mitted to the subject by the operator by use of
an FM "wireless microphone" tuned to the frequency
on which the music was being broadcast. All
equipment was situated so that the subject could
not observe the actions of the operator, the in-
dication of any Instrument, or the manipulation
of any valve or control. Air from a compressed
air tank was allowed to escape into the room dur-
ing the periods when the stimulus mixture was not
filling the reservoir bag so that the subject
would not get an auditory cue when the stimulus
was applied or removed. Subjects were not told
which stimulus mixture .they were to receive, and
most underwent a "blank" experimental run in which
compressed air was used in place of the C02 stim-
ulus gas In order to detect the presence of vol-
untary effort, psychic efforts, etc., on the part
of the subject. . I
The stimulus gas mixture was allowed to come to
temperature equilibrium with the room air by pas- .
sage through two series humidifier/heat exchangers:
and the reservoir balloon. Gas flow rates were
kept low enough to prevent positive pressure from i
developing in the balloon and to allow time for
temperature equilibrium with the room air to be
achieved. The degree of humidificatlon provided
by the humidifers was such that subjects were
unable to differentiate between room air and hu-
midified compressed air from the reservoir balloon
in several runs.
The experimental results for tidal volume,
respiratory frequency, and minute ventilation are
plotted in Figures 3-5. It can be seen from fig-
ures 3 and 4 that a characteristic dissociation
of the frequency and tidal volume on-transients
occurs at each stimulus concentration with tidal
volume increasing rapdily to a stable plateau
while the frequency rises very gradually through-
out the stimulus period. Alveolar PcO2 and Po2
transients for all stimulus levels are given in
Figure 6.
The steady-state values and transient half-
times for the ventilatory variables are summa-
rized in Table 1 and those for the gas pressures
in Table 2. Several trends can be noted. The on-
transient half-times for respiratory frequency
steadily increase with increasing stimulus level
vhile those for tidal volume increase in a nearly
linear fashion. Ventilation on-transient half-
times also steadily Increase with increasing
stimulus level. The on-transient half-times for
alveolar PO2 become progressively smaller as the
stimulus level is Increased. The half-times for
the Pc02 on-transients remain essentially constant
until the 7 per cent level is reached. At this
concentration the half-time becomes significantly
larger. The off-transient half-times for respira-
tory frequency, tidal volume and minute ventila-
tion all decrease with increasing stimulus concen-
tration. Again it can be noted that the trend of
the alveolar oxygen half-time is opposite to that
of the other variables. The half-times for alve-
olar Pco2 are essentially constant for all in-
spired C(>2 values. As the PCO2 on-transients,
the PC02 off-transients are the fastest ones
observed. The off-transients for every varibale
except alveolar P02 are faster than the on-tran-
sient.
Computer Simulation
The model vas divided into a controlled system
and a controlling system. The former is Illus-
trated in Figure 7. It consists of a lung com-
partment, a cerebrosplnal fluid compartment, a
peripheral sensor compartment, and a lumped tis-
auc compartment. Arterial blood and venous blood
were given their own CO2 dissociation curves, and
all tissues, for simplicity, were assumed to have
the dissociation curve of brain tissue. In actu-
ality, this is not a bad assumption when this
curve is compared to those of the other major
tissues. Cerebral blood flow was assumed to be
a steady-state function of arterial Pco2 and a
first-order lag, as was the blood flow to the
lumped tissue compartment. Blood flow to the
peripheral sensor compartment was assumed to be
constant. Cardiac output was then the sum of the
Individual flows. Circulation times were con-
sidered to be variable depending on the instan-
•ous flow rates.
The controlling system is shown in Figure 8.
Ventilation is considered to be the sura of two
components, a peripheral chemoreceptor component
and a central chemoreceptor component. Each of
these is determined by use of a function curve
and a weighting function (w=0.88). The inputs to
the two functions are assumed to be peripheral
chemoreceptor hydrogen ion concentration (Cpgw^ .)
and central chemoreceptor hydrogen ion concentra-
tion (CCS(,-f). Alveolar ventilation (VA) is
determined from minute ventilation as follows:
Tidal volume Is computed from minute ventilation
by use of a function curve based on data from
the literature2"^!?. Physiological deadspace (Vn)
is then computed from tidal volume based on data
from the literature*. Minute ventilation is
divided by tidal volume to obtain respiratory fre-
quency. Respiratory frequency is then multiplied
by deadspace to obtain minute deadspace (fVn)
which is substracted from minute ventilation to
give alveolar ventilation.
Viewing the central chimoreceptor as being
located somewhere between cerebrosplnal fluid
and deep brain tissue, a Pco2 gradient between
cerebrospinal fluid Pco2 (PcSFcoj) and deeP brain
tissue Pco2 can be described by
X/D) (1)
in which Qcs is the blood flow in the neighbor-
hood of the central sensor, S is the slope of the
COJ dissociation curve, D is the diffusion coeffi-
cient of CC>2, and X is the depth beneath the sur-
facelO. Pco2 in this equation becomes the central
receptor PcO2 (Pcs ) at a value of X equals to
its depth beneath tfte surface. The pH at this
point Is
P«cs -
and the hydrogen Ion concentration is
CCSH+ " «xp(-2.303pHcs) (3)
The sensor depth is determined as shown in
Figure 9. The solid lines were obtained from the
model by fixing the sensor depth a various values.
The number associated with each curve is the sen-
sor depth in microns. Zero microns represents the
surface of the medulla and 1000 microns is ap-
proaching the deep brain tissue level. The dots
are experimental data from 14 human subjects.
As can be seen, the 280 micron transient falls in
the neighborhood of the experimental data. The
sensor depth was, therefore, fixed at this value
In the model. :
Figure 10 shows the simulation results for •
step inputs of 3, 5, 6, and 7 per cent C02.
Comparison of this figure to Figure 5 shows that,
in general, agreement between experimental data
and model is good at all concentrations of In-
spired C02.
Figure 11 shows the response of the model to '.
step perfusion of the "surface of the medulla" i
with mock cerebrospinal fluid high in C02. Data
from human subjects, as might be expected, is not
available for comparison. However, Mitchell et
a_l. *" did perform a similar experiment in anes-
thetized cats (Figure 12). A qualitative compar-
ison can, therefore, be made. As can be seen,
the response of the model appears to be similar
in form to the response of the anesthetized cat.
In addition, using responses of the model to
both CC>2 inhalation and CSF perfusion, the con-
troller relationships of previous models^.** were
compared to the present one. Although differences
in responses to C02 inhalation did occur with each
controller relationship, they were not greatly
different. The responses to CSF perfusion, how-
ever, varied greatly, the present relationship
giving the most satisfactory result.
The responses of the model were also similar
for CO2 inhalation when the single central sensor
vas replaced by one monitoring ccrebrospinal fluid
H* concentration and contributing 23 per cent of
the central ventilatory drive and another monitor-
Ing deep brain tissue H4' concentration and con-
tributing 77 per cent of the central ventilatory
drive. The responses to cerebrospinal fluid per-
fusion, however, were considerably different in
each case.
References
1. Asnussen, E. and Nlelson, M. Physiological
dead space at rest and during muscular exer-
cise. Acta Physiol. Scand. 38:1-21. 1956.
2. Drlpps, R. D. and Comroe, J. H., Jr. The
respiratory and circulatory response of normal
man to inhalation of 7.6 and 10.4% CO2 with
• comparison of the maximum ventilation
provided by severe muscular exercise, inhala-
tion of C02 and maximum voluntary hyperventl-
latlon. Am. J. Physiol. 149:43-51. 1947.
3. Grodins, F. S., Buell, J., and Bart, A. Math-
en* t leal analysis and digital simulation of
the human respiratory system. J. Appl.
Physiol. 22:260-275, 1967.
4. Hey, E. N., Lloyd, B. B., Cunningham, D. J. C,
Jukes, M. G. H., and Bolton, D. P. G. Effects
of various respiratory stimuli on the depth
•nd frequency of breathing in man. Resp.
Fhystol. 1:193-205. 1966.
5. Holloman, G. H., Jr. and Milhorn, H. T., Jr.
Data acqulslon and digital computation of
respiratory transients. Proc. Ann. Symp.
Biomath. Comp. Sci. Life Set.. 8th. pp 53-56,
1970.
6. Horgan, J. D., and Lange, R. L. Digital
computer simulation of respiratory responses
to cerebrospinal fluid Pco2 in the cat.
Blophys. J. 6:935-945. 1965.
7. Laobertsen, C. J. Carbon dioxide and respira-
tion In acid-base homeostasis. Anestheslology
21:642-651, 1960.
8. Milhorn, H. T., Jr., Benton, R., Ross, R., and
Cuyton, A. C. A mathematical model of the
hunan respiratory control system. Biophys.
J.. 5:27-46, 1965.
9. Milhorn, H. T., Jr., Reynolds, W. J., «nd
Holloman, G. H., Jr. Digital computer .simula-
tion of C02 inhalation and CSF perfusion.
Coup, and Blomed. Res. In Press.
10. Mitchell, R. A., Loeschcke, H. H., Masslon,
W. H., and Severinghaus, J. W. Respiratory
responses mediated through superficial super-
ficial chemosensitlve areas on the medulla.
J. Appl. Physiol. 18:523-533, 1963.
11. Reynolds, W. J., and Milhorn, H. T., Jr.
Transient ventilatory responses to hypoxla
with and without controlled alveolar Pco2>
J. Appl. Physiol. Submitted. '
12. Reynolds, W. J., Milhorn, H. T., Jr. and
Holloman, G. H., Jr. Transient ventilatory
response to graded hypercapnla in the human.
J. Appl. Physiol. In Press.
TABLE 1. Summary of steady-state values and half-times for minute ventilation, tidal volume, and respiratory
frequency.
VARIABLE
Minute
Ventilation
(liters/min)
Tidal
Volume
(liters)
Respiratory
Frequency
(breaths /min)
pico2
0.03
0.05
0.06
0.07
0.03
0.05
0.06
0.07
0.03
0.05
0.06
0.07
PRESTIMULUS
CONTROL
6.3
5.7
5.8
6.0
0.61
0.59
0.58
0.60
11.0
11.5
11.8
12.1
25-MINUTE
VALUE
11.25
17.40
27.41
41.44
0.97
1.15
1.53
1.79
13.1
17.9
21.0
25.5
ON -TRANSIENT
tu (seconds)
64
93
123
135
62
72
75
78
*
206
210
225
OFF -TRANSIENT
tv (seconds)
43
24
16
12
50
27
23
19
*
29
24
23
* Not sufficiently well-defined to measure transient half-times.
2.;*StMMry of steady-state value* and half-tin** for alveolar I^ >2 *nd FCOo
*IZABI* *C02
0.03
i : 0.05
WP «W 0.06
- 4
' : ' . °'07
0.03
**X>2 0.05
(•iHg)
0.06
0.07
PRESTTMDLUS
CONTROL
102.5
102.0
100.9
102.8
42.2
43.6
42.5
43.1
2 5 -MINUTE
VALUE
126.0
131.8
132.1
144.0
44.3
47.5
48.9
56.2
OH-TKAMSIEMT
ti (seconds)
72
64
61
45
6.6
6.0
5.7
13.0
%
OVERSHOOT
0
0
0
0
24
20
0
0
OFF-TRANSIENT
ti (seconds)
49
57
75
84
6.0
4.9
4.7
6.0
T.
UNDERSHOOT
0
0
0
0
27
54
63
72
Figure Captions
1. The respirator; system as a black boxlZ.
1 22. Data collection system  .
3. Transient tidal volume responses to steps of
3, 5, 6, and 7 per cent C(>2 in Inspired air12.
4. Transient respiratory frequency responses to
steps of 3, 5, 6, and 7 per cent C&2 ln
Inspired atr!2.
5. Transient minute ventlla tlon responses to
steps of 3, 5. 6, and 7 per cent C02 in
Inspired air12.
6. Transient responses of alveolar PCO2 and Po2
to steps of (a) 37., (b) 57., (c) 67., and (d)
71 COj in Inspired air12.
7. The controlled system'.
8. The controlling system'.
9. Determination of central receptor depth (see
text for explanation)9.
UX Transient minute ventilation responses of the
model to steps of 3, 5, 6, and 7 per cent CO2
In Inspired air9.
11. Transient tidal volume and alveolar Fco2
responses of the model to a step of C(>2 in
cerebrospinal fluid9.
12, Transient tidal volume and alveolar Pco2
responses of an anesthetized cat to a step
of CX>2 in cerebrosplnal fluid10.
coz
Fi02
RESPIRATORY
SYSTEM
VT
i
Figure 1
Figure 2
05
15 2O 25
TIME (minutes)
30 40
10 ft to
TIME (minuf«»)
40
Figure 4
10 15 20 23
TIME (minutes)
Figure 5
j ')v»—* v
.1
i *
1 1 1^ ""^  I 1 1 _L . J^l .
8 » g 5 § S| 5 8 ? 8 «
. . A . . . . . V .
i
* <•
*9
>*
•iS
0)
S_
Figure 8
100-
8 12 16 20 24
TIME (mimifes)
26 32 96 40
Figure 9
50r
4O
50
c
'i
20
IO
T%
KD 15 20 25
TIME (mmut«)
90 35 40
Figure 10
50 r
O. 30
0
Figure 11
2 4 6
TIME (minutes)
Figure 12


Digital simulation and experimental evaluation of the CO2-H(plus) control of pulmonary ventilation

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