The human ventilatory response to step changes in end-tidal PO2 of differing amplitude

Respiration Physiology, 94 (1993) 0

1993 Elsevier

Science

309

309-321

Publishers

B.V. All rights reserved.

0034-5687/93/$06.00

RESP 02077

The human ventilatory response to step changes in end-tidal PO2 of differing amplitude D.H. Paterson”Tb, I.D. Clement”, L.S. Howard”, Robbins”,” I’ Ukwrsity

Lahorator~

B. Nagyova”

of Physiology, Parks Road, O.xjiird, OXI 3PT, University,

of

Westem Onturio. London,

(Accepted

UK; h Faculty

and P.A. of Kinesiology,

Canada

19 July 1993)

Abstract. This study assessed

whether the form of the peripheral chemoreflex response to hypoxia depends on the magnitude of the stimulus. Two amplitudes of square-wave hypoxic stimulation were employed: small amplitude (SO) PETE, from 63.2 to 54.9 Torr, and large amplitude (LO) PET,, from 73.0 to 48.0 Torr. Each was studied at two I&els of PET,,:: 2 Torr above resting PETE,,? (EC), and-7 Torr above resting PET,,,, (HC). Each protocol was repeated 6 times on 5 subjects. To assess the form of the response. a simple first-order model was fitted to the data which incorporated a pure delay (Td) and time constant (T). Average parameter values (set) were: ECSO r= 4.07, Td = 6.69; ECLO r= 8.82, Td = 4.91; HCSO r= 5.22, Td = 7.08; HCLO r= 9.96, Td = 4.39. ANOVA demonstrated modest but significant differences for log,(r) (P
Chemoreceptors,

peripheral;

Control

of breathing;

Hypoxia;

Stimulus

magnitude;

Mammals,

humans

A first-order linear model has previously been used to describe the ventilatory responses to isocapnic hypoxia (Robbins, 1984). More recently a number of first-order model structures have been examined by Clement and Robbins (1993) using the ventilatory responses to periodic hypoxic input stimuli presented at a number of different frequencies. They found that the values for the first-order model parameters varied with the frequency of the hypoxic input stimulus suggesting that the model was incomplete. The purpose of this study was to investigate the same model of the ventilatory response to hypoxia to determine whether there was any variation in the model parameters with the amplitude of the hypoxic stimulus. To do this the ventilatory response in human subjects to a periodic hypoxic square-wave stimulus in the alveolar gas has been studied using the dynamic end-tidal forcing technique. The square-wave hypoxic stimulus was presented at constant frequency but at two different amplitudes (step sizes). Experi-

*Corresponding

author.

Tel.: 0865-272490;

Fax: 0865-272469

310 ments were performed both near eucapnia and in moderate lar advantage of the square-wave protocol is that it provides latory transients from which to obtain reliable estimates parameters (Clement and Robbins, 1993).

hypercapnia. A particua large number of ventiof the dynamic model

Methods Subjects. Five healthy men of mean age 27.12 9.5 (mean + S.D.) years, height 1.79 + 0.01 m, and mass 70.5 + 1.3 kg served as subjects. Subjects received both a verbal and written explanation of the study before consenting to take part. The study was approved by the Central Oxford Research Ethics Committee. Preliminary experiments. These were undertaken to gauge the individual subject’s “steady-state” responses to hypoxia and hypercapnia. The data were used to estimate the four parameters of the Lloyd-Cunningham equation (Lloyd et al., 1958),

iTE = D (P,,>

- B) + DA

(P,oz

- B)

(Pr& - C) namely A, B, C and D. These parameter values were used in the prediction of the inspiratory gas profiles for CO, and 0, required to generate the desired stimuli in the alveolar gas in the main experiments. In these experiments each trial lasted 26 min and consisted of a series of step changes in PEToZ with isocapnia maintained throughout. Each trial started with an 8 min period at PETIT = 100 Torr followed by successive 2 min test periods at PETE, = 60, 100, 45, 300 and 50 Torr, each separated by 2 min periods at PETIT = 100 To&. Four of these trials were completed on each subject, two near eucapnia (PET,,? = rest + 2 Torr) and two in hypercapnia (PET,,? = rest + 7 Torr). The advantage of this protocol is that it allows acute hypoxic responses to be assessed whilst avoiding any hypoxic ventilatory depression (Clement and Robbins, 1993). The breath-by-breath ventilations were averaged over the second minute of each of the 2 min test periods. The average ventilations at each PETE> and PET,-~~ were used in a non-linear regression to determine values for the parameters of the LloydCunningham equation for the ventilatory response to hypoxia and hypercapnia. Main experimental protocol. Two different step sizes for PETE, were studied at two different levels of PETALS. Thus, the four protocols were: ECSO (eucapnic small 0, step), ECLO (eucapnic large 0, step), HCSO (hypercapnic small O2 step), and HCLO (hypercapnic large 0, step). The PETE, levels employed for the large 0, step were 48.0 and 73.0 Torr which corresponded to haemoglobin saturations (Sa,,) of 83.4 and 94.5 % respectively when calculated by the Severinghaus equation (Severinghaus, 1979). The PETE, levels employed for the small 0, step were 54.9 and 63.2 Torr (Sao, val-

311 ues of 88.1 and 91.8%). Thus the magnitude of the hypoxic steps, in terms of oxygen desaturation, differed by a factor of 3.0, with the mean Sac,, for both being approximately 90.0% (89 to 90%). These step changes in Paz were presented at eucapnia + 2 Torr (EC, PETIT,= 39, 41, 48, 42, and 44, in subjects 868, 888, 876, 880, and 886, respectively) and at eucapnia + 7 Torr (HC, PETIT, = 44,46, 53,47, and 49 in subjects 868, 888, 876, 880 and 886, respectively). The period of the PETE, cycle was chosen at 90 set for all four protocols. Each protocol was of 42 min duration and each was repeated to achieve six acceptable trials on each subject. Subjects completed 2 to 5 trials per session (2 to 5 hours) and the total of 24 successful trials was completed on a subject over a period of 3 to 5 months. At each session the protocols were presented in a varied order.

Respiratory measurements. Subjects were seated comfortably in a chair breathing through a mouthpiece with the nose occluded. Respiratory volumes were measured with a turbine device (Howson et al., 1986) and respiratory flows and durations were obtained using a pneumotachograph. Respired gases were sampled continuously at a port just proximal to the turbine to determine Paz and Pco2 by mass spectrometry. Data were sampled every 20 ms by computer. Expired ventilation was calculated breathby-breath by dividing the expired volume by the breath duration measured from the start of inspiration. Throughout, breath-by-breath data for VT~ and VT~, PETE, and were displayed on a six channel recorder. PET,02

Control of inspiratory gas composition. A computer-controlled fast gas-mixing system (Robbins et al., 1982; Howson et al., 1987) was used to vary the inspiratory gas composition in order to elicit accurate dynamic changes in end-tidal gas composition. A model of the cardio-respiratory system was used to estimate for each subject the second-by-second ventilation expected in response to hypoxic steps and the level of PETcoI. This model was supplied with the parameter values for each subject describing the steady state responses to hypoxia and hypercapnia obtained from the preliminary experiments. The cardio-respiratory model was then used with these calculated ventilations to predict the pattern of changes (second-by-second) in the inspiratory partial pressures required to produce the required end-tidal values. During an experiment values for PET,> and PETIT* were calculated by the data acquisition computer and sent to the controlling computer. These data were compared with the desired end-tidal values, and together with the predicted values for inspirafeedback routine was used to calculate the tory PCO* and Paz an integral-proportional new requirements for the inspiratory gas (Robbins et al., 1982). The gas mixture was then generated via the fast gas-mixing system (Howson et al., 1987). Fig. 1 shows a sample experimental tracing, and it illustrates the quality of a couple of step changes in end-tidal Po2, the changing inspiratory gas mixtures required to achieve the desired end-tidal values, the control of the PETIT?, and the subject’s ventilatory responses.

312 HCSO

1

I

0

1

1 min.

Fig. I. Sample chart recording of breath-by-breath responses to cyclic step changes of hypoxia with PET,,, held constant. Upper panels, cxpiratory tidal volume (VT~ );middle panels, P,,,? at the mouth; and lower panels. P,,? at the mouth. Left panels are from an ECLO protocol, and right panels from an HCSO protocol.

Selection of data for malysis. For each 42 min trial the first 21 min were omitted, to allow the slow dynamic changes associated with hypoxic ventilatory decline (HVD) time to develop (Weil and Zwillich, 1976). Data analysis and model fitting was therefore limited to minutes 22 to 42, consisting of 14 cycles of the 90 set hypoxic steps. In order to examine the quality of end-tidal gas control, graphs of the average cycle for each experimental trial were constructed. For this purpose the data were divided into 1 set time bins and end-tidal gas values and ventilation assumed to be constant for the duration of each breath. The graph was then examined by two investigators for the quality of the input and the trial rejected if either investigator felt the GOI control or hypoxic steps were not satisfactory. In general one trial of each of the four protocols in each subject was needed to produce the modifications to the inspiratory Pco and P,? predictions in order to produce subsequent trials of adequate input quality, with the PETIT, controlled within 0.5 Torr ofthe desired value, and with the PETE, following a square wave pattern of the desired values. Overall it required approximately 31 trials (29 to 34) on a subject to complete 6 acceptable trials on each of the four protocols. Model.fitting.

compartment

The ventilatory response for each trial in each subject was fit by a single model represented by first-order, linear differential equations as detailed

313 by Clement and Robbins (1993). Briefly, the model of the ventilatory poxia regards the total iTE as consisting of \ip, the hypoxia-dependent

response to hyventilation re-

lated to the peripheral chemoreflex, and Qc, the hypoxia-independent ventilation related for the most part to the central chemoreflex (Miller et al., 1974). As isocapnia was maintained in each of the protocols ?c was regarded as constant. The dynamic behaviour of the hypoxia dependent component of the ventilation was described by: 7’ d+pldt

+ +p = Gp . (Hyp,,

T.d)),

where Gp is the hypoxic gain, Hyp the hypoxic stimulus, a function of PETE,, T is the time constant and Td the pure delay. The pure delay term (Td) is related to the circulation time from the lungs to the carotid bodies. The hypoxic function (Hyp) is the calculated haemoglobin desaturation (Severinghaus, 1979) given by: Hyp = 1.0 - {(2340O/(P~~,~’

+ 150.P~~o~))

+ 1)

I.

This expression for the hypoxic function has been shown to have an approximately linear relationship with the ventilatory response (Clement and Robbins, 1993). In this model, based on the results of Clement and Robbins (1993) the non-linear conversion of the P, to hypoxia is performed before the dynamics associated with the first order model are introduced into the calculation of the model ventilation (model 3 of Clement and Robbins, 1993). The technique used to fit the model to the data was the same as that described by Clement and Robbins (1993). The differential equation was solved over a single breath to give a difference equation which describes the model ventilation for each breath in terms of the PET,, and breath duration for that breath. This method has the advantage that the actualbreath-by-breath PET o, is used in calculating the model ventilation. The parameters to be estimated for the model (r, Td, Gp, ?c) were constrained to be greater than zero with z not exceeding 60 set and Td not exceeding 20 sec. The best fit parameters were estimated by non-linear regression using the NAG (Numerical Algorithms Group, Oxford, UK) Fortran library routine E04FDF to minimize the residual sum of squares for each breath weighted by the breath duration. Fitting of the model of the ventilatory response was carried out individually for each of the six trials of each protocol (ECSO, ECLO, HCSO, HCLO) in each subject. Additionally the breath-by-breath data and model results of each of the six trials (with 14 step cycles in the trial) were each averaged in the same way to obtain a composite graph of the ventilatory response and model fitting from a total of 84 step cycles of hypoxia for each protocol type in each subject. Statistical analyses. For each parameter, the total set of values obtained for all subjects was subjected to a repeated-measures three way analysis of variance performed with CO,-level (EC, HC) and 0, step amplitude (SO, LO) as fixed factors and subjects as a random factor. As the fitted time constant of the model could be non-normally

314 distributed (with the possibility of some time constants being very long) the distributions of the time constant data were compared to distributions predicted for a normal distribution of the same mean and variance. The upper values of the data were larger than predicted by the normal distribution on 18 out of 20 occasions (PtO.OO1) and the lower values of the data were smaller than predicted on 4 out of 20 occasions (P 0.05). Analysis of variance was therefore also conducted on the log,(z) data.

Results Quality of input. The dynamic end-tidal forcing system (after adjustment of the input model for each subject) produced the cyclic step changes in PETE, every 45 set as desired, with the PETITE controlled to within approximately + 0.5 T&r of the desired value throughout the 90 set cycle. Fig. 2 shows the PETIT, the calculated haemoglobin desaturation and the PETIT, as averaged over the 84 cycles of each protocol in one subject (888). The step amplitudes and means for the calculated haemoglobin desaturations are shown in Table 1. The mean ratio of the large and small O2 step amplitudes, in terms of haemoglobin desaturation, was 2.7 for the near-eucapnic protocol and 2.8 for the hypercapnic protocol (intended ratio 3.0). Ventilatory results. The ventilatory response and in hypercapnia are shown for the mean tocol) for one subject (880) in Fig. 3. For all ventilatory response was 2.70 L.min-’ for for L.min-’ for HCSO, and 9.64 L.min-’ clearly higher for the HC protocols than for

to the cycles of hypoxia in near eucapnia data (average of 84 cycles for each prosubjects combined, the amplitude of the ECSO, 9.26 L.min-’ for ECLO, 3.09 HCLO. The baseline ventilations were the EC protocols.

Modelfitting results. Model fitting of the ventilatory responses was performed for each trial of each protocol in each subject. Fig. 3 illustrates the average ventilatory and model responses for each protocol in a single subject (880). Table 2 shows the mean values for each of the parameters of the model for each subject. Table 3 shows the average parameter values for the model across all subjects for each of the four protocols together with the results of the analysis of variance for the COZ level and the O2 step size. The interactive term between CO2 level and 0, step size did not reach significance for any of the parameters. In all subjects the baseline ventilation was significantly higher in HC versus EC trials. There was no significant difference between the baseline ventilations for the SO versus LO trials. For the small 0, steps, the magnitude of the gain was greater in all subjects in the HC trials compared with the EC trials, but for the large 0, steps this was true only for 3 of the 5 subjects. Overall these differences did not reach significance. There was a tendency for the gain term to be higher for the large 0, steps than

315 Subject

888

B. ECLO

A. ECSO

II

(

0

c.

HCSO

0

153045607590

Time

I

1

1

1

1

60

75

90

153045607590

D. HCLO

0

(set)

15

30

Time

45

(set)

Fig. 2. The input stimulus averaged over 84 cycles for each protocol (EGO, ECLO, HLSO, HCLO) in one subject (888). In each panel the upper plot shows the PETIT> (solid line), the lower plot the PETE, (solid line), and the middle plot the calculated oxygen desaturation (broken line and right hand scale; Severinghaus, 1979).

for the small 0, steps (all 5 subjects in eucapnia, 3 out of 5 subjects in hypercapnia). Again this did not quite reach significance. For the time constant, there did not appear to be any consistent effect of the degree of hypercapnia upon its value, but there was a tendency for the larger 0, steps to be associated with larger values for the time constant (all 5 subjects in eucapnia, 4 out of 5 subjects in hypercapnia). This did not quite reach significance. Since the estimates for the time constants were shown to have a distribution significantly different from normal (see Methods) the analysis of variance was repeated on the log, values of the time constants (Table 4). Under these conditions, the time constant was found to be significantly longer for the large 0, steps (P
316 TABLE 1 Target

and actual experimental

Target values Amplitude

Small sleps Large steps

3.7 11.1

haemoglobin

(“;) for each protocol

Actual values Mean

90.0 89.0

Eucapnia

for all 5 subjects.

Hypcrcapnia

Amplitude

Mean

Amplitude

4.1

90.0

3.9

90.0

(3.7-4.4)

(89.9-90.0)

(3.7-4.4)

(89.9-90.1)

89.0

11.0

89.0

(88.9-89.4)

(10.8-11.6)

(88.9-89.0)

I I.0 (10.7-I

Values arc means

desaturations

1.7)

Values in brackets

are maximum

O2 steps (all 5 subjects for EC, 4 out of 5 subjects for the group as a whole (Table 3, P-cO.05).

and minimum

Mean

of range.

for HC). This trend was significant

Discussion Qualit_v qf input. The averaged PET,~ transients approximated a square-wave input with reasonable precision (Fig. 2). However, this approximation is not perfect and, in addition, there was some variation between the individual cycles. In order to allow for this, the model fitting procedure used the actual breath-by-breath PETE, in calculating the model ventilation (see Clement and Robbins, 1993). The fitting procedure did not take into account variations in PETIT,. However, these variations were small and there did not appear to be any systematic variations in PETIT? throughout the hypoxic cycle (Fig. 3). In their study of the responses of the peripheral chemoreflex to isocapnic hypoxic stimuli, Clement and Robbins (1993) found that consideration of the effects of CO1 variations on the peripheral chemoreflex contribution to ventilation did not appreciably improve the fit of the model. They also argued that the low amplitude and high frequency variations in PETIT> should have little effect on the central chemoreflex because of the slow time constant of this chemoreflex (Bellville et al., 1979). Fitting qf model. As shown in Fig. 3, the ventilatory responses were reasonably well fit by the model with the residuals generally close to zero across the cycle. The use of many cycles of hypoxia (84 per protocol per subject) helped reduce the influence of noise in the model fitting process. The major finding arising from the model fitting was that there was a modest but significant variation in t and Td with the step size, with a longer time constant and shorter pure delay associated with the greater amplitude of the ventilatory response to the large 0, steps compared with the small 0, steps. This suggests that the model is incomplete, as these parameter values should not vary with the type of input. A similar observation was evident in the data of Dahan (1990)

317

Subject A.

.E \

880

8. I

ECLO

ECSO

I 5Ot 40 _-

d

-

30 .>w

In

2ot 0

(set)

-3

-

C.

Time

-3

D.

HCSO

.E

(set)

0

.I! $ CL

153045607590

3

m 0 2

0

0

: oz

Time

3r

VI 0 3

0

153045607590

50

40

HCLO

f---L._

‘= .>y

30

20

l-J

0 3

v) 0 3

I

I

1

153045607590

Time

I

1

J

0

(set)

r

I

I

I

I

I

I

153045607590

Time

(set)

0

.z : (L

I

-3

Fig. 3. Upper plots: Vcntilatory responses (solid line) and model fit (broken line) averaged over 84 cycles for each protocol (EGO, ECLO, HCSO, HCLO) in the same subject (880). Lower plots: Averaged residuals (L,min-‘) calculated from mode1 minus data (broken line) k 2SE (solid line).

wherein an hypoxic step during exercise yielded a significantly longer time constant than an hypoxic step at rest. Again, the longer time constant was associated with the greater amplitude of response. Painter et al. (1993), in a study of models of hypoxic depression, found that the rapid time constant associated with the onset and relief of hypoxia was longer when a hypercapnic background was present compared with a eucapnic background. In the present experiments, however, the CO, background did not alter the time constant. This latter finding of the current study might suggest that the lengthening of the time constant was related to a larger hypoxic stimulus per se, rather than to the magnitude

318 TABLE

2

Mean parameter values for individual subjects. ECSO = eucapnia, Ox step; HCSO = hypercapnia, small 0, step; HCLO = hypercapnia, Parameter

Expt

Baseline +E (+c) (L.min-

‘)

Gain (Gp) (L.min

888

876

880

886

ECSO

28.9

19.1

22.3

12.7

14.8

ECLO

(3.5) 24.3 (3.2)

(1.9) 19.0

(4.0) 21.6

(1.2) 16.0

(1.5) 17.2

39.5

(1.4) 37.5

(2.4) 41.5

(2.8)

HCSO

42.8

(1.5) 33.5

HCLO

(3.3) 47.8

(2.5) 35.0

(3.0) 36.5

(3.3) 33.2

(2.6) 33.8

(3.4)

(1.7)

(2.2)

(3.1)

(2.9)

ECSO ECLO HCSO HCLO

constant (see)

ECSO (T) ECLO HCSO HCLO

Pure delay

ECSO

(Td) (set)

Subjects 868

’ “,)- ’

Time

small 0, step; ECLO = eucapnia, large large 0, step. Values are means ( k SE).

0.50

0.31

0.96

0.73

0.72

(0.09)

(0.09) 1.01

(0.14)

(0.17)

0.79

(0.07) 0.68

0.81

0.93

(0.24)

(0.10)

(0.09)

(0.12)

0.59

0.41

1.12

0.82

(0.07) 1.17

(0.08)

(0.08)

0.60

(0.10) 0.60

1.05

(0.12) 1.43

(0.29) 1.14

(0.03)

(0.06)

(0.08)

(0.37)

(0.11)

8.08

2.60

3.54

2.19

3.94

(5.59)

(0.94)

(2.32)

(0.81)

(1.89)

20.12

6.91

6.75

2.94

7.39

(6.15)

(2.05)

(1.73)

(0.78)

(0.48)

8.48

6.81

1.59

4.74

4.49

(3.77)

(0.73)

(1.04)

(1.83)

13.46

(3.10) 21.15

5.49

2.80

6.90

(2.56)

(7.94)

(1.94)

(0.57)

(1.24)

6.51

1.43

6.44

5.90

7.19

(1.49)

(1.07)

(0.54)

(0.53)

(0.82)

ECLO

4.25

4.34

5.79

5.35

4.83

(0.59) 7.23

(0.42) 5.16

(0.78) 6.49

(0.35)

HCSO

(0.94) 8.92

HCLO

(2.71) 3.76

(1.18) 5.20

(0.41) 5.25

(0.62) 2.87

(1.04) 4.87

(0.75)

(0.26)

(0.33)

(0.74)

(0.72)

7.59

of the ventilatory response. However, in the current study the increase in the value of Gp with hypercapnia was surprisingly small (Table 3) and not significant, and consequently it is not possible to distinguish between these possibilities. The parameter estimates for the first-order model in the present study can be compared with those obtained by Clement and Robbins (1993). In that study, square waves

319 TABLE Mean parameter

Parameter

3

values for all subjects combined together with results of analysis of variance. HC = hypercapnia; SO = small PO2 step; LO = large PO1 step. Expt

Mean

EC = cucapnia;

O2 comparison

CO2 comparison

(SE)

Baseline iiE, \ic (L~min-

ECSO

co2 Level

Mean

EC

19.6

F-ratio (p-value)

0,

step

Mean

type

F-ratio (p-value)

19.6 (1.5)

‘) ECLO

so

29.3

19.6 (1.1) 207.2

HCSO

39.0

0.6

(0.000)

(0.42)

(1.4) HC HCLO

I

LO

0.74

so

38

28.4

37.3 (1.5)

Gain, Gp (L.min

ECSO

I “,,) ’

0.64 (0.06) EC

ECLO

0.73

0.84 (0.06) 3.3

HCSO

0.82 (0.09)

HCLO

0.96

6.8

(0.144)

(0.059)

HC

0.89

LO

0.90

EC

6.45

so

4 65

(0.10) Time constant,

ECSO T

4.07 (1.26)

(=) ECLO

8.82 (1.66)

HCSO

HCLO

Pure delay,

ECSO

Td (set)

0.3

5.22 (1.09)

6.6

(0.623)

(0.062)

HC

7.59

LO

9.39

EC

5.80

so

6.88

9.96 (2.02) 6.69 (0.41)

ECLO

4.91 (0.29) 0.1

HCSO

7.08

16.1 (0.016)

(0.860)

(0.64) HC HCLO

4.39 (0.30)

5.73

LO

4.65

320 TABLE 4 A: Mean values (shown as antilog, set) for log,(r) for individual subjects. B: Results of analysis of variance on log,(r). EC = eucapnia; HC = hypercapnia; SO = small Po, step; LO = large Po. step. A: Expt

Subject 868

ECSO ECLO HCSO HCLO

888

876

880

886

1.80

1.05

0.47

0.74

I .40

(1.09)

(1.51)

(2.64)

(2.48)

(2.16)

16.61

3.63

4.10

2.34

7.32

(1.30)

(2. IO)

(1.88)

(1.38)

(1.07)

2.20

1.79

0.55

3.97

2.34

(2.77)

(3.10)

(2.18)

(1.35)

(1.88)

11.94

16.44

2.48

2.48

6.49

(1.27)

(1.34)

(1.25)

(1.24)

(1.16)

B: Expt

Mean

ECSO

0.98

ECLO

5.31

co, level

Mean

EC

2.29

F-ratio

0,

(p value)

type

so

Step

Mean

1.34

2.9

23.2 (0.009)

(0.164) HCSO

1.82

HCLO

6.30

HC

3.39

F-ratio (p value)

LO

5.81

with periods ranging from 30 to 120 set, with the lower and upper values for PETE, ranging from 47 and 69 Torr to 51 and 55 Torr, yielded a mean value for z of 6.5 set and a mean value for Td of 5.6 sec. These values are very similar to the overall means (all protocols combined) in the present study where t= 7.1 set and Td = 5.8 sec. However, this similarity disguises the marked difference in the current study between the average values for the small 0, amplitude experiments (T = 4.7 set, Td = 6.9 set) and the large O2 amplitude experiments (z= 9.4 set, Td = 4.7 set). Clement and Robbins (1993) found shorter values for z at higher frequencies with a sawtooth input, but no such relationship was observed with the square-wave protocols. However, the square wave amplitudes in their study were varied with frequency (amplitudes were smaller at the lower frequency inputs). In the current study we have shown z increases with increasing amplitude. Thus, it is possible that the lack of significant variation in the values for r obtained from the square wave data of Clement and Robbins (1993) may be explained by two opposing effects, those of amplitude and those of frequency.

321 This study and the previous study of Clement and Robbins (1993) describe some of the ways in which a very simple and fundamental model of the dynamics of the peripheral chemoreflex failed to fit the observed data when a range of different input functions was employed. The particular manner in which the model fails to fit the data may suggest mathematically how the model could be modified to describe the data more accurately. Apart from this, modifications to the model may be suggested from basic physiology, such as the effect of hypoxia on cardiac output (and hence circulation delay) and the form of the response of the carotid sinus nerve to step changes of hypoxia at the carotid body. The challenge is to understand the relations between the mathematical modifications and the basic physiological mechanisms, and in this way learn more about what determines the form of the dynamic ventilatory response to hypoxia.

This work was supported

Acknowledgements.

neering Research

Council of Canada.

him as a sabbatical

scientist.

by the Wellcome

D.H. Paterson

The authors

Trust and the Natural

Sciences

extends thanks to Dr. P.A. Robbins

wish to thank each of the subjects

and Engi-

for accommodating

for their efforts in completing

the experiments.

References Bellville, J.W., B.J. Whipp, and peripheral

R.D. Kaufman,

chemoreflex

G.D.

Swanson,

loop gain in normal

K.A. Aqleh and D.M. Wiberg (1979). Central

and carotid

body- resected

subjects. J. Appl. Physiol. 46:

843-853. Clement,

I.D. and P.A. Robbins

(1993). Dynamics

of the ventilatory

response

to hypoxia in humans.

Respir.

Physiol. 92: 253-276. Dahan, A. (1990). The Ventilatory versity of Leiden. Howson,

M.G.,

S. Khamnei,

for measuring Howson,

volumes

Dioxide

and P.A. Robbins

M.E. McIntyre,

Jukes and D.J.C.

and the respiratory Miller, J.P., D.J.C. man of sudden

response

Cunningham, changes

R., S. Khamnei

and Oxygen in Man. Ph.D. Thesis. (1986). The properties

D.F. O’Connor

Cunningham

to carbon

and P.A. Robbins control.

Robbins,

(1987). A rapid computer-

(1958). The relation between alveolar oxygen pressure

dioxide in man. Quart. J. Exp. Physiol. 43: 217-227.

CO, in hypoxia

and P.A. Robbins

and in high oxygen.

(1993). A mathematical

time courses.

P.A. (1984). The ventilatory

respiratory

effects in

Respir. Physiol. 20: 17-31,

model of the human ventilatory

to isocapnic hypoxia. d. Appl. Physiol. 74: 2007-2015. Robbins, P.A., G.D. Swanson and M.G. Howson (1982). A prediction-correction veolar gases along certain

of a turbine device

J. Physiol. (London). 394: 7P.

B.B. Lloyd and J.M. Young (1974). The transient

in alveolar

Uni-

in man. J. Physiol. (London) 382: 12P.

binary gas mixing system for studies in respiratory

Lloyd, B.B., M.G.M.

Painter,

to Carbon

D.F. O’Connor

respiratory

M.G., S. Khamnei,

controlled

Response

response

scheme for forcing

al-

J. Appl. Phy.yiol. 52: 1353-1357.

response

of the human

respiratory

system to sine waves of alveolar

carbon dioxide and hypoxia. J. PhyJiol. (London) 350: 461-474. Severinghaus, J.W. (1979). Simple, accurate equations for human blood 0, dissociation

computations.

J.

Appl. Physiol. 46: 599-602. Weil, J.V. and C.W. Zwillich pretation.

(1976). Assessment

Chesr 70 (Suppl.):

124-128.

of ventilatory

response

to hypoxia:

methods

and inter-