Development of an anaesthetized‐rat model of exercise hyperpnoea: an integrative model of respiratory control using an equilibrium diagram

Abstract

New Findings

• What is the central question of this study?

  The lack of useful small‐animal models for studying exercise hyperpnoea makes it difficult to investigate the underlying mechanisms of exercise‐induced ventilatory abnormalities in various disease states.

• What is the main finding and its importance?

  We developed an anaesthetized‐rat model for studying exercise hyperpnoea, using a respiratory equilibrium diagram for quantitative characterization of the respiratory chemoreflex feedback system. This experimental model will provide an opportunity to clarify the major determinant mechanisms of exercise hyperpnoea, and will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models.

Abstract

Exercise‐induced ventilatory abnormalities in various disease states seem to arise from pathological changes of respiratory regulation. Although experimental studies in small animals are essential to investigate the pathophysiological basis of various disease models, the lack of an integrated framework for quantitatively characterizing respiratory regulation during exercise prevents us from resolving these problems. The purpose of this study was to develop an anaesthetized‐rat model for studying exercise hyperpnoea for quantitative characterization of the respiratory chemoreflex feedback system. In 24 anaesthetized rats, we induced muscle contraction by stimulating bilateral distal sciatic nerves at low and high voltage to mimic exercise. We recorded breath‐by‐breath respiratory gas analysis data and cardiorespiratory responses while running two protocols to characterize the controller and plant of the respiratory chemoreflex. The controller was characterized by determining the linear relationship between end‐tidal CO₂ pressure ($P_{\mathrm{ETC}{\mathrm{O}}_2}$) and minute ventilation (${\dot{V}}_{\mathrm{E}}$), and the plant by the hyperbolic relationship between ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$. During exercise, the controller curve shifted upward without change in controller gain, accompanying increased oxygen uptake. The hyperbolic plant curve shifted rightward and downward depending on exercise intensity as predicted by increased metabolism. Exercise intensity‐dependent changes in operating points (${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$) were estimated by integrating the controller and plant curves in a respiratory equilibrium diagram. In conclusion, we developed an anaesthetized‐rat model for studying exercise hyperpnoea, using systems analysis for quantitative characterization of the respiratory system. This novel experimental model will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models.

1. INTRODUCTION

Exercise‐induced ventilatory abnormalities in various disease states seem to arise from pathological changes in respiratory regulation (Arzt et al., 2003; Dempsey & Smith, 2014; Guazzi et al., 2007). Many experimental studies have attempted to determine the control mechanisms responsible for generating the ventilatory responses observed during exercise (Ainslie & Duffin, 2009; Dempsey, Miller, & Roman, 2006; Eldridge & Waldrop, 1991; Mateika & Duffin; 1995; Kao, 1963; Krogh & Lindhard., 1913; Wasserman, Whipp, & Casaburi, 1986). However intense debate remains over the major physiological mechanisms responsible for controlling ventilation during exercise (Dempsey & Smith, 2014; Forster, Haouzi, & Dempsey, 2012). Consequently, the pathophysiological mechanisms of abnormal ventilation during exercise under pathological conditions, such as congestive heart failure and chronic obstructive pulmonary disease, are also still unknown. Furthermore, the lack of useful small‐animal models for investigating respiratory control during exercise makes it difficult to investigate the underlying mechanisms of exercise hyperpnoea and respiratory abnormalities.

The respiratory chemoreflex controlling ventilation is a negative feedback system that can be divided into two subsystems: a controller (controlling element) and a plant (controlled element) (Figure 1; Berger, Mitchell, & Severinghaus, 1977; Defares, 1964; Folgering, 1988; Lloyd & Cunningham, 1963; Milhorn, 1966). Briefly, the controller element approximates a straight line and represents the linear increase in minute ventilation (${\dot{V}}_{\mathrm{E}}$; output) in response to an increase in arterial partial pressure of CO₂ ($P_{\mathrm{aC}{\mathrm{O}}_2}$ input). The plant element approximates a hyperbola with a positive asymptote, and represents the asymptotic decrease of $P_{\mathrm{aC}{\mathrm{O}}_2}$ (output) in response to an increase in ${\dot{V}}_{\mathrm{E}}$ (input). Since respiration is determined from the intersecting point of the controller and the plant curves on the respiratory equilibrium diagram (Figure 1), quantitative analysis of the two subsystems of respiratory chemoreflex provides a framework by which we can analytically evaluate how the unique value of ${\dot{V}}_{\mathrm{E}}$ during exercise is determined by the respiratory chemoreflex system, how changes in the controller element affect exercise hyperpnoea, and how changes in the plant element affect exercise hyperpnoea (Cummin & Saunders., 1987; Cunningham, Robbins, & Wolff, 1986). In human studies, we developed an experimental method for quantitative characterization of the respiratory control system at rest (Miyamoto et al., 2004, 2014, 2015) and during exercise (Miyamoto et al., 2012; Ogoh, Hayashi, Inagaki, Ainslie, & Miyamoto, 2008). Subsequently, we succeeded in characterizing these subsystems in an open‐loop condition and constructed a respiratory equilibrium diagram to illustrate the mechanisms of respiratory regulation at rest in normal and CHF rats under anaesthesia (Miyamoto et al., 2006). However, there is no appropriate small‐animal experimental model to investigate the exercise adaptation and/or pathophysiological key mechanisms responsible for controlling ventilation. The primary purpose of this study was to develop an anaesthetized‐rat model for studying exercise hyperpnoea during electrically induced muscular contraction, using systems analysis for quantitative characterization of the respiratory chemoreflex feedback system.

Figure 1.

Block diagram of the respiratory chemoreflex feedback system and equilibrium diagram analysis characterizing the system. The respiratory chemoreflex system consists of two subsystems: the controller (controlling element) and the plant (controlled element). In the controller, the input parameter is $P_{\mathrm{C}{\mathrm{O}}_2}$ and the output parameter is minute ventilation (${\dot{V}}_{\mathrm{E}}$). The controller can be characterized by observing changes in ${\dot{V}}_{\mathrm{E}}$ in response to changes in arterial $P_{\mathrm{C}{\mathrm{O}}_2}$ ($P_{\mathrm{aC}{\mathrm{O}}_2}$). In the plant, the input is ${\dot{V}}_{\mathrm{E}}$ and the output is $P_{\mathrm{aC}{\mathrm{O}}_2}$. The plant can be characterized by observing changes in $P_{\mathrm{aC}{\mathrm{O}}_2}$ in response to changes in ${\dot{V}}_{\mathrm{E}}$ (a). Since both relationships share common variables, the resultant operating point of the ventilatory or $P_{\mathrm{aC}{\mathrm{O}}_2}$ response under the closed loop condition is determined by the intersection of these two factors (b). $P_{\mathrm{a}{\mathrm{O}}_2}$, arterial $P_{{\mathrm{O}}_2}$

2. METHODS

2.1. Ethical approval

All experimental procedures and protocols were performed in accordance with the Guiding Principles for Care and Use of Animals in the Field of Physiological Sciences, approved by the Physiological Society of Japan. Animals were housed on a 12 h–12 h light–dark cycle at 19–23°C and 55 ± 10% humidity and had ad libitum access to food and water. The experiments were approved by the Animal Subjects Committee of the Morinomiya University of Medical Sciences (No. 2014A005). Every attempt was made to reduce animal suffering and discomfort and to reduce the number of animals needed to obtain reliable results. All surgery was performed under general anaesthesia as described in the Experimental preparation section and no animals were reused for different protocols. At the end of the experiments, animals were killed by an overdose of sodium pentobarbitone (200 mg kg⁻¹ i.v.).

2.2. Experimental preparation

In two experimental protocols, 24 male Sprague–Dawley rats (body weight, 340–670 g) were used. Anaesthesia was initiated by an intraperitoneal bolus injection of a mixture of urethane (500 mg kg⁻¹; Sigma‐Aldrich, St Louis, MO, USA) and α‐chloralose (80 mg kg⁻¹; Sigma‐Aldrich). The rats under anaesthesia were intubated and spontaneous breathing was preserved. The depth of anaesthesia was assessed by observing the presence or absence of a significant withdrawal reflex to pinching a paw and the absence of alterations in arterial blood pressure and heart rate. Throughout the experiment, a stable level of these variables was used as an indication of the anaesthetic level. All experimental protocols were completed within 3.5 h and supplemental dosing was not required during the experiment.

2.3. Experimental set‐up

Figure 2 shows the experimental set‐up used for characterizing the respiratory chemoreflex feedback system in rats. The ventilatory responses were measured continuously using an open circuit apparatus. In protocol 1, 12 rats breathed through a tube attached to a low‐resistance one‐way valve. The electromagnetic valve mechanism attached to the inspiratory port allowed the rat to inspire room air or a selected gas mixture from a 40‐litre Douglas bag containing CO₂ in O₂ with N₂ balance [fractional concentration of inspired CO₂ ($F_{\mathrm{IC}{\mathrm{O}}_2}$) = 0.00, 0.03 and 0.05; fractional concentration of inspired ($F_{\mathrm{I}{\mathrm{O}}_2}$) = 0.21 with N₂ balance]. The total apparatus dead space was 0.05 ml. In protocol 2, the other 12 rats breathed through a tube attached to small‐animal ventilator (volume‐controlled mechanical ventilator; model CIV‐101, Columbus Instruments, Columbus, OH, USA). In both protocols, expired gas was sampled continuously, and O₂ and CO₂ concentrations were measured by a mass spectrometer (ARCO2000‐MET, Arcosystem, Chiba, Japan). Expired gas flow was measured using a differential pressure transducer with sufficient sensitivity and frequency response, and a high precision soap‐film flow meter (SF‐1U/2U, Horiba Ltd, Kyoto, Japan). End‐tidal CO₂ partial pressure ($P_{\mathrm{ETC}{\mathrm{O}}_2}$) was used as a surrogate for arterial partial pressure of CO₂ ($P_{\mathrm{aC}{\mathrm{O}}_2}$). Flow signals were converted to single breath data by matching to gas concentrations identified as single breaths using $P_{\mathrm{ETC}{\mathrm{O}}_2}$, after accounting for the time lag (950 ms) in gas concentration measurements. The corresponding O₂ uptake (${\dot{V}}_{{\mathrm{O}}_2}$) and CO₂ output (${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$) for each breath were calculated from the differences of inspired–expired gas concentrations and by expired ventilation, with inspired ventilation being calculated by N₂ correction. A catheter was placed in the right carotid artery and connected to a pressure transducer (BSM‐7201, DX‐200, Nihon Kohden, Tokyo, Japan) to measure arterial pressure. Heart rate was measured using a cardiotachometer (AT601G, Nihon Kohden) triggered by the R‐wave on the electrocardiogram. The heart rate series were checked by visual inspection. Body temperature was monitored with a thermometer placed in the rectum, and was maintained at 38°C using a heating pad throughout the experiment. Oxygen and CO₂ measurements were calibrated using a standard gas of known concentrations before each test. Signals from the mass spectrometer, flow sensor, pressure transducer and cardio‐tachometer were synchronized on‐line using a personal computer, and displayed continuously during all experiments. The signals were logged at 200 Hz using a 12‐bit analog‐to‐digital converter (AD12‐8(PM) CONTEC Co., Ltd, Osaka, Japan). The analytical software program was custom‐made.

Figure 2.

Experimental set‐up used for characterizing the respiratory chemoreflex feedback system in an anaesthetized rat. We recorded breath‐by‐breath gas analysis data during electrically induced exercise at low and high voltage, while running two protocols to characterize the controller [protocol 1, hypercapnia test: end‐tidal CO₂ tension ($P_{\mathrm{ETC}{\mathrm{O}}_2}$) to ${\dot{V}}_{\mathrm{E}}$ relationship] and plant (protocol 2, hypo/hyperventilation test: ${\dot{V}}_{\mathrm{E}}$ to $P_{\mathrm{ETC}{\mathrm{O}}_2}$ relationship) of the respiratory system at rest and during electrically induced exercise. f, respiratory rate; $F_{\mathrm{IC}{\mathrm{O}}_2}$, fractional concentration of inspired CO₂; V _T, tidal volume

2.4. Electrically induced muscle contraction mimicking exercise

Under the above experimental conditions, we simultaneously induced muscle contraction by stimulating bilateral distal sciatic nerves at low and high voltage (0.1–0.5 and 3.0 V, respectively) in the anaesthetized rat. Thus, the intensity of muscle contraction was controlled by varying the voltage (SEN‐7130, Nihon Kohden) as shown in Figure 3. The stimulation electrodes and nerves were secured with silicone glue (Kwik‐ Sil, World, Precision Instruments, Sarasota, FL, USA). Electrically induced muscle contraction mimicking exercise was continued for 24 min using a stimulator. The muscles contracted rhythmically at stimulation frequency of 5 Hz (interval, 150 ms; duration, 2 ms) (Bassols, Carreras, & Cussó, 1986).

Figure 3.

Experimental protocols. Protocol 1: the hypercapnia test consisting of 3 separate fractional concentrations of inspired CO₂ ($F_{\mathrm{IC}{\mathrm{O}}_2}$) trials ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00, 0.03 and 0.05, $F_{\mathrm{I}{\mathrm{O}}_2}$ = 0.21 with N₂ balance) at rest and during electrically induced exercise. Protocol 2: the hypo/hyperventilation test consisting of 3 trials (1 hypoventilation trial and 2 hyperventilation trials) under resting and exercising conditions. Ex (L), induced low‐intensity exercise; Ex (H), induced high‐intensity exercise; Rest, resting (no induced exercise)

2.5. Study design

2.5.1. Methodological approaches to open feedback system in rats

The properties of a closed feedback system can be fully elucidated by examining its open‐loop characteristics. One direct way is to open the loop physically. However, this approach is not always possible in a living body, because the exact location of CO₂ sensors is not known and the brain has to be isolated for that purpose. Therefore, we adopted a more practical approach. In previous small‐animal studies (Bin‐Jaliah, Maskell, & Kumar, 2005; Hayashi, Yoshida, Fukuda, & Honda, 1982), it is well known that arterial CO₂ tension can be manipulated easily by altering the inspiratory CO₂ tension, and ${\dot{V}}_{\mathrm{E}}$ seems to have no effect on arterial CO₂ tension unless ventilation is greatly decreased. Based on this concept, we effectively opened the feedback loop and successfully examined the $P_{\mathrm{aC}{\mathrm{O}}_2}$ to ${\dot{V}}_{\mathrm{E}}$ relationship by changing the inspiratory CO₂ tension at rest and during muscle contraction. In humans, the ${\dot{V}}_{\mathrm{E}}$ to $P_{\mathrm{aC}{\mathrm{O}}_2}$ relationship can be obtained easily by voluntarily changing ${\dot{V}}_{\mathrm{E}}$ to open the feedback loop (Miyamoto et al., 2004, 2012, 2014, 2015; Ogoh et al., 2008). The same method can be used in anaesthetized animals, using a mechanical ventilator.

2.5.2. Assessment of respiratory equilibrium diagram

To characterize the respiratory chemoreflex system in normal rats, we divided the total system into two elements, the controller and plant (Figure 1a). The controller detects changes in $P_{\mathrm{aC}{\mathrm{O}}_2}$ and alters ${\dot{V}}_{\mathrm{E}}$ accordingly. Therefore, we can characterize the controller by observing changes in ${\dot{V}}_{\mathrm{E}}$ in response to changes in $P_{\mathrm{aC}{\mathrm{O}}_2}$. The plant operates according to the command from the controller and expires carbon dioxide accordingly. As a result, $P_{\mathrm{aC}{\mathrm{O}}_2}$ changes in response to changes in ${\dot{V}}_{\mathrm{E}}$. Thus, the plant can be characterized by observing changes in $P_{\mathrm{aC}{\mathrm{O}}_2}$ in response to changes in ${\dot{V}}_{\mathrm{E}}$. The characteristics of the controller are equivalent to central chemosensitivity, and those of the plant correspond to pulmonary efficiency. Since both relationships share common variables, ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$, the intersection of the two curves represents the operating point of the ventilatory response under the closed‐loop condition (Figure 1b).

2.6. Experimental procedures

In order to characterize the controller and plant elements at rest and during stimulation of bilateral distal sciatic nerves under anaesthesia in rats, a hypercapnia test (protocol 1) and a hypo/hyperventilation test (protocol 2) were conducted on two different days.

2.6.1. Protocol 1. Hypercapnia test: controller system characterization

To characterize the controller, we changed $P_{\mathrm{ETC}{\mathrm{O}}_2}$ in 12 anaesthetized normal rats with preserved spontaneous breathing (body weight, 429 ± 42 g). The rats inspired a normoxic gas mixture with increasing inspiratory CO₂ fraction through a ventilatory circuit equipped with a one‐way valve. By this method, we induced hypercapnia in the rats. A hypercapnia test was performed to characterize the controller elements by measuring steady‐state ${\dot{V}}_{\mathrm{E}}$. This test consisted of three separate trials with different $F_{\mathrm{IC}{\mathrm{O}}_2}$ ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00, 0.03 and 0.05; $F_{\mathrm{I}{\mathrm{O}}_2}$ = 0.21 with N₂ balance) each under resting and low‐ and high‐intensity mimicked exercise conditions (Figure 3). Baseline data were recorded at $F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00, before starting the hypercapnia test. Each $F_{\mathrm{IC}{\mathrm{O}}_2}$ trial lasted 8 min. The $F_{\mathrm{IC}{\mathrm{O}}_2}$ in the inspiration gas was increased stepwise every 8 min, and ${\dot{V}}_{\mathrm{E}}$ was plotted against $P_{\mathrm{ETC}{\mathrm{O}}_2}$. After completing each hypercapnia test under each condition followed by a ‘CO₂ washout’ period of 20 min, and confirming that values for ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$ had returned to pre‐test baseline values, the next hypercapnia test was performed (Figure 4a).

Figure 4.

Time courses of cardiorespiratory responses at rest and during electrically induced exercise at low and high intensities in the hypercapnia test (a; protocol 1) and in the mechanical hypo‐ and hyper‐ventilation test (b; protocol 2). f, respiratory rate; HR, heart rate; MBP, mean blood pressure; $P_{\mathrm{ETC}{\mathrm{O}}_2}$, end‐tidal CO₂ partial pressure; ${\dot{V}}_{\mathrm{E}}$, minute ventilation; ${\dot{V}}_{{\mathrm{O}}_2}$, oxygen uptake; V _T, tidal volume. Bold continuous lines represent the mean, and dashed lines indicate ± SD

2.6.2. Protocol 2. Hypo/hyper ventilation test: plant system characterization

To characterize the plant, we altered ${\dot{V}}_{\mathrm{E}}$ by changing the setting of the artificial ventilator in another 12 normal rats (body weight, 446 ± 32 g). The hypo/hyperventilation test was performed to characterize the plant elements by measuring steady‐state $P_{\mathrm{ETC}{\mathrm{O}}_2}$ responses to hypo/hyperventilation. Each hypo/hyperventilation test consisted of three trials (1 hypoventilation trial and 2 hyperventilation trials) at resting and exercising conditions (Figures 3 and 4b). For hyperventilation trials, tidal volume and respiratory frequency (respiratory pattern) were predetermined to match those obtained in protocol 1, in order to match the effect of dead volume (Figure 5). For the hypoventilation trial, we altered ${\dot{V}}_{\mathrm{E}}$ by setting both tidal volume and respiratory frequency 3% lower than the values for the 0.00 $F_{\mathrm{IC}{\mathrm{O}}_2}$ condition. After stabilization, we measured the baseline steady‐state $P_{\mathrm{ETC}{\mathrm{O}}_2}$. We then altered ${\dot{V}}_{\mathrm{E}}$ level stepwise and plotted $P_{\mathrm{ETC}{\mathrm{O}}_2}$ against ${\dot{V}}_{\mathrm{E}}$. Each trial lasted 8 min. All trials were performed under normoxic conditions ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00; $F_{\mathrm{I}{\mathrm{O}}_2}$ = 0.21 with N₂ balance). A 20 min recovery period of room air breathing was set before each increase in exercise intensity.

Figure 5.

The relationship between respiratory rate and tidal volume under spontaneous breathing at rest and during electrically induced exercise at low and high intensities in the hypercapnia test (protocol 1)

2.7. Assessment of respiratory equilibrium diagram and arterial blood samples

On a separate day, we verified the validity of using steady‐state $P_{\mathrm{ETC}{\mathrm{O}}_2}$ as a surrogate for $P_{\mathrm{aC}{\mathrm{O}}_2}$ throughout the hypercapnic and hypocapnic range under the resting condition in five anaesthetized rats (body weight, 493 ± 38 g). In each rat, we positioned a catheter in the carotid artery to obtain arterial blood samples without stasis. The experiment started 20‒30 min after catheter placement. Four hypercapnia tests ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00, 0.03, 0.06 and 0.09; $F_{\mathrm{I}{\mathrm{O}}_2}$  = 0.21 with N₂ balance) and five hypo/hyperventilation tests (1 hypoventilation trial, 1 normal ventilation trial, 3 hyperventilation trials) were conducted in all five rats. For the hypercapnia test, the rats inspired gas with increasing $F_{\mathrm{IC}{\mathrm{O}}_2}$ through a ventilatory circuit equipped with a one‐way valve. The $F_{\mathrm{IC}{\mathrm{O}}_2}$ in the inspiration gas was increased stepwise every 8 min. After completing all of the hypercapnia test followed by a ‘washout’ period of 30 min, and confirming that values for ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$ have returned to pre‐test baseline values, hypo/hyperventilation tests were performed in the same rats. For hypo/hyperventilation tests, we changed the artificial ventilator settings according to ventilation curves at respiratory rates and tidal volumes mimicking those recorded during the hypercapnia trials. Each trial lasted 8 min. All cardiorespiratory parameters were measured using the same methods as in protocols 1 and 2. An arterial blood sample (90 μl) was collected during the last 2 min of each steady‐state trial.

Thereafter we characterized the controller and plant elements, and thus ventilatory regulation, by the respiratory chemoreflex system using an equilibrium diagram. The measured values of the operating point in each rat were defined to be the steady‐state values for ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$ that were obtained during the 0.00 $F_{\mathrm{IC}{\mathrm{O}}_2}$ trial (during spontaneous breathing).

2.8. Data analysis

In each protocol, steady‐state cardiorespiratory data were obtained by averaging the respective data for the last 2 min of each experimental duration. In protocol 1, to characterize the controller system, we performed linear regression of ${\dot{V}}_{\mathrm{E}}$ against $P_{\mathrm{ETC}{\mathrm{O}}_2}$ [${\dot{V}}_{\mathrm{E}}$ = S × ($P_{\mathrm{ETC}{\mathrm{O}}_2}$ − B), where S is the slope and B is the $P_{\mathrm{ETC}{\mathrm{O}}_2}$ intercept]. In protocol 2, to characterize the plant system, we fitted a metabolic hyperbola ($P_{\mathrm{ETC}{\mathrm{O}}_2}$ = A/${\dot{V}}_{\mathrm{E}}$ + C, where A is the numerator and C is the asymptote of the modified metabolic hyperbola (see Appendix), modified from the original metabolic hyperbola, to the measured data including normal spontaneous breathing data. The operating points obtained at rest and during electrically induced exercise were defined as the steady‐state values of ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$ obtained in the trial of $F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.00 (during spontaneous breathing) of the hypercapnia test in protocol 1 (Table 1). The plant gain (G _P) was calculated as the reciprocal of the slope of the modified metabolic hyperbola at the operating point. The total loop gain at the operating point (G _Total) was estimated by the product of the gains of the controller and the plant.

Table 1.

Cardiorespiratory parameters (data averaged over the last 2 min of each trial) at the operating points during the pre‐experimental baseline period in each protocol, and during experimental periods at rest and during mimicked exercise in protocol 1

	Pre‐experimental baseline ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.0%)		Experimental trial periods in protocol 1 ($F_{\mathrm{IC}{\mathrm{O}}_2}$ = 0.0%); data at operating points
Parameter	Protocol 1 (n = 12)	Protocol 2 (n = 12)	Rest (n = 12)	Ex (L) (n = 12)	Ex (H) (n = 12)
$P_{\mathrm{ETC}{\mathrm{O}}_2}$ (mmHg)	44.2 ± 2.8	43.9 ± 4.1	44.6 ± 2.7	44.1 ± 2.4	38.9 ± 4.0**,††
${\dot{V}}_{\mathrm{E}}$ (ml min−1)	77.0 ± 26.4	79.5 ± 25.1	83.0 ± 13.3	124 ± 19**	204 ± 45**,††
V T (ml)	1.6 ± 0.9	1.6 ± 0.5	1.7 ± 0.2	1.9 ± 0.2*	2.4 ± 0.3**,††
f (breaths min−1)	50.1 ± 11.3	51.5 ± 8.3	49.8 ± 10.8	65.0 ± 8.8**	84.4 ± 16.5**,††
${\dot{V}}_{{\mathrm{O}}_2}$ (ml min−1)	3.4 ± 1.2	3.3 ± 1.0	3.7 ± 0.7	4.7 ± 0.7**	6.4 ± 1.2**,††
${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$ (ml min−1	2.8 ± 1.0	2.7 ± 0.8	3.0 ± 0.5	4.2 ± 0.5**	5.7 ± 1.0**,††
MBP (mmHg)	81.8 ± 21.4	79.7 ± 19.8	79.7 ± 19.7	86.9 ± 13.6	116 ± 19**,††
HR (beats min−1)	363 ± 58.1	383 ± 38.5	353 ± 56	386 ± 40	460 ± 30**,††

Values are presented as means ± SD. Ex (H), induced high‐intensity exercise; Ex (L), induced low‐intensity exercise; f, respiratory rate; HR, heart rate; MBP, mean blood pressure; $P_{\mathrm{ETC}{\mathrm{O}}_2}$, end‐tidal pressure for CO₂; Rest, resting (no induced exercise); ${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$, carbon dioxide output; ${\dot{V}}_{\mathrm{E}}$, minute ventilation; ${\dot{V}}_{{\mathrm{O}}_2}$, oxygen uptake; V _T, tidal volume. ^* P < 0.05; ^** P < 0.01 vs. Rest; ^†† P < 0.01 vs. Ex (L).

2.9. Statistical analysis

In each protocol, depending on the purpose of comparison, one‐way, factorial and repeated measures ANOVA followed by Tukey's test were conducted on each response variable using mean data of an individual rat. Fitted parameters for the controller and plant elements were obtained by fitting response curves using linear and non‐linear least‐squares regression analysis. Pearson's product‐moment correlations were calculated between $P_{\mathrm{ETC}{\mathrm{O}}_2}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$ values. Comparisons between $P_{\mathrm{aC}{\mathrm{O}}_2}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$ measures were also evaluated using Bland–Altman analysis (Bland & Altman, 1986). The Bland–Altman plot was subsequently analysed by linear regression analysis to determine if the slope of the relationship was greater than zero, which would indicate that a proportional bias was present (i.e. the difference between two methods changes as the average values from the two methods becomes smaller or larger). Furthermore, a fixed bias is present if the 95% confidence limit of the Bland–Altman plot does not include zero. All data are presented as the mean ± SD and significance for all two‐tailed tests was set at P < 0.05.

3. RESULTS

Hereinafter, electrically induced muscle contraction mimicking exercise is referred to as exercise. Table 1 shows cardiorespiratory parameters at the operating points during the pre‐experimental baseline periods in protocols 1 and 2, and during experimental periods at rest and during muscle contraction induced by electrical stimulation of bilateral distal sciatic nerves at low (0.1–0.5 V) and high voltage (3.0 V) under spontaneous breathing in protocol 1 ($F_{\mathrm{IC}{\mathrm{O}}_2}$; 0.0%). During the baseline period in protocols 1 and 2, there were no significant differences in all cardiorespiratory parameters between protocols 1 and 2. During the experimental period in protocol 1, although $P_{\mathrm{ETC}{\mathrm{O}}_2}$ was regulated at constant level causing exercise hyperpnoea, the exercise stimulus induced voltage‐dependent increases in all cardiorespiratory and metabolic parameters. ANOVA revealed a significant main effect of exercise intensity for ${\dot{V}}_{\mathrm{E}}$, tidal volume (V _T), respiratory rate (f), ${\dot{V}}_{{\mathrm{O}}_2}$, ${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$, mean blood pressure (MBP) and heart rate (HR), indicating that electrically induced exercise at higher intensity significantly increased the above parameters compared to the resting state (P < 0.01). A post hoc analysis revealed that higher exercise intensity increased ${\dot{V}}_{\mathrm{E}}$, V _T, f, ${\dot{V}}_{{\mathrm{O}}_2}$, ${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$, MBP and HR, and decreased $P_{\mathrm{ETC}{\mathrm{O}}_2}$ (P < 0.01) (Table 1).

Figure 4 shows the averaged data of the time courses of cardiorespiratory responses at rest and during electrically induced exercise in the hypercapnia test (protocol 1) and the mechanical hypo‐ and hyperventilation test (protocol 2). In the hypercapnia test both at rest and during exercise at low and high intensities, stepwise increase of $F_{\mathrm{IC}{\mathrm{O}}_2}$ from 0 to 0.05 was accompanied by increases of $P_{\mathrm{ETC}{\mathrm{O}}_2}$, ${\dot{V}}_{\mathrm{E}}$, V _T and f at each $F_{\mathrm{IC}{\mathrm{O}}_2}$ increase, reaching steady states in 3–6 min (Figure 4a). Figure 4b illustrates the effects of changes in ${\dot{V}}_{\mathrm{E}}$ on cardiorespiratory parameters at rest and during electrically induced exercise at low and high intensities. Hypoventilation increased $P_{\mathrm{ETC}{\mathrm{O}}_2}$ while hyperventilation decreased $P_{\mathrm{ETC}{\mathrm{O}}_2}$, and the changes reached steady states in 6–8 min in each trial both at rest and during exercise (Figure 4b).

Figure 5 shows the relationships between respiratory rate and tidal volume during spontaneous breathing in the hypercapnia test both at rest and during exercise in protocol 1. There were no significant differences in the breathing pattern (V _T vs. f relationship) during all trials for both resting and exercise conditions.

Figure 6 shows the characteristics of the controller and the plant at rest and during electrically induced exercise obtained from the averaged steady‐state data shown in Figure 4a and b. For the controller curve, ${\dot{V}}_{\mathrm{E}}$ increased linearly with increase in $P_{\mathrm{ETC}{\mathrm{O}}_2}$ at rest and during exercise (r ² = 0.808–0.995; pooled data of all rats) (Figure 6a). The plant curve approximated the modified metabolic hyperbola reasonably well (r ² = 0.962–0.996; all rats) (Figure 6b). Table 2 shows the estimated parameters of the controller and plant properties, and respiratory total loop gain at rest and during electrically induced exercise at low and high intensities. For the controller, the regression line of the ${\dot{V}}_{\mathrm{E}}$–$P_{\mathrm{aC}{\mathrm{O}}_2}$ relationship shifted upward depending on exercise intensity without significant change in controller gain (S). ANOVA revealed that a significant main effect was observed for the $P_{\mathrm{ETC}{\mathrm{O}}_2}$ intercept (B) (F _[2,22] = 3.94, P = 0.035). A post hoc analysis revealed that the $P_{\mathrm{ETC}{\mathrm{O}}_2}$ intercept (B) during electrically induced high‐ and low‐intensity exercise was markedly reduced compared to the resting condition, but there was no difference between both intensities (Table 2). The fitted plant curve shifted rightward and downward depending on exercise intensity as predicted by increase in metabolic rate (Figure 6b). ANOVA revealed that a significant main effect was observed for the numerator A of the modified metabolic hyperbola (F _[2,22] = 35.80, P < 0.001) and also for the asymptote parameter C (F _[2,22] = 20.02, P < 0.001). A post hoc analysis revealed that electrically induced high‐ and low‐intensity exercise significantly increased A and decreased C compared to resting condition. Furthermore, both A and C values showed a significant difference between both intensities (Table 2).

Figure 6.

Characteristics of the controller (a) and the plant (b) systems at rest and during electrically induced exercise at low and high intensity. Exercise intensity‐dependent changes in operating points (${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$) were estimated by integrating the controller and plant curves in a respiratory equilibrium diagram (c)

Table 2.

Parameters of controller and plant properties, and respiratory total loop gain at rest and during electrically induced exercise at low and high intensities

Parameter	Rest	Ex (L)	Ex (H)
Controller (n = 12)
S (ml min−1 mmHg−1)	6.2 ± 2.0	6.4 ± 2.1	7.2 ± 2.7
B (mmHg)	30.7 ± 5.6	23.4 ± 6.6*	−2.5 ± 52.1**
Plant (n = 12)
A (ml min−1 mmHg−1)	2440 ± 627	4252 ± 1306**	7389 ± 2044**,††
C (mmHg)	18.0 ± 6.1	12.1 ± 4.7*	2.8 ± 4.7**,††
G P (mmHg ml−1 min−1)	0.36	0.26	0.18
G Total	2.0	1.6	1.3

Values are expressed as means ± SD. Controller: ${\dot{V}}_{\mathrm{E}}$ = S × ($P_{\mathrm{ETC}{\mathrm{O}}_2}$− B); S, controller gain; B, $P_{\mathrm{ETC}{\mathrm{O}}_2}$ intercept. Plant: $P_{\mathrm{ETC}{\mathrm{O}}_2}$ = A/${\dot{V}}_{\mathrm{E}}$ + C. A is the numerator and C is the asymptote of the modified metabolic hyperbola. Ex (H), induced high‐intensity exercise; Ex (L), induced low‐intensity exercise; G _P, plant gain at operating point; G _Total, total loop gain at operating point; Rest, resting (no induced exercise). ^* P < 0.05; ^** P < 0.01 vs. Rest; ^†† P < 0.01 vs. Ex (L).

The respiratory equilibrium diagram was constructed by plotting the controller and plant curves together on the same graph, at rest and during electrically induced exercise at low and high intensities (Figure 6c). The intersecting point between the controller and plant curves predicts the closed‐loop respiration operating point. Induced exercise shifted the operating point upward, which effectively stabilized $P_{\mathrm{ETC}{\mathrm{O}}_2}$ within the normal range, and decreased the plant gain (G _P) calculated by the reciprocal of the slope of the modified metabolic hyperbola at the operating point, while the controller gain remained unchanged (S) (Table 2). The significant main effect indicated that the absolute value of G _P at low‐intensity exercise was smaller than at high‐intensity exercise. The estimated total loop gain at the operating point (product of the controller and plant gain) was lower at high‐intensity exercise.

In five rats, the relationships between steady‐state $P_{\mathrm{ETC}{\mathrm{O}}_2}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$ for four $F_{\mathrm{IC}{\mathrm{O}}_2}$ trials as well as one hypoventilation, one normal ventilation and three hyperventilation trials are illustrated in Figure 7. $P_{\mathrm{ETC}{\mathrm{O}}_2}$ correlates tightly with $P_{\mathrm{aC}{\mathrm{O}}_2}$ (n = 45, $P_{\mathrm{aC}{\mathrm{O}}_2}$ = 0.928 × $P_{\mathrm{ETC}{\mathrm{O}}_2}$ + 4.8, r ² = 0.910, P < 0.001) throughout the hypercapnic and hypocapnic range under the resting condition, but $P_{\mathrm{ETC}{\mathrm{O}}_2}$ consistently underestimates $P_{\mathrm{aC}{\mathrm{O}}_2}$ (Figure 7a). In addition, a one‐way repeated‐measures ANOVA revealed no difference between measured values of $P_{\mathrm{ETC}{\mathrm{O}}_2}$ (48.5 ± 16.7 mmHg) and $P_{\mathrm{aC}{\mathrm{O}}_2}$ (49.8 ± 16.2 mmHg). For the Bland–Altman plot, there was a small bias between measurement devices (bias, −1.3 mmHg) and 95% confidence limits of −11.1 and 8.5 mmHg (Figure 7b).

Figure 7.

The relationships between steady‐state $P_{\mathrm{ETC}{\mathrm{O}}_2}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$ for 4 $F_{\mathrm{IC}{\mathrm{O}}_2}$ trials as well as 1 hypoventilation, 1 normal ventilation and 3 hyperventilation trials in five rats. $P_{\mathrm{ETC}{\mathrm{O}}_2}$ correlates tightly with $P_{\mathrm{aC}{\mathrm{O}}_2}$ (n = 45, $P_{\mathrm{aC}{\mathrm{O}}_2}$ = 0.928 × $P_{\mathrm{ETC}{\mathrm{O}}_2}$ + 4.8, r ² = 0.910, P < 0.001) throughout the hypercapnic and hypocapnic range under resting condition. Measures of $P_{\mathrm{ETC}{\mathrm{O}}_2}$ (48.5 ± 16.7 mmHg) and $P_{\mathrm{aC}{\mathrm{O}}_2}$ (49.8 ± 16.2 mmHg) were similar, but $P_{\mathrm{ETC}{\mathrm{O}}_2}$ consistently underestimates $P_{\mathrm{aC}{\mathrm{O}}_2}$. The linear regression analysis (a) and the Bland–Altman plot (b) also revealed a close relationship between $P_{\mathrm{aC}{\mathrm{O}}_2}$ and $P_{\mathrm{ETC}{\mathrm{O}}_2}$. For the Bland–Altman plot, there was a small bias between measurement devices (bias, −1.3 mmHg) and 95% confidence limits of −11.1 and 8.5 mmHg. Different symbols represent results from individual rats (n = 5). A regression analysis was performed on pooled data. Bold line, identity line; fine line, linear regression

Furthermore, we characterized the controller (S = 8.9 ± 2.5 ml min⁻¹ mmHg⁻¹, B = 29.4 ± 2.7 mmHg) and plant elements (A = 3398 ± 851 ml min⁻¹ mmHg⁻¹, C = 13.6 ± 1.7 mmHg) in each rat. Their operating points estimated by the equilibrium diagram (the intersection between the two relationship lines) were very close to those during closed‐loop spontaneous breathing. Consequently, mean estimated $P_{\mathrm{ETC}{\mathrm{O}}_2}$ and ${\dot{V}}_{\mathrm{E}}$ values at the operating point were statistically indistinguishable from the measured values (42.9 ± 3.0 vs. 42.8 ± 2.8 mmHg, and 112.7 ± 11.5 vs 110.4 ± 9.8 ml•min⁻¹, respectively). The gain of the plant estimated by the reciprocal of the slope of the hyperbola curve at the operating point was 0.30 ± 0.07 mmHg ml⁻¹ min⁻¹. The estimated total loop gain at the operating point, i.e. the product of the gains of the controller and the plant, was 2.6 ± 0.3.

4. DISCUSSION

The present study clearly showed that exercise intensity‐dependent increases in cardiorespiratory responses are adjusted to ${\dot{V}}_{{\mathrm{O}}_2}$ increase by evoking muscular activity through electrical stimulation of the peripheral ends of severed bilateral sciatic nerves. Furthermore, under each experimental condition in spontaneously breathing anaesthetized rats (Table 1), the absolute values of ${\dot{V}}_{\mathrm{E}}$ and averaged breathing pattern (V _T–RR relationship in Figure 5) were well within the range reported by Crosfill & Widdicombe (1961) and Palecek et al. (1969). In addition, we experimentally demonstrated that exercise hyperpnoea, i.e. normal isocapnic ventilatory response to electrically induced exercise, can be determined by integrating the controller and plant properties in the respiratory equilibrium diagram.

4.1. Interpretation of the operating point of respiration using the respiratory equilibrium diagram

In this study, electrically stimulated exercise shifted the plant curve rightward and upward, reflecting increased metabolism (${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$ increase). If the exercise stimulus had not affected the controller element, the operating point during exercise would have been the intersecting point between the fine straight line and the bold hyperbola in Figure 6c. In that case, $P_{\mathrm{ETC}{\mathrm{O}}_2}$ would have increased to above 50 mmHg. However, the electrically induced exercise can produce an isocapnic ventilatory response. These results show that the exercise stimulus shifts the controller element toward higher ${\dot{V}}_{\mathrm{E}}$, which effectively stabilizes $P_{\mathrm{ETC}{\mathrm{O}}_2}$ within the normal range, at the expense of exercise hyperpnoea (Figure 6c).

Several decades ago, Cunningham et al. (1986) proposed a model of chemoreflex control of respiration at rest and during exercise. The concept of using the respiratory equilibrium diagram has also been proposed by Berger et al. (1977), Folgering (1988) and Mahamed, Ali, Ho, Wang, & Duffin (2001), Milhorn (1966). Previously, we have demonstrated that the operating point of respiration at rest and during exercise can be described by the point of intersection of the controller and plant curves in the respiratory equilibrium diagram in humans (Miyamoto et al., 2004, 2012, 2014, 2015, Ogoh et al., 2008). In the present investigation using anaesthetized small animals, we succeeded in characterizing these subsystem under an open‐loop condition and constructed a respiratory equilibrium diagram to illustrate the mechanisms of respiratory regulation at rest and during electrically induced exercise. Therefore, the present investigation extends previous animal studies of respiratory control by demonstrating the exercise intensity‐dependent shift of the operating points in the respiratory equilibrium diagram. Indeed, the operating $P_{\mathrm{ETC}{\mathrm{O}}_2}$ and ${\dot{V}}_{\mathrm{E}}$ estimated from the intersection point on the respiratory equilibrium diagram conformed reasonably well to the values actually measured regardless of rest and exercise conditions (Figure 6c).

4.2. Exercise‐induced shift in the controller element

In the present study, we found that the controller curve shifts upward to compensate for the plant curve shift accompanying increased metabolism. Furthermore, the exercise stimulus did not change the controller gain (S) despite an increase in metabolic demand. However, the $P_{\mathrm{ETC}{\mathrm{O}}_2}$ intercept (B) during electrically induced high‐intensity exercise was smaller compared to resting and low‐intensity exercise conditions, indicating that the exercise‐induced upward shift of the controller curve was exercise intensity‐dependent (Table 2; Figure 5).

As verified in the present study, many physiologists concur on the exercise‐induced upward shift of the controller curve in both humans (Clark, Sinclair, & Lenox, 1980; Duffin et al., 1980; Miyamoto et al., 2012; Ogoh et al., 2008; Weil et al., 1972) and anaesthetized mammals (Asmussen, 1957, 1965; Kao, 1963), although the effect of exercise stimulus on the controller gain (CO₂ sensitivity) varies among studies.

In a human study, Casey, Duffin, and McAvoy (1987) demonstrated that exercise did not change the central chemoreceptor threshold, supporting the neuro‐humoral theory of exercise ventilation. The concept of an additional drive to breathe during exercise apart from the chemoreflex is now considered common knowledge. These findings thus suggest that the additional drive to breathe during exercise is greater at high‐intensity exercise, which is not necessarily due to a change in central chemoreflex threshold.

Despite almost 100 years of intensive study, the pathways that mediate exercise hyperpnoea have not been clearly defined (Eldridge, 1994; Eldridge & Waldrop, 1991; Kao, 1963; Krogh & Lindhard, 1913; Mateika & Duffin, 1995; Strange et al., 1993; Wasserman et al., 1986; Forster et al., 2012). As a result, a fundamental conflict seems to exist in the literature on exercise hyperpnoea, and a variety of mechanisms have been postulated to explain the exercise‐induced upward shift of the controller curve during exercise, which leads to exercise hyperpnoea.

In this experimental study, although the drives to breathe in addition to the chemoreflex drive have not been defined, the neural drives originating from the central and peripheral nervous system (Forster et al., 2012); afferents from the working limbs (Comroe & Schmidt, 1943; Kao, 1963; McCloskey & Mitchell, 1972; Smith, Mitchell, & Garry, 2006) and afferents from the heart (Wasserman, Whipp, & Castagna, 1974, Wasserman, Whipp, & Casaburi, 1986) may be involved in the exercise‐induced upward shift of the controller curve, leading to exercise hyperpnoea. Recent findings that support critical contributions from cortical central command and muscle afferent feedback to exercise hyperpnoea are reviewed (Forster et al., 2012). On the other hand, in our current model, despite the absence of the central command, the fact that involuntary muscle activation was sufficient to elicit isocapnic exercise hyperpnoea indicated that central motor activity/central command does not contribute to the hyperpnoea under this experimental condition. Brice et al. (1988) also indicated that central command is not requisite for the precise matching of alveolar ventilation to increases in ${\dot{V}}_{\mathrm{C}{\mathrm{O}}_2}$ during low‐intensity muscle contractions in humans. Although their study limitation is that 50–100% increase in metabolic rate is within the physiological variation that occurs at rest, their results were consistent with our findings.

4.3. Exercise‐induced shift in the plant element

In the present study, exercise induced by electrical stimulation shifted the plant curve rightward and downward reflecting increased metabolism, and the exercise intensity‐dependent changes in the plant element is characterized by an increase in A and a decrease in C (Appendix, Equation (2)).

In the past, some researchers have explained the exercise‐induced changes in the plant element using the conventional metabolic hyperbola (Wasserman et al., 1986; Whipp & Pardy, 1986). In the conventional method, the equation that expresses the relation between ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$ during exercise ignores the scaling factors representing ventilatory work‐related CO₂ production. However, because ventilatory work‐related CO₂ production occurs and V _D/V _T changes with variation in ${\dot{V}}_{\mathrm{E}}$ in ‘real‐life’ physiological systems (Aaron, Seow, Johnson, & Dempsey, 1992; Crosfill & Widdicombe, 1961; Harms, Wetter, St Croix, Pegelow, & Dempsey, 2000), we modified the conventional metabolic hyperbola to explain the exercise‐induced changes in plant element (see Appendix). In the modified metabolic hyperbola ($P_{\mathrm{ETC}{\mathrm{O}}_2}$ = A/${\dot{V}}_{\mathrm{E}}$ + C]), the increase in A may result from increases in basal metabolic demand (α) and/or V _D/V _T (Appendix, Equation (3)). The decrease in C may result from decreases in V _D/V _T and/or metabolic cost of breathing (β) (Appendix Equation (3); Miyamoto et al., 2004). V _D/V _T is unlikely to increase during exercise, because the exercise stimulus increases V _T but decreases V _D due to improved ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ mismatch. Therefore, β probably decreases accompanying reduced airway resistance, consequently reducing the oxygen cost of breathing. On the other hand, exercise intensity‐dependent increase in A may be mainly due to increase in basal metabolic demand and decrease in C, which decrease both V _D/V _T and β. Therefore, plant system characteristics curves obtained show unique changes according to given conditions. Although we did not evaluate such physiological measurement in this experiment, these ‘metabolic factors’ (A and C) may explain the leftward shift of the operating point during electrically induced exercise at high intensity (Figure 6c).

In the living body, since the input‒output relationship is finally determined according to many elements including the anatomical and physiological dead space [respiratory pattern, ventilation to perfusion ratio (${\dot{V}}_{\mathrm{A}}/\dot{Q}$) mismatch], airway resistance and CO₂ output (metabolic level), an accurate description of the functional characteristics of the plant system can be important, especially in patients with cardiopulmonary lesions. Therefore, this diagram can be useful in understanding not only the mechanism of respiratory control at rest and during exercise, but also the pathophysiological mechanism of diseases manifesting breathing disorders.

4.4. Clinical perspectives

We demonstrated that respiration is determined from the intersecting point of the controller and the plant curves on the respiratory equilibrium diagram. Consequently, the quantitative analysis of the two subsystems of respiratory chemoreflex provides a framework by which we can analytically evaluate how the unique value of ${\dot{V}}_{\mathrm{E}}$ during exercise is determined by the respiratory chemoreflex system, how changes in model parameters of controller (S and B) and plant (α, β, A, and C) elements affect exercise hyperpnoea. Using this conceptual diagram, it is possible to analytically estimate with high precision whether (abnormal) changes of the controlling element and the controlled element cause (abnormal) changes in ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$, or conversely, how (abnormal) changes in ${\dot{V}}_{\mathrm{E}}$ and $P_{\mathrm{aC}{\mathrm{O}}_2}$ alter the characteristics of the system. Indeed, we have already constructed a respiratory equilibrium diagram to illustrate the respiratory abnormalities in CHF rats under anaesthesia, and suggested the potential difference between normal and CHF rats in exercise‐induced changes in controller and plant (Miyamoto et al., 2006). Therefore, using this experimental model, systematic evaluation of their integrated function would also help elucidate the pathophysiological key mechanisms responsible for controlling ventilation.

In the future, quantitative analysis of the dynamic properties of the respiratory chemoreflex system may play a role in elucidating the adaptive mechanism of the exercise ventilatory response during training and the mechanism of respiratory abnormality in CHF. The mechanisms of their occurrence have been attributed to a change in sensitivity to carbon dioxide (gain) or an increase in lung‐chemoreceptor circulation time associated with central respiratory disorder. Especially, in CHF patients, the increase in central and peripheral chemoreflex sensitivity (controller gain) and the increase in peripheral plant gain because of an increase in dead space/tidal volume ratio are speculated to cause a total loop gain increase in the system.

4.5. Experimental limitations

There are several limitations to the present study. First, we obtained data from anaesthetized animals. If data had been obtained from conscious animals, the results might have been different. However, because human studies have observed the same exercise‐induced upward shift of the controller curve during exercise, which leads to exercise hyperpnoea (Miyamoto et al., 2012; Ogoh et al., 2008), the interpretation of the observed changes in the operating points may be reasonable. Second, the present study consistently showed that electrical stimulation to involuntarily contract skeletal muscles in rats increases mean arterial pressure, heart rate and ventilation. Some components of this constellation of responses to involuntary contraction may be the result of the reflex arising either from the working muscles or from direct activation of afferent fibres. Alternatively, a metabolic byproduct of involuntary muscular contraction may have circulated to other regions such as the lung and carotid bodies to evoke these responses. Although there is a paucity of data concerning the effects of possible abnormal sensory stimulation resulting from electrically induced exercise, our result in general agrees with other physiological studies using direct electrical stimulation to evoke muscular activity, which has been widely used in anaesthetized mammals (Kao, 1963; Lamb, 1966; Linton, Miller, & Cameron, 1976; Waldrop, Mullins, & Millhorn, 1986). In addition, our quantitative observation of isocapnic ventilatory response and intensity‐dependent change in the controller and plant elements during exercise may be evidence that neural and/or metabolic factors account for the isocapnic exercise hyperpnoea. Third, in the present study, the estimation of $P_{\mathrm{aC}{\mathrm{O}}_2}$ using $P_{\mathrm{ETC}{\mathrm{O}}_2}$ may have limitations. However, our validation experiment revealed that $P_{\mathrm{ETC}{\mathrm{O}}_2}$ correlated closely with $P_{\mathrm{aC}{\mathrm{O}}_2}$ (n = 45, $P_{\mathrm{aC}{\mathrm{O}}_2}$ = 0.93 × $P_{\mathrm{ETC}{\mathrm{O}}_2}$ + 4.8, R ² = 0.910, P < 0.001) (Figure 5a). Therefore, the change in $P_{\mathrm{ETC}{\mathrm{O}}_2}$ observed during experimental conditions likely reflects $P_{\mathrm{aC}{\mathrm{O}}_2}$. However, $P_{\mathrm{ETC}{\mathrm{O}}_2}$ was shown to slightly underestimate $P_{\mathrm{aC}{\mathrm{O}}_2}$ across all experimental conditions, a finding that is consistent with a previous report (Jones, Robertson, & Kane, 1979). Furthermore, Jones and Campbell (1982) reported that $P_{\mathrm{ETC}{\mathrm{O}}_2}$ is higher than $P_{\mathrm{aC}{\mathrm{O}}_2}$ when $F_{\mathrm{IC}{\mathrm{O}}_2}$ and ${\dot{V}}_{\mathrm{E}}$ increase, but is lower under normal conditions. Therefore, the values of controller gain, plant gain and total loop gain may be underestimated using $P_{\mathrm{ETC}{\mathrm{O}}_2}$ as a surrogate for $P_{\mathrm{aC}{\mathrm{O}}_2}$. Finally, another limitation is that to characterize the plant element, the rats were subject to non‐physiological respiration using a mechanical ventilator, which might have affected the $P_{\mathrm{ETC}{\mathrm{O}}_2}$ response to ${\dot{V}}_{\mathrm{E}}$. However, the combinations of tidal volume and respiratory frequency were predetermined in order to match the spontaneous breathing pattern, because we tried to match the effect of dead volume as well. Thus, our conceptual interpretation of the observed changes in plant system properties, and assessment of the respiratory equilibrium diagram are likely to be valid.

5. CONCLUSIONS

We developed an anaesthetized‐rat model for studying exercise hyperpnoea during electrically induced muscular contraction, using systems analysis for quantitative characterization of the respiratory chemoreflex feedback system. This small‐animal experimental model will provide an opportunity to clarify the major determinant mechanisms of exercise hyperpnoea, and will be useful for understanding the mechanisms responsible for abnormal ventilation under various pathophysiological conditions.

COMPETING INTERESTS

None declared.

AUTHOR CONTRIBUTIONS

Conception or design of the work: T.M. Acquisition, analysis, or interpretation of data for the work: T.M., K.M., S.U., H.N. Drafting the work or revising it critically for important intellectual content: T.M. All authors approved the final version of the manuscript and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

APPENDIX 1.

1.1.

The metabolic hyperbola has been described conventionally by:

$$P_{\mathrm{aC}{\mathrm{O}}_2}=863\times {\dot{V}}_{\mathrm{C}{\mathrm{O}}_2\left(\mathrm{STPD}\right)}/{\dot{V}}_{\mathrm{A}\left(\mathrm{BTPS}\right)}$$ (1)

where ${\dot{V}}_{\mathrm{A}}$ is alveolar ventilation, and 863 is a correction factor (Whipp & Pardy, 1986). This conventional metabolic hyperbola ignores the scaling factors representing ventilatory work‐related CO₂ production.

We modified the conventional metabolic hyperbola as follows. If we approximate ${\dot{V}}_{\mathrm{A}}$ by ${\dot{V}}_{\mathrm{E}}$ × (1 − V _D/ V _T) and take into consideration the work of breathing (Aaron et al., 1992; Crosfill & Widdicombe, 1961; Harms et al., 2000), Equation (1) can be rewritten as

$$P_{\mathrm{aC}{\mathrm{O}}_2}=863\times (\alpha +\beta \times {\dot{V}}_{\mathrm{E}})/\left({\dot{V}}_{\mathrm{E}}\times \left[1-V_{\mathrm{D}}/V_{\mathrm{T}}\right]\right)$$ (2)

where V _D/V _T represents dead space ventilation, and α and β are the respective scaling factors representing CO₂ production unrelated and related to work of breathing. Rearranging Equation (2) yields

$$P_{\mathrm{aC}{\mathrm{O}}_2}=A/{\dot{V}}_{\mathrm{E}}+C$$ (3)

where A = 863 × α/(1 − V _D/V _T) and C = 863 × β/(1 − V _D/V _T)

Equation (3) is the modified metabolic hyperbola. The fitted parameters of A and C for the plant element (Equation (3)) take into account the metabolic changes incurred through ventilatory work‐related CO₂ production as well as physiological dead space ventilation accompanying changes in respiration pattern and/or ventilation to perfusion ratio (${\dot{V}}_{\mathrm{A}}/\dot{Q}$). These changes are significant under specific environments and pathophysiological conditions.

Miyamoto T, Manabe K, Ueda S, Nakahara H. Development of an anaesthetized‐rat model of exercise hyperpnoea: an integrative model of respiratory control using an equilibrium diagram. Experimental Physiology. 2018;103:748–760. https://doi.org/10.1113/EP086850