Linear programming analysis of VA/Q distributions: average distribution

The defining equations of the multiple inert gas elimination technique are underdetermined, and an infinite number of VA/Q ratio distributions exists that fit the same inert gas data. Conventional least-squares analysis with enforced smoothing chooses a single member of this infinite family whose features are assumed to be representative of the family as a whole. To test this assumption, the average of all ventilation-perfusion ratio (VA/Q) distributions that are compatible with given data was calculated using a linear program. The average distribution so obtained was then compared with that recovered using enforced smoothing. Six typical sets of inert gas data were studied. In all sets but one, the distribution recovered with conventional enforced smoothing closely matched the structure of the average distribution. The single exception was associated with the broad log-normal VA/Q distribution, which is rarely observed using the technique. We conclude that the VA/Q distribution conventionally recovered approximates a simple average of all compatible distributions. It therefore displays average features and only that degree of fine structural detail that is typical of the family as a whole.     

Linear programming analysis of VA/Q distributions: limits on central moments

Linear programming examines the boundaries of infinite sets. We used this method with the multiple-inert gas-elimination technique to examine the central moments and arterial blood gases of the infinite family of ventilation perfusion (VA/Q) distributions that are compatible with a measured inert gas-retention set. A linear program was applied with Monte-Carlo error simulation to theoretical retention data, and 95% confidence intervals were constructed for the first three moments (mean, dispersion, and skew) and the arterial PO2 and PCO2 of all compatible blood flow distributions. Six typical cases were studied. Results demonstrate narrow confidence intervals for both the lower moments and predicted arterial blood gases of all test cases, which widen as moment number or error increase. We conclude that the blood gas composition and basic structure of all compatible VA/Q distributions are tightly constrained and that even subtle changes in this structure, as may occur experimentally, can be identified.     

A statistical model of the VA/Q distribution

A "blocks model" is proposed to model the distribution of the ventilation-perfusion ratio (VA/Q distribution). This model is developed from statistical principles and enables the estimated VA/Q distribution to be interpreted in a straightforward and intuitive manner. Estimation of parameters of the blocks model uses a constrained weighted least-squares procedure. Although developed initially to estimate VA/Q distributions from data generated by the multiple inert gas elimination technique (P. D. Wagner, H. A. Saltzman, and J. B. West, J. Appl. Physiol. 36: 588-599, 1974), the blocks method is applicable to any problem in which the unknown distribution is related to the data through an ill-posed integral equation and is particularly suited for problems in which the data are scarce. The method is illustrated with several examples--hypothetical data representing a wide range of VA/Q distributions as well as some real data.     

Ventilation-perfusion inequality in normal humans during exercise at sea level and simulated altitude

To investigate the effects of both exercise and acute exposure to high altitude on ventilation-perfusion (VA/Q) relationships in the lungs, nine young men were studied at rest and at up to three different levels of exercise on a bicycle ergometer. Altitude was simulated in a hypobaric chamber with measurements made at sea level (mean barometric pressure = 755 Torr) and at simulated altitudes of 5,000 (632 Torr), 10,000 (523 Torr), and 15,000 ft (429 Torr). VA/Q distributions were estimated using the multiple inert gas elimination technique. Dispersion of the distributions of blood flow and ventilation were evaluated by both loge standard deviations (derived from the VA/Q 50-compartment lung model) and three new indices of dispersion that are derived directly from inert gas data. Both methods indicated a broadening of the distributions of blood flow and ventilation with increasing exercise at sea level, but the trend was of borderline statistical significance. There was no change in the resting distributions with altitude. However, with exercise at high altitude (10,000 and 15,000 ft) there was a significant increase in dispersion of blood flow (P less than 0.05) which implies an increase in intraregional inhomogeneity that more than counteracts the more uniform topographical distribution that occurs. Since breathing 100% O2 at 15,000 ft abolished the increased dispersion, the greater VA/Q mismatching seen during exercise at altitude may be related to pulmonary hypertension.     

Contributions of ventilation and perfusion inhomogeneities to the VA/Q distribution.

The anatomic distributions of ventilation (VA) and perfusion (Q) in prone and supine dogs have been described in the literature. These data also provide frequency distributions, i.e., the distribution of lung units as a function of VA or Q. A comprehensive distribution that encompasses these two distributions is described, and the properties of the comprehensive distribution that determine the width of the VA/Q distribution are identified. Using data on the VA and Q distributions taken from various sources in the literature, we estimated the widths of the VA/Q distributions. The widths estimated from the independent data on the VA and Q distributions agree well with the widths obtained from gas exchange data. The analysis provides information about the relative contributions of the VA and Q distributions to the width of the VA/Q distribution. In the prone dog, the VA and Q distributions, as described by the available data, have different length scales, and we argue that these distributions are therefore not highly correlated. As a result, the variance of the VA/Q distributions is approximately the sum of the variances of the VA and Q distributions. Two-thirds of the variance in VA/Q is a result of nonuniform Q, and one-third is a result of nonuniform VA. In the supine dog, the variance of VA is larger than in the prone dog because of a vertical gradient and the variance of Q is larger, in part, because of a vertical gradient. Because the magnitudes of the vertical gradients of VA and Q are about equal, the vertical gradient of VA/Q is small, and these components of the VA and Q inhomogeneities contribute little to the width of the VA/Q distribution. The other components of Q inhomogeneity cause the additional variance of VA/Q in the supine dog.     

Spectral analysis of inert gas elimination data: resolution limits

A new method of analyzing inert gas data for recovery of the pulmonary ventilation-perfusion ration (VA/Q) distribution is proposed. It is shown that the conventional inert gas elimination equation takes the form of a convolution integral, and the relationship between VA/Q distribution and inert gas elimination resembles that of a noncausal low-pass filter with infinite zero-frequency gain. With the use of this formulation, characteristic features of VA/Q distribution may be represented in the frequency domain in terms of the corresponding energy spectrum. It is shown that the lack of resolution associated with finite data samples and measurement error is caused by distortions in the high-frequency contents of the resulting VA/Q distribution. With six inert gases, the technique cannot resolve a log SD less than 0.21 decade and a modal separation less than 0.87 decade. In the presence of measurement error, the degree of resolution is even less. It is suggested that for maximum resolution the number of discrete and duplicate data samples should be chosen so that the resulting noise and sampling cutoff frequencies are approximately equal.     

Reproducibility of the multiple inert gas elimination technique

Although measurement errors in the multiple inert gas elimination technique have a coefficient of variation of approximately 3%, small biological fluctuations in ventilation, blood flow, or other variables must contribute additional variance to this method of assessing ventilation-perfusion (VA/Q) mismatch. To determine overall variance of computed indices of VA/Q mismatch, an analysis of variance was carried out using a total of 400 duplicate pairs of inert gas samples obtained from canine (N = 118) and human (N = 282) studies in the past 2 years. In both sets VA/Q mismatch ranged from minimal (2nd moment of ventilation and blood flow distributions, log SDV and log SDQ, respectively approximately equal to 0.3 each) to severe (log SDV and log SDQ approximately equal to 2.0). Differences between duplicate log SD values were computed and found to be a constant fraction of the mean log SD of each duplicate pair, averaging 13% for both canine and human ventilation and blood flow data. The resultant coefficient of variation for a single measurement of log SD about its mean averaged 8.6% for all data combined. This analysis demonstrates excellent reproducibility of these dispersion indices over a wide range of conditions, and if the mean of duplicate values is used, thus reducing variability by square root 2 to 6.1%, log SD can be estimated with an approximately 95% confidence limit of +/- 12%.     

Calculating the distribution of ventilation-perfusion ratios from inert gas elimination data

It is well known that the major cause of hypoxemia in lung disease is ventilation-perfusion (VA/Q) inequality, but it has been extremely difficult to measure the distribution of ventilation-perfusion ratios except in terms of unrealistically simple (albeit useful) models. The multiple inert gas elimination technique provides considerable information concerning the shape, position, and dispersion of the VA/Q distribution, although it cannot precisely define all features of the distribution. Although there are many techniques for obtaining information about the distribution from inert gas elimination data, we have found the most flexible and useful approach to be a multicomponent analysis with enforced smoothing, sometimes known as ridge regression. This presentation describes in some detail the physiological and mathematical principles principles involved in the transformation of inert gas elimination data into a representative distribution of ventilation-perfusion ratios by enforced smoothing techniques. It is important to realize that with this approach and any other approach aimed at estimating the distribution of ventilation-perfusion ratios, the results must be properly interpreted.     

Pulmonary gas exchange in humans exercising at sea level and simulated altitude

In a previous study of normal subjects exercising at sea level and simulated altitude, ventilation-perfusion (VA/Q) inequality and alveolar-end-capillary O2 diffusion limitation (DIFF) were found to increase on exercise at altitude, but at sea level the changes did not reach statistical significance. This paper reports additional measurements of VA/Q inequality and DIFF (at sea level and altitude) and also of pulmonary arterial pressure. This was to examine the hypothesis that VA/Q inequality is related to increased pulmonary arterial pressure. In a hypobaric chamber, eight normal subjects were exposed to barometric pressures of 752, 523, and 429 Torr (sea level, 10,000 ft, and 15,000 ft) in random order. At each altitude, inert and respiratory gas exchange and hemodynamic variables were studied at rest and during several levels of steady-state bicycle exercise. Multiple inert gas data from the previous and current studies were combined (after demonstrating no statistical difference between them) and showed increasing VA/Q inequality with sea level exercise (P = 0.02). Breathing 100% O2 did not reverse this increase. When O2 consumption exceeded about 2.7 1/min, evidence for DIFF at sea level was present (P = 0.01). VA/Q inequality and DIFF increased with exercise at altitude as found previously and was reversed by 100% O2 breathing. Indexes of VA/Q dispersion correlated well with mean pulmonary arterial pressure and also with minute ventilation. This study confirms the development of both VA/Q mismatch and DIFF in normal subjects during heavy exercise at sea level. However, the mechanism of increased VA/Q mismatch on exercise remains unclear due to the correlation with both ventilatory and circulatory variables and will require further study.     

Operation Everest II: pulmonary gas exchange during a simulated ascent of Mt. Everest

Eight normal subjects were decompressed to barometric pressure (PB) = 240 Torr over 40 days. The ventilation-perfusion (VA/Q) distribution was estimated at rest and during exercise [up to 80-90% maximal O2 uptake (VO2 max)] by the multiple inert gas elimination technique at sea level and PB = 428, 347, 282, and 240 Torr. The dispersion of the blood flow distribution increased by 64% from rest to 281 W, at both sea level and at PB = 428 Torr (heaviest exercise 215 W). At PB = 347 Torr, the increase was 79% (rest to 159 W); at PB = 282 Torr, the increase was 112% (108 W); and at PB = 240 Torr, the increase was 9% (60 W). There was no significant correlation between the dispersion and cardiac output, ventilation, or pulmonary arterial wedge pressure, but there was a correlation between the dispersion and mean pulmonary arterial pressure (r = 0.49, P = 0.02). When abnormal, the VA/Q pattern generally had perfusion in lung units of zero or near zero VA/Q combined with units of normal VA/Q. Alveolar-end-capillary diffusion limitation of O2 uptake (VO2) was observed at VO2 greater than 3 l/min at sea level, greater than 1-2 l/min VO2 at PB = 428 and 347 Torr, and at higher altitudes, at VO2 less than or equal to 1 l/min. These results show variable but increasing VA/Q mismatch with long-term exposure to both altitude and exercise. The VA/Q pattern and relationship to pulmonary arterial pressure are both compatible with alveolar interstitial edema as the primary cause of inequality.     

Ventilation-perfusion inhomogeneity increases gas uptake in anesthesia: computer modeling of gas exchange.

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on overall gas exchange during maintenance-phase N(2)O anesthesia with an inspired O(2) concentration of 30%. A multialveolar compartment computer model was used based on physiological log normal distributions of VA/Q inhomogeneity. Increasing the log standard deviation of the distribution of perfusion from 0 to 1.75 paradoxically increased O(2) uptake (VO(2)) where a low mixed venous partial pressure of N(2)O [high N(2)O uptake (VN(2)O)] was specified. With rising mixed venous partial pressure of N(2)O, a threshold was observed where VO(2) began to fall, whereas VN(2)O began to rise with increasing VA/Q inhomogeneity. This phenomenon is a magnification of the concentrating effects that VO(2) and VN(2)O have on each other in low VA/Q compartments. During "steady-state" N(2)O anesthesia, VN(2)O is predicted to paradoxically increase in the presence of worsening VA/Q inhomogeneity.     

Distribution of ventilation-perfusion ratios in dogs with normal and abnormal lungs.

We have recently described a new method for measuring distributions of ventilation-perfusion ratios (VA/Q) based on inert gas elimination. Here we report the initial application of the method in normal dogs and in dogs with pulmonary embolism, pulmonary edema, and pneumonia. Characteristic distributions appropriate to the known effects of each lesion were observed. Comparison with traditional indices of gas exchange revealed that the arterial PO2 calculated from the distributions agreed well with measured values, as did the shunts indicated by the method and by the arterial PO2 while breathing 100 per cent 02. Also the Bohr dead space closely matched the dispersion of ventilation in realtion to VA/Q. Assumptions made in the method were critically evaluated and appear justified. These include the existence of a steady state of gas exchange, an alveolar-end-capillary diffusion equilibration, and the fact that all of the observered VA/Q inequality occurs between gas exchange units in parallel. However, theoretical analysis suggests that the method can detect failure of diffusion equilbration across the blood-gas barrier should it exist. These results suggest that the method is well-suited to clinical investigation of patients with pulmonary disease.     

Effect of common dead space on VA/Q distribution in the dog

Several previous studies have shown worsening ventilation-perfusion (VA/Q) relationships in humans during heavy exercise at sea level. However, the mechanism of this deterioration remains unclear because of the correlation with ventilatory and circulatory variables. Our hypothesis was that the decrease in the series dead space-to-tidal volume ratio during exercise might be partly responsible because mixing in the common dead space can reduce apparent inequality. We tested this notion in 10 resting anesthetized normocapnic dogs passively hyperventilated by increase tidal volume and a) inspired CO2 or b) external dead space. We predicted less apparent VA/Q inequality in condition b because of mixing in the added dead space. After base-line measurements, conditions a and b were randomly assigned, and after a second set of base-line measurements they were repeated in the reverse order in each dog. VA/Q inequality was measured by the multiple inert gas elimination technique. Comparison of conditions a and b demonstrated that additional external dead space improved (P less than 0.001) the blood flow distributions as hypothesized [log standard deviation of perfusion = 0.49 +/- 0.02 (SE) in condition b and 0.61 +/- 0.03 in condition a with respect to 0.52 +/- 0.03 at base line]. This study suggests that the increased tidal volume during exercise could uncover VA/Q inequality not evident at rest because of the higher ratio of common dead space to tidal volume at rest.     

Multiple inert gas elimination technique

The understanding of pulmonary gas exchange has undergone several major advances since the early 1900's. One of the most significant was the development of the multiple inert gas elimination technique for assessing the ventilation-perfusion (VA/Q) distribution in the lung. By measuring the mixed venous, arterial, and mixed expired concentrations of six infused inert gases, it is possible to distinguish shunt, dead space, and the general pattern of VA/Q distribution. As with all mathematical models of complex biological phenomena, there are limitations that can result in errors of interpretation if the technique is applied uncritically. In addition, methodological limitations also can lead to both experimental error and errors of interpretation. Despite these limitations, the multiple inert gas elimination technique remains the most powerful tool developed to date to analyze pulmonary gas exchange.     

Effects of inspired CO2, hyperventilation, and time on VA/Q inequality in the dog.

In a recent study by Tsukimoto et al. (J. Appl. Physiol. 68: 2488-2493, 1990), CO2 inhalation appeared to reduce the size of the high ventilation-perfusion ratio (VA/Q) mode commonly observed in anesthetized mechanically air-ventilated dogs. In that study, large tidal volumes (VT) were used during CO2 inhalation to preserve normocapnia. To separate the influences of CO2 and high VT on the VA/Q distribution in the present study, we examined the effect of inspired CO2 on the high VA/Q mode using eight mechanically ventilated dogs (4 given CO2, 4 controls). The VA/Q distribution was measured first with normal VT and then with increased VT. In the CO2 group at high VT, data were collected before, during, and after CO2 inhalation. With normal VT, there was no difference in the size of the high VA/Q mode between groups [10.5 +/- 3.5% (SE) of ventilation in the CO2 group, 11.8 +/- 5.2% in the control group]. Unexpectedly, the size of the high VA/Q mode decreased similarly in both groups over time, independently of the inspired PCO2, at a rate similar to the fall in cardiac output over time. The reduction in the high VA/Q mode together with a simultaneous increase in alveolar dead space (estimated by the difference between inert gas dead space and Fowler dead space) suggests that poorly perfused high VA/Q areas became unperfused over time. A possible mechanism is that elevated alveolar pressure and decreased cardiac output eliminate blood flow from corner vessels in nondependent high VA/Q regions.     

Lobar contribution to VA/Q inequality during constant-flow ventilation

Previous studies have shown that normal arterial PCO2 can be maintained during apnea in anesthetized dogs by delivering a continuous stream of inspired ventilation through cannulas aimed down the main stem bronchi, although this constant-flow ventilation (CFV) was also associated with a significant increase in ventilation-perfusion (VA/Q) inequality, compared with conventional mechanical ventilation (IPPV). Conceivably, this VA/Q inequality might result from differences in VA/Q ratios among lobes caused by nonuniform distribution of ventilation, even though individual lobes are relatively homogeneous. Alternatively, the VA/Q inequality may occur at a lobar level if those factors causing the VA/Q mismatch also existed within lobes. We compared the efficiency of gas exchange simultaneously in whole lung and left lower lobe by use of the multiple inert gas elimination technique in nine anesthetized open-chest dogs. Measurements of whole lung and left lower lobe gas exchange allowed comparison of the degree of VA/Q inequality within vs. among lobes. During IPPV with positive end-expiratory pressure, arterial PO2 and PCO2 (183 +/- 41 and 34.3 +/- 3.1 Torr, respectively) were similar to lobar venous PO2 and PCO2 (172 +/- 64 and 35.7 +/- 4.1 Torr, respectively; inspired O2 fraction = 0.44 +/- 0.02). Switching to CFV (3 l.kg-1.min-1) decreased arterial PO2 (112 +/- 26 Torr, P less than 0.001) and lobar venous PO2 (120 +/- 27 Torr, P less than 0.01) but did not change the shunt measured with inert gases (P greater than 0.5).(ABSTRACT TRUNCATED AT 250 WORDS)     

Cardiogenic oscillations in He and SF6 expirograms during airway and venous loading

Cardiogenic oscillations in the expired partial pressure profiles of two inert gases (He and SF6) were monitored in seven anesthetized paralyzed mechanically ventilated dogs. He and SF6 were administered either intravenously by a membrane oxygenator and partial arteriovenous bypass [venous loading (VL)] or by washin into lung gas [airway loading (AL)]. The single-breath expirograms obtained during constant-flow expiration after inspiration of test gas-free air displayed distinct and regular cardiogenic oscillations. The relative oscillation amplitude (ROA), calculated as oscillation amplitude divided by mixed expired-inspired partial pressure difference, was in the range of 1-8%. The ROA for both He and SF6 was approximately 4.2 times higher in VL than in AL, which indicated that among lung units that emptied sequentially in the cardiac cycle, the effects of alveolar ventilation-perfusion (VA/Q) inequality were more pronounced than those of alveolar ventilation-alveolar volume (VA/VA) inequality. In AL, He and SF6 oscillations were 180 degrees out of phase compared with CO2 and O2 oscillations and with He and SF6 oscillations in VL, which suggests that regions with low VA/VA had high VA/Q and very low Q/VA. The ROA was practically unaffected by breath holding in both AL and VL, which indicates that there was little diffusive or convective (cardiogenic) mixing between the lung units that were responsible for cardiogenic oscillations. The ROA was consistently higher for He than for SF6, and the He-to-SF6 ratio was independent of route of test gas loading, averaging 1.6 in both AL and VL. This result may be explained by laminar Taylor dispersion, whereby oscillations generated in peripheral lung regions are dissipated in inverse proportion to diffusion coefficient during transit through the proximal (larger) airways.     

Ventilation-perfusion relationships in isolated blood-free perfused rabbit lungs.

The multiple inert gas elimination technique (MIGET) was applied to blood-free perfused isolated rabbit lungs. Commonly accepted criteria for reliability of the method were found to be fulfilled in this model. Ventilation-perfusion (VA/Q) distributions in isolated control lungs corresponded to those repeatedly detected under physiological conditions. In particular, a narrow unimodal dispersion of perfusate flow was observed: perfusion of low-VA/Q areas ranged below 1% and shunt flow approximately 2-3%; perfusion of high-VA/Q regions was not detected. Gas flow was characterized by narrow dispersion in the midrange-VA/Q areas. Application of a low level of PEEP (1 cmH2O) reduced shunt flow to less than 1%, and low-VA/Q areas were no longer noted. By using this PEEP-level, stable gas exchange conditions were maintained for greater than 5 h of extracorporeal perfusion. Graded embolization with small air bubbles caused a typical rightward shift (to higher VA/Q ratios) of mean ventilation, associated with the appearance of high-VA/Q regions and an increase in dead space ventilation. Mean perfusion was shifted leftward, and shunt flow was approximately doubled. Whole lung lavage with saline for washout of surfactant evoked a progressive manifold increase in shunt flow, accompanied by a moderate rise of perfusate flow to low-VA/Q areas. We conclude that the MIGET can be applied to isolated blood-free perfused rabbit lungs for assessment of gas exchange and that typical patterns of VA/Q mismatch are reproduced in this model.     

Effect of regional alveolar hypoxia on gas exchange in dogs

We studied the effects of left lower lobe (LLL) alveolar hypoxia on pulmonary gas exchange in anesthetized dogs using the multiple inert gas elimination technique (MIGET). The left upper lobe was removed, and a bronchial divider was placed. The right lung (RL) was continuously ventilated with 100% O2, and the LLL was ventilated with either 100% O2 (hyperoxia) or a hypoxic gas mixture (hypoxia). Whole lung and individual LLL and RL ventilation-perfusion (VA/Q) distributions were determined. LLL hypoxia reduced LLL blood flow and increased the perfusion-related indexes of VA/Q heterogeneity, such as the log standard deviation of the perfusion distribution (log SDQ), the retention component of the arterial-alveolar difference area [R(a-A)D], and the retention dispersion index (DISPR*) of the LLL. LLL hypoxia increased blood flow to the RL and reduced the VA/Q heterogeneity of the RL, indicated by significant reductions in log SDQ, R(a-A)D, and DISPR*. In contrast, LLL hypoxia had little effect on gas exchange of the lung when evaluated as a whole. We conclude that flow diversion induced by regional alveolar hypoxia preserves matching of ventilation to perfusion in the whole lung by increasing gas exchange heterogeneity of the hypoxic region and reducing heterogeneity in the normoxic lung.     

VA/Q distribution during heavy exercise and recovery in humans: implications for pulmonary edema.

Ventilation-perfusion (VA/Q) inequality has been shown to increase with exercise. Potential mechanisms for this increase include nonuniform pulmonary vasoconstriction, ventilatory time constant inequality, reduced large airway gas mixing, and development of interstitial pulmonary edema. We hypothesized that persistence of VA/Q mismatch after ventilation and cardiac output subside during recovery would be consistent with edema; however, rapid resolution would suggest mechanisms related to changes in ventilation and blood flow per se. Thirteen healthy males performed near-maximal cycle ergometry at an inspiratory PO2 of 91 Torr (because hypoxia accentuates VA/Q mismatch on exercise). Cardiorespiratory variables and inert gas elimination patterns were measured at rest, during exercise, and between 2 and 30 min of recovery. Two profiles of VA/Q distribution behavior emerged during heavy exercise: in group 1 an increase in VA/Q mismatch (log SDQ of 0.35 +/- 0.02 at rest and 0.44 +/- 0.02 at exercise; P less than 0.05, n = 7) and in group 2 no change in VA/Q mismatch (n = 6). There were no differences in anthropometric data, work rate, O2 uptake, or ventilation during heavy exercise between groups. Group 1 demonstrated significantly greater VA/Q inequality, lower vital capacity, and higher forced expiratory flow at 25-75% of forced vital capacity for the first 20 min during recovery than group 2. Cardiac index was higher in group 1 both during heavy exercise and 4 and 6 min postexercise. However, both ventilation and cardiac output returned toward baseline values more rapidly than did VA/Q relationships. Arterial pH was lower in group 1 during exercise and recovery. We conclude that greater VA/Q inequality in group 1 and its persistence during recovery are consistent with the hypothesis that edema occurs and contributes to the increase in VA/Q inequality during exercise. This is supported by observation of greater blood flows and acidosis and, presumably therefore, higher pulmonary vascular pressures in such subjects.