The effect of inspired oxygen concentration on the ventilation-perfusion distribution in inhomogeneous lungs

The coupled conservation of mass equations for oxygen, carbon dioxide and nitrogen are written down for a lung model consisting of two homogeneous alveolar compartments (with different ventilation-perfusion ratios) and a shunt compartment. As inspired oxygen concentration and oxygen consumption are varied, the flux of oxygen, carbon dioxide and nitrogen across the alveolar membrane in each compartment varies. The result of this is that the expired ventilation-perfusion ratio for each compartment becomes a function of inspired oxygen concentration and oxygen consumption as well as parameters such as inspired ventilation and alveolar perfusion. Another result is that the "inspired ventilation-perfusion ratio and the "expired ventilation-perfusion ratio differ significantly, under some conditions, for poorly ventilated lung compartments. As a consequence, we need to distinguish between the "inspired ventilation-perfusion distribution, which is independent of inspired oxygen concentration and oxygen consumption, and the "expired ventilation-perfusion distribution, which we now show to be strongly dependent on inspired oxygen concentration and less dependent oxygen consumption. Since the multiple inert gas elimination technique (MIGET) estimates the "expired ventilation-perfusion distribution, it follows that the distribution recovered by MIGET may be strongly dependent on inspired oxygen concentration.     

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)     

Pulmonary blood flow and ventilation-perfusion heterogeneity

We studied the independent influence of changes in perfusion on pulmonary gas exchange in the left lower lobe (LLL) of anesthetized dogs. Blood flow to the LLL (QLLL) was raised 50% (increased QLLL) or reduced 50% (decreased QLLL) from baseline by partial occlusion of the right or left pulmonary artery, respectively. Minute ventilation and alveolar PCO2 of the LLL remained constant throughout the study. We determined ventilation-perfusion distributions of the LLL using the multiple inert gas elimination technique. Increased QLLL impaired LLL pulmonary gas exchange. All dispersion indexes and all arterial-alveolar difference areas increased (P less than 0.01). Decreased QLLL increased the log standard deviation of the perfusion distribution (P less than 0.05) and reduced the log standard deviation of the ventilation distribution (P less than 0.01) but did not affect the dispersion indexes or alveolar-arterial difference areas. We conclude that ventilation-perfusion heterogeneity is increased by independent changes in perfusion from normal baseline blood flow, even when ventilation and alveolar gas composition remain constant.     

Ventilation-perfusion distribution and shunt fraction during one-lung ventilation: effect of different inhaled oxygen levels

Ventilation with higher fraction of inspired oxygen (F(I)O2) is one of the commonly-chosen strategies executed for treatment of hypoxemia during one lung ventilation (OLV) for thoracic surgery. In this study, we investigated the effect of F(I)O2 on pulmonary ventilation-perfusion (VA/Q) distribution during OLV. Six pigs, weighing 27 to 34 kg, were selected for this study. Following by a steady-state period, randomized administrations of F(I)O2 with 0.4, 0.6 and 1.0 were performed for 30 minutes at the right lateral decubitus position during OLV, while hemodynamic data and lung mechanics were simultaneously monitored. The VA/Q distributions of the lung(s) were assessed by the multiple inert gas elimination technique (MIGET). PaO2 at F(I)O2 of 100% was significantly reduced in OLV compared with two-lung ventilation (TLV) (522 +/- 104 vs. 653 +/- 21 mmHg; P < 0.001) at right lateral decubitus position. MIGET algorithms demonstrated a wider VA/Q distribution during OLV at F(I)O2 of 40%, as compared with distribution during TLV at F(I)O2 of 100%, but a bimodal perfusion distribution shifted to lower VA/Q component during OLV at F(I)O2 of 100%. There was an increase of pulmonary shunting in OLV, as compared with TLV at F(I)O2 of 100% (1.94 +/- 2.2% vs. 9.5 +/- 9.7%; P < 0.01). In addition, OLV caused a significant increase in the dispersion of perfusion at F(I)O2 of 100% (0.62 +/- 0.20 vs. 0.44 +/- 0.23; P < 0.01), but ventilation showed no denoting changes (1.06 +/- 0.20 vs. 0.98 +/- 0.35; P > 0.01). During OLV with right lateral decubitus position, there were no significant changes in the pulmonary shunt, the dispersion of perfusion and ventilation at different F(I)O2. OLV resulted in an increase in pulmonary shunting and heterogeneity compared with TLV. Furthermore, the PaO2 decreased during OLV regardless of the postural changes. At different F(I)O2, there were no significant changes in the pulmonary shunt, the dispersion of perfusion and ventilation during OLV with right lateral decubitus posture.     

Determination of the distribution of ventilation-perfusion ratios: technic of elimination of multiple inert gases

The multiple inert gas elimination technique (MIGT) facilitates the estimation of the distributions of ventilation-perfusion (VA/Q) ratios in the experimental and clinical setting. The most relevant technical aspects and equipment and operational requirements needed to measure a mixture of inert gases in both the gas phase and the blood phase using gas chromatography are overviewed with detail. Results obtained in 3 dogs and 4 syringe-homogeneous lung models were entirely consistent with data formerly reported in the literature. Particular attention is paid to the linearity of the gas chromatograph detectors, reproducibility of inert gases sampling, and analysis of brands of heparin to detect acetone content. The errors of measurement (coefficients of variation) in blood were: 1.4 for sulfur hexafluoride; 1.8% for ethane; 2% for cyclopropane and halothane, each; 2.4% for diethyl ether; and, 3.6% for acetone. Important practical points are also emphasized in order to draw attention to potential problems and issues that should be concentrated upon to minimize the error in the measurements. It is concluded that the setting up of the MIGT is well established and validated.     

Quantification of regional V/Q ratios in humans by use of PET. II. Procedure and normal values

Regional measurements of tissue isotope concentration, made using positron emission tomography (PET), allow tracer models to be used in a quantitative manner to provide topographic distributions of many structural and functional parameters, each derived for the same well-defined lung element. In this paper we describe a technique to measure regional ventilation-perfusion ratios (V/Q), in absolute units, by use of PET and the continuous intravenous infusion of an inert gas isotope, 13N, and report on measurements made in 12 normal subjects (4 smokers). Data were obtained from a single lung section (slice thickness, 1.7 cm full width at half-maximum response to a line source) at the level of the right ventricle in the supine posture during quiet breathing. For the 12 subjects, volume-weighted mean values of V/Q, averaged over individual right and left lung fields, ranged from 0.50 to 1.29. Analysis of these means showed no difference between lungs: right, 0.80 +/- 0.23 SD; left, 0.76 +/- 0.20 SD. Topographically, a systematic fall of V/Q in the ventrodorsal direction was observed in eight of the subjects (mean ventrodorsal difference 0.39, range 0.19-0.90), whereas two showed a clear increase toward dependent lung regions (range 0.16-0.26). Seven of the subjects with a falling ventrodorsal V/Q gradient also exhibited discrete regions of low V/Q at the dorsal lung border. We conclude that, in normal subjects, ventilation and perfusion are generally well matched in the supine posture, but isolated mismatching often occurs in dependent lung regions.     

Information content of multiple inert gas elimination measurements

The multiple inert gas elimination technique provides a fundamental assessment of the distribution of ventilation-perfusion (VA/Q) ratios in the lung. The resolution of the finer structure of this distribution is limited however. This study examines the theoretical basis of this limitation and presents an objective method for evaluating the independence of inert gas measurements. It demonstrates the linear dependence of the inert gas kernels and their filtering characteristics to be the factors most limiting information content. The limited number of gases available for measurement and experimental error are lesser limitations. At usual levels of experimental error, no more than seven different inert gases having partition coefficients between those of SF6 and acetone will provide independent information, and information content will be maximized by choosing gases with partition coefficients spaced equally on a logarithmic scale. A fivefold reduction in experimental error will not significantly alter the information content of the measurements. The analysis applies equally to other methods of multiple inert gas elimination data interpretation.     

Hypoxic pulmonary vasoconstriction as a regulator of alveolar-capillary oxygen flux: A computational model of ventilation-perfusion matching

The relationship between regional variabilities in airflow (ventilation) and blood flow (perfusion) is a critical determinant of gas exchange efficiency in the lungs. Hypoxic pulmonary vasoconstriction is understood to be the primary active regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply. However, it is not understood how the integrated action of hypoxic pulmonary vasoconstriction affects oxygen transport at the system level. In this study we develop, and make functional predictions with a multi-scale multi-physics model of ventilation-perfusion matching governed by the mechanism of hypoxic pulmonary vasoconstriction. Our model consists of (a) morphometrically realistic 2D pulmonary vascular networks to the level of large arterioles and venules; (b) a tileable lumped-parameter model of vascular fluid and wall mechanics that accounts for the influence of alveolar pressure; (c) oxygen transport accounting for oxygen bound to hemoglobin and dissolved in plasma; and (d) a novel empirical model of hypoxic pulmonary vasoconstriction. Our model simulations predict that under the artificial test condition of a uniform ventilation distribution (1) hypoxic pulmonary vasoconstriction matches perfusion to ventilation; (2) hypoxic pulmonary vasoconstriction homogenizes regional alveolar-capillary oxygen flux; and (3) hypoxic pulmonary vasoconstriction increases whole-lobe oxygen uptake by improving ventilation-perfusion matching.     

Diffusion limitation in normal humans during exercise at sea level and simulated altitude

The relative roles of ventilation-perfusion (VA/Q) inequality, alveolar-capillary diffusion resistance, postpulmonary shunt, and gas phase diffusion limitation in determining arterial PO2 (PaO2) were assessed in nine normal unacclimatized men at rest and during bicycle exercise at sea level and three simulated altitudes (5,000, 10,000, and 15,000 ft; barometric pressures = 632, 523, and 429 Torr). We measured mixed expired and arterial inert and respiratory gases, minute ventilation, and cardiac output. Using the multiple inert gas elimination technique, PaO2 and the arterial O2 concentration expected from VA/Q inequality alone were compared with actual values, lower measured PaO2 indicating alveolar-capillary diffusion disequilibrium for O2. At sea level, alveolar-arterial PO2 differences were approximately 10 Torr at rest, increasing to approximately 20 Torr at a metabolic consumption of O2 (VO2) of 3 l/min. There was no evidence for diffusion disequilibrium, similar results being obtained at 5,000 ft. At 10 and 15,000 ft, resting alveolar-arterial PO2 difference was less than at sea level with no diffusion disequilibrium. During exercise, alveolar-arterial PO2 difference increased considerably more than expected from VA/Q mismatch alone. For example, at VO2 of 2.5 l/min at 10,000 ft, total alveolar-arterial PO2 difference was 30 Torr and that due to VA/Q mismatch alone was 15 Torr. At 15,000 ft and VO2 of 1.5 l/min, these values were 25 and 10 Torr, respectively. Expected and actual PaO2 agreed during 100% O2 breathing at 15,000 ft, excluding postpulmonary shunt as a cause of the larger alveolar-arterial O2 difference than accountable by inert gas exchange.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pulmonary shunt: a comparison between oxygen and inert gas infusion methods.

Pulmonary shunt measurement was compared using the standard oxygen (Berggren) technique and a new multiple inert gas infusion (Wagner et al.) technique in 11 mongrel dogs with either regional atelectasis or diffuse pulmonary edema. Relative retentions of sulfur hexafluoride, ethane, cyclopropane, halothane, diethyl ether, and acetone were used to calculate intrapulmonary shunt. Relative dilution of oxygen (Berggren method) was used to calculate total right to left shunt. The two methods gave similar results in the range of 20-80%. At low shunts the oxygen method measured higher values. This is because of the greater relative importance of fixed extrapulmonary shunts at this level and, as well, error in the measurement of PO2. Both techniques are suitable for normal clinical use.     

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.     

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.     

Conducting airway gas exchange: diffusion-related differences in inert gas elimination.

We studied CO2 and inert gas elimination in the isolated in situ trachea as a model of conducting airway gas exchange. Six inert gases with various solubilities and molecular weights (MW) were infused into the left atria of six pentobarbital-anesthetized dogs (group 1). The unidirectionally ventilated trachea behaved as a high ventilation-perfusion unit (ratio = 60) with no appreciable dead space. Excretion of higher-MW gases appeared to be depressed, suggesting a MW dependence to inert gas exchange. This was further explored in another six dogs (group 2) with three gases of nearly equal solubility but widely divergent MWs (acetylene, 26; Freon-22, 86.5; isoflurane, 184.5). Isoflurane and Freon-22 excretions were depressed 47 and 30%, respectively, relative to acetylene. In a theoretical model of airway gas exchange, neither a tissue nor a gas phase diffusion resistance predicted our results better than the standard equation for steady-state alveolar inert gas elimination. However, addition of a simple ln (MW) term reduced the remaining residual sum of squares by 40% in group 1 and by 83% in group 2. Despite this significant MW influence on tracheal gas exchange, we calculate that the quantitative gas exchange capacity of the conducting airways in total can account for less than or equal to 16% of any MW-dependent differences observed in pulmonary inert gas elimination.     

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.     

Ventilation-perfusion relationships in the lung during head-out water immersion.

Water immersion can cause airways closure during tidal breathing, and his may result in areas of low ventilation-perfusion (VA/Q) ratios (VA/Q less than or equal to 0.1) and/or shunt and, ultimately, hypoxemia. We studied this in 12 normal males: 6 young (Y; aged 20-29 yr) with closing volume (CV) less than expiratory reserve volume (ERV), and six older (O; aged 40-54 yr) with CV greater than ERV during seated head-out immersion. Arterial and expired inert gas concentrations and dye-dilution cardiac output (Q) were measured before and at 2, 5, 10, 15, and 20 min in 35 degrees C water. During immersion, Y showed increases in expired minute ventilation (VE; 8.3-10.3 l/min), Q (6.1-8.2 l/min), and arterial PO2 (PaO2; 91-98 Torr; P less than or equal to 0.05). However, O2 uptake (VO2), shunt, amount of low-VA/Q areas (% of Q), and the log standard deviation of the perfusion distribution (log SDQ) were unchanged. During immersion, O showed increases in shunt (0.6-1.8% of Q), VE (8.5-11.4 l/min), and VO2 (0.31-0.40 l/min) but showed no change in low-VA/Q areas, log SDQ, Q, or PaO2. Throughout, O showed more VA/Q inequality (greater log SDQ) than Y (O, 0.69 vs. Y, 0.47).(ABSTRACT TRUNCATED AT 250 WORDS)     

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 posture on regional gas exchange in pigs.

Although recent high-resolution studies demonstrate the importance of nongravitational determinants for both pulmonary blood flow and ventilation distributions, posture has a clear impact on whole lung gas exchange. Deterioration in arterial oxygenation with repositioning from prone to supine posture is caused by increased heterogeneity in the distribution of ventilation-to-perfusion ratios. This can result from increased heterogeneity in regional blood flow distribution, increased heterogeneity in regional ventilation distribution, decreased correlation between regional blood flow and ventilation, or some combination of the above (Wilson TA and Beck KC, J Appl Physiol 72: 2298-2304, 1992). We hypothesize that, although repositioning from prone to supine has relatively small effects on overall blood flow and ventilation distributions, regional changes are poorly correlated, resulting in regional ventilation-perfusion mismatch and reduction in alveolar oxygen tension. We report ventilation and perfusion distributions in seven anesthetized, mechanically ventilated pigs measured with aerosolized and injected microspheres. Total contributions of pulmonary structure and posture on ventilation and perfusion heterogeneities were quantified by using analysis of variance. Regional gradients of posture-mediated change in ventilation, perfusion, and calculated alveolar oxygen tension were examined in the caudocranial and ventrodorsal directions. We found that pulmonary structure was responsible for 74.0 +/- 4.7% of total ventilation heterogeneity and 63.3 +/- 4.2% of total blood flow heterogeneity. Posture-mediated redistribution was primarily oriented along the caudocranial axis for ventilation and along the ventrodorsal axis for blood flow. These mismatched changes reduced alveolar oxygen tension primarily in the dorsocaudal lung region.     

The secretion of inert gas into the swim-bladder of fish

The composition of the gas mixture secreted into the swim-bladders of several species of fish has been determined in the mass spectrometer. The secreted gas differed greatly from the gas mixture breathed by the fish in the relative proportions of the chemically inert gases, argon, neon, helium, and nitrogen. Relative to nitrogen the proportion of the very soluble argon was increased and the proportions of the much less soluble neon and helium decreased. The composition of the secreted gas approaches the composition of the gas mixture dissolved in the tissue fluid. A theory of inert gas secretion is proposed. It is suggested that oxygen gas is actively secreted and evolved in the form of minute bubbles, that inert gases diffuse into these bubbles, and that the bubbles are passed into the swim-bladder carrying with them inert gases. Coupled to a preferential reabsorption of oxygen from the swim-bladder this mechanism can achieve high tensions of inert gas in the swim-bladder. The accumulation of nearly pure nitrogen in the swim-bladder of goldfish (Carassius auratus) is accomplished by the secretion of an oxygen-rich gas mixture followed by the reabsorption of oxygen.     

Ventilation distribution in rats: Part I - The effect of gas composition as measured with electrical impedance tomography

ABSTRACT: The measurement of ventilation distribution is currently performed using inhaled tracer gases for multiple breath inhalation studies or imaging techniques to quantify spatial gas distribution. Most tracer gases used for these studies have properties different from that of air. The effect of gas density on regional ventilation distribution has not been studied. This study aimed to measure the effect of gas density on regional ventilation distribution. METHODS: Ventilation distribution was measured in seven rats using electrical impedance tomography (EIT) in supine, prone, left and right lateral positions while being mechanically ventilated with either air, heliox (30% oxygen, 70% helium) or sulfur hexafluoride (20% SF6, 20% oxygen, 60% air). The effect of gas density on regional ventilation distribution was assessed. RESULTS: Gas density did not impact on regional ventilation distribution. The non-dependent lung was better ventilated in all four body positions. Gas density had no further impact on regional filling characteristics. The filling characteristics followed an anatomical pattern with the anterior and left lung showing a greater impedance change during the initial phase of the inspiration. CONCLUSION: It was shown that gas density did not impact on convection dependent ventilation distribution in rats measured with EIT.     

The effect of the width of the ventilation-perfusion distribution on arterial blood oxygen content

We investigate the effect of the width of ventilation-perfusion distributions on arterial blood oxygen content. We assume that the perfusion within the alveolar volume is a continuous function of ventilation-perfusion ratio, known as the continuous ventilation-perfusion distribution, and then write down the conservation of mass equations in the lung incorporating the nonlinear relationship between oxygen concentration in the gas phase and blood oxygen content. We solve these equations for various unimodal and bimodal ventilation-perfusion distributions believed to occur in practice and calculate the arterial blood oxygen content in each case. When a subject has a unimodal ventilation-perfusion distribution we show that the fraction of cardiac output to that mode (i.e. the fraction of non-shunted blood) has a large effect on arterial oxygen blood content. However, the width of the distribution has only a negligible effect on arterial oxygen blood content. For a bimodal ventilation-perfusion distribution the location and fraction of cardiac output to each mode has a large effect on arterial oxygen blood content. Again, the width of each mode of the distribution has little effect on arterial oxygen blood content. As a result there is little point, from a clinical perspective, in developing techniques for investigating the width of modes of these distributions since all relevant clinical information is contained in the nature (i.e. unimodal or bimodal) and in the location of the modes.