Kazuhiro Yamaguchi; Takao Tsuji; Kazutetsu Aoshiba; Hiroyuki Nakamura; Shinji Abe

Review Article

Austin J Pulm Respir Med 2019; 6(1): 1060.

Insights into Anatomical Basis Prescribing Ventilation- Perfusion Distribution in Lung Periphery

Kazuhiro Yamaguchi*¹, Takao Tsuji¹, Kazutetsu Aoshiba², Hiroyuki Nakamura² and Shinji Abe¹

¹Department of Respiratory Medicine, Tokyo Medical University, Japan

²Department of Respiratory Medicine, Tokyo Medical University Ibaraki Medical Center, Japan

*Corresponding author: Kazuhiro Yamaguchi, Department of Respiratory Medicine, Tokyo Medical University, 6-7-1 Nishi-Shinjuku, Shinjuku-ku, Tokyo 160-0023, Japan

Received: May 02, 2019; Accepted: June 14, 2019; Published: June 21, 2019

Abstract

Some crucial problems regarding structural (anatomical) basis on functional parameters describing gas exchange in lung periphery have remained unsolved. Although many definitions for anatomical gas exchange unit (i.e., acinus) have been proposed, there are no authentic study for certifying that anatomicallydefined acinus indeed acts as functional gas exchange unit, as well. Among different acini reported so far, we selected acinus of Haefeli-Bleuer (HB acinus) as the most reliable organization. This is simply because microstructures of HB acinus were precisely examined by aid of scanning electron microscopy in addition to light microscopy. Therefore, we first coped with the issue of whether anatomically-defined HB acinus would meet the definition of functional gas exchange unit, i.e., the gas concentration is constant in any region of this organization. We were confronted with an interesting phenomenon that spatial PO₂ gradient exists along the axial direction of HB acinus over inspiration, but it almost disappears over expiration, leading to the conclusion that anatomicallydefined HB acinus indeed acts as functional gas exchange unit on expiration but not on inspiration. This fact certainly indicates that functional gas exchange parameters measured on expiration, such as V_A/Q heterogeneity investigated from Multiple Inert Gas Elimination Technique (MIGET), can be considered to reflect microstructural abnormalities at the level of HB acinus. Subsequently, we tried to validate the issue of whether V_A/Q heterogeneities estimated from MIGET would well explain the structural abnormalities in patients with pathologicallyand/ or radiologically-confirmed lung diseases.

Keywords: Acinus; Anatomical gas exchange unit; Functional gas exchange unit; V_A/Q heterogeneity; Multiple inert gas elimination technique

Abbreviations

V_A: Alveolar or Effective Ventilation, or Alveolar Volume; Q: Pulmonary Capillary Perfusion; V_A/Q: Ventilation-Perfusion Ratio; MIGET: Multiple Inert Gas Elimination Technique; acinus of HB: acinus of Haefeli-Bleuer and Weibel; TB: Terminal Bronchiole; TrB: Transitional Bronchiole; RB: Respiratory Bronchiole; AD: Alveolar Duct; AS: Alveolar Sac; Z: Generation of Airway From Trachea; Z’: Generation of Acinar Airway From Transitional Bronchiole; PFT: Pulmonary Function Test; VC: Vital Capacity; FVC: Forced Vital Capacity; FEV₁: Forced Expiratory Volume During One Second; ATI: Air Trapping Index defined as 100.(VC-FVC)/VC; PEF: Peak Expiratory Flow Rate; FEF₅₀: Forced Expiratory Flow Rate at 50% of FVC; TLC: Total Lung Capacity; FRC: Functional Residual Capacity; RV: Residual Volume; PaO₂: PO₂ in Arterial Blood; AaDO₂: Alveolar-Arterial PO₂ Difference; PaCO₂: PCO₂ in Arterial Blood; D_LCO: Pulmonary Diffusing Capacity For Carbon Monoxide (CO); K_CO: Krogh Factor for CO defined as D_LCO/V_A, where V_A denotes alveolar volume; Hb: Hemoglobin; Pe: Peclet number; d: diameter of airway tube; u: mean convective flow velocity; D: Binary Diffusion Coefficient of Gas; x: axical distance from terminal alveolar sacs; t: time; C: Concentration of Gas; MBNW: Multi-Breath N₂ Washout; DCDI: Diffusion-Convection-Dependent Inhomogeneity; P: Partial Pressure of Gas; P_A: Partial Pressure of Gas in Alveolar Gas Phase; P_C: Partial Pressure of Gas in Pulmonary Capillary; P_V: Partial Pressure of Gas in Mixed Venous Blood; E: Excretion of Gas (P_A/ P_V); R: Retention of Gas (P_C/P_V); λ: Blood-Gas Partition Coefficient; SF₆: Sulfur Hexafluoride; L: Objective Variable Minimized with Respect to Fractional Perfusion; q_j: fractional perfusion; v_j: fractional ventilation; R_i: Measured Arterial Gas Concentration Divided by its Mixed Venous Concentration; W_i: Coefficient For Weight of Each Gas; μ: Lagrange Multiplier; φ_j: Compartmental Weight of each V_A/Q Unit; S: Smoothing Term; V_D/V_T: Dead Space Ventilation; Q_S/ Q_T: Right-to-Left Shunt; MRI: Magnetic Resonance Imaging; ASL: Arterial Spin Labeling; HPV: Hypoxic Pulmonary Vasoconstriction; COPD: Chronic Obstructive Pulmonary Disease; IP: Interstitial Pneumonia; ARDS: Acute Respiratory Distress Syndrome; PE: Pulmonary Embolism; BO: Bronchiolitis Obliterans; PPFE: Pleuroparenchymal Fibroelastosis; HSCT: Hematopoietic Stem Cell Transplantation; HPS: Hepatopulmonary Syndrome; IVL: Intravascular Lymphomatosis; PVOD: Pulmonary Veno-Occlusive Disease; PCH: Pulmonary Capillary Hemangiomatosis; LCH: Langerhans Cell Histiocytosis; LAM: Lymphangioleiomyomatosis; ANCA: Anti-Neutrophil Cytoplasmic Antibodies; PAP: Pulmonary Alveolar Proteinosis; DOE: Dyspnea on Exertion; CT: Computed Tomography; GGO: Ground Glass Opacity; VATS: Video-Assisted Thoracoscopy; ^99mTc-MAA: Perfusion Scan using ^99mTechnetium (Tc) Labeled Macro-Agglutinated Albumin (MAA); ^81mKr: ^81mKripton; NO: Nitric Oxide; FeNO: Fractional Concentration of Exhaled NO

Introduction

Among the functional parameters that estimate gas exchange dynamics in the lung periphery, the continuous distribution of ventilation to perfusion (V_A/Q) gives a particularly important information while diagnosing the functional abnormalities in patients with a variety of lung diseases [1,2]. The heterogeneity of V_A/Q distribution is the key mechanism that gives rise to hypoxemia and/ or hypercapnia in patients with a variety of lung diseases. It is worth noting that pulmonary physiology, which stresses the heterogeneity of functional properties leading to impaired overall function, is well ahead of other areas of physiology. In other organs, the heterogeneous distribution of functional properties in an organ is well known but little interest has been directed toward the consequences of such functional heterogeneity. As such, the developmental process of pulmonary physiology is unique in comparison with that of other organs [2]. However, there remains the serious problem in pulmonary gas exchange physiology represented by V_A/Q heterogeneity; that is, the endeavors to ensure the relationship between functional heterogeneity and structural lesion do not end successfully [1]. Although the great efforts of elucidating the direct communication (i.e., the establishment of one-to-one relationship) between structural and functional abnormalities in the lung periphery have been made in the era of the 20^th century, particularly from the 1950’s to the 1980’s, it is hard to say that the efforts to unite them in a variety of directions are successfully enough. Furthermore, it is of clinical necessity to have a profound knowledge about the issue of what structural abnormality is detected from the functional V_A/Q heterogeneity while physicians should do a pathophysiological decision-making against a patient with a certain lung disease. In view of these historical facts and clinical requirements, the present review highlights the issue of specifying the structural (anatomical) backgrounds underlying the functional parameter of continuous distribution of V_A/Q that has been used for estimating gas exchange dynamics in the lung periphery. For accomplishing this purpose, the three matters were comprehensively addressed. (1) What is the most appropriate organization serving as the functional gas exchange unit, which is certainly backed by the structural design of the lung periphery? (2) Is the V_A/Q distribution, which is quantified by means of the Multiple Inert Gas Elimination Technique (MIGET), indeed supported by the structural (anatomical) facts? (3) Based on the measurements of continuous distribution of V_A/Q in patients with pathologically- and/or radiologically-confirmed lung diseases, the attempt was made to certify the structure-function relationships in the lungs with various kinds of specific diseases in a precise fashion.

What is the Most Appropriate Organization Serving as Functional Gas Exchange Unit?

Anatomical design for estimating gas transport in conductive airways: From the anatomical standpoint, the lung is divided into two parts. The region with conductive airways (central and peripheral airways) with a dichotomous branching geometry having no alveoli configures the anatomical dead space, through which environmental air is transported to the lung periphery. On the other hand, the region having a tremendous number of alveoli engaging in gas exchange is defined as the acinus. The morphometric data of airway trees can be abstracted into two types of models that extend from the trachea to the terminal alveolar sacs [3-5]. Model A stresses the basic properties of airway branching by assuming the regular dichotomy and thus defining a symmetric typical-path model, while model B defines the irregularities of tree architecture with asymmetric branching and defines the properties of a variable path model.

In the symmetrical typical-path model of A (equivalent to the model A of Weibel [1,5]), the airway branches in a certain generation are assumed to have the same diameter and length. Thus, the diameterto- length ratio is also treated to be similar in all generations. The total cross-sectional area of all airways in each generation increases tremendously toward the airways located in the periphery. For this feature, the typical-path model of A has been called “trumpet” or “thumbtack” model, as well [6]. In this case, it is necessary to note that the essential factor that defines the airway dimension is the number of generations. The detailed criticisms on the typical-path model of A was found elsewhere [1,5]. Briefly, (1) this model assumes that all anatomical gas exchange units (i.e., acini) are found at an equal distance from the trachea. This is a gross simplification if we gaze the anatomical fact that some terminations of conductive airways end after a shorter distance than others. (2) While the diameter shows a relatively symmetric distribution in airways belonging to the same generation, the segment length is highly skewed. (3) The diameter of acinar airways precisely examined by Haefeli-Bleuer and Weibel [7] is not predicted from the regression line constructed for estimating the diameter of conductive airways.

The starting point for defining the asymmetrical model of B is based on the anatomical finding that airways with a certain diameter occur in several generations and at different distances from the origin of airways [5]. For instance, airways of 2 mm diameter are found in generations 4 to 14, with a maximum in generation 8. Alternatively, these bronchi are located at 18 to 31 cm from the origin of trachea with a maximum at 24 cm. Note that in the symmetrical typicalpath model of A, bronchi with 2 mm diameter are located maximally in generation 8 corresponding to 23.6 cm from the trachea, which is in a close agreement with the distance that shows the maximum distribution of bronchi having 2 mm diameter in the variable path model of B [5]. Based on these facts, one may conceive that although the symmetrical typical-path model of A has various limitations, it works approximately as an acceptable model for predicting airway branching, at least in lower conductive airways from trachea to terminal bronchioles. When attempting to precisely evaluate the convection-related gas transport dynamics in conductive airways toward terminal bronchioles, a more realistic model such as variable path model of B with an asymmetrical branching architecture should be applied. However, when considering the gas mixing dynamics in the acinar region, the difference in models for conductive airways may exert little impact. This is because the relative contribution of diffusion is equivalent to, or predominates, that of convective flow in the acinar region [6].

Anatomical design for estimating gas exchange in lung periphery: The alveolus cannot be taken as a ventilation unit mostly because each alveolus is not independent of other alveoli. Two adjoining alveoli share the alveolar wall and each alveolus adjoins several alveoli, some of which are connected to different alveolar ducts. Furthermore, there are communications at the level of respiratory bronchioles or alveolar ducts defined as Martin channels [8]. In addition, there is a serious problem concerning a perfusion unit formed by the pulmonary microcirculation. The dense, intertwined capillary network embedded in the alveolar wall forms a continuum of blood flow that is not partitioned into independent perfusion units, resulting in that the story one likes to present, i.e., the anatomical gas exchange unit is organized into an alveolus associated with a separated capillary network in the alveolar wall, is highly fictitious. The capillary network is supplied by the arteriole penetrating the acinus along acinar airways and is drained into the venule in the acinar periphery. The distance between an arteriole and a venule is of an order between 0.5 and 1.0 mm [9], resulting in that the perfusion unit given by the area surrounded by an arteriole and a venule extends over several alveoli. These facts are in accord with the idea that the perfusion unit is not congruent with the ventilation unit if it is composed of an alveolus, giving rise to difficulty in anatomically defining the gas exchange unit from an alveolus and a capillary network, in which the ventilation and perfusion units should be matched.

The traditional rationale for anatomical ventilation unit was evolved based on the concept of acinus, the ventilation into which is supplied by a terminal bronchiole (corresponding to the 14^th generation in typical-path model of A) that is the last peripheral airway without alveoli. This type of ventilation unit is generally called the acinus of Loeschcke (Figure 1). There are many other terms that define the region equivalent to the acinus of Loeschcke [10-16]. The size of acinus of Loeschcke averages 7 to 10 mm in diameter and roughly 30,000 acini configure the lung. An acinus contains alveoli ranging from 3,000 to 4,000 [7], resulting in that the lung consists of about a hundred million alveoli.

Figure 1: Anatomical characteristics of various acini. Acinus of Loeschcke is supplied by terminal bronchiole (14^th generation). Acinus of Haefeli-Bleuer (HB) and acinus of Aschoff are supplied by transitional bronchiole (15^th generation) and first-order respiratory bronchiole (16^th generation), respectively. Primary lobule of Miller is served by alveolar duct (19^th generation). Z in right panel indicates the number of airway generations from zero (trachea) to 23 (terminal alveolar sac) in model A of Weibel. Z’ is the number of airway generations from zero (transitional bronchiole) to 8 (alveolar sacs) in HB acinus. Figure in right side is modified from Reference [5].

    
    
    Figure 1: Anatomical characteristics of various acini.
Acinus of Loeschcke is supplied by terminal bronchiole (14^th generation).
Acinus of Haefeli-Bleuer (HB) and acinus of Aschoff are supplied by
transitional bronchiole (15^th generation) and first-order respiratory bronchiole
(16^th generation), respectively. Primary lobule of Miller is served by alveolar
duct (19^th generation). Z in right panel indicates the number of airway
generations from zero (trachea) to 23 (terminal alveolar sac) in model A
of Weibel. Z’ is the number of airway generations from zero (transitional
bronchiole) to 8 (alveolar sacs) in HB acinus. Figure in right side is modified
from Reference [5].

Miller [17] proposed the different anatomical concept that is precious for understanding what the secondary and primary lobules are. The secondary lobule of Miller is the area supplied by a lobular bronchiole having dimeter of about 1.0 mm (corresponding to the 12th generation) and surrounded by the fibrous connective tissue septa (i.e., the interlobular septa). The size of secondary lobule of Miller varies from 1.0 to 2.5 cm, each of which is comprised of varying number of acini defined by Loeschcke, ranging from three to 24 depending on the region selected [10,18], while the primary lobule of Miller is expressed by the area governed by an alveolar duct (corresponding to the 19th generation). However, it may be a mistake to take the primary lobule of Miller as the ventilation unit constituting the anatomical gas exchange unit. This is because there are many alveoli that are not included in the primary lobule of Miller.

Reid [19,20] proposed a different definition about the secondary lobule. The secondary lobule of Reid is the region distal to any bronchiole with a mm-branching pattern. The size of the secondary lobule of Reid is constant (approximately 1.0 cm) in comparison with that of Miller and contains three to five acini of Loeschcke. The Reid’s secondary lobule is useful when interpreting the bronchogram but not evaluating the gas exchange in the lung periphery.

The acinus of Aschoff is defined as the ventilation unit supplied by the first-order respiratory bronchiole (the 16th generation), the size of which is about half of the acinus of Loeschcke [21].

The extensive analysis on the microscopic structure of the acinus was made by Haefeli-Bleuer and Weibel [7], who defined the acinus as the region severed by the proximal part of a transitional bronchiole without identifiable alveoli (the 15^th generation). The authors [7] showed that the transitional bronchiole contains the segments both with and without alveoli. We shall name this type of acinus “the acinus of HB” in the present review, which may be larger than the acinus of Aschoff but is smaller than the acinus of Loeschcke. However, as it is extremely difficult to surely separate the transitional bronchiole from the first-order respiratory bronchiole in a microscopic examination [7], there is a certain possibility that the acinus of HB is practically the same as that of Aschoff. Therefore, when the term of the acinus of HB is used in the present review, it also includes the acinus of Aschoff.

The difficult problem concerning the anatomical unit for perfusion was resolved by König et al. [22], who demonstrated that the entire region of Loeschcke is perfused almost homogeneously by a plasma tracer, indicating that all capillary networks existing in the acinus of Loeschcke are connected to each other. Since the acinus of HB is smaller than that of Loeschcke, the fact identified by König et al. [22] holds true for the acinus of HB, as well. Therefore, we addressed the acinus of HB as the most appropriate anatomical gas exchange organization (Table 1). The acinar airways of HB are characterized by asymmetrical, irregular dichotomy (rarely, trichotomy), which branch over 9 generations. The internal airway dimeter falls as the branching progresses, while the outer diameter, including the sleeve of alveoli, remains almost constant. The total path length from the transitional bronchiole to the terminal alveolar sac averages 8.8 mm, while the total acinar volume averages 0.2 cm3. The total alveolar surface area participating in gas exchange reaches about 70 cm². However, it should be noticed that these values are measured at an almost full expansion of the lung tissue specimens, corresponding to a Total Lung Capacity (TLC) level. Therefore, under physiological condition, i.e., at a Functional Residual Capacity (FRC) level, the dimensions of acinar structures, including acinar volume and total alveolar surface area, should be considered about half of the values depicted in (Table 1) [23].

Table 1: Microstructural characteristics of HB acinus.




  
    Structural parameters
    Comments
  
  
    Entrance
    Transitional Bronchiole (TrB)
  
  
    Airway branching pattern
    Irregular, asymmetrical    dichotomy (trichotomy: rare)
  
  
    Number of branches (Z’)
      Transitional bronchiole: Z’ = zero
    Average: 9.1 (ranging from 6 to 12)
  
  
    Total longitudinal path length
    8.8 ± 1.4 mm (from TrB to terminal alveolar sacs)
  
  
    Internal airway diameter
    Decrease from 500 mm (Z’ = 0) to 270 mm (Z’ = 10)
  
  
    Outer airway diameter
    Approximately constant over    acinar airways including alveolar sleeve (700 mm)
  
  
    Total surface area of alveoli
    Average: 69 cm²
  
  
    Total volume of an acinus
    187 ± 79 mm³
  
  
    Total number of acini in human lung
    26,000 to 32,000
  
  
    Values are measured under condition at full expansion    of lung tissue specimen. Data are extracted from those reported in ref. 7.



Table 1: Microstructural characteristics of HB acinus.

Collateral ventilation in the acinus: Three pathways provide the collateral ventilation in the acinus, i.e. alveolar pores (pores of Kohn), channels of Lambert, and channels of Martin. Although the size of alveolar pores ranges from 2 to 30 μm, there are many studies certifying that the alveolar pores are not potent in air-filled lungs [24,25]. These studies indicate that the alveolar pores take no part in maintaining alveolar ventilation.

Lambert [26] described accessory communications between bronchioles and alveoli in the normal human lung. The diameter of Lambert channels varies from zero to 30 μm, and they are considered to serve as collateral ventilation to adjacent alveoli when airway obstruction occurs at the level of terminal bronchioles [25]. Supporting this consideration, the important role of Lambert channels was identified in patients with pneumoconiosis, in which a striking accumulation of macrophages was found in the Lambert channels and their adjacent alveoli [27].

Martin [8] reported intra-acinar communications at the level of respiratory bronchioles or alveolar ducts in the canine lung. The Martin channels were also found in human lungs [13,28]. As the Martin channels have sufficiently low resistance to gas flow, they act as the primary pathway for inducing collateral ventilation in the acinus [25]. Therefore, one can conceive that only the Martin channels but neither the alveolar pores nor the Lambert channels serve to equalize the acinar ventilation.

Anatomical and functional boundaries between dead space and alveolar region: The anatomical boundary between dead space and alveolar region is very simple, lying at the level of terminal bronchiole having no alveoli, corresponding to the entrance of acinus of Loeschcke. Namely, the dead space is anatomically conceptualized as the space configured by upper and lower conductive airways up to terminal bronchioles [29]. The anatomically-determined dead space volume varies from 140 to 260 mL depending on the extent of lung inflation and age [30-32]. The anatomical studies consistently showed that 50% of the dead space exists in extrathoracic upper airways, indicating that the volume of lower conductive airways, including central and peripheral airways up to terminal bronchioles, ranges between 70 and 130 mL.

The functional boundary between dead space and alveolar region has been examined by many investigators based on singlebreath measurements using CO2, N2, and foreign inert gases [33- 36]. The functional boundary may be better understood to use the term of “imaginary boundary”. The results obtained therefrom are comparable to those reported for the anatomical dead space. In this case, the following fact should be recognized, i.e., in addition to the convective transport by ventilation, the contribution of diffusion to overall gas transport rises substantially in acinar regions. The respective importance of convection and diffusion for gas transport in a certain part of the lung can be appreciated from the Peclet number (Pe) as;

Pe = d·(u/D) ⋅⋅⋅⋅⋅⋅ Equation 1

where d is diameter of an airway tube, u is convective flow velocity, and D is binary diffusion coefficient of a gas. When the Pe number reaches 1.0, the diffusive transport is the same order of magnitude as the convective transport [37]. Under resting condition with air breathing, the convective flow velocity at the trachea is about 100 cm/sec while about 1 cm/sec at the acinar entrance, indicating that the convective flow velocity falls 100-fold from the trachea to the acinar airways and the contribution of diffusion to gas transport significantly surpasses that of convection within the acinus [5,37]. The position where the Pe is equal to 1.0 is called the critical zone originally proposed by Gomez [38]. The most informative study aiming at specifying the essential mechanism forming the functional boundary between dead space and alveolar region was expanded by Paiva [39]. Incorporating convection, diffusion, and their interaction into the basic mechanism for gas mixing in airways below the 13^th> generation of symmetrical typical-path model of A (i.e., corresponding closely to the secondary lobule of Miller) [6,40-44], Paiva [39] found that on inspiration, the front of a gas (alternatively called diffusion front), which is the concentration profile of a gas having the sigmoid shape against the axial distance from the terminal position of the acinus, lags far behind the front of tidal volume. The font of tidal volume reaches the 22^th generation of airways (i.e., the alveolar duct) at end-inspiration, whereas the diffusion front remains almost stationary in the secondorder respiratory bronchiole during inspiration except for the time point just after beginning of inspiration. The relatively stationary diffusion front indicates that during inspiration, the convective advancement of a gas into the periphery is counterbalanced by the diffusion-elicited proximal retreat of a gas in the acinus [1,6,39]. Qualitatively the similar results were obtained by Swan and Tawhai [23], who applied the asymmetrical branching model of acinar airways (i.e., the acinus of HB) for theoretical analysis. We also estimated the time- and axial distance-dependent PO₂ profiles in an acinus of HB during inspiration and expiration under resting condition with air breathing. We obtained qualitatively the same results as those reported by Swan and Tawhai [23] (Figure 2). These findings suggest that the dead space can be functionally described as the inspiratory volume decided by the diffusion front, but not by the front of tidal volume. The classical gas exchange theory assumes that the dead space has a sharp, all-or-nothing transition boundary as if it is formed only by the ventilation-elicited convection (i.e., the effective ventilation). The effective ventilation may be decided by converting the effect of diffusion to the equivalent effect of convection. The location of effective ventilation is intuitively appreciated by drawing the straight line along the vertical axis, which crosses the representative point of diffusion front. The representative point of diffusion front is given by the inflation point of the sigmoid concentration profile of a gas, which is characterized by the maximal concentration gradient for an intended gas. The inflation point of the symmetrical sigmoid curve is approximated by the point corresponding to the midpoint of the total change in the concentration of a gas generated between acinar entrance and terminal alveolar sacs. When simplifying the complicated results shown in (Figure 2) by considering the effective ventilation point, the functional (imaginary) boundary between dead space and alveolar gas exchange region lies in the second-order respiratory bronchiole, which is distal to the terminal bronchiole and close to the entrance of acinus of HB. This fact suggests that the acinus of HB might also serve as the gas exchange unit in a functional sense.

Figure 2: Temporal and spatial PO₂ profiles in HB acinus during inspiration. Theoretical calculations were done based on geometrical data of HB acinus (Table 1). Various conditions for theoretical calculations are the same as taken by ref. 23 except for PO₂ transfer through alveolocapillary membrane. For simplicity, O₂ is assumed to be not absorbed through alveolocapillary membrane in our calculations. Calculations were done under conditions of room air breathing, resting condition, tidal volume of 500 mL, FRC of 3,000 mL, and one respiratory cycle of 5 sec (inspiration: 2.5 sec and expiration: 2.5 sec). We used equations demonstrated by ref. 37, in which convection, axial diffusion, influence of acinar structures on gas mixing, and transitional change of alveolar cross-sectional area during respiration are taken into consideration. To know representative point of diffusion front at a certain time, we calculated inflation point solving equation of ∂²C/∂x² = 0 under steady state condition (∂C/∂t = 0). Inflation point gives functional (imaginary) boundary between dead space and alveolar gas exchange region. TB: Terminal Bronchiole; TrB: Transitional Bronchiole; RB: Respiratory Bronchiole; AD: Alveolar Duct; AS: Alveolar Sac.

    
    
    Figure 2: Temporal and spatial PO₂ profiles in HB acinus during inspiration.
Theoretical calculations were done based on geometrical data of HB acinus
(Table 1). Various conditions for theoretical calculations are the same as
taken by ref. 23 except for PO₂ transfer through alveolocapillary membrane.
For simplicity, O₂ is assumed to be not absorbed through alveolocapillary
membrane in our calculations. Calculations were done under conditions of
room air breathing, resting condition, tidal volume of 500 mL, FRC of 3,000
mL, and one respiratory cycle of 5 sec (inspiration: 2.5 sec and expiration:
2.5 sec). We used equations demonstrated by ref. 37, in which convection,
axial diffusion, influence of acinar structures on gas mixing, and transitional
change of alveolar cross-sectional area during respiration are taken into
consideration. To know representative point of diffusion front at a certain time,
we calculated inflation point solving equation of ∂²C/∂x² = 0 under steady state
condition (∂C/∂t = 0). Inflation point gives functional (imaginary) boundary
between dead space and alveolar gas exchange region. TB: Terminal
Bronchiole; TrB: Transitional Bronchiole; RB: Respiratory Bronchiole; AD:
Alveolar Duct; AS: Alveolar Sac.

The Most Appropriate Organization Serving as Functional Gas Exchange Unit: The absolute condition that should be met while defining the functional gas exchange unit is the homogeneous distribution of a gas over the region that forms the unit. The important message derived from the study of Paiva [39] and that of Swan and Tawhai [23] is that a series, stratified inhomogeneity of a gas concentration along acinar airways from entrance to terminal alveolar sacs exists during inspiration, resulting in that regardless of the type of acinus, the anatomically-defined acinus does not satisfy the absolute condition indispensable for establishing the functional gas exchange unit during inspiration. However, the situation is clearly different during expiration. A couple of groups of investigators [23,39,45] demonstrated that the inspirationelicited stratified inhomogeneity for a gas diminishes rapidly during expiration. Swan and Tawhai [23] identified that the spatial variation of PO₂ in the acinus of HB under resting condition at air breathing is only 3% during expiration, which is qualitatively coincided with our analytical results (Figure 3). Furthermore, the Martin channels, the communications locating at respiratory bronchioles or alveolar ducts, may further promote the homogenization of spatial gas difference in the acinus. Thus, joining together the result for the functional (imaginary) boundary between dead space and alveolar gas exchange region argued above and the result found by Swan and Tawhai [23], we can infer that the anatomically-defined acinus of HB serves as the functional gas exchange unit during expiration in a first approximation. However, we should be aware of the fact that there is no acinar region rigorously satisfying the definition of the functional gas exchange unit during inspiration. These ideas lead to a critical conclusion that the steady-state gas exchange parameters estimated from the gas samples harvested on expiration can be interpreted based on a concept of the functional gas exchange unit, which implies that the expiration-associated gas exchange parameters, such as the continuous distribution of V_A/Q, reflect the structural abnormalities of bronchioles and microvessels occurring at the acinar level of HB.

Figure 3: Spatial distribution of PO₂ at end-inspiration and at end-expiration. Temporal and spatial PO₂ profiles shown in (Figure 2) identified that substantial stratified inhomogeneity of PO₂ along axial distance from transitional bronchiole (acinar entrance) to terminal alveolar sacs exists at end-inspiration (upper panel). However, stratification of PO₂ is almost fully eliminated at end-expiration (lower panel).

    
    
    Figure 3: Spatial distribution of PO₂ at end-inspiration and at end-expiration.
Temporal and spatial PO₂ profiles shown in (Figure 2) identified that
substantial stratified inhomogeneity of PO₂ along axial distance from
transitional bronchiole (acinar entrance) to terminal alveolar sacs exists at
end-inspiration (upper panel). However, stratification of PO₂ is almost fully
eliminated at end-expiration (lower panel).

Determination of Ventilation-Perfusion (V_A/Q) Distribution in the Lung

There are a couple of important examinations that detect the functional abnormalities occurring at the acinar level, including the normalized N₂ alveolar plateau estimated from the first few breaths of the Multi-Breath N₂ Washout (MBNW), the Multiple Inert Gas Elimination Technique (MIGET), and so on. Although the normalized N₂ alveolar plateau in the few breaths just after beginning of the MBNW is promising for detecting the Diffusion-Convection- Dependent Inhomogeneity (DCDI) in the acinar regions, which reflects the intra-acinar maldistribution of ventilation [37,46,47], we would like to focus on the MIGET in the present review. This is because the VA/Q distribution recovered from the MIGET identifies functional abnormalities evoked both by maldistribution of microcirculation and that of alveolar ventilation. The detection of microcirculatory abnormalities is not possible from the MBNW.

Basic rationale for V_A/Q distribution: Under a steady state condition in which there is no change in the Partial Pressure of a gas (P) against the elapsed time (t) at any portion of the lung (i.e., ∂P/∂t = zero)), the partial pressure of a foreign inert gas in gas phase (P_A) and that in blood phase (P_C) in a given micro region of the lung periphery (compartment) are described by the simple equation in accordance with the law of mass balance [48,49];

P_A/P_V = P_C/P_V = λ/(λ + V_A/Q) ⋅⋅⋅⋅⋅⋅⋅ Equation 2

where P_V denotes the partial pressure of a given inert gas in mixed venous blood, whereas λ is the blood-gas partition coefficient of a gas [50]. The (Equation 2) is valid when an intended gas is not contained in the inspired gas. The (Equation 2) implies that the partial pressure of an inert gas in a microregion of the lung periphery simply decided by the ratio of effective ventilation (V_A) and perfusion (Q) distributed there (Figure 4) [2,51-53]. Although there are many physiological assumptions required for the establishment of (Equation 2) [52- 54], they were extensively addressed elsewhere [1,2]. However, the fundamentally important issue that should be emphasized is that the (Equation 2) is implicitly prerequisite for the presence of microregional compartment satisfying the definition of functional gas exchange unit. As extensively argued in the previous section, the microregion given by the acinus of HB encounters the definition of functional gas exchange unit in expiration (Figure 3). However, one should be careful about the fact that the acinus of HB does not satisfy the definition of functional gas exchange unit in inspiration. Fortunately, the MIGET measures inert gas concentrations collected only in expiration so that the V_A/Q distribution investigated from this method can be interpreted based on the concept of functional gas exchange unit, which corresponds to the anatomically-defined microregion really existing in the lung periphery.

Figure 4: Relationships between blood-gas partition coefficients (λ) of inert gases and V_A/Q values. Ordinate: excretion (E = P_A/P_V) or retention (R = P_C/P_V) of inert gases. Abscissa: logarithmic V_A/Q value. E or R of each inert gas sharply changes in a certain range of V_A/Q depending on λ. Sharp change in SF₆ is found at V_A/Q ranging between 0.001 and 0.01. As such, SF₆ has high sensitivity to detecting gas exchange units with very low V_A/Q values. On the contrary, acetone sharply changes at V_A/Q ranging from 10 to 100, indicating that acetone is susceptible to gas exchange units with very high V_A/Q values.

    
    
    Figure 4: Relationships between blood-gas partition coefficients (λ) of inert
gases and V_A/Q values.
Ordinate: excretion (E = P_A/P_V) or retention (R = P_C/P_V) of inert gases.
Abscissa: logarithmic V_A/Q value. E or R of each inert gas sharply changes
in a certain range of V_A/Q depending on λ. Sharp change in SF₆ is found at
V_A/Q ranging between 0.001 and 0.01. As such, SF₆ has high sensitivity to
detecting gas exchange units with very low V_A/Q values. On the contrary,
acetone sharply changes at V_A/Q ranging from 10 to 100, indicating that
acetone is susceptible to gas exchange units with very high V_A/Q values.

Determination of continuous distribution of V_A/Q by MIGET: Saline containing a small quantity of six foreign inert gases with a wide variety of λ, including Sulfur Hexafluoride (SF₆), ethane, cyclopropane, halothane, diethyl ether, and acetone (Table 2), is infused through the peripheral vein at a constant rate of 2 mL/min [52,54]. After a steady state is established (about 30 min after starting the infusion), expired gas, arterial blood, and mixed venous blood are simultaneously collected and the concentrations of six inert gases in these samples are measured by gas chromatography [55]. Using the data measured for six inert gases, Wagner and colleagues [52- 54] established a novel method allowing for predicting a continuous distribution of V_A/Q in a representative manner. In this method, they assumed 50 functional gas exchange units with different V_A/Q values, including right-to-left shunt with V_A/Q of zero, dead space with infinite V_A/Q composed of series (common) and parallel (alveolar) dead space, and 48 units with finite values of V_A/Q ranging from 0.005 to 100, all of which are arranged in parallel and are equally spaced on a logarithmic scale (Figure 5). The basic equation used for determining the continuous distribution of fractional Q (q) along the V_A/Q axis is described below [52-54,56];

Figure 5: Acinar model for estimating continuous distribution of V_A/Q. In MIGET, representative 50 functional gas exchange units configured by collective of HB acini, including acini with right-to-left shunt (V_A/Q = zero), acini with dead space (V_A/Q = infinite), and 48 acini with V_A/Q values raging between 0.005 and 100, are postulated.

    
    
    Figure 5: Acinar model for estimating continuous distribution of V_A/Q.
In MIGET, representative 50 functional gas exchange units configured by
collective of HB acini, including acini with right-to-left shunt (V_A/Q = zero),
acini with dead space (V_A/Q = infinite), and 48 acini with V_A/Q values raging
between 0.005 and 100, are postulated.

Table 2: Blood-gas partition coefficients (λ) of six inert gases used for MIGET.




  
    Species of inert gases
    l (mL/mL at 37°C)
  
  
    (1) Sulfur hexafluoride (SF₆)
    0.009
  
  
    (2) Ethane
    0.091
  
  
    (3) Cyclopropane
    0.583
  
  
    (4) Halothane
    2.82
  
  
    (5) Diethyl ether
    14.4
  
  
    (6) Acetone
    304



Table 2: Blood-gas partition coefficients (λ) of six inert gases used for MIGET.

L = ΣW_i[R_i - Σq_j.(λ_i/(λ_i + (V_A/Q)_j))]² +μ.(1 - Σq_j) + S.ΣΦ_jq_j² ..........Equation 3

where L is the objective variable that should be minimized with respect to the fractional perfusion (q_j, j=1, 2 ... 50) distributed to each functional gas exchange unit with a certain V_A/Q value. R_i is the measured value of arterial gas concentration for each inert gas divided by its mixed venous concentration (i=1, 2, … 6). W_i is the coefficient for weight of each inert gas, which is given by the reciprocal of variance of R_i. The second term of the equation denotes the equality constrain for q_j, the sum of which should amount to 1.0. μ is the Lagrange multiplier that is determined and replaced by an adequate value during computation. The third term designates the correction based on the enforced smoothing using the Lagrange multiplier of Φ_j, which is the value related to the compartmental weight of each V_A/Q unit, while S is the smoothing term that is empirically assumed to be 40. The enforced smoothing is applied for stabilizing the resultant V_A/Q distribution. Replacing q_j in the (Equation 3) by fractional ventilation (v_j), the ventilation distribution along the V_A/Q axis is readily decided, as well.

New Method for Quantitating V_A/Q Distribution: The basic concept on proton Magnetic Resonance Imaging (MRI) for measuring V_A/Q distribution was first proposed about six years ago [57]. This technique combines Arterial Spin Labeling (ASL) measures of regional pulmonary blood flow [58] with oxygen enhanced measures of regional specific ventilation [59] and fast gradient echo measures of regional proton density [60,61] to quantify the regional distribution of V_A/Q ratios. Although the spatial resolution of the V_A/Q image examined by the original proton MRI method was not enough, it has been improved considerably by applying a highprecision MRI such as a 1.5 Tesla system. Using the high-performance proton MRI, Sá et al. [62] measured the regional V_A/Q distribution along the 15-mm sagittal slice located in the mid-clavicular line of the right lung in normal adults. The slice measures approximately 8% of the total lung volume and about 20 min is necessary for completing one examination. The collected image matrix size is 256 x 256, giving the voxel size of 0.04 cm³ and the spatial resolution of 1.0 cm³, the latter of which corresponds to the volume composed of 5~6 acini (Table 1). Sá et al. [62] demonstrated that in normal subjects with no lung diseases, the V_A/Q distribution recovered from the proton MRI method does not differ largely from that measured with the classical MIGET. However, there are several disadvantages in the proton MRI method. This method acquires the data from the lung region corresponding to 8% of the entire lung. Although in normal subjects, the V_A/Q distribution in the lung can be considered relatively uniform so that the V_A/Q distribution estimated from the 8% lung region may approximately represent the overall V_A/Q distribution, this assumption is not allowed for the patients with lung diseases, in whom the V_A/Q distribution in a certain region differs substantially from other regions. When attempting to measure the V_A/Q distribution in the whole lung in terms of the proton MRI method, it may require about four hours for a single observation, which is too long as the clinical examination. Furthermore, from several technical reasons, it is difficult to measure the region with very low V_A/Q (i.e., the shunt) and that with very high V_A/Q (i.e., the dead space) in terms of the proton MRI method [62]. Based on these facts, we consider that at present, the newly-developed proton MRI method does not outweigh the classical MIGET as the examination in a clinical situation.

V_A/Q Distributions in Patients with Pathologically- and/or Radiologicallyconfirmed Lung Diseases

According to the concept of the functional gas exchange unit expanded in the previous sections, we can conclude that the V_A/Q distribution harvested from the MIGET reflects the inter-regional heterogeneity of V_A/Q distribution at the acinar level. The basic rationale for the clinical interpretation of V_A/Q heterogeneity is summarized in (Table 3). The lesions forming abnormal acini with low V_A/Q values are primarily yielded by obstruction and/ or destruction of acinar airways as well as microvascular injury accompanied by paralysis of Hypoxic Pulmonary Vasoconstriction (HPV). The HPV is the major mechanism for matching between perfusion and ventilation, thus preventing the progressive formation of low V_A/Q acini [63-66]. However, if the HPV is paralytic in injured microvasculature, the perfusion there is not decreased so that the formation of low V_A/Q acini advances. The HPV paralysis was identified in some specific lung diseases, including Hepatopulmonary Syndrome (HPS), Acute Respiratory Syndrome (ARDS), pneumonias, granulomatous disease, and some types of lung cancer [63,66-75]. On the other side, the HPV paralysis was not certified in patients with bronchial asthma, Chronic Obstructive Pulmonary Disease (COPD), Idiopathic Pulmonary Fibrosis (IPF), and Pulmonary Embolism (PE) [76-81].

Table 3: Pathological causes for forming low and high V_A/Q acini.




  
    Low V_A/Q acini
    High    V_A/Q acini
  
  
    Primary lesions
    Primary lesions
  
  
    1)    Destruction or obstruction of acinar airways
    1)    Microvascular loss
  
  
    .Acinar    Bronchiolitis (COPD)
      × Atelectasis/pneumonia
      × Interstitial Pneumonia (IP)
      × Alveolar edema (ARDS, heart failure,
      .Pulmonary    Alveolar Proteinosis (PAP))
      × Alveolar Hemorrhage/Infarction (ANCA-related    angiitis, Goodpasture, PE)
    × COPD
      × Interstitial Pneumonia (IP)
      × Pulmonary Embolism (PE)
      × Cystic disease
      × Langerhans Cell Histiocytosis (LCH)
      × Lymphangioleiomyomatosis (LAM)
  
  
    2)    Microvascular injury with HPV paralysis
    2)    Microvascular occlusion without HPV paralysis
  
  
    × Hepatopulmonary Syndrome (HPS)
      × ARDS
      × Pneumonia (pneumococcus, pseudomonas)
      × Granulomatous disease
      × Lung cancer
    × Intravascular Lymphomatosis (IVL)
      × Pulmonary Veno-Occlusive Disease (PVOD)
      × Pulmonary Capillary    Hemangiomatosis (PCH) 
  
  
    3) Aqueous-phase diffusion limitation (shunt)
      × HPS, ARDS
     
  
  
    Secondary lesions
    Secondary lesions
  
  
    1) Shift of    perfusion from acini with microvascular loss or microvascular occlusion    without HPV paralysis to normal acini
      × COPD, IP, PE, LCH, LAM
      × IVL, PVOD, PCH
    1) Shift of    ventilation from affected acini to normal acini
      × Bronchiolitis Obliterans (BO)
      × Emphysema/bulla (COPD)
      × Cystic disease (LCH, LAM)
      × Pleuroparenchymal Fibroelastosis (PPFE)
  
  
     
    2) Shift of perfusion    from normal acini to those
      with    microvascular injury with HPV paralysis
      × HPS, ARDS



Table 3: Pathological causes for forming low and high V_A/Q acini.

Since microvessels in HPS are largely dilated, the thickness of plasma layer is considerably increased, leading to the augmented aqueous-phase diffusion limitation (shunt) that causes formation of low V_A/Q acini. In ARDS, airspaces are flooded by edematous fluid, which yields aqueous-phase diffusion limitation, as well [56].

The secondary cause for producing low V_A/Q acini is the redistribution of perfusion from affected to non-affected regions. This phenomenon is recognized in patients with microvascular loss or microvascular occlusion without HPV paralysis, who have the acini with high V_A/Q values (primary lesion) in concomitance with those with low V_A/Q values (secondary lesion).

The microvascular loss or microvascular occlusion without HPV paralysis primarily produces the acini with high V_A/Q values because of reduction in acinar perfusion there.

The secondary cause for forming high V_A/Q acini is the redistribution of ventilation from affected to non-affected regions. This is observed in patients with Bronchiolitis Obliterans (BO), COPD, cystic disease, or Pleuroparenchymal Fibroelastosis (PPFE). The reduction (redistribution) of ventilation at embolized regions in severe Pulmonary Embolism (PE) is sometimes attributed to the hypocapnia-elicited bronchoconstriction [82,83]. However, we cannot agree with this opinion, because CO₂-sentive bronchial smooth muscles are predominantly located along central airways but neither peripheral nor acinar airways, indicating that the hypocapnia-related shift of ventilation, if any, occurs far away from the acinar region, thus lacking in an ability for precisely adjusting the distribution of acinar ventilation. Instead, we think that the reduction in ventilation at embolized regions of PE may be explained from the atelectasis, hemorrhage, and/or infarction formed there. This aspect of PE should be taken as a kind of the primary, but not secondary, cause (Table 3).

In a patient with microvascular injury with HPV paralysis, the perfusion in normal acini may be redistributed to the acini with HPV-paralytic microvascular lesions, thus converting the acini with normal V_A/Q values to those with relatively high V_A/Q values.

To address the considerations as described above in a more practical fashion, we presented the continuous V_A/Q distributions in three cases with pathologically- and radiologically-confirmed lung diseases with specific lesions.

Bronchiolitis Obliteration (BO): The case is a 21-year-old, non-smoking woman, who underwent the allogeneic Hematopoietic Stem Cell Transplantation (HSCT) against the chronic myeloid leukemia. After HSCT, she was progressively conscious of Difficulty in Breathing on Exertion (DOE). She died one year after HSCT. The CT examination confirmed the mosaic perfusion in the right lung field at the level of secondary lobule of Miller (Figure 6). Although the ventilation and perfusion scans revealed large reduction in both ventilation and perfusion in the lower lung fields, the mismatch between the two distributions were not evident (Figure 6). The postmortem autopsy identified the remarkable constriction of membranous bronchioles, including lobular and terminal bronchioles, whereas the acinar structures, including acinar airways, alveolar septa, and microcirculation, were spared. These pathological findings are in accordance with the diagnosis of HSCT-induced BO.

Structural parameters	Comments
Entrance	Transitional Bronchiole (TrB)
Airway branching pattern	Irregular, asymmetrical dichotomy (trichotomy: rare)
Number of branches (Z’) Transitional bronchiole: Z’ = zero	Average: 9.1 (ranging from 6 to 12)
Total longitudinal path length	8.8 ± 1.4 mm (from TrB to terminal alveolar sacs)
Internal airway diameter	Decrease from 500 mm (Z’ = 0) to 270 mm (Z’ = 10)
Outer airway diameter	Approximately constant over acinar airways including alveolar sleeve (700 mm)
Total surface area of alveoli	Average: 69 cm²
Total volume of an acinus	187 ± 79 mm³
Total number of acini in human lung	26,000 to 32,000
Values are measured under condition at full expansion of lung tissue specimen. Data are extracted from those reported in ref. 7.

Species of inert gases	l (mL/mL at 37°C)
(1) Sulfur hexafluoride (SF₆)	0.009
(2) Ethane	0.091
(3) Cyclopropane	0.583
(4) Halothane	2.82
(5) Diethyl ether	14.4
(6) Acetone	304

Low V_A/Q acini	High V_A/Q acini
Primary lesions	Primary lesions
1) Destruction or obstruction of acinar airways	1) Microvascular loss
.Acinar Bronchiolitis (COPD) × Atelectasis/pneumonia × Interstitial Pneumonia (IP) × Alveolar edema (ARDS, heart failure, .Pulmonary Alveolar Proteinosis (PAP)) × Alveolar Hemorrhage/Infarction (ANCA-related angiitis, Goodpasture, PE)	× COPD × Interstitial Pneumonia (IP) × Pulmonary Embolism (PE) × Cystic disease × Langerhans Cell Histiocytosis (LCH) × Lymphangioleiomyomatosis (LAM)
2) Microvascular injury with HPV paralysis	2) Microvascular occlusion without HPV paralysis
× Hepatopulmonary Syndrome (HPS) × ARDS × Pneumonia (pneumococcus, pseudomonas) × Granulomatous disease × Lung cancer	× Intravascular Lymphomatosis (IVL) × Pulmonary Veno-Occlusive Disease (PVOD) × Pulmonary Capillary Hemangiomatosis (PCH)
3) Aqueous-phase diffusion limitation (shunt) × HPS, ARDS
Secondary lesions	Secondary lesions
1) Shift of perfusion from acini with microvascular loss or microvascular occlusion without HPV paralysis to normal acini × COPD, IP, PE, LCH, LAM × IVL, PVOD, PCH	1) Shift of ventilation from affected acini to normal acini × Bronchiolitis Obliterans (BO) × Emphysema/bulla (COPD) × Cystic disease (LCH, LAM) × Pleuroparenchymal Fibroelastosis (PPFE)
	2) Shift of perfusion from normal acini to those with microvascular injury with HPV paralysis × HPS, ARDS

PFT parameters	BO	HPS	IVL
VC (L)	2.6	3.0	3.2
FVC (L)	2.2	3.0	3.2
FEV₁ (L)	0.8	2.7	2.4
FEV₁/FVC (%)	36	91	75
ATI (%)	15.4	0.4	0.6
PEF (L/sec)	2.2	8.9	7.0
FEF₅₀ (L/sec)	0.3	5.1	3.8
TLC (L)	3.9	not determined	not determined
RV (L)	1.3	not determined	not determined
RV/TLC (%)	35	not determined	not determined
PaO₂ (mmHg)	72	56^*	56
PaCO₂ (mmHg)	58	36^*	35
AaDO₂ (mmHg)	7.1	101^*	49
D_LCO (mL/min/mmHg)	27.8	9.7	10.0
K_CO (mL/min/mmHg/L)	5.8	1.9	2.6
*: Values are measured at inspired O₂concentration of 28%.

Insights into Anatomical Basis Prescribing Ventilation- Perfusion Distribution in Lung Periphery

Abstract

Abbreviations

Introduction

What is the Most Appropriate Organization Serving as Functional Gas Exchange Unit?

Determination of Ventilation-Perfusion (V_A/Q) Distribution in the Lung

V_A/Q Distributions in Patients with Pathologically- and/or Radiologicallyconfirmed Lung Diseases

Conclusion

References

Insights into Anatomical Basis Prescribing Ventilation- Perfusion Distribution in Lung Periphery

Abstract

Abbreviations

Introduction

What is the Most Appropriate Organization Serving as Functional Gas Exchange Unit?

Determination of Ventilation-Perfusion (VA/Q) Distribution in the Lung

VA/Q Distributions in Patients with Pathologically- and/or Radiologicallyconfirmed Lung Diseases

Conclusion

References

Determination of Ventilation-Perfusion (V_A/Q) Distribution in the Lung

V_A/Q Distributions in Patients with Pathologically- and/or Radiologicallyconfirmed Lung Diseases