Figure 1. The relationship between the partial pressure of oxygen and carbon dioxide and ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. When the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio is low, the partial pressures approach that of mixed venous blood. When the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio is high, the partial pressure is close to inspired. Note that there is little change in PO₂ when the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio is less than 0.1 or greater than 10. Redrawn, with permission, from West JB. 1977 332.

Figure 2. The O₂ CO₂ diagram. The relationship between oxygen and carbon dioxide partial pressures in alveolar gas or capillary blood. The points along this line are determined by the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. The blue dots indicate mixed venous (0) and inspired (∞) points as well as a normal mean ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio (1.3) for the lung as a whole. Note the marked curvilinear behavior of the plot. Redrawn, with permission, from Rahn H and Fenn WO. 1955 258.

Figure 3. Respiratory exchange ratio (R) measured at the mouth with a rapid‐response analyzer during a slow exhalation from vital capacity to residual volume. The change in R during a slow exhalation from total lung capacity is described in four phases. First pure dead space gas is cleared, with R indeterminant (Phase I). In Phase II, R rapidly rises as the dead space is mixed with alveolar gas. As the expiration progresses, dead space is cleared further and gas exchange is ongoing throughout the maneuver with oxygen being removed and CO₂ being added. R progressively falls (Phase III) since more oxygen is being consumed than carbon dioxide is being produced. The final phase (Phase IV) is a terminal rise associated with dependent airways closure in lung regions that are close to residual volume. Phase III is also characterized by marked cardiogenic oscillations reflecting the effect of the heartbeat on pulmonary blood flow and lung mechanics. Modified, with permission, from Prisk GK, et al. 2003 251.

Figure 4. Intrabreath R and iVQ as a function of lung volume measured at the mouth during a slow exhalation from total lung capacity. The data from Figure 3 showing the change in R during a slow exhalation from total lung capacity are replotted in the top tracing (thin line). Dotted lines represent the modeled R assuming differing ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratios. The thick tracing represents the intrabreath ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ (iV/Q) derived by interpolating measured R line between the three dotted modeled R lines. Reused, with permission, from Prisk GK, et al. 2003 251.

Figure 5. Determination of iVQ slope as a measure of ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ heterogeneity. The intrabreath ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio (iV/Q) obtained by interpolating the measured intrabreath R with the modeled R isopleths from Figure 4 showing the region of Phase III. A line is fitted to the two halves of Phase III by least squares regression (thick line). The slope of the first half of phase three has been shown to correlate with ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ heterogeneity measured by MIGET and become steeper with methacholine administration 251. The solid vertical bar represents the intrabreath V_A/Q, iV/Q range over Phase III, and this is also used as an index of heterogeneity but is only weakly associated with MIGET metrics of heterogeneity. Reused, with permission, from Prisk GK, et al. 2003 251.

Figure 6. Single breath nitrogen washout and Fowler dead space. (a) A schematic drawing of an expirogram showing the change in expired nitrogen measured at the mouth following the inspiration of pure oxygen. Initially, there is no nitrogen, as the previously inspired pure oxygen is cleared (Phase I). There is rapid rise in nitrogen concentration as resident gas partially mixed with oxygen is expired (Phase II). Phase III is a relative plateau in nitrogen, reflecting the mixing of inspired oxygen with resident gas 87,88,89, and the slope of this reflects ventilation heterogeneity 314. Phase IV is a terminal rise in nitrogen concentration again representing dependent airways closure. The red box indicates the portion of the plot represented in (b). (b) A schematic of the expirogram in a normal subject with little Phase III slope. The concentration of nitrogen in the Phase III plateau (top dotted blue line) is used as the concentration of alveolar nitrogen. The area under the curve divided by the volume expired is used as the concentration of mixed expired nitrogen to solve the Bohr equation for dead space. The simplified graphical method uses the straight line along Phase III and a vertical line intersecting Phase II (red line) such that the two areas A and B defined by this are equal. The intersection of the red line with the x‐axis is dead space. This approach is problematic in patients with lung disease because ventilation heterogeneity, which is almost always present, means that there will be a significant upward slope in Phase III and thus difficulty in estimating alveolar nitrogen 88.

Figure 7. Retention of inert gases of differing solubility used in MIGET. Retention, the ratio of arterial concentration to mixed venous concentration of inert gases of differing blood‐gas partition coefficient (λ) in a homogeneous lung without ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ mismatch a mean ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio of 1. The plot is constructed by solving Eq. 32 for gases of differing λ. The six gases shown are ones commonly used in MIGET and cover most of the retention curve. Redrawn, with permission, from Hopkins SR and Wagner PD. 2017 160.

Figure 8. Retention of inert gases in lung units of differing ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. (A) Individual Inert gas retention curves for a three‐compartment lung with three different ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratios, 0.1, 1.0, and 10. Similar to Figure 7, the plot is constructed by solving Eq. 32 for gases of differing λ, and now, different ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratios. The plot for ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio of 0.1 and 10 have the same shape as the one for the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio of 1 but are displaced a decade higher and lower. Note that when retention is 0.5 (dotted horizontal black line), ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ = λ (colored arrows) for each curve. (B) A three‐compartment lung with the same ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratios (dashed lines) as in (A) with equal blood flow to each compartment. The composite retention curve for this three‐compartment lung is the flow weighted average of each individual curve (black solid line).

Figure 9. Recovered ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ distributions from a normal subject (A) and a patient with COPD (B). The normal subject has a smooth and unimodal distribution of ${\dot{V}}_{\mathrm{A}}$ and $\dot{Q}$ versus ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio, with a mean slightly greater than 1. There is no shunt (compare to Figure 10) or low or high ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ regions and by convention the dead space compartment is omitted from the distribution plots. This patient with COPD has a tri‐modal distribution with regions of low ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio and regions of high ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. Again, shunt is absent, and a large shunt is not typically observed in COPD patients. Modified, with permission, from Hopkins SR and Wagner PD. 2017 160 and Wagner PD, et al. 1977 321.

Figure 10. Quantitative data obtained from the MIGET 50‐compartment model. The distribution of ventilation and perfusion are plotted as a function of ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. In this case, the distributions are smooth and unimodal with the mean of both distributions close to 1. The width of the distributions represented by the standard deviation on a log scale (LogSD) of the distributions is used as an index of heterogeneity, with LogSD$\dot{V}$ representing the heterogeneity in the ventilation versus ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ distribution and LogSD$\dot{Q}$ in the perfusion versus ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ distribution. Shunt and dead space are represented as single points at a ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio less than 0.005 and greater than 100, respectively. Typically, dead space is omitted from these plots because the ventilation to this compartment is so large relative to the other compartments.

Figure 11. Site of particle deposition in the airways by particle size. These complex relationships between particle diameter and site of deposition highlight the importance of the selection of appropriate particle or aerosol size for measurements of alveolar ventilation. Technigas^® graphite particles are 0.005 to 0.2 μm 24,303 and thus are an optimum size. Care must be taken to keep nebulized liquids such as 99mTc‐DTPA at an aerosol diameter less than 2 μm 24. Aerosolized fluorescent microspheres used in destructive tissue techniques are approximately 1 μm 11. Adapted, with permission from Tsuda A, et al. 2013 311.

Figure 12. SPECT measurement of ${\dot{V}}_{\mathrm{A}}/\dot{Q}$. Dual‐isotope SPECT with ^133mIn‐MAA albumin was used to measure perfusion (top) and Technegas^® to measure ventilation (bottom). Data were acquired on a SPECT CT system, which allows for attenuation correction, and the underlying CT image can be seen in gray surrounding the colored lung field. The left‐hand images are the axial projection, the center images are coronal and right‐hand ones sagittal. The color scale represents relative intensity (i.e., ventilation or perfusion). Reused, with permission, from Petersson J, et al. 2007 242.

Figure 13. ¹³N‐Nitrogen tracer kinetics. (A) Washout of ¹³N‐Nitrogen plotted on a log scale showing activity versus time in a voxel exhibiting uniform behavior modeled and as a single compartment. The compound is injected during an apnea, and the tracer is delivered to the alveolus in proportion to regional blood flow thus the plateau in activity at the time of the first appearance, is proportional to regional perfusion in the voxel. Then, as the subject begins breathing, the tracer in the alveolus will washout proportional to regional specific ventilation ($S\dot{V}$) and the slope of the washout is equal to $–1/S\dot{V}$. The area under the curve (light blue) is proportional to the ratio of perfusion/specific ventilation $\dot{Q}/S\dot{V}$. (B) Washout of ¹³N‐Nitrogen plotted on a log scale showing activity versus time in a voxel exhibiting two‐compartment behavior, with compartment one having high specific ventilation (rapidly clearing) and compartment 2 having low specific ventilation. During washout, compartment 1 clears tracer rapidly and the initial slope (slope 1) of the activity versus time plot is quite steep. The total blood flow in the voxel (${\dot{Q}}_1$ + ${\dot{Q}}_2$) is again reflected in the plateau but is apportioned between the two compartments based on the back extrapolated point to the onset of the second compartment washout. The $\dot{Q}/S\dot{V}$ is distributed for compartment 1 as shown in light blue and for compartment 2 as shown in gray. Adapted, with permission, from Vidal Melo MF, et al. 2003 317.

Figure 14. Example axial images from a 13N Nitrogen PET animal study (sheep) in a normal animal and in one representative animal after each of pulmonary embolism, saline lung lavage, and bronchoconstriction. Slices in each condition are arranged from apical to basal. The animals are prone in all except the lung lavage condition. In the first column, regional perfusion images are shown representing activity during the apnea portion of the data collection for each condition. Regions of reduced perfusion (dark areas) are seen in the pulmonary embolism and lung lavage conditions. The second column shows images obtained at the end of the washout lung images. Note higher tracer activity in the lung lavage and bronchoconstriction conditions. The third column shows the time‐activity plots for each condition. The peak occurring early, followed by a plateau indicates the presence of significant intrapulmonary shunt in the lung lavage condition. Reprinted, with permission, from Vidal Melo MF, et al. 2003 317.

Figure 15. The basic magnetic resonance experiment. (A) In the presence of a strong magnetic field (B₀) protons show a net alignment of their magnetic moments (M₀) along the axis of B₀, with the magnitude of M₀ proportional to the local proton density. (B) With a radiofrequency (RF) excitation pulse, the protons are tipped out of their alignment in a plane perpendicular to the static magnetic field, with the flip angle (α) describing the extent to which the net magnetization is tipped relative to B₀. (C) This new alignment of the protons has a longitudinal component (M_L) and a transverse component (M_T), in red. The precession of the transverse component along the axis of B₀ creates a signal which can be detected. (D) Immediately after the excitation pulse, protons gradually relax to their equilibrium alignment (M₀) and the transverse magnetization decays, and the longitudinal magnetization is recovered with two separate time constants: T₁ is the time constant for recovery of longitudinal magnetization and T₂, the time constant for the decay of transverse magnetization. Adapted, with permission, from Buxton RB. 2009 47.

Figure 16. The basis of the specific ventilation imaging experiment. Top: Schematic depiction of specific ventilation of two lung units. The unit on the right has a large change in volume, ΔV, during inspiration compared to V₀, the end‐expiratory (local FRC) volume of the unit, and thus a high specific ventilation, SV, defined as the ratio ΔV/V₀. The unit on the right has a relatively low specific ventilation. Bottom: Since the change in volume is large relative to the resting volume in the high specific ventilation unit the initial concentration of oxygen C₀, at end expiration rises rapidly when the subject breathes 100% oxygen. The high specific ventilation unit equilibrates faster (continuous line, SV = 0.8) than the lower specific ventilation unit (dashed line, SV = 0.2). Reused, with permission, from Sa RC, et al. 2010 283.

Figure 17. Time series of signal intensity for a single voxel during a specific ventilation experiment. When the subject changes from breathing air to oxygen, the T₁ is shortened and the signal intensity increases. The dashed line change indicates the change in F_IO₂, termed the driving function. Units with higher specific ventilation equilibrate faster; thus, signal intensity more closely follows the driving function than for units with lower specific ventilation. The time required for the signal to reach a new equilibrium is the rise time and is measured as the time delay which maximizes the correlation of the time course of the signal from each voxel with the driving function (after accounting for delay in delivering the new F_IO₂ to the mouth. The correlation delay for each voxel is converted to specific ventilation based on modeling voxels of differing specific ventilation. Reused, with permission, from Sa RC, et al. 2010 283.

Figure 18. Regional measurement of fractional ventilation measured with MRI using hyperpolarized ³Helium in a coronal slice of a healthy rat lung. Fractional ventilation, r, represents the delivery of fresh gas divided by the resident gas at the end of inspiration (specific ventilation is the delivery of fresh gas divided by resident gas at end expiration). (A) Quantified image. The trachea and large conducting airways can be seen as regions of high r. (B) Histogram of the resultant r values, showing a bimodal distribution showing a main mode of normal lung parenchyma on the left and a second high r mode representing trachea and conducting airways on the right. Reused, with permission, from Hopkins SR, et al. 2007 156.

Figure 19. Signal intensity in a normal volunteer within a region of interest in lung parenchyma following bolus injection of contrast during dynamic contrast‐enhanced MR imaging of pulmonary perfusion. After a transit delay, a sharp rise in signal intensity is followed by rapid washout. The late peak reflects recirculation of indicators into the region of interest. After gamma‐variate fitting, the first moment of the curve represents mean transit time, and area under the curve represents blood volume of the region of interest. Reused, with permission, from Hopkins SR, et al. 2007 156.

Figure 20. An example of arterial spin labeling (ASL) in a coronal slice of lung in a healthy human. The sequence used to acquire data is ASL‐FAIRER (flow sensitive alternating inversion recovery). Two EKG gated images are acquired approximately 5 s apart. (A) A 180° selective inversion radiofrequency pulse is applied in diastole to the desired slice of lung. After waiting for a complete systolic ejection of blood the image is acquired, and protons from outside the slice that have not seen the 180° inversion pulse and enters the slice fully relaxed giving strong signal. (B) The nonselective inversion image is acquired after the 180° inversion pulse is applied to the entire torso and the magnetization of arterial blood outside the slice is recovering from the inversion pulse and the signal is very low. (C) The subtraction of the selective and nonselective inversion images yields a map of the amount of blood delivered to each voxel during the delay time between the inversion pulse and image acquisition, as stationary structures such as the spine, liver, etc. subtract out. Reprinted, with permission, from Hopkins SR and Levin DL. 2006 155.

Figure 21. Example images of density (A), alveolar ventilation (B), perfusion (C), and ventilation‐perfusion ratio (D) in a sagittal slice of the right lung in a normal subject in the supine posture. Images are also shown for the prone posture (E–H, respectively). Images representing regional specific ventilation (not shown) are combined with proton density to get regional alveolar ventilation. Voxels contained within larger, conduit, blood vessels, and voxels that correlate perfectly with the driving function in specific ventilation (representing large airways) are removed as they are not part of gas exchange and are seen as dark tubular structures in the three right‐hand columns of images. The resultant ventilation image is combined with the perfusion image to give an image of regional ventilation‐perfusion ratio. Note the gravitational gradients in all images. Reused, with permission, from Henderson AC, et al. 2013 135.

Figure 22. (A) The relationship between gas partial pressure and ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio for respiratory gases and Sulphur Hexafluoride (SF₆) for a mammalian lung. The relationship between oxygen and carbon dioxide was also shown previously in Figure 1. In lung units where the ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio is high, since SF₆ is insoluble in blood, comparatively little oxygen is transferred out of the alveolus and the SF₆ concentration is stable. In lung units with low ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio, as the oxygen partial pressure falls the insoluble SF₆ (λ ∼ 0.005) remains behind in the alveolar space. (B) The relationship between SF₆ partial pressure and T₁. As the concentration of SF₆ increases, T₁ becomes longer. (C) The relationship between the T₁ for SF₆ and ${\dot{V}}_{\mathrm{A}}/\dot{Q}$ ratio. Data are for an inhaled gas mixture of 30% SF₆/70% O₂ and an ambient barometric pressure of 626 mmHg (Albuquerque, NM, elevation 1600 m). Reused, with permission, from Kuethe DO, et al. 1998 190.

Figure 23. Mass attenuation coefficient, as a function of energy for different materials. The mass attenuation coefficient is the fraction of a beam of photons that are absorbed per unit volume of the absorbing tissue or material (called the linear attenuation coefficient, μ), divided by density of the tissue, ρ. The sudden change in the iodine curve reflects the K‐edge. the K‐edge denotes the point at which the photon energy matches the binding energy of the K‐shell electron of the atom. At the K‐edge, there is a sudden increase in attenuation due to photoelectric absorption of the photons, thus changing the ability of the photon to penetrate iodine. Green Shading indicates CT energy range. Reprinted, with permission, Xia T, et al. 2014 345.

Figure 24. Computed tomography enhancement [ΔCT] measured in Hounsfield Units (HU) induced by differing concentrations of xenon in air at 80 and 120 kV, showing a linear relationship between xenon concentration and the change in attenuation. Reused, with permission, from Marcucci C, et al. 2001 212.

Figure 25. Regional pulmonary blood volume (PBV) measured after an injection of iodinated contrast by dual‐energy source dual detector CT. The configuration of dual‐energy computed tomography (DECT) uses 80‐ and 140‐kVp energies, with detectors 95° apart to acquire contrast‐enhanced CT images at the two energies, (A). A test bolus of contrast is injected to determine the time delay and Axial CT images are acquired (Ba). A region of interest is located in the left atrium (red circle) and a time versus contrast density curve (Bb) is constructed to establish a delay time, the time between the start of the injection and time it takes the contrast density to reach 100 Hounsfield units (HU) (vertical line in the Bb). The delay time accounts for the difference between the start of contrast injection and the start of the DECT acquisition. Images derived from DECT at 80‐ and 140‐kVp are used to calculate PBV maps (C). (D) Global and regional PBV analysis, showing lung mask outlining only the lung parenchyma. Large vessels and airways are excluded. Data were acquired before and after the administration of sildenafil, a potent pulmonary vasodilator (E). To evaluate changes, images are registered by warping the 140‐kVp images post sildenafil images to pre sildenafil to evaluate heterogeneity (coefficients of variation, CV, also known as relative dispersion) before and after sildenafil. Reprinted, with permission, from Iyer KS, et al. 2016 166.

Figure 26. Images of pulmonary blood volume (PBV), calculated from three‐material decomposition of the iodine contrast‐enhancement signal and pulmonary blood flow (PBF) measured with four‐dimensional (dynamic) electrocardiographically gated axial CT. Data are from a pig model evaluated at five different levels of airway pressure. Top row grayscale images, middle row pulmonary blood volume, bottom row, pulmonary blood flow. Color scale indicates with lower values in blue and higher values in red. There is close agreement between blood volume and blood flow. Reprinted, with permission, from Fuld MK, et al. 2013 95.

Figure 27. Model of tracer gas delivery and loss for a voxel of lung. With inhalation of the tracer, the concentration is determined by the concentration in inspired gas, the concentration in expired gas, the amount of tracer that diffuses out of the voxel across the alveolar wall, and the amount that recirculates in mixed venous blood. $\dot{V}$, ventilation; $\dot{Q}$, perfusion; C_I, inspired concentration; C_A, alveolar concentration C_cap, end‐capillary blood concentration; $C_{\bar{V}}$, pulmonary mixed venous blood concentration; t, time. Reused, with permission, from Kreck TC, et al. 2001 188.

Figure 28. Schematic diagram of an EIT acquisition. Current (I) is applied between adjacent surface electrodes (in this case 15 and 16), and the voltages (U) are measured between the remaining pairs, in this case 5 and 6. It should be noted that in this instance, electrode pairs 1 and 2 and 13 and 14, will have the greatest sensitivity to monitor the resultant voltage. Reused, with permission, from Frerichs I, et al. 2001 91.

Figure 29. Electrical impedance tomography (EIT) data obtained from the dorsal region of the dependent (A) and nondependent lungs (B) in a single subject. The relative impedance (rel. ΔZ) changes due to ventilation are greater than those associated with heartbeat which are seen during apnea. Changes in rel. ΔZ during breathing are great in the dependent than in the nondependent lung consistent with the gravitational gradient in regional specific ventilation 283. The decrease in EIT signal during breath holding is consistent with loss of gas volume consistent with ongoing gas exchange in the presence of a RER less than 1, such that less CO₂ is produced than O₂ is taken up. Reused, with permission, from Frerichs I, et al. 2017 90.

Figure 30. Regional ventilation and perfusion measured with fluorescent microspheres in a pig. View is looking at the anterior surface of the lung, and the cardiac fossa is visible as the indented region in the upper portion of the lung fields. The color scale indicates ventilation or perfusion in ml/min/mg of dried lung. Reprinted, with permission, from Altemeier WA, et al. 2000 9.