Real-time measurement of alveolar size and population using phase contrast x-ray imaging

Andrew F.T. Leong; Genevieve A. Buckley; David M. Paganin; Stuart B. Hooper; Megan J. Wallace; Marcus J. Kitchen

doi:10.1364/BOE.5.004024

1. Introduction

The lung is comprised of bifurcating hollow branches that carry air to the terminal airways (alveoli) where gas exchange takes place. Lung injury and diseases, such as ventilation-induced lung injury and emphysema, compromise the structure of the alveoli and consequently their function. Here we present a non-invasive phase contrast x-ray (PCX) imaging technique to measure the size and population of alveoli in situ. To do this we exploit the image texture associated with the speckle pattern that results from propagation-based phase contrast x-ray (PB-PCX) imaging of the lungs [1]. Repeating this measure over several time points during breathing provides functional information regarding the changing morphology of lung tissue. This has potential benefit for the diagnosis and treatment of lung diseases and the development of safer ventilation strategies to reduce the incidence of ventilation-induced lung injury [2].

Previous investigation of lung structure at the alveolar scale have been done using imaging techniques that include; optical coherence tomography (OPCT), confocal laser scanning microscopy (CLSM) and endoscopy microscopy [3–5]. These techniques provide highly spatially-resolved images of individual alveoli that are used to assess alveolar structure during respiration. However, they have short penetrative depth even after invasive manoeuvres to bypass the skin. Endoscopy microscopy is relatively non-invasive as it places an endoscope in the pleura visceralis. However, that was shown to alter the intrapleural pressure, which artificially changes the alveolar morphology [6]. Ultrasound measures scatterer sizes in the lungs from backscattered sound waves, but has yet to be proven to be that of alveolar sacs [7]. The deep penetrative power of synchrotron x-rays has previously enabled non-invasive imaging of the alveoli but was still restricted to less concentrated regions of alveoli that undergo minimal movement to accurately track them individually [8].

Tomographic-based imaging modalities provide insight into alveolar mechanics of the entire lung. However, the acquisition time for these modalities are long compared to the length of a single spontaneous breathing cycle, which makes dynamic imaging of the alveoli in real-time unfeasible because of motion artefacts. Although there has been progress towards improving the imaging acquisition frame rate, there is always a trade-off against poor spatial resolution and signal-to-noise ratio (SNR) to resolve the alveoli [9]. Alternatively, post-hoc respiratory gating, where projections from similar time points in the respiratory cycle are grouped together during post-processing, allows multiple reconstructions per respiratory cycle with comparable temporal resolution to x-ray imaging, but requires stable ventilation [10]. Another drawback to these modalities is the high exposure to ionizing radiation, either in the form of a radionuclide contrast agent in positron emission tomography [11, 12], or an x-ray source in x-ray computed tomography (CT) [13].

PCX imaging converts changes in the phase of an x-ray wavefield into visible intensity modulations [14]. The air-tissue interfaces of the lung are ideal for PCX imaging as they yield significant phase shifts [1]. This markedly increases the contrast of tissue compared to that seen in absorption-based x-ray images. PB-PCX imaging has the simplest PCX experimental setup. It requires only a sufficiently spatially coherent x-ray source and a detector placed some distance behind the sample. The boundary between materials with different refractive index decrements becomes enhanced by Fresnel interference fringes upon free space propagation. The Fresnel fringes arising from many alveoli are projected onto the imaging plane to form a speckled pattern (Figs. 1(a) and 1(b)) [1]. Roughly textured materials and spatially random samples, such as colloidal glass particles, also produce speckled images. The parameters of speckle patterns (for example, size, intensity and contrast) have been shown to depend on the structural properties of the illuminated object [15–17]. Here, we devise a way to extract structural properties of the alveoli, specifically their size and population from PB-PCX lung speckle images, which is quantified via analysis in the Fourier domain.

Fig. 1 19.8 $\times$ 22.8 mm² 2D propagation-based phase contrast x-ray (PB-PCX) image of the chest at (a) low and (b) high lung air volumes of the same rabbit kitten. These PB-PCX images were one of 1800 projections used to reconstruct 27.6 $\times$ 26.4 mm² CT slices as shown in (c) and (d), respectively. ODD = 1 m. Energy = 24 keV. Exposure time per projection = 50 ms. (See section 3 for further experimental details).

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Previous evidence on how human alveoli behave during respiration has been inconclusive, partly due to the inherently complicated interconnecting nature of alveoli, but also because previous studies used different experimental techniques, animal subjects and morphemetrics techniques [18]. While it was initially believed alveolar size varied monotonically with lung volume, there has been some evidence of alveoli opening and closing during respiration [19]. This is often termed alveolar recruitment/de-recruitment although, in the neonatal lung, aeration and reflooding may be more accurate terminology [20].

The theoretical basis of our work is presented in section 2. This is validated using colloidal soda-lime glass (SLG) microspheres, which closely resemble alveoli in size and shape, then applied to newborn rabbit kittens to measure alveolar size and compared with a gold standard using high-resolution CT images (see section 3 for details). The results and analysis from both microspheres and rabbit lungs is presented in section 4. The prospect of applying our work to human patients forms part of our discussion in section 5. We conclude with section 6.

2. Background theory

Here we show how the alveolar size and population can be determined from lung speckled PB-PCX chest images if the lung air volume is known. This derivation follows closely to that developed in Leong et al. [21], but in that derivation alveoli were assumed to be randomly distributed. In Figs. 1(c) and 1(d) we see that the alveoli become relatively closely packed and therefore less randomly ordered at increasing volume. Herein, we take into account potential short-range ordering associated with close packing.

Consider an object comprised of a single material with complex refractive index, n = 1-δ + iβ, where δ and β are the refractive index decrement and attenuation index, respectively. The imaginary number is denoted by i. The power spectrum of its PB-PCX image ( $I ({\overset{⇀}{r}}_{⊥}, z = L)$ ) in the plane ${\vec{r}}_{⊥} = (x, y)$ that is normalized against its contact image ( $I ({\overset{⇀}{r}}_{⊥}, z = 0)$ ), at object-to-detector propagation distance (ODD) L, along the optic axis z can be expressed as [21]:

{| F {\frac{I ({\overset{⇀}{r}}_{⊥}, z = L)}{I ({\overset{⇀}{r}}_{⊥}, z = 0)} - 1} |}^{2} = L^{2} δ^{2} k_{⊥}^{4} {| F {T ({\vec{r}}_{⊥})} |}^{2} .

Here, $T ({\overset{⇀}{r}}_{⊥})$ is the projected thickness of the object, $F$ is the Fourier transform with respect to spatial variables x and y, $k_{⊥} = \sqrt{k_{x}^{2} + k_{y}^{2}}$ is the transverse wavenumber in ${\vec{r}}_{⊥}$ where $(k_{x}, k_{y})$ are vectors in two-dimensional (2D) Fourier space. The technique employed to determine $I ({\overset{⇀}{r}}_{⊥}, z = 0)$ is detailed in section 3.4.

In deriving Eq. (1), two assumptions were made regarding the object: (1) lateral displacement of the x-ray beam at the exit surface due to scattering within the object must be less than the detector spatial resolution, and (2) it weakly absorbs (i.e., µT<1 where µ is the attenuation coefficient of the object). These assumptions have been shown to be valid when imaging the thorax of a newborn rabbit kitten using 24 keV x-rays [21]. Equation (1) is restricted to the near-field regime, which is where the Fresnel number, N_F, defined by,

N_{F} = \frac{a^{2}}{L λ},

to be such that N_F ≥ max{1,|φ|_max} [22]. Here, a is the characteristic length scale of the object over which

I ({\overset{⇀}{r}}_{⊥}, z = 0)

varies appreciably, λ is the incident wavelength, and the maximum magnitude of the phase gradient in

{\vec{r}}_{⊥}

is defined by |φ|_max. Note that the reciprocal of ‘a’ in the near-field condition quantifies the area of the 2D Fourier support.

To determine the form of Eq. (1) for lungs, the lung is modeled as N air-filled spherical cavities of radius R (representing alveoli) that are randomly distributed in lung tissue volume with refractive index decrement δ. This model provides a simple analytic solution to Eq. (1) for the lungs. Highly magnified images of the alveoli show they resemble pseudo-randomly orientated dodecahedrons, which for our purpose are sufficiently close to being spherical [23]. To that end, the object function of the modeled lung can be expressed as a sum of convolutions:

\tilde{T} (\vec{r}) = V (\vec{r}) - \sum_{n = 0}^{N} \int_{\vec{r}} δ (\vec{r} - {\vec{r}}_{n}) G (\vec{r}) d \vec{r},

where

δ (\vec{r})

is the unit impulse function and

{\vec{r}}_{n} = (x_{n}, y_{n}, z_{n})

is a vector in 3D Cartesian space representing the random position of the n^th alveoli in the volume

V (\vec{r})

, where

V (\vec{r})

is the object function of lung tissue and is equal to unity everywhere in the volume and zero everywhere else. The integral of the modeled lung

\tilde{T} (\vec{r})

along the optic axis z gives the projected thickness

T ({\vec{r}}_{⊥})

. The object function of a sphere is represented by

G (\vec{r})

where G = 1 for

| \vec{r} | \leq R

and G = 0 everywhere else. The power spectrum of Eq. (3) is written as:

| F {\tilde{T} (\vec{r})}^{2} | = {| \int_{V} \tilde{T} (\vec{r}) e^{- i 2 π \vec{k} \cdot \vec{r}} d \vec{r} |}^{2},

where

\overset{⇀}{k} = (k_{x}, k_{y}, k_{z})

are vectors in 3D Fourier space.

The first term of Eq. (3) is a constant function and so contributes only to the zero (DC) frequency. The DC frequency, however, is not relevant to our analysis and will be ignored hereafter. To derive an analytic solution of the integral in Eq. (4), and hence obtain explicit dependence on N and R, Eq. (3) (minus $V (\vec{r})$ ) is substituted into Eq. (4), and making use of the convolution theorem and the sifting property of the unit impulse, we arrive at,

{| F {\tilde{T} (\vec{r})} |}^{2} = {| F {G (\vec{r})} |}^{2} [N + \sum_{n = 1}^{n \neq m} \sum_{m = 1} \cos (2 π \vec{k} \cdot {\vec{D}}_{n m})],

where

{| F {G (\vec{r})} |}^{2}

is the power spectrum of a sphere and

{\vec{D}}_{n m}

is the vector from sphere n to m. The arrangement of alveoli is macroscopically isotropic making their power spectrum rotationally symmetric. Thus, the sum in Eq. (5) is averaged over the polar angle defined between

| \vec{k} |

and

| {\vec{D}}_{n m} |

, and the azimuthal angle formed by the plane containing

\vec{k}

and

{\vec{D}}_{n m}

with an arbitrary plane. Furthermore, the power spectrum of a sphere is also rotationally symmetric. Thus, Eq. (5) can be simplified into one-dimensional form with independent variable

| \vec{k} |

, to give a result equivalent to the Debye scattering formula, which was derived for predicting the diffraction patterns of gases and liquids [24]:

\bar{{| F {\tilde{T} (\vec{r})} |}^{2}} = {| F {G (\vec{r})} |}^{2} [N + \sum_{n = 1}^{n \neq m} \sum_{m = 1} \frac{\sin (| \vec{k} | | {\vec{D}}_{n m} |)}{| \vec{k} | | {\vec{D}}_{n m} |}] .

The overbar represents the rotational average of ${| F {\tilde{T} (\vec{r})} |}^{2}$ , hereafter the overbar will be dropped for notational simplicity. According to the Fourier slice theorem, ${| F {\int_{z} \tilde{T} (\vec{r}) d z} |}^{2} (k_{x}, k_{y}) = {| F {\tilde{T} (\vec{r})} |}^{2} (k_{x}, k_{y},0)$ . This is also true for ${| F {G (\vec{r})} |}^{2}$ and therefore allows $| \vec{k} |$ to be replaced with $k_{⊥} = | {\vec{k}}_{⊥} |$ in Eq. (6) to give an expression for the power spectrum of $T ({\overset{⇀}{r}}_{⊥})$ . Substituting this 2D form of Eq. (6) into Eq. (1), and given that the power spectrum of a sphere is ${| F {G (\vec{r})} |}^{2} = {| \frac{4 π R^{3}}{{(k_{⊥} R)}^{2}} [\frac{\sin (k_{⊥} R)}{k_{⊥} R} - \cos (k_{⊥} R)] |}^{2}$ [25], we arrive at the main equation of this study, the PB-PCX speckle image power spectrum,

\begin{array}{l} {| F {\frac{I (x, y, z = L)}{I (x, y, z = 0)} - 1} |}^{2} = L^{2} δ^{2} k_{⊥}^{4} N {| \frac{4 π R^{3}}{{(k_{⊥} R)}^{2}} [\frac{\sin (k_{⊥} R)}{k_{⊥} R} - \cos (k_{⊥} R)] |}^{2} \\ \times [1 + \int_{V} ρ (D) \frac{\sin (k_{⊥} D)}{k_{⊥} D} d V] . \end{array}

Here, the summation term in Eq. (6) has been rewritten as an integral, over the volume $V (\overset{⇀}{r})$ , weighted by the function ρ(D) that is defined as the frequency of occurrence of alveoli separated by distance $D = | \vec{D} |$ . For randomly distributed alveoli, ρ(D)≈constant. Consequently, the integral in Eq. (7) becomes the Fourier transform of $V (\overset{⇀}{r})$ (remember that the sinc term is the polar and azimuthal average of the exponential term in Fourier space). If the ratio of the sphere size $G (\vec{r})$ to the dimension of $V (\vec{r})$ is much less than unity then the integral tends to zero everywhere except at $k_{⊥} = 0$ , and given the DC frequency is irrelevant for our analysis, this reduces Eq. (7) to the expression first derived by Leong et al. [21]:

{| F {\frac{I (x, y, z = L)}{I (x, y, z = 0)} - 1} |}^{2} = L^{2} δ^{2} k_{⊥}^{4} N {| \frac{4 π R^{3}}{{(k_{⊥} R)}^{2}} [\frac{\sin (k_{⊥} R)}{k_{⊥} R} - \cos (k_{⊥} R)] |}^{2} .

Leong et al. [21] showed that the area under the first peak in the spectrum, which is bounded by adjacent minima k_⊥R = 0 and k_⊥R = 4.493, is given by,

P S_{A r e a} = 34 π^{2} L^{2} δ^{2} N R .

This is approximately equivalent to integrating over all $k_{⊥}$ , except at $k_{⊥} = 0$ , of experimentally measured power spectra as the higher order peaks are suppressed by the detector point spread function (d-PSF) and penumbral blurring. If the total lung air volume (V_L) within the alveoli is known, which is approximated under the assumption of N isolated spheres of radius R,

V_{L} = \frac{4}{3} N R^{3},

then N and R can be solved, given if δ is known, which can be readily calculated for a given material at a given x-ray energy using the National Institute of Standards and Technology (NIST) database, as described in section 3.4. An alternative method to calculating R from PS_Area is using the position of the maximum value of the first order peak (PS_Peak) defined by PS_PeakR = 2.74 (see Eq. (8)). N could then be calculated from either the known V_L or PS_Area, but in this study, V_L was used. However, as is apparent from Figs. 1(c) and 1(d), at increasing V_L, alveoli exhibit short-range order as the alveoli become more closely packed. Equation (7) accounts for this reduction in randomness. Comparing Eqs. (7) and (8), it can be shown that both are oscillatory functions in Fourier space. As the packing fraction increases, their first order peaks differ in position as do the area under their curves. Calculating R from the position of the first order peak using Eq. (8) would become less accurate for increasing alveolar density. A more accurate expression for PS_Peak and PS_Area can be derived from Eq. (7); however, ρ(D) will likely vary during breathing and is difficult to determine exactly. To test the effect of short-range ordering, SLG microspheres, randomly arranged and closely packed, were imaged. Equations (9) and (10) were then used to measure N and R and compared with their known values (see section 4). This would indicate if Eq. (9) provides sufficiently accurate measures of N and R for closely packed alveoli.

Our team has devised several methods to calculate V_L from 2D images [21, 26–28]. Here we employ the algorithm of Kitchen et al. [26], that is simple, accurate and robust for this type of imaging. It measures the change in regional lung air volumes between pairs of PB-PCX images by using a single image phase retrieval algorithm (SIPR) [29]. Having an image of non-aerated lungs enables us to calculate absolute regional lung air volumes [26]. V_L represents the lung air volume within the alveoli while the volumetric technique employed measures the previously mentioned volume plus the volume of air in the airway branches. Nevertheless, given that approximately 90% of the total lung air volume resides in the alveoli, the algorithm by Kitchen et al. [26] can be used to adequately approximate V_L.

3. Methodology

3.1 Image acquisition

The Medical and Imaging centre of beamline 20B2 (Hutch 3) at the SPring-8 synchrotron radiation source in Japan was used for all imaging experiments. A Si (111) non-dispersive monochromator was tuned to different energies for imaging glass particles and rabbit kittens with relative energy width of ΔE/E~10⁻⁴ and photon flux density ~2 × 10⁸ photons/s/mm². Images were flat field corrected using flat and dark field images recorded at the beginning of each image sequence to normalize against the incident intensity of the x-ray beam and to offset the intrinsic detector noise, respectively. For long image sequences (>2 mins), the intensity of each frame was rescaled to the first frame. This corrected for synchrotron beam fluctuations caused by periodic injections of electrons into the storage ring, and heating/cooling of optical elements.

Two detectors were used in this study: a 2560 × 2160 pixel tandem lens-coupled scientific-CMOS (sCMOS) imaging sensor (pco.edge; PCO AG, Germany) coupled to a 25 µm thick gadolinium oxysulfide (Gd₂O₂S:Tb⁺;P43) powdered phosphor, and a 2048 × 2048 pixel sCMOS imaging sensor (ORCA-Flash4.0; Hamamatsu, Japan) with a direct fiber optic coupling the sensor to a 150 µm thick columnar CsI scintillator. Their effective pixel sizes were 15.23 µm and 6.38 µm, respectively.

3.2 Glass particles

SLG microspheres (Whitehouse Scientific Ltd.) were used to test and validate our theory. They are a good model for alveoli and their average size and population are accurately known. Both detectors were used for imaging microspheres to test the robustness of our technique against detector types. Microspheres were imaged at 30 keV and with an exposure time of 1.2 s. 150-180 µm sized microspheres were sprinkled onto a cover slip to produce a sparse random distribution and then sealed with another cover slip placed on top. A hollow step-wedge made of polymethylmethacrylate was designed with the height (i.e. thickness) of the steps at 1 mm, 2 mm, 5 mm, 10 mm and 20 mm. The hollow step-wedge was separately filled with closely packed microspheres of sizes 43-55 µm, 63-75 µm, 75-90 µm, 90-106 µm, 106-125 µm, 150-180 µm, 180-212 µm and 250-300 µm.

3.3 Rabbit kittens

All animal experiments performed were approved by the Monash University Animal Ethics Committee and the SPring-8 Animal Care and Use Committee. Pregnant New Zealand white rabbits (27-30 days of gestation, term = 31-32 days; n = 4) were anaesthetized initially using propofol (i.v; 12 mg/kg bolus, 150-500 mg/h infusion), then via inhalation following intubation (Isoflurane 1.5-4%). Rabbit kittens (n = 10) were delivered by caesarean section, then humanely killed using an overdose of sodium pentabarbitone (>100 mg/kg i.p.). Immediately after euthanasia, they were surgically intubated before being placed upright in a water-filled cylinder with their head out and supported by a rubber diaphragm around their necks. A custom-built mechanical ventilator was connected to the endotracheal tubes, which were inserted into the trachea of the rabbit kittens, and sent out trigger signals for gated imaging [30]. Before ventilation several non-aerated images of the chest were recorded. Thereafter ventilation was initiated with an initial airway pressure (AP) of 16 cmH₂O. AP was then gradually increased to 27 cmH₂O and decreased back to 16 cmH₂O via 1 cmH₂O increments, each of which was held for 5 s. The images were recorded at 24 keV with a frame rate of 20 Hz, 40 ms exposure time, and 1 m ODD. This amounts to an absorbed radiation dose per PB-PCX image of ~1 mGy. While this is more than the standard chest x-ray image, the spatial resolution is significantly higher and the dose is still much lower than a standard chest CT [13]. Furthermore, the SNR was measured to be ~10 from several regions that were away from the rabbit kitten but within the water-filled cylinder.

The ventilator was disconnected with AP last set at 2 cmH₂O. High resolution CT images (1800 projections from 0 to 180° with 50 ms exposures and 1 m ODD) were then acquired for a gold standard comparison. Additional CT images were recorded after the kitten’s lungs were filled with 100% N₂ (to prevent absorption of gas into the pulmonary capillaries) at 29 cmH₂O AP with the intubation tube then tied off to prevent lung collapse. Each rabbit kitten was fixed in a test tube filled with agar to reduce motion blur. PB-PCX images of the same animal were also recorded at different ODDs to measure the degree of validity of Eq. (1) at large ODD. The pco.edge detector was used because only it had a sufficiently large field of view to image the entire chest of a rabbit kitten in a single exposure.

3.4 Image analysis

Equation (8) does not account for the d-PSF and penumbral blurring. Given that the synchrotron source size of the beamline used for this study was 150 µm × 10 µm, the source-to-object distance was 210 m, and the maximum ODD set was 2 m, the degree of penumbral blurring is less than a pixel width for both detectors [14]. However, the d-PSF alters the power spectrum significantly, and was therefore measured and corrected for each PB-PCX image before subsequent image analysis. The edge spread function was measured both vertically and horizontally using a 5.25 mm thick lead block. The transverse spatial derivatives of the resulting images were averaged over many pixels, extruded azimuthally to construct the d-PSF, and fitted with a 2D Pearson type VII distribution function (PVII) [31]. The Wiener deconvolution algorithm was used to deconvolve the PB-PCX images with the fitted d-PSF [32]. This algorithm is stable against the input parameter, the SNR of the deconvolved image, particularly at low spatial frequencies where the first order peak of the power spectrum of lung speckle presides, thus it need not be known exactly. An optimal SNR value of 500 was found to provide consistent values of N and R for microspheres and alveoli. Wiener deconvolution amplifies high frequency noise but the degree of noise amplification is similar between frames of the same animal. To suppress this effect, the power spectra of images without speckle (e.g. the non-aerated lung images) were subtracted from that of the speckled image (e.g. aerated lung images).

The contact (absorption) image ( $I ({\overset{⇀}{r}}_{⊥}, z = 0)$ ) is required to calculate PS_Area. This was estimated using SIPR [29]. It requires both µ and δ as inputs for the filter, which were calculated from the NIST database [33]. For SLG microspheres (30 keV), µ_SLG = 197 m⁻¹ and δ_SLG = 5.09 × 10⁻⁷, and for lung tissue (24 keV), µ_LT = 54.74 m⁻¹ and δ_LT = 3.99 × 10⁻⁷. SIPR assumes a single-material object, but the chest comprises of bone and soft tissue. Setting the parameters of SIPR for lung tissue will accurately reverse the lung tissue-induced phase contrast but over-smooth that of the bone [28]. To that end, dividing PB-PCX chest images by their contact image (using SIPR) will accurately remove the absorption contrast of lung tissue but not entirely that of the bone, particularly along the edges of the bone. Nevertheless, its contribution to the power spectra is small compared to the lung speckle signal.

To summarize, PS_Area was calculated using the following sequence of steps applied to the PB-PCX lung speckle image: (i) deconvolving the d-PSF, (ii) dividing by its contact image, (iii) computing its azimuthally averaged power spectrum, (iv) subtracting from that of its non-aerated PB-PCX image, and (v) integrating between 2 mm⁻¹ and the Nyquist frequency. The lower limit was chosen to exclude the peak at the origin of Fourier space but still included the first order peak.

Grayscale 3D granulometry [34] was considered the ‘gold standard’ for our technique for measuring alveolar dimensions. Spheres of various sizes were created as structural elements to survey the lung for alveoli of similar size using the morphological opening operator on 7.5 mm³ CT volumes of rabbit kitten lungs. The CT volumes were magnified by a factor of 4 and bilinearly interpolated beforehand to increase the spatial sampling rate. Alveolar dimensions were measured from our technique by calculating PS_Area from one of the CT projection images. For this data set V_L was calculated by intensity thresholding the CT images to segment the airways before counting the total voxels within them.

4. Results

Three types of 150-180 µm microsphere samples were investigated: single and multiple particles randomly dispersed between cover slips, and a hollow step-wedge filled with particles. These samples were recorded at 15 cm ODD using the pco.edge detector and are shown in Figs. 2(a-c). Both N and R were calculated using Eqs. (9) and (10). N and R were also determined from the position of the first order peak in the speckle power spectrum, that is, PS_Peak. The calculated values of N and R along with their expected values are presented in Table 1.

Fig. 2 3.83 $\times$ 3.83 mm² propagation-based phase contrast x-ray images of 150-180 µm sized (a) single glass particle, (b) multiple glass particles and (c) a 1 mm thick container of glass particles with volume packing density $\approx 55 %$ . (d) shows the corresponding power spectra of (a)-(c), after deconvolving to remove the detector point spread function, dividing by their contact image, normalizing against the total pixels in the image and the number of microspheres. ODD = 15 cm. Energy = 30 keV. Exposure time = 1 s.

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Table 1. The number and mean radius of glass particles calculated from the propagation-based phase contrast x-ray images in Figs. 2(a)-2(c) compared with the expected values shown in brackets.

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For single and multiple particles placed between cover slips, V_L was calculated using Eq. (10) with N and an average value for R measured directly from their images for comparison with our technique. The calculated and expected values of N and R for a single microsphere agree poorly because the image noise masked its signal (Fig. 2(d)). However, as the number of microspheres increased, a clear peak in the power spectrum becomes evident above the noise in Fig. 2(d). This resulted in excellent agreement between the calculated and expected values of N and R using both the PS_Area and PS_Peak (Table 1). The uncertainties in N and R were propagated from the uncertainty in V_L, which was the difference in using the average rather than the distribution of R, except for R calculated from PS_Peak which was determined from weighted fitting a PVII function to the centroid. Comparing the uncertainties in N and R, at low packing fraction, they are more precisely measured from PS_Peak than from PS_Area as PS_Peak does not depend on how precisely V_L is measured.

Microspheres poured into a container inevitably stack on top of one another to produce some short-range order. V_L was determined using SIPR to calculate the projected thickness of glass at each pixel then summed and multiplied by the pixel area [29]. Surprisingly, the presence of short-range order did not adversely affect the calculation of N and R using PS_Area. The uncertainty was propagated from that of V_L, which was determined using a calibration curve that plots the uncertainty in V_L against the image size, developed by Leong et al. [28]. Conversely, PS_Peak shifted to higher frequencies (Fig. 2(d)), thereby underestimating R and overestimating N. Again, the uncertainty of the former was determined from weighted fitting a PVII function to the centroid while that of the latter was determined in a similar manner to N that was calculated from PS_Area. Two important and consequential points arise from these findings: (1) there is short-range order in closely packed particles, as indicated by the shift in PS_Peak, and (2) despite this, Eqs. (9) and (10) can still accurately calculate N and R. Figure 2(d) provides a clue to why Eqs. (9) and (10) remain valid. There we see that the shape and position of the first order peak is altered by short-range order, but the area under the curve remains virtually unchanged. This presents a favourable outcome, since the packing density of alveoli will vary during respiration.

PB-PCX images of the 1 mm thick region of the step-wedge, each containing different sized microspheres, were recorded using the ORCA detector to better resolve the smaller sized microspheres. N and R were calculated from PS_Area for each and are plotted in Fig. 3(a) and are in close agreement with the expected values. However, at increasing sample thickness (that is, at increasing |φ|_max) and ODD, large errors accumulated in the calculation of R as N_F reduces below max{1,|φ|_max}. This is shown in Fig. 3(b). A similar trend (not shown) was found when plotting N as a function of ODD. The accuracy of calculating $R$ of a single layer of microspheres also decreases despite N_F ≥ max{1,|φ|_max} of up to 2 m ODD (R≈165 µm, |φ|_max = |-kδ_SLG2R| = 13.5, L = 2 m, a = 2R, N_F = 61.6). The consistent overestimation of PS_Area with respect to that obtained experimentally, which we denote as large distance error, could be due to a number of possible effects. While partial coherence (penumbral blurring) was deemed negligible based on the source size given by Goto et al. [35], the effects on speckle contrast may be larger than expected. Our group has also found discrepancies between simulated lung speckle contrast using the projection approximation and the more rigorous multi-slice diffraction method, which may also account for the differences. Finally, Nugent et al. [36] showed a loss of contrast from imaging random phase screens (akin to the lungs) can be caused by limited spatial resolution. A complete study of these competing effects is warranted, but is beyond the scope of this paper.

Fig. 3 Evaluating the accuracy of calculating the number and mean radius of microspheres from propagation-based phase contrast x-ray images of (a) 1 mm thick container filled separately with different sized microspheres at 15 cm object-to-detector distance (ODD) and (b) containers with variable thickness filled with 150-180 µm sized microspheres, and a single layer of 150-180 um microspheres, at various ODDs.

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Considering that the typical alveolar radius and projected thickness of a fully aerated lung of a rabbit kitten are 75 µm and 10 mm, respectively, and given that the ODD used in our experiments was 1 m, N_F = 435 and |φ|_max = |-kδ_SLG2R| = 363. Since N_F ≥ max{1,|φ|_max}, this shows the PB-PCX lung images recorded in this study satisfy the near-field condition. To account for the large distance error for the lungs, images of sets of lungs aerated to various degrees of the same rabbit kitten were acquired at multiple ODDs. The PS_Area was calculated at each ODD and compared with the expected PS_Area, which was determined by assuming the calculated PS_Area at the lowest ODD of 15 cm was accurate and subsequent PS_Area were extrapolated to larger ODD using Eq. (1). This was done for several rabbit kittens at 1 m ODD, and on average their calculated PS_Area differed by a factor of 2.3 $\pm$ 0.6 from the expected value. This factor was accounted for in all PB-PCX rabbit kitten images recorded at 1 m to give a more reliable measure of the alveolar dimensions and number.

3D granulometry was utilized to test the accuracy of measuring alveolar dimensions from PS_Area and PS_Peak, although it does not yield their number, N. Figure 4(a) shows typical granulometry curves that correspond to a 7.5 mm³ cube region-of-interest (ROI) in Figs. 1(c) and 1(d). The maximum value represents the dominant alveolar dimension. 3D granulometry was performed on several more rabbit kittens and compared with PS_Area and PS_Peak (Fig. 4(b)). The uncertainty in R measured from 3D granulometry was determined by the width of the flat top of the peak while that measured from PS_Area was propagated from the uncertainty in the factor, 2.3 $\pm$ 0.6, used to correct for the large distance error. The uncertainty in PS_Peak, determined from weighted fitting to the PVII function, was negligible (<1 µm). The gradients for PS_Area and PS_Peak against 3D granulometry were 0.9 ± 0.3 (Pearson product-moment correlation coefficient ρ = 0.6) and 0.2 ± 0.1 (ρ = 0.3), respectively. The gradient of the latter indicates the insensitivity of PS_Peak with R, which is likely caused by short-range ordering of alveoli affecting the measured size (see section 2), while the former shows a strong positive correlation. From the results of the SLG microspheres, this further demonstrates our technique is immune to short-range ordering effects.

Fig. 4 (a) Distribution of alveolar dimensions determined from 7.5 mm³ regions centred about the two CT slices in Figs. 1(c) and 1(d), respectively, using 3D granulometry. (b) The average alveoli size was measured both from PS_Area and PS_Peak and was compared with that measured from 3D granulometry for several rabbit kittens. (c) The alveolar number was approximated by manually counting the number of alveoli surface profiles from one transaxial slice per CT of a ventilating kitten and plotted against the total lung air volume determined by intensity thresholding the entire CT.

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To demonstrate the presence of alveolar recruitment and de-recruitment, the number of alveoli was manually counted from a transaxial slice for each CT recorded of a rabbit kitten at different stages of respiration, which in stereology shows that it is approximately proportional to the alveolar number in 3D (see section 5 for automated methods trialled as gold standards for validating N) [37]. The transaxial slices were chosen to be approximately at the same axial position in the lung. Figure 4(c) shows alveolar number correlated with the total lung volume of the entire CT.

The ability of our technique to dynamically measure N and R during ventilation is demonstrated in Fig. 5; from the first breath and several respiratory cycles later. From the first breath (Fig. 5(a)), Fig. 5(b) shows that N (calculated from PS_Area) first increases then plateaus after t = 5 s. This increase in N coincides with the clearing of fetal lung liquid and consequent recruitment of alveoli [20]. An increase in R, computed from PS_Area, follows the same trend as V_L. Conversely, R that was derived from PS_Peak, remains largely unchanged, which may be caused by alveoli becoming more closely packed. At t≥27 s, a sudden drop in V_L sees R decreasing (calculated from PS_Area), but interestingly N concomitantly increased. The increase in N may be caused by the trapping of air as the airways collapse to produce the appearance of additional alveoli in the form of air bubbles. During a second respiratory cycle of the partially aerated lung (Fig. 5(c)), the independent calculations of R shown in Fig. 5(d) closely agree, but after t≥8 s they diverge. This is likely due to effects of short-range order affecting peak position. N (calculated from PS_Area) remains approximately constant throughout except at the beginning and end of the respiratory cycle. This shows evidence of alveolar opening/recruitment followed by flooding/de-recruitment.

Fig. 5 Lung air volumes from PB-PCX chest images of a kitten mechanically ventilated (a) from its first breath, and (c) over a single respiratory cycle several breaths after its first. The corresponding calculation of number and mean radius of alveoli are shown in (b) and (d).

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5. Discussion

The structural and functional complexity of the lung makes it both intriguing to understand yet difficult to study. Many lung imaging techniques are limited to studying only small regions of the lungs accessible to invasive instruments, or lungs that are effectively stable which therefore precludes the extraction of dynamic information. Here, the method developed by Leong et al. [21] was applied, after accounting for the large distance error and d-PSF, to measure the N and R of alveoli from the speckle patterns of PB-PCX ventilated chest images. Highly spatially resolved PB-PCX images can be recorded in real-time during a respiratory cycle by using intense and coherent synchrotron light coupled with detectors with high spatial resolution and quantum efficiency. Our technique can therefore provide valuable insight into the structural lung changes during respiration, which could prove useful for developing safe ventilation strategies or studying lung diseases.

In this study, N and R were measured for the whole lungs. However, a key benefit of this technique is its ability to also measure N and R locally, if PS_Area and V_L are regionally measured. The minimum size of the ROI from which that V_L can be measured, using the technique adapted in this study, is limited by the differential movement of the bone. Previously, Leong et al. [28] developed a cross correlation-based technique that aligned the bones between two PB-PCX chest images, which effectively removes the bone, before applying the volumetric analysis of Kitchen et al. [26] to calculate V_L on a pixel-by-pixel basis. For calculating PS_Area, the ROI must be large enough to adequately sample the power spectrum. Given the detector pixel size of 15.23 µm and typical alveolar size of 150 µm, N and R can be calculated from a ROI as small as ~0.5 mm² compared to that of the entire lung being 230 mm². This would be important in optimizing ventilation strategies to ensure all parts of the lung are adequately aerated without over-distending the alveoli leading to conditions such as ventilation-induced lung injury and bronchopulmonary dysplasia. Diagnosis and treatment of respiratory diseases including emphysema could also benefit by better localizing and targeting the diseased region.

Non-aerated PB-PCX images of the lungs are required for our technique but are not always accessible, particularly for studying subjects that are not newborn. One alternative is intensity thresholding a low dose chest CT image reconstructed from phase retrieved PB-PCX images (using SIPR) to remove the aerated alveoli, with the resulting image being Radon-transformed then propagated using Eq. (1) to obtain the non-aerated PB-PCX chest image. While CT can provide information on N and R, our technique can achieve this using single projections. Consequently, the temporal resolution of our technique is far superior in allowing dynamic measures at a significantly lower radiation dose than CT. Similarity in anatomical structure of the chest within a species should also make it possible to use a non-aerated PB-PCX image for different subjects of the same species. This would avoid doing CT and imparting unnecessary radiation dose to every subject.

Grayscale 3D granulometry cannot be used to measure the number of alveoli from CT images. To that end, an automated algorithm, watershedding [38], was tried in this study on the CT images. This image processing technique can measure both N from the number of local minima and R from the size of the valleys centring those minima. However, watershedding was found to be unstable against image noise as the dominant spatial frequency of the noise was comparable to that of the alveoli.

The success of translating our technique for clinical use will depend on achieving adequate SNR at short exposure times. This would be important for in vivo imaging of the rapid rate of spontaneous breathing as opposed to controlled ventilation that was performed in our study. Moreover, human lungs are significantly larger than those of the rabbit kittens used in this study. While this lowers the image signal from an increase in attenuation, the x-ray energy can be increased without significant loss in phase contrast [14]. There is potential for synchrotron imaging of human patients, but the cost and limited availability of synchrotrons makes this unfeasible. Lower powered laboratory-based x-ray sources have been shown to produce well defined lung speckle in mice [39]. The challenge here will be optimizing the x-ray source spot size and ODD first for imaging animals and then human patients to produce speckles minimally affected by penumbral or motion blur. Also, while laboratory x-rays sources are polychromatic and the technique presented herein has only been developed for quasi-monochromatic sources, it has been shown that the transport-of-intensity equation, from which Eq. (1) was derived, can be generalized for a polychromatic source given the projection approximation is valid across the x-ray energy spectra [40]. For larger lungs, higher x-ray energies may be required to ensure the projection approximation holds.

6. Conclusions

We have demonstrated a novel non-invasive in situ imaging-based technique that is able to quantify the number and average size of densely packed particles and cavities. We have applied this technology to measure the same parameters of alveoli in the lungs. This information is encoded in the speckle pattern seen in propagation-based phase contrast x-ray images in which multiple particles and cavities overlap in projection. The morphological parameters were extracted by calculating the area under the image power spectrum of the speckled images and by simultaneously measuring the particulate volume from the image. Our technique revealed recruitment and de-recruitment of alveoli in mechanically ventilating newborn rabbit kittens. 3D grayscale granulometry was employed as a gold standard for alveolar dimensions and agreed well with our technique. As well as furthering our conceptual understanding of the structural behaviour of the lung, our technique has potential to be performed with a laboratory-based x-ray source and consequently applied to clinical diagnosis of respiratory diseases, evaluating the effect of therapeutic treatments, and monitoring of assisted ventilation.

Acknowledgment

The authors would like to thank Kentaro Uesugi and Naoto Yagi for assistance with the experiments, and SPring-8 for providing access to their facility and equipment. AFTL acknowledges the support of an Australian Postgraduate Award. SBH and MJK acknowledge funding from the Australian Research Council (ARC; Grant Nos. DP110101941 and DP130104913) and National Health & Medical Research Council (NHMRC; APP1064973). MJK is an ARC Australian Research Fellow. SBH is a NHMRC Principal Research Fellow. This research was partially funded by the Victorian Government's Operational Infrastructure Support Program. We acknowledge travel funding provided by the International Synchrotron Access Program managed by the Australian Synchrotron and funded by the Australian Government.

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	Number		Radius (µm)
Microspheres	PS_Area	PS_Peak	PS_Area	PS_Peak
Single (Fig. 2(a))	0.67±0.03(1)	2.7 ± 0.1	96 ± 4(83 ± 8)	59.55 ± 0.01
Multiple (Fig. 2(b))	52 ± 3(59)	59.63 ± 0.08	87 ± 4(83 $\pm$ 8)	83.47 ± 0.08
Packed (Fig. 2(c))	3730 ± 460(3600 ± 800)	7500 ± 1600	82 ± 9(83 $\pm$ 8)	64.90±0.01

Real-time measurement of alveolar size and population using phase contrast x-ray imaging

Abstract

1. Introduction

2. Background theory

3. Methodology

3.1 Image acquisition

3.2 Glass particles

3.3 Rabbit kittens

3.4 Image analysis

4. Results

5. Discussion

6. Conclusions

Acknowledgment

References and links

Cited By

Figures (5)

Tables (1)

Equations (10)

Biomedical Optics Express