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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 27905–27923
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Measurement of absolute regional lung air volumes from near-field x-ray speckles

Andrew F. T. Leong, David M. Paganin, Stuart B. Hooper, Melissa L. Siew, and Marcus J. Kitchen  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 27905-27923 (2013)
http://dx.doi.org/10.1364/OE.21.027905


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Abstract

Propagation-based phase contrast x-ray (PBX) imaging yields high contrast images of the lung where airways that overlap in projection coherently scatter the x-rays, giving rise to a speckled intensity due to interference effects. Our previous works have shown that total and regional changes in lung air volumes can be accurately measured from two-dimensional (2D) absorption or phase contrast images when the subject is immersed in a water-filled container. In this paper we demonstrate how the phase contrast speckle patterns can be used to directly measure absolute regional lung air volumes from 2D PBX images without the need for a water-filled container. We justify this technique analytically and via simulation using the transport-of-intensity equation and calibrate the technique using our existing methods for measuring lung air volume. Finally, we show the full capabilities of this technique for measuring regional differences in lung aeration.

© 2013 OSA

1. Introduction

X-ray imaging is commonly used to reveal the internal structure of the chest, differentiating materials such as soft tissue and bone by their densities. Lung diseases in their early stages, such as emphysema, cystic fibrosis and cancer are difficult to detect in a conventional x-ray image [1

1. H. Kauczor and A. Bankier, Functional Imaging of the Chest (Springer, 2004). [CrossRef]

]. Since early diagnosis of lung disease is a critical factor for patient prognosis, improved diagnostic methods during the early stages underpins advances in the treatment of these diseases [1

1. H. Kauczor and A. Bankier, Functional Imaging of the Chest (Springer, 2004). [CrossRef]

]. Lung functional x-ray imaging is more sensitive for detecting lung diseases than anatomical imaging, making it a prospective complementary diagnostic tool to x-ray imaging [2

2. A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. W Siu, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40, 1160–1169 (2012). [CrossRef]

].

Pulmonary functional tests, such as the forced oscillation and spirometry techniques, are performed in clinical diagnostics of respiratory diseases together with x-ray imaging [3

3. M. J. Tobin, G. Jenouri, B. Lind, H. Watson, A. Schneider, and M. A. Sackner, “Validation of respiratory inductive plethysmography in patients with pulmonary disease,” Chest 83, 615–620 (1983). [CrossRef] [PubMed]

5

5. E. Oostveen, D. MacLeod, H. Lorino, R. Farr, Z. Hantos, K. Desager, and F. Marchal, and on behalf of the ERS Task Force on Respiratory Impedance Measurements, “The forced oscillation technique in clinical practice: methodology, recommendations and future developments,” Eur. Respir. J. 22, 1026–1041 (2003). [CrossRef] [PubMed]

]. However, these tests give limited information on the location and extent of the abnormality. The need to detect regional lung pathology has produced many different tomographic-based volumetric techniques [6

6. A. Kyriazis, I. Rodriguez, N. Nin, J. Izquierdo-Garcia, J. Lorente, J. Perez-Sanchez, J. Pesic, L. Olsson, and J. Ruiz-Cabello, “Dynamic ventilation 3He MRI for the quantification of disease in the rat lung,” IEEE Trans. Biomed. Eng. 59, 777–786 (2012). [CrossRef]

8

8. T. J. Wellman, T. Winkler, E. L. Costa, G. Musch, R. S. Harris, J. G. Venegas, and M. F. V. Melo, “Measurement of regional specific lung volume change using respiratory-gated PET of inhaled 13N-nitrogen,” J. Nucl. Med. 51, 646–653 (2010). [CrossRef] [PubMed]

]. Some of these techniques have been combined with k-edge subtraction to help resolve small airways [9

9. S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjld-Nordenstam, and A. R. A. Sovijrvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46, 3287–3299 (2001). [CrossRef]

, 10

10. L. Porra, S. Monfraix, G. Berruyer, G. Le Duc, C. Nemoz, W. Thomlinson, P. Suortti, A. R. A. Sovijrvi, and S. Bayat, “Effect of tidal volume on distribution of ventilation assessed by synchrotron radiation CT in rabbit,” J. Appl. Physiol. 96, 1899–1908 (2004). [CrossRef] [PubMed]

]. However, they require inhalation of a contrast agent to assess regional lung ventilation except when using computed tomography (CT). Yet, CT imparts a relatively large dose of radiation particularly when several three-dimensional (3D) images need to be reconstructed from many projections in order to measure regional lung air volume (VL) over time. The length of time involved in recording the projected images to reconstruct a three-dimensional (3D) image of the chest reduces temporal resolution significantly and so, to minimize motion blurring, breath holds or gated imaging is required. Although CT and magnetic resonance imaging (MRI) techniques can acquire and reconstruct images in real-time on the order of milliseconds, the spatial resolution achievable is only of the order of millimeters, which is insufficient to resolve the minor airway structures [11

11. E. M. Law, A. F. Little, and J. C. Salanitri, “Non-vascular intervention with real-time CT fluoroscopy,” Australas. Radiol. 45, 109–112 (2001). [CrossRef] [PubMed]

, 12

12. M. Uecker, S. Zhang, D. Voit, A. Karaus, K.-D. Merboldt, and J. Frahm, “Real-time MRI at a resolution of 20 ms,” NMR Biomed. 23, 986–994 (2010). [CrossRef] [PubMed]

].

Regional volumetric analysis techniques using two-dimensional (2D) phase contrast x-ray (PCX) imaging from a synchrotron x-ray source have emerged to offer superior temporal resolution over those that use tomography [13

13. M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53, 6065–6077 (2008). [CrossRef] [PubMed]

15

15. A. F. T. Leong, A. Fouras, M. S. Islam, M. J. Wallace, S. B. Hooper, and M. J. Kitchen, “High spatiotemporal resolution measurement of regional lung air volumes from 2D phase contrast x-ray images,” Med. Phys. 40, 041909 (2013). [CrossRef] [PubMed]

]. PCX is a class of imaging modalities that produce phase-induced intensity variations between the boundary of materials exhibiting different complex refractive indices. With a sufficiently spatially coherent x-ray source they provide high contrast images of soft tissues. When employed to image the chest, the boundaries of the conducting airways and alveoli are rendered highly visible (see Fig. 6). Thus, performing volumetric analysis on 2D PCX images simultaneously provides a detailed image of the chest and information on regional lung aeration with high spatial and temporal resolution. One major benefit of this is allowing mechanical ventilators to be adjusted in real time and on a breath-by-breath basis to avoid lung injury [16

16. M. L. Siew, A. B. te Pas, M. J. Wallace, M. J. Kitchen, M. S. Islam, R. A. Lewis, A. Fouras, C. J. Morley, P. G. Davis, N. Yagi, K. Uesugi, and S. B. Hooper, “Surfactant increases the uniformity of lung aeration at birth in ventilated preterm rabbits,” Pediatr. Res. 70, 50–55 (2011). [CrossRef] [PubMed]

18

18. K. Wheeler, M. Wallace, M. Kitchen, A. te Pas, A. Fouras, M. Islam, M. Siew, R. Lewis, C. Morley, P. Davis, and S. Hooper, “Establishing lung gas volumes at birth: interaction between positive end-expiratory pressures and tidal volumes in preterm rabbits,” Pediatr. Res. 73, 734–741 (2013). [CrossRef] [PubMed]

].

Kitchen et al. [13

13. M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53, 6065–6077 (2008). [CrossRef] [PubMed]

] developed a technique to measure changes in VL from 2D propagation-based phase contrast x-ray (PBX) images using a single image phase retrieval algorithm (SIPRA) [19

19. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microscopy 206, 33–40 (2002). [CrossRef]

]. PBX imaging is the simplest of the PCX modalities as only a partially coherent source and a sufficiently large object-to-detector propagation distance (ODD) is required [20

20. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996). [CrossRef]

]. In that technique the animal is immersed upright in water and it is assumed that only the volume of air/water changes within the field of view of the detector. This is an accurate assumption for measuring the total change in VL as the volume of all other materials, namely bone, can be made to remain constant by choosing a sufficiently large region of interest (ROI) to encompass the entire chest. Reducing the size of the ROI to measure regional changes in VL can result in bone moving inside and outside the ROI leading to incorrect measures of VL. Thus, that technique was shown to accurately measure changes in VL over areas as small as one quarter of the lung, where the change in volume of air was not significantly affected by relative displacement of bones. Leong et al. [15

15. A. F. T. Leong, A. Fouras, M. S. Islam, M. J. Wallace, S. B. Hooper, and M. J. Kitchen, “High spatiotemporal resolution measurement of regional lung air volumes from 2D phase contrast x-ray images,” Med. Phys. 40, 041909 (2013). [CrossRef] [PubMed]

] improved on this by removing the bone using a temporal subtraction-based algorithm to measure VL on a pixel-by-pixel basis of micron-scale spatial resolution. That technique, however, is prone to misregistrations when the differential motion of the chest becomes overly complex at large VL. Regional VL has also been measured from analyzer-based phase contrast x-ray images [14

14. M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “Phase contrast image segmentation using a Laue analyser crystal,” Phys. Med. Biol. 56, 515–534 (2011). [CrossRef] [PubMed]

]. A Laue crystal was used to split the x-ray beam to produce two complementary images that were used to create separate images of bone and soft tissue, thus enabling regional VL measurement. That technique does not require anatomical registration, but it is experimentally more challenging and also requires the chest to be immersed in water for VL extraction [14

14. M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “Phase contrast image segmentation using a Laue analyser crystal,” Phys. Med. Biol. 56, 515–534 (2011). [CrossRef] [PubMed]

].

The planar imaging-type volumetric techniques described above work only when the chest is upright and enclosed in water. Moreover, these techniques are limited to measuring changes in VL unless an image of a non-aerated lung is available, which is not always easily attainable. This restricts the type of studies that can be performed, for example, it would not be possible to analyze VL if the animal was ventilated in a supine/prone position or determining its functional residual capacity (FRC; the volume of air at end-expiration). The attenuating medium also reduces the signal-to-noise ratio (SNR). Whilst SNR can be improved by increasing the intensity of the x-ray source, a concomitant increase in radiation dose ensues. In this study, we developed a novel approach for measuring regional VL of PBX chest images without needing to immerse the object in a water bath. This technique relates the power spectra of lung speckle patterns directly to VL.

1.1. Lung speckle

Spatially random samples such as particles suspended in liquid and optically rough surfaces of textured materials produce rapid complex refractive index fluctuations [21

21. R. P. Carnibella, M. J. Kitchen, and A. Fouras, “Determining particle size distributions from a single projection image,” Opt. Express 20, 15962–15968 (2012). [CrossRef] [PubMed]

26

26. S. J. Kirkpatrick, D. D. Duncan, R. K. Wang, and M. T. Hinds, “Quantitative temporal speckle contrast imaging for tissue mechanics,” J. Opt. Soc. Am. A 24, 3728–3734 (2007). [CrossRef]

]. The phase of an incident wavefield is randomly altered as it traverses through or reflects off such an object [22

22. J. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co., 2007).

]. Downstream of the exit surface of the object, the intensity of the randomized wavefield exhibits bright and dark spots, known as speckles, formed by constructive and destructive interferences, respectively. This is the most likely explanation, for the origin of lung speckle observed using PBX imaging, as the lung contains many air-filled alveoli that are pseudo-randomly distributed and enclosed by thin regions of tissue.

Yagi et al. [27

27. N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26, 2190–2193 (1999). [CrossRef] [PubMed]

] were one of the first to encounter lung speckle, which was observed using PBX imaging, in a mouse model. They hypothesized that speckles formed as a consequence of alveoli present in the lungs. Kitchen et al. [28

28. M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49, 4335–4348 (2004). [CrossRef] [PubMed]

] investigated the origin of these speckles by simulating projected PBX images of lung tissue. Here they modeled the alveoli as spheres and generated synthetic PBX images of a lung by numerically propagating the wavefield at the contact plane to the detector surface using the angular spectrum formalism of scalar wave optics. Speckles similar to those seen in PBX chest images of a rabbit pup were observed, and it was shown that this was because the alveoli acted locally as aberrated compound refractive lenses.

1.2. Theory

Consider a lung being made of non-overlapping air-filled voids, where the projected thickness of each void with radius R is described by the object function G(x,y)=2Rx2y2, embedded randomly in soft tissue (or equivalently in water), as shown in Fig. 1. We assume that the x-rays follow a straight path from the x-ray source to the exit surface of the object. This is known as the projection approximation and it is used to fully describe the phase and intensity changes of the x-ray wave traversing the lung at the exit surface [19

19. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microscopy 206, 33–40 (2002). [CrossRef]

]. Using Monte Carlo simulations, Kitchen et al. [28

28. M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49, 4335–4348 (2004). [CrossRef] [PubMed]

] showed that for the lungs of a mouse the projection approximation was valid at diagnostic x-ray energies (i.e. >6 keV). In the near-field regime, the altered x-ray wave produces a speckled PBX image (I(x,y,z = L)) whose power spectrum can be described as (see Appendix A):
|F{I(x,y,z=L)I(x,y,z=0)1}|2=L2δT2k4N|F{G(x,y)}|2,
(1)
where I(x,y,z = 0) is the absorption contrast image, T(x,y) is the projected thickness of the object function, δT is the refractive index decrement of lung tissue, L is the ODD, k=kx2+ky2 is the transverse wavenumber in the (x,y) plane, N is the number of voids, and F is the Fourier transform with respect to x and y. I(x,y,z = 0) was recovered using SIPRA [19

19. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microscopy 206, 33–40 (2002). [CrossRef]

]:
I(x,y,z=0)=F1{F[I(x,y,z=L)]1+(δlTLμlT)k2},
(2)
where F−1 is the inverse Fourier transform with respect to x and y, and μT is the absorption coefficient of lung tissue. μT and δT were set to 54.7 m−1 and 3.99× 10−7(24 keV), respectively. The former was calculated using the National Institute of Standards and Technology database (NIST) [31

31. NIST, “National institute of standards and technology, physical reference data,” (2010)

] and the latter was calculated using [32

32. R. W. James, The Crystalline State: The Optical Principles of the Diffraction of X-Rays (Cornell University, 1965).

]:
δ=reλ22πini(f1)i,
(3)
where re is the classical electron radius, ni is the concentration of type i atoms per unit volume and f1 is the real part of the atomic scattering factor in the forward direction provided by NIST [31

31. NIST, “National institute of standards and technology, physical reference data,” (2010)

].

Fig. 1 Alveoli in lung tissue, modeled by voids randomly embedded within an absorbing medium, is illuminated by a coherent x-ray source and a PBX image is recorded a distance L from the exit surface of the object.

The definition of what is considered near-field depends on multiple factors. These can be succinctly summarized by the Fresnel number (NF) [33

33. J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase shifts,” Opt. Express 19, 12066–12073 (2011). [CrossRef] [PubMed]

]:
NF=aLλ|φ|max,
(4)
where a is a characteristic length scale of the object over which the intensity changes appreciably and |∇φ|max is the maximum phase gradient transverse to the direction of propagation. The near-field regime is defined to be at Lmax<aλ|φ|max.

The alveoli were modeled as spheres with radius R. To determine the 2D power spectrum of its PBX image, the following integral was solved:
|F{G˜(x,y,z)}|2=|G˜(x,y,z)exp(2πikr)dr|2,
(5)
where k = (kx, ky, kz) and r = (x, y, z) are 3D vectors in Fourier and real space, respectively. The shape function (x,y,z) = 1 for R ≤ 1 and (x,y,z) = 0 elsewhere. The evaluation of Eq. (5) is simplified by the radial symmetry of (x,y,z), which effectively reduces it to a one-dimensional problem. The integral in Eq. (5) can then be expressed analytically by first expanding then evaluating the exponential term as a Taylor series to give an exact solution [34

34. S. Sýkora, “K-space images of n-dimensional spheres and generalized sinc functions,” 2008, http://www.ebyte.it/library/docs/math07/SincN.html.

]:
|F{G(x,y,z)}|2=|V3(kR)2[sin(kR)kRcos(kR)]|2,
(6)
where k=|k|=kx2+ky2+kz2 and V=4πR33 is the volume of a sphere.

According to the Fourier slice theorem, the 2D power spectrum of a projected sphere is a slice of its 3D power spectrum through the origin. Since the 3D power spectrum is radially symmetric, the equation of the 2D power spectrum is identical to Eq. (6) but the z-coordinate is dropped and k is redefined as k=kx2+ky2.

The 2D version of Eq. (6) is combined with Eq. (1) to give:
|F{I(x,y,z=L)I(x,y,z=0)1}|2=L2δw2k4N|4πR3(kR)2[sin(kR)kRcos(kR)]|2.
(7)

Equation (7) assumes there is only one alveolus size whereas a realistic lung model would have a distribution of sizes typically with a coefficient of variation as large as 0.6; however, the error introduced in assuming an average alveolus size is small (< 5%) [35

35. L. Brancazio, G. Franz, E. Petsonk, and D. Frazer, “Lung area-volume models in relation to the recruitment-derecruitment of individual lung units,” Ann. Biomed. Eng. 29, 252–262 (2001). [CrossRef] [PubMed]

]. To determine the area under the power spectrum (PSArea), Eq. (7) is integrated over a select domain of radial frequencies, k⊥0 ≤ |k| ≤ kN, then ξ = kR is substituted to give:
PSArea=16π2L2δw2NRξ0/RξN/R|[sin(ξ)ξcos(ξ)]|2dξ.
(8)

The limits of the integral in Eq. (8) are dependent on R. However, under experimental conditions, the higher order peaks of the oscillatory function in the integral are suppressed by the detector point spread function (PSF) and penumbral blurring. Consequently, PSArea is dominated by the lowest order peak (see Fig. 2(a)). This means the limits can be fixed, and be independent of R, so long as it includes the first peak. The area under the first peak bounded by the minimas ξ = 0 and ξ = 4.493 (these are the first two solutions to ( sin(ξ)ξcos(ξ)=0) is 2.141. Hence, the integral is approximately 2.141, and Eq. (8) can be simplified to:
PSArea=34π2L2δw2NR.
(9)

There are additional factors that we have not entirely accounted for in deriving Eq. (9): penumbral blurring, detector PSF and asymmetrically shaped alveoli. If the imaging setup remains unchanged between recordings over time then the power spectra are equally affected by penumbral blurring and the detector PSF. While alveoli are not perfectly spherical, but resemble more like polyhedra, they are randomly positioned and oriented. Consequently, the derivations above is still valid and the only aspect altered is the solution for Eq. (8). The alveoli were modelled as spheres because a simple analytic solution for Eq. (8) exists. Unless these factors are accounted for, Eq. (9) cannot be directly used to measure VL. Instead, PSArea can be calibrated against known VL values as described in section 2.3. As well as accounting for the factors listed above, the calibration curve would also account for the alveoli changing shape during respiration.

Fig. 2 Lung speckle simulations. (a) Azimuthally averaged power spectra of a random distribution of 45 μm air-filled voids simulated within a 10 mm thick water-filled container with a volume packing density of 54%. Under ideal conditions (black), the power spectrum is a damped oscillatory function. To mimic our experimental conditions, ODD was increased from 0.1 m to 2 m, the PBX image was convolved with a Gaussian function, with FWHM=20 um, to simulate the PSF of a detector, and white noise was added, with a standard deviation (σnoise) of 0.1 intensity. This yielded an image with SNR ≈ 10, which was determined from taking the ratio of the mean intensity of the image and σnoise. This results in only one prominent peak in the power spectrum (red). (b) A plot displaying the PSArea of the same sample, but with mean void size of 130 μm, against ODD. (for details on the simulation of lung speckles, see section 2.1)

The relationship between VL and PSArea will depend on how N and R vary over time (t). That is, if N and R were parameterized to Ntn and Rtr, respectively, where n and r are constants, then,
VLPSArean+3rn+r
(10)

Having presented the theoretical background of near-field lung speckle and how it relates to VL in this section, we test this model by simulating lung tissue in section 2 and present the results and analysis in section 3. Also in section 3, we evaluate how accurately our model can measure changes in VL in a rabbit pup model. Some directions for future work are provided in section 4 and we conclude with section 5.

2. Methodology

2.1. Simulated lung tissue

To directly validate our theory, simulations were performed with conditions set similarly to that of imaging real lung tissue. The conditions for our simulations are summarized in Table 1. 11.8 mm × 11.8 mm projected lung thickness images, with pixel size 0.59μm, were simulated for two different sets of samples. The pixel size was chosen to adequately sample the phase map of the exit surface and propagated wavefield (that is, the maximum wavefield phase gradient is less than π2 radians per pixel). In the first set of samples, spherical voids of mean radius 65μm were randomly suspended in a rectangular water-filled volume of thickness 1mm. Several non-identical 1mm thick samples were generated and stacked to achieve different sample thicknesses. This was to simulate lung tissue with varying N while R was fixed. In the second set of samples, for each of the different mean sized voids, 5900 voids were suspended in a rectangular water-filled volume of thickness 10mm. In contrast to the first set, this was to simulate lung tissue with varying R while N was fixed. A maximum volume packing fraction of 75% was achieved from the largest mean size void (70μm).

Table 1. Parameters used for simulating PBX images of lung tissue.

table-icon
View This Table

2.2. Rabbit pup lungs

All imaging experiments took place in Hutch 3 of beamline 20B2 at the SPring-8 synchrotron in Japan [37

37. S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res., Sect. A 467–468, 682–685 (2001). [CrossRef]

] with a Si (111) double-bounce monochromator tuned to 24 keV. The x-ray source-to-sample distance was set at 210 m. All animal procedures were conducted in accordance with the protocol approved by the Monash University Animal Ethics Committee and the SPring-8 Animal Care and Use Committee. At 31 days of gestation, pregnant New Zealand white rabbits were anesthetized initially by an intravenous injection (Rapinovet [Schering-Plough Animal Health, USA]; 12 mg kg−1 bolus, 40 mg h−1 infusion) and anesthesia was maintained via isoflurane inhalation (1.5– 4%; Isoflurane, Delvet Pty. Ltd., Australia). Pups were delivered by caesarean section, sedated and surgically intubated. Pups in the first group (Group-Water, n = 15) were immersed in a water-filled cylindrical poly-methyl methacrylate container (plethysmograph) with their head out and the chamber sealed with a rubber diaphragm enclosing their necks. The plethysmograph is routinely used for VL measurement. At birth, the lungs of the newborn are completely liquid-filled and so imaging the lungs in their fluid-filled state was performed as soon as possible after the pup’s delivery. Two different detectors were used to acquire PBX images: (i) a large format (4000×2672 pixels) Hamamatsu CCD camera (C9300-124F21) with a tapered fiber optic (FOP) coupling the sensor to a 20 μm thick gadolinium oxysulfide (Gd2O2S : Tb+; P43) phosphor, and (ii) a tandem lens-coupled scientific-CMOS imaging sensor coupled to a 50 μm thick gadolinium oxysulfide (Gd2O2S : Tb+; P43) phosphor (pco.edge; 2560×2160 pixels). The effective pixel sizes were for these two detectors 16.2 μm, based on the taper ratio of 1.8:1, and 15.23 μm, respectively. Imaging sequences were respiratory gated, with timing controlled by a custom-designed pressure-controlled ventilator [38

38. M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5, T02002 (2010). [CrossRef]

] at a frame rate of 3 Hz, with a respiratory cycle of 2.5 s and exposure time of 40 ms. All animals were humanely killed at the end of each experiment via anesthetic overdose of Nembutal (Abbott Laboratories, USA, 100 mg/kg).

Pups in the second group (Group-Air, n=3) were initially used for studying the effect of different mechanical ventilation strategies on lung aeration and humanely killed via anesthetic overdose at the end of experiment. The deceased pups were supported in an upright position and connected to a pneumotach (flowmeter) to measure differential airflow at the mouth opening throughout each respiratory cycle. The pups were imaged in air under identical conditions to the first group imaged in water but at a frame rate of 10 Hz, using only the sCMOS camera.

The optimal ODD to image the pups was determined by modeling a 10 mm thick container packed with 130 μm sized voids. The size of the void and container thickness corresponds closely to that of an alveolus [39

39. S. B. Hooper, M. J. Kitchen, M. J. Wallace, N. Yagi, K. Uesugi, M. J. Morgan, C. Hall, K. K. W. Siu, I. M. Williams, M. Siew, S. C. Irvine, K. Pavlov, and R. A. Lewis, “Imaging lung aeration and lung liquid clearance at birth,” FASEB J. 21, 3329–3337 (2007). [CrossRef] [PubMed]

] and a rabbit pup’s lung, measured from a lateral PBX image of the chest, respectively. Using the steps and conditions as described in section 2.1, several PBX images were simulated from the model at different ODD. Figure 2(b) shows, based on Eq. (9), the near-field regime extends up to ∼3 m but not beyond 5 m. Lmax was computed to be 2.7 m. This is consistent with Fig. 2(b). PBX images of pups were therefore recorded at a propagation distance 3 m. While choosing propagation distances much less than 2.7 m would ensure the TIE approximation was well satisfied, the contrast-to-noise ratio of lung speckles would be small and weaken the correlation between VL and PSArea.

2.3. Image processing and analysis

Immediately before imaging each pup, multiple dark field (no x-rays) and flat field (x-rays; no sample) images were recorded then averaged to correct for the detector dark current and to normalize against the incident beam intensity, respectively. Nonlinear spatial distortions arising from the FOP camera, as a result of imperfect alignment of the fiber bundles at each end of the taper, were corrected by the use of Delaunay triangulation with bilinear interpolation [40

40. M. S. Islam, R. A. Lewis, K. Uesugi, and M. J. Kitchen, “A high precision recipe for correcting images distorted by a tapered fiber optic,” J. Instrum. 5, P09008 (2010). [CrossRef]

].

3. Results & analysis

3.1. Validation of theory using simulated lung tissue

Before validating our theory, simulated lung speckles were qualitatively compared with real lung speckles in real and reciprocal space. The intensity contrast of real speckles in Fig. 3(a) is lower than that of simulated speckles in Fig. 3(b). This is reflected in their azimuthally averaged power spectra, where for real lungs (see Fig. 3(c)) the peak is broader and weaker than that of simulated lungs (see Fig. 3(d)). We believe this could be due to incoherent scattering from the alveoli and in air between the object and detector, and that in real lungs, the alveoli are closely packed rather than randomly positioned as in our simulated lung tissue.

Fig. 3 3.24 mm × 3.24 mm PBX images of a ∼10 mm thick sample (a) of real and (b) simulated (mean diameter of 130 μm) lung tissue normalized against their phase retrieved absorption image. Their corresponding power spectra are shown in (c) and (d), respectively.

To verify the linear relationship between N and PSArea, PSArea was plotted against the sample thickness of simulated lung tissue from the first sample set at 1 m and 3 m ODD (see Fig. 4(a)). The sample thickness is essentially proportional to N as the total volume fraction was made approximately constant throughout the sample. At 3 m ODD, Fig. 4(a) shows N at first varies linearly with PSArea but begins to breakdown at N = 3000 as |∇φ|max increases, resulting in NF approaching and then being less than unity. Pogany et al. [41

41. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997). [CrossRef]

] showed that phase contrast decreases beyond the near-field region, which is reflected in reduction of the rate of increase of PSArea in Fig. 4(a) with respect to N. At 1 m ODD, NF remained >1 for all sample thickness, thus PSArea was proportional to N throughout. The dependance between R and PSArea was investigated by plotting PSArea against R of simulated lung tissue from the second sample set packed in a 10 mm thick container at 3 m ODD, as shown in Fig. 4(b). As predicted by Eq. (9), PSArea varies linearly with R even at this large ODD.

Fig. 4 Plots of PSArea of simulated lung tissue versus (a) number of voids, of size 130 μm (at 1 m and 3 m ODD), and (b) radius of voids with a maximum volume packing density of 75% (at 3 m), all at energy 24 keV.

3.2. Regional lung air volume measurements

A PSAreaVL calibration curve was generated from the 15 newborn rabbit pups in Group-Water. Since for each pup a PBX image of its lung in a fluid-filled state was recorded, PSArea was calibrated against absolute VL. Two cameras were used that had slightly dissimilar spatial frequency responses, or modulation transfer functions (MTFs). The MTF represents the camera’s ability to accurately preserve the amplitudes of each of the spatial frequencies in an image and this depends on the design of the camera. This resulted in two distinct calibration curves originating from the two cameras, which differed by a multiplicative factor of 3.35. This is likely due to the different phosphor thicknesses coupled to the two detectors. Thus, PSArea calculated from using the sCMOS camera was multiplied by 3.35 to align with the calibration curve attained from the FOP camera. While this highlights the need to produce a calibration curve for each of the detectors, a calibration curve would also be needed for other different experimental configurations. This includes different types of animals due to variability in lung morphology and imaging setups since the power spectrum of the speckle produced would be affected by factors such as beam characteristics. A direct plot of VL against PSArea showed a non-linear relationship. It was found that raising VL to the power 34 best linearized the curve based on the chi-square goodness-of-fit test.

Figure 5(a) shows the linearized PSAreaVL calibration curve. A weighted linear trend ( VL3/4=a×PSArea+b) was fitted with coefficients a = (1.345 ± 0.001) × 10−4 and b = (−6.84 ± 0.02) × 10−7. The uncertainty in VL3/4 was determined by measuring the standard deviation (σ) of the volume change over time of a water-only ROI against the ROI size (N × M pixel). A rational exponent function was fitted to give σ = 3.5×10−7 ×[N × M]3/4 +3.7×10−6 (see [15

15. A. F. T. Leong, A. Fouras, M. S. Islam, M. J. Wallace, S. B. Hooper, and M. J. Kitchen, “High spatiotemporal resolution measurement of regional lung air volumes from 2D phase contrast x-ray images,” Med. Phys. 40, 041909 (2013). [CrossRef] [PubMed]

, section IIE]). The same ROIs were used to measure σ of PSArea to determine its uncertainty. A PSAreaVL curve from the quadrants from one of the pups used for Fig. 5(a) is plotted in Fig. 5(b). This shows the PSAreaVL curve from the quadrants diverge from each other at large VL. This divergence was observed in other pups at different VL that depended on their total lung capacity. However, this degree of divergence is comparable to that of the points in Fig. 5(a).

Fig. 5 (a) A calibration curve between VL and the PSarea from PBX chest images divided into quadrants consisting of (a) a subset of points (∼ 10%) from multiple pups and (b) a single pup. A weighted linear fit was performed on (a) and is shown as a red line.

The phase gradient across the interface between water and tissue is considerably smaller than between air and tissue. When the PBX chest images of rabbit pups were divided by their absorption images to remove the absorption-induced intensity trends, the boundary of the skin was enhanced for pups imaged in air (see Fig. 6(a)) compared to those imaged in water (see Fig. 6(b)). Consequently, the azimuthally averaged power spectra of pups imaged in air showed a larger amplitude between frequencies 0 mm−1 and 2 mm−1 compared to that of pups imaged in water (see Fig. 6(c)). Beyond the frequency 2 mm−1, the shape of the power spectra were of similar magnitude, which was the range PSArea is calculated in. Thus, the calibration curve in Fig. 5(a) generated from pups imaged in water was used to measure the total change in VL of 3 pups imaged in air and then compared with the volume measured using a flowmeter (see Fig. 7(a)). A straight line was fitted to Fig. 7(a) with a gradient of 1.06 ±0.06 (R2= 0.978). This shows the calibration curve to be a highly accurate tool for determining the total change in VL without needing to immerse the animal in water. This gives us confidence for retrieving accurate regional volumetric information.

Fig. 6 A pair of 24 mm × 21 mm PCX chest images of a newborn rabbit pup in (a) a water-filled tube and in (b) air. (c) shows their respective power spectra after dividing by their absorption image reconstructed using phase retrieval.
Fig. 7 (a) A representation of the accuracy of using the calibration curve to measure the change in total VL of pups imaged in air in comparison to using a flowmeter. The red line is the line of best fit. (b) Regional lung volume measurements from a lung image sequence after partitioning the images into quadrants. Note that the lower quadrant curves have been offset by 0.1 ml to better distinguish them from the upper quadrant curves.

A quadrant-based analysis of a single pup imaged in air (see Fig. 7(b)) reveals non-uniform lung aeration. Figure 6(a) shows how the quadrants were delineated. As expected, the volumetric curves of each quadrant oscillates in phase with the mechanical ventilator. However, there are subtle but important physiological differences between quadrants. The upper left quadrant shows a lack of increase in tidal volume (i.e. volume of air entering the lungs) despite the increasing volume of air supplied by the ventilator, while the upper right quadrant is the only quadrant showing a significant increase in FRC. This quantification of non-uniform aeration using regional analysis is critical for assessing the efficacy of resuscitation strategies for newborn infants.

Fig. 8 14.6 mm ×14.6 mm regional volumetric maps from a mechanically ventilated rabbit pup in air ventilated using three different tidal volumes: (a) 0.12 ml, (b) 0.24 ml and (c) 0.35 ml. Map demonstrate the distribution of air when it enters the lung.

4. Discussion

There are three limitations that we foresee in our technique: (i) motion blur, (ii) the multi-valued relationship between PSArea and VL, and (iii) the minimum size of the region from which VL can be measured. The motion of the chest wall causes blurring in images; which results in a reduction in PSArea [22

22. J. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co., 2007).

]. The zero spatial frequency is however largely unchanged, which is why those techniques previously discussed that measure VL from the intensity of pixels/voxels are unaffected by motion blur. Reducing the exposure time can reduce the degree of motion blur but this coincides with a decrease in SNR. There are techniques that could measure and correct the degree of motion blur [42

42. J. Wang, G. Wang, and M. Jiang, “Blind deblurring of spiral CT images based on ENR and wiener filter,” J. x-ray sci. technol. 13, 49–60 (2005).

]. However, respiratory-induced motion blur is non-linear and difficult to correct. Motion blur can also be avoided through patient breath holds or taking measurements towards the end of inspiration/expiration when there is minimal chest motion.

The difference in the dependance of R and N with VL and PSArea means a dynamic relationship exists between VL and PSArea. The calibration curve in Fig. 5(a) showed PSArea was approximately proportional to VL3/4. From Eq. (10), the exponent ( 43) is close to 1, which indicates the lungs accommodated the flow of air by changing the number of alveoli. This is expected since we are imaging the lungs from an non-aerated state, hence new alveoli are being recruited as the lungs fill with air, thereby increasing N It was found, however, a PSAreaVL curve of a single breath showed subtle changes in the exponent (other than 43). This was masked in the calibration curve as it was made up of multiple single breath curves from pups mechanically ventilated with different positive inspiratory and positive end-expiratory pressures. This allowed a single calibration curve to approximate VL. At large volumes (≥10 ml/kg) however, a slight divergence in the calibration curve between quadrants appears (see Fig. 5(b)). This may either be the variable relationship between VL and PSArea or the breakdown of the TIE approximation. The average projected thickness between quadrants is different in that the apical region the lungs is thinner than that adjacent to the diaphragm. Thus, the TIE approximation may breakdown sooner for the lower quadrants at large volumes as the lungs increase in thickness.

When performing regional VL analysis, the region must be large enough to sufficiently sample the spatial frequencies of a power spectrum. As detector technology continues to improve, we expect that detectors with larger numbers of pixels producing lower noise levels coupled with better detector spatial resolution to be available. Hence we anticipate being able to measure VL in smaller ROIs in the future. Another major benefit of having lower noise level detectors is a reduced ODD. In our study, the ODD was set at 3 m to produce a sufficiently strong speckle contrast-to-noise ratio (CNR), but this distance was found to be at the edge of the near-field regime. To that end, PBX chest images were also recorded at 1.5 m ODD but were not included in this manuscript because VL weakly correlated with PSArea due to the weak CNR of the speckle. Thus, a lower noise level will allow PBX images to be recorded at shorter ODD while still having a short exposure time to minimize chest-induced motion blur.

Since our technique does not require the subject to be immersed in water, the much improved SNR allows significant reduction in the exposure time. The SNR of an image of a pup imaged in air was measured to be ∼ 1.4× larger than a pup imaged in water. The region chosen in calculating SNR was at the thickest (central) portion of the body below the lungs. This improvement in SNR will be important for translating this research for use with lower power laboratory-based x-ray machines [43

43. J. Ewald and T. Wilhein, “Source size characterization of a microfocus x-ray tube used for in-line phase-contrast imaging,” AIP Conf. Proc. 1365, 81–83 (2011). [CrossRef]

45

45. A. B. Garson III, E. W. Izaguirre, S. G. Price, and M. A. Anastasio, “Characterization of speckle in lung images acquired with a benchtop in-line x-ray phase-contrast system,” Phys. Med. Biol. 58, 4237 (2013). [CrossRef] [PubMed]

].

5. Conclusions

Appendix A: Power spectrum of a near-field 2D intensity map of a 3D random distribution of identical voids

Consider N voids randomly embedded in an absorbing medium, as shown in Fig. 1. We assume the path of the rays within the object is unperturbed, this is known as the projection approximation, and it allows the absorption (I(x,y,z = 0)) and phase shift (φ(x,y,z = 0)) induced by the object up to its exit surface to be considered projections through, respectively, the absorption index (β) and refractive index decrement (δ) with:
IA(x,y,z=0)=exp[2kβ(x,y,z)dz]
(11)
and
φ(x,y,z=0)=kδ(x,y,z)dz.
(12)
Here, k = 2π/λ is the wavenumber and λ is the wavelength of the source illuminating the object along the z direction. We assume the medium is composed of a single material of projected thickness T(x,y) along the z direction, and since any voids are non-absorbing (i.e. βvoid = δvoid = 0), Eqs. (11) and (12) reduce to:
I(x,y,z=0)=exp[2kβT(x,y)]
(13)
and
φ(x,y,z=0)=kδT(x,y),
(14)
where μ = 2 is the linear attenuation coefficient of the medium. At short distances (L) along the z direction from the exit surface of the object, the free space evolution of the intensity distribution can be described by the transport-of-intensity equation (TIE) [46

46. M. R. Teague, “Deterministic phase retrieval: a green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]

]:
kI(x,y,z)z=[I(x,y,z=0)φ(x,y,z=0)],
(15)
where =x^x+y^y.

The TIE assumes paraxial wave propagation (i.e. kkx2+ky2 where (kx, ky, kz) is the x, y, z components of the wavevector k). The validity of the TIE is given by the Fresnel number when, NF=aLλ|φ|max1 [33

33. J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase shifts,” Opt. Express 19, 12066–12073 (2011). [CrossRef] [PubMed]

]. Here, a is the characteristic length scale over which the object changes appreciably and |∇φ|max is the maximum absolute transverse phase gradient. This form of NF is very similar to another commonly used condition a2Lλ1, but this condition does not consider |∇φ|max. From the ray optics perspective, the degree of deflection of the rays depends on both a and |∇φ|max. The importance of this in the context of lung imaging is that NF can be overestimated if |∇φ|max > 1 radians per unit length was not considered, thus unknowingly imaging outside the near-field region.

To remove any dependency on absorption in Eq. (15), we begin with a finite difference approximation on the left hand side, dI(x,y)dzI(x,y,z=L)I(x,y,z=0)L, while the the right hand side (RHS) is expanded, with Eqs. (13) and (14) substituted into Eq. (15), to give:
I(x,y,z=L)I(x,y,z=0)1=Lδ[2T(x,y)μ|T(x,y)|2],
(16)
where 2=2x2+2y2 denotes the Laplacian, respectively, in the xy plane. The second, and only, term on the RHS of Eq. (16) is dependent on but can be neglected if μ|T(x,y)|2|2T(x,y)|. To explicitly show when this is true, we make the substitutions |∇T||ΔT|/a where |ΔT| is the maximum magnitude of the difference in projected thickness across the length a, and |2T||ΔT|/a2. This simplifies the inequality to μΔT(x,y) ≪ 1, that is, the object is weakly absorbing [47

47. L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960–2965 (2004). [CrossRef] [PubMed]

]. The lung tissue thickness in rabbit pups is typically on average 6 mm and at 24 keV, μ = 54.7 m−1 for lung tissue, thus μT(x,y)| ≤ 0.328. Consequently, the second term on the RHS of Eq. (16) can be ignored, hence the absolute square of the Fourier transform of Eq. (16) gives the power spectrum:
|F{I(x,y,z=L)I(x,y,z=0)1}2|=L2δ2k4|F{T(x,y)}|2.
(17)

Here we have made use of the Fourier derivative theorem to replace 2 with k2=(kx)2+(ky)2. Returning to our object of interest, for a random distribution of N air-filled voids, described by the object function (x,y,z) where (x,y,z) = 1 for x2+y2+z2R and (x,y,z) = 0 elsewhere, embedded in an absorbing medium (V(x,y,z) = 1 everywhere), the object can be expressed as a sum of convolutions:
T˜(x,y,z)=V(x,y,z)n=0Nδ(xxn)δ(yyn)δ(zzn)G˜(x,y,z),
(18)
where δ’s are the unit impulse functions and (xn,yn,zn) represents the random position of the nth void within the dimensions of the medium. For simplicity, the first term on the RHS of Eq. (18) will be dropped as it affects only the zero frequency in its corresponding power spectrum, which is unimportant for our analysis. Generally the random positions of the voids are unknown but the expectation value of the power spectrum of (x,y,z) can be evaluated without this information [48

48. J. H. Talbot, “Fraunhofer diffraction pattern of a random distribution of identical apertures in a plane screen,” Proc. Phys. Soc. 89, 1043–1053 (1966). [CrossRef]

]. With equal probability of finding a void within the medium, we have for the expectation value of the power spectrum of (x,y,z):
|F{T˜(x,y,z)}|2=[N2δ^(0,0,0)+N]|F{G˜(x,y,z)}|2,
(19)
where δ̂(0, 0, 0) has a value of unity at (0,0,0) and zero elsewhere (Kronecker delta). The expected value operator will be dropped for notational simplicity and the first term inside the square brackets of Eq. (19) will also be dropped as it only affects the zero frequency. It can then be seen that the power spectrum of the random distribution of voids is N times the power spectrum of a single void for k ≠ 0. This remains valid if the voids are randomly positioned and do not overlap with neighboring voids [48

48. J. H. Talbot, “Fraunhofer diffraction pattern of a random distribution of identical apertures in a plane screen,” Proc. Phys. Soc. 89, 1043–1053 (1966). [CrossRef]

].

To determine T(x,y) = z(x,y,z)dz, we make use of the Fourier slice theorem [49

49. D. Paganin, Coherent X-ray Optics (Oxford University, 2006). [CrossRef]

],
|F{T˜(x,y,z)}|2(kx,ky,0)=|F{zT˜(x,y,z)dz}|2(kx,ky)=|F{T(x,y)}|2(kx,ky),
(20)
with a similar conclusion made for |F{G(x,y)}|2. If (x,y,z) is azimuthally symmetric (i.e. spherical) then G(x,y) is independent of the orientation of (x,y,z). However, if (x,y,z) is not azimuthally symmetric, but randomly orientated, like the alveoli, then 〈|F{(x,y,z)}|2〉 is approximately azimuthally symmetric with |F{(x,y,z)}|2 being the azimuthal average of the power spectrum of a single void replicated azimuthally. Thus, Eq. (19) can be reduced to 2D,
|F{T(x,y)}|2=N|F{G(x,y)}|2.
(21)

This shows that even though increasing the number of voids results in an increase in the amount of overlap between them seen in the projected thickness image, the power spectrum only changes by a factor. This may seem counter-intuitive as the more voids there are the shorter the characteristic length scale of the image, which would shift the peaks in the power spectra to higher frequencies. But this is untrue as long as there is no physical overlap between neighboring voids and the positions of the voids are sufficiently random.

Finally, substituting Eq. (21) into Eq. (17) we arrive at the power spectrum of the near-field intensity map of a 3-dimensional random distribution of identical voids normalized against its absorption image:
|F{I(x,y,z=L)I(x,y,z=0)1}|2=L2δ2k4N|F{G(x,y)}|2.
(22)

Acknowledgments

The authors would like to thank Kentaro Uesugi and Naoto Yagi for assistance with the experiments. 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). 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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28.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49, 4335–4348 (2004). [CrossRef] [PubMed]

29.

J. García, Z. Zalevsky, P. García-Martínez, C. Ferreira, M. Teicher, and Y. Beiderman, “Three-dimensional mapping and range measurement by means of projected speckle patterns,” Appl. Opt. 47, 3032–3040 (2008). [CrossRef] [PubMed]

30.

E. R. Weibel, Morphometry of the Human Lung (Academic, 1963).

31.

NIST, “National institute of standards and technology, physical reference data,” (2010)

32.

R. W. James, The Crystalline State: The Optical Principles of the Diffraction of X-Rays (Cornell University, 1965).

33.

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase shifts,” Opt. Express 19, 12066–12073 (2011). [CrossRef] [PubMed]

34.

S. Sýkora, “K-space images of n-dimensional spheres and generalized sinc functions,” 2008, http://www.ebyte.it/library/docs/math07/SincN.html.

35.

L. Brancazio, G. Franz, E. Petsonk, and D. Frazer, “Lung area-volume models in relation to the recruitment-derecruitment of individual lung units,” Ann. Biomed. Eng. 29, 252–262 (2001). [CrossRef] [PubMed]

36.

D. S. Wilks, Statistical Methods in the Atmospheric Sciences (Elsevier Science, 2011).

37.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res., Sect. A 467–468, 682–685 (2001). [CrossRef]

38.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5, T02002 (2010). [CrossRef]

39.

S. B. Hooper, M. J. Kitchen, M. J. Wallace, N. Yagi, K. Uesugi, M. J. Morgan, C. Hall, K. K. W. Siu, I. M. Williams, M. Siew, S. C. Irvine, K. Pavlov, and R. A. Lewis, “Imaging lung aeration and lung liquid clearance at birth,” FASEB J. 21, 3329–3337 (2007). [CrossRef] [PubMed]

40.

M. S. Islam, R. A. Lewis, K. Uesugi, and M. J. Kitchen, “A high precision recipe for correcting images distorted by a tapered fiber optic,” J. Instrum. 5, P09008 (2010). [CrossRef]

41.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997). [CrossRef]

42.

J. Wang, G. Wang, and M. Jiang, “Blind deblurring of spiral CT images based on ENR and wiener filter,” J. x-ray sci. technol. 13, 49–60 (2005).

43.

J. Ewald and T. Wilhein, “Source size characterization of a microfocus x-ray tube used for in-line phase-contrast imaging,” AIP Conf. Proc. 1365, 81–83 (2011). [CrossRef]

44.

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode micro-focus source,” Appl. Phys. Lett. 91, 074104 (2007). [CrossRef]

45.

A. B. Garson III, E. W. Izaguirre, S. G. Price, and M. A. Anastasio, “Characterization of speckle in lung images acquired with a benchtop in-line x-ray phase-contrast system,” Phys. Med. Biol. 58, 4237 (2013). [CrossRef] [PubMed]

46.

M. R. Teague, “Deterministic phase retrieval: a green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]

47.

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960–2965 (2004). [CrossRef] [PubMed]

48.

J. H. Talbot, “Fraunhofer diffraction pattern of a random distribution of identical apertures in a plane screen,” Proc. Phys. Soc. 89, 1043–1053 (1966). [CrossRef]

49.

D. Paganin, Coherent X-ray Optics (Oxford University, 2006). [CrossRef]

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.6150) Imaging systems : Speckle imaging
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(290.5850) Scattering : Scattering, particles
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: August 28, 2013
Revised Manuscript: October 21, 2013
Manuscript Accepted: October 21, 2013
Published: November 6, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Andrew F. T. Leong, David M. Paganin, Stuart B. Hooper, Melissa L. Siew, and Marcus J. Kitchen, "Measurement of absolute regional lung air volumes from near-field x-ray speckles," Opt. Express 21, 27905-27923 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-27905


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  27. N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys.26, 2190–2193 (1999). [CrossRef] [PubMed]
  28. M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol.49, 4335–4348 (2004). [CrossRef] [PubMed]
  29. J. García, Z. Zalevsky, P. García-Martínez, C. Ferreira, M. Teicher, and Y. Beiderman, “Three-dimensional mapping and range measurement by means of projected speckle patterns,” Appl. Opt.47, 3032–3040 (2008). [CrossRef] [PubMed]
  30. E. R. Weibel, Morphometry of the Human Lung (Academic, 1963).
  31. NIST, “National institute of standards and technology, physical reference data,” (2010)
  32. R. W. James, The Crystalline State: The Optical Principles of the Diffraction of X-Rays (Cornell University, 1965).
  33. J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase shifts,” Opt. Express19, 12066–12073 (2011). [CrossRef] [PubMed]
  34. S. Sýkora, “K-space images of n-dimensional spheres and generalized sinc functions,” 2008, http://www.ebyte.it/library/docs/math07/SincN.html .
  35. L. Brancazio, G. Franz, E. Petsonk, and D. Frazer, “Lung area-volume models in relation to the recruitment-derecruitment of individual lung units,” Ann. Biomed. Eng.29, 252–262 (2001). [CrossRef] [PubMed]
  36. D. S. Wilks, Statistical Methods in the Atmospheric Sciences (Elsevier Science, 2011).
  37. S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res., Sect. A467–468, 682–685 (2001). [CrossRef]
  38. M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum.5, T02002 (2010). [CrossRef]
  39. S. B. Hooper, M. J. Kitchen, M. J. Wallace, N. Yagi, K. Uesugi, M. J. Morgan, C. Hall, K. K. W. Siu, I. M. Williams, M. Siew, S. C. Irvine, K. Pavlov, and R. A. Lewis, “Imaging lung aeration and lung liquid clearance at birth,” FASEB J.21, 3329–3337 (2007). [CrossRef] [PubMed]
  40. M. S. Islam, R. A. Lewis, K. Uesugi, and M. J. Kitchen, “A high precision recipe for correcting images distorted by a tapered fiber optic,” J. Instrum.5, P09008 (2010). [CrossRef]
  41. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum.68, 2774–2782 (1997). [CrossRef]
  42. J. Wang, G. Wang, and M. Jiang, “Blind deblurring of spiral CT images based on ENR and wiener filter,” J. x-ray sci. technol.13, 49–60 (2005).
  43. J. Ewald and T. Wilhein, “Source size characterization of a microfocus x-ray tube used for in-line phase-contrast imaging,” AIP Conf. Proc.1365, 81–83 (2011). [CrossRef]
  44. T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode micro-focus source,” Appl. Phys. Lett.91, 074104 (2007). [CrossRef]
  45. A. B. Garson, E. W. Izaguirre, S. G. Price, and M. A. Anastasio, “Characterization of speckle in lung images acquired with a benchtop in-line x-ray phase-contrast system,” Phys. Med. Biol.58, 4237 (2013). [CrossRef] [PubMed]
  46. M. R. Teague, “Deterministic phase retrieval: a green’s function solution,” J. Opt. Soc. Am.73, 1434–1441 (1983). [CrossRef]
  47. L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express12, 2960–2965 (2004). [CrossRef] [PubMed]
  48. J. H. Talbot, “Fraunhofer diffraction pattern of a random distribution of identical apertures in a plane screen,” Proc. Phys. Soc.89, 1043–1053 (1966). [CrossRef]
  49. D. Paganin, Coherent X-ray Optics (Oxford University, 2006). [CrossRef]

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