We present phase contrastx-ray tomography of functional soft tissue within the bony cochlear capsule of mice, carried out at laboratory microfocus sources with well-matched source, detector, geometry, and reconstruction algorithms at spatial resolutions down to 2 μm. Contrast, data quality and resolution enable the visualization of thin membranes and nerve fibers as well as automated segmentation of surrounding bone. By complementing synchrotron radiation imaging techniques, a broad range of biomedical applications becomes possible as demonstrated for optogenetic cochlear implant research.

The cochlea is the auditory end organ in the inner ear designed to encode sound into neuronal activity. Detailed knowledge about the delicate and complex cochlea morphology is necessary to understand malformations caused by genetic defects, improve the treatment of hearing diseases, and optimize the design of cochlear implants.2,3 Optogenetic stimulation of spiral ganglion neurons (SGNs) using light-gated ion channels is a promising approach to overcome the limited sound frequency resolution of current cochlear implants.1 In this research, a central challenge is to determine the position and orientation of the light emitter(s) (e.g., an optical fiber) relative to the spiral ganglion. Therefore, three dimensional (3D) visualization with sufficient contrast and resolution for functional soft tissues is required. Since cochlea morphology comprises soft tissue within surrounding bone, most methods to determine its 3D structure, such as classical histology,4 optical coherence tomography,5 orthogonal-plane optical fluorescence6 and magnetic resonance imaging,7 require invasive sample preparation (e.g., slicing,4 staining,4,6,7 dehydration,4 opening the bony cochlea wall5) or lack sufficient contrast or spatial resolution. Specific advantages of x-ray imaging on the other hand concern the combination of high resolution and compatibility with unsliced, unstained, and hydrated specimens. Microtomography based on x-ray absorption contrast has been used for non-destructive 3D structure determination of human cochleae.2,10–12 For small scale soft tissues, e.g., within the mouse cochlea, absorption is weak and the interaction with x-rays results predominantly in a shifted phase. Therefore, coherent x-ray methods8,9,13 exploiting the phase shift induced by the sample are particularly well suited for cochlea imaging, as shown by recent synchrotron studies.3,14,15 Nevertheless, these studies rely on the (limited) availability of third generation synchrotron facilities, inhibiting a routine use in the laboratory, which is needed for long-term biomedical research. Even though grating-based imaging enables phase contrast with laboratory sources,18–22 the reported resolution range above 30 μm is not sufficient to identify thin membranes or nerve fibers within the cochlea.

Here, we present 3D imaging of functional mouse cochlear soft tissue within surrounding bone at high resolution down to 2 μm using compact laboratory microfocus x-ray sources. The method is based on cone-beam in-line phase contrast tomography9 and a fast Fourier-based phase reconstruction procedure.16 Compared to absorption imaging, in-line phase contrast enables increased spatial resolution, along with higher contrast for low absorbing features due to edge-enhancement.8,9,23,24 However, tomographic reconstruction of phase contrast projection images results in disturbing edge-artifacts in the 3D data, inhibiting automatic segmentation. To overcome this limitation, we apply a phase retrieval algorithm which removes those artifacts and improves the signal-to-noise ratio.16 As a result, the obtained data allow automatic histogram-based segmentation between bone and soft tissue, in contrast to previously reported synchrotron-based phase contrast studies of the cochlea which skipped the phase reconstruction step.3,15 This enables fast and convenient data visualization, which is a key requisite for batch analysis of several cochleae, e.g., as part of a biomedical study.

Based on the transport of intensity equation (TIE), the measured intensity distribution Izθ(x,y) at small propagation distances z for an object with slowly varying absorption in x and y directions can be expressed as26–28 

Izθ(x,y)=I0θ(x,y)[1zλ2π2ϕθ(x,y)],
(1)

where θ is the projection angle and λ is the x-ray wavelength. ϕθ(x,y) and I0θ(x,y) denote the phase function and intensity distribution right behind the object. For low-absorbing objects, the modified Bronnikov algorithm (MBA)29,30 was proposed to obtain an approximation ϕ̃θ(x,y) of the phase function without the knowledge of I0θ(x,y) using a Fourier filter of the form q(ξ,η)=1/(ξ2+η2+α), where ξ and η are the spatial frequencies and α is an absorption-dependent regularization parameter.30 However, the bony capsule of the cochlea gives rise to strong absorption which results in blurred phase reconstructions using the MBA.25 We obtain superior image quality by subsequent reconstruction of the amplitude I0θ(x,y)=exp[μ(x,y,z)]dL right behind the object using Eq. (1)

I0θ(x,y)=Izθ(x,y)1γ2ϕ̃θ(x,y),
(2)

known as Bronnikov Aided Correction (BAC),16 where zλ/2π was replaced by the α-dependent control parameter γ.16 Cone-beam filtered back projection using I0θ(x,y) then yields the attenuation coefficients μ(x, y, z) in 3D.17 

We first discuss results obtained at a solid target microfocus source (17.5 keV characteristic photon energy, 60 kVp, 4.2 W e-beam power, 6 μm source size (FWHM)).17 Several mouse cochleae were investigated as part of an optogenetic study. In essence, prior to the imaging experiment, the spiral ganglion neurons (genetically rendered sensitive to light) of each cochlea were stimulated by an optical fiber which was inserted through a small window in the bony cochlear capsule (cochleostomy) and brainstem responses were recorded.1 After the optogenetic experiment, the fiber was fixed in place with dental cement and the cochlea was carefully dissected from the skull and chemically fixed. Phase contrast images at 916 projection angles distributed among 183° were obtained in a conventional cone-beam geometry (Fig. 3(a)). The sample was placed at a distance z1=78mm behind the source and the detector was placed at a distance z2=116mm behind the sample. Geometric magnification M=1+z2/z1 resulted in an effective propagation distance zeff=z1z2/(z1+z2) and an effective pixel size peff=P/M=2.6μm, with detector pixel size P.17 Figure 1(a) shows a slice through the reconstructed 3D volume revealing several functional structures. Notably, resolution and contrast is high enough to identify nerve tissue as well as the basilar membrane and the thin Reissner Membrane, which allows to locate all three cavities (scala tympani, scala vestibuli, scala media). Importantly, due to phase reconstruction, no edge-artifacts disturb the data quality enabling threshold-based automated segmentation of bony structures. The 3D visualisation of bone, basilar membrane, Reissner's membrane, and Rosenthal's canal (Fig. 2(a)) allows to readily evaluate the positioning of the optical fiber in the investigated cochleae (Figs. 2(c)–2(e)). Fig. 2(b) shows how nerve fibers of the spiral ganglion reach out towards the basilar membrane where the organ of Corti and the sensory hair cells are located (not visible in the data). The position of the optical fiber relative to the tonotopic map of the cochlea was measured using such visualisations, complementing the analysis of brainstem responses to light stimulation.

FIG. 1.

(a) Slice through the reconstructed 3D volume of a mouse cochlea with basilar membrane (BM), Reissner's membrane (RM), scala tympani (ST), scala vestibuli (SV), scala media (SM), spiral ligament (SL), stria vascularis (STV), spiral ganglion (SG) within Rosenthal's canal (RC), nerve fibers (NF), helicotrema (H), and surrounding bone (B). (b) Tomogram obtained within 30 min exposure time. The fast acquisition enables observation of soft tissue structures in the region of the organ of Corti and the tectorial membrane (dashed circles). (c) The same tomogram was repeated after 1 h. Due to dehydration of the cochlear cavities, these structures are not observed anymore (dashed circles) and Reissner's membrane ruptured at the basal turn. Scale bars: 200 μm.

FIG. 1.

(a) Slice through the reconstructed 3D volume of a mouse cochlea with basilar membrane (BM), Reissner's membrane (RM), scala tympani (ST), scala vestibuli (SV), scala media (SM), spiral ligament (SL), stria vascularis (STV), spiral ganglion (SG) within Rosenthal's canal (RC), nerve fibers (NF), helicotrema (H), and surrounding bone (B). (b) Tomogram obtained within 30 min exposure time. The fast acquisition enables observation of soft tissue structures in the region of the organ of Corti and the tectorial membrane (dashed circles). (c) The same tomogram was repeated after 1 h. Due to dehydration of the cochlear cavities, these structures are not observed anymore (dashed circles) and Reissner's membrane ruptured at the basal turn. Scale bars: 200 μm.

Close modal
FIG. 2.

(a) 3D visualisation of a mouse cochlea with bone (brown, semi-transparent), basilar membrane (green), Reissner's membrane (yellow), Rosenthal's canal (blue), and optical fiber (gray).(b) Magnified view showing nerve tissue (orange). The nerve fibers of the spiral ganglion pass out between the two layers of the lamina spiralis ossea (bottom layer shown in magenta). (c)-(e) Position and orientation of the optical fiber relative to the spiral ganglion in Rosenthal's canal for three different investigated cochleae. Scale bars: (a) 800 μm, (b) 400 μm, (c) 1 mm.

FIG. 2.

(a) 3D visualisation of a mouse cochlea with bone (brown, semi-transparent), basilar membrane (green), Reissner's membrane (yellow), Rosenthal's canal (blue), and optical fiber (gray).(b) Magnified view showing nerve tissue (orange). The nerve fibers of the spiral ganglion pass out between the two layers of the lamina spiralis ossea (bottom layer shown in magenta). (c)-(e) Position and orientation of the optical fiber relative to the spiral ganglion in Rosenthal's canal for three different investigated cochleae. Scale bars: (a) 800 μm, (b) 400 μm, (c) 1 mm.

Close modal

Drying of the liquid-filled cavities and the attached soft tissue is difficult to avoid during long tomographic acquisitions (typically 5 h) using the solid target source. This may also be the reason why we did not observe the organ of Corti so far. To this end, we demonstrate a substantial reduction in accumulation time, using high-brilliance liquid-metal-jet x-ray source technology31–33 (9.25 keV characteristic photon energy, 60 kVp, 40 W e-beam power, asymmetric spot size of about FWHMsrc,h.=4μm and FWHMsrc,v.=7μm) and a fast complimentary metal–oxide–semiconductor detector.17 A tomogram with 2 μm voxel size (z1=77mm,z2=168mm) which reveals soft tissue structures in the region of the organ of Corti and the tectorial membrane (Fig. 1(b)) was recorded within 30 min. A subsequent replicate of the measurement 1 h later does not show these structures (Fig. 1(c)). Moreover, Reissner's membrane exhibits a rupture at the basal turn. These observations illustrate the advantage of fast tomography using a liquid-metal-jet source and motivate future work directed at improved structure preservation using agarose embedding. So far, the low photon energy of the current liquid-metal source inhibits embedding. However, a 24 keV metal-jet has recently been developed,34 which may further extend the potential of 3D cochlea imaging with short exposure times using compact laboratory sources.

Finally, spatial resolution can be further optimized. The variance of the imaging system point-spread function (PSF) in the sample plane can be written as σsys2=(M1)2M2σsrc2+M2σdet2, where σsrc and σdet indicate the standard deviation of the source intensity and detector PSF, respectively.35,36 Hence, spatial resolution is dominated by the lateral source dimensions for high geometric magnifications (σsysσsrc if M, Fig. 3(a)) and by the detector PSF for low geometric magnifications (σsysσdet if M → 1, Fig. 3(b)). By using M = 1.03 and a high-resolution detector system17 instead (Fig. 3(b)), we achieve spatial resolutions well below the source size as shown for an absorbing test structure in Figs. 3(c)–3(f). Importantly, phase contrast can also be exploited in this geometry, due to the symmetry of zeff with respect to z1 and z2. In fact, the parallel beam geometry employed in most synchrotron phase contrast experiments (from early demonstrations8,13,23 to recent cochlea studies3,15) corresponds to the limit z1z2. Nonetheless, in contrast to synchrotron instrumentation, for compact microfocus setups z1 and z2 can continuously be changed, including an optimal setting with Mopt=1+c2,c=σdet/σsrc, where the imaging system PSF

σsys,opt=(σsrc2σdet2)/(σsrc2+σdet2)
(3)

is simultaneously below both the lateral source dimensions and the detector PSF35,36

σsys,optσsrc=c2c2+1<1,σsys,optσdet=1c2+1<1.
(4)

Despite these experimental design options, the vast majority of in-line phase contrast tomography work at compact sources is based on z1<z2 (conventional geometry), while only few authors have previously used z2<z1,37 which we denote as inverse geometry. The fact that the inverse geometry has not been exploited for tomography of biological samples may be due to the reduced efficiency of high-resolution scintillator-based detectors. We show that combination with a high-brilliance liquid-jet source renders this geometry a promising approach for phase contrast imaging applications. The detector PSF was measured to about FWHMdet=22ln2σdet=3μm resulting in optimal magnifications Mopt,h.=1.56 and Mopt,v.=1.18 for the vertical and horizontal direction, respectively (assymetric x-ray spot). Phase contrast images of mouse cochlea were recorded at an intermediate value of M = 1.23 (z1=77mm,z2=18mm,peff=0.6μm) as a trade-off between vertical and horizontal directions. The superior spatial resolution of phase contrast imaging in the inverse geometry is illustrated in Fig. 3 for 10 μm polystyrene spheres. Consequently, phase contrast tomography of mouse cochlea in the inverse geometry exhibits higher spatial resolution and reveals smaller features (e.g., better resolution of nerve fibers, Figs. 3(i) and 3(j)) when compared to conventional geometry results (z1=77mm,z2=168mm,M=3.2,peff=2μm). The 3D (half-period) resolution for the high resolution setup is about 1.75 μm (determined by the azimuthally averaged power spectral density, corresponding to three voxels).

FIG. 3.

(a) Conventional and (b) inverse geometry with sample (S), x-ray source (X), and detector (D). A high resolution detector system is used in (b) (scintillator (SC), objective (O), mirror (M), optical CCD). (c) and (f) Absorbing test structure (4 μm line period along the direction corresponding to a source size of 7 μm (FWHM)) recorded with (c) source-size limited (z1=72mm,z2=418mm,peff=0.96μm) and (f) detector limited (z1=95mm,z2=3mm,peff=0.72μm) spatial resolution. (d) and (g) Phase contrast image of 10 μm polystyrene spheres along with (e) and (h) reconstructed amplitudes (BAC) for conventional (z1=70mm,z2=1930mm,peff=0.7μm) and inverse (z1=65mm,z2=20mm,peff=0.57μm) geometry, respectively. (i) and (j) 3D cochlea imaging (region of interest) revealing scala tympani (ST), basilar membrane (BM), scala vestibuli et media (SVM), and spiral ganglion (SG) for (i) conventional and (j) inverse geometry. Finer nerve fibers are resolved in the inverse geometry (see inset). Scale bars: 200 μm and 20 μm (inset).

FIG. 3.

(a) Conventional and (b) inverse geometry with sample (S), x-ray source (X), and detector (D). A high resolution detector system is used in (b) (scintillator (SC), objective (O), mirror (M), optical CCD). (c) and (f) Absorbing test structure (4 μm line period along the direction corresponding to a source size of 7 μm (FWHM)) recorded with (c) source-size limited (z1=72mm,z2=418mm,peff=0.96μm) and (f) detector limited (z1=95mm,z2=3mm,peff=0.72μm) spatial resolution. (d) and (g) Phase contrast image of 10 μm polystyrene spheres along with (e) and (h) reconstructed amplitudes (BAC) for conventional (z1=70mm,z2=1930mm,peff=0.7μm) and inverse (z1=65mm,z2=20mm,peff=0.57μm) geometry, respectively. (i) and (j) 3D cochlea imaging (region of interest) revealing scala tympani (ST), basilar membrane (BM), scala vestibuli et media (SVM), and spiral ganglion (SG) for (i) conventional and (j) inverse geometry. Finer nerve fibers are resolved in the inverse geometry (see inset). Scale bars: 200 μm and 20 μm (inset).

Close modal

The results demonstrate that functional soft tissue within surrounding bone can be imaged in 3D with unprecedented quality at compact laboratory microfocus x-ray sources using in-line phase contrast, as demonstrated for mouse cochleae which constitute particularly challenging samples. Phase retrieval yields data quality which allows automatic histogram-based segmentation between bone and soft tissue. This enables fast and convenient data visualization as required by biomedical studies and demonstrated here for cochlear implant research. The advantage of using a liquid-metal-jet source is evident both in terms of short accumulation times in conventional geometry as well as for high spatial resolutions down to 2 μm in an optimized (inverse) geometry. The presented approach can be applied to a broad range of biomedical problems, where 3D data with high resolution and contrast for soft tissue are required on a routine laboratory basis.

We thank André Beerlink for configuration of the high-resolution detector system and Christian Olendrowitz for scintillator commissioning and related measurements. The work was supported by the excellence cluster 172 Molecular Physiology of the Brain/Microscopy at the Nanometer Range and the Collaborative Research Center 755 Nanoscale Photonic Imaging of the German science foundation (DFG), and the Bernstein Focus for Neurotechnology (01GQ0810).

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Supplementary Material