Lucas Lavenir
email: lucas.lavenir@lirmm.fr

João Cavalcanti Santos

Nabil Zemiti
email: nabil.zemiti@lirmm.fr

Fr éd éric Venail Akil Kaderbay
email: kaderbay@chu-montpellier.fr

Frederic Venail
email: frederic.venail@inserm.fr

Philippe Poignet
email: philippe.poignet@lirmm.fr

Jo Ão

C Santos

Miniaturized endoscopic 2D US transducer for volumetric ultrasound imaging of the auditory system

Keywords: Auditory system, ultrasound imaging, volumetric reconstruction. I

est destinée au dépôt

estimated the prevalence of hearing loss to more than 1.5 billion people [START_REF]World report on hearing[END_REF]. Since this number is expected to rise over 2.5 billion by 2050, hearing impairment has been elevated to a major public health issue. In parallel with the prevention of hearing loss, WHO consequently promotes the development of low-cost technologies for facilitating diagnosis and treatment, especially in low-and middle-income countries [START_REF] Davis | Hearing loss: rising prevalence and impact[END_REF].

Overall, hearing loss can be categorized as either conductive or sensorineural [START_REF] Cunningham | Hearing loss in adults[END_REF]. The first one refers to pathologies that hinder sound transmission through the eardrum or the ossicular chain to the inner ear while the latter is typically responsible for permanent hearing impairment and results from a dysfunction of the cochlear sensory cells or the hearing nerve.

Despite the increased use of magnetic resonant imaging and computed tomography (CT) for the study of the temporal bone [START_REF] Juliano | Imaging review of the temporal bone: part i. anatomy and inflammatory and neoplastic processes[END_REF], such modalities lack resolution for accurate identification of middle and inner ear pathologies. In some conductive hearing loss cases, the accurate diagnosis can only be made during a surgical exploratory tympanotomy [START_REF] Robertson | Findings at exploratory tympanotomy for conductive hearing loss[END_REF], which allows for a direct visualization of the tympanic cavity and the auditory ossicles [START_REF] Paparella | Exploratory tympanotomy revisited[END_REF]. To overcome those spatial resolution issues, conebeam CT (CBCT) has emerged in the ear, nose, and throat (ENT) area, providing an isotropic spatial resolution up to 0.150 mm, and is now commonly used for postoperative verification of cochlear implantation [START_REF] Miracle | Conebeam ct of the head and neck, part 2: clinical applications[END_REF]. However, the high investment cost of the apparatus, the radiation hazards and the inability to provide functional information significantly limit the application of CBCT as a cost-effective modality for early diagnosis. From this perspective, optical coherence tomography (OCT) appears as a promising alternative. OCT is a safe modality based on white light interferometry that provides real-time rendering with a spatial resolution of a few tens of microns. Recently, it has gained interest for the imaging of both the middle [START_REF] Macdougall | Optical coherence tomography system requirements for clinical diagnostic middle ear imaging[END_REF] and inner ears [START_REF] Gurbani | Robot-assisted three-dimensional registration for cochlear implant surgery using a common-path swept-source optical coherence tomography probe[END_REF], but its limited penetration depth in scattering media impedes its application for intraoperative imaging of the auditory system [START_REF] Bance | New imaging modalities in otology[END_REF].

Although also limited in depth, ultrasound (US) imaging allows to image further than OCT and was even shown to evaluate the functionality of the ossicles through the eardrum [START_REF] Rainsbury | High frequency ex vivo ultrasound imaging of the middle ear to show simulated ossicular pathology[END_REF]. Besides, depending on the applied frequency, US imaging is capable to achieve sufficient spatial resolution to visualize anatomical landmarks of the ear that range from the ossicular chain [START_REF] Rainsbury | High frequency ex vivo ultrasound imaging of the middle ear to show simulated ossicular pathology[END_REF], [START_REF] Landry | Real-time imaging of in-vitro human middle ear using high frequency ultrasound[END_REF] to cochlear structures such as the basilar membrane [START_REF] Brown | High-frequency ex vivo ultrasound imaging of the auditory system[END_REF], [START_REF] Landry | Real-time intracochlear imaging of automated cochlear implant insertions in whole decalcified cadaver cochleas using ultrasound[END_REF]. Combined with the low-cost, ease of use and safety of the corresponding imaging systems, these features make US an appropriate modality for initial contact with the patient. Yet, the large housing of commercially available US transducers makes the use of US for the imaging of the ear inapplicable in clinical practice since the auditory system is deeply anchored in the temporal bone. In fact, studies that reported ex vivo imaging of the middle ear actually required prior removal of the external auditory canal (EAC) [START_REF] Rainsbury | High frequency ex vivo ultrasound imaging of the middle ear to show simulated ossicular pathology[END_REF], [START_REF] Landry | Real-time imaging of in-vitro human middle ear using high frequency ultrasound[END_REF].

In this paper, we introduce a new miniaturized endoscopic 2D US transducer whose dimensions are compatible with the EAC. Since the anatomy of the middle and inner ears is one of the most complex of the human body, conventional 2D US imaging may actually result in a mental workload for the medical practitioner who must picture the organ of interest from various planar images. For instance, the operator in [START_REF] Rainsbury | High frequency ex vivo ultrasound imaging of the middle ear to show simulated ossicular pathology[END_REF] had to visualize cross-sections from different angles to construct a mental representation of the imaged structures. A proper solution then is to resort to three-dimensional (3D) US imaging, which provides a better understanding of the anatomy and facilitates the decision-making process. Various technologies based on 2D transducers are reported in the literature, where the main dichotomy lies in the use of position sensing. Sensorless techniques, such as mosaicing, rely on the sole intrinsic contents of the acquired images to deduce their global alignement. Best results, however, come with a high computational cost due to the use of specific similarity measures [START_REF] Wachinger | Three-dimensional ultrasound mosaicing[END_REF]. On the contrary, sensor-based techniques consist in reconstructing a volume based on the relative pose of collected data. In freehand US, the localization of each B-scan is achieved using a tracking device, which leads to inaccuracies and a high computational cost in reconstruction due to the sparsity of acquired data [START_REF] Solberg | Freehand 3d ultrasound reconstruction algorithms-a review[END_REF]. In scan-conversion US, frame acquisitions are conversely performed using a motor stage that includes an encoder. By directly refering to the geometry of the probe, this technique thus benefits from a high degree of precision as well as a short reconstruction time, both of which are of interest for diagnosis purposes [START_REF] Duan | Fast interpolation algorithms for real-time threedimensional cardiac ultrasound[END_REF]- [START_REF] Pospisil | 4-d x 3-d ultrasound: real-time scan conversion, filtering, and display of displacement vectors with a motorized curvilinear transducer[END_REF]. Synthetic aperture has also been studied for 3D US using mechanically translated [START_REF] Andresen | Precise time-of-flight calculation for 3-d synthetic aperture focusing[END_REF] or rotated [START_REF] Nikolov | Three-dimensional real-time synthetic aperture imaging using a rotating phased array transducer[END_REF] 2D transducers since it increases both the resolution and acquisition rate. Yet, this method requires to access RF signals from the individual transducer elements, which is difficult to fulfill on commercial devices and may necessitate dedicated equipment [START_REF] Jensen | Ultrasound research scanner for real-time synthetic aperture data acquisition[END_REF]. In this paper, we present a new imaging platform that takes advantages of our newly miniaturized endoscopic 2D US transducer to provide minimally invasive volumetric US imaging of the auditory system using scan-conversion. The actuation of the probe is based on an existing robotic system called RobOtol that is dedicated to middle ear surgery. As for robot-assisted 3D US imaging [START_REF] Monfaredi | Robot-assisted ultrasound imaging: Overview and development of a parallel telerobotic system[END_REF], [START_REF] Salcudean | Robot-assisted medical imaging: A review[END_REF], the use of such a system enables both the precise and repetable positioning of the probe, which is of particular interest for the insertion along the EAC.

Since it is meant for medical purposes, we consider of primary importance to validate both quantitatively and qualitatively the proposed acquisition setup. As a result, this study additionally incorporates a two-fold validation stage. Firstly, we focus on assessing the correctness of the reconstructed volume's geometry compared to the reality of acquisition using a dedicated phantom. Beyond the lack of a clear methodology in the literature, a significant difficulty for quantifying the reconstruction error is due to the unusual small dimensions of the imaging probe and, thereby, of the corresponding acquisition window. To adress this point, a new evaluation protocol is presented in this work as well. It consists in the automatic detection and registration of pairs of lines of a custom 3D-printed cross-wire phantom from US and micro-CT acquisitions, the latter being the reference model. The accuracy of the reconstruction procedure is then computed as the mean distance between the registered sets of lines. Secondly, we demonstrate the clinical potential of our system by performing ex vivo acquisitions with a complete anatomical context on a cadaveric head.

The contributions of this paper lie in both the carrying out and validation of minimally invasive 3D US imaging of the auditory system using a miniaturized endoscopic 2D US transducer whose dimensions are compatible with the EAC. To our knowledge, this is the first time that 3D US imaging of the auditory system is reported without prior deterioration of the EAC. Although our imaging platform has already been introduced in [START_REF] Santos | Geometric calibration of a new miniaturized endoscopic ultrasound probe[END_REF], this previous study only addressed the issue of calibrating such a miniaturized US transducer. In this paper, we focus on a detailed description of the system and its applicability for medical purposes with a special attention on the validation aspect.

II. MATERIALS AND METHODS

A. Imaging platform

The imaging platform is based on a custom designed 2D US transducer (Fig. 1), whose fabrication was subcontracted to Vermon, a world leader in composite piezoelectric transducers. The dimensions of the distal part were optimized to enable adequate access to the middle ear by raising a tympanomeatal flap. This procedure, which is routinely performed for exploratory tympanotomy [START_REF] Robertson | Findings at exploratory tympanotomy for conductive hearing loss[END_REF], [START_REF] Paparella | Exploratory tympanotomy revisited[END_REF], consists in elevating the annulus in order to expose the tympanic cavity. To preserve the functionality of the ossicular chain while running surgical instruments and endoscopes into the EAC, the maximum allowable diameter was set to 4 mm [START_REF] Miroir | Design of a robotic system for minimally invasive surgery of the middle ear[END_REF]. Thereby, the manufactured probe consists in a 4 mm diameter 24 elements curved array transducer with a field of view of 47.55°and a center frequency of 18 MHz ± 10%. The center frequency value was motivated by the fact that a compromise between compactness and spatial resolution had necessarily to be done. From that perspective, a center frequency of 18 MHz allows to operate at frequencies that provide a spatial resolution of a few tens of microns while remaining close to the frequency range of the 5-14 MHz US transducer we used in a previous study [START_REF] Lavenir | Hfus imaging of the cochlea: A feasibility study for anatomical identification by registration with microct[END_REF] to prove the feasability of using US for imaging an ex vivo human cochlea. The probe is also compatible with the SonixTouch® Ultrasound System (BK Medical formerly Ultrasonix, Peabody, United States) that provides real-time rendering by online conversion of the acquired raw data into 2D B-mode images.

Regarding the actuation of the US transducer, we used a RobOtol system (Collin Medical, Bagneux, France), a commercial 6 degrees of freedom robotic arm that was specifically designed for middle ear surgery [START_REF] Miroir | Robotol: from design to evaluation of a robot for middle ear surgery[END_REF]. As depicted in Fig. 2, the probe was inserted into the optical system holder and secured with an additional mechanical assembly which was fabricated by means of additive manufacturing with polyactic acid. Since RobOtol is a teleoperated system, a master joystick allowed the operator to adapt the pose of the probe tip in order to adjust the imaging plane. Once the pose was estimated to be satisfying, the transducer was rotated around the distal axis of the arm to collect a set of B-scans. The rotational speed and the frame rate were respectively set to 1°/s and 10 images per second, leading to an angular resolution of 0.1°. The frequency of the probe was also set to 20 MHz to achieve high spatial resolution. All the acquired 2D frames were transferred to a workstation using Ethernet through the OpenIGTLink protocol and then stacked in a DICOM file for further processing. In the following sections, we refer to the stack of acquired B-scans as the pre-scan converted image I pre and the corresponding reconstructed volume as the post-scan converted image I post .

B. Reconstruction procedure

Scan-conversion (SC) consists in resampling the collected B-scans on a regular Cartesian grid using coordinate system transformation derived from the geometry of the probe. In summary, the reconstruction procedure can be summarized in three steps [START_REF] Duan | Fast interpolation algorithms for real-time threedimensional cardiac ultrasound[END_REF]. Firstly, for each sample of the volume to be reconstructed, one must compute the corresponding point in the transducer coordinate system thanks to backward mapping. Secondly, since the resulting point may fall at non-grid location, interpolation is then necessary to estimate its associated gray value from the pre-scan converted data. Finally, the interpolated intensity value is assigned to the studied sample.

Despite a clear outline of the procedure, SC lacks methodology and remains cumbersome to perform. Reported implementations are actually transducer specific [START_REF] Pospisil | 4-d x 3-d ultrasound: real-time scan conversion, filtering, and display of displacement vectors with a motorized curvilinear transducer[END_REF] as, for instance, there is no systematic and automatic way to derive the coordinate system transformation regardless of the used probe. Thanks to our expertise as roboticists, we propose in the following sections an adequate method for implementing SC that is not only meant to be straightforward for the nonspecialist reader but also can be extended to any transducer geometry.

Forward mapping: The objective of forward mapping is to allow for the conversion of the transducer coordinates (x I , y I , ϕ) into the world coordinates (x, y, z). x I and y I denote the coordinates of a point in an acquired B-scan relative to the US transducer coordinate frame F 4 and ϕ the rotation angle of the transducer while the 3-tuple (x, y, z) corresponds to the coordinates of the same point expressed in the world coordinate frame F 0 (Fig. 3). F 0 is chosen so that the y-axis is collinear to the rotation axis of the probe pointing forward, whereas the x-axis passes through the transducer array focus (TAF) when ϕ = 0. In order to derive the (4 × 4) homogeneous transformation matrix 0 T 4 that defines F 4 relative to F 0 , we introduce intermediary frames as depicted in Fig. 3. As F 0 is subjected to four consecutive transformations, 0 T 4 can be deduced from the postmultiplication

0 T 4 = 0 T 1 . 1 T 2 . 2 T 3 . 3 T 4 = Rot y (ϕ) . Tr x (-r) . Rot z (-θ 0 ) . Tr y (∆y).Tr x (-∆x) =     -c ϕ . [∆x.c θ0 -∆y.s θ0 + r] R y (ϕ).R z (-θ 0 ) ∆x.s θ0 + ∆y.c θ0 s ϕ . [∆x.c θ0 -∆y.s θ0 + r] 0 1×3 1     (1)
with c α = cos(α) and s α = sin(α). r is the radius of the endoscopic part of the US probe (r = 4 mm) and θ 0 the elevation angle up to half of the field of view (θ 0 = 0.50 rad). ∆x and ∆y correspond to the offsets in the x and y directions, respectively, between the origins of the frames F 3 and F 4 and depend on both the spatial spacing and the extent of the acquired B-scans. Rot y and Tr y denote respectively the (4 × 4) transformation matrices of pure rotation and translation about the y-axis and similarly for other axes whereas R y and R z represent the (3 × 3) rotation matrices about the y-and z-axes. Following [START_REF]World report on hearing[END_REF], it is possible to derive the F 0 relative world coordinates 0 p = (x, y, z, 1) from the F 4 relative US transducer coordinates 4 p = (x I , y I , 0, 1) thanks to the Fig. 3: Successive transformations corresponding to forward mapping.

relation 0 p = 0 T 4 . 4 p, (2)
which, after simplification, yields the forward mapping system

  x y z   =   c ϕ [(x I -∆x).c θ0 + (y I + ∆y).s θ0 -r] -(x I -∆x).s θ0 + (y I + ∆y).c θ0 -s ϕ [(x I -∆x).c θ0 + (y I + ∆y).s θ0 -r]   . (3)
This step is required to generate the sampling domain Ω post of the volume to be reconstructed, which is based on the physical extent of the pre-scan converted image and the spacing that we want to achieve.

Backward mapping: On the contrary, backward mapping denotes the relation that allows to pass from world to transducer coordinates. To derive the inverse relationship, we first determined the rotational angle ϕ from (3) using the x and z coordinates:

ϕ = -tan -1 z x (4)
After finding ϕ, we determined the x I and y I coordinates in the corresponding B-scan by solving the linear system formed by the first and third lines of (3), which yields:

x I y I = ( x cϕ + r).c θ0 -y.s θ0 + ∆x ( x cϕ + r).s θ0 + y.c θ0 -∆y . ( 5
)
Implementation: According to ( 4) and ( 5), each sample x post that belongs to the regular grid Ω post of the 3D image I post : Ω post → [0, 255] to be reconstructed can then be mapped to its corresponding location x pre in the stack of the acquired B-scans I pre : Ω pre → [0, 255]. For a given voxel that may not fall at grid locations, the estimation of the associated gray is performed using trilinear interpolation, which provides a good compromise between reconstruction quality and computational time [START_REF] Thévenaz | Interpolation revisited [medical images application[END_REF]. From an algorithmic perspective, the SC procedure can be described by the following pseudocode:

Algorithm Scan-conversion

Require: Ω post , Ω pre , I pre for all x post = (x, y, z) ∈ Ω post do compute x pre = (x I , y I , ϕ) using ( 4) and ( 5)

if x pre ∈ Ω pre then
Compute the voxel intensity I post (x post ) from I pre evaluated at the eight corner points surrounding x pre using trilinear interpolation else I post (x post ) = 0 end if end for return I post By working with a stack of already converted B-scans instead of directly using the raw radio frequency signals collected by the transducer, this implementation of SC allows for a shorter reconstruction time at the expense of an additional interpolation step [START_REF] Zhuang | Real-time 3-d ultrasound scan conversion using a multicore processor[END_REF].

The complete reconstruction procedure was implemented using the C++ Insight Tool Kit (ITK) library and run on an Intel® Xeon T M i7-8750H 2.20GHz processor.

C. Evaluation of system performances

Resolution measurement: The spatial resolution that is achievable by a 2D transducer is defined as the axial, or lateral, full width at half maximum (FWHM). This corresponds to the -6 dB width, along either the axial or lateral direction respectively, of a punctual object that is imaged at the optimal focus. In order to replicate such a punctual information, we designed a single 0.18 mm thick wire phantom (Fig. 4a) that is meant to be imaged perpendicularly to the acquisition plane of the transducer. Thus, the obtained B-scan contains a shape that comes closest to a point and from which we can compute the FWHM. Since the objective is to characterize the FWHM as a function of the distance from the probe, the phantom was placed on a positionning Z stage (Fig. 4c), which allows sub-mm control over the height of the linear platform.

For any given cross-section of the wire, the associated FWHM values (axial and lateral) were computed following the measurement protocol defined in [START_REF] Thijssen | Objective performance testing and quality assurance of medical ultrasound equipment[END_REF]. First, we estimated the position of the maximal intensity pixel and placed a rectangular measurement box around it. Then, the gray level profiles centered on the previous pixel position and bounded by the box were retrieved along the axial (y-axis) and lateral (x-axis) directions and recalculated to dB scale. Finally, a parabola was fitted to each profile using least squares based on the gray level points above -20 dB with respect to the 0 dB level maximum, from which we deduced the FWHM as the -6 dB width. For each position of the phantom, a rotational sweep of 4°was collected and used for computing the FWHM values so that to quantify the precision of the resolution measurement.

Correctness of reconstructed volume's geometry measurement: Beyond assessing the resolution of the 2D B-mode images, this paper also aims to quantitatively evaluate the correctness of volumetric reconstruction since this new imaging platform is meant for medical purposes. To the best of the authors' knowledge, there is no agreed standard in the literature, and existing works on SC actually rely only on visual inspection for validation [START_REF] Duan | Fast interpolation algorithms for real-time threedimensional cardiac ultrasound[END_REF]- [START_REF] Pospisil | 4-d x 3-d ultrasound: real-time scan conversion, filtering, and display of displacement vectors with a motorized curvilinear transducer[END_REF]. The only paper that presents such a quantitative test is a freehand US related work [START_REF] Solberg | 3d ultrasound reconstruction algorithms from analog and digital data[END_REF]. The proposed protocol consists in measuring to what extend the volumetric reconstruction is capable of reproducing the geometry of a well-known phantom. This evaluation test, though, induces a bias in the reported accuracy since measurements needs to be performed manually in the reconstructed volumes. In that sense, this technique would benefit from being automatized. Besides, a stumbling block for extending the test presented in [START_REF] Solberg | 3d ultrasound reconstruction algorithms from analog and digital data[END_REF] to our need arises from the fact that the phantom geometry must fit into the unusual small acquisition window of our setup.

To adress the abovementioned issues, we propose in this section a novel operator-independent protocol for evaluating the correctness of the reconstructed volume's geometry, which is based on a dedicated phantom that fits our acquisition window. Ideally, such a phantom should include point-like reflectors distributed in space as the reference geometry. Yet, its design remains a challenging task and even more so because of the unusual small dimensions of the acquisition window. Consequently, lines were chosen as the reference geometry as they both provides redudant information in 3D and are easy to build. The phantom consists of a cross-wire structure including two pairs of 2-mm-distant parallel wires that were mounted in orthogonal directions (Fig. 5). The plastic support was fabricated with 3D printing and metal wiring was used to enhance the constrast between the wires and the background. In addition, a reference volume of the studied phantom was required in order to account for both the 3D printing and wiring positioning errors that may occur during the fabrication. This would then serve as a ground truth in our evaluation protocol. Accordingly, we resorted to micro-CT that not only can provide high resolution images but also benefits from a high signal-to-noise ratio. Thus, the reference volume was acquired with an EasyTom 150® scanner (RX Solutions, Chavanod, France), which resulted in a volume of 389 × 1897 × 1243 voxels with an isotropic spacing of 29.35 µm.

For any given US volume, our evaluation protocol is organized as follows. First, each of the four 0.18 mm thick wires imaged in both US and micro-CT volumes was modelled by a line segment, which we represented by the 3-tuple S i = {c i , e i , l i } with i ∈ {1, 2, 3, 4}. c i denotes the position vector of the center of the segment line, e i the unit vector along its direction and l i its length. Following the resulting sets of line segments S U S = S U S i and S µCT = S µCT i , we then computed the transformation that allows to match line segments of both modalities. Finally, we estimated the accuracy of volumetric reconstruction by computing the mean distance from the registered US set of lines to the micro-CT one. To our knowledge, no similar quantitative and automatic evaluation protocol for volumetric US imaging has been reported in the literature.

The evaluation protocol was implemented using the same C++ library as for the reconstruction procedure.

1) Line segment fitting: For both the US and micro-CT modalities, the modelling of the set of wires was performed in two stages. First, each wire was isolated separately using a cylinder defined by two selected endpoints to provide a set of voxels V with coordinates X ⊂ R 3 to work on and then modelled by a line corresponding to the subset

L = {x ∈ R 3 | ∃λ ∈ R, x = p + λe}, ( 6
)
where p is the position vector of a point belonging to the line and e the unit vector along its direction. Finally, according to the estimated parameters, we deduced the end points of the studied set of voxels p min = p + λ min e and p max = p + λ max e such as

λ min = min x∈X (x -p) e λ max = max x∈X (x -p) e , (7)
from which we derived the center of the corresponding line segment c = pmax+pmin 2 and its length l = p max -p min .

For the micro-CT acquisition, the wiring part was extracted from the volume using simple thresholding due to the high density of metal compared to plastic. Then, the best line model was derived by principal component analysis (PCA) [START_REF] Wold | Principal component analysis[END_REF].

Regarding the US volumetric reconstruction, PCA was not applicable since US imaging suffers from various artifacts such as speckle and distortion that may hinder the line modelling step. Consequently, we applied a modified version of the procedure described in [START_REF] Uherčík | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF], in which a random sample consensus (RANSAC) is used to robustly localize a thin surgical tool in US volumes. The RANSAC approach is preferred to using Hough transform techniques as it does not suffer from a high computational effort in the 3D case. First, in each RANSAC iteration, two control points p A and p B are randomly selected from X U S to fit a line so that p = p B -p A 2 and e = p B -p A p B -p A in [START_REF] Paparella | Exploratory tympanotomy revisited[END_REF]. From the estimated line L U S , each voxel of coordinates x ∈ X U S is then classified as either belonging to the model (m = 1) or not (m = 0) following the classification function

m(x, L U S ) = 1, if d(x, L U S ) ≤ r wire 0, otherwise , (8)
where d(x, L U S ) represents the orthogonal distance of the point x to the line L U S and r wire the radius of the studied wire (r wire = 0.09 mm). Thanks to [START_REF] Macdougall | Optical coherence tomography system requirements for clinical diagnostic middle ear imaging[END_REF], it is then possible to define the set of inliers

X inl = {x ∈ X U S | m(x, L U S ) = 1} , (9)
which is involved in the selection of the best model across the iterations. However, contrary to the method described in [START_REF] Uherčík | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF], whose voting process is based on the usual number of estimated inliers, we decided to weight the vote of each inlier voxel by their corresponding intensity value. Accordingly, this RANSAC procedure no longer consists in maximizing |X inl | but the cost function

C(X inl ) = x∈X inl I post (x), (10)
which relies on the fact that the intensity of the wire's voxels is maximal at its center. Unlike Uhervčík et al. in [START_REF] Uherčík | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF], using this specific cost function allows to avoid prior segmentation to extract the set of voxels V U S and, thereby, eliminates the need for an additional tuning stage of the threshold that may be volume specific.

2) Model matching: Regarding the matching of the resulting sets of line segments, we used the approach presented in [START_REF] Kamgar-Parsi | Algorithms for matching 3d line sets[END_REF]. For conciseness purposes, we only discuss here the outline of the technique we implemented and refer readers to the original paper for further details.

The proposed algorithm in [START_REF] Kamgar-Parsi | Algorithms for matching 3d line sets[END_REF] takes as input two line sets: one referred as the model set S M and the other as the image set S I . The output corresponds to the rigid transformation M T I that allows to align S I with S M such that

M T I : S I = Rc I i + t, Re I i , l i , (11)
where R and t are the (3 × 3) rotation matrix and the translation vector associated to M T I , respectively. Depending on whether the model and/or the image line sets consist of sets of finite line segments or infinitely long lines, the authors distinguish several cases that lead to different derivations of the matching transformation. Since we previously estimated the length of each US line segment, the Finite Model Finite Image (FMFI) algorithm, when model and image line sets both consist of finite line segments, was the most relevant for our application. Yet, according to the authors' instructions, the FMFI algorithm performs best when initialized with the Infinite Model Infinite Image approach (IMII), which applies when model and image both consist of infinite lines. Consequently, we proceeded in two steps by first estimating an initial guess of M T I using the IMII algorithm and then refining it using the FMFI algorithm. In the next step, we denote by S mU S the matched set of line segments resulting from operating the transformation M T I on S U S .

3) Accuracy evaluation: When it comes to quantifying the spatial consistency between volumes after multimodal matching, the target registration error (TRE) is considered as the most relevant evaluation tool in the literature. Still, this metric does not apply for our phantom since it requires detected features to be points and is no longer applicable on line segments. As a result, we introduce in this section a new metric that is meant to quantify the accuracy (ACC) of volumetric reconstruction by measuring the difference between the reconstructed US and the micro-CT volumes based on the matched sets of line segments.

Since two matched lines may not be strictly parallel with each other, we defined the relative distance D i between them as the mean squared integral of the distance

d i (λ) = p mU S i -c µCT i × e µCT i ( 12
D i = 1 λ i,2 -λ i,1 λi,2 λi,1 d 2 i (λ)dλ. (13)
The values λ i,1 and λ i,2 of the interval for integration were defined such that the projections of both points p mU S i (λ i,1 ) and p mU S i (λ i,2 ) on the line segment S µCT i exactly coincide with the endpoints c µCT i ± li 2 e µCT i . Thereby, [START_REF] Brown | High-frequency ex vivo ultrasound imaging of the auditory system[END_REF] allows us to obtain the ACC as the mean value of the relative distances D i from S mU S i to S µCT i line segments:

ACC = 1 4 4 i=1 D i (14)
Although the proposed evaluation protocol only applies to wire phantoms, it allows to validate the constructability of more complicated structures than just line segments. Indeed, in case of an error in the reconstruction of either the orientations or the interdistances between the wires, the reconstruction procedure would worsen the line segment fitting, which would then impact the model matching and finally result in a degraded accuracy value. Consequently, the metric defined in [START_REF] Landry | Real-time intracochlear imaging of automated cochlear implant insertions in whole decalcified cadaver cochleas using ultrasound[END_REF] enables to quantify to what extent the reconstruction procedure allows to preserve both the orientations and distance, which holds true for any structure.

D. Evaluation of clinical potential

To assess the clinical potential of the proposed setup, we carried out additional acquisitions on the left ear of a cadaveric head to account for a representative intraoperative context. Four volumetric acquisitions requiring prior anatomical preparation were actually performed with the help of an ENT surgeon.

First acquisition: The first acquisition was conducted on a left ear featuring an intact tympanic membrane (TM). A posterior incision was performed to elevate the pinna. This was required to insert the probe into the EAC without damage, since the cadaveric rigidity of the pinna prevents the normal stretching of the cartilaginous structures. This provided a visual feedback on the positioning of the tip of the transducer. Finally, a transtympanic injection of saline solution was carried out to allow for acoustic coupling, and the acquisition was launched.

Second acquisition: For this acquisition, the TM was entirely removed using tympanotomy. In the absence of this opaque membrane, it was then possible to adjust more properly the pose of the tip and thus to focus on middle ear structures. Again, a transtympanic injection of saline solution was performed before starting the rotational sweep.

Third and fourth acquisitions: Afterwards, we concentrated on investigating the potential of volumetric US imaging applied to cochlear implants by placing a Neuro ZTI CLASSIC electrode array (Oticon Medical, Vallauris, France) in a representative anatomical context. To that end, a mastoidectomy with posterior tympanotomy was performed on the same ear to enable the access to the tympanic cavity as it is routinely done in cochlear implantation, and the implant was inserted through the round window into the scala tympani. Following the implantation, two volumetric reconstructions (third and fourth acquisitions) were performed using the same sweep settings, imaging parameters and pose of the probe: one with the electrode array in place and the other after its removal. This step enabled to extract the implant from the acquired data by subtracting the corresponding reconstructed volumes. Volumetric reconstruction of the same implant outside any anatomical context in a water tank was also performed for comparison purposes.

The handling and imaging of the cadaveric tissues were conducted with the approval of the local ethics committee of the Faculty of Medicine of the University of Montpellier (FRANCE).

III. RESULTS

A. Resolution measurement

Fig. 6 shows the FWHM values (axial and lateral) obtained from the single wire phantom images as functions of the axial distance from the probe. Overall, a total of 80 acquisitions were performed with an incremental step of 0.2 mm in the axial direction between two successive rotational sweeps, leading to a study range of 16 mm. For each distance, the axial and lateral FWHM are plotted with a central point representing the mean value computed over the rotational sweep while whiskers indicate the corresponding standard deviation. The axial distance from the probe was automatically measured from the acquired images in order to be operator-independent. According to the figure, the FWHM have different behaviors along the two directions. The lateral FWHM (blue) tends to degrade linearly with the distance from the probe, ranging from 0.23 mm in the near-field to 1.04 mm in the far-field, whereas the axial FWHM (red) does not vary significantly with a mean value of 0.16 ± 0.01 mm. Fig. 6: Measurements of the axial and lateral resolutions as the full-width at half maximum (FWHM) of the single wire phantom at various distances from the probe.

B. Correctness of reconstructed volume's geometry measurement

Three-dimensional renderings of the volumetric reconstructions of the custom 3D printed cross-wire phantom using micro-CT and US are shown in Fig. 7. As mentioned in section II-C, the density of metal wiring provides a high contrast between the background and wires. Yet, the US acquisition window remains limited since the proposed setup only allowed to image a small subpart of the phantom compared to micro-CT (Fig. 7b). Qualitatively, Fig. 7 indicates that the acquisition setup allows to preserve the orientations since the rendered wires 1 and 2 (resp. 3 and 4) look parallel with each other, which is consistent with the designed phantom. Although the pair of parallel wires a (wires 1 and 2) may also look perpendicular to the pair b (wires 3 and 4), orthogonality is more difficult to assess from visual inspection as it depends on the rendered pose.

Regarding the evaluation protocol, Fig. 8 illustrates the processing steps we described in section II-C. On the micro-CT side, the reference volume was first thresholded in order to extract the wiring part from the rest of the image (Fig. 8a). In addition, the segmented wires were cropped according to the central square (dotted diamond in Fig. 5) so that to provide similar extent line segments than the acquired with volumetric US. Then, line fitting was performed on the corresponding subpart using PCA (Fig. 8b). On the US side, the result obtained from line fitting performed on the reconstructed US volume using RANSAC is depicted in Fig. 8c. Finally, Fig. 8d presents a rendering of the two matched sets of line segments resulting from applying successively the IMII and FMFI algorithms.

Overall, a total of 12 US reconstructed volumes were used for the quantitative evaluation with varying orientations and depths of the probe with respect to the phantom. In order to study the influence of the incidence of the transducer relative to the phantom on the ACC, the spherical coordinates of the transducer array focus (TAF in Fig. 3) were derived from each reconstructed volume and reported in Table I. To that end, we adopted the following convention (Fig. 9): the radial distance r from the intersection point between the wires 1 and4; the elevation angle θ measured from a reference plane; the azimuthal angle ϕ between the position vector projected onto the reference plane and the z-axis. To provide a broad picture of the range of adopted configurations, the extreme poses of the tip of the transducer are also depicted in Fig. 10. Fig. 9: Spherical coordinates (r, θ, ϕ) used to determine the incidence of the US tranducer relative to the phantom: radial distance r, elevation angle θ and azimuthal angle ϕ.

For each acquisition, the phantom was placed in a container filled with water to allow for acoustic coupling. The rotational sweep was set to ∆ϕ = 120°to enable a complete scan of the wires. Regarding the imaging parameters, the frequency was set to 20 MHz, the B-mode gain to 30% and the imaging depth to 1.6 cm. Thereby, each reconstructed volume resulted in a 3D image of 609 × 645 × 722 voxels with a spatial spacing of 31 µm.

The calculations of the ACC on the complete set of scans are given in Table I. The reconstruction errors range from 0.08 to 0.43 mm with a mean value of 0.20 ± 0.09 mm. The lowest ACC was obtained on the US volume 2 while the highest one was obtained on the US volume 11. The spherical coordinates of the TAF were (r 2 , θ 2 , ϕ 2 ) = (16.62, 3.54, 1.40) and (r 11 , θ 11 , ϕ 11 ) = (14.28, 12.70, 3.12), respectively. These results were obtained by setting the threshold value to 30 for the micro-CT while the iterative procedures were stopped after reaching a total of 10 4 iterations for the RANSAC and 10 2 iterations for the FMFI algorithm.

C. Acquisitions on the cadaveric head

The results presented in this section refer to the acquisitions described in section II-D.

First acquisition: Imaging of the auditory system with an intact TM is presented in Fig. 11. The first volumetric reconstruction resulted in an image of 586 × 658 × 625 voxels with an isotropic spacing of 28 µm. The TM with its typical cone shape is clearly visible in the cross-sectional B-scan as well as the cochlear promontory, which results in a brighter structure due to its high density (Fig. 11a). Yet, because of bone distortion, localization of the round window (RW) remains cubersome considering only 2D images. On the contrary, 3D rendering of the reconstructed volume easily allows to identify the RW niche (RWN) by highlighting the corresponding cavity in the cochlear promontory (Fig. 11b).

Parts of the malleus are also identified such as the umbo, which is located at the tip of the conic TM, and the lateral process of the malleus. In Fig. 11b, the malleus manubrium is not continuously delineated as it does not entirely lie within the acquisition window. Second acquisition: Fig. 12 presents the imaging of the auditory system after complete removal of the TM. properly the pose of the probe tip thanks to visual feedback. A significant part of the ossicular chain is clearly visible such as the malleus manubrium, long process of incus and stapes. Again, the cavity in the bottom part suggests the location of the RWN which overlooks the RW.

Third and fourth acquisitions: Results of the investigation on cochlear implants are presented in Fig. 13 by depicting 3D US imaging of the electrode array in a water bath (Fig. 13a) and after implantation through the RW (Fig. 13b). The third volumetric reconstruction resulted in an image of 609 × 643 × 724 voxels with a spatial spacing of 34 µm. Fig. 13a shows that the used imaging parameters are adequate for the detection of the electrode array in water. Fig. 13b, however, depicts a composite rendering of the electrode array (green) and the middle ear (gray). Since no change in the sweep settings and imaging parameters was applied before and after the implantation, third and fourth volumetric reconstructions led to images of 558 × 609 × 599 voxels with a spatial spacing of 38 µm. Compared to Fig. 13a, only small segments of the implant are visible in the clinical setting. This may be due to the fact that the electrode array is no longer placed perpendicularly to the probe. As a result, only the eletrodes that are localized outside the cochlea can be imaged since they are the most echogenic parts of the implant.

As a lone 2D view of a 3D rendering may not allow for a clear understanding of volumetric reconstruction, we also provide videos of the corresponding reconstructed volumes as supplementary materials.

IV. DISCUSSION

In this paper, we presented a novel imaging platform for the 3D US imaging of the auditory system, which is based on the motorization of a miniaturized endoscopic US transducer specially developped for fitting the EAC.

Regarding the performances of the system, 2D B-mode imaging was shown to achieve a lateral resolution of 0.23 mm in the near-field that degrades as the distance increases and a stable axial resolution of 0.16 mm ± 0.01 mm. Consequently, volumetric imaging requires a tradeoff to be made between the spatial resolution to be achieved and the size of the acquisition window since the latter enlarges with the distance due to the conical shape of the collected B-scans. As regards with volumetric imaging, typical 3D scans were acquired within 2 minutes with an angular range of 120°at a rotational speed of 1°/s. We are perfectly aware that such a scanning time is not suited for clinical applications and, as a result, future works should focus on its reduction. One possibility could be to explore synthetic aperture since it allows to significantly increase the data rate and has been studied for achieving realtime 3D US imaging using 2D arrays transducers [START_REF] Lockwood | Real-time 3-d ultrasound imaging using sparse synthetic aperture beamforming[END_REF], [START_REF] Yang | Separable beamforming for 3-d medical ultrasound imaging[END_REF]. Concerning the reconstruction time, it ranged from 50 to 72 s on CPU depending on the physical extent and the desired spacing. As for the rotational sweep, such a computational time is excessive for a clinical use. However, implementing the SC algorithm on GPU could be a relevant solution to achieve almost real-time reconstruction.

Concerning volumetric imaging, the correctness of the reconstruction procedure was evaluated using a novel operatorindependent protocol that relies on the matching of a micro-CT volume of a reference geometry. A modified version of the RANSAC procedure described in [START_REF] Uherčík | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF] was used for the modelling of line segments in 3D US images. The rationale for modifying the original procedure was to avoid any prior segmentation of the data so that to automatize the evaluation. The calculations performed on the validation set composed of a total of 12 reconstructed US volumes (Table I) demonstrated that our setup allows to reconstruct 3D US data with a mean maximum error of 0.2 mm. It is actually crucial to understand that the reported ACC does not reflect the error of reconstruction itself but its highest bound since the incertainties of each step composing the evaluation protocol are contained in this measure. Indeed, line fitting in US still remains a challenging task that may lead to outliers due to the presence of artifacts while model matching based on the FMFI algorithm may converge to a local optimum. All of these are error prone tasks that impact the matching of the reference geometry in both modalities, even in case of a perfect reconstruction. According to Table I, the lowest and highest ACC were obtained on the volumes 2 and 11 with spherical coordinates (16.62, 3.54, 1.40) and (14.28, 12.70, 3.12), respectively. These results suggest that, above a certain value, the elevation angle tends to deteriorate the ACC and that the transducer should be positioned perpendicularly for optimal reconstruction. Measures performed on the volumes 9 and 10 tend to confirm this observation since the ACC significantly deviate from the mean value for azimuthal angles above 20°. Consequently, the more the axis of the transducer is close to the normal of the structure to be imaged, the better the correctness of the reconstructed volume. To our knowledge, this is the first time that such a quantitative and operator-independent validation protocol is reported for 3D US imaging techniques. Regarding the evaluation metric, a relevant alternative would have been to use the gold standard TRE instead of our tailored ACC by taking advantages of the intersections of lines as target points and increasing the number of wires of the phantom. In order for the TRE to account for local reconstruction errors, target points should yet be distributed in the acquisition space, which would thus require a 3D net of wires for the validation phantom. Given the unusual small dimensions of the acquisition window of our imaging platform, such a phantom would however remain difficult to build. Besides, the measurability of such a net of wires, and so target points, would also be hindered by the intrinsic features of our imaging platform considering the degraded lateral resolution in the far-field (Fig. 6) as well as the narrowed and conical acquisition window in the near-field.

The main strength of our setup lies in the minimally invasive aspect of this imaging technique. Contrary to [START_REF] Rainsbury | High frequency ex vivo ultrasound imaging of the middle ear to show simulated ossicular pathology[END_REF] and [START_REF] Landry | Real-time imaging of in-vitro human middle ear using high frequency ultrasound[END_REF], in which prior removal of the EAC was required due to the footprint of the utilized US probes, no ablation of the surrounding bone was needed in our experiments. From the clinician's viewpoint, the use of such a modality could facilitate the diagnostic process of the patient. Volumetric reconstruction of the auditory system could actually allow to assess the integrity of the ossicles and thus identify cases of CHL that may be caused by otosclerosis or chronic ear infections. Yet, since the real-time aspect of the acquired images is lost during the rotational sweep, 3D scans are currently restricted to structural information. As a result, clinical applications may also benefit from 2D B-scans that could provide functional information about the ossicular chain and enable to detect impairments at the incudomalleolar joint, which cannot be imaged (Fig. 12).

Regarding ENT surgeries, one possible application could be for ossicular chain reconstruction where functional information could allow to verify the prosthesis placement after putting the eardrum back in place. We also investigated the potential use of this modality for inner ear surgery by imaging a cochlear implant in different conditions (Fig. 13). As depicted in Fig. 13b, segmentation of the implant parts was possible by merely substracting acquired volumes before and after the insertion. Combined with a registered preoperative scan, this information could allow to maintain an appropriate axis of insertion, which was shown to be a critical factor in intracochlear trauma during cochlear implantation [START_REF] Torres | Cochlear implant insertion axis into the basal turn: a critical factor in electrode array translocation[END_REF]. Additionally, 3D registration between pre-and intra-operative imaging of the tympanic cavity could enable surgical navigation, which would be of great use for the surgeon given the complexity of the ear anatomy.

Since calibration is inherent to the development of any surgical navigation system, we actually conducted in a previous paper a feasability study on the calibration of such an imaging apparatus [START_REF] Santos | Geometric calibration of a new miniaturized endoscopic ultrasound probe[END_REF]. Despite the unusual small dimensions of the acquisition window, effective calibration of our setup was shown to be possible using a classic scheme based on a phantom with the same reference geometry than the one used in section II-C. However, in the absence of a reliable ground truth, no conclusion could be drawn regarding the accuracy of the procedure.

Consequently, future works will focus on the evaluation of a calibration procedure of our acquisition setup and, if necessary, on improving its accuracy for the further development of a navigation system intended for otological surgery. In this perspective, a US / CBCT registration algorithm will also be needed to be investigated, with a special focus on achieving sub-mm accuracy and a quantitative validation using cadaver datasets.

V. CONCLUSION

In this article, we focused on the carrying out of minimally invasive 3D US for the imaging of the auditory system using a new miniaturized endoscopic 2D US transducer. The latter consists of a 18 MHz 24 elements curved array transducer with a distal diameter of 4 mm that can be inserted into the EAC. Volumetric acquisition was achieved by rotating this very probe around its own axis using a RobOtol system.

Since this acquisition setup is meant for medical purposes, we focused on evaluating the correctness of the acquired volume's geometry. To that end, we introduced a new protocol that relies on the automatic registration and comparison of US volumes to a ground truth micro-CT acquisition of a custom phantom including a set of wires as reference geometry. US acquisitions obtained with twelve different probe poses were used to quantify the accuracy of volumetric reconstruction, which was estimated to achieve a maximum error of 0.2 mm. This value is consistent with the dimensions of the anatomical structures of the auditory system to be imaged.

To explore its clinical applicability in a representative anatomical context, our system was also tested on a cadaveric head. Typical structures such as the ossicles and the round window could be identified from the obtained US volumes. These results confirm that this technique enables the imaging of the middle and inner ears without requiring prior removal of the EAC. Such a system could then facilitate the minimaly invasive diagnosis and surgical navigation for otology in a fast, cost-effective and safe way.

Fig. 1 :

 1 Fig. 1: Technical specifications of the miniaturized endoscopic 2D US transducer. Distances are expressed in mm.

Fig. 2 :

 2 Fig. 2: Imaging platform with the endoscopic probe mounted onto the end-effector of a RobOtol system.

Fig. 4 :

 4 Fig. 4: Experimental setup for the measurement of the full width at half maximum. (a) CAD view of the 0.18 mm thick wire phantom. (b) Top view of the phantom after being secured in a recipient with some clay. (c) Positionning Z stage for controlling the height of the phantom.

Fig. 5 :

 5 Fig. 5: Top view of the 3D printed phantom used for evaluating the accuracy of the reconstruction procedure.

  the variable λ, which yields

Fig. 7 :

 7 Fig. 7: 3D renderings of the phantom with (a) micro-CT and (b) volumetric US.

Fig. 8 :

 8 Fig. 8: Processing steps of the evaluation protocol. (a) Segmentation of the wiring part in the micro-CT volume after thresholding and (b) line segment modelling (green) on the cropped part using PCA. (c) Line segment modelling (red) in the US volume using RANSAC. (d) Matching of both micro-CT (green) and US (red) sets of line segments.

Fig. 10 :

 10 Fig. 10: Renderings of the extreme poses of the tip of the probe (colors) with regard to the phantom for the complete set of scans. (a) Isometric view. (b) Front view. (c) Right view. (d) Top view. Red, green, cyan and magenta colors correspond to acquisitions 1, 9, 11 and 12, respectively.

Fig. 11 :

 11 Fig. 11: US imaging of the auditory system with an intact eardrum. (a) B-scan. (b) 3D rendering.

  Fig. 12a and Fig. 12b depict otomicroscopy and CBCT views of the corresponding tympanic cavity in order to facilitate the identification of the imaged structures with 3D US (Fig 12c). The second volumetric reconstruction led to an image of 558 × 609 × 599 voxels with a spatial spacing of 38 µm. Compared to Fig. 11b, additional structures of the middle ear were included within the acquisition window by adjusting

Fig. 12 :

 12 Fig. 12: Imaging of the tympanic cavity after tympanotomy with (a) otomicroscopy, (b) CBCT and (c) volumetric US highlighting the malleus manubrium (MM), the long process of the incus (LPI), the stapes, the round window niche (RWN) and the round window (RW).

Fig. 13 :

 13 Fig. 13: 3D rendering of US acquisitions of a cochlear implant (a) placed in a water bath and (b) after insertion into the cochlea. The platinum contacts of the electrode array are depicted in green outside the cochlea.

TABLE I :

 I Accuracy of volumetric reconstruction for each US volume with regard to the micro-CT reference.

ACKNOWLEDGMENT

The authors would like to thank Tony Blo, Frédéric Guérin and thanatopractitioner Maud Moulin (Faculty of Medecine of Montpellier) for their assistance in the evaluation of the acquisition setup on the cadaveric head and Dr Renaud Lebrun (Montpellier Rio Imaging platform and LabEx CeMEB -Institut des Sciences de l'Evolution -Université de Montpellier -CNRS UMR 5554 -Campus Triolet Place Eugène Bataillon 34095 Montpellier Cedex 5) for his contribution in the micro-CT acquisition.

2021, the World Health Organization (

This work was supported by the French "Fondation pour l'Audition" (FPA RD-2017-4), the French Occitanie Region and European Council (RR19093FF FEDER found), the Labex CAMI (ANR


Pawan Kumar Jha

Valérie Pralong

Maximilian Fichtner

Prabeer Barpanda
email: prabeer@iisc.ac.in

P3 type layered oxide frameworks: An appealing family of insertion materials for K-ion batteries

Keywords: K-ion batteries, cathodes, Layered oxides, P3 frameworks

K-ion batteries (KIBs) offer an efficient technological alternative to the state-of-the-art Li-ion batteries (LIBs) as energy storage devices with similar chemistry, comparable energy densities, elemental economy and uniformly distributed abundant resources. Nonetheless, their practical implementation warrants robust cathode materials that can yield high gravimetric/volumetric energy density, stable cycle life, and high-rate capability. In this scenario, P3 type layered oxides form an appealing family of KIB cathodes, which includes single transition metal based KxMO2 (M =transition metals) and multiple transition metals based KxMn1-yMyO2. They possess easy and scalable synthesis, high reversible capacity, and adequate operating potential.

The current review attempts to capture the most recent advancements in the P3 type KIB cathodes focusing on structural stability, structure-property correlation, and electrochemical performance with suggestions for further material optimization. Finally, the challenges and potential of these P3 type oxide cathodes have been addressed to guide their future research and development as intercalation materials.

Introduction

The effective transition from fossil fuels to a carbon-free and sustainable future depends on the advancement of energy storage technologies. The significance of effective and reliable systems for storing energy sporadically produced by renewable resources cannot be overstated. At present, the current state-of-the-art Li-ion battery (LIB) systems propel the consumer electronics, electric vehicles, grid-scale storage and are currently getting increasing deployment in aviation sector [START_REF] Armand | Building better batteries[END_REF][START_REF] Dunn | Electrical energy storage for the grid: A battery of choices[END_REF][START_REF] Whittingham | History, evolution, and future status of energy storage[END_REF][START_REF] Whittingham | Ultimate limits to intercalation reactions for lithium batteries[END_REF]. However, due to the exponential rise in their usage, Li-ion batteries significantly suffer from drawbacks related to low abundance in the earth's crust and sparse supply chains, resulting in a markedly higher price rise. At this juncture, it is important to develop alternate post-Li-ion battery systems with elemental abundance, operational safety, comparable energy densities without any geographic supply chain constraints. One such feasible alternatives to Li-ion batteries is K-ion batteries (KIB) that employ K + as an intercalant species instead of Li + [START_REF] Hosaka | Research development on K-ion batteries[END_REF][START_REF] Hwang | Recent progress in rechargeable potassium batteries[END_REF][START_REF] Kim | Recent progress and perspective in electrode materials for K-ion batteries[END_REF][START_REF] Yabuuchi | Research development on sodium-ion batteries[END_REF]. In principle, KIB can be economically deployed considering the relative abundance of K element in the earth's crust (20000 ppm for K vis-à-vis 20 ppm for Li) and resulting lower cost of K-based precursors (e.g., 1000 USD/ton of K2CO3 vis-à-vis 23000 USD/ton of Li2CO3). The standard redox potential of K/K + (-2.93 V vs. the standard hydrogen electrode [SHE]) is equivalent to Li/Li + (-3.04 V vs. SHE) and is lower than Na/Na + (-2.71 V vs. SHE), leading to higher operating potential in KIBs. Also, owing to the low stoke radius, K + possesses higher mobility in electrolytes as compared to Li + or Na + [START_REF] Hosaka | Research development on K-ion batteries[END_REF][START_REF] Hwang | Recent progress in rechargeable potassium batteries[END_REF][START_REF] Kim | Recent progress and perspective in electrode materials for K-ion batteries[END_REF]. Unlike sodiumion batteries (NIBs), employing KIB is relatively simple as the well-known graphite anode can be readily used. However, identifying suitable cathodes that reversibly (de)intercalate K + ions with high capacity, optimum voltage, efficient rate kinetics, and consistent cycle life is a key challenge for the advancement and implementation of KIBs. K + ions can stabilize different structural types than Li + and Na + ions owing to their larger ionic radius (1.38 Å) in comparison to Li + (0.76 Å) and Na + (1.02 Å) ions. Accordingly, the respective cathode materials and their working voltages are likely to differ from those for Li + and Na + analogues. Similar to the LIBs, layered oxide materials form the major type of cathodes for KIBs with organic electrolytes. Because of their high energy density and two-dimensional open frameworks, layered oxide materials can offer fast K + migration rendering them viable cathode candidates for potassium-ion batteries [START_REF] Delmas | Evolution cristallochimique et propriétés physiques de quelques oxydes lamellaires[END_REF][START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF][11]. Especially, P3-type layered oxides have gained tremendous attention in the pursuit to develop potential KIB cathode systems [START_REF] Hosaka | Research development on K-ion batteries[END_REF][START_REF] Zhang | Layered oxide cathode for potassium-ion battery: Recent progress and prospective[END_REF][START_REF] Kim | Next-generation cathode materials for non-aqueous potassium-ion batteries[END_REF].

They (i) can be easily prepared by large-scale (dry) solid-state synthesis, (ii) offer high K + ionic conductivity, and (iii) have superior structural integrity than the P2 and O3 counterparts. (blue and green balls) available for K + ions in P3 structure leading to potential ordering in Kmetal layers upon depotassiation [START_REF] Kaufman | Ordering and structural transformations in layered KxCrO2 for K-ion batteries[END_REF]. (e) Antiphase boundary diffusion mechanism in P3 layered oxides. Arrow marks (black) indicate the migration of antiphase boundary (APB) [START_REF] Kaufman | Antiphase boundary migration as a diffusion mechanism in a P3 sodium layered oxide[END_REF].

Reproduced with permission from Ref. [START_REF] Kaufman | Ordering and structural transformations in layered KxCrO2 for K-ion batteries[END_REF][START_REF] Kaufman | Antiphase boundary migration as a diffusion mechanism in a P3 sodium layered oxide[END_REF].

Structure stabilization

There are two proposed hypotheses for understanding the favored stacking sequence of anion (oxygen) which determines the type of structure. Based on the critical parameter β (beta) as proposed by Rouxel, the trigonal prismatic environment of alkali-metal ions is preferable at non-stichometry states (KxMO2; x<1) [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF]. This can be explained by the ionic radius of cation (RK + and RM 3+ /RM 4+ ) and the ionicity of K-O and M 3+ /M 4+ -O bonds which are directly correlated to the degree of ionicity or covalence of crystal lattice. The structure stabilization can also be understood from the "cationic potentials" as proposed by Hu group, which expresses the extent of the cation electron density and its polarizability finally normalized to the ionic potential of anion or oxygen [16]. Notably, the P3 type structure is the most stable structure at the intermediate states, as evidenced by the two aforementioned governing parameters and the phase diagram derived by Delmas as presented in Figure 1b [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF]16].

The structure types (depending on K-vacancy orderings) of layered KxMO2, as characterized by the coordination environment and periodicity of MO2 layer or KO2 layer in repeated units as reported in the literature, are summarized in Figure 1c [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF]. It can be defined using an alphanumeric formulation as proposed by Delmas, with a letter designating the alkali site coordination (ca. octahedral [O] or prismatic [P]) and a number defining the oxygen stacking sequence. The monoclinic distorted O'3-, P'3-, and P'2-type materials are also included with the undistorted types (where ' refers to structural distortion). Notably, the co-existence of several layered stacking suggests the existence of stacking faults as a result of synthesis conditions and/or K + (de)intercalation. When M = Sc or Cr, the oxide systems exclusively assume O3-type structure in KMO2 although they form during the electrochemical (de)charge process [START_REF] Delmas | Les phases KxCrO2 (x ⩽ 1)[END_REF][START_REF] Hoppe | Oxoscandate der alkalimetalle: KScO2 und RbScO2[END_REF]. KMnO2, on the other hand, has a nonlayered structure composed of chains of [MnO5] edge-sharing square pyramids [START_REF] Jansen | Zur kenntnis von KMnO2[END_REF]. While in KFeO2, tetrahedrally coordinated Fe 3+ ions are connected through three-dimensional corner sharing fashion [START_REF] Han | KFeO2 with corner-shared FeO4 frameworks as a new type of cathode material in potassium-ion batteries[END_REF]. Furthermore, there are numerous reports on the synthesis of P3-(P'3) KxMO2 for single transition elements (Cr, Mn, and Co) as well as for mixed transition elements. Owing to the bigger size of K + -ion and high cation-cation electrostatic repulsion, P3 type stacking is thermodynamically more favored in case of K-based layered oxides [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF][START_REF] Kim | Stoichiometric layered potassium transition metal oxide for rechargeable potassium batteries[END_REF]. Although the P3 structure has twice as many prismatic sites as MO6 octahedral sites, all prismatic sites cannot be occupied at once due to strong K + -K + electrostatic repulsions, resulting in an ordering of occupied K sites (Figure 1d) [START_REF] Kaufman | Ordering and structural transformations in layered KxCrO2 for K-ion batteries[END_REF][START_REF] Kaufman | NaxCoO2 phase stability and hierarchical orderings in the O3/P3 structure family[END_REF][START_REF] Toriyama | Potassium ordering and structural phase stability in layered KxCoO2[END_REF].

In the P3-type layered structure, all the K + ions occupy a single type of prismatic site, sharing a face with an MO6 octahedron on one side and three edges with surrounding MO6 octahedra on the opposite side. In the oxygen stacking array AB BC CA along the c-axis, K-metal ions fill the prismatic sites in the inter-slab space between the MO2 slabs. The (x,y) coordination of oxygen atoms are the same between the interslab space forming a hexagonal unit cell with an R3m or R-3m space group containing three MO2 slabs. Hexagonal symmetry in the unit cell is obtained when the lattice undergoes monoclinic distortion [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF]. To denote distortion, a prime sign is placed between the letter and the number, however, the number of MO2 slabs is estimated assuming a pseudohexagonal unit cell. For example, the O3-type KCrO2 transforms into O'3-, P3-, and P'3-type KxCrO2 during electrochemical K extraction [START_REF] Kim | Stoichiometric layered potassium transition metal oxide for rechargeable potassium batteries[END_REF]. Notably, P'3type K0.8CrO2 can be easily synthesized via a simple solid-state reaction [START_REF] Naveen | Highly stable P′3-K0.8CrO2 cathode with limited dimensional changes for potassium ion batteries[END_REF]. As O3 and P3 share the same space group, it is possible for the O3 phase to transform into the P3 phase by gliding MO2 slabs by (1/3,2/3,0) without breaking the M-O bond and vice-versa [START_REF] Komaba | Study on the reversible electrode reaction of Na1-xNi0.5Mn0.5O2 for a rechargeable sodium-ion battery[END_REF][START_REF] Kubota | Electrochemistry and solid-state chemistry of NaMeO2 (Me = 3d Transition Metals)[END_REF].

Single transition metal-based cathodes

Nonstoichiometric KxMO2 oxides crystallize as P3-and P2-type phases, with the K content and calcination temperature having a substantial influence on the final structure type. P3 polymorphs are characterized as low-temperature phase [27]. Indeed, P3-KxCoO2 can be synthesized by calcination at a lower temperature than that required for the P2-KxCoO2 phase [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF]. Furthermore, Delmas et al. reported the synthesis of the P'3-and P'2-types for x = 0.5 and 0.55 < x < 0.67, respectively, by heating a homogenous mixture of K2O, MnO2, and Mn2O3 in a sealed gold tube at 700 °C [START_REF] Delmas | Les Phases KxMnO2 (x ≤ 1)[END_REF]. Recent work by Liu et al. reports the P3-and P'2-type phases for x = 0.45 and 0.3, respectively, by calcining a K-Mn oxalate coprecipitation precursor at 900 °C in air [START_REF] Liu | Layered potassium-deficient P2-and P3-type cathode materials KxMnO2 for K-ion batteries[END_REF].

The (dis)charge behavior of different polymorphs of KxMO2 displayed a lower average voltage of K|| KxMO2 than NaxMO2 and LixMO2 along with a more inclined (sloping) voltage curve [START_REF] Hosaka | Research development on K-ion batteries[END_REF]. Goodenough et al. discovered that the electrostatic interaction of the alkali ions in the interslab gap affects the M-O bond length. The stronger electrostatic repulsion leads to the elongation of the M-O bond [START_REF] Goodenough | Solid-solution oxides for storage-Battery electrodes[END_REF]. As a result, the lower binding energy or lower Madelung stabilization of oxygen with respect to transition metal energy states lead to lower voltage in KxMO2 as compared to LixCoO2 and NaxCoO2. Further, P3 type intercalation host crystal tends to stabilize cation-vacancy orderings over a wide range of K concentrations negatively impacting the fast ion transport [START_REF] Kaufman | Ordering and structural transformations in layered KxCrO2 for K-ion batteries[END_REF][START_REF] Kaufman | NaxCoO2 phase stability and hierarchical orderings in the O3/P3 structure family[END_REF][START_REF] Toriyama | Potassium ordering and structural phase stability in layered KxCoO2[END_REF]. The simplest nearest-neighbor hops in K-vacancy ordered phases are prohibited because they are directed to unstable configurations. Van der Ven group identified an alternative mechanism of K + ion transport mediated by antiphase boundary (APB) migration via the formation and expansion of kinks along domain boundaries as displayed in Figure 1e. In fact, it relies on extended defects that are inherent to the stable phases rather than vacancy cluster defects and have much lower kinetic barriers for the migration [START_REF] Kaufman | Antiphase boundary migration as a diffusion mechanism in a P3 sodium layered oxide[END_REF][START_REF] Kaufman | Cation diffusion facilitated by antiphase boundaries in layered intercalation compounds[END_REF].

KxMnO2

Mn-based compounds are appealing cathode materials because of the elemental/ precursor abundance. The electrochemical K (de)intercalation performance of layered P3-KxMnO2 was first reported by Kim et al. in 2017 [33], whereas its crystal structure was earlier reported by Delmas back in 1976 [START_REF] Delmas | Les Phases KxMnO2 (x ≤ 1)[END_REF]. The K0.5MnO2, which was synthesized via a simple solid-state method, has a rhombohedral lattice with R3m symmetry exhibiting 140 and 106 mAhg -1 capacity in a K-metal half-cell in the voltage range of 1.5-4.2 V and 1.5-3.9 V respectively vs. K as presented in Figure 2a-d. The narrow operating voltage window yields better cycling stability and retains ~70% (≈70 mAhg -1 ) of the initial discharge capacity with ~95% of coulombic efficiency at a current rate of 20 mAg -1 at the end of 50 th cycle. In-situ XRD measurement suggests the structural transition occurred from P3 to O3 type stacking via twophase mechanism (0.425<x<0.395) and further transforms from O3 to an unknown phase (O-3 like) via two-phase reaction (0.364<x<0.316) (Figure 2e-f) [START_REF] Kim | Investigation of potassium storage in layered P3-type K0.5MnO2 cathode[END_REF]. Notably, the irreversible transition metal migration from the slab to the interslab is less favorable as the interslab distance of KxMnO2 monotonically increases during the complete charge process. Less stepwise voltage curve (irreversible) and intensity weakening of (00l) peak at higher voltage (4.2 V) during K-removal suggest the stacking fault and other defect induction in a lattice, responsible for the capacity fading during cycling. The discharge process reversibly traces the charging process and indicates feasible K + ion (de)insertion from the KxMnO2 host. In addition, van der Wall corrected DFT calculations were also in sync with the experimental phase transformation during the (de)insertion process (Figure 2f). Even if the upper cut-off voltage is set to a lower value, the capacity fade cannot be avoided entirely [START_REF] Liu | Layered potassium-deficient P2-and P3-type cathode materials KxMnO2 for K-ion batteries[END_REF][START_REF] Kim | Investigation of potassium storage in layered P3-type K0.5MnO2 cathode[END_REF]. Similar to most Mn-based systems, KxMnO2 suffers from two significant flaws: the inevitable Jahn-Teller distortion and Mn 3+ disproportionation (2Mn 3+  Mn 2+ + Mn 4+ ), which significantly reduce the cycling stability. While the former triggers an asymmetric elongation in the bond lengths of Mn-O in [MnO6] octahedra, the latter leads to the dissolution of Mn 2+ into electrolytes. To address these concerns, recent research suggests that tunable interfacial structure and the induction of a synergistic interaction between particle size, shape, and hollow interior can alleviate structural stress and further provide a shorter K + diffusion pathway [START_REF] Lei | Dual interphase layers in situ formed on a manganese-based oxide cathode enable stable potassium storage[END_REF].

KxCoO2

Although P3 type KxCoO2 compounds have been studied since the 1970s, their electrochemical K + (de)intercalation was reported by the Komaba group as shown in Figure 2g-h [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF]. The electrochemical properties of KxCoO2 follow a similar trend as NaxCoO2. Both P2 and P3 phases confirm the comparable capacities of ~60 mAhg -1 and 70 mAhg -1 , respectively having similar voltage profiles in the voltage window of 1.5-3.9 V [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF]. A discharge capacity of ≈ 55 mAhg -1 or ~92 % of the initial discharge capacity is maintained at the end of 30 th cycle by the P3 phase at 11.5 mAg -1 rate. The small ionic size (Shannon radius) of Co leads to higher ionic potential of Co (as explained in the above section). As a result, the larger size of K + prefers a wide prismatic interslab space that weakens the K + -K + repulsion (or the interaction of K + ions).

The favorable stability in the prismatic site for K produces a similar charge-discharge profile for P2 and P3 type KxCoO2. Due to the stability of the prismatic site, it is reasonable to infer that the P3 type phase was maintained during the (dis)charge process, which is consistent with DFT predicted results [START_REF] Toriyama | Potassium ordering and structural phase stability in layered KxCoO2[END_REF]. Notably, the fluctuation in K1-xCoO2 interslab lengths caused by the extraction of large K + ions is nearly equivalent to Na1-xCoO2. Even with a small amount of residual potassium, the large potassium ions most likely act as pillars while maintaining the wide interslab distance [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF]. Additionally, strong K + -K + repulsion is responsible for the differing site energies for K and vacancy, which further results in the stabilization of the K +vacancy ordering at various K-contents and undergo several first-order phase transformation steps during cycling. (a-d) and phase evolution during cycling from (e) in-situ XRD study, and (f) DFT calculations [START_REF] Kim | Investigation of potassium storage in layered P3-type K0.5MnO2 cathode[END_REF]. (gh) Typical galvanostatic charge and discharge curves and cycling performance of KxCoO2 [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF]. (i-k) Galvanostatic voltage-capacity profiles, convex Hull plot and calculated voltage plot (DFT) compared to the experimentally obtained charge-discharge profiles for P3 type KCrO2 [START_REF] Hwang | Development of P3-K0.69CrO2 as an ultra-high-performance cathode material for K-ion batteries[END_REF]. (l-n) Galvanostatic (dis)charge curves and in-situ XRD patterns of P'3 KxCrO2 synthesized by solid-state method [START_REF] Naveen | Highly stable P′3-K0.8CrO2 cathode with limited dimensional changes for potassium ion batteries[END_REF].

KxCrO2

As a reasonably abundant element with high electrochemical potential, chromium plays an important role in K-based oxides, which displays all three polymorphs, namely P3, P2, and O3. K-deficient P3 K0.69CrO2 phase was prepared via an electrochemical ion-exchange (chimie douce) method from parent O3 type NaCrO2 material [START_REF] Hwang | Development of P3-K0.69CrO2 as an ultra-high-performance cathode material for K-ion batteries[END_REF]. While retaining its original crystal structure, the cathode displayed an initial capacity of 100 mAh g -1 with reasonable cycling stability (65% capacity retention over 1000 cycles at 1C) as shown in Figure 2i-k. Further, P'3 type K0.8CrO2 with the space group C2/m was prepared using a simple solid-state method as reported by Pyo's group [START_REF] Naveen | Highly stable P′3-K0.8CrO2 cathode with limited dimensional changes for potassium ion batteries[END_REF]. In-situ XRD study revealed that the monoclinic distorted framework was converted into undistorted (or P3 phase) at the intermediate stage of K + extraction and this process was completely reversible during subsequent K + insertion process as depicted in Figure 2l-n [START_REF] Naveen | Highly stable P′3-K0.8CrO2 cathode with limited dimensional changes for potassium ion batteries[END_REF].

Despite the inherent advantages of unary KxMO2 compounds outlined in the preceding section, most of these materials exhibit low capacity, low operating voltage, rapid capacity fading, and several stepwise phase transitions upon charge-discharge process, which limits their practical utility. Fewer voltage steps and smooth voltage curves are desired for the practical applications of KxMO2. Based on the experience and knowledge gained from NaxMO2 systems [START_REF] Yabuuchi | Research development on sodium-ion batteries[END_REF], fewer voltage steps can be partially obtained in binary, ternary, and quaternary transition-metal systems, as well as by partial substitution with redox inactive metals.

Mixed transition metal-based cathodes

Binary oxides (KxM1M2O2)

Mn(M1)/M2-based layered oxides combine the large specific capacity of Mn 4+ /M2 3+ and the high operating voltage of M2 (=Fe, Co, and Ni). The presence of M2 forms an efficient strategy to suppress the strong cooperative Jahn-Teller distortion associated with high-spin Mn 3+ (3d 4 ) species. Thus, structural instability during (de)potassiation can be efficiently avoided even with a small amount of M2 substitutions. However, higher Co substitution can result in poor cycling performance and rate capability associated with first-order phase transition occurring by simply gliding the MO2 layer (Figure 3a-d) [START_REF] Choi | Co0.5Mn0.5O2: New cathode with high power capability for potassium-ion batteries[END_REF][START_REF] Sada | P3-type layered K0.48Mn0.4Co0.6O2: a novel cathode material for potassium-ion batteries[END_REF][START_REF] Ramasamy | Superior potassium-ion hybrid capacitor based on novel P3-type layered K0.45Mn0.5Co0.5O2 as high capacity cathode[END_REF][START_REF] Zhang | Structural insight into layer gliding and lattice distortion in layered manganese oxide electrodes for potassium-ion batteries[END_REF]. Furthermore, increasing the K-content leads to a smoother voltage curve and improved structural stability. Doping of Co greater than x= 0.5 results in lower capacity, even with a K-content of 0.48 per formula unit [START_REF] Sada | P3-type layered K0.48Mn0.4Co0.6O2: a novel cathode material for potassium-ion batteries[END_REF]. On the other hand, Ni substitution enables the multi-electron redox reaction in addition to high voltage, giving rise to energy density. Despite this, the lattice parameter, particularly along the c-axis, varies slightly in K0.5Ni0.1Mn0.9O2 as Ni substitution can reduce the anisotropic change of the Mn-O bond along the c-axis in MnO6 octahedra (Figure 3e-h) [START_REF] Cho | Cycling stability of layered potassium manganese oxide in nonaqueous potassium cells[END_REF]. Inherent Ni comes up with a small amount of NiO as an impurity owing to limited solubility and thermodynamic stability of the NiO compound [START_REF] Yabuuchi | Research development on sodium-ion batteries[END_REF]. Noticeably, the electrochemical K + intercalation capabilities of KxMO2 can be altered by substitution of redox-inactive metals such as Mg, Cu, and Zn. Since the K + -K + electrostatic repulsion is higher than that of Li + -Li + and Na + -Na + species, these metals can successfully accommodate in the MO2 slab [START_REF] Weng | Construction of hierarchical K0.7Mn0.7Mg0.3O2 microparticles as high capacity & long cycle life cathode materials for low-cost potassium-ion batteries[END_REF][START_REF] Liu | Low-cost layered K0.45Mn0.9Mg0.1O2 as a high-performance cathode material for K-ion batteries[END_REF]. Even though Ni, Co or Mg/Mnbased oxides exhibit promising K + storage ability at useful working potentials (Figure 3 i-k), a more profound comprehension of phase evolution and a practical structural design suitable for these materials is still notably missing.

Ternary oxides (KxM1M2M3O2)

The drawbacks of the Mn-based layered cathode materials, such as low voltage, structural and capacity degradation, can be partially solved by replacing Mn 3+ with Fe 3+ , Mg 2+ and Ni 2+ [START_REF] Choi | Facile migration of potassium ions in a ternary P3-type K0.5[Mn0.8Fe0.1Ni0.1O2 cathode in rechargeable potassium batteries[END_REF][START_REF] Liu | 67Ni0.17Co0.17Mn0.66O2: A cathode material for potassium-ion battery[END_REF][START_REF] Liu | A P3type K1/2Mn5/6Mg1/12Ni1/12O2 cathode material for potassium-ion batteries with high structural reversibility secured by the Mg-Ni pinning effect[END_REF]. For example, ternary K0.5Mn0.8Fe0.1Ni0.1O2 oxide has a high reversible discharge capacity (120 mAh g -1 ) involving P3-O3 phase transition along with good structural integrity over 300 cycles (74% capacity retention) at 50 mA g -1 (Figure 4a-c

Conclusion and perspectives

P3-type layered oxides and their derivatives form a promising group of cathode insertion materials for advanced potassium-ion batteries (KIBs) aimed at large-scale energy storage. In recent years, significant progress has been achieved in harnessing these P3 oxide cathodes, but there are still numerous concerns that must be addressed before KIBs can be realized in the future. The low coulombic efficiency, chemical stability, K-deficiency, lower voltage owing to strong K + -K + repulsion, and several first-order phase transformations (including guiding) or K + /vacancy ordering results in a stepwise voltage profile. Along this line, coating the active layer can be a viable solution in achieving chemical stability since it improves rate capability and cycling stability by mitigating side reactions at the electrode interface. The proper selection of cation substituents with large ionic radius should be beneficial to accommodate more K + in pristine layer structure. The presence of larger transition metal (M) leads to higher lattice parameters, thereby favoring the introduction of larger cations and stabilization of pristine layered structure with higher K + content, which in turn is beneficial to yield higher capacity.

For instance, if the charge ordering of M layers in KxMO2 is disrupted, the K + /vacancy ordering could be effectively avoided. Slight differences in the ionic radii of different dopants and significant differences in the redox potentials are conducive to form disordered configurations. Moreover, high entropy P3 type oxides made up of several transition metals might exhibit greater cycling stability and higher capacity, as reported in case of sodium-ion batteries.

Another technique to improve battery performance can be tweaking the particle size, shape, and morphology. Caution must be exercised during materials handling as K-based compounds have lower moisture stability than Na and Li counterparts as they can accommodate crystal water when exposed to open air. Poor moisture stability can affect the cycling performance and rate performance necessitating careful storage and handling conditions. We anticipate this review offers fresh perspectives for further development of P3-type layered oxide cathodes for rechargeable potassium-ion batteries.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figure

  Figure1adepicts a schematic layout of a typical KIB, which includes positive [e.g., P3 K0.5MO2] and negative (e.g., graphite) electrodes with current collectors and electrolyte (e.g., KPF6 in EC:DEC) soaked separator between the electrodes[START_REF] Hosaka | Research development on K-ion batteries[END_REF]. The current article overviews the recent advancements in the P3-type K-based cathodes stressing on their structural stability, structure-performance correlation, and overall electrochemical performance. After a sneak peek on mono, binary and ternary transition metal-based oxides, the limitation and potential of these P3 type oxide cathodes have been discussed to offer guidelines for future research and development of these layered insertion materials.

Figure 1 .

 1 Figure 1. (a) Schematic illustration of operation of typical K + -ion batteries. (b) Phase diagram vs. content of alkali ions (Na and K) as derived by Delmas [10]. (c) Schematic illustrations of the O3-, P3-, and P2-frameworks for AxMO2 layered oxides. (d) Two triangular lattice sites

Figure 2 .

 2 Figure 2. Electrochemical performance of KxMnO2 in different potential windows (a-d) and phase evolution during cycling from (e) in-situ XRD study, and (f) DFT calculations [33]. (gh) Typical galvanostatic charge and discharge curves and cycling performance of KxCoO2 [28]. (i-k) Galvanostatic voltage-capacity profiles, convex Hull plot and calculated voltage plot

Figure 3 .

 3 Figure 3. (a) Typical galvanostatic (dis)charge profiles of P3-Kx[Co0.5Mn0.5]O2 on K + (de)insertion, corresponding (b) cyclic voltammetry plots and (c) operando XRD phase evolution during cycling revealing (d) the change in c-lattice parameter [36]. (e) Galvanostatic (dis)charge profiles of K0.5Ni0.1Mn0.9O2, (f) corresponding dQ/dV curves and (g-h) operando XRD patterns during cell cycling [40]. (i) Galvanostatic (dis)charge profiles, and respective (j) cyclic voltammogram and (k) ex situ XRD patterns for Mg-doped KxMnO2 [42].

  ). It could be attributed to slight structural variation and facile migration of K + ions. From a structural standpoint, the shared oxygen atoms in MnO6, FeO6, and NiO6 (O-Mn-O-Fe-O-Ni-O) could preclude the introduction of structural defects like the Jahn-Teller phenomenon in MnO6 octahedra. Conversely, P3-type ternary K0.67Ni0.17Co0.17Mn0.66O2 oxide delivers a discharge capacity of 77 mAhg -1 in the range 4.3-2 V with a lower interslab distance as evidenced by ex situ XRD patterns after charging to 4.3 V (Figure 4d-f).

Figure 4 (

 4 Figure 4 (a) Galvanostatic (dis)charge profiles of K0.5Mn0.8Fe0.1Ni0.1O2 oxide, (b) DFT calculations-based formation energy plot depicting the structural evolution in of K0.5Mn0.8Fe0.1Ni0.1O2 in a K-half cell. The formation energies are normalized per formula unit.(c) Corresponding evolution of phases and lattice parameter c during K + (de)insertion[START_REF] Choi | Facile migration of potassium ions in a ternary P3-type K0.5[Mn0.8Fe0.1Ni0.1O2 cathode in rechargeable potassium batteries[END_REF]. (d) Galvanostatic (dis)charge curves of P3 K0.67Ni0.17Co0.17Mn0.66O2, corresponding (e) dQ/dV profiles, and (f) ex situ XRD patterns during the first cycle in a K-half cell[START_REF] Liu | 67Ni0.17Co0.17Mn0.66O2: A cathode material for potassium-ion battery[END_REF].

Acknowledgements

The first author is grateful to the Ministry of Human Resource Development (MHRD, Government of India) for graduate fellowship. PKJ, VP and PB acknowledge the Indian-French Laboratory of Solid State Chemistry (LaFICS) for financial support. The work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany´s Excellence Strategy -EXC 2154 -Project number 390874152. It also contributes to the research performed at CELEST (Center for Electrochemical Energy Storage Ulm-Karlsruhe) and was funded by the German Research Foundation (DFG) under Project ID 390874152 (POLiS Cluster of Excellence). PB is grateful to the Alexander von Humboldt Foundation (Bonn, Germany) for a 2022 Humboldt fellowship for experienced researchers. CRediT author statement Pawan Kumar Jha: Conceptualization, Writing-Original draft preparation. Valerie Pralong, Maximilian Fichtner, Prabeer Barpanda: Supervision, Writing-Reviewing and Editing.