Method for calculating the three-dimensional ROTO-translation of transparent microscopic objects while they flow and rotate in a microfluidic channel

Abstract

The present invention relates to a method to precisely retrieve the rotating angles of transparent microscopic objects flowing along a microfluidic channel within a tomographic imaging flow cytometry system. The measured angles are obtained without any prior information about the said transparent microscopic objects (i.e. shape, density, size, etc.) with the aim of attaining tomograms of their refractive index values.

Description

[0001] SIB BI5961R METHOD FOR CALCULATING THE THREE-DIMENSIONAL ROTO-TRANSLATION OF TRANSPARENT MICROSCOPIC OBJECTS WHILE THEY FLOW AND ROTATE IN A MICROFLUIDIC CHANNEL

[0002] TECHNICAL FIELD OF THE INVENTION

[0003] The present invention relates to a method to precisely retrieve the rotating angles of transparent microscopic objects flowing along a microfluidic channel within a tomographic imaging flow cytometry system. The measured angles are obtained without any prior information about the said transparent microscopic objects (i.e. shape, density, size, etc.) with the aim of attaining tomograms of their refractive index values.

[0004] BACKGROUND OF THE INVENTION

[0005] Holo-tomographic imaging flow cytometry (HTIFC) is based on the recording of digital holograms, through an interferometric microscopy system, of single cells from different angles, i.e. while they simultaneously flow and rotate in a microfluidic channel. The sequence of holographic images acquired for each cell is then processed to reconstruct 2D quantitative phase-contrast maps (QPMs) which, together with the 3D orientation of the cell, are used as the inputs of any 3D tomographic reconstruction algorithm. Unlike other state-of-the-art holo-tomographic techniques, in which the acquisition of a cell is achieved through the illumination source’s scanning while the cell is fixed in a certain position, thus accurately knowing the illumination angle, in HTIFC the 3D orientation of the cells when they rotate around the axis perpendicular to the flow direction and the optical axis is unknown a priori.

[0006] Tomographic Imaging Flow Cytometry (TIFC) exploits a combination of active elements and fluid dynamic effects to induce full particles’ rotation during the acquisition of microscopy images. The introduction of external forces into the microchannel always requires an adjustment of the operating parameters to the properties of the particle’s suspension. On the other hand, high throughput applications require continuous imaging of all particles passing through the imaged Field of View (FoV). Therefore, one option to achieve tomographic imaging of continuously flowing particles is to force their continuous self-rotation in shear flow during images acquisition. This requires the particle’s transport at a distinct off-center position of the microchannel, which can be realized by a preceding flow focusing step, e.g. hydrodynamic or acoustophoretic effect. Several technological solutions have been proposed to induce controlled particle rotation in microfluidicSIB BI5961R

[0007] channels. For example, the generation of particle rotation in microchannels can be realized by guiding all the particles through a capillary in an off-center position of a microchannel, i.e. without any focusing. The particles will be statistically distributed within the parabolic flow profile and undergo self-rotation with different rotation frequencies depending on their location within the flow profile. A different solution can be achieved by guiding all the particles directly to the channel side walls by hydrodynamic focusing. However, even though all the particles will undergo self-rotation, the particle rotation is still not controlled (known a priori) due to the direct particle-wall contact. Particles focusing into a single file arrangement with a unique focal plane can also be achieved by inertial focusing in a high aspect ratio microchannel, i.e. width > height. All these approaches, along with others using external forces, provide only partial control of both 3D positioning and 3D orientation dynamics of flowing particles, therefore a computational methodology to precisely calculate the complete pose of particles is needed, especially when the imaging is finalized to perform 3D shape reconstructions such as tomography.

[0008] This topic is well addressed in HTIFC thanks to the use of holographic imaging. In fact, the uniqueness of holographic microscopy to provide a posteriori quantitative multiple refocusing capability and phase-contrast imaging allows the complete 3D pose estimation of flowing and rotating particles in microfluidic channels. For the 3D particles positioning, well-established methods allow the calculation of both transversal and optical axis positions for all particles imaged in the FoV.

[0009] Concerning the 3D orientation dynamics, currently four different numerical methods have been developed to recover the unknown rotating angles of flowing particles in HTIFC. However, these approaches require prior knowledge of the particles shape and / or refractive index (Rl) to identify correlations among 2D QPMs of the recorded sequence, thus calculating the rotation frequency in the hypothesis of quasi homogeneous rotation dynamic. Very recently, deep convolutional neural networks (DCNNs) have been employed to recover the orientation of flowing red blood cells in digital in-line holographic microscopy, even if also these solutions lack in the generalization capabilities when the shape and / or subcellular components are too diverse from the ones used in the training stage of the DCNN model.

[0010] In the HTIFC system, hundreds of digital holograms per particle are typically (but not exclusively) recorded along a fixed beam direction while they are flowing and rotating in suspension through a microfluidic channel. An example of recorded digital hologram is shown in Figure 1, where the xyz Cartesian reference system has been reported. In particular, z is the optical axis along which digital holograms are recorded, and y is theSIB BI5961R

[0011] flow direction. From each digital hologram, regions of interest (ROIs) containing the flowing particles are cropped and converted into the corresponding QPMs. Let cells be considered as example of possible particles in HTIFC, to reconstruct the 3D tomogram of the RIs of a single cell, the hundreds of its QPMs are given in input to a tomographic algorithm (e.g., the Filtered Back Projection) along with the corresponding viewing angles. In the HTIFC paradigm, the viewing angles correspond to the rotating angles of the cell, as the illumination beam direction is fixed. However, the cell poses, including both the 3D positions inside the FoV and the rolling angles, are not a priori known in a HTIFC setup. Therefore, this information must be numerically retrieved for performing the tomographic reconstruction. As regards the cell’s positions, they can be computed for each frame using any of the existing particle tracking methods. The microfluidic system setting can ensure that cells flow along the y-axis and that they rotate around the x-axis only. Moreover, the roto-translation is hypothesized to be continuous and quasi-uniform, and the recording frame rate is supposed to be high enough to have small angular changes between two successive frames. Therefore, it can be assumed that the angular variation (around the x-axis) between two successive frames is proportional to the position variation along the y-axis. So far, the unknown rotating angles have been recovered by exploiting the latter property as

[0012] 0k= (yk-yi)~ y — / m-yi (1) where ykis the retrieved y-position at the frame k = 1,..., K, m is an integer number, and fmis the frame at which a ml80° rotation has occurred with respect to the first one k = 1 (0! is arbitrarily fixed as 0°).

[0013] To implement this formula, the fmframe must be identified.

[0014] At this aim, all the QPMs 'PK with k = 2,..., K are compared to the first one

[0015]

[0016] by means of an ad hoc image similarity metric, for example the Tamura Similarity Index (TSI). For this reason, this method is termed as matching-based rolling angles recovery method. In fact, the TSI has been demonstrated outperforming other conventional image similarity metrics, like the correlation coefficient or the structure similarity index. For example, if m = 2, a full rotation (i.e., 360°) is searched. However, this method has some important drawbacks that limit its application in HTIFC, related both to the automation and the accuracy.

[0017] In fact, in HTIFC, a fundamental requirement is that all the numerical processing from the holograms to the tomographic reconstruction is fully automatic, since HTIFC aims to the high-throughput reconstruction of big datasets of 3D Rl tomograms in small times. Instead, finding the correct fmvalue often requires a double-check by a human operatorSIB BI5961R

[0018] for two main reasons. In particular, it often happens that the correct / ^ value corresponds to a local minimum close to the absolute one due to high noise levels and / or to a quasi- spherical shape and / or a quasi-homogeneous inner content of the cell, which makes very difficult the detection of phase similarities. Another major source of disturbance is due to multiple rotations of the cell, that can lead to the formation of several local minima related to the several rotations. An example in which the TSI fails in computing the f2frame in an automatic way is displayed in Figure 2 for an ovarian cancer cell. In fact, in this case the visual analysis of the QPMs sequence by a human operator is required to detect f2= 41 as the frame at which a 360° rotation has occurred with respect to the first frame of the QPMs sequence, otherwise impossible through an automatic analysis of the TSI trend.

[0019] However, it is worth underlining that, even if the correct fmframe is identified by the TSI metric, angles are still corrupted by an approximation error, that is intrinsic to the formula in Eq. (1). In fact, Eq. (1) is assuming that the ml80° rotation has been exactly sampled, but this is not true in most cases. Hence, usually a rotation ml80° + s is recorded at the fmframe, instead of the exact ml 80° rotation. The s error belongs to the interval

[0020]

[0021] is the mean angular sampling acquired by the HTIFC system. Hence, the s error propagates throughout the overall sequence of angles ekcomputed through Eq. (1).

[0022] In the light of the problems of the prior art, it is necessary to provide a method for determining the roto-translation dynamics of cells in continuous flow in a microfluidic channel with the aim of calculating the 3D orientation of the sequence of 2D QPMs of a spherical object, for example a cell, for an accurate and precise reconstruction of the 3D tomogram.

[0023] SUMMARY OF THE INVENTION

[0024] The Authors of the present invention overcame the problems of the prior art with a reprojection-based rotating angles recovery method, to solve both the automation and the accuracy issues related to the matching-based rolling angles recovery method of the prior art.

[0025] At this aim, the proportionality between the angular variation (around the x-axis) and the translational variation (along they-axis) has been formulated in a different way, i.e.

[0026] 0fc= (yfc-yi)

[0027]

[0028] where A0 and Ay are the mean angular sampling and the mean y-translational sampling acquired by the HTIFC system, respectively, i.e. the mean angular increment and theSIB BI5961R

[0029] mean y-translational increment that occurs between two successive frames. The d / Tiy value can be interpreted as the average angular increment performed by the cell during its rotation for each pixel of translation along the y-axis. Hence, the formula in Eq. (2) is a generalization of the formula in Eq. (1), and they coincide if a ml80° rotation is exactly acquired at the fmframe.

[0030] The invention has the advantage of allowing accurate estimation of the angle of rotation of objects in flow and therefore being able to obtain, by means of such measurements, refractive index (Rl) tomograms of the single object, through a label-free imaging flow cytometry system. To the best of the inventors’ knowledge, there are no elements, even potential ones, which could constitute a limitation in the use and exploitation of the invention.

[0031] Objects of the present invention are:

[0032] a computer-implemented method for determining the three-dimensional roto-translation of a transparent microscopic object while flowing and rotating along a fluidic channel to obtain the three-dimensional tomographic reconstruction of said object, preferably the three-dimensional refractive index tomographic reconstruction of said transparent microscopic object, comprising the steps of:

[0033] a) retrieving quantitative phase-contrast maps (QPMs) 'PK from corresponding regions of interest (ROIs) in an interferometric image obtained by tomographic imaging flow cytometry recording of said transparent microscopic object imaged along the z-axis, flowing along the y-axis and rotating around the x-axis in a microfluidic channel, wherein k is an integer;

[0034] b) computing the positions ykof said transparent microscopic object, wherein k is an integer;

[0035] c) determining the mean y-translational increment Ay of said transparent microscopic object from the vector of ykpositions through equation (3):

[0036]

[0037] d) determining the mean angular increment (A0) of said transparent microscopic object;

[0038] e) determining the unknown rolling angles ekof said transparent microscopic object, wherein k is an integer, through equation (2):

[0039] 0fc= (yfc-yi) (2),SIB BI5961R f) reconstructing the three-dimensional refractive index tomogram of said transparent microscopic object using the QPMs 4^ retrieved in step a) and the rolling angles 6kdetermined in step e);

[0040] a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of the present invention; an apparatus suitable for carrying out tomographic analysis on a microscopic object as defined in the present invention, comprising a data processing device configured to execute the computer program of the present invention, and / or the computer-readable data carrier of the present invention.

[0041] DETAILED DESCRIPTION OF THE FIGURES

[0042] Figure 1. Example of holographic frame recorded along the optical z-axis by the HTIFC system, containing cells flowing along the y-axis and rotating around the x-axis.

[0043] Figure 2. Trend of the TSI for computing the f2frame in the case of an ovarian cancer cell. The correct f2value is 41 (black circle).

[0044] Figure 3. 3D numerical cell phantom, (a) Isolevels representation of the simulated organelles, i.e. the cell membrane, the cytoplasm, the nucleus, 5 nucleoli, and 10 lipid droplets, (b) Histogram of the Rl distribution assigned to each organelle in (a), (c) Central slice of the 3D Rl tomogram obtained after assigning the Rl distributions in (b) to the organelles in (a).

[0045] Figure 4. Scheme of the steps for building the functional (79L, <p^.

[0046] Figure 5. Minimization problem for retrieving the unknown rolling angles through the reprojection-based method in the simulated case (A0 = 6°). (a) Functional

[0047]

[0048] with highlighted the A0 and the p values corresponding to the global minimum, (b) Filtered functional E(J 0i'), with highlighted the minimum value (circle), corresponding to the simulated A0 = 6°.

[0049] Figure 6. Minimization problem for retrieving the unknown rolling angles through the reprojection-based method in the simulated case (A0 = 9.75°). (a) Functional E(A0j, <p7), with highlighted the A0 and the p values corresponding to the globalSIB BI5961R

[0050] minimum, (b) Filtered functional E(A0(), with highlighted the minimum value (circle), corresponding to the simulated A0 = 9.75°.

[0051] Figure 7. Minimization problem for retrieving the unknown rolling angles through the reprojection-based method in the simulated case (A0 = 2.70°). (a) Functional

[0052]

[0053] with highlighted the A0 and the p values corresponding to the global minimum, (b) Filtered functional E(A0(), with highlighted the minimum value (circle), corresponding to the simulated A0 = 2.70°.

[0054] Figure 8. Minimization problem for retrieving the unknown rolling angles through the reprojection-based method in the experimental case of an ovarian cancer cell. (a) Functional E(A0j,<p7), with highlighted the A0 and the p values corresponding to the global minimum, (b) Filtered functional E(J 0i'), with highlighted the minimum value (circle), corresponding to A0 = 9.25°.

[0055] Figure 9. Refinement of the minimization problem for retrieving the unknown rolling angles through the reprojection-based method in the experimental case of an ovarian cancer cell, (a) Functional E(A0j, <p7), with highlighted the A0 and the p values corresponding to the global minimum, (b) Filtered functional E(J 0i'), with highlighted the minimum value (circle), corresponding to A0 = 9.15°.

[0056] DETAILED DESCRIPTION OF THE INVENTION

[0057] The present invention relates to a computer-implemented method for the three- dimensional tomographic reconstruction of a transparent microscopic object by determining the three-dimensional roto-translation of said transparent microscopic object while flowing and rotating along a microfluidic channel, comprising the steps of:

[0058] a) retrieving quantitative phase-contrast maps (QPMs) 'PK from corresponding regions of interest (ROIs) in an interferometric image obtained by tomographic imaging flow cytometry recording of said transparent microscopic object imaged along the z-axis, flowing along the y-axis and rotating around the x-axis in a microfluidic channel, wherein k is an integer;

[0059] b) computing the positions ykof said transparent microscopic object, wherein k is an integer;

[0060] c) determining the mean y-translational increment Ay of said transparent microscopic object from the vector of yfcpositions through equation (3):SIB BI5961R

[0061]

[0062] d) determining the mean angular increment (A0) of said transparent microscopic object;

[0063] e) determining the unknown rolling angles 0kof said transparent microscopic object, wherein k is an integer, through equation (2):

[0064]

[0065] f) reconstructing the three-dimensional refractive index tomogram of said transparent microscopic object using the QPMs

[0066]

[0067] retrieved in step a) and the rolling angles 0kdetermined in step e).

[0068] In a preferred embodiment, the three-dimensional tomographic reconstruction of said transparent microscopic object is the three-dimensional refractive index tomographic reconstruction of said transparent microscopic object.

[0069] In a preferred embodiment, holo-tomographic imaging flow cytometry (HTIFC) based on digital holography is the interferometric imaging technique for quantitative phase imaging.

[0070] In other words, the method of the present invention allows to precisely measure the 3D orientation dynamics, i.e. rotating angle, of flowing particles in a microfluidic channel within a tomographic imaging flow cytometry system, without any prior knowledge about particle’s shape or biophysical / chemical information, by calculating the 3D orientation of the sequence of 2D QPMs of a microscopic object. Therefore, it is necessary to calculate the mean y-translational increment (Ay) (or mean translational sampling) of said transparent microscopic object from the vector of ykpositions through equation (3), and the mean angular increment (A0) (or mean angular sampling) acquired by the HTIFC system.

[0071] Unless otherwise defined herein, scientific, and technical terms used in connection with the present invention shall have the meanings that are commonly understood by those of ordinary skill in the art. Further, unless otherwise required by context, singular terms shall include pluralities and plural terms shall include the singular.

[0072] According to the present invention, the term “rotating angle” and the term “rolling angle” have the same meaning and refer to the angular displacement of a microscopic object as it moves along the microfluidic channel.

[0073] According to the present invention, the term “transparent microscopic object’’ refers to a fully transparent object or a weak scattering object (biological, organic or inorganic object) having a characteristic size in the micrometer range, in particular from 1 to 1000SIB BI5961R

[0074] m, and for which it is possible to measure the phase map of optical path lengths, thus interacting with an imaging system in a manner that allows the extraction of its three- dimensional structural information through phase- contrast tomographic reconstruction techniques.

[0075] Holographic regions of interest (ROIs) in a digital hologram obtained by HTIFC recording of said transparent microscopic object refer to specific spatial areas within a digitally recorded hologram that contain relevant phase and amplitude information about the microscopic object being imaged. These regions are selected for further processing, analysis, or reconstruction, allowing for enhanced focus on areas of interest while reducing computational complexity and improving imaging accuracy. Identified within the holographic dataset, these ROIs enable targeted tomographic reconstruction of the three-dimensional refractive index distribution of the object, facilitating detailed morphological and structural analysis in applications such as biomedical imaging, flow cytometry, and label-free optical microscopy.

[0076] Quantitative phase-contrast map (QPM) refers to a computationally generated representation of the phase shift induced by a microscopic object when light passes through it, providing quantitative information about the optical path length variations across the sample. This map is obtained through interferometric or digital holographic imaging techniques and encodes the Rl distribution and thickness variations of the object with high precision.

[0077] Segmentation of a microscopic object while flowing and rotating in a microfluidic channel refers to the identification and isolation of the microscopic object from its surrounding environment in the QPMs computationally generated from HTIFC recordings. Segmentation enables precise differentiation of the object from background noise, facilitating quantitative analysis, classification, and visualization for applications such as optical imaging and flow cytometry.

[0078] Three-dimensional recovery of a microscopic object by determining the 3D roto-translation of said transparent microscopic object while flowing and rotating in a microfluidic channel refers to the process of reconstructing the three-dimensional structure of a microscopic object by tracking its translational movement and rotational changes as it flows through a microfluidic system. This reconstruction enables the extraction of morphological and Rl information, allowing for detailed analysis of the object's structural properties.

[0079] In an embodiment, the method to recover a QPM from a holographic ROI is termed phase retrieval, which is an iterative algorithm in the case of in-line holographic recordingSIB BI5961R

[0080] configuration and a single-shot processing in the case of off-axis holographic recording configuration. Both approaches share the following steps: automatic refocusing, phase aberration compensation and phase unwrapping. Alternative methods involve deep convolutional neural networks to predict a QPM from a holographic ROI.

[0081] In an embodiment, three main steps may be identified to implement a 3D holographic particle-tracking analysis: 1) particle detection, where elements standing out from the background are labeled by implementing suitable image detection approaches, 2) axial localization of particles through automatic refocusing criteria, 3) transverse particle localization based on image segmentation techniques.

[0082] In a preferred embodiment, the mean angular increment (A0) (or mean angular sampling) of said transparent microscopic object in step d) is determined by a method comprising the following steps:

[0083] i) fixing a search range for the A0 value, by providing Ae values, wherein i is an integer;

[0084] ii) for each Ae:

[0085] ii-a) computing all the corresponding angles ekl= 6k( 6 of said microscopic object through equation (2);

[0086] ii-b) constructing a tomogram Tk=2 Kof said transparent microscopic object by using all the QPMs except the first one, wherein k is an integer; ii-c) rotating backwards the tomogram Tk=2 Kobtained in step ii-b) around the x-axis by a reprojection angle pj wherein j is an integer, thereby obtaining a rotated tomogram Tk 2 K

[0087] ii-d) for each reprojection angle pj,

[0088] ii-d-1) retro-projecting the rotated tomogram Tk 2 Kobtained in step ii-c) along the optical z-axis wherein digital holograms are registered in order to emulate a quantitative phase-contrast map (QPM) formation, thus obtaining a reprojected QPM

[0089]

[0090] ii-d-2) comparing the reprojected QPM

[0091]

[0092] obtained in step ii-d-1) to the QPM 'Pfc with k=1 obtained in step a);

[0093] iii) creating a functional E(A9L, <pj), wherein i and j are integers.

[0094] According to the present invention, “using all the QPMs except the first one” means that the QPM having k=1 is not used.SIB BI5961R

[0095] Fixing a search range in the context of defining a mean angular increment A0 refers to establishing a predefined interval within which the mean angular increment values A0 are selected for determining the rotation of a microscopic object in a tomographic reconstruction process.

[0096] In other words, in step ii) each discrete angular increment value A0 within the fixed search range is taken and used to calculate all the corresponding absolute rotation angles eklof the microscopic object. This means that, for each specific A0, the complete set of angles eklthat describe the object's orientation in space is determined through a predefined mathematical equation.

[0097] The phrase "constructing a tomogram Tk=2 Kof said transparent microscopic object, wherein k is an integer" refers to the process of generating a three-dimensional (3D) reconstruction (tomogram) of the microscopic object by combining multiple two-dimensional (2D) QPMs taken at different orientations except the first one. The tomogram is built using the computed set of angles eklfrom the previous step, where k = 2,..., K represents discrete time frames or image acquisitions during the rotation of the object.

[0098] The subsequent step, "rotating backwards the tomogram Tk=2 Kobtained in the previous step by a reprojection angle pj wherein j is an integer, thereby obtaining a rotated tomogram Tk 2 K", means that the initially reconstructed tomogram is further processed by applying a corrective rotation (backward rotation) based on a reprojection angle pj. This rotation accounts for the property that the tomogram Tk=i K= T(k, 8k\k = 1,

[0099]

[0100] reconstructed by using all the QPMs, is rotated around the x-axis by an angle ■~A01= ~(02- 0-i) = “02 with respect to the tomogram Tk 2,..., K ~ TQ¥k,dk\k ~ 2,

[0101]

[0102] reconstructed by using all the QPMs except the first one. “Applying a corrective rotation” refers to the process of transforming a tomographic reconstruction by modifying its orientation in three-dimensional space according to a specified rotation angle and rotation axis. In particular, “a backward rotation based on a reprojection angle” refers to the adjustment of a reconstructed tomogram by rotating it in the opposite direction of a previously estimated rotational motion.

[0103] In an embodiment, said reprojection angle pj in step ii-c) is taken from a fixed reprojection range, made of J angles pj, preferably with a step of at least the angular resolution of the recording system, that is the minimum angular variation of the rotating object detectable by the imaging system.

[0104] In the subsequent step, for each reprojection angle <p7:SIB BI5961R

[0105] The previously rotated tomogram T^’2 Kis processed by retro-projecting it along the optical axis used during the digital hologram acquisition.

[0106] In an embodiment, said retro-projection is preferably the integration of the rotated tomogram along the optical z-axis.

[0107] " Retro-projecting along the optical axis used during the digital hologram acquisition" means projecting in the two-dimensional (2D) space the three-dimensional (3D) tomographic data along the same direction in which the optical system captured the original holograms. In the context of holographic tomography, the optical axis refers to the direction in which the imaging system records the light that interacts with the microscopic object. Since digital holography captures phase information in a 2D plane, the 3D tomogram must be mathematically collapsed or projected along this axis to simulate how the quantitative phase-contrast map (QPM) would appear if the object were imaged under the same conditions as the original acquisition. This integration simulates the way a quantitative phase-contrast map (QPM) is formed, effectively reconstructing a synthetic phase map that mimics the actual imaging conditions. The result of this integration is a reprojected QPM(P1,7, which represents how the reconstructed microscopic object would appear in a phase contrast imaging system. The reprojected QPM O'1,7obtained in the previous step is then compared to the reference QPM 'PK with k=1, which corresponds to the actual QPM acquired from the first recorded hologram. In one embodiment, said step ii-d-2) is carried out through an imaging similarity metric. In an embodiment, such imaging similarity metric is selected from Tamura Similarity Index (TSI) metric, Spatial Correlation Coefficient (SCC), Structural Similarity Index Measure (SSIM), Universal Image Quality Index (UIQI) or Gradient Magnitude Similarity Deviation (GMSD)

[0108] The Tamura Similarity Index (TSI) is a computational metric based on the Tamura Coefficient (TC), which quantifies the local contrast of an image by computing the ratio of the standard deviation to the mean of pixel intensity values within a defined local neighborhood. The TSI is used to compare two phase images by evaluating the similarity of their local contrast distributions.

[0109] The Spatial Correlation Coefficient (SCC) is a similarity metric that evaluates the degree of linear correlation between corresponding pixel intensity values of two images. It is computed as the normalized cross-correlation, where values close to 1 indicate strong spatial similarity, and values near 0 indicate little or no correlation. The SCC is particularly useful for assessing global structural similarity in grayscale images.

[0110] The Structural Similarity Index Measure (SSIM) is a perceptual similarity metric that compares two images based on luminance, contrast, and structural information. It isSIB BI5961R

[0111] designed to model the human visual perception of image quality and is calculated within local windows across the image. SSIM values range from -1 to 1, with 1 indicating perfect structural similarity.

[0112] The Universal Image Quality Index (UIQI) is a full-reference image similarity metric that evaluates image quality based on three components: correlation, luminance distortion, and contrast distortion. It provides a single scalar value between -1 and 1 that quantifies the overall similarity between two images. The UIQI is effective in measuring perceptual degradation due to processing operations such as compression or reconstruction. The Gradient Magnitude Similarity Deviation (GMSD) is an image quality assessment metric that measures the deviation in gradient magnitude similarity between two images. It captures local structural changes by comparing the edge and texture information encoded in gradient magnitudes. GMSD produces a single quality score, where lower values indicate higher similarity. It is especially sensitive to structural distortions and is suitable for evaluating tomographic image reconstructions.

[0113] “Creating a functional

[0114]

[0115] wherein i and j are integers” refers to defining a mathematical function that evaluates the accuracy of the tomographic reconstruction by quantifying the alignment between a reprojected quantitative phase-contrast map and a reference quantitative phase-contrast map. The functional takes as input a mean angular increment (Ae ) representing a mean rotational step used in the reconstruction process, and a reprojection angle pj, applied to adjust the tomogram's alignment. The function computes a scalar value representing an error or similarity measure between the reprojected quantitative phase-contrast map, obtained from the tomographic reconstruction after applying the mean angular increment and the reprojection angle, and the original reference quantitative phase-contrast map acquired during HTIFC imaging. The functional is used to optimize the selection of mean angular increments and reprojection angles by minimizing the discrepancy between the computed and reference phase-contrast maps, thereby enhancing the accuracy of the tomographic reconstruction.

[0116] Theoretically, the functional

[0117]

[0118] is minimum when, given the correct A0 value, the corresponding tomogram Tk,zz2K has been rotated backward by the angle <p ~ 02- However, due to the approximation errors introduced by the linear model for the light propagation and by the numerical rotation of the tomogram, the minimization with respect to the reprojection angle <p may be wrong. Nevertheless, this is not a problem because, according to Eq. (2), the sole A0 value is enough to retrieve the unknown rotating angles.SIB BI5961R

[0119] Therefore, in one embodiment the determination of the A0 value of said transparent microscopic object in step d) further comprises the steps of:

[0120] iv) averaging the functional E ebp^ with respect to the p variable through the equation (4):

[0121]

[0122] v) applying a moving average to the functional E(E9j thereby obtaining a filtered functional

[0123]

[0124] vi) computing the A0 value by minimizing the filtered functional E(J Oi').

[0125] “Averaging the functional

[0126]

[0127] respect to the variable cp” refers to the process of computing a representative value of the functional E( ebp^ over multiple values of the reprojection angle pj, thereby reducing the dependence on individual pj values and obtaining a more stable measure of error or similarity. Mathematically, this means integrating or summing the functional over all considered values of pj and normalizing it by the number of terms, so that the resulting expression provides an averaged error or similarity measure associated with the sole mean angular increment A0.

[0128] “Applying a moving average to the functional E(A0j, <p7)” refers to the process of smoothing the functional by computing an average of its values over a predefined window of neighboring angular increments, thereby reducing local fluctuations and obtaining a filtered functional E Ot). The filtered functional represents a smoothed version

[0129]

[0130] , wherein noise and abrupt variations due to individual values of the reprojection angle pj are attenuated, ensuring a more stable and continuous function for further processing in the optimization of mean angular increments.

[0131] In an embodiment, in said step v), said moving average has a length of at least 3, preferably 3. Applying a moving average of 3 to the functional refers to the process of smoothing the functional by replacing each of its values with the average of the corresponding value and its two neighboring values, thereby obtaining a filtered functional, thereby reducing noise and local fluctuations by computing, for each index i, the arithmetic mean

[0132]

[0133] Moreover, the last step of computing the Ae value by minimizing the filtered functional E(A0j) refers to the process of determining the optimal angular increment A0 by identifying the value of Ae that results in the minimum value of the filtered functional E(A0j) through the Grid Search method.SIB BI5961R

[0134] The Grid Search Method is a computational optimization technique used to identify the minimum (or maximum) of a functional by systematically evaluating the functional over a discrete set of candidate solutions defined across a multi-dimensional parameter space. The method operates by constructing a finite grid of parameter combinations within pre-defined bounds and computing the value of the functional at each grid point. The parameter set yielding the lowest functional value is selected as the optimal solution.

[0135] The tomographic reconstruction is obtained by implementing an algorithm fed by the QPMs and the retrieved rotating angles, preferably the Filtered Back Projection algorithm, or diffraction- based algorithms or total variation algorithms or iterative algorithms or machine learning-based algorithms.

[0136] The Filtered Back Projection (FBP) algorithm is a tomographic reconstruction method that computes a volumetric representation of an object from a set of two-dimensional projection images acquired at different viewing angles. The algorithm operates by first applying a filtering operation — typically a high-pass filter such as a Ram-Lak or Shepp-Logan filter — to each projection in the frequency domain, enhancing high-frequency components. The filtered projections are then back-projected along their respective acquisition angles to reconstruct the spatial distribution of a physical property, such as the refractive index.

[0137] Diffraction-based algorithms are computational reconstruction methods that model the propagation of light through a sample according to the principles of wave optics, typically using approximations such as the Rayleigh-Sommerfeld, Fresnel, or angular spectrum methods. These algorithms account for phase delays and interference effects induced by the internal structure of the sample, enabling the reconstruction of its three-dimensional refractive index distribution from phase images.

[0138] Total Variation algorithms are iterative reconstruction techniques that minimize the total variation norm of the reconstructed volume, promoting piecewise-smooth solutions while preserving sharp structural boundaries. These algorithms are particularly effective in suppressing noise and reducing reconstruction artifacts, especially when the number of input projections is limited. In the context of microscopic phase imaging, total variation algorithms are used to recover high-fidelity three-dimensional morphologies of microscopic entities by regularizing the reconstruction process with spatial sparsity constraints.

[0139] Iterative algorithms are reconstruction methods that progressively refine an estimated volumetric representation of an object by repeatedly updating it to minimize theSIB BI5961R

[0140] discrepancy between simulated and measured data. Examples include the Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), and Expectation-Maximization approaches.

[0141] Machine learning-based algorithms are data-driven reconstruction techniques that utilize trained models to infer the three-dimensional structure of an object from two-dimensional projection data.

[0142] A microscopic object refers to any object of a size that requires optical or electron microscopy for observation and analysis, in particular object having a characteristic size in the micrometer range, in particular from 1 to 1000 µm, which is capable of interacting with an imaging system in a manner that allows the extraction of its three-dimensional structural information through phase-contrast tomographic reconstruction techniques. Such an object may be biological, organic, or inorganic. Biological microscopic objects include individual cells, cellular aggregates, microorganisms, biological tissue samples and other biological structures, while inorganic microscopic objects may comprise synthetic microparticles, colloidal suspensions, or other finely divided materials with dimensions at the microscale. Organic microscopic objects may include polymeric microparticles or naturally occurring microscopic structures of organic origin.

[0143] In a preferred embodiment, the microscopic object is a cell or a spheroidal cluster of cells, which can be either a eukaryotic cell or a prokaryotic cell. Eukaryotic cells include those found in multicellular organisms such as plants, animals, and fungi, while prokaryotic cells refer to unicellular organisms such as bacteria and archaea.

[0144] In certain embodiments, the microscopic object is selected from diatoms, pollen grains, algae, yeast cells, fungi, or fungal spores or other transparent microscopic objects for which it is of interest to obtain a 3D Rl tomogram.

[0145] In another embodiment, the microscopic object is a mammalian cell, which may include cells derived from tissues of multicellular organisms. In a more specific embodiment, the mammalian cell is a human cell, which can encompass a broad range of cell types, including somatic cells, stem cells, and blood cells. Among human cells, particular interest lies in cancer cells and blood cells.

[0146] Forms part of the present invention a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method described in the present description.SIB BI5961R

[0147] Further object of the present invention is a computer-readable data carrier having stored there on the computer program described by any one of the embodiments herein disclosed.

[0148] In an embodiment, said computer-readable data carrier is in the form of a USB pen-drive, an external hard disk (HDD), a compact disc (CD), a digital versatile disc (DVD).

[0149] Another object of the present invention is an apparatus suitable for carrying out tomographic analysis on a microscopic object, i.e. a cell or on a group of cells, comprising a data processing device configured to execute the computer program herein described, and / or the computer-readable data carrier according to the previous embodiments. In an embodiment, said apparatus is a flow cytometer comprising a microfluidic modulus. In a further embodiment, said apparatus comprises means of a light source to illuminate the cells flowing in the said microfluidic modulus, having the appropriate features of coherence such that an interference pattern, preferably a digital hologram, can be recorded on the digital camera, and a microscope objective to image the cells with the appropriate resolution and magnification and project said in focus or out of focus images on the sensor of the camera.

[0150] In an embodiment according to the present description, said light source can be selected among any source having appropriate coherence, preferably lasers, diode pumped solid state lasers, and Light Emitting Diodes (LEDs).

[0151] In another embodiment, said light source can be selected among any wavelength in the visible range or any other regions of the electromagnetic spectrum including X-ray regions.

[0152] Furthermore, in an embodiment of the present invention, the polarization state of said light source can be selected among any possible polarization state. The polarization is the phenomenon in which waves of light or other radiation are restricted in direction of vibration.

[0153] In an embodiment of the present invention, according to any of the embodiments herein disclosed, said apparatus is used with a single illumination source or with multiple sources having the same wavelength or multiple wavelengths.

[0154] In an additional embodiment, said apparatus is used with a single polarization state or with multiple sources having multiple polarization states.

[0155] In an embodiment of the present description, said apparatus is characterized in that the imaged Field of View of the digital hologram is such that the flowing cell experiences an enough amount of rotation angle while it travels inside the said field of view in order toSIB BI5961R

[0156] retrieve a useful tomogram. Field of View of the digital hologram is the interference area imaged by the sensor of the camera.

[0157] In an embodiment, said apparatus is further characterized in that the acquisition frame rate of the camera is fast enough with respect to the longitudinal and angular cell velocity, to record the cells at different rotating positions with enough angle resolution in order to retrieve a useful tomogram of each cell.

[0158] Additionally, in an embodiment of the present invention, said apparatus has said microfluidic modulus which operates and is engineered or customized in the appropriate way in order to guarantee that the flowing cells rotate along the microfluidic channel in a way that assures the recovery of the tomogram.

[0159] In another embodiment according to the present description, said microfluidic modulus has channel dimensions selected according to the size of the object and the flow properties in order to guarantee the rotation around a single axis perpendicular to flow axis and optical axis.

[0160] In an embodiment, said biological fluid sample is selected from the following ones: blood, urine, cerebrospinal fluid, saliva, tear fluid.

[0161] In an embodiment, the apparatus of the present invention is used in liquid biopsy for detection and classification of circulating tumor cells (CTCs) in a biological fluid sample taken from a patient.

[0162] In an embodiment, the apparatus of the present invention is used in drug testing to evaluate the drug effects on biological samples from a patient. This also allows to personalize the therapeutic approach for the patient.

[0163] In an embodiment, the apparatus of the present invention is used in single-cell analysis to statistically evaluate cellular populations in a biological sample. This enables the qualitative characterization of the cell heterogeneity in a 3D and label-free manner.

[0164] In compliance with Art. 170bis of the Italian patent law it is herein declared that all experiments involving cells were carried out on commercially available cells.

[0165] In any part of the present description and claims, the term comprising can be substituted by the term “consisting of”.

[0166] Examples are reported below which have the purpose of better illustrating the methodologies disclosed in the present description, such examples are in no way to be considered as a limitation of the previous description and the subsequent claims.SIB BI5961R

[0167] EXAMPLES

[0168] Here it is proposed a reprojection-based rolling angles recovery method to solve both the automation and the accuracy issues related to the matching-based rolling angles recovery method summarized above. At this aim, the proportionality between the angular variation (around the x-axis) and the translational variation (along the y-axis) has been formalized in a different way, i.e.

[0169]

[0170] where 0 and Ay are the mean angular sampling and the mean y-translational sampling acquired by the HTIFC system, respectively, i.e. the mean angular increment and the mean y-translational increment that occurs between two successive frames. The A9 / Ay value can be interpreted as the average angular increment performed by the cell during its rotation for each pixel of translation along the y-axis. Hence, the formula in Eq. (2) is a generalization of the formula in Eq. (1), and they coincide if a ml80° rotation is exactly acquired at the fmframe.

[0171] In order to present and validate the reprojection-based rolling angles recovery method, the 3D numerical cell phantom displayed in Figure 3 has been considered. As shown in Figure 3(a), several organelles have been simulated, i.e. the cell membrane, the cytoplasm, the nucleus, 5 nucleoli, and 10 lipid droplets. The Rl distributions reported in Figure 3(b) have been assigned to each organelle, thus obtaining the 3D Rl tomogram displayed in Figure 3(c). To simulate an angular sequence, without loss of generality, it has been fixed Ay = 24 pixels. Then, starting from y ~ 0, an array of equidistant ykpositions has been created, with k = 1, K. To consider a non-uniform roto-translation, each ykposition has been perturbed by a 6kvalue randomly drawn from the integer uniform distribution U(-6,6), with k - 2,

[0172]

[0173] Finally, K = 61 rolling angles 6khave been computed through Eq. (2) by fixing AS ~ 6°. This means that an average roto-translation of the cell of 0.25° / pixel has been simulated. Note that the 360° rotation has not been sampled, as the cell passes from 06O= 356° to 061= 361.5°. Finally, the QPMs

[0174]

[0175] have been simulated, with k ~ 1,

[0176]

[0177] by integrating the tomogram along the simulated 8kangles, according to the linear approximation of the light propagation.

[0178] It is worth pointing out that in a real experimental problem:

[0179] 1. the QPMs TT are numerically extracted from the corresponding holographic ROIs,

[0180]

[0181] 2. the ykpositions are computed through the holographic tracking algorithms, with k = 1,... CSIB BI5961R

[0182] 3. the Ay value is measured from the vector of yfepositions as

[0183]

[0184] 4. the A0 value is estimated through the reprojection-based method;

[0185] 5. the θkunknown rolling angles, with k = 1,

[0186]

[0187] are retrieved through Eq. (2).

[0188] Hereafter it is discussed the reprojection-based method to estimate the ’8 value at step 4 by using the K QPMs

[0189]

[0190] the corresponding ykpositions and the Ay value. The proposed method is based on the property that the tomogram Tk,:=1 K= T(k, 8k\k = 1,

[0191]

[0192] reconstructed by using all the QPMs, is rotated around the x-axis by an angle -A0-! = ~(62~0i) = ~~ 2 with respect to the tomogram Tfe=,2,..., K ” TQ¥k, 9k\k ~ 2,

[0193]

[0194] reconstructed by using all the QPMs except the first one

[0195] 4.1 A search range for the AA value is fixed, made of AS, values, with i = 1,.... N (in this example, the search range is [0.25°, 12°] with step 0.25°).

[0196] 4.2 For each

[0197]

[0198] a. all the corresponding angles 6k= 8k(&9i) are computed according to Eq. (2); b. the tomogram T^=2 Kis reconstructed;

[0199] c. the tomogram

[0200]

[0201] rotated backwards by an angle pj taken from a fixed reprojection range, made of j =

[0202]

[0203] angles <p,, thus obtaining the rotated tomogram Tkl2 K(in this example, the reprojection range is [0.25°, 12°] with step 0.25°);

[0204] d. for each reprojection angle <pj,

[0205] i. the rotated tomogram T^:2 kis integrated along the optical z-axis in order to emulate the QPM formation, thus obtaining the reprojected

[0206]

[0207] is compared to the first real QPM % through the TSI metric.

[0208] 4.3 A functional E( 0, <p,) is built,

[0209]

[0210] Theoretically, the functional E( 9b<p ) is minimum when, given the correct At? value, the corresponding tomogram 7=2,... has been rotated backward by the angle <p ~ 62. However, due to the approximation errors introduced by the linear model for the light propagation and by the numerical rotation of the tomogram, the minimization with respect to the reprojection angle <p may be wrong. Nevertheless, this is not a problem because,SIB BI5961R

[0211] according to Eq. (2), the sole A0 value is enough to retrieve the unknown rolling angles. Therefore

[0212] 4.4 The functional E(Keit<p;) is averaged with respect to the (p variable, i.e.

[0213]

[0214] 4.5 A moving average with length 3 is applied to the functional E(A0£), thus obtained the filtered functional E(A0£).

[0215] 4.6 The A9 value is finally computed by minimizing the filtered functional E(A6h).

[0216] The steps 4.1-4.3 for building the functional

[0217]

[0218] are sketched in Figure 4. In Figure 5(a) it is reported the functional E( 0£, <p;) related to the simulation described above, carried out by fixing A6 = 6°. It can be seen that the functional E(A0(, y?,) is minimized in the correct A( = 6° but in the wrong <p ~ 7.75° (the simulated value

[0219]

[0220] = 6.25°). Even if the searched solution At? = 6° is already obtained at this step in this example, to boost the robustness of the proposed method towards an experimental case, the functional E’(A0 (pi') is further averaged (step 4.4) and filtered (step 4.5), thus obtaining the filtered functional E(A0£) displayed in Figure 5(b), which minimum (step 4.6) is again the correct A0 = 6°. Other two simulations are reported in Figure 6 and Figure 7. In particular, the reprojection-based method is able to recover the correct A0 = 9.75° in Figure 6 and the correct AS = 2.70° in Figure 7. In Figure 7, the search range is [0.1°, 12°] with step 0.1°. As regards the experimental case discussed in Figure 2 about the ovarian cancer cell, a first search range [0.25°, 12°] has been fixed with step 0.25° and the functionals reported in Figure 8 are obtained by using all the K = 120 recorded QPMs. It is worth highlighting that, in this case, the A9 value which minimizes the functional

[0221]

[0222] in Figure 8(a) is 1.75°, which instead should be close to 9° according to the matching-based method in Figure 2. instead, the average and the filtering operations allow overcoming this error, thus reaching the AS = 9.25° solution in Figure 8(b). Moreover, to refine the At? value, the same pipeline can be repeated by considering a narrower and thicker search range and reprojection range around 9.25°, i.e. [8.25°, 10.25°] with step 0.05°, as shown in Figure 9. However, in order to obtain a more accurate solution, in this refinement case it has been considered only the first K ~ 42 recorded QPMs, that correspond to the frames requested by the cell to perform a full 360° rotation, according to the Eq. (2) if A0 = 9.25° is used. In this way, the refined solution is A0 = 9.15°. By applying Eq. (2), the unknown rolling angles 9kare retrieved. Hence, it has been obtained that a full rotation occurs between frames 40 and 41, since we have that 640- 3 6.4° and 041= 365.9°, accordingSIB BI5961R to the solution obtained through the human inspection of the matching-based method, i.e. f2- 41

Claims

SIB BI5961RCLAIMS1. A computer-implemented method for determining the three-dimensional roto-translation of a transparent microscopic object while flowing and rotating along a fluidic channel to obtain the three-dimensional tomographic reconstruction of said transparent microscopic object, preferably the three-dimensional refractive index tomographic reconstruction of said transparent microscopic object, comprising the steps of:a) retrieving quantitative phase contrast maps (QPMs)from corresponding regions of interest (ROIs) in an interferometric image obtained by tomographic imaging flow cytometry recording of said transparent microscopic object flowing along the y-axis and rotating around the x-axis in a microfluidic channel, wherein k is an integer;b) computing the positions ykof said transparent microscopic object, wherein k is an integer;c) determining the mean y-translational increment Ay of said transparent microscopic object from the vector of yfcpositions through equation (3):d) determining the mean angular increment ( 0) of said transparent microscopic object;e) determining the unknown rolling angles 6kof said transparent microscopic object, wherein k is an integer, through equation (2):f) reconstructing the three-dimensional refractive index tomogram of said transparent microscopic object using the QPMsretrieved in step a) and the rolling angles 6kdetermined in step e).

2. The method according to claim 1, wherein the A0 value of said transparent microscopic object in step d) is determined by a method comprising the following steps:i) fixing a search range for the A0 value, by providing Ae values, wherein i is an integer;ii) for each e:ii-a) computing all the corresponding angles ekl= Gn^ Gt) of said microscopic object through equation (2);ii-b) constructing a tomogram Tk=2 Kof said transparent microscopic object by using all the QPMs except the first one, wherein k is an integer;SIB BI5961Rii-c) rotating backwards the tomogram T^=2 Kobtained in step ii-b) around the x-axis by a reprojection angle pj wherein j is an integer, thereby obtaining a rotated tomogram T^2 K.ii-d) for each reprojection angle pj,ii-d-1) retro-projecting the rotated tomogram T^2 Kobtained in step ii-c) along the optical z-axis wherein digital holograms are registered in order to emulate a quantitative phase-contrast map (QPM) formation, thus obtaining a reprojected QPM T71,7;ii-d-2) comparing the reprojected QPM O'1’7obtained in step ii-d-1) to the QPM 'Pfc with k=1 obtained in step a);iii) creating a functional E(A0j, <p7), wherein i and j are integers.

3. The method according to claim 2, wherein said method of determination of A0 value in step d) further comprises the steps of:iv) averaging the functional E ebp^ with respect to the p variable through the equation (4):v) applying a moving average to the functional E ebp^ thereby obtaining a filtered functionalvi) computing the A0 value by minimizing the filtered functional E(J Oi').

4. The method according to anyone of claims 2 or 3, wherein said reprojection angle pj in step ii-c) is taken from a fixed reprojection range, made of ] angles pj, preferably with a step of at least the angular resolution of the recording system, wherein said angular resolution of the recording system is the minimum angular variation of the rotating object detectable by the imaging system.

5. The method according to anyone of claims 3 or 4, wherein in said step ii-d-1), said retro-projection is the integration of the rotated tomogram along the optical z-axis.

6. The method according to anyone of claims 2 to 5, wherein said step ii-d-2) is carried out through an imaging similarity metric, preferably selected from Tamura Similarity Index (TSI), Spatial Correlation Coefficient (SCC), Structural Similarity Index MeasureSIB BI5961R(SSIM), Universal Image Quality Index (U I QI) or Gradient Magnitude Similarity Deviation (GMSD).

7. The method according to anyone of claims 3 to 6, wherein in said step v), said moving average has a length of at least 3.

8. The method according to anyone of claims 3 to 7, wherein said step vi) is carried out through the Grid Search method.

9. The method according to anyone of claims 1 to 8, wherein said step f) is carried out by a tomographic reconstruction algorithm fed by the QPMs and the retrieved rotating angles, preferably wherein the tomographic reconstruction algorithm is the Filtered Back Projection algorithm, or diffraction-based algorithms or total variation algorithms or iterative algorithms or machine learning-based algorithms.

10. The method according to anyone of claims 1 to 9, wherein said tomographic imaging flow cytometry system to record interferometric images is holo-tomographic imaging flow cytometry (HTIFC).

11. The method according to anyone of claims 1 to 10, wherein said transparent microscopic object is a cell or a spheroidal cluster of cells.

12. The method according to claim 11, wherein said cell is a eukaryotic cell or a prokaryotic cell.

13. The method according to anyone of claims 11 or 12, wherein said transparent microscopic object is selected from diatom, pollen grain, algae, yeast cell, a fungi or fungal spore.

14. The method according to anyone of claims 11 to 13, wherein said transparent microscopic object is a mammalian cell, preferably is a human cell, a blood cell or a cancer cell.

15. The method according to anyone of claims 1 to 14, wherein the size of said microscopic object is from 1 to 1000 m, preferably from 1 to 100 pm,SIB BI5961R16. The method according to anyone of claims 1 to 15, wherein said transparent microscopic object is a fully transparent object or a weak scattering object for which it is possible to measure the phase map of optical path lengths.

17. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any one of claims 1 to 16.

18. A computer-readable data carrier having stored there on the computer program of claim 17.

19. An apparatus suitable for carrying out tomographic reconstruction of a microscopic object as defined in claims 11-16, comprising a data processing device configured to execute the computer program of claim 17, and / or the computer-readable data carrier of claim 18.

20. The apparatus according to claim 19, wherein said apparatus is a flow cytometer comprising a microfluidic modulus21. The apparatus according to anyone of claims 19 or 20, for use in liquid biopsy for detection and classification of circulating tumor cells (CTCs) in a biological fluid sample taken from a patient.

22. The apparatus according to anyone of claims 19 or 20, for use in drug testing to evaluate the drug effects on biological samples from a patient.

23. The apparatus according to anyone of claims 19 or 20, for use in single-cell analysis to statistically evaluate cellular populations in a biological sample.

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