Algorithms for automated characterization of cell populations in thick specimens from 3-D confocal fluorescence microscopy data

Methods are presented for the automated, quantitative and three-dimensional (3-D) analysis of cell populations in thick, essentially intact tissue sections while maintaining intercell spatial relationships. This analysis replaces current manual methods which are tedious and subjective. The thick sample is imaged in three dimensions using a confocal scanning laser microscope. The stack of optical slices is processed by a 3-D segmentation algorithm that separates touching and overlapping structures using localization constraints. Adaptive data reduction is used to achieve computational efficiency. A hierarchical cluster analysis algorithm is used automatically to characterize the cell population by a variety of cell features. It allows automatic detection and characterization of patterns such as the 3-D spatial clustering of cells, and the relative distributions of cells of various sizes. It also permits the detection of structures that are much smaller, larger, brighter, darker, or differently shaped than the rest of the population. The overall method is demonstrated for a set of rat brain tissue sections that were labelled for tyrosine hydroxylase using fluorescein-conjugated antibodies. The automated system was verified by comparison with computer-assisted manual counts from the same image fields.     

Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy

Confocal scanning laser microscopy (CSLM) provides optical sectioning of a fluorescent sample and improved resolution with respect to conventional optical microscopy. As a result, three-dimensional (3-D) imaging of biological objects becomes possible. A difficulty is that the lateral resolution is better than the axial resolution and, thus, the microscope provides orientation-dependent images. However, a theoretical investigation of the process of image formation in CSLM shows that it must be possible to improve the resolution obtained in practice. We present two methods for achieving such a result in the case of 3-D fluorescent objects. The first method applies to conventional CSLM, where the image is detected only on the optical axis for any scanning position. Since the resulting 3-D image is the convolution of the object with the impulse-response function of the instrument, the problem of image restoration is a deconvolution problem and is affected by numerical instability. A short introduction to the linear methods developed for obtaining stable solutions of these problems (the so-called regularization theory of ill-posed problems) is given and an application to a real image is discussed. The second method applies to a new version of CSLM proposed in recent years. In such a case the full image must be measured by a suitable array of detectors. For each scanning position the data are not single numbers but vectors. Then, in order to recover the object, one must solve a Fredholm integral equation of the first kind. A method for the solution of this equation is presented and the possibility of achieving super-resolution is demonstrated. More precisely, we show that it is possible to improve by about a factor of 2 the resolution of conventional CSLM both in the lateral and axial directions.     

Visualization of volume data in confocal microscopy: comparison and improvements of volume rendering methods

Confocal microscopes routinely produce three-dimensional data sets. The visualization of these digital volumes is currently performed by one surface rendering or volume rendering approach. In this paper, we describe improvements developed in the field of volume rendering. We focused on three methods: parallelepiped face mapping: the rotation-projection method (with or without stereoscopy, with different matters and transparencies); the voxel ray-tracing method. We compared the possibilities of these different algorithms, in terms of quality of rendering, of computation load and as an essential aid to study the 3D organization of biological specimens.     

The significance of 3-D transfer functions in confocal scanning microscopy

The three-dimensional (3-D) transfer function is a useful concept for describing image formation in confocal scanning microscopy. From it we can derive the corresponding 2-D transfer function for in-focus imaging. In confocal transmission this can be derived analytically. The 1-D transfer function for on-axis imaging, which can be expressed in an analytical form even for confocal fluorescence with differing wavelengths of excitation and fluorescence, can be derived from the 3-D transfer function. The 2-D transfer function for in-focus imaging in confocal fluorescence microscopy with a finite-sized detector is also presented, which is shown to exhibit sign changes and can therefore result in reversals of image contrast.     

Modelling and analysis of 3-D arrangements of particles by point processes with examples of application to biological data obtained by confocal scanning light microscopy

Within the concept of point processes, a review is presented of quantities which can be used in studies of three-dimensional (3-D) aggregates of particles. Suitable characteristics and estimators are given for both unmarked and marked point processes. To demonstrate the feasibility of such quantitative approaches, an application in histology, dealing with 3-D arrangements of cell nuclei in rat liver, is described. Using a confocal scanning light microscope, 3-D images are recorded and image analysis used to obtain the coordinates of the centroid, together with the volume and DNA content, of each cell nucleus. Examples of results are given, using both unmarked and marked point processes. In the latter case, cell type, nuclear volume and ploidy group are suitable marks.     

An FFT-based method for attenuation correction in fluorescence confocal microscopy

A problem in three-dimensional imaging using a confocal scanning laser microscope (CSLM) in the (epi)fluorescence mode is the darkening of the deeper layers due to absorption and scattering of both the excitation and the fluorescence light. A new method is proposed to correct for these effects. The approach, valid for weak attenuation, consists of multiplying the measured fluorescence intensity by a correction factor involving a convolution integral of the measured signal, which can be computed efficiently by the fast Fourier transform. Analytical and numerical estimates are given for the degree of attenuation under which the method is valid, and the method is applied to various test images. A real CSLM image is restored. Finally, the method is compared with a recent iterative method with regard to numerical accuracy and computational efficiency.     

Axial resolution of confocal fluorescence microscopy

A simple analytic expression is given for the axial resolution of a confocal fluorescence microscope. The expression, which is based on the spatial frequency cut-off criterion of resolution, is valid for high aperture optics and arbitrary fluorescence wavelength.     

The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data

We have measured the point-spread function (PSF) for an MRC-500 confocal scanning laser microscope using subresolution fluorescent beads. PSFs were measured for two lenses of high numerical aperture—the Zeiss plan-neofluar 63 × water immersion and Leitz plan-apo 63 × oil immersion—at three different sizes of the confocal detector aperture. The measured PSFs are fairly symmetrical, both radially and axially. In particular there is considerably less axial asymmetry than has been demonstrated in measurements of conventional (non-confocal) PSFs. Measurements of the peak width at half-maximum peak height for the minimum detector aperture gave approximately 0·23 and 0·8 μm for the radial and axial resolution respectively (4·6 and 15·9 in dimensionless optical units). This increased to 0·38 and 1·5 μm (7·5 and 29·8 in dimensionless units) for the largest detector aperture examined. The resulting optical transfer functions (OTFs) were used in an iterative, constrained deconvolution procedure to process three-dimensional confocal data sets from a biological specimen—pea root cells labelled in situ with a fluorescent probe to ribosomal genes. The deconvolution significantly improved the clarity and contrast of the data. Furthermore, the loss in resolution produced by increasing the size of the detector aperture could be restored by the deconvolution procedure. Therefore for many biological specimens which are only weakly fluorescent it may be preferable to open the detector aperture to increase the strength of the detected signal, and thus the signal-to-noise ratio, and then to restore the resolution by deconvolution.     

Three-dimensional laser scanning two-photon fluorescence confocal microscopy of polymer materials using a new,efficient upconverting fluorophore

Three-dimensional confocal imaging of polymer samples was achieved by the use of two-photon excited fluorescence in both positive and negative contrast modes. The fluorophore was a new and highly efficient two-photon induced upconverter, resulting in improved signal strength at low pumping power. Because of the relatively long wavelength of the excitation source (798 nm from a mode-locked Ti:Sap-phire laser), this technique shows a larger penetration depth into the samples than provided by conventional single-photon fluorescence confocal microscopy. Single-photon and two-photon images of the same area of each sample show significant differences. The results suggest the possibility of using two-photon confocal microscopy, in conjunction with highly efficient fluorophores, as a tool to study the surface, interface, and fracture in material science applications.     

Automated imaging of extended tissue volumes using confocal microscopy

Confocal microscopy enables constitutive elements of cells and tissues to be viewed at high resolution and reconstructed in three dimensions, but is constrained by the limited extent of the volumes that can be imaged. We have developed an automated technique that enables serial confocal images to be acquired over large tissue areas and volumes. The computer-controlled system, which integrates a confocal microscope and an ultramill using a high-precision translation stage, inherently preserves specimen registration, and the user control interface enables flexible specification of imaging protocols over a wide range of scales and resolutions. With this system it is possible to reconstruct specified morphological features in three dimensions and locate them accurately throughout a tissue sample. We have successfully imaged various samples at 1-mum voxel resolution on volumes up to 4 mm3 and on areas up to 75 mm2. Used in conjunction with appropriate embedding media and immuno-histochemical probes, the techniques described in this paper make it possible to routinely map the distributions of key intracellular structures over much larger tissue domains than has been easily achievable in the past.     

3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis

The imaging properties of a confocal fluorescence microscope are considered on the basis of a theoretical model. The model takes into account high-aperture objectives, the polarization state of the excitation light and a finite detector pinhole. Electromagnetic diffraction theory of the field near focus as developed by Richards and Wolf is used to compute the optical properties of the model. These are shown to be dependent on the polarization of the light. With the resulting three-dimensional point spread function we have studied the imaging of point, line and plane objects as a function of their orientation with respect to the confocal plane. In addition, the effect of the pinhole size on the image formation of these objects is discussed. The results indicate the necessity to take object orientation into account during image processing activities such as segmentation or analysis.     

Comparison of the axial resolution of practical Nipkow-disk confocal fluorescence microscopy with that of multifocal multiphoton microscopy: theory and experiment

We compare the axial sectioning capability of multifocal confocal and multifocal multiphoton microscopy in theory and in experiment, with particular emphasis on the background arising from the cross‐talk between adjacent imaging channels. We demonstrate that a time‐multiplexed non‐linear excitation microscope exhibits significantly less background and therefore a superior axial resolution as compared to a multifocal single‐photon confocal system. The background becomes irrelevant for thin (< 15 µm) and sparse fluorescent samples, in which case the confocal parallelized system exhibits similar or slightly better sectioning behaviour due to its shorter excitation wavelength. Theoretical and experimental axial responses of practically implemented microscopes are given.     

Automated quantification and reconstruction of collagen matrix from 3D confocal datasets

The geometrical structure of fibrous extracellular matrix (ECM) impacts on its biological function. In this report, we demonstrate a new algorithm designed to extract quantitative structural information about individual collagen fibres (orientation, length and diameter) from 3D backscattered‐light confocal images of collagen gels. The computed quantitative data allowed us to create surface‐rendered 3D images of the investigated sample.     

Comparison and accuracy of methods to determine the confocal volume for quantitative fluorescence correlation spectroscopy

Single molecule detection based on fluorescent labels offers the possibility to gain not only qualitative but also quantitative insight into specific functions of complex biological systems. Fluorescence correlation spectroscopy is one of the favourite techniques to determine concentrations and diffusion constants as well as molecular brightness of molecules in the pico‐ to nano‐molar concentration range, with broad applications in biology and chemistry. Although fluorescence correlation spectroscopy in principle has the potential to measure absolute concentrations and diffusion coefficients, the necessity to know the exact size and shape of the confocal volume very often hampers the possibility to obtain quantitative results and restricts fluorescence correlation spectroscopy to relative measurements mainly. The determination of the confocal volume in situ is difficult because it is sensitive to optical alignment and aberrations, optical saturation and variations of the index of refraction as observed in biological specimen. In the present contribution, we compare different techniques to characterize the confocal volume and to obtain the confocal parameters by fluorescence correlation spectroscopy curve fitting, a fluorescence correlation spectroscopy dilution series and confocal scanning of fluorescent beads. The results are compared in the view of quantitative fluorescence correlation spectroscopy measurement and analysis. We investigate how unavoidable artefacts caused by a non‐ideal confocal volume can be experimentally determined and validated.     

High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy

This study presents a method for high-precision distance measurements and for the volume-conserving segmentation of fluorescent objects with a size of the order of the microscopic observation volume. The segmentation was performed via a model-based approach, using an algorithm that was calibrated by the microscopic point spread function. Its performance was evaluated for three different fluorochromes using model images and fluorescent microspheres as test targets. The fundamental limits which the microscopic imaging process imposes on the accuracy of volume and distance measurements were evaluated in detail. A method for the calibration of the axial stepwidth of a confocal microscope is presented. The results suggest that in biological applications, 3D distances and radii of objects in cell nuclei can be determined with an accuracy of ≤ 60 nm. Using objects of different spectral signature, 3D distance measurements substantially below the lateral half width of the confocal point spread function are feasible. This is shown both theoretically and experimentally.     

Three-dimensional analysis of cell nucleus structures visualized by confocal scanning laser microscopy

Studies of the three-dimensional (3-D) organization of cell nuclei are becoming increasingly important for the understanding of basic cellular events such as growth and differentiation. Modern methods of molecular biology, including in situ hybridization and immunofluorescence, allow the visualization of specific nuclear structures and the study of spatial arrangements of chromosome domains in interphase nuclei. Specific methods for labelling nuclear structures are used to develop computerized techniques for the automated analysis of the 3-D organization of cell nuclei. For this purpose, a coordinate system suitable for the analysis of tri-axial ellipsoidal nuclei is determined. High-resolution 3-D images are obtained using confocal scanning laser microscopy. The results demonstrate that with these methods it is possible to recognize the distribution of visualized structures and to obtain useful information regarding the 3-D organization of the nuclear structure of different cell systems.     

Data-driven, simultaneous blur and image restoration in 3-D fluorescence microscopy

A novel algorithm for simultaneous blur and image restoration (SBIR)* in three-dimensional (3-D) fluorescence microscopy is presented. All the internal parameters including the point spread function essential for the restoration are estimated from the data. Validation of the SBIR algorithm using simulated signals/images and known real world specimens is provided. Both lateral and axial resolution of images are improved by the application of the algorithm. Finally, the results of the application of the algorithm to unknown specimens are shown, demonstrating the potential of the algorithm in practical applications. Furthermore, evidence is provided to show that this algorithm can provide a turn-key system to deblur images in 3-D fluorescence microscopy.     

3-D model of vascular network in rat skin obtained by stereo vision techniques

The quantitative analysis of the depth of injury, penetration of therapeutic agents in tissues, and the regeneration of vascular patency after a graded degree of thermal injury requires a knowledge of the shape and spatial configuration of the vascular networks in the tissue. We have applied computational stereo vision techniques to describe the 3-D configuration of microvessels in full thickness rat skin vascular casts produced by perfusion of Yellow Microfil latex solution through the aorta. The principal concern is to describe the 3-D structure of vascular networks using a set of 3-D space curves. This representation is computed by integrating monocular and binocular processing; the 2-D curve representation of blood vessels computed through monocular analysis is integrated with disparity data to yield a space curve representation for each vessel. A connection diagram is also computed to indicate the connections existing among the computed space curve representations.     

Image compression and data integrity in confocal microscopy

To manage large volumes of image data generated routinely using real-time confocal microscopy, compressing image data using a lossy algorithm prior to sustained video rate transferring and/or storing is proposed. Test criteria for determining the acceptability of uncompressed data, both qualitatively and quantitatively, are described, and an empirical demonstration of the use of lossy compression in data management is provided. It is found that, if appropriately used, the lossy compression scheme could retain all the useful information in the data while providing better compression ratios (memory for the original/ memory for the compressed) when compared with a lossless scheme.