Fluorescence microscopy is commonly implemented for observation of biological samples. A number of different microscopy methods have been developed over the last two decades. Among these, confocal laser scanning microscopy (CLSM) currently prevails as the technique of choice for studying specimens which exhibit fluorescence. CLSM allows for rapid and non-invasive scanning of three-dimensional structures. Interference, incidental quenching and stray light can be reduced due to confocality. Furthermore, modern CLSMs are equipped with computerized controls for magnification, aperture size, detector bandwidth and gain. Thus, high resolution images can be generated allowing for the observation of specimens in three-dimensions.

Principle of CLSM

In CLSM the sample is scanned by laser light and the emitted fluorescence after excitation is collected onto a photo-detector. As shown in the following figure, an aperture is positioned in the image plane in front of the detector at a position confocal with the in-focus plane. Light emanating from the in-focus plane passes through the aperture to the detector, while artifactual emission from any region above or below the focal plane is physically excluded from reaching the detector. It is this ability to reduce the out-of-focus blur, and thus permit accurate non-invasive optical sectioning that makes confocal scanning microscopy so well suited for the imaging and three-dimensional tomography of samples.

Figure 1. Principle of confocal microscopy

CLSM and 3D reconstruction

Figure 2. 3D reconstruction based on confocal microscopy sections.

Accurate reconstruction requires a sufficiently small distance in the z-direction between successive sections. The sampling rate (number of optical sections per mm) should be set at least equal to the Nyquist rate. This rate is the minimal sampling at which a signal must be recorded to ensure that all information present in the signal is represented in the samples. In this case, as stated by the Shannon theorem, it is possible to reconstruct the digitized analog signal completely. In confocal microscopy, the Nyquist rate depends on various factors including the excitation wavelength, the numerical aperture of the objective and the refractive index of the immersion and mounting medium. Usually, the calculated sampling rate is close to the axial resolution of CLSM. Thus, the presence of out-of-focus information in each focal plane is unavoidable. The problem is further compounded by geometric distortion, glare and noise which inhibit the complete of extraneous information.

Figure 3. SEM of a hepatocyte aggregate and confocal micrograph of enzymatic activity with this aggregate. Haze is apparent as the result of out-of-focus information from the bottom layers of the aggregate.

 Deconvolution

The issues concerning the use of CLSM for 3D reconstruction of biological samples, can be tackled with computational methods collectively known as deconvolution methods. A multitude of such techniques has been developed for the deblurring of fluorescence images. The underlying algorithms are commonly characterized as computationally intensive since processing can take anywhere from minutes to hours. In addition, a substantial amount of memory is required because of the large number of 2D planes necessary for accurate 3D reconstruction. Nearest-neighbor methods can circumvent this problem by using a significantly smaller subset of planes for deconvolution. However, nearest-neighbor approaches are impeded primarily by steep local intensity gradients, which may cause artifacts during the deblurring process. Thus, it is necessary to implement a deconvolution method which is applied over the entire data set.

The amount of time for the deblurring of large data sets can be dramatically reduced with the parallel implementation of deconvolution schemes. Parallel computing can also alleviate the excessive demand in memory. The image sections from a single data volume can be distributed on interconnected nodes for concurrent processing allowing real-time analysis and 3D reconstruction of the observed object.

In our laboratory, we have used a constrained iterative method based on van Cittert's algorithm. Compared to linear methods, constrained iterative methods are advantageous since a set of constrains can be incorporated to enhance the quality of the processed image. Typically, a non-negativity constraint is imposed prohibiting the presence of negative image intensities, which are commonly observed in linear methods and confound any sort of quantitative or qualitative analysis. Spatial constraints can also be enforced depending on geometry or other special characteristics of the sample. In addition, we have incorporated an algorithm for correcting noise artifacts during the deconvolution process.

A large number of deconvolution methods requires a point spread function (PSF). Many deconvolution methods, including van Cittert's, require a point spread function (PSF), which models the introduction of artifacts during image acquisition. PSF can be either calculated from theoretical models or measured experimentally. Generation of a theoretical PSF is based on standard parameters such as objective lens magnification and numerical aperture, excitation and emission wavelength, pinhole aperture size and refractive index of immersion and mounting medium. Measurement of PSF experimentally can be more accurate since factors which are unique for the particular microscope including noise from the electronic components are also taken into account.

Regardless of the method used for generation of the PSF, the stacks of sample and PSF images are transferred to a 256-processor IBM SP2 computer at the Minnesota Supercomputer Institute (MSI). An MPI-Fortran code is written for parallel implementation of the constraint iterative deconvolution algorithm. The optical sections are distributed to an array of interconnected processors, and deconvolution is performed concurrently on all confocal sections.

Figure 4. Parallel deconvolution scheme.

The quality of the processed images is assessed both visually and by calculating the mean square error (MSE), which is defined as the residual discrepancy between the processed solution and the observed data. The deconvolution procedure is terminated when there is no significant change in the MSE between successive iterations. The algorithm scales up almost linearly with the number of processors. The required time is singificantly smaller compared to execution times reported in the literature or in tests with commercially available software for data sets of similar size.

Figure 5. Deconvolution scalability. Actual processing time (seconds/iteration) versus the number of processing elements is shown for two separate data sets.

A sample before and after deconvolution is shown in the next figure. The top row shows the original images whereas processed images are on the bottom row. Hepatocyte aggregates are probed for liver-specific activities (in this case for the activity of a biotransformation enzyme). Multiple planes are scanned and the resulting images are used for three-dimensional reconstruction after deconvolution. A volume containing sections after deconvolution is used for three-dimensional reconstruction performed with software available at MSI.

Figure 6. Confocal micrographs of enzymatic activity in spheroids after deconvolution. The colorbar indicates the level of activity. Different sections are shown (in mm) from the top aggregate surface. Bars are in mm.

Coming soon:

We have also developed a PC version of the deconvolution program, which is currently under testing. The execution is multithreaded since the program utilizes shared-memory threads. The code can be executed on single-processor machines. Nevertheless, optimal results in terms of speed and memory management are obtained in multiprocessor PC computers. A free version of this code will soon be available to download and use with fluorescence microscopy images.