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Biomedical Optics & Medical Imaging

Improved fluorescence optical projection tomography reconstruction

A physical model of image formation combined with a reconstruction algorithm results in superior optical projection tomography reconstructions.
6 November 2008, SPIE Newsroom. DOI: 10.1117/2.1200810.1329

Introduced in 2002,1 optical projection tomography (OPT) is a relatively new technique for high-resolution three-dimensional imaging of fluorescent and non-fluorescent biological specimens in the micrometer to centimeter range. Ranging from studies of anatomy to gene expression, applications have been reported in many areas where 3D images of biological samples are required or offer additional insight.2–12

Fluorescence OPT works by capturing images of the fluorescence emanating from within a specimen from a number of equidistant angular orientations. Figure 1 illustrates the process. The information contained in these images, referred to as projections, is combined to produce a 3D image of the auto-fluorescent anatomy and/or fluorescent-labeled parts of the specimen. Figure 2 illustrates that this 3D image can be rendered and cross-sectioned in useful and enlightening ways, without the need for time-consuming and destructive physical sectioning of the specimen.

Figure 1. A sample is excited using light of an appropriate wavelength (blue), causing the fluorescent labeled parts of the sample to emit light of a longer wavelength (green). Images of the fluorescent emission are captured for a number of equidistant angular positions of the sample. (Click to enlarge figures.) 

The information contained in a set of OPT projections is generally re-combined one slice at a time using the filtered back projection (FBP) algorithm. For a single slice, the FBP algorithm builds up an approximation of the slice by additively smearing the information contained in the corresponding row of each projection across an initially blank image. However, FBP does not account for optical effects such as blurring, which has been shown to result in qualitative and quantitative inaccuracies in fluorescence OPT reconstructions.13–15

Figure 2. (A) OPT projection of a mouse embryo labeled with green fluorescent protein. (B) FBP reconstruction of the highlighted slice of the embryo. (C) OPT projection of an amphipod crustacean Parhyale hawaiensis with auto-fluorescent cuticle. (D) FBP reconstruction of the highlighted slice of the crustacean.

The use of an iris to increase the depth of field and reduce blurring is common practice and overcomes some of the limitations of the FBP algorithm. However, this approach inevitably leads to a lower signal-to-noise ratio in the projections and does not fully resolve the blurring issue.

Theoretical advances have focused on pre-processing OPT projections for use with FBP13 and modifications to the FBP algorithm itself, which result in quantitatively correct reconstructions, but at the cost of image quality.14 An approach that takes the effects of the optics into account could lead to superior reconstructions.

Consider a discrete spatial domain of voxels (‘volumetric pixels’) encompassing the depth of field (DOF) of the imaging system. A system matrix S can be calculated to describe the numbers of photons emitted within each voxel being detected at each CCD detector pixel.

Figure 3. The maximum-likelihood expectation-maximization algorithm for emission tomography. An initial estimate B of the body is used to start the first iteration of the algorithm. In projection space, the error is calculated as the quotient of the recorded projections P and the projections resulting from the current estimate of the body B where S is the system matrix. The error is back-projected into image space and used to update the current estimate of the body B.

Given a system matrix S and projection data P, the maximum likelihood expectation maximization (ML-EM) algorithm starts with an initial estimate B of the body and iteratively computes successive improved estimates. The algorithm consists of the repetition of two key steps: the expectation and maximization steps, the derivations of which lead to a mathematical formula for the iterative procedure outlined in Figure 3.16 The expectation step uses forward projection to calculate expected projections given the current estimate of the body. The maximization step calculates a more likely estimate of the body given the expected projections from the previous estimate of the body.

Figure 4 shows a digital test sample (phantom) consisting of three areas of fluorescence against a zero fluorescence background, which we used to compare the performance of the ML-EM algorithm against that of the standard FBP algorithm.

Figure 4. The digital fluorescence OPT phantom consists of a grid of voxels all of zero fluorescence intensity except for three groups of voxels on slice 5 of intensity 100.

Figure 5. The FBP reconstruction of the digital phantom. Note the reduced intensity and lower resolution towards the edge of the volume.

We calculated 100 fluorescence OPT projections of the phantom and used the FBP and ML-EM algorithms to reconstruct the phantom. The ML-EM algorithm performed considerably better than FBP, assigning very low fluorescence intensities outside the original areas of fluorescence and yielding high contrast fluorescence without the streak artifact associated with FBP, as can be seen in Figures 5 and 6. Intensity analysis revealed that the FBP reconstruction contained significantly lower intensity fluorescence than the original phantom whereas the ML-EM reconstruction contained the correct intensities.

In conclusion, optical projection tomography is a relatively new imaging modality that can be used to obtain 3D images both of absorption and fluorescence in biological samples on the micron to centimeter range. When used to reconstruct OPT data the standard FBP algorithm can produce quantitatively unreliable images that also suffer from qualitative drawbacks such as blurring and streak artifacts. Using a model of image formation for fluorescence OPT, the ML-EM algorithm can produce reconstructions that are both quantitatively correct and qualitatively superior to those produced by the FBP algorithm.

In addition to the improvements described above, the explicit modeling of the OPT optics in the system matrix should allow the use of wider optical apertures, thereby achieving a higher signal-to-noise ratio in both the projections and the reconstructions.

Figure 6. The ML-EM reconstruction of the digital phantom. Note the high resolution and approximately constant intensity of fluorescence throughout the volume.
Alex Darrell would like to acknowledge support from E.U. Integrated Project "Molecular Imaging" LSHG-CT-2003-503259.

Alex Darrell
BMI Laboratory
Institute of Computer Science, FORTH
Heraklion, Greece
Medical Vision Laboratory
Department of Engineering Science
University of Oxford
Oxford, England  

Alex Darrell is a doctoral candidate at the Medical Vision Laboratory at the University of Oxford and a Marie Curie grant recipient at the FORTH research institute in Greece. He has published four papers.

Jim Swoger, Laura Quintana, James Sharpe
EMBL-CRG Systems Biology Program
Centre for Genomic Regulation
Barcelona, Spain

James Sharpe developed OPT in 2002 while working at the MRC Human Genetics Unit in Edinburgh, UK. Since then he has been a group leader at the same institute, and in 2006 moved as a senior group leader to the EMBL-CRG Systems Biology Program within the Centre for Genomic Regulation (CRG) in Barcelona, Spain.

Kostas Marias
BMI laboratory
Institute of Computer Science, FORTH
Heraklion, Greece

Kostas Marias currently holds a principal researcher position in the Institute of Computer Science, ICS-FORTH, Greece. Previously he worked as a research assistant in the Medical Vision Laboratory, University of Oxford, UK. He completed his PhD in the field of Medical Image Analysis/ Medical Physics in 2001 at UCL, London in collaboration with the University of Oxford and has an MSc from Imperial College London. His research interests include medical image analysis, multi-modality data fusion and registration, molecular and gene-expression imaging. He has published more than 40 papers in these fields in international journals and is a member of the IEEE Engineering in Medicine and Biology Society (EMBS).

Michael Brady
Medical Vision Laboratory
Department of Engineering Science
University of Oxford
Oxford, England

Michael Brady is professor of Information Engineering at the University of Oxford, where he founded the Robotics Research Laboratory and the Wolfson Medical Vision Laboratory. He has published over 450 papers, 24 patents, and is author/editor of 10 books. He has been elected a fellow of the Royal Society, the Royal Academy of Engineering, the Academy of Medical Sciences, and has six honorary doctorates. Professor Brady founded the companies Mirada Solutions (now the Advanced Applications Laboratory of Siemens Molecular Imaging) and Guidance Ltd. He is a director of Ixico, Dexela, and Oxford Instruments.

Jorge Ripoll
Institute of Electronic Structure & Laser, FORTH
Heraklion, Greece