Tomographic imaging was pioneered as x-ray computed tomography (CT), for which Godfrey Hounsfield received the Nobel prize in Medicine in 19791 . The mathematics of x-ray CT can be extended to other forms of tomography, including optical tomography. Essentially the 3-D structure (a stack of X-Z slices) of a sample is reconstructed from a series of angularly-resolved wide-field 2-D projections (X-Y images).  These images acquired at different angles are known as “projections” and in x-ray CT are effectively a map of the sample attenuation of the radiation integrated along the line of the projection. In the simplest implementation, photographic or digital angularly-resolved images of the specimen are acquired throughout a full rotation (360o) and a filtered back-projection (FBP) algorithm is used for image reconstruction2. This assumes parallel projection corresponding to parallel ray (or plane wave) propagation of the signal with negligible scattering in the sample, which can be a reasonable assumption for X-ray CT of small (<10 cm) scale samples of biological tissue. There are many other approaches to CT and many implementations for X-ray and other modalities including PET and SPECT approach to CT provides isotropic 3-D resolution. 

The mathematics developed for X-ray computed tomography can be directly applied to optical tomography of transparent samples - and approach described as optical projection tomography (OPT).  For in vivo imaging of, e.g. mammalian tissue, opticla tomography is severely challenged by absorption and scattering of visible/near infrared radiation and image reconstuction must take account of the light scattering. Typically, imaging mammalian tisue must account for multiple scattering of the detected photons and this approach is described as diffuse optical tomography. 

2 Kak, A. C., Slaney, M., “Principles of computerized tomographic imaging,” O’Malley, R. E. ed. (SIAM, IEEE Press, New York, 1988).

Optical tomography

Optical projection tomography

OPT is the direct optical equivalent of X-ray computed tomography (CT), in which parallel ray projection is assumed and 3-D image stacks can be reconstructed using the FBP algorithm as long as the sample is contained within the depth of field of the imaging lens (i.e. in focus) such that the illuminating light approximates to parallel ray projection. It can be directly applied to samples that have been rendered transparent by a chemical clearing process3 or which are inherently transparent.  Important examples of the latter include live organisms that can be genetically manipulated to serve as disease models such as d. melanogaster4, c. elegans5 and danio rerio (zebrafish) larvae6. Thus OPT complements other mesoscopic imaging techniques such as LSFM. OPT can be applied to reconstruct the absorption as well as the fluorescence distributions in optically transparent samples and can be applied over sub-mm to ~cm scales, although the requirement to approximate to parallel projection means that the achievable optical resolution decreases with increasing sample size as the depth of field must be increased proportionately. This trade-off between sample size and resolution can be mitigated by “focal scanning”, which entails translating the focus of a high NA imaging lens such that all parts of the sample are in focus for some time during the acquisition of each projection image7. The FBP reconstruction process suppress the out of focus light although it can impact the signal to noise ratio of the OPT image stacks. An alternative approach to address this trade-off is to use multiple imaging set-ups focussed to different depths in the sample such that different sub-volumes of the sample are simultaneously imaged in focus during a single OPT acquisition8. This significantly increases the light collection efficiency and therefore the imaging speed, which is important when imaging live organisms. OPT also offers the opportunity to decrease image acquisition times through the use of compressive sensing techniques originally developed for X-ray CT, where fewer angularly resolved projection images are acquired than is necessary to meet the Nyquist sampling criterion set by the spatial resolution of the detectors. Providing the data is sparse, 3-D images can be reconstructed without loss of information using iterative algorithms. We have implemented this for OPT9 of live zebrafish in order to reduce the time that they need to be maintained under anaesthetic.

3 Sharpe, J., Ahlgren, U., Perry, P., Hill, B., Ross, A., Hecksher-Sørensen, J., Baldock, R. and Davidson, D., Science, 296 (2002) 541
4 Vinegoni, C., Pitsouli, C., Razansky, D., Perrimon, N. and Ntziachristos, V., Nature Methods, 5 (2008) 45
5 Birk, U. J., Rieckher, M., Konstantinides, N., Darrell, A., Sarasa-Renedo, A., Meyer, H., Tavernarakis, N. and Ripoll, J., Biomedical Optics Express, 1 (2010) 87
6 McGinty, J., Taylor, H. B., Chen, L., Bugeon, L., Lamb, J. R., Dallman, M. J. and French, P. M. W., Biomedical Optics Express, 2 (2011) 1340
7 L Chen, S. Kumar, D. Kelly, N. Andrews, M.J. Dallman,  P. M W French and J. McGinty, Biomed Optical Express, 5 (2014) 3367-3375 DOI:10.1364/BOE.5.003367g
8 L. Chen. J. McGinty and P. M. W. French, Opt Lett 38, (2013) 851
9 Correia et al. PLoS ONE 10(8): e0136213, doi:10.1371/journal.pone.0136213,

Diffuse fluorescence tomography

When applying optical tomography to larger and more highly scattering samples, the filtered back-projection algorithm for tomographic image reconstruction becomes less valid, although it still can provide useful 3-D images in the presence of moderate scattering, as is encountered in live adult zebrafish.  For strongly scattering samples, it is beneficial to take into account the multiple scattering of the detected photons and to use statistical diffuse light propagation algorithms to reconstruct the 3-D fluorescence quantum efficiency and lifetime distributions based on the probable trajectories of the detected photons.  Diffuse fluorescence tomography (DFT), also described as fluorescence molecular tomography (FMT)10 presents significantly decreased spatial resolution compared to OPT of transparent samples but, nevertheless, it is able to reconstruct fluorescence lifetime distributions in scattering phantoms11, 12 and in ex vivo13 and live mice14, 15 and recently we reported the first FLIM FRET tomography of genetically expressed fluorescent proteins in a live mouse16. We note that the precision of fluorophore localization is still compromised by the absorption and scattering of excitation and fluorescence radiation and by the background autofluorescence of the biological tissue. The impact of absorption and scattering could be mitigated in future by engineering new FRET probes with donor-acceptor combinations utilizing fluorophores that are both excited and emit at longer wavelengths, such as red and near infrared fluorescent proteins. These advances towards the practical application of FLIM FRET to read out molecular interactions and biosensors in vivo would facilitate longitudinal in vivo studies for a variety of research fields, including drug discovery, and could lead to a significant reduction in the number of animals needed for biomedical research.

10 Ntziachristos, V., Annu Rev Biomed Eng, 8 (2006) 1
11 Kumar, A. T. N., Raymond, S. B., Bacskai, B. J. and Boas, D. A., Optics Letters, 33 (2008) 470
12 McGinty, J., Soloviev, V. Y., Tahir, K. B., Laine, R., Stuckey, D. W., Hajnal, J. V., Sardini, A., French, P. M. W. and Arridge, S. R., Optics Letters, 34 (2009) 2772
13 Venugopal, V., Chen, J., Lesage, F. and Intes, X., Optics Letters, 35 (2010) 3189
14 Nothdurft, R. E., Patwardhan, S. V., Akers, W., Ye, Y., Achilefu, S. and Culver, J. P., Journal of Biomedical Optics, 14 (2009) 024004
15 Rusanov, A. L., Ivashina, T. V., Vinokurov, L. M., Fiks, I. I., Orlova, A. G., Turchin, I. V., Meerovich, I. G., Zherdeva, V. V. and Savitsky, A. P., Journal of Biophotonics, 3 (2010) 774
16 McGinty, J., Stuckey, D. W., Soloviev, V. Y., Laine, R., Wylezinska-Arridge, M., Wells, D. J., Arridge, S. R., French, P. M. W., Hajnal, J. V. and Sardini, A., Biomedical Optics Express, 2 (2011) 1907