pinhole spect provides high - resolution images of small animals that can be used to quantitatively study the in vivo distribution of a new tracer or drug , for example to determine whether and how molecules reach the target area or what receptors are available in the animal .
spect can also be employed for function or lesion detection with the help of a wide range of available radiolabelled molecules . in many cases
far fewer animals need to be sacrificed in spect studies than in post - mortem tissue distribution studies , because spect allows for dynamic imaging and longitudinal studies and provides 3-d images with slices that are perfectly aligned to each other .
most of them ( e.g. [ 19 ] ) employ ( multi-)pinhole collimation instead of parallel - hole collimation that is used clinically , taking advantage of the magnification of pinholes to improve resolution [ 1 , 10 ] .
small - animal spect images are typically much less degraded by photon scattering and absorption than clinical spect images because of smaller body dimensions . nevertheless , the degradation in small - animal spect images is not negligible .
for example in the centre of a rat - sized cylinder of water , photon attenuation can reduce the measured concentration of activity up to 25% when imaging with tc . for clinical spect devices
several attenuation correction [ 1215 ] and scatter correction methods [ 1420 ] have been developed .
several of these systems are now commercially available and their accuracy has been improved by the availability of integrated spect / ct devices [ 21 , 22 ] .
there are few publications about quantitative small - animal spect however ( e.g. [ 11 , 23 , 24 ] ) .
recently , vanhove et al .   presented their studies with an average error of 7.9    10.4% between the activity concentrations measured on their scatter- and attenuation - corrected pinhole spect mouse images and in a dose calibrator .
they used microct imaging for producing attenuation maps , which has the advantage that non - uniformities can be taken into account but at the cost of increased dose to animals and need for additional hardware .
furthermore , the attenuation correction was incorporated in the iterative reconstruction process , which in some reconstruction algorithms may cause problems since they require a new system matrix for each subject to be imaged .
post - reconstruction attenuation correction algorithms , such as the chang method , had been proposed decades ago .
the first - order correction provided by the chang algorithm is often not accurate enough for clinical use because effects of attenuation in patients are very strong .
the aim of this paper is ( 1 ) to investigate the accuracy of the chang algorithm in rodents and ( 2 ) to present a practical chang - based method using body outline contours obtained with optical cameras .
the method was tested for the case of focusing pinhole spect [ 5 , 27 ] and in combination with correction of other effects such as scatter and distance - dependent collimator blurring and sensitivity .
u - spect - ii   is a stationary focusing multi - pinhole spect system for small - animal organ and total - body imaging studies .
exchangeable cylindrical collimators containing 75 focusing pinholes can be mounted in the centre and are surrounded by three nai gamma cameras .
optical photos are acquired by three integrated optical cameras for volume of interest ( voi ) selection before spect acquisition ( fig .  1 ) .
with an xyz stage , an animal can be moved inside the collimator during imaging in order to also enable obtaining total - body images . 

b three integrated optical cameras . c user interface , showing optical photos for voi selection u - spect - ii .
c user interface , showing optical photos for voi selection the u - spect - ii system can reach sub - half - millimetre resolution . with tc , the image resolution is better than 0.35  mm in any part of a mouse - sized object or better than 0.8  mm in any part of a rat - sized object . with the scanner hardware and acquisition software , the information , including scintillation time , position and photon energy , etc .
this offers great flexibility for image reconstruction , such as implementing decay and spectrum- ( e.g. window- ) based scatter correction .
more detailed descriptions , evaluations and examples of applications of the u - spect systems were given in [ 5 , 9 , 28 , 29 ] .
the scanning focus method ( sfm ) described in   was used for acquisition . with the sfm
, a total - body scan can be carried out with a sequence of bed positions , and its image can be reconstructed with a single series of iterations . the system matrix used for computing re - projections and backprojections during iterative reconstruction with pixel - based ordered subset expectation maximization ( posem ) is derived from point spread function ( psf ) measurements . within these psf - based matrices ,
we define the calibration factor to be the ratio of the activity concentration to the voxel value in reconstructed spect images .
since the various distance - dependent pinhole sensitivities are already modelled in the system matrix and subsequently compensated in the reconstruction process , the calibration factor should be theoretically homogeneous throughout all voxels of reconstructions if attenuation and scatter can be neglected .
it means that the calibration factor is a global scaling factor ; thus we can obtain the factor by measuring and reconstructing a point source that is almost attenuation free .
the activity of the source was 69.0  mbq measured in a vik-202 dose calibrator .
the calibration scan lasted for 200  min , and then a volume of 10    10    10  mm containing the point source in the centre was reconstructed by running 6 posem iterations with 16 subsets .
the calibration factor , cf , was given by 
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				 \begin{document}$$ cf = \frac{a}{{v \cdot \sum r } } , $ $ \end{document}where a is the activity of the point source measured in the dose calibrator , r is the summation of voxel values all over the image and v is the volume of a voxel .
if a has a unit of mbq , v is expressed in millilitres , and voxel value r is considered to be dimensionless , then the cf has a unit of mbq / ml . for scatter- and attenuation - free acquisitions and reconstructions , after scaling by the cf ,
however , in practice , scatter correction and attenuation correction should be carried out apart from the global scaling of voxel values . in the u - spect - ii system
since data are acquired in list mode , scatter and photopeak windows can be set after acquisition .
we employed the triple energy window ( tew ) technique   in both phantom and animal experiments for this paper . a photopeak window ( 140  kev , 20% width )
two background windows ( centred at 117  kev , 10% width and centred at 163  kev , 7% width , respectively ) were set adjacent to the photopeak for estimating the number of scattered photons of which the energies ranged inside the photopeak window .
the scatter images were scaled by the ratio of the window widths , and added to the estimated scatter - free projections in the denominator of the posem formula along the lines proposed in bowsher et al . .
in this way the contributions of scattered photons in projections were taken into account in order to eliminate their detriment to the images as much as possible .
this scatter correction scheme was also performed during the reconstruction of the point source used for obtaining the calibration factor . that scatter needs to be taken into account here is because although probability of scattering inside the point source is quite small , the amount of scattering by the imaging system , especially by the collimator , is not negligible [ 35 , 36 ] . in a reconstruction of the point source without scatter correction
, we found that the calibration factor is 4.35% smaller than the one with scatter correction .
it can be implemented as a post - reconstruction processing method , so that no new system matrix is needed . in recent clinical spect software , it has often been replaced by more accurate iterative attenuation correction . however , due to the small amount of attenuation in rodents , the chang algorithm could be sufficient .
if the over- and/or undercorrection problems of the chang algorithm can be ignored , the attenuation correction process may benefit from the method s simplicity and high computation speed .
the consequence of attenuation is a reduction in the number of gamma photons which can arrive directly at the detectors , caused by photon scattering and absorption .
the amount of attenuation depends on the photon energy , medium properties and the travelling distance of gamma photons in the medium .
the transmitted fraction ( tf ) is therefore represented as 
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				 \begin{document}$$ t{f_l } = \exp \left ( { - \int\limits_l { \mu ( l)dl } } \right ) , $ $ \end{document}where l denotes the travelling path of a gamma photon inside the attenuation medium , and  is the attenuation coefficient .
the number of counts detected in that path is then reduced to 
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				 \begin{document}$$ n = { n_0}t{f_l } , $ $ \end{document}where n0 represents the number of counts detected without attenuation .
chang   provided an approximation here : the tf of a voxel over all possible projection paths is the average of all tfls , or 
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				 \begin{document}$$ tf = \frac{1}{m}\sum\limits_{m = 1}^m { \exp \left ( { - \int\limits_{{l_m } } { \mu ( l)dl } } \right ) } , $ $ \end{document}where m is the total number of projections taken in acquisition . in small - animal spect , a small m could be sufficient due to the small amount of attenuation . to estimate a sufficiently large m for a rat - sized object , we calculated the tfs with different m on a single slice with an attenuation coefficient of 0.151  cm (=  of 140  kev photon travelling in water ) inside an area of an ellipse with its major and minor axes equal to 4 and 2  cm , respectively .
then we took the tfs of the voxels calculated with m  =  1,024 as reference data and inspected the normalized root mean square deviation ( nrmsd ) when m is smaller .
we found that by increasing m above 32 gamma ray directions , the nrmsds are below 0.2% .
therefore , we considered m  =  32 as sufficiently large for a rat - sized object and applied it in our studies . 

table  1nrmsd of tfs on an elliptic cross section between different m and m  =  1,024m481632641282565121,024nrmsd(%)10.631.310.290.140.080.040.020.000 nrmsd of tfs on an elliptic cross section between different m and m  =  1,024 an attenuation map was needed to determine the attenuation coefficient  in different locations of the image volume . in order to simplify the process , we considered the  to be homogeneous and equal to 0.151  cm (=  of 140  kev photon travelling in water ) inside the regions of the objects scanned .
an application program was developed for defining top view and side view 2-d contours of animals on the optical photos that standardly are taken before u - spect acquisition , e.g. for the purpose of voi selection and activity localization .
2a , the three optical photos are displayed on the graphical user interface of the software , with a closed bzier spline curve lying on top of each .
the curves are initialized with standard shapes and can be deformed to fit animal outlines by dragging several anchor points . after proper 2-d contours were made , the software measured the width p and height q of the animal on the top view and side view contours , respectively , in each position of those transverse slices ( fig . 
then it created an ellipse of which the horizontal and vertical axes were equal to p and q , respectively , determined by the following equation : 
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				 \begin{document}$$ \frac{{{x^2}}}{{{p^2 } } } + \frac{{{y^2}}}{{{q^2 } } } = 4 .
$ $ \end{document}all those ordered ellipses were stacked together to form a 3-d contour of the object ( fig . 
c a mesh plot of 3-d contours based on a stack of ellipses generating a 3-d contour . a graphical user interface .
c a mesh plot of 3-d contours based on a stack of ellipses with this 3-d contour and some extra information , such as voxel size and attenuation coefficient  , the software was able to compute the tf of every voxel : 
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				 \begin{document}$$ tf = \frac{1}{{32}}\sum\limits_{m = 1}^{32 } { \exp \left ( { - \mu { l_m } } \right ) } .
$ $ \end{document } it is important to compute tfs for not only the voxels inside a 3-d contour , but also the ones outside .
a source can exist outside an attenuation medium , e.g. due to an overly tight body contour , and gamma rays emitted by that source and penetrating the medium will still be attenuated , so that the tfs for that source outside the 3-d contour should not be simply set to 1 .
another advantage is that it makes the tf change continuously across the border of the contour , which reduces the error brought in by an inaccurate contour .
finally we computed the activity concentration ac at the location of every voxel of the reconstructed image , with the equation 
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				 \begin{document}$$ ac = \frac{{r \cdot cf}}{{tf } } , $ $ \end{document}in which r was the scatter - corrected voxel value .
we first used a simple cylindrical phantom to validate the accuracy of absolute quantification with u - spect - ii .
the phantom ( 45  mm diameter and 40  mm height ) was filled with tc solution with activity concentration equal to 2.88  mbq / ml .
a scan was then performed with u - spect - ii , and the image was subsequently reconstructed by using 6 posem iterations with 16 subsets , a 0.375-mm voxel size , and with decay and scatter corrections integrated .
a cadaver of a 250-g female wistar rat was used to test our method in a realistic complex attenuation distribution .
twelve tc sphere - like sources were made from tips of microcentrifuge tubes ( container ) , cotton balls ( solution absorber ) , tc solution ( radioactive source ) and parafilm ( seal ) .
their diameters were around 5  mm and activities ranged from 7.29 to 9.87  mbq , measured in the same dose calibrator employed in the phantom experiment . these sources were inserted into the rat ( mouth , neck , shoulder    2 , lung    2 , liver , right kidney , intestine , bladder and back    2 ) by surgery .
the image was reconstructed by using 6 posem iterations combining with 16 subsets and a 0.375-mm voxel size .
u - spect - ii   is a stationary focusing multi - pinhole spect system for small - animal organ and total - body imaging studies .
exchangeable cylindrical collimators containing 75 focusing pinholes can be mounted in the centre and are surrounded by three nai gamma cameras .
optical photos are acquired by three integrated optical cameras for volume of interest ( voi ) selection before spect acquisition ( fig .  1 ) .
with an xyz stage , an animal can be moved inside the collimator during imaging in order to also enable obtaining total - body images . 

b three integrated optical cameras . c user interface , showing optical photos for voi selection u - spect - ii .
c user interface , showing optical photos for voi selection the u - spect - ii system can reach sub - half - millimetre resolution . with tc , the image resolution is better than 0.35  mm in any part of a mouse - sized object or better than 0.8  mm in any part of a rat - sized object . with the scanner hardware and acquisition software , the information , including scintillation time , position and photon energy , etc .
this offers great flexibility for image reconstruction , such as implementing decay and spectrum- ( e.g. window- ) based scatter correction .
more detailed descriptions , evaluations and examples of applications of the u - spect systems were given in [ 5 , 9 , 28 , 29 ] .
the scanning focus method ( sfm ) described in   was used for acquisition . with the sfm , a total - body scan can be carried out with a sequence of bed positions , and its image can be reconstructed with a single series of iterations . the system matrix used for computing re - projections and backprojections during iterative reconstruction with pixel - based ordered subset expectation maximization ( posem ) is derived from point spread function ( psf ) measurements . within these psf - based matrices ,
we define the calibration factor to be the ratio of the activity concentration to the voxel value in reconstructed spect images .
since the various distance - dependent pinhole sensitivities are already modelled in the system matrix and subsequently compensated in the reconstruction process , the calibration factor should be theoretically homogeneous throughout all voxels of reconstructions if attenuation and scatter can be neglected .
it means that the calibration factor is a global scaling factor ; thus we can obtain the factor by measuring and reconstructing a point source that is almost attenuation free .
the activity of the source was 69.0  mbq measured in a vik-202 dose calibrator .
the calibration scan lasted for 200  min , and then a volume of 10    10    10  mm containing the point source in the centre was reconstructed by running 6 posem iterations with 16 subsets .
the calibration factor , cf , was given by 
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				 \begin{document}$$ cf = \frac{a}{{v \cdot \sum r } } , $ $ \end{document}where a is the activity of the point source measured in the dose calibrator , r is the summation of voxel values all over the image and v is the volume of a voxel .
if a has a unit of mbq , v is expressed in millilitres , and voxel value r is considered to be dimensionless , then the cf has a unit of mbq / ml . for scatter- and attenuation - free acquisitions and reconstructions , after scaling by the cf ,
however , in practice , scatter correction and attenuation correction should be carried out apart from the global scaling of voxel values .
in the u - spect - ii system , scatter correction is integrated into the reconstruction step .
since data are acquired in list mode , scatter and photopeak windows can be set after acquisition .
we employed the triple energy window ( tew ) technique   in both phantom and animal experiments for this paper . a photopeak window ( 140  kev , 20% width )
two background windows ( centred at 117  kev , 10% width and centred at 163  kev , 7% width , respectively ) were set adjacent to the photopeak for estimating the number of scattered photons of which the energies ranged inside the photopeak window .
the scatter images were scaled by the ratio of the window widths , and added to the estimated scatter - free projections in the denominator of the posem formula along the lines proposed in bowsher et al . .
in this way the contributions of scattered photons in projections were taken into account in order to eliminate their detriment to the images as much as possible .
this scatter correction scheme was also performed during the reconstruction of the point source used for obtaining the calibration factor . that scatter needs to be taken into account here is because although probability of scattering inside the point source is quite small , the amount of scattering by the imaging system , especially by the collimator , is not negligible [ 35 , 36 ] . in a reconstruction of the point source without scatter correction , we found that the calibration factor is 4.35% smaller than the one with scatter correction .
it can be implemented as a post - reconstruction processing method , so that no new system matrix is needed . in recent clinical spect software , it has often been replaced by more accurate iterative attenuation correction . however , due to the small amount of attenuation in rodents , the chang algorithm could be sufficient .
if the over- and/or undercorrection problems of the chang algorithm can be ignored , the attenuation correction process may benefit from the method s simplicity and high computation speed .
the consequence of attenuation is a reduction in the number of gamma photons which can arrive directly at the detectors , caused by photon scattering and absorption .
the amount of attenuation depends on the photon energy , medium properties and the travelling distance of gamma photons in the medium .
the transmitted fraction ( tf ) is therefore represented as 
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				 \begin{document}$$ t{f_l } = \exp \left ( { - \int\limits_l { \mu ( l)dl } } \right ) , $ $ \end{document}where l denotes the travelling path of a gamma photon inside the attenuation medium , and  is the attenuation coefficient . the number of counts detected in that path is then reduced to 
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n = { n_0}t{f_l } , $ $ \end{document}where n0 represents the number of counts detected without attenuation .
chang   provided an approximation here : the tf of a voxel over all possible projection paths is the average of all tfls , or 
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				 \begin{document}$$ tf = \frac{1}{m}\sum\limits_{m = 1}^m { \exp \left ( { - \int\limits_{{l_m } } { \mu ( l)dl } } \right ) } , $ $ \end{document}where m is the total number of projections taken in acquisition . in small - animal spect , a small m could be sufficient due to the small amount of attenuation . to estimate a sufficiently large m for a rat - sized object , we calculated the tfs with different m on a single slice with an attenuation coefficient of 0.151  cm (=  of 140  kev photon travelling in water ) inside an area of an ellipse with its major and minor axes equal to 4 and 2  cm , respectively .
then we took the tfs of the voxels calculated with m  =  1,024 as reference data and inspected the normalized root mean square deviation ( nrmsd ) when m is smaller .
we found that by increasing m above 32 gamma ray directions , the nrmsds are below 0.2% .
therefore , we considered m  =  32 as sufficiently large for a rat - sized object and applied it in our studies . 

table  1nrmsd of tfs on an elliptic cross section between different m and m  =  1,024m481632641282565121,024nrmsd(%)10.631.310.290.140.080.040.020.000 nrmsd of tfs on an elliptic cross section between different m and m  =  1,024 an attenuation map was needed to determine the attenuation coefficient  in different locations of the image volume . in order to simplify the process , we considered the  to be homogeneous and equal to 0.151  cm (=  of 140  kev photon travelling in water ) inside the regions of the objects scanned .
an application program was developed for defining top view and side view 2-d contours of animals on the optical photos that standardly are taken before u - spect acquisition , e.g. for the purpose of voi selection and activity localization . as shown in fig . 
2a , the three optical photos are displayed on the graphical user interface of the software , with a closed bzier spline curve lying on top of each .
the curves are initialized with standard shapes and can be deformed to fit animal outlines by dragging several anchor points .
after proper 2-d contours were made , the software measured the width p and height q of the animal on the top view and side view contours , respectively , in each position of those transverse slices ( fig . 
then it created an ellipse of which the horizontal and vertical axes were equal to p and q , respectively , determined by the following equation : 
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				 \begin{document}$$ \frac{{{x^2}}}{{{p^2 } } } + \frac{{{y^2}}}{{{q^2 } } } = 4 .
$ $ \end{document}all those ordered ellipses were stacked together to form a 3-d contour of the object ( fig .  2c ) . 

c a mesh plot of 3-d contours based on a stack of ellipses generating a 3-d contour . a graphical user interface .
with this 3-d contour and some extra information , such as voxel size and attenuation coefficient  , the software was able to compute the tf of every voxel : 
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				 \begin{document}$$ tf = \frac{1}{{32}}\sum\limits_{m = 1}^{32 } { \exp \left ( { - \mu { l_m } } \right ) } .
$ $ \end{document } it is important to compute tfs for not only the voxels inside a 3-d contour , but also the ones outside .
a source can exist outside an attenuation medium , e.g. due to an overly tight body contour , and gamma rays emitted by that source and penetrating the medium will still be attenuated , so that the tfs for that source outside the 3-d contour should not be simply set to 1 .
another advantage is that it makes the tf change continuously across the border of the contour , which reduces the error brought in by an inaccurate contour .
finally we computed the activity concentration ac at the location of every voxel of the reconstructed image , with the equation 
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				 \begin{document}$$ ac = \frac{{r \cdot cf}}{{tf } } , $ $ \end{document}in which r was the scatter - corrected voxel value .
we first used a simple cylindrical phantom to validate the accuracy of absolute quantification with u - spect - ii .
the phantom ( 45  mm diameter and 40  mm height ) was filled with tc solution with activity concentration equal to 2.88  mbq / ml .
a scan was then performed with u - spect - ii , and the image was subsequently reconstructed by using 6 posem iterations with 16 subsets , a 0.375-mm voxel size , and with decay and scatter corrections integrated .
a cadaver of a 250-g female wistar rat was used to test our method in a realistic complex attenuation distribution .
twelve tc sphere - like sources were made from tips of microcentrifuge tubes ( container ) , cotton balls ( solution absorber ) , tc solution ( radioactive source ) and parafilm ( seal ) .
their diameters were around 5  mm and activities ranged from 7.29 to 9.87  mbq , measured in the same dose calibrator employed in the phantom experiment .
these sources were inserted into the rat ( mouth , neck , shoulder    2 , lung    2 , liver , right kidney , intestine , bladder and back    2 ) by surgery . then a total - body spect scan was carried out .
the image was reconstructed by using 6 posem iterations combining with 16 subsets and a 0.375-mm voxel size .
figure  3 shows reconstructed slices of the cylindrical phantom to illustrate the effect of the attenuation correction .
the summation of ten transverse slices ( decay corrected ) without attenuation correction ( fig . 
this can be observed more clearly on the line profiles through the diameters of the phantom along the x direction ( fig . 
the activity concentration measured in the dose calibrator as a gold standard is indicated by a horizontal line at 2.88  mbq / ml . 

the grey scales of a  d are the same , from black ( 0  mbq / ml ) to white ( 3.5  mbq / ml ) .
the line mc indicates the concentration measured with a dose calibrator , as a gold standard averages of ten transverse spect slices of the cylindrical phantom .
the grey scales of a  d are the same , from black ( 0  mbq / ml ) to white ( 3.5  mbq / ml ) .
the line mc indicates the concentration measured with a dose calibrator , as a gold standard without corrections , the difference between the activity concentrations calculated on the reconstructed spect image and measured in the dose calibrator was significantly underestimated by 0.54  mbq / ml , or 18.7% . with scatter correction only ,
the difference worsened to 0.77  mbq / ml ( 26.8% ) . applying only attenuation correction led to an overestimation by 0.26  mbq / ml ( 9.2% ) . applying attenuation correction in combination with
scatter correction resulted in a small underestimation of 0.05  mbq / ml ( 1.7% ) .
these numbers were calculated on the voxels in a cylindrical volume with a diameter of 42  mm , which was slightly smaller than the phantom size in order to avoid the influence of partial volume effect .
since the sources inserted into the rat were isolated well , it is possible to segment sub - volumes for individual sources on the reconstructed spect image .
the activity of each source was calculated by adding all the voxel values in the sub - volume containing that source and then multiplying the resulting sum , the cf , and the voxel size together .
eleven volunteers were invited to carry out the attenuation corrections on the reconstructed image individually , using the application program that is shown in fig . 
after a 15-min training session , all volunteers were able to finish their testing within 5  min .
table  2 lists the activities of the sources measured in the dose calibrator and their quantitative results calculated on the decay , scatter and attenuation - corrected image .
the averages , standard deviations and percent errors of those results over the 11 testers are also listed . 

table  2activities of sources measured in dose calibrator and corrected results by 11 individual testerssource no.activity ( mbq)quantified results by 11 individual testers ( mbq)aver .
( mbq)sd ( mbq)error ( % ) 18.758.918.789.008.438.868.548.698.698.508.318.808.680.21 - 0.828.777.928.258.237.828.098.238.388.028.518.188.878.230.29 - 6.238.758.828.778.658.808.698.658.228.748.588.738.888.680.18 - 0.847.878.078.198.138.258.277.968.348.098.048.338.158.160.123.758.168.308.158.318.048.258.018.008.237.988.088.268.150.13 - 0.267.948.217.947.787.948.037.637.528.027.767.927.977.880.19 - 0.779.7310.479.8710.2610.2910.009.939.599.629.9710.029.9910.000.262.887.297.827.597.827.787.687.607.457.317.637.687.657.640.154.898.969.198.899.178.818.958.748.618.778.738.568.948.850.20 - 1.2109.279.639.479.689.399.499.329.299.409.299.179.539.420.151.7119.699.739.669.789.449.609.539.649.549.339.079.719.550.21 - 1.5129.879.919.8810.029.649.979.629.729.849.629.609.859.790.15 - 0.8max .
error6.2 activities of sources measured in dose calibrator and corrected results by 11 individual testers figure  4 shows the decay - corrected activities of the sources calculated on the reconstructed spect image without and with scatter and attenuation correction , as well as the activities measured in the dose calibrator .
the quantification errors on the uncorrected images ranged from 23.6 to 9.3% . with attenuation correction only ,
these errors of the 11 testers average results ranged from 1.4 to 10.3% , with an average magnitude of 5.6% over all 12 sources . with scatter and attenuation correction ,
these errors ranged from 6.3 to + 4.3% , and the average magnitude decreased to 2.1% . 

nc no correction was performed , sc  +  ac scatter and attenuation correction was performed , ma activities measured by dose calibrator a planar images showing positions of sources .
nc no correction was performed , sc  +  ac scatter and attenuation correction was performed , ma activities measured by dose calibrator
figure  3 shows reconstructed slices of the cylindrical phantom to illustrate the effect of the attenuation correction .
the summation of ten transverse slices ( decay corrected ) without attenuation correction ( fig . 
this can be observed more clearly on the line profiles through the diameters of the phantom along the x direction ( fig . 
the activity concentration measured in the dose calibrator as a gold standard is indicated by a horizontal line at 2.88  mbq / ml . 

the grey scales of a  d are the same , from black ( 0  mbq / ml ) to white ( 3.5  mbq / ml ) .
the line mc indicates the concentration measured with a dose calibrator , as a gold standard averages of ten transverse spect slices of the cylindrical phantom .
the grey scales of a  d are the same , from black ( 0  mbq / ml ) to white ( 3.5  mbq / ml ) .
the line mc indicates the concentration measured with a dose calibrator , as a gold standard without corrections , the difference between the activity concentrations calculated on the reconstructed spect image and measured in the dose calibrator was significantly underestimated by 0.54  mbq / ml , or 18.7% . with scatter correction only ,
the difference worsened to 0.77  mbq / ml ( 26.8% ) . applying only attenuation correction led to an overestimation by 0.26  mbq / ml ( 9.2% ) . applying attenuation correction in combination with
scatter correction resulted in a small underestimation of 0.05  mbq / ml ( 1.7% ) .
these numbers were calculated on the voxels in a cylindrical volume with a diameter of 42  mm , which was slightly smaller than the phantom size in order to avoid the influence of partial volume effect .
since the sources inserted into the rat were isolated well , it is possible to segment sub - volumes for individual sources on the reconstructed spect image .
the activity of each source was calculated by adding all the voxel values in the sub - volume containing that source and then multiplying the resulting sum , the cf , and the voxel size together .
eleven volunteers were invited to carry out the attenuation corrections on the reconstructed image individually , using the application program that is shown in fig . 
after a 15-min training session , all volunteers were able to finish their testing within 5  min .
table  2 lists the activities of the sources measured in the dose calibrator and their quantitative results calculated on the decay , scatter and attenuation - corrected image .
the averages , standard deviations and percent errors of those results over the 11 testers are also listed . 

table  2activities of sources measured in dose calibrator and corrected results by 11 individual testerssource no.activity ( mbq)quantified results by 11 individual testers ( mbq)aver .
( mbq)sd ( mbq)error ( % ) 18.758.918.789.008.438.868.548.698.698.508.318.808.680.21 - 0.828.777.928.258.237.828.098.238.388.028.518.188.878.230.29 - 6.238.758.828.778.658.808.698.658.228.748.588.738.888.680.18 - 0.847.878.078.198.138.258.277.968.348.098.048.338.158.160.123.758.168.308.158.318.048.258.018.008.237.988.088.268.150.13 - 0.267.948.217.947.787.948.037.637.528.027.767.927.977.880.19 - 0.779.7310.479.8710.2610.2910.009.939.599.629.9710.029.9910.000.262.887.297.827.597.827.787.687.607.457.317.637.687.657.640.154.898.969.198.899.178.818.958.748.618.778.738.568.948.850.20 - 1.2109.279.639.479.689.399.499.329.299.409.299.179.539.420.151.7119.699.739.669.789.449.609.539.649.549.339.079.719.550.21 - 1.5129.879.919.8810.029.649.979.629.729.849.629.609.859.790.15 - 0.8max .
error6.2 activities of sources measured in dose calibrator and corrected results by 11 individual testers figure  4 shows the decay - corrected activities of the sources calculated on the reconstructed spect image without and with scatter and attenuation correction , as well as the activities measured in the dose calibrator . the quantification errors on the uncorrected images ranged from 23.6 to 9.3% .
with attenuation correction only , these errors of the 11 testers average results ranged from 1.4 to 10.3% , with an average magnitude of 5.6% over all 12 sources . with scatter and attenuation correction , these errors ranged from 6.3 to + 4.3% , and the average magnitude decreased to 2.1% . 

nc no correction was performed , sc  +  ac scatter and attenuation correction was performed , ma activities measured by dose calibrator a planar images showing positions of sources .
nc no correction was performed , sc  +  ac scatter and attenuation correction was performed , ma activities measured by dose calibrator
quantification of spect imaging in absolute terms becomes possible when physical effects like collimator blurring , sensitivity , scatter and photon absorption are all modelled during iterative reconstruction or compensated afterwards . in clinical spect imaging ,
non - uniform attenuation maps ( e.g. from x - ray ct ) need to be acquired for accurate quantitative results .
our work shows that attenuation compensation can be performed well in small - animal spect applications , despite the fact that no ct scanner was used .
uniform attenuation maps were created with the help of body contour information from optical cameras . at the current stage of this research , the 2-d contours were defined manually with deformable closed spline curves on the optical photos .
this could possibly be further automated by using certain image processing techniques , such as image segmentation , pattern recognition and an anatomical body contour model .
experiments were performed to validate our method , first with a simple uniform phantom , and then with a rat cadaver .
although the animal model of a rat with artificial sources is still different from a realistic set - up of pre - clinical studies ( with injections and region of interest measurements , etc . ) , it is very well suited for evaluating the accuracy of correction methods , since the exact amounts of activity in specific regions of interest are known ( which is in contrast to using living animals with a tracer injected ) .
the results from the phantom and animal experiments demonstrated that without compensation an approximately 1030% underestimation of the activity concentration could be achieved , varying with the diameters of the objects and the depth of the sources .
note that even if the sources were just under the skin of the rat , i.e. the common positions of transplanted tumours for pre - clinical cancer research , there was still more than 10% underestimation . applying a first - order uniform attenuation correction with
the chang algorithm resulted in accurate quantifications in our experiments , especially when combining together with scatter correction ( 1.7% in the phantom study and from 6.3 to + 4.3% in the animal study ) . in table  2
we notice that the magnitudes of most errors are below 5% except for source no . 2 which has an underestimation of 6.3% .
this source was in the rat s mouth and we found that the mouth can be hardly seen on the optical photos , due to the obstruction of the tissue and tape around the rat , which makes the 2-d contours at that region uncertain .
in fact , the source is not even enclosed with the contours made by 7 of the 11 testers .
this apparently leads to an underestimation of the attenuation and thus to a negative bias of the quantitative result .
therefore , we suggest trying to keep a clear sight of the animal contour in a study that requires absolute quantification . on the other hand ,
the standard deviations of the 11 testers results are small (  3% ) , which supports the observation that the proposed attenuation correction method is not very sensitive to the contour differences introduced by some subjective judgments of individuals . when imaging with tc , scatter correction is usually not performed in normal studies due to the small amount of compton photons within the photopeak window .
however , for absolute quantitative studies , it is better to apply scatter correction in order to avoid the overestimation caused by scattered photons . by using attenuation correction in combination with scatter correction ,
about 7.5 and 3.5% improvement of quantitative accuracy over the accuracy with only attenuation correction was gained in our phantom and rat cadaver experiments , respectively .
there are two things in our experiments which may cause a bias to the results .
different photopeak window settings will affect the proportion of gamma counts which contribute to the reconstructed images and thus change the calibration factor . to avoid this we employed the same window settings for all of the reconstructions .
the other one is the inaccuracy of the dose calibrator . by using the same dose calibrator to measure the sources for computing the calibration factor and for the validation experiments , the system error , or bias , of the dose calibrator cancels out in the final results of relative errors .
however , accurate calibration of the dose calibrator is essential to obtain the exact calibration factor and absolute quantitative results in applications . in order to simplify our method and to facilitate rapid correction ,
the pinhole geometry of the u - spect - ii system and associated attenuation paths were roughly ( 2-d ) approximated during the chang - like attenuation correction .
the actual projection paths of a voxel are very complicated considering both the multi - pinhole geometry and the use of multiple bed positions during acquisition .
it was shown that this approximation provides good quantitative accuracy in small - animal images . that still good results were obtained
can partly be explained by the fact that changes of transmitted fraction due to the length differences between oblique paths and perpendicular paths are small ( around 5% at the most ) . in clinical studies , the chang algorithm is known to cause over- and undercorrection , and therefore an additional iterative step for compensation is implemented , however at the cost of noise increase . since in small - animal spect the results are accurate without additional iterations , we restricted our method to pure post - reconstruction processing which ( 1 ) is much easier to implement and ( 2 ) does not increase noise .
we introduced a contour - based attenuation correction method for small - animal spect . to validate this method ,
phantom and animal experiments were performed and subsequently quantified with a practical software tool by 11 testers . from the results ( average error of 1.7 and 2.1% for phantom and animal studies , respectively ) , we conclude that this body contour - based uniform attenuation correction method derived from the chang algorithm , in combination with scatter correction , is sufficient for accurate absolute quantification in small - animal spect imaging .
the information of 3-d contours for generating the attenuation maps can be obtained from optical photos instead of from x - ray ct images .
this gives opportunities to do absolute quantitative spect with stand - alone spect systems and to reduce the dose to the animals caused by x - rays which can be limiting in longitudinal studies .
we introduced a contour - based attenuation correction method for small - animal spect . to validate this method ,
phantom and animal experiments were performed and subsequently quantified with a practical software tool by 11 testers . from the results ( average error of 1.7 and 2.1% for phantom and animal studies , respectively ) , we conclude that this body contour - based uniform attenuation correction method derived from the chang algorithm , in combination with scatter correction , is sufficient for accurate absolute quantification in small - animal spect imaging .
the information of 3-d contours for generating the attenuation maps can be obtained from optical photos instead of from x - ray ct images .
this gives opportunities to do absolute quantitative spect with stand - alone spect systems and to reduce the dose to the animals caused by x - rays which can be limiting in longitudinal studies .
 purposein pinhole spect , attenuation of the photon flux on trajectories between source and pinholes affects quantitative accuracy of reconstructed images . 
 previously we introduced iterative methods that compensate for image degrading effects of detector and pinhole blurring , pinhole sensitivity and scatter for multi - pinhole spect . 
 the aim of this paper is ( 1 ) to investigate the accuracy of the chang algorithm in rodents and ( 2 ) to present a practical chang - based method using body outline contours obtained with optical cameras.methodshere we develop and experimentally validate a practical method for attenuation correction based on a chang first - order method . 
 this approach has the advantage that it is employed after , and therefore independently from , iterative reconstruction . 
 therefore , no new system matrix has to be calculated for each specific animal . 
 experiments with phantoms and animals were performed with a high - resolution focusing multi - pinhole spect system ( u - spect - ii , milabs , the netherlands ) . 
 this spect system provides three additional optical camera images of the animal for each spect scan from which the animal contour can be estimated.resultsphantom experiments demonstrated that an average quantification error of 18.7% was reduced to 1.7% when both window - based scatter correction and chang correction based on the body outline from optical images were applied . without scatter and attenuation correction , quantification errors in a sacrificed rat containing sources with known activity ranged from 23.6 to 9.3% . 
 these errors were reduced to values between 6.3 and + 4.3% ( with an average magnitude of 2.1% ) after applying scatter and chang attenuation correction.conclusionwe conclude that the modified chang correction based on body contour combined with window - based scatter correction is a practical method for obtaining small - animal spect images with high quantitative accuracy . 
Introduction
Materials and methods
U-SPECT-II: a focusing pinhole small-animal SPECT system
Image reconstruction
Calibration factor
Scatter correction
Attenuation correction
Quantification
Experiments
Results
Phantom experiment
Animal experiment
Discussion
Conclusion