dramatic advances in imaging technology , especially for small animal imaging , have been an important driving force in establishing the field of molecular and genomic imaging .
micro - ct system for small animal imaging has been studied since 1990s [ 27 ] and has played a critical role in the evolution of molecular imaging [ 8 , 9].it can obtain high - resolution anatomic information and can be combined with other modalities [ 10 , 11 ] , such as nuclear imaging [ 12 , 13 ] and optical imaging .  
a prototype cone - beam micro - ct system for small animal imaging has been developed by our group . in this system
, we use a microfocus x - ray source and a complementary metal oxide semiconductor ( cmos ) based flat - panel detector .
fdk   method is adopted for 3d reconstruction . in order to accelerate ct reconstruction speed ,
we develop reconstruction software using graphics processing unit ( gpu ) hardware .   the aim for building such
a system is to develop a dual modality system integrated with a micro - ct scanner and a bioluminescence tomography ( blt ) system .
however , the spatial resolution of blt is about several millimeters or submillimeters , so the anatomic structure with less than 100 micron is enough .
moreover , main organs , such as lung , bone , kidney , and liver , should be discriminated in ct image .   in this paper , the prototype micro - ct system is introduced , including overview of the system , geometric misalignment calibration , gpu - based image reconstruction and post - processing software .
system performances have been evaluated in terms of spatial resolution , image uniformity and noise , and low contrast resolution .
furthermore , some mouse images with and without contrast agent are presented to show the overall performance of the system .
the prototype micro - ct system consists of a microfocus x - ray source , a three - dimensional ( x - y translation and rotation ) programmable stage with mouse holder and a flat - panel x - ray detector .
all of them are mounted on an optical bench in a shielded laboratory and controlled by a host computer .
a schematic diagram of the system is shown in figure 1 . the source to detector distance ( sdd ) and source to object distance ( sod ) are variable to change the magnification ratio , cone - beam angle , and field of view ( fov ) of the system . in most cases ,
the sdd is set to 498 mm and the magnification ratio m is set to 1.3 , where m = sdd / sod . the x - ray source ( ultrabright , oxford instruments , usa ) has a microfocus continuously adjustable from 13 m to 40 m and the power density has been rated to 2.5 w/m .
the target voltage of the x - ray tube is 20 to 90 kvp , with maximum output power 80 w. the x - ray flat panel detector ( c7942ca-02 , hamamatsu , japan ) , based on cmos technology with a column csi scintillator plate , has a 120 mm      120 mm photodiode area with 50 m pixel size .
the image data are transferred to the host computer by a frame grabber card ( imaq pci-1424 , national instruments , usa ) in the system .  
the three - dimensional programmable stage consists of two motorized translation stages ( psa200 - 11 , zolix instruments , china ) and one motorized rotation stage ( rak-100 , zolix instruments , china ) .
the resolution of the rotation stage is up to 0.00125. the magnification ratio can be changed by adjusting the position of the object ( mouse or rat ) using the motorized translation stages , which will significantly affect the spatial resolution and the fov .
the fov is usually large enough to acquire the whole body imaging of a normal size mouse in a single scan with a small magnification ratio .
several methods [ 1719 ] have been proposed to evaluate and calibrate the geometric misalignment . in our system , the method proposed by yang   is used . as is stated in ,
the rotation axis is defined as the z axis of the system . the axis which passes through the cone vertex ( x - ray tube focal spot ) and perpendicular to the z axis
the axis perpendicular to the x - z plane is defined as the y axis .
there are seven parameters to describe the system geometry : source to detector distance ( sdd ) , source to object distance ( sod ) , 
 u0 , horizontal location of the intersection of the x axis and detector plane , 
 v0 , vertical location of the intersection of the x axis and detector plane , 
  , in - plane rotation angle , the rotation angle of the detector plane along x axis , 
  , out - of - plane rotation angle , the rotation angle of the detector plane along the axis of v = v0 , 
  , out - of - plane rotation angle , the rotation angle of the detector plane along the axis of u = u0 ,   the two out - of - plane rotation angles ,  and  , are quite difficult to determine with reasonable accuracy and have only a small influence on image quality , so  and  could be assumed to zero during geometric calibration , and then five other parameters need to be estimated . therefore , the method with multiple projection images acquired from rotating point - like objects ( metal ball bearings ) are used to estimate these five parameters . during experiments , it is found that the horizontal location parameter u0 has a great influence on image quality .
though yang 's method could achieve high accuracy , there still exists a small residual detector horizontal offset sometimes , which may be caused by the projection noise in the geometric evaluation .
we denote the residual horizontal offset as u , which is the difference between the actual and estimated value of u0 after yang 's geometric calibration .
if the residual offset value is large , it will degrade the reconstruction image , especially when high resolution is desired . in the developed system ,
a wire phantom is utilized to assess the geo - calibration result , and a simple method is proposed to evaluate the horizontal offset through the wire phantom reconstruction image . considering a wire phantom with the wire diameter significantly smaller than the system spatial resolution ,
cross - sectional view of the phantom reconstruction image can be regarded as the point spread function ( psf ) of the system . through 1d psf , the profile of the psf image , one can access geometric calibration effect quantitively .
if there is no detector residual horizontal offset , the wire in the cross - sectional view will be a point . while if a small horizontal offset exists after geometric calibration , psf will be spreaded and its intensity will become smaller .
camparing the peak value of psf with different geometry calibration , we can determine which one leads to a better calibration result .
if the residual horizontal offset is large enough , a ring will appear in the cross - sectional view instead of a point , and the radius of the ring is related to the horizontal offset value .
we have proposed a simple method to assess the horizontal offset , which is derived as follows .
let s , o and od be the focal spot of the x - ray source , the center of the rotational stage and the center of the flat panel detector , respectively .
we use p to denote a point in the tungsten wire near horizontal mid - plane of the cone beam , where the cone angle can be neglected .
the distance between the wire and the rotational axis is l. figure 2 shows that the rotational stage turns an angle  ( 0 
 < 2 ) , and the projection of the point p will be along the radial sp or sn which makes an angle  with the center ray so . owing to the effect of the horizontal offset u ,
back - projection will start from n and along the radial ns which makes an angle  with sp .
the distance from point p to the line ns is r. figure 3 illuminates that the tail portions of the line are cancelled and a ring with radius r around the point p is formed when the neighboring views are closely placed . as u is very small , the following relationships can be derived : 
								 ( 1)usdd,(2)=arctan(l  sin  sod+l  cos  ),(3)=2,(4)r=rsin  ,(5)ur=sddsod+l  cos  . substituting ( 3 ) and ( 4 ) into ( 5 ) , we have 
								 ( 6)ur = sdd(sod+l  cos  )sin(/2 ) . 
							
as the wire is near the phantom center , the value l will be very small , only a few millimeters , when the phantom is put in the center of the rotational stage , thus l  sod .
u is significantly smaller than sdd , u  sdd , then ( 6 ) can be simplified to 
								 ( 7)ur = sddsod = m , 
							 where m is the magnification ratio of the system . by ( 7 ) , the horizontal offset can be evaluated and the ring radius value can be measured from the wire reconstruction image . reconstruction image with smaller voxel
though the offset value could be calculated , yet the offset direction could not be determined .
so the offset needs to be calibrated in both left and right to confirm the correct direction .
it should be noted that the above analysis is an ideal case . in real experiments
, the ring may be not very clear because of the effects of noise and wire size .
so we have to average many cross - sectional slices to identify the ring clearly .
in addition , when the horizontal offset is small , the ring may not appear in the image . in this condition , if one wants to dertermine whether the calibration result is good or not , a small horizontal offset ( about a pixel ) should be added artificially .
if the evaluted value is equal to the added one , it indicates that the former geometric calibration is good .
due to dark imaging offset , pixel gain and defective pixels , raw data from x - ray detector show spatial variation , therefore it is necessary to perform data preprocessing before reconstruction , including dark current subtraction , flat field division , and defective pixels interpolation .   after data pre - processing , fdk method is adopted for 3d reconstruction in the developed system . because an exact reconstruction is impossible for circular cone - beam scans due to data insufficiency [ 20 , 21 ]
, fdk is an approximate algorithm and the reconstruction images using fdk algorithm have artifacts such as low - intensity drop when the cone angle is large .
however , our experiments and other literatures [ 22 , 23 ] have suggested that the reconstruction images are acceptable when the cone angle is relatively small ( about less than 10 ) . it is well known that 3d ct image reconstruction is computationally demanding , so a software using gpu hardware is developed to improve the reconstruction speed .
it takes about 5.2 seconds to reconstruct a 512 cubed volume from 360 views of the size of 512  512 on a 2.66 ghz dual - core intel pc with 2 gb ram hosting a nvidia geforce 8800gtx card .
large data reconstruction may need tens of or hundreds of seconds , because data reading from hard disk to ram costs lots of time .
we use 3d medical image processing and analyzing software 3dmed ( v. 2.2.0 ) , developed by the medcal image group , institute of automation , chinese academy of sciences ( http://www.3dmed.net/ , http://www.mitk.net/ ) , to display and post - process the 3d micro - ct data .
it is a free software and combines the function of medical image segmentation , registration and visualization .
furthermore , it supports the creation of plug - ins to incorporate new processing algorithms .
in order to evaluate the system characteristics , the reconstruction images are assessed in terms of modulated transfer function ( mtf ) , uniformity and noise level , and low contrast resolution .
phantoms and mouse scanning protocols are listed detailedly in table 1 . a wire phantom ( micro - ct wire phantom , qrm , germany ) , as shown in figure 4 , is utilized to measure the psf and mtf of the micro - ct system in our study .
the cylinder phantom contains two tungsten wires in solid material aligned parallel to the phantom axis of rotation .
one of the wires is slightly off center , the other 12 mm away from the center in order to allow estimating image quality in the periphery .
the two tungsten wires in the phantom are designed to parallel to the phantom axis . when the cylinder phantom is put on the rotation stage perpendicularly ,
we can judge whether the wire slopes or not by the sagittal and coronal view of the reconstruction image .
if there is no slope observed from the sagittal view and coronal view , we assume that the wire is perpendicular to the horizontal plane .
the wire phantom is scanned according to the above protocols to acqure the system modulation transfer function .
the reconstruction image of the wire can be regarded as the psf of the system . calculating the modulus of the fourier transform of the psf and normalizing to 1 at spatial frequency at zero
different magnification ratios , 1.3 and 2.36 , are set to observe geometric position effect on spatial resolution .
as there are two wires in the phantom , one could evaluate the spatial resolution both near the rotation axis and off away from the axis in a single scan measurement .
ramp function and cosine window function ( hamming window ) are used respectively as the filter kernel during 3d reconstruction to study the influence of different filter kernels .
imaging uniformity and noise of the reconstruction image are investigated with a cylindrical phantom filled with distilled water ( micro - ct water phantom , qrm , germany ) , as shown in figure 5 . the radial profile of the reconstruction image is plotted to illuminate the uniformity qualitatively . a quantitative assessment of the signal variation , from center to periphery , is performed by calculating the mean values and standard deviations in five regions of interest ( rois ) , one in the center of phantom and four in the periphery , and the average differences in signal intensity values between the central and the perihperal regions are calculated .
five different exposure intensities are used to determine the relationship between exposure and image noise .
the tube is set at 50 kvp with the tube current varying from 0.4 ma to 1.2 ma , which corresponds to exposure from 0.24 mas to 0.72 mas for a single projection .
beam hardening correction is implemented to reduce artifacts caused by polychromatic x - ray beam .
the total measured noise can be considered as a quadrature summation of photon noise and system noise , then one can obtain 
								 ( 8)m2=ae+s2 , 
							 where m is the measured noise variance , m is standard deviation . also , e is the exposure for a single view in mas , and a and s are constant terms . in our system ,
if we want to distinguish the low - contrast objects from their background with false positive and false negative rate 5% , the means of the two distributions should be separated by 3.29 m .
for 50% false - positive and false - negative rate , 0.83 m separation are needed . for in vivo small animal imaging ,
to reduce the motion blurring due to breathing or heart beating , the systems with high framing rate or respiratory gating has been studied [ 25 , 28 , 29 ] . none of these techniques has been implemented in our system and great efforts have been made to reduce motion effects under the current condition .
in addition , as the purpose of the system is to provide anatomic structure for blt , which resolution is about several millimetres or submillimetres , so some slight motion artifacts are acceptable
. the overall performance of the micro - ct system is assessed by mouse scanning .
the mouse was anesthetized with pentobarbital sodium and no contrast agent was used during scanning .
the cross - sectional view , coronal view , sagittal view , and the bone structure of the mouse are illuminated in the following section . in order to enhance soft tissues contrast resolution ,
after fasting for 24 hours , a 20 g balb / c mouse is slowly injected fenestra lc ( art , montreal , canada ) at a dose of 15 ml / kg over a period of 3060 seconds via the lateral tail vein .
it is anesthetized with urethane and scanned by our micro - ct system at 3.5 hours postinjection .
the wire phantom shown in figure 4 is used to assess the geometric calibration results .
it is reconstructed with ram - lak filter and the voxel size is 0.01  0.01  0.05 mm .
however , 100 slices near the horizontal mid - plane are averaged to reduce the noise effect .  
 figure 6(a ) shows that a ring exists in the cross - sectional view of the wire phantom , which arises from a small horizontal offset after geometric calibration . in figure 6(a ) , the radius of the ring is mesured about 0.035 mm .
the magnification ratio is 1.3 . according to ( 7 ) , the horizontal offset can be determined , that is , 0.045 mm , about 0.9 pixel .
because the misalignment direction is unknown , the calibration have to be implemented in left and right to determine the correct direction .
figure 6(c ) gives an excellent geometric calibration results , where a point appears in the image instead of a ring .   in order to assess the geometric results quantitively
, normalized 1d psfs are ploted in figure 7 , which are corresponding to figures 6(a )   and 6(c ) . due to horizontal geometric offset
it should be noted that when the horizontal offset is not large , the forked peak will not appear but the peak value will be still lower than the excellent geometric calibration result .
campared the psf peak values obtained with different horizontal offsets , the optimal geometric configration can be determined . 

figure 8 shows the modulation transfer function of the cone - bean micro - ct system .
the effects of the magnification ratio and filter kernel are illuminated in the figure clearly .
the spatial resolution in the periphery of the phantom is a little lower than that near the center , but not obviously .   at a lower magnification ratio ( m = 1.3 ) ,
the spatial resolution is about 9 lp / mm at 10% of the mtf curve with ramp function kernel and 6.5 lp / mm with cosine window kernel , while it reaches about 14.5 lp / mm with ramp function kernel and 10.5 lp / mm with cosine window kernel at a higher magnification ratio ( m = 2.36 ) .
the radial profile of the reconstruction water phantom is plotted in figure 9 to illuminate the uniformity of the image .
table 2 gives the mean value and standard deviation of the signals in five different rois with different exposure intensities .
signal average values acquired in different exposure intensities share almost the same value , while the standard deviation decreases with the increment of the exposure intensity . for all exposure intensities ,
the differences of the average signal intensities from center to periphery are all less than one standard deviation of the signals .  

figure 10 shows the relationship between standard deviation of voxel noise ( in hu ) and the exposure intensity ( in mas ) , which has been fitted to ( 8) and obtains 
								 ( 9)m2=883e , 
							 where the system noise variance s is neglected because it is significant small .
equation ( 9 ) indicates that the voxel noise variance is inversely proportional to the exposure intensity . as shown in figure 10 , the standard derivation of the signal noise is about between 35 hu and 60 hu .
take 50 kvp , 1.2 ma for example , the standard derivation is 34.8 hu , which means that 114.5 hu difference is needed to distinguish the low contrast objects from their background with false positive and false negative rate 5% , and 28.9 hu is needed to reach 50% false positive and false negative rate . 

. figures 11(a ) , 11(b ) , and 11(c ) are the transaxial view , the sagittal view , and the coronal view of the mouse , respectively . figure 11(d ) shows the bone structure of the mouse segmented from the reconstruction data using the software 3dmed .
while figure 12 shows excellent liver contrast enhancement which is achieved at 3.5 hours postinjection fenestra lc at the dose of 15 ml / kg . it is possible to distinguish liver from surrounding soft tissues in this image .
a prototype cone - beam micro - ct system for small animal imaging is described in this paper . to acquire images with high spatial resolution and low artifacts , data preprocessing and geometry calibration
system spatial resolution is investigated in terms of mtf , which reaches about 14.5 lp / mm at a magnification ratio of 2.36 with ram - lak filter .
water phantom study shows that the voxel noise variance is inversely proportional to the exposure intensity .
low contrast resolution is also studied in the paper . some living mouse imaging results with and without contrast agents
are presented to give an overall performance of the system . for micro - ct , relative low soft tissue contrast resolution is a drawback which hinders its widespread .
as is measured in water phantom experiments , the standard deviation is about 35 hu for 50 kvp , 1.2 ma , while ct number of human 's main organs , except lung and bone , are mostly in the range from 20 hu to 80 hu .
so it is a big challenge to distinguish one from others , especially for the liver .
fortunately , exogenous contrast agent overcomes this problem to some extent . with specific micro - ct contrast agent fenestra lc
beside contrast agent method , techniques to reduce image noise could also be used in micro - ct to improve contrast resolution .   at present , several commercial micro - ct systems have been developed .
compared with these systems , one characteristic of our system is reconstruction using gpu hardware , which reaches a high reconstruction speed with relative low cost , and will achieve software upgrade easily .
a simple method has been proposed to access geometric calibration results and evaluate the detector horizontal offset utilizing a wire phantom .
in addition , as mentioned , the final purpose is to build a blt - ct dual modality system .
a prototype micro - ct system will be more conveniently to integrate with blt system .
 a prototype cone - beam micro - ct system for small animal imaging has been developed by our group recently , which consists of a microfocus x - ray source , a three - dimensional programmable stage with object holder , and a flat - panel x - ray detector . 
 it has a large field of view ( fov ) , which can acquire the whole body imaging of a normal - size mouse in a single scan which usually takes about several minutes or tens of minutes . 
 fdk method is adopted for 3d reconstruction with graphics processing unit ( gpu ) acceleration . in order to reconstruct images with high spatial resolution and low artifacts , raw data preprocessing and geometry calibration 
 are implemented before reconstruction . a method which utilizes a wire phantom to estimate the residual horizontal offset of the detector 
 is proposed , and 1d point spread function is used to assess the performance of geometric calibration quantitatively . 
 system spatial resolution , image uniformity and noise , and low contrast resolution have been studied . 
 mouse images with and without contrast agent are illuminated 
 in this paper . 
 experimental results show that the system is suitable for small animal imaging and is adequate to provide high - resolution anatomic information for bioluminescence tomography to build a dual modality system . 
1. Introduction
2. System Description
3. System Performance Evaluation
4. Results
5. Conclusion