due to its short acquisition time and high temporal resolution , echo - planar imaging ( epi ) is often the method of choice for data acquisition in fast imaging including diffusion - weighted imaging ( dwi ) , diffusion tensor imaging ( dti ) , perfusion mri , and functional mri ( fmri ) .   however , epi is extremely sensitive to magnetic field inhomogeneities ( e.g. , close to tissue / bone or tissue / air interfaces ) because of the prolonged readout and hence low bandwidth in the phase encoding ( pe ) direction .
in addition to time - invariant off - resonance effects such as b0 field inhomogeneities , dynamic field variations induced by eddy currents may further contribute to the observed image distortions .  
several methods to overcome limitations of geometric image distortions can be found in literature [ 2 , 3 ] .
techniques based on the field mapping approach  though elegant and intuitive  face implementation difficulties related to the need for phase unwrapping , particularly at high fields and when imaging small objects .
multireference methods [ 4 , 5 ] offer a greater degree of stability at expense of prolonged imaging time . among these methods ,
the point spread function- ( psf- ) based approach for distortion correction ( dico ) by robson et al .
is often used in mri . using an extended epi acquisition with an additional gradient encoding on the phase encoding ( pe ) axis
based on the psf information , a pixel shift map ( psm ) can be calculated and applied to conventional epi data for image distortion correction .  
the psf mapping is a very robust method and allows the quantification of distortions in regions of low- and high - field inhomogeneities .
in addition , epi inherent eddy currents and concomitant gradients cause identical distortions of the psf data as in epi and , thus , are also mapped faithfully .  
the acquisition steps for the psf data depends directly on the matrix size and can result in a substantial acquisition time increase .
however , there are several further developments to speed up psf mapping including the application of parallel imaging techniques ( e.g. , grappa ) and the reduced field of view ( rfov ) approach to psf data acquisition . with regard to postprocessing
, the calculation of the pixel shift map is computationally cheap and fast and shows a high stability .
another reason for the choice of the psf - based method is several years of the positive experience with the method in routine human epi examinations at our 3 t systems .   in this paper
we present an implementation of the psf - based distortion correction methodology on an animal imaging system and its application to epi at high fields .
the inaccuracies of the phase information in epi  and hence , the geometric distortions  increase with the field strength and if measured in pixels , the geometric distortions increase in an over - proportional manner at higher resolutions that are typical for high - field animal mri .
thus , the aim of this work is to investigate the performance of the psf - based correction method for high - field epi applications in animal mri .
unfortunately epi distortion correction in animal mr imaging has received extremely scant attention of the research community , and the fair comparison between different known correction methods given the special requirements of animal imaging has not been performed elsewhere . therefore the choice was made to implement the psf technique , which has proven its stability over several years of experience at our institution   and was also recommended by previous publications from other groups .
for the acquisition of psf data , a standard epi method was extended by an additional gradient encoding on the phase encoding axis as described in .
in addition , the method was adapted such that raw data ( later called  psf raw data  )
are stored after all postprocessing steps ( e.g. , ramp sampling correction , grappa reconstruction of missing k - space lines , etc . ) but before image reconstruction .
the described method was implemented on a bruker biospin 94/20 system in paravision 5 ( bruker biospin , ettlingen , germany ) .  
in addition , our implementation allowed for automatic psf encoding settings ( gradient strength and number of repetitions ) and acquisition time reduction using rfov .
postprocessing of psf raw data was performed offline on a standard pc running fedora linux ( fedora 8) using the matlab software package ( matlab r2007b , the mathworks inc . , natick , ma , usa ) .
the psf raw data can be considered as a 3d data set with dimensions of epi frequency , epi phase encoding , and psf encoding .   in order to get complex image data a two - dimensional fourier transformation
is applied in epi frequency and phase encoding directions . in the case of multichannel data ,
this step is performed separately for each coil element and the resulting images are combined complex using adaptive reconstruction from walsh et al .   in order to preserve the phase information necessary for the following processing steps .   in order to calculate the psf ,
next , the shift of the psf is determined to subpixel resolution using the fourier shift theorem [ 7 , 11 ] for every point in image space .
this results in a pixel shift map ( psm ) , which is later used to correct for image distortions .  
the nondistorted image has the same echo time and , thus , image contrast as the corresponding echo - planar image .
it represents a spin echo ( se ) or gradient echo ( ge ) image corresponding to whether an se - epi or ge - epi is used .
in addition , an object mask is generated from the nondistorted image using threshold segmentation that is later used during the distortion correction procedure . in the last postprocessing step , conventional epi data ( e.g. , fmri or dwi )
therefore , a pixel inside the object mask retrieves a value determined by its original position and the corresponding shift in the pixel shift map from the original image ( epi ) . due to the subpixel shifts present in the pixel shift map ,
a piecewise cubic spline interpolation procedure was used to determine the corrected pixel intensity values .  
as stated above , this operation is only performed for pixels inside the object mask to prevent artifact generation outside of the distortion - corrected object .
note that the data inside of the object mask can not be damaged by incorrect mask generation .  
the corrected image data are stored inside the original data folder as an additional reconstruction for this examination .
the distortion correction was applied to conventional spin - echo ( se - epi ) and gradient - echo ( ge - epi ) echo - planar imaging on phantoms as well as to functional magnetic resonance imaging with diffusion - weighted echo - planar imaging ( dw - epi ) on mice and rats in vivo .
all experiments were performed on a 9.4 t bruker biospin animal system equipped with a bga12s gradient system capable of 675  mt / m .
a transmit / receive 1h mouse quadrature birdcage resonator with an inner diameter of 35  mm was used for mice and phantom imaging . for rat imaging , a transmit 1h quadrature birdcage resonator with an inner diameter of 70  mm was used for rf excitation and a 4-channel phased array head coil was used for signal detection .   for phantom experiments ,
a phantom was built using a plastic cylinder with an inner diameter of 30  mm ( falcon tube ) .
the tube was filled with two different agarose concentrations ( inner part : 1% ; outer part 2% ) in order to provide contrast between the two compartments .  
acquisition parameters for a single - shot se - epi were tr = 3000 milliseconds , te = 52.18 milliseconds , bw = 200  khz , and 10 repetitions .
ten consecutive slices with 1  mm slice thickness , an fov of 40  mm      40  mm , and a matrix size of 192      96 were acquired in 30 seconds .
total acquisition time for psf data with 96 images for each slice was 4 : 48 minutes .   for in vivo data acquisition
, animals were narcotized using an isofluran - oxygen mixture ( ~2vol% isofluran for rats ,   ~2.5vol% isofluran for mice ) .
ecg , respiration , and core temperature of the animals were monitored during the experiments .
all experiments were in concordance with the local ethics committee ( approval g-08/54 ) .  
acquisition of mice images was performed using a single - shot , diffusion - weighted se - epi , and the following parameters : tr = 4000 milliseconds , te = 18.3 milliseconds , and bw = 400  khz .
geometric settings were 8 consecutive slices , 0.6  mm slice thickness , fov = 30  mm      20  mm , and 96      64 image matrix , resulting in an isotropic in - plane resolution of 0.3125      0.3125  mm .
however , in order to reduce se - epi acquisition duration , partial fourier encoding with an acceleration factor of 1.6 and 8 overscan lines was employed .
five b = 0  s / mm images without diffusion weighting and 34 diffusion - weighted images were acquired in ta = 2 : 36 minutes . for diffusion weighting , different b - values ranging from 100 to 3400
acquisition parameters for psf data using conventional se - epi were tr = 3000 milliseconds and te = 8.8 milliseconds , with the geometric settings equal to the respective parameters in dw - epi . for each slice
, 64 images were acquired in ta = 3 : 12 minutes . in this context
diffusion - weighted rat images were acquired with a 4-shot se - epi , and parameters of tr = 3000 milliseconds , te = 17 milliseconds , and bw = 300  khz .
geometric settings were 12 slices , 0.5  mm slice thickness , fov = 40  mm      40  mm , and 128      96 matrix size .
in addition to one b = 0 image , 5 diffusion - weighted images were acquired with b = 200 , 400 , 600 , 800 , and 1000  s / mm .   in order to derive correct distortion information ,
psf data were also acquired using a 4-shot se - epi sequence . for full psf data sampling ,
to shorten acquisition time for psf data acquisition , the rfov functionality was utilized , as described in .
two additional psf datasets were acquired with an rfov acceleration factor of 2 and 4 .
this reduced the psf data acquisition time from 19:12 minutes to 9:36 minutes ( acceleration factor of 2 ) and 4 : 48 minutes ( acceleration factor of 4 ) , respectively .
the resulting pixel shift maps and distortion corrected images using the psf data with rfov were compared to results calculated from full psf data .  
all epi data were transferred to the offline linux - pc for distortion correction and stored on the acquisition computer for further postprocessing .
this included the calculation of adc maps directly in paravision for the original and corrected datasets .

 figure 3 shows exemplary results for distortion correction on phantoms using se - epi . the upper row shows the conventional se - epi ( a ) in comparison to the distortion corrected se - epi ( b ) .
the computation time for distortion correction was below 1 minute . the nondistorted se image ( c ) and corresponding image mask ( d )
in addition , figure 3(e ) shows the pixel shift map ( psm ) with shifts from black ( 16 pixels ) to white ( 0 pixels ) .
the shim values and b0 settings were adjusted to increase the effect on geometric distortions .  
the correction of in vivo dw - epi mice data is presented in figure 4 . the conventional dw - epi image ( a ) shows strong distortions in the head resulting in an  inflated  brain .
in contrast , the distortion - corrected image ( b ) looks similar to the nondistorted se image ( c ) , which was directly calculated from the psf data and used to generate the image mask .
figure 4(d ) shows the corresponding psm with shift values ranging from 16 ( white , only inside image mask ) to 0 ( black ) .  

figure 5 shows exemplary results of the distortion correction applied on multishot dw - epi in rats .
the conventional dwi - epi ( figure 5(a ) ) shows strong image distortions , which were corrected using the described method ( figure 5(b ) ) .
the resulting adc maps are given in figure 5(c ) calculated from the original dw - epi and in figure 5(d ) calculated from the corrected dw - epi .  
the psms were calculated from full psf data acquisition ( figure 6(a ) ) and with an acceleration factor of 2 ( figure 6(b ) ) and 4 ( figure 6(c ) ) using the rfov functionality .
in addition , the lower row shows the difference between figure 6(a ) and the images with acceleration ( figures 6(b ) and 6(c ) ) .
this paper presents our work on the implementation and application of a psf - based distortion correction for echo - planar imaging as used in functional animal imaging .
the method works reliably and delivers a significant increase in image quality while correcting for geometric image distortions . even readjusting the shim settings
while the psf data acquisition is directly integrated into the epi method , the dico postprocessing is performed offline on an additional linux - computer . further and
more intensive usage of this method may motivate a direct implementation in the paravision reconstruction pipeline . in this case
the correction procedure can be performed on the acquisition computer automatically during the reconstruction process and the corrected and uncorrected datasets can both be stored as independent reconstructions .
the additional postprocessing time would be on the order of seconds . in this case , copying the data to the offline pc , manual start of the correction and transferring the data back to the acquisition computer would not be necessary .
this would also allow the use of the correction method routinely without much effort in order to increase the workflow performance . in this context , we would like to mention our quality experience in using the method on our human 3 t system where the psf distortion correction is applied completely automatic for all routine epi acquisitions .  
it is appropriate to compare the psf mapping technique to the most commonly used distortion correction approach based on field mapping [ 2 , 3 ] .
the field mapping technique is built upon a solid theoretical basis ( 3 ) and is in principle capable of correcting local pixel shifts in both the read - out and phase - encode directions .
however , due to the high bandwidth in the read - out direction and alternating readout polarities , distortions are mainly affecting the phase - encoding direction , where the psf - based methods provide accurate corrections [ 1 , 7 , 12 ] .
although field mapping is a relatively fast and easy to implement technique , the need to balance between field map snr and resolution and the phase unwrapping complexity has prevented it from reaching the robustness required for day - to - day practice .
specifically , at the high field of 9.4 t and in small animals , phase unwrapping may cause significant difficulties .
in addition , field mapping ignores the time - dependent magnetic field variations such as those caused by eddy currents and replaces the true field evolution with a value estimated at the echo time .
since the psf method is based on the original epi readout timing , the inherent eddy currents and concomitant gradients cause identical distortions of the psf data as in epi and , thus , are also mapped faithfully .  
animal movement during data acquisition or between the acquisition of psf data and epi data presents a limitation for the current implementation .
however , this is a common problem of all pre- or postscan - based correction methods where the information of distortions is sampled before or after the functional imaging . in order to overcome this limitation
one may use a proper fixation of the animals or image - based motion correction .   depending on geometric parameters
however , in comparison to the prolonged acquisition times of dti experiments , the additional time on the order of a couple of minutes is not significant and can surely be accepted . in this context , it is also to be noted that shimming may sometimes take several minutes . in fmri , there is often a time gap during which the animal is lead over from isofloran anesthesia to paralysis using meditomedin .
this time gap is on the order of 20 to 40 minutes , and during this gap no fmri acquisition can be performed .
however , this time gap is more than enough for the acquisition of the psf data , even without using the rfov functionality .
if the acquisition time for psf data is still too long , there are several methods to further reduce it .
parallel imaging can be applied also in the psf encoding direction and depending on the coil settings and other rf channels ; an acceleration of 2 and more can be applied .
in addition , this time saving method can be combined with the rfov functionality without any limitations .
while the contrast of the resulting images is not the determining factor for the calculation of the psm , a t1-weighted psf data acquisition is sufficient for the distortion correction of t2w- , dwi- , or fmri - epi as long as bandwidth and geometry settings are not affected .   in this study ,
the acceleration of psf data acquisition using rfov showed no major differences in later distortion corrected epi .
smaller differences were identified , but all were located outside the brain and on parallel lines in the pe direction on both sides of the throat .
we assume that these differences are derived from different psf data due to the breathing or swallowing of the animal .  
in conclusion , our work demonstrated benefits in improving image quality on high - field animal epi for different kinds of functional imaging like fmri and dwi imaging .
the psf data acquisition and correction procedure works reliably and quickly and the additional acquisition time needed is worth the enhancement in geometric accuracy of the reconstructed images .
 the purpose of this work is to demonstrate the functionality and performance of a psf - based geometric distortion correction for high - field functional animal epi . 
 the epi method was extended to measure the psf and a postprocessing chain was implemented in matlab for offline distortion correction . 
 the correction procedure was applied to phantom and in vivo imaging of mice and rats at 9.4 t using different se - epi and dwi - epi protocols . 
 results show the significant improvement in image quality for single- and multishot epi . using a reduced fov in the psf encoding direction 
 clearly reduced the acquisition time for psf data by an acceleration factor of 2 or 4 , without affecting the correction quality . 
1. Introduction
2. Methods
3. Results
4. Discussion