advanced acquisition strategies and image reconstruction have become major research topics in cardiovascular magnetic resonance ( cmr ) . new techniques are commonly validated using numerical phantoms . however , computer simulations are often based on oversimplified and unrealistic models . furthermore , the lack of standardized reference models has resulted in a large diversity in simulation methods hampering appropriate cross - validation . comparability is , however , of particular relevance in cmr , where cardiac and respiratory motions add to simulation complexity . considerable efforts have been invested into the development of non - cartesian and accelerated data acquisition strategies , as they permit reduced scan time , increased spatial and/or temporal resolution or a combination of these benefits  . despite the growth of the research field , it remains difficult to benchmark the various image reconstruction approaches . among others , one reason for this is the lack of comparability between simulation setups . the first analytical phantom to be used widely for imaging simulations was the shepp - logan head phantom . further development led to computationally more complex cerebral phantoms specifically designed for mri , using elliptical shapes  or combinations of different geometrical contours . voxel based phantoms , on the other hand , are usually derived from acquired images of a single volunteer or patient , with a few segmented tissue types only and adapted to the purpose of the study . voxel based phantoms are realistic and easily accessible , but limited to the acquisition parameters they are based on , such as spatial and temporal resolution . furthermore , for voxel based phantoms the image to k - space relation is approximated by the discrete fourier transform , which ignores k - space truncation errors . these effects are omitted with analytical phantoms , where the continuous fourier transform is well - defined . in contrast , analytical phantoms usually do not incorporate motion as required in cmr . a practical approach to numerical phantoms is the integration of advantages of both analytical and voxel - based methods into hybrid phantoms . hybrid phantoms address the key limitations of analytical and voxel - based approaches , leading to a versatile , realistic and reproducible simulation framework . the mathematical cardiac - torso ( mcat ) and the extended cardiac - torso ( xcat ) phantoms present such approaches by combining voxel - based in - vivo data with non - uniform rational b - splines ( nurbs ) or polygon meshes to define anatomical objects  . the anatomical information in xcat is based on the visible human project of the national library of medicine . several numerical phantoms for cmr applications have been proposed so far , including analytical , voxel based   and hybrid models  . these in part allow for reproducible figures of merit based on known simulation parameters such as spatial resolution . despite the attempt to generate versatile and realistic phantoms , none of the above - mentioned studies have made their phantoms available to the community . therefore , reproducibility is limited and reimplementation of the phantom is cumbersome . in this paper , mrxcat is a simulation framework designed for research on cmr sampling and reconstruction strategies in the presence of motion . in order to promote comparability and reproducibility in cmr simulation research , mrxcat cine and myocardial perfusion mrxcat implementations are presented alongside with reconstruction and post - processing examples as showcase applications . the xcat software   allows generation of realistic human anatomical masks including cardiac contraction and respiratory motion . spatial resolution , matrix size , temporal resolution , coverage , geometry and non - rigid object motion are adjustable . for the mrxcat implementation , each tissue mask is assigned mr properties as illustrated in figures  1 and 2 . tissue masks in desired orientation with optional cardiac and respiratory motion are generated using xcat . optional gridding to non - cartesian trajectories and resampling , followed by image reconstruction and post - processing complete the simulation procedure . the tissue and sequence operators depend on tissue properties , sequence parameters and the signal model m. the coil operator and noise object use coil geometry and snr as input . the trajectory governs the effect of the gridding and sampling operators . mathematically , the mrxcat phantom dk?,t in k - t space is expressed as(1)dk?,t=?i=1nsri?g?f?snc , rc , x?c?cmte , tr,?,nr?tt1,t2,?,ct?oix?,t+nix?,t , where oix?,t is the xcat object , which is a function of space and time , and nix?,t denotes object noise . the circle denotes application of the operator on the left hand side of ? onto the object on the right hand side . t is the tissue operator , which depends on relaxation times t1 , t2 , the proton density ? and the contrast agent concentration c(t ) . the sequence operator cm implements the signal model m with various parameters including echo time te , repetition time tr , flip angle ? and number of repetitions nr . coil operator s applies coil sensitivities of nc receive coils with radius rc and location x?c as input . after fourier transform f , the gridding operator g and the sampling operator ri convert the raw k - space phantom into simulated mri data , as detailed below . the full xcat and noise objects are created for each segment i and the sampling operator ri extracts the segment i from the full k - space data . a number of physiological parameters such as heart beat and respiratory cycle duration can be adjusted in xcat . several parameters are defined at the xcat input including spatial and temporal resolution , matrix size , slice offcentres and angulation and the number of simulated heart beats . the timing information allows setting the temporal resolution during the heart phase and the number of segments needed to acquire the full k - space . the blood pool and myocardial tissue of the atria and ventricles in the left and right heart are divided into eight individual partitions . arteries , veins and pericardium form separate compartments . using the tissue and sequence operators t and cm the organ masks ( xcat object oi ) are assigned realistic mr signal intensities based on tissue properties t1 , t2 , proton density ? and contrast agent concentration c(t ) . sequence timing parameters such as repetition time tr , echo time te , number of repetitions nr and the flip angle ? examples of available signal models are balanced ssfp , and saturation - recovery gradient echo sequences , . dynamic contrast enhancement during first - pass myocardial perfusion is simulated based on a population average arterial input function ( aif ) from six healthy volunteers . a contrast dose of 0.025  mmol / kg b.w . and a short saturation delay ( 30  ms ) mid - ventricular signal intensity vs. time curves were extracted from the left ventricle and manually shifted in time to the same bolus arrival time before averaging , which mitigates temporal broadening of the aif peak by averaging . the population average aif was fitted by a 3-parameter gamma - variate function to obtain a first - pass aif of the contrast bolus . the myocardial concentration - time curve is obtained by convolution with a fermi function . the blood pool and myocardial concentrations are then converted to signal intensities using the relationship between t1 and concentration c(t),(2)r1=1t1,0+ct?r , where t1,0 is the baseline tissue t1 in the absence of contrast agent and r the relaxivity of the contrast agent . three - dimensional coil sensitivities are simulated using the biot - savart law,(3)b?r?=?04??coilidl?r??r?'r??r?'3 , by discretising the integral and calculating the effective magnetic field at the voxel positions of the xcat masks . adjustable parameters in this module are the number of receive coils nc , the radius rc and position x?c of the individual coil elements . the coil elements are arranged on one or more circles around the mrxcat phantom to mimic typical cardiac coil arrays around the chest . note that the biot - savart law is only valid in the near field approximation , i.e. for field strengths?<?4  t. since most cmr protocols are designed for 3  t or lower field strength the approximation is considered a valid assumption . a spatial low - pass filter option is implemented at this point with variable filter strength to obtain realistic signal intensities at tissue interfaces . white gaussian noise is added to obtain the desired signal - to - noise ratio ( snr ) . in case of dynamic contrast enhancement , the noise level is defined by the contrast - to - noise ratio ( cnr ) . after this step , the image - domain phantom is transformed into k - space via discrete fourier transform f. the gridding operator g allows interpolation of the data onto non - cartesian trajectories . to apply these trajectories , the non - uniform fast fourier transform ( nufft ) implementation by j. fessler   and the nufft wrapper by m. lustig the sampling operator r defines the sampled k - space profiles and enables application of undersampling schemes by omitting certain k - space lines . if the simulated acquisition consists of multiple k - space segments , the required segment is extracted from the full k - space . the mrxcat phantom production is repeated for each segment to yield the final mrxcat phantom , which is saved as matlab output . other output formats such as the ismrmrd data structure   are possible . to allow comparison of the numerical phantoms with in - vivo cmr , cine and first - pass myocardial perfusion cmr was performed on two philips achieva scanners ( philips healthcare , best , the netherlands ) at 1.5  t and 3  t field strengths . cine in - vivo parameters were : spatial resolution : 1.561.56  mm , 10  mm slice thickness , field - of - view : 400400 mm , tr?=?3.4  ms , te?=?1.7  ms , flip angle?=?50 , 20 heart phases . parameters for in - vivo myocardial perfusion imaging were : spatial resolution : 2.142.255 mm , field - of - view : 36036080 mm , tr?=?1.97  ms , te?=?0.78  ms , flip angle?=?15. perfusion image acquisition was performed using a 10-fold accelerated saturation - recovery gradient echo sequence with a saturation delay of 150  ms followed by k - t pca reconstruction . a gadolinium bolus ( gadovist , bayer healthcare , zurich , switzerland ) with a contrast agent dose of 0.025  mmol / kg b.w . was applied during a breathhold acquisition of 30 time frames . example cine and myocardial perfusion mrxcat phantoms were generated with t1 and t2 values according to textbook literature . relative proton densities were extracted from a proton - density weighted in - vivo measurement . two - dimensional ( 2d ) cine mrxcat parameters were equal to the in - vivo measurement , except for the number of heart phases , which was set to 24 to enable 8-fold undersampling and k - t reconstruction without zero - filling ( cf . parameters for simulated first - pass myocardial perfusion imaging were as in - vivo except for the in - plane resolution , which needed to be isotropic in xcat and was set to 2.142.14  mm . further parameters were : cnr of 30 , 40 profiles from acquisition start to k - space centre , contrast agent dose : 0.075  mmol / kg b.w . , contrast agent relaxivity : r?=?5.6 rest and stress myocardial blood flow were set to 1.0 and 3.5  ml / g / min , respectively . both the 2d cine and the 3d myocardial perfusion fully sampled cartesian phantoms were retrospectively undersampled and reconstructed using k - t pca   and k - t sparse . for both cases , an acceleration factor of r?=?8 was chosen . to visualise local variations in reconstruction accuracy , error maps were calculated by subtracting the reconstructed images from the fully sampled reference phantom reconstruction . all error maps were normalized by the average signal intensity over all time frames of the reference image to yield percentage errors . root mean square error ( rmse ) values were calculated for each case to estimate the total error . quantification of myocardial blood flow ( mbf ) was performed on the myocardial perfusion reconstruction results . using the xcat masks , signal intensity - time curves were extracted from left ventricle and myocardium and converted back to contrast agent concentration using equation ( 2 ) and the signal model . the signal intensity - time curves allow display of temporal filtering effects introduced by image reconstruction from undersampled data . analysis of the mbf from fully sampled versus undersampled data enabled estimation of the additional uncertainty introduced by undersampling compared to measurement noise . the mrxcat extension for xcat was implemented in matlab ( mathworks , natick , ma , usa ) . all computations were run on a laptop pc equipped with an intel i7 m620 2.67  ghz cpu with 2 cores and 8  gb memory . a number of physiological parameters such as heart beat and respiratory cycle duration can be adjusted in xcat . several parameters are defined at the xcat input including spatial and temporal resolution , matrix size , slice offcentres and angulation and the number of simulated heart beats . the timing information allows setting the temporal resolution during the heart phase and the number of segments needed to acquire the full k - space . the blood pool and myocardial tissue of the atria and ventricles in the left and right heart are divided into eight individual partitions . using the tissue and sequence operators t and cm the organ masks ( xcat object oi ) are assigned realistic mr signal intensities based on tissue properties t1 , t2 , proton density ? and contrast agent concentration c(t ) . the concentration is used to simulate dynamic contrast enhancement by shortening t1 . sequence timing parameters such as repetition time tr , echo time te , number of repetitions nr and the flip angle ? examples of available signal models are balanced ssfp , and saturation - recovery gradient echo sequences , . dynamic contrast enhancement during first - pass myocardial perfusion is simulated based on a population average arterial input function ( aif ) from six healthy volunteers . a contrast dose of 0.025  mmol / kg b.w . and a short saturation delay ( 30  ms ) mid - ventricular signal intensity vs. time curves were extracted from the left ventricle and manually shifted in time to the same bolus arrival time before averaging , which mitigates temporal broadening of the aif peak by averaging . the population average aif was fitted by a 3-parameter gamma - variate function to obtain a first - pass aif of the contrast bolus . the blood pool and myocardial concentrations are then converted to signal intensities using the relationship between t1 and concentration c(t),(2)r1=1t1,0+ct?r , where t1,0 is the baseline tissue t1 in the absence of contrast agent and r the relaxivity of the contrast agent . three - dimensional coil sensitivities are simulated using the biot - savart law,(3)b?r?=?04??coilidl?r??r?'r??r?'3 , by discretising the integral and calculating the effective magnetic field at the voxel positions of the xcat masks . adjustable parameters in this module are the number of receive coils nc , the radius rc and position x?c of the individual coil elements . the coil elements are arranged on one or more circles around the mrxcat phantom to mimic typical cardiac coil arrays around the chest . note that the biot - savart law is only valid in the near field approximation , i.e. for field strengths?<?4  t. since most cmr protocols are designed for 3  t or lower field strength the approximation is considered a valid assumption . a spatial low - pass filter option is implemented at this point with variable filter strength to obtain realistic signal intensities at tissue interfaces . white gaussian noise is added to obtain the desired signal - to - noise ratio ( snr ) . in case of dynamic contrast enhancement , the noise level is defined by the contrast - to - noise ratio ( cnr ) . after this step the image - domain phantom is transformed into k - space via discrete fourier transform f. the gridding operator g allows interpolation of the data onto non - cartesian trajectories . to apply these trajectories , the non - uniform fast fourier transform ( nufft ) implementation by j. fessler   and the nufft wrapper by m. lustig the sampling operator r defines the sampled k - space profiles and enables application of undersampling schemes by omitting certain k - space lines . if the simulated acquisition consists of multiple k - space segments , the required segment is extracted from the full k - space . the mrxcat phantom production is repeated for each segment to yield the final mrxcat phantom , which is saved as matlab output . to allow comparison of the numerical phantoms with in - vivo cmr , cine and first - pass myocardial perfusion in - vivo data were acquired in two healthy volunteers . cmr was performed on two philips achieva scanners ( philips healthcare , best , the netherlands ) at 1.5  t and 3  t field strengths . cine in - vivo parameters were : spatial resolution : 1.561.56  mm , 10  mm slice thickness , field - of - view : 400400 mm , tr?=?3.4  ms , te?=?1.7  ms , flip angle?=?50 , 20 heart phases . parameters for in - vivo myocardial perfusion imaging were : spatial resolution : 2.142.255 mm , field - of - view : 36036080 mm , tr?=?1.97  ms , te?=?0.78  ms , flip angle?=?15. perfusion image acquisition was performed using a 10-fold accelerated saturation - recovery gradient echo sequence with a saturation delay of 150  ms followed by k - t pca reconstruction . a gadolinium bolus ( gadovist , bayer healthcare , zurich , switzerland ) with a contrast agent dose of 0.025  mmol / kg b.w . example cine and myocardial perfusion mrxcat phantoms were generated with t1 and t2 values according to textbook literature . relative proton densities were extracted from a proton - density weighted in - vivo measurement . two - dimensional ( 2d ) cine mrxcat parameters were equal to the in - vivo measurement , except for the number of heart phases , which was set to 24 to enable 8-fold undersampling and k - t reconstruction without zero - filling ( cf . parameters for simulated first - pass myocardial perfusion imaging were as in - vivo except for the in - plane resolution , which needed to be isotropic in xcat and was set to 2.142.14  mm . further parameters were : cnr of 30 , 40 profiles from acquisition start to k - space centre , contrast agent dose : 0.075  mmol / kg b.w . , contrast agent relaxivity : r?=?5.6 rest and stress myocardial blood flow were set to 1.0 and 3.5  ml / g / min , respectively . both the 2d cine and the 3d myocardial perfusion fully sampled cartesian phantoms were retrospectively undersampled and reconstructed using k - t pca   and k - t sparse . for both cases , an acceleration factor of r?=?8 was chosen . to visualise local variations in reconstruction accuracy , error maps were calculated by subtracting the reconstructed images from the fully sampled reference phantom reconstruction . all error maps were normalized by the average signal intensity over all time frames of the reference image to yield percentage errors . root mean square error ( rmse ) values were calculated for each case to estimate the total error . quantification of myocardial blood flow ( mbf ) was performed on the myocardial perfusion reconstruction results . using the xcat masks , signal intensity - time curves were extracted from left ventricle and myocardium and converted back to contrast agent concentration using equation ( 2 ) and the signal model . the signal intensity - time curves allow display of temporal filtering effects introduced by image reconstruction from undersampled data . analysis of the mbf from fully sampled versus undersampled data enabled estimation of the additional uncertainty introduced by undersampling compared to measurement noise . the mrxcat extension for xcat was implemented in matlab ( mathworks , natick , ma , usa ) . all computations were run on a laptop pc equipped with an intel i7 m620 2.67  ghz cpu with 2 cores and 8  gb memory . temporal profile plots of breathhold mrxcat cine , free - breathing mrxcat cine and in - vivo breathhold cine data are demonstrated ( figure  3c ) . individual coil maps of a simulated 8-element cardiac coil array are displayed in figure  3f . full field - of - view at systole and expiration ( a ) and at diastole and inspiration breathhold ( b ) . ( c ) profiles along dashed line in ( b ) for 24 heart phases for breathhold and free - breathing mrxcat with 15 segments and the breathhold in - vivo case for comparison . ( d - e ) cardiac region - of - interest at different cardiac phases for breathhold mrxcat ( d ) and in - vivo scan ( e ) . ( f ) single coil images from 8 individual coils . in figure  4 the whole - heart myocardial perfusion mrxcat phantom is displayed . apical , mid - ventricular and basal slices at the time points of bolus arrival in the right and left ventricle as well as in the myocardium are shown in figure  4a . in - plane profiles as a function of time extracted from the breathhold , free - breathing phantom and in - vivo acquisition are demonstrated in figure  4b . a cardiac region - of - interest ( roi ) in addition , the effect of timing of the saturation pulse with respect to the image acquisition is shown for a long saturation to acquisition delay of 150 ms relative to a short saturation delay of 10 ms to demonstrate the non - linearity between mr signal and contrast agent concentration . ( a ) three slices from apex to base at maximum contrast agent enhancement in the right ventricle , left ventricle and myocardium . ( b ) anterior - posterior profiles along dashed line in ( a ) for all heart beats for breathhold mrxcat , free - breathing mrxcat and in - vivo breathhold myocardial perfusion images ( left - right ) . ( c ) 16 slices of the mrxcat perfusion phantom , covering the whole left ventricle at a time frame during contrast enhancement . ( d - e ) signal intensity curves extracted from the left ventricle ( aif ) and the myocardium of stress and rest mrxcat perfusion phantoms generated with saturation delays of 150 ms ( d ) and 10 ms ( e ) . figure  5 shows the results of image reconstruction of the breathhold 2d cine mrxcat phantom with 8-fold data undersampling . a cardiac roi and a profile through the slice as a function of heart phase are shown . absolute error maps reveal that both k - t pca and k - t sparse yield reconstructed images of good quality . reconstruction errors are found at the borders of the myocardium , where cardiac contraction causes most motion . the rmse in the cardiac roi was 10.0% and 10.2% for k - t pca and k - t sparse , respectively . diastolic and systolic heart phases and profile along the dashed line in ( a ) for all heart phases . reference images ( a ) , reconstruction results and difference maps using 8x k - t pca ( b ) and 8x k - t sparse ( c ) . figure  6 illustrates reconstruction results for the 8x undersampled myocardial perfusion phantom at time points of bolus enhancement in the left ventricle and myocardium . error maps show pronounced edge effects for k - t sparse , whereas the error distribution in k - t pca is more homogeneous . the rmse was 16.1% and 14.4% for k - t pca and k - t sparse , respectively . fermi model based mbf quantification in eight mid - ventricular slices of the simulated stress perfusion image is shown for reference , k - t pca and k - t sparse reconstructions in six angular sectors per slice . mean and standard deviation of mbf were 3.48??0.13  ml / g / min in the reference image , 3.48??0.36  ml / g / min for 8 k - t pca and 3.55??0.33  ml / g / min for 8x k - t sparse . fully sampled reference ( a ) , 8x k - t pca ( b ) and 8x k - t sparse ( c ) reconstruction results and error maps . a mid - ventricular slice at peak left - ventricular ( lv ) and myocardial enhancement and profile along the dashed red line for 32 time frames are shown . ( d - f ) signal intensity - time curves for reference and reconstructed data from 4 voxels ( inset ) . ( g - i ) fermi mbf quantification of stress perfusion simulation in 8 slices with 6 angular sectors per slice ( inset ) . total computation times for mrxcat generation were 38 and 124 minutes for the breathhold and free - breathing cine phantom , respectively . for the perfusion phantom , calculations took 13.6 and 10.7  minutes for breathhold and free - breathing simulations . in all cases the large difference between cine and perfusion computation times mainly stems from the fact that 360 xcat time frames were created for cine ( 24 heart phases , 15 segments ) , while only 32 time frames were needed for perfusion . by executing only the matlab part of mrxcat , calculation times spanned from 54 s ( breathhold cine ) to 166 s ( free - breathing perfusion ) in this work a cmr extension to the xcat phantom has been proposed to enable realistic simulation to aid and benchmark image reconstruction and quantitative post - processing approaches . the mrxcat framework is composed of several sequential software modules , which enable user interaction via parameters at each stage of the simulation . the xcat hybrid phantom , which is used to simulate anatomy and motion , delivers realistic and generalized tissue masks . although the xcat object is rasterised , the drawbacks of voxel based phantoms can be addressed by increasing the spatial resolution in xcat . thus , the 0.330.331 mm voxel size of the visible human segmentation   is sufficient for most cmr applications . all subsequent software parts act on that rasterised xcat object , which simplifies implementation and data handling in array - based numerical software . the individual operators or software modules allow setting parameters specific for tissue and sequence , receiver coils , measurement noise and k - space characteristics . the independency between modules potentially enables parallel computing and division of large data portions into chunks on computers with less available memory . the use of mrxcat phantoms for research on accelerated imaging was exemplified using k - t pca and k - t sparse . the effect of cardiac contraction in conjunction with image acceleration was showcased with the cine phantom , where the biggest residual errors after reconstruction remain at the inner and outer border of the myocardium . using the myocardial perfusion showcase , the effect of signal changes due to contrast agent administration was demonstrated . in this example , residual reconstruction errors mainly stem from temporal filtering of the signal - time curves . moreover , mrxcat phantoms can be used for the development of post - processing methods such as myocardial blood flow quantification . a key advantage of quantification using mrxcat is that noiseless ground truth is always at hand and available for assessment of errors this issue was accounted for by adding a low - pass filter module before noise addition . a similar problem is the missing organ texture in xcat , which has recently been addressed . however , mrxcat assumes instantaneous acquisition of the individual segments . extending the framework to enable individual timing of single k - space lines would require full xcat masks for each k - space line . since the xcat part of mrxcat is the computationally most time - consuming step , this would yield unacceptably long simulation times . as such , it is suitable for the simulation of sampling strategies , trajectory optimization and post - processing methods . however , a number of error sources are excluded , such as magnetic field inhomogeneity , magnetization evolution across time frames or signal alteration due to motion during sampling . for those applications , other simulation frameworks based on solving bloch equations may be more suitable . extending the framework to enable individual timing of single k - space lines would require full xcat masks for each k - space line . since the xcat part of mrxcat is the computationally most time - consuming step , this would yield unacceptably long simulation times . , it is suitable for the simulation of sampling strategies , trajectory optimization and post - processing methods . however , a number of error sources are excluded , such as magnetic field inhomogeneity , magnetization evolution across time frames or signal alteration due to motion during sampling . for those applications , other simulation frameworks based on solving bloch equations may be more suitable . extensions to other cmr modalities , such as diffusion or flow encoded mri , are possible . aif : arterial input function cmr : cardiovascular magnetic resonance cnr : contrast - to - noise ratio mbf : myocardial blood flow mcat : mathematical cardiac - torso mrxcat : magnetic resonance extended cardiac - torso nufft : non - uniform fast fourier transform nurbs : non - uniform rational b - splines rmse : root mean square error roi : region - of - interest snr : signal - to - noise ratio xcat : extended cardiac - torso lw , cs , sk devised mrxcat in matlab , created phantom examples , performed image reconstruction and post - processing .
backgroundcomputer simulations are important for validating novel image acquisition and reconstruction strategies . in cardiovascular magnetic resonance ( cmr ) , 
 numerical simulations need to combine anatomical information and the effects of cardiac and/or respiratory motion . to this end 
 , a framework for realistic cmr simulations is proposed and its use for image reconstruction from undersampled data is demonstrated.methodsthe extended cardiac - torso ( xcat ) anatomical phantom framework with various motion options was used as a basis for the numerical phantoms . 
 different tissue , dynamic contrast and signal models , multiple receiver coils and noise are simulated . arbitrary trajectories and undersampled acquisition can be selected . 
 the utility of the framework is demonstrated for accelerated cine and first - pass myocardial perfusion imaging using k - t pca and k - t sparse.resultsmrxcat phantoms allow for realistic simulation of cmr including optional cardiac and respiratory motion . 
 example reconstructions from simulated undersampled k - t parallel imaging demonstrate the feasibility of simulated acquisition and reconstruction using the presented framework . 
 myocardial blood flow assessment from simulated myocardial perfusion images highlights the suitability of mrxcat for quantitative post - processing simulation.conclusionthe proposed mrxcat phantom framework enables versatile and realistic simulations of cmr including breathhold and free - breathing acquisitions .