a method for evaluating or quantifying resolution of a volumetric imaging system such as for example , a multislice ct ( msct ) scanner is disclosed . during the method , volumetric image data of an image phantom is acquired and processed to determine the modulation transfer function ( mts ) of the volumetric imaging system as well as the directional dependence of the mts . the image phantom provides for the simultaneous measurement of volumetric imaging system resolution in virtually all directions as well as the independent measure of resolution in any direction , without the need for repositioning or alignment of the image phantom . during display of reconstructed volumetric images , a graphical object or icon is also displayed identifying the resolution of the volumetric imaging system in the direction of the volumetric image being viewed . further specifics will now be described with reference to fig1 to 3 . fig1 a and 1 b show an msct scanner generally identified by reference numeral 50 . as is well known to those of skill in the art , msct scanner 50 comprises a gantry 52 accommodating an x - ray source 54 and collimator 56 . rows of detectors 58 are also accommodated by the gantry 52 diametrically opposite the x - ray source 54 and collimator 56 . in this embodiment , the gantry 52 accommodates at least thirty - two ( 32 ) rows of detectors 58 . an image reconstruction computer 60 communicates with the detectors 58 and reconstructs volumetric images from the volumetric image data output by the detectors 58 . a monitor 62 communicates with the image reconstruction computer 60 and displays the generated volumetric images . the gantry 52 has a central opening 64 into which a patient supporting table 66 extends . the gantry 52 is rotatable about the table 66 and tiltable with respect to the table 66 to allow a full compliment of images of a patient or object supported on the table 66 to be acquired . in order to evaluate the resolution of the msct scanner 50 , the msct scanner 50 is conditioned to scan an image phantom using the selected scanning protocol . during scanning , the x - ray source 54 outputs an x - ray beam 70 that is fanned by collimator 56 . the fanned x - ray beam 70 , after passing through the image phantom , impinges on the multiple rows of detectors 58 . in response , the detectors 58 output volumetric image data ( voxels ) that are received by the image reconstruction computer 60 . at the same time , the gantry 52 is rotated about the table 66 and the table 66 is translated relative to the opening 64 in the gantry 52 so that the image phantom is fully scanned . the gantry 52 in this case is rotated about the table 66 at a rate less than or equal to one ( 1 ) rotation per second . the image reconstruction computer 60 in turn processes the volume image data received from the detectors 58 thereby to reconstruct volumetric images of the image phantom that are displayed on monitor 62 . as mentioned above , the configuration of the image phantom is such so as to allow the resolution of the msct scanner 50 to be evaluated . turning now to fig2 a and 2 b , the image phantom is shown and is generally identified by reference numeral 100 . as can be seen , image phantom 100 comprises a sphere 102 generally centrally positioned within a cylinder or puck 104 . the sphere 102 and cylinder 104 are formed of generally uniform materials having low atomic numbers to help produce volumetric image data sets that are free from x - ray beam hardening artifacts . in this embodiment , sphere 102 is formed of teflon ® which has an effective atomic number equal to 8 . 47 and a mean value of 900 houndsfield units ( hu ). as will be appreciated the effective atomic number of teflon ® is very close to that of soft tissue . the increased hu mean value of the sphere 102 as compared to soft tissue is primarily due to its density . the cylinder 104 is formed of curable liquid silicone having a mean value equal to 190 hu . the attenuation coefficient of the sphere 102 is at least three times greater than the attenuation coefficient of the cylinder 104 . the sphere contrasts the cylinder sufficiently to allow the sphere to be differential from the cylinder in acquired volumetric images . the diameter of the sphere 102 is selected to be at least three times greater than the voxel spacing of the volumetric images of the image phantom 100 . in this embodiment , the sphere 102 has a diameter equal to 0 . 5 inches . the cylinder 104 has a diameter equal to 4 inches and a height equal to 4 inches . as will be appreciated , the shape of the sphere 102 has a curvature that emulates biological structures making it particularly suited to msct scanner resolution evaluation . also , the symmetry of the sphere 102 permits measurement of blur in virtually any direction without requiring special alignment as will be described . during formation of the image phantom 100 , the image phantom 100 is molded in a two - part procedure under low pressure to position centrally and immerse the sphere 102 within the cylinder 104 and to ensure the cylinder 104 is free of entrapped air bubbles . in order to evaluate the resolution of the msct scanner 50 , the reconstructed volumetric image data is processed to generate a surface spread function ( ssf ) representing the edge response function for the msct scanner 50 that is used to quantify the resolution of the msct scanner in all directions . the ssf is a graphical plot which maps the intensity value of each voxel as a function of the voxel &# 39 ; s distance from the centroid of the sphere 102 . the ssf is then differentiated to produce a plane spread function ( pisf ). the results are then interpreted using full width at half maximum ( fwhm ), and fourier transforming to generate a modulation transfer function ( mtf ). the fwhm represents the apparent width ( blur ) in the image space of an infinitely thin sheet while the mtf quantifies how spatial frequencies are modulated as they pass through the msct scanner 50 . turning now to fig3 , the processing of reconstructed volumetric image data in order to evaluate the resolution of the msct scanner 50 will be further described . initially , the volumetric image data of the image phantom 100 is thresholded into voxels interior to and exterior to the sphere 102 , by comparing the gray - level values of the voxels with a threshold value that is intermediate the mean interior and exterior gray - level values of the sphere ( step 200 ). voxels within the sphere 102 are set to an intensity of one , while voxels outside of the sphere 102 are set to an intensity of zero . following the thresholding procedure , the voxels within the sphere 102 are processed to calculate the centre of mass of the sphere 102 thereby to determine the centroid of the sphere 102 ( step 202 ). the thresholded volumetric image data is also used to calculate the radius of the sphere 102 by determining the extent of the voxels that are set to unity intensity ( step 204 ). the original unthresholded volumetric image data is then used for the remainder of the analysis . all voxels a distance greater than eight voxel dimensions from the centroid of the sphere 102 and less than three sphere radii from the sphere centroid are used to assemble the surface spread function ( ssf ) ( step 206 ). the distance of each of these voxels from the sphere centroid is calculated and the distances are placed into the bins of a histogram one tenth the size of the in - plane resolution . the gray - level values of the voxels are accumulated into one set of bins , and the numbers of voxels at given distances are accumulated into another set of bins . following this procedure , the accumulated gray - level values are divided by the numbers of voxels in the bins to yield an averaged ssf curve ( step 208 ). a bspline algorithm using cubic basis functions is used to smooth the averaged ssf curve ( step 210 ). control points are placed at four times the spacing in the averaged ssf curve ( still two and a half times the original in - plane image resolution ). the smoothed ssf curve is evaluated from the bspline coefficients at the original coordinates , preserving the spacing at one tenth the original in - plane resolution . the binned , smoothed ssf curve is digitally differentiated by evaluating the difference between successive ssf values thereby to yield a resulting pisf curve ( step 212 ). the full width at half maximum ( fwhm ) is then determined from the pisf curve ( step 214 ). the pisf curve is fourier transformed using an algorithm adapted from the realfi routine from numerical recipes ( step 216 ). this algorithm replaces a real - valued function with the positive - frequency half of its complex fourier transform . for this algorithm , the data must be radix 2 , so the pisf curve data is zero padded to increase the array size to the nearest power of two prior to fourier transforming . the magnitude of the resulting complex array is calculated , and normalized to unity at zero spatial frequency thereby to yield the mtf ( step 218 ). the 10 % mtf represents the limiting spatial resolution of the msct scanner 50 . the directional dependence of the mtf is then evaluated by approximating the mtf along the positive and negative directions of each coordinate axis , in other words , by evaluating six independent mtf curves ( step 220 ). in particular , axial and trans - axial resolution of the msct scanner is evaluated . during axial resolution evaluation , a ray is drawn from the sphere centroid subtending 30 degrees to the positive axial direction ( superior ) rotated to produce a cone . similarly , a second cone is drawn subtending 30 degrees to the negative axial direction ( inferior ). the voxels within these two cones are used to assemble the ssf curves in the positive and negative axial directions , respectively . fig4 shows the cones from which the voxels are recruited to assemble the ssf curves . the procedure for assembling the ssf curves is the same as that described above , with the exception that the contribution from each voxel is weighted by the squared ratio of its axial coordinate to its distance from the sphere centroid , thereby assigning increased weight to voxels located closer to the axial axis . for trans - axial resolution evaluation , a ray is drawn from the centroid subtending 60 degrees to the positive axial direction rotated to produce a cone . however , in this case the anti - cone outside this cone and above the transverse plane is used . the union of the anti - cone and the similar anti - cone below the transverse plane is further subdivided into four quadrants defined by the planes x = y and y =− x . the voxels within these four quadrants are used to assemble the ssf curves in the positive and negative x ( right - left ) and y ( anterior - posterior ) directions . the anti - cone from which voxels are recruited to assemble the ssf curves is shown as the shaded volume in the left side of fig5 . the x = y and y =− x planes that bisect the anti - cone are shown in the right side of fig5 . once again , the contribution from each voxel is weighted by the squared ratio of its coordinate along the relevant axis to its distance from the sphere centroid , thereby assigning greater weight to voxels located closer to the axis in question . following the assembly of the six independent ssf curves , the procedure of smoothing the ssf curves with bsplines , differentiating the smoothed ssf curves to obtain the pisf curves , and fourier transforming to obtain the mtf curves , is the same as that described above . the axial and trans - axial resolutions evaluated for the msct scanner are recorded . during subsequent imaging of patients using the msct scanner , the recorded resolutions are used to update a graphical icon presented on the monitor 62 with the displayed volumetric image so that the resolution of the msct scanner in the particular direction being viewed is also displayed . in this manner , variations in image quality resulting from changes in msct scanner resolution can be visually determined inhibiting such variations from being wrongly interpreted as image artifacts . imaging of the image phantom 100 may be repeated by varying the position of the image phantom radially , and axially , to evaluate the resolution of the volumetric imaging system throughout the scan field . for example , the image phantom may be placed at the middle of the scan field , 20 % of the radius , 50 % and 80 % of the radius to evaluate the spatial resolution as a function of radial position within the scan field . in addition , the resolution loss due to table motion in helical scans may be quantified by scanning the image phantom using a helical scanning protocol . turning now to fig9 and 10 , alternative embodiments of an image phantom are shown . in these embodiments , the spheres are suspended in one dimension within cylindrical contours by support structures . the spheres in these cases may be surrounded by air or the volume encompassed by the containers may be evacuated to create a vacuum therein . volumetric scans of the image phantom 100 were acquired with two commercially available clinical volumetric ct scanners , namely a general electric healthcare lightspeed vct ( ge vct ) and the siemens medical systems somatom sensation 64 - slice ( sms 64 ). scanning parameters were matched as closely as possible for the two ct scanners , and reflect typical protocols used in 30 clinical practice at hfhs . the spiral scanning protocol used to acquire the volumetric scans is shown in table 1 below . during scanning , the image phantom 100 was positioned such that sphere 102 was located approximately at iso - centre . volumetric scans were acquired using the spiral scanning protocol of table 1 with a table speed of 20 mm / sec and a pitch of 1 . 0 for three ( 3 ) sphere diameters , namely 0 . 5 inches , 1 inch and 1 . 5 inches in order to investigate the influence of sphere diameter on measured resolution . a larger sphere diameter is desirable due to increased over - sampling but should be constrained to a size that does not cause significant x - ray beam hardening which would distort the measurement of spatial resolution five ( 5 ) additional scans of the image phantom 100 having a 1 inch sphere diameter were acquired with the ge vct to determine the precision of the measurement technique . to study azimuthal blur , the image phantom 100 was positioned at the periphery of the scan field of view with the sphere 102 located at approximately 180 mm from iso - centre in the right - left direction . volumetric image data was acquired with gantry speeds of 1 . 0 and 0 . 4 seconds per rotation . the diameter of the spheres 102 was measured at 8 points , along 6 lines of longitude , to assess sphericity . the variation in diameter was found to be less than 25 gm , for a given sphere . visual inspection of the clear silicone cylinders 104 did not show any inclusions of air . reconstructed images of the image phantom were copied from the ct scanner console in the slice based dicom file format and converted into a single volume data file . voxel values from the single volume data set were used to assemble the ssf in order to compute the fwhm and 10 % mtf for the scanning modes which were investigated . fig6 shows an image slice through a reconstructed volumetric image of the image phantom together with a profile line plot taken through the image slice . fig7 shows the resulting ssf curve derived from the profile line plot of fig6 . fig8 shows the resulting pisf curve from which the fwhm is measured together with the derived mtf identifying the limiting spatial frequency of the ct scanner . precision measurements were made for the ge vct only . the variability of measurement of fwhm and 10 % mtf was higher for axial ( superior - inferior ) measurements than trans - axial ( left - right , anterior - posterior ) measurements . this is likely due to the fact that fewer points are used to assemble the axial ssf curves and therefore there is less noise averaging in the binning procedure as compared to the formation of the trans - axial ssf curves . the respective mean values and standard deviations for the ge vct are shown in table 2 below . the variation in measurement of resolution as a function of sphere size is shown in table 3 below for sphere diameters of 0 . 5 inch , 1 inch and 1 . 5 inches , for both the ge vct and sms 64 . the variation in measurements of resolution as a function of sphere size is shown in the table 4 below for sphere diameters of 0 . 5 inch , 1 inch and 1 . 5 inches , for the ge vct . table 5 below compares the fwhm and the 10 % mtf spatial frequency for protocols with no table motion during scanning ( axial ) and a table speed of 20 mm / sec ( spiral ). those of skill in the art will appreciate that the described resolution evaluation method may be applied to other volumetric imaging modalities such as for example magnetic resonance imaging , ultrasound , optical , spect and pet imaging . although a preferred embodiment has been described with reference to the accompanying drawings , those of skill in the art will appreciate that variations and modifications may be made without departing from the spirit and scope thereof as defined by the appended claims .
a method for evaluating the spatial resolution of a volumetric medical imaging system comprises imaging an image phantom including a sphere surrounded by a uniform medium . the image phantom is imaged and the resulting volumetric data set is used to generate an edge response function in three dimensions . differentiating the edge response function produces a plane spread function . the method simultaneously measures the spatial resolution in all directions , providing a bulk measurement resolution . alternatively , the edge response function may be assembled in a manner so as to independently measure the axial and trans - axial resolution of the volumetric imaging system .