as discussed in detail above , quantitative mismatches can arise from the incorrect conversion of radiodensity measurements - for example , ct numbers obtained in conventional ct scanning - to linear attenuation coefficients at 511 kev . the presence of contrast agent ( s ) in the patient during the ct scan can cause significant errors in the 511 kev attenuation map when using the bilinear or hybrid conversion methods . in cancer imaging , for example , iodinated intravenous contrast agents are necessary for detection of lesions in solid organs and to better identify lymph nodes . as another example , oral contrast agent is typically administered to differentiate normal from abnormal bowel and to differentiate bowel from mesenteric masses . concurrent intravenous and oral contrast enhancement is therefore critical for cancer staging with ct scanning and often is necessary for correlation with fdg ( fluorodeoxyglucose ) pet staging studies . intravenous contrast agents generally have iodine concentrations of 300 to 380 mg / ml . oral contrast agents are usually based on barium . contrast agents have a high atomic number ( 53 for iodine and 56 for barium ) and radiodensity , which results in a high mass attenuation coefficient at x - ray photon energies because of photoelectric absorption . in the absence of intravenous contrast , vascularized tissues have ct numbers , or radiodensity , in the range of 30 to 60 hu . immediately after a bolus injection of iodinated contrast media , the ct numbers can reach up to 200 to 300 hu for the aorta or the renal cortex . however , at 511 kev , the mass attenuation coefficient of iodine and barium is essentially the same as water or tissue . the values of contrast - enhanced ct numbers range from 0 to 300 hu , although the true linear attenuation coefficient at 511 kev for iodine varies little . thus any scale factor that correctly predicts the attenuation coefficient at 511 kev for bone or soft tissue will overestimate the attenuation at 511 kev for contrast agent and vice - versa . focal accumulation of contrast agent — for example , in an artery during a bolus injection — can result in artifactual hot spots in the pet emission image in the same location . an accumulation of contrast agent , however , does not significantly affect pet emission images that are not attenuation corrected . even at lower concentrations , with the overlap in ct numbers for contrast - enhanced and non - enhanced tissues , it is difficult to decide on the true attenuation coefficient based solely on the ct number . as a first approach to ct - based attenuation correction (“ ctac ”) in pet imaging the scaling method discussed above and illustrated in fig2 , was developed . an improved scaling method is disclosed herein that provides a robust method that is particularly suitable when contrast agent is present in the scanned region . the method enables the clinician to distinguish bone from contrast agent , even when the ct numbers for the bone and contrast agent overlap in a particular ct scan . refer now to fig3 , illustrating a block diagram providing an overview of a method 100 for calculating attenuation factors . in this embodiment , a ct scan of a region of a patient or object is taken at a relatively low energy level or voltage potential — for example , 80 kvp — to generate a first ct data set 110 . it will be appreciated by the artisan that in an x - ray generator the high - voltage potential between the cathode and the anode affects the speed at which electrons travel and strike the anode . the higher the kilovoltage potential ( kvp ), the more speed and , therefore , energy the electrons have when they strike the anode . electrons striking with more energy results in x - ray with more penetrating power . the high - voltage potential is measured in kilovolts , and this is typically controlled with a voltage or kilovoltage control on a control console . an increase in the kilovoltage will also result in an increase in the peak energy of the radiation , which is distributed over a continuous spectrum or range . typically , the ct image data set comprises a three - dimensional set of ct numbers corresponding to each voxel in the data set . a second ct scan of the region is taken at a different kvp setting to generate a second three - dimensional ct data set 120 . corresponding points in the first and second ct data sets 110 , 120 are differenced to generate a ct difference data set 130 . the ct difference data set 130 , relative to the values in the first ( or second ) ct image ( e . g ., fig6 ), is used to identify portions of the first or second ct data sets corresponding to locations in the scanned region that are primarily bone and to similarly identify portions of the ct data sets corresponding to locations in the scanned region that are primarily contrast agent 140 . different scaling conversions may then be used to convert the ct numbers in the first ct data set and / or second ct data set from hu to attenuation coefficients at 511 kev . in one embodiment of the present invention , the difference data set is also used to identify locations in the scanned region corresponding to water / air / soft tissue , such regions having a difference value that is usually substantially equal to or near zero . alternatively , water / air / soft tissue may be identified from one of the ct data sets ( preferably the higher kvp data set ) as regions wherein the ct number is less than or equal to zero ( or another appropriate threshold value , as discussed above ). having identified for each relevant voxel in the difference data set the primary composition of the corresponding location in the scanned region , each corresponding voxel in either ( or both ) of the two ct data sets can now be converted from the ct number to an appropriate linear attenuation coefficient at 511 kev , using known or readily obtainable conversions . that is , the value in each voxel in the selected ct data set is converted to an attenuation coefficient based on the scanned ct number , and the determined composition . for example , fig4 a - 4c show three illustrative curves for converting ct numbers to linear attenuation coefficients at 511 kev . fig4 a shows a curve for converting ct numbers obtained for soft tissue , water , and air ; fig4 b shows a curve for converting ct numbers obtained for contrast agent ; and fig4 c shows a curve for converting values obtained for bone . this method extends the scaling method described in the background section above to distinguish voxels having values for locations that are dominated by contrast agent from voxels having values for locations dominated primarily by bone . the calculated attenuation coefficients are then used to interpret the pet data for the region in a conventional manner as is well known in the art . this scaling method utilizes two different - energy ct data sets and takes advantage of the large differences in the photoelectric cross sections of the contrast agent as compared with calcium or bone , to determine how to scale each voxel in the ctac image . fig5 is a sketch of a cross section of a 20 cm diameter test phantom 150 that was used as a test model to acquire ct number measurements at 80 , 100 , 120 , and 140 kvp . the test phantom 150 is a tube containing water 152 , a 5 cm - diameter cylinder containing air 154 , a 5 cm - diameter cylinder containing dilute iodine - based contrast agent 156 , and a 5 cm - diameter cylinder containing cacl 2 in solution 158 ( simulating bone equivalent atomic number ). the resulting ct numbers ( from a conventional clinical reconstruction ) were evaluated at each tube voltage . for example , when the ct numbers corresponding to the air and water were differenced between the values obtained from a scan at 80 kvp and a scan obtained at 140 kvp , there was essentially no variation in ct number for air 154 or water 152 with tube voltage . as noted above , this aspect permits identification of the air / water / soft tissue solely from the difference between two data sets . for the cacl 2 solution 158 simulating bone , however , the ct numbers increased by about 278 hu as the tube voltage was dropped from 140 to 80 kvp . the contrast agent 156 ct numbers increased by about 700 hu as the tube voltage was dropped from 140 to 80 kvp . therefore , when the ct number data set obtained from the 140 kvp scan is differenced from the ct number data set obtained from the 80 kvp scan , the resulting difference data set was essentially zero for the air 154 and water 152 , but contained significantly different values for the cacl 2 158 and contrast agent 156 . in particular , the difference data set values for contrast agent differed from the difference data set values for cacl 2 by more than 400 hu . based on these results , a classification scheme for difference data sets was derived using a midpoint of the relative change in ct numbers . the difference data set values were plotted against the ct numbers from one of the ct scans , and were found to increase approximately linearly with the ct numbers , wherein the ct number values account for variable concentrations of contrast agent and variable bone density , as indicated in fig6 . fig6 shows the measured ct numbers plotted against the corresponding ct difference values , e . g ., the ct number measured for the 80 kvp scan minus the ct number measured for the 120 kvp scan . the corresponding curve for the contrast agent 166 is generally steeper than the curve for the bone equivalent ( cacl 2 ) 168 . the currently preferred classification scheme uses the midpoint between these curves 166 and 168 shown as a dashed line 169 in fig6 as a threshold , so that voxels having a difference above the dashed line 169 are classified and scaled as contrast agents ( e . g ., from fig4 b ), whereas voxels having a difference below the dashed line 169 are classified and scaled as bone ( e . g ., from fig4 c ). for example , in fig6 , the threshold dashed line 169 may be characterized by the equation diff = 0 . 53 * ctn , where diff is the difference between the ct numbers at 120 kvp from the corresponding ct numbers at 80 kvp , and ctn is the ct number at 120 kvp . to identify voxels corresponding to contrast agent , therefore , if diff is greater than ( 0 . 53 * ctn ) for a voxel , then it corresponds to contrast agent and an appropriate conversion of the corresponding ct number to an attenuation coefficient at 511 kev can be made . if diff is less than ( 0 . 53 * ctn ) and the voxel does not correspond to soft tissue ( e . g ., near zero value ), then it corresponds to bone and an appropriate conversion of the ct number to attenuation coefficient can be made . it will be appreciated that zero - value voxels in the difference data set correspond to air and water . therefore , in a variation on the present method , the classification voxels corresponding to air and water may be based on a minimum value for the difference data , rather than relying on the raw data in one or both of the ct data sets . this hybrid / bilinear scaling method was tested with measured ct and pet transmission data to evaluate the effect of increased statistical noise with 100 times fewer photons on classification errors and impact of statistical reconstruction methods . in this revised testing , we have found that with this dual - energy hybrid method it is possible to discriminate contrast versus bone in the ct attenuation correction images and apply the correct scale factor for accurate calibration and attenuation correction even at very low exposure levels for the second ct scan . although the method described is suitable for calculating suitable attenuation factors in regions having a single high - z material , such as a contrast agent present , it is contemplated that the method may be readily extended to include more than two ct scans at different energies to discriminate between multiple high - z materials present in a particular application . while illustrative embodiments have been illustrated and described , it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention .
a method is disclosed for obtaining linear attenuation coefficients for interpreting a pet scan of a region . the method is suitable for use when high molecular weight materials are present in the region , such as contrast agents or metal objects . the method includes obtaining first and second x - ray ct data sets of the region of interest at two different energies or voltage potentials and differencing corresponding ct numbers . the difference values are used to distinguish portions of the region that are bone from portions of the region that are contrast agent or other high molecular weight material . the obtained ct data set is then used to obtain an attenuation coefficient map of the region at the pet energy of 511 kev , for example , using a linear scaling factor suited to the particular identified material . difference values at or near zero may be used to identify soft tissue portions of the region .