Patent Application: US-9941608-A

Abstract:
a system for three - dimensional tomosynthesis imaging of a target element is provided having an image acquisition element and a processor . the image acquisition element obtains a plurality of images of the target element from a plurality of angles and includes a radiation source that is positionable at a plurality of angles with respect to the target element and a radiation detector . the radiation detector is positioned so as to detect radiation emitted by the radiation source passing through the target element and determine a plurality of attenuation values for radiation passing through the target element to establish a radiation absorbance projection image of the target element for a particular radiation source angle . the processor is configured to apply an iterative reconstruction algorithm to the radiation absorbance projection images of the target element obtained from a plurality of radiation source angles to generate a three - dimensional reconstruction of the target element . the system can gain further accuracy where the iterative reconstruction algorithm is applied using cone - beam forward projection and back projection .

Description:
the systems and methods of the present invention address the needs of the art by providing tomosynthesis apparatus and techniques for imaging target elements that overcome the problems of conventional three - dimensional imaging systems . the present invention enables the use of tomosynthesis to efficiently provide accurate three - dimensional imaging of a target element in which overlapping sub - elements having differing attenuation characteristics by applying a 3d reconstruction algorithm having a novel combination of features . the algorithm can employ a cone - beam geometry lacking in geometric simplification such as parallel - beam based approximation methods . the algorithm can further apply the cone - beam geometry in an iterative forward - projection and back - projection method based on maximum - likelihood image estimation using an estimation - maximization algorithm . the invention is applied below to one preferred embodiment in which the system is used for tomosynthesis mammography ; however , the invention will be useful in a variety of three - dimensional imaging situations . for example , the invention can be applied to a variety of patient imaging problems such as heart imaging , or imaging of the soft tissues or bones of the hand . the imaging system of the invention can be used for diagnoses ( as is described below for tomosynthesis mammography ) or it may be used for other applications such as three - dimensional modeling for the purpose of fitting an implant ( whether orthopedic , such as a hip or knee implant , an artificial heart , or other type of implant ) or for use in surgical navigation systems . what follows is a description of one preferred embodiment of the invention . tomosynthesis mammography is a three - dimensional breast imaging technique . it involves acquiring projection images of a breast at a plurality of viewpoints , typically over an arc or linear path . three - dimensional distribution of x - ray attenuation coefficient of the breast volume is reconstructed from these projections . a prototype tomosynthesis system 10 for breast imaging is illustrated in fig1 . in this exemplary system , eleven projections are acquired by moving the x - ray tube 12 over a 50 ° arc (− 25 ° to + 25 °) above the target element , in this case breast tissue 18 which may be compressed by compression paddle 16 , in 5 ° angular steps about axis of rotation 14 . breast tissue 18 and digital detector 20 are stationary during the image acquisition . certain characteristics of this exemplary embodiment of a tomosynthesis system of the invention are described below : spatial resolution and contrast resolution : the tomosynthesis system uses an amorphous - silicon - based flat panel digital detector 20 on which a csi crystal phosphor is grown epitaxially . it reads out 2304 × 1800 pixels ( 100 μm pixel pitch ) via a tft array . the detector has a linear response over exposure levels up to 4000 mr and 12 bits of working dynamic range . each plane of the 3d reconstruction has about the same resolution as the detector ( 100 um ) but the depth resolution is on the order of a millimeter . dose : the target / filter combination is rh / rh and the accelerating potential is 25 ˜ 33 kvp to image breasts with 3 ˜ 8 cm range of thickness . the total x - ray dose for acquiring 11 projections is approximately 1 . 5 times of that used for one film - screen mammogram . each projection is a low dose breast image ( approximately 1 / 11 of the does per projection ). patient motion : patient motion is reduced by fast image acquisition . using cone - beam x - ray geometry and area detector , a projection of the whole breast can be recorded with one x - ray exposure at each angle . for each projection , the exposure time is 0 . 1 ˜ 0 . 2 s and detector readout time is about 0 . 3 s . rotation to the next angle is performed during the detector readout . the total image acquisition time for 11 projections is about 7 sec . breast compression also helps to reduce patient motion . image acquisition geometry : the design of the tomosynthesis system can be based on the conventional mammography system . the mlo views have been used in most cases since it provides the most complete coverage of the whole breast . tomosynthesis can take advantage of the high efficiency of a digital detector in acquiring low dose breast images . prior to the present invention , appropriate reconstruction methods that make good use of the low dose projections and the acquisition geometry of the tomosynthesis system 10 have not been deployed . for an initial evaluation , niklason implemented a “ shift - and - add ” method that is similar to backprojection [ niklason et al , 1997 ]. methods used by others [ chakraborty et al , 1984 ; haaker et al , 1985 ; suryanarayanan et al , 2000 ] essentially did not handle the limited statistics in low dose projection images . in theory , they were not suitable in the case of limited number of projections and limited angular range . therefore , the three - dimensional information extracted by these methods was limited , which resulted in poor quality reconstructions . the maximum likelihood ( ml ) algorithm is an iterative reconstruction method [ rockmore , 1977 ; shepp et al , 1982 ; levitan et al , 1987 ; herbert et al , 1989 ; browne et al , 1992 ; manglos et al , 1995 ; pan et al 1997 ; zhou et al , 1997 ]. it is well suited for tomosynthesis reconstruction , which is an ill - conditioned problem ( only 11 low dose projections are available ). the ml algorithm incorporates the stochastic nature of the x - ray transmission process so that the statistical noise in projection images is taken into consideration in the case of low x - ray flux . it also incorporates the information of the object into the reconstruction in the form of constraints . in ml reconstruction , the likelihood function , which is the probability of obtaining the projections y obtained in a measurement , given a certain model for the three - dimensional map of attenuation coefficients u is : the ml solution is the 3d reconstruction that maximizes the probability of the measured projections . because an analytical solution is usually intractable , an iterative algorithm is a better choice . the incident and transmitted x - rays follow poisson statistics and the log - likelihood is described by : where u is the linear attenuation coefficient ; n i is the number of incident x - ray photons to projection pixel i , before attenuation ; y i is the number of transmitted x - ray photons to projection pixel i , after attenuation ; l ij is the path length of beam ray i in the object ( reconstruction voxel j ; and the algorithm by lange and fessler [ lange and fessler , 1995 ] can be selected to solve the ml problem . at the n - th iteration , the value of an object voxel μ is updated by : cone - beam forward projection and back projection can form the basis for iterative reconstruction according to the invention . at the forward projection step , the projection images at 11 angles are calculated based on the current 3d reconstruction model . at the backprojection step , the calculated projections and the measured projections are compared and the 3d reconstruction model is updated according to their difference . the forward projection to a detector pixel i at a projection angle can be used to illustrate the whole forward projection problem . an x - ray beam containing n i photons is incident from the source to the center of the selected detector pixel . this beam penetrates a series of object voxels and is sequentially attenuated by them . the total aggregate attenuation is & lt ; l , u ( n ) & gt ; i and the number of transmitted photons is n i e −& lt ; l , u ( n ) & gt ; i , which is the forward projection to the pixel . this operation is repeated for all detector pixels that form the forward projection at this angle . the forward projections at all angles can be done in the same way except that the “ pseudo - beam ” is rotated . the 3d reconstruction model is updated at the backprojection step . equation 3 describes the update of a voxel j at the n - th iteration of reconstruction . the whole image is updated by doing the same operation on every voxel in it . at a projection angle , the center of the voxel is projected from the source to a detector pixel containing the attenuation information of this voxel . this operation is repeated at other angles and totally 11 detector pixels are found . in equation 3 , the values of these 11 pixels , both in forward projection and in measured projection are used to update the object ( reconstruction ) voxel ( the summation is on the set of these 11 pixels ). the origin of the coordinate system is at the axis of rotation 14 as illustrated in fig2 . the rotation plane of the x - ray 12 source is the yz - plane ( x = 0 ). the detector 20 is parallel to the xy - plane at z = 21 . 7 cm . the distance between the source 12 and the axis of rotation 14 is d sa and the distance between the detector 20 and the axis of rotation 14 is d da . at projection angle θ , the position of the x - ray source 12 is : the reconstructed object 24 is a rectangular volume , represented by a three - dimensional array of voxels 26 . the breast volume 18 is contained in this rectangular volume 24 . in a reconstructed image , the value of a voxel is positive if it represents breast tissue ; zero if it represents the empty space out of the breast . in the coordinate system , the position of a voxel 26 indexed by ( m x , m y , m z ) is : where ( x obj , y obj , z obj ) is the position of the center of the rectangular volume 24 ; d x , d y and d z are the size of the voxel 26 in three dimensions . the position of a detector pixel 28 indexed by ( n x , n y ) is : where ( x p , y p ) is the position of the center of the detector 20 ; d ′ x and d ′ y are the size of the pixel 28 in x and y dimensions . the forward projection is implemented by ray tracing from the x - ray source 12 to detector pixel 28 . at a projection angle , the x - ray beam to a detector pixel 12 is attenuated from the point where the beam enters the volume 24 to the point where it goes out . the total attenuation along the beam & lt ; l , u ( n ) & gt ; i is calculated by accumulating the attenuation l · u ( n ) by each voxel 26 on the beam line . the number of transmitted x - rays to the pixel 28 is n i e −& lt ; l , u ( n ) & gt ; i . the forward projection of the object 18 at this angle is obtained by repeating this operation for all detector pixels 28 . the forward projections at other angles are calculated in the same way except the x - ray source 12 is at a different location . the first step of forward projection is to determine the orientation of the x - ray beam 30 as illustrated in fig3 . at an angle , the position of the x - ray source ( x s , y s , z s ) 12 and detector pixel ( x p , y p , z p ) 28 are determined by equation 4 and 6 . the orientation of the beam p ( x , y , z ) 30 from source 12 to the detector pixel 28 can be described by two parameters : ( 1 ) β , the angle made by the beam and the yz - plane ; ( 2 ) α , the angle made by the projection of the beam in yz - plane and the z - axis . these two parameters are determined by : α = tan − 1 (( y p − y s )/( z p − z s )) β = tan − 1 ( x p /√{ square root over (( y p − y s ) 2 +( z p − z s ) 2 )}{ square root over (( y p − y s ) 2 +( z p − z s ) 2 )}) ( 7 ) the path length |{ right arrow over ( p 1 p 4 )}| of the x - ray beam 30 through a voxel 26 , as illustrated in fig4 , is also the distance between the centers of two successive voxels along the beam . the position of the next voxel along the beam can be located by shifting δx , δy and δz ({ right arrow over ( p 1 p 2 )}, { right arrow over ( p 2 p 3 )} and { right arrow over ( p 3 p 4 )} in fig4 ) along three dimensions from the current voxel 26 . δ x ={ right arrow over ( p 1 p 2 )}={ right arrow over ( p 1 p 4 )}· cos β · cos α δ y ={ right arrow over ( p 2 p 3 )}={ right arrow over ( p 1 p 4 )}· cos β · sin α ( 8 ) δ z ={ right arrow over ( p 3 p 4 )}={ right arrow over ( p 1 p 4 )}· sin β to calculate { right arrow over ( p 1 p 4 )}, its projection in the yz - plane { right arrow over ( p 1 p 3 )}, illustrated in fig5 , is calculated first : { right arrow over ( p 1 p 3 )}= d y / sin α if α & gt ; tan − 1 ( d y / d z ); ( 9 ) { right arrow over ( p 1 p 3 )}= d x / cos α if α ≦ tan − 1 ( d y / d z ) in a similar way , the path length { right arrow over ( p 1 p 4 )} can be calculated by : { right arrow over ( p 1 p 4 )}= d x / sin β if β & gt ; tan − 1 ( d x /{ right arrow over ( p 1 p 3 )}); ( 10 ) { right arrow over ( p 1 p 4 )}= d x / cos β if β ≦ tan − 1 ( d x /{ right arrow over ( p 1 p 3 )}) there are exceptions to the two cases illustrated in fig5 . in a case shown in fig6 , the path lengths through voxel 3 and 4 cannot be described by equation 10 . but the total path length of them is equal to the path length in voxel 2 . the total attenuation by voxel 3 and 4 is equivalent to the attenuation by the shaded area in fig6 , which has the same path length as voxel 2 . the equivalent attenuation is estimated by a linear interpolation of attenuations by voxel 3 and 4 . the weighting for the interpolation is proportional to the inverse of the distance from the voxel center to the beam line . the ratio of the weighting for voxel 3 to that for voxel 4 is d 4 / d 3 , equivalent to r 4 / r 3 , where d 3 and d 4 are the distances from the voxel center to the beam ; r 3 and r 4 are the distances from the voxel center to the projection of the beam along the y - axis . the total attenuation along a beam to a detector pixel i is the summation from the first voxel at the point where the beam enters the volume to the voxel at the point where the beam goes out of the volume . for a beam with orientation ( α , β ), the position of the voxel at entering point is : x 0 = x s +√{ square root over (( y 0 − y s ) 2 +( z 0 − z s ) 2 )}{ square root over (( y 0 − y s ) 2 +( z 0 − z s ) 2 )}· tan β where d is the thickness of the reconstruction volume . the attenuation l · u 0 by the first voxel at ( x 0 , y 0 , z 0 ) is calculated and then the tracing point is shifted forward by ( δx , δy , δz ) to the next voxel along the beam , where the attenuation l · u 1 is calculated and added to l · u 0 . at the n - th step , the position being search is : the number of steps of forward projection is v = int ( d / δz )+ 1 . after v steps , the total attenuation along the beam to detector pixel i is ( represented by & lt ; l , u ( n ) & gt ; i ). the number of transmitted x - ray photons is the value of the object voxel is updated at the backprojection step as illustrated in fig7 . at this step , projection pixels containing the attenuation information of the selected object voxel are found and used to update the value of this voxel . at a projection angle , the position of the detector pixel ( x p , y p , z p ) which contains the information of a selected voxel is : x p = x s +( x obj − x s )·( z p − z s )/( z obj − z s ) y p = y s +( y obj − y s )·( x p − x s )/( x obj − x s ) ( 13 ) where ( x s , y s , z s ) is the position of the x - ray source at this angle . this operation is repeated to find detector pixels related to this voxel at other angles . the value of this voxel is updated by equation 3 , using these detector pixels . a phantom 38 is composed of a piece of mastectomy specimen 40 and a feature plate 42 from an american college of radiology ( acr ) accredited mammography phantom and placed on detector 20 as illustrated in fig8 a . the feature plate 42 , further illustrated in fig8 b , contained nylon fibers ( labeled 1 to 6 on the plate ), simulated micro - calcifications ( labeled 7 to 11 on the plate ) and tumor - like masses ( labeled 12 to 16 on the plate ). the mastectomy specimen 40 is a surgically removed breast tissue containing lesions . the combination of the feature plate 42 with the mastectomy specimen 40 makes it very hard to find features of the acr phantom 42 . the reconstructed feature plate demonstrates how the three - dimensional reconstruction works to improve the visibility of features . ten features ( fiber 1 , 2 , 3 , 4 ; micro - calcification cluster 7 , 8 , 9 and mass 12 , 13 , 14 ) can be seen very well in a projection of the 4 cm thick acr phantom 42 itself ( rh / rh , 28 kvp and 160 mas ) as shown in fig9 a . with the superimposed mastectomy specimen 40 , only one feature ( micro - calcification cluster 7 ) is visible in a projection ( rh / rh , 30 kvp and 140 mas ) as can be seen in fig9 b . the reconstruction of the feature layer after 10 iterations is shown in fig9 c . the x - ray energy and exposure are the same as that used to create the image of fig9 b . more features ( micro - calcification cluster 7 , 8 , 9 and mass 12 ) can be seen in the reconstruction . even some low contrast features ( fiber 1 , 2 , 3 , 4 ) are recognizable . the number “ 503 059 ” on the label is clearer . it is clear that the visibility of features are significantly improved . clinical imaging of volunteers conducted at massachusetts general hospital under irb approved protocols have been reconstructed for comparison of conventional film - screen mammography and to tomosynthesis mammography . as an example , a mediolateral oblique ( mlo ) mammogram from a volunteer was obtained using film - screen system ( mo / mo , 25 kv and 330 mrad average glandular dose ). the x - ray film image is shown in fig1 . the patient was found to have a non - palpable 10 mm invasive ductal cancer with associated in situ tumor and this was proved by biopsy . the cancer was difficult to see in the conventional screening mammogram and was found primarily because the calcifications associated with it drew the attention of the radiologist . a tomosynthesis image dataset was taken with rh / rh target / filter at 28 kvp and a total dose of 307 mrad . three reconstructed slices from the 3d reconstruction are shown in fig1 . blood vessels are seen near the breast skin in fig1 a . a tumor that has intraductal as well as invasive ductal cancer elements is just out of the plane of section in fig1 b . the invasive tumor mass , marked by an arrow , with associated calcifications in the in situ portion is clearly seen in fig1 c , as is a benign intramammary lymph node in the upper portion of the image . it is apparent from this volunteer &# 39 ; s dataset that overlapping structures in the conventional two - dimensional projection images ( fig1 ) were spacially separated . a reconstructed image provided at three different depths ( fig1 a illustrating a depth of z = 2 mm , fig1 b illustrating a depth of z = 22 mm , and fig1 c illustrating a depth of z = 32 mm ) makes it easier to see the tumor and calcifications and their relative geometry . a person of ordinary skill in the art will appreciate further features and advantages of the invention based on the above - described embodiments . accordingly , the invention is not to be limited by what has been particularly shown and described , except as indicated by the appended claims or those ultimately provided in a utility application claiming priority to this provisional application . a number of references have been referred to in the specification by last name of the first listed author and year of publication ; those references are listed by full citation in the bibliography below . all publications and references cited herein are expressly incorporated herein by reference in their entirety , in particular , each of the references listed in the bibliography below is expressly incorporated for the teachings referred to in the sections of the application above for which they are cited . u . s . pat . no . 5 , 872 , 828 to niklason et al ., entitled “ tomosynthesis system for breast imaging .” j . a . browne , and t . j . holmes , “ developments with maximum likelihood x - ray computed tomography ,” ieee transactions on medical imaging , 11 ( 1 ): 40 - 52 ( 1992 ). d . p . chakraborty , m . v . yester , g . t . barnes and a . v . lakshminarayanan , “ self - masking subtraction tomosynthesis ,” radiology , 150 : 225 - 229 ( 1984 ). p . haaker , e . klotz , r . koppe , r . linde and h . moller , “ a new digital tomosynthesis method with less artifacts for angiography ,” medical physics , 12 ( 4 ): 431 - 436 ( 1985 ). t . j . herbert and r . m . leahy , “ a generalized em algorithm for 3 - d bayesian reconstruction from poisson data using gibbs priors ,” ieee transactions on medical imaging , 8 ( 2 ): 194 - 202 ( 1989 ). k . lange and j . a . fessler , “ globally convergent algorithm for maximum a posteriori transmission tomography ,” ieee transactions on image processing , 4 : 1430 - 1438 ( 1995 ). e . levitan and g . t . herman , “ a maximum a posteriori probability expectation maximization algorithm or image reconstruction in emission tomography ,” ieee transactions on medical imaging , mi - 6 ( 3 ): 185 - 192 ( 1987 ). s . h . manglos , g . m . gagne , f . d . thomas and r . narayanaswamy , “ transmission maximum - likelihood reconstruction with ordered subsets for cone beam ct ,” physics in medicine and biology , 40 : 1225 - 1241 ( 1995 ). l . t . niklason , b . t . christian , l . e . niklason , d . b . kopans , d . e . castleberry , b . h . opsahl - ong , c . e . landberg , p . j . slanetz , a . a . giardino , r . m . moore , d . albagi , m . c . dejule , p . a . fitzgerald , d . f . fobare , b . w . giambattista , r . f . kwasnick , j . liu , s . j . lubowski , g . e . possin , j . f . richotte , c - y weinad r . f . wirth , “ digital tomosynthesis in breast imaging ,” radiology , 205 : 399 - 406 ( 1997 ). l . t . niklason , b . t . christian , l . e . niklason , d . b . kopans , p . j . slanetz , d . e . castleberry , b . h . opsahl - ong , c . e . landberg , b . w . giambattista , “ digital breast tomosynthesis : potentially a new method for breast cancer screening ,” digital mammography , edited by n . karssemeijer , m . thijssen , j . hendriks and l . van erning , 13 : 51 - 56 ( kluwer academic publishers , 1998 ). t . pan , b . m . w . tsui and c . l . byrne , “ choice of initial conditions in the ml reconstruction of fan - beam transmission with truncated projection data ,” ieee transactions on medical imaging , 16 ( 4 ): 426 - 438 ( 1997 ). a . j . rockmore and a . macovski , “ a maximum likelihood approach to transmission image reconstruction from projections ,” ieee transactions on nuclear science , 24 : 1929 - 1935 ( 1977 ). l . a . shepp and y . vardi , “ maximum likelihood reconstruction for emission tomography ,” ieee transactions on medical imaging , mi - 1 : 113 - 122 ( 1982 ). s . suryanarayanan , a . karellas , s . vedantham , s . j . glick , c . j . d &# 39 ; 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