with reference to fig2 and 3 , a centerline 14 is drawn through a vessel 16 ( e . g . a blood vessel ) within the body of a living being ( e . g . a human ) within the field of view 18 of an ultrasound probe ( not shown ). the centerline 14 is defined as a plurality of statistical “ centers ” of the vessel 16 throughout the field of view 18 . the centerline 14 is derived from measured ultrasound parameters such as 4 - d power doppler or 4 - d color flow data . it can be , for instance , the mean ( average ), median ( central value ), or mode ( location of maximum ) of samples of ultrasound measurements taken over successive cross - sections of areas 20 along the vessel 16 . the mean of a dimension x representing the x dimension in the coordinate system of the frame of reference of the ultrasound probe using a ( x ) as a density of some desirable ultrasound parameter is ∫ xa ( x ) dx , provided that a ( x ) is normalized so that it integrates to unity . the median is the value x 0 such that ∫ - ∞ x 0 ⁢ a ⁡ ( x ) ⁢ ⁢ ⅆ x = ∫ x 0 ∞ ⁢ a ⁡ ( x ) ⁢ ⁢ ⅆ x , max x ⁢ { a ⁡ ( x ) } = a ⁡ ( x p ) . now referring to fig3 and 4 , the cross - section of area 20 forms a circle 22 in a plane 24 for 3 - d or 4 - d imaging if the vessel 16 can be modeled in a small region as a right - circular cylinder 26 and is perpendicular to the direction of fluid flow 28 through the vessel 16 . in contrast , a doppler ultrasound probe 30 propagates ultrasound waves in a direction 32 through the vessel 16 . that ultrasound energy can be thought of as projecting onto an area 34 of the vessel 16 which forms an ellipse 36 in a plane 38 which contains the direction 32 of wave propagation . the direction of the centerline 14 is the same as the direction of fluid flow 28 , which is taken to be the average direction of all flow of fluid ( e . g . blood ) in any cross - section plane 24 through the centerline 14 . if fluid flow is measured as an average velocity of fluid flowing past the area 20 by the ultrasound equipment , and if that velocity were not along the centerline 14 , fluid would have to leak out of the vessel 16 . in any plane 22 , 38 drawn through the vessel 16 , the components of velocity perpendicular to the centerline 14 are assumed to average to zero . if not , there would be a net flow of fluid through the vessel walls . since the average velocity direction is along the centerline 14 and only the component of velocity in the direction of wave propagation 32 of the ultrasound probe emitted energy can be measured , then it can be assumed , in the case of blood as the fluid , that all blood cells are moving parallel to the centerline 14 . it does not matter if this is not correct for every blood cell ; it will be correct on average . the net flow or flux ( integrated over the cross - sectional area 20 , 34 ) will be in the direction of the centerline 14 . the direction of wave propagation 32 of the ultrasound probe emitted energy forms an angle θ with the direction of fluid flow 28 . similarly , the plane 38 forms an angle φ with plane 24 . since doppler cannot measure true velocity s , but only its radial component , s cos θ , it is necessary to find the direction of fluid flow 34 and thus the direction of the centerline 14 relative to the direction 32 of wave propagation in order to correct for the angle θ . likewise to find the proper orientation of cross - section of area 20 from the orientation of area 34 in order to find , say , the lumen area , then it is necessary to correct for the angle φ . with reference to fig5 and 6 , to correct for θ and φ , it is necessary to impose a coordinate system of the reference frame of the ultrasound probe 30 onto the vessel 16 . the vessel 16 , in three dimensions is referenced , for example , by a rectangular coordinate system with dimensions x *, y *, z *, where x * and z * are the dimensions of the cross - section plane 24 perpendicular to the centerline 14 , and y * is measured parallel to the centerline 14 . the dimensions x , y , and z are the axes with reference to the ultrasound probe 30 where z is in the direction of ultrasound propagation from the probe 30 , the x - y plane at z = 0 is the plane of the transducers ( not shown ) of the probe 30 , and the x - z plane at a fixed value of y cuts through the vessel 16 under examination , i . e ., the plane 38 through the vessel 16 ( to create the ellipse 36 if the vessel 16 is a circular cylinder ). if the plane 38 is divided into a large number of rectangular regions 40 , then each region 40 represents a three dimensional pixel known as a voxel . if the centerline 14 is defined with reference to a mean position of x and z dimensions at a fixed y on the plane 38 , then a point on the centerline 14 is given by the mean of the center , i . e . a point with dimensions x ( y ), y , z ( y ) such that x _ ⁡ ( y ) = ∑ n ⁢ ⁢ x n ⁢ a n ∑ n ⁢ ⁢ a n = ∑ x , z ⁢ ⁢ xa ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ a ⁡ ( x , y , z ) ( 1 ) z _ ⁡ ( y ) = ∑ n ⁢ ⁢ z n ⁢ a n ∑ n ⁢ ⁢ a n = ∑ x , z ⁢ ⁢ za ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ a ⁡ ( x , y , z ) ( 2 ) at a given time t where n is the n th voxel within the ellipse 36 . the centerline 14 is calculated from the density variable a ( x , y , z ) which is based on 2 - d , 3 - d , or 4 - d power doppler or color doppler image data ( after a wall filter ). the power doppler or color doppler densities a ( x , y , z ) are derived with the use of the method disclosed in international patent publication no . wo 00172756 ( i . e ., international patent application no . pct / us00 / 14691 ) and u . s . pat . no . 6 , 524 , 253 b1 , the disclosures of which are incorporated herein by reference in their entirety . with reference to page 34 , lines 18 - 21 , of international patent publication no . wo 00 / 72756 , a generalized doppler spectrum can be denoted by a 5 - dimensional data set a 1 ( r , a , e , f , t ) which is the real - time signal return amplitude of what is being measured ( to obtain blood flow velocity ), where r = depth ( or range ), a = azimuth , e = elevation , f = doppler frequency , and t = time . such a data set can be readily converted to rectangular coordinates , where it becomes a 2 ( x , y , z , f , t ) or a 3 ( x , y , z , v , t ) where v is the radial velocity , the component of velocity of fluid flow in the direction 32 , and v is related to doppler frequency by the relation where c and f 0 are the sonic propagation speed and frequency , respectively . a still more interesting 5 - d data set would be a 4 ( x , y , z , s , t ) where s is the fluid speed ( e . g . blood speed ), i . e ., the signed magnitude of the true total vector velocity of fluid flow where v = s cos θ and θ is the angle described above for fig3 and 4 . a 4 - d doppler ultrasound machine as described in international patent publication no . wo 00 / 72756 and u . s . pat . no . 6 , 524 , 253 b1 will produce three different 4 - d data sets corresponding to the three common vascular imaging modes : b ⁡ ( x , y , z , t ) = a 2 ⁡ ( x , y , z , 0 , t ) ⁢ ⁢ “ 4 ⁢ - ⁢ d ⁢ ⁢ b ⁢ - ⁢ mode ⁢ ⁢ data ” ( 3 ) p ⁡ ( x , y , z , t ) = ∫ f & gt ; f0 ⁢  a 2 ⁡ ( x , y , z , f , t )  2 ⁢ ⁢ ⅆ f ⁢ ⁢ “ 4 ⁢ - ⁢ d ⁢ ⁢ power ⁢ ⁢ doppler ” ( 4 ) v ⁡ ( x , y , z , t ) ⁢ ⁢ “ 4 ⁢ - ⁢ d ⁢ ⁢ color ⁢ ⁢ doppler ” ⁢ ⁢ or ⁢ ⁢ “ 4 ⁢ - ⁢ d ⁢ ⁢ color ⁢ ⁢ flow . ” ( 5 ) with reference to fig7 , as is customary in modern doppler ultrasound , p plotted vs . frequency in fig7 , which has a peak surrounding the carrier frequency f 0 and another peak around f 0 + f c where f c is the shift in frequency due to the doppler effect . when passed through a wall ( high pass ) filter ( the dotted line in fig7 ), the resulting plot of p vs . frequency is shown in fig8 , which is the density to be obtained ( usually after first maximizing p ( or v ) with respect to t — a process called “ peak hold ”). the centerline 14 is the mean , mode , or median of x ( or y ) and z as a function of y ( or x ) using p as a density . for the case of a point on the centerline 14 given by the mean of the center , i . e . a point with dimensions x ( y ), y , z ( y ) based on density p , values of the dimensions x and z are thus : x _ ⁡ ( y ) = ∑ n ⁢ ⁢ x n ⁢ p n ∑ n ⁢ p n = ∑ x , z ⁢ ⁢ xp ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ p ⁡ ( x , y , z ) ( 6 ) z _ ⁡ ( y ) = ∑ n ⁢ ⁢ z n ⁢ p n ∑ n ⁢ p n = ∑ x , z ⁢ ⁢ zp ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ p ⁡ ( x , y , z ) ( 7 ) the quantity v is the mean radial velocity of fluid flow corresponding to the measured amplitude a 3 as already discussed above , which is obtained using the autocorrelation function described in “ real - time two - dimensional blood flow imaging using an autocorrelation technique ,” c . kasai , k . nemakawa , a . koyano , and r . omoto , ieee transactions on sonics and ultrasonics , vol . su - 32 , no . 3 , pp . 458 - 463 , may 1985 , which is incorporated herein by reference in its entirety . the centerline 14 for v is the mean , mode , or median of x ( or y ) and z as a function of y ( or x ) using v as a density . for the case of a point on the centerline 14 given by the mean of the center , i . e . a point with dimensions x ( y ), y , z ( y ) based on density v , values of the dimensions x and z are thus : x _ ⁡ ( y ) = ∑ n ⁢ ⁢ x n ⁢ v n ∑ n ⁢ v n = ∑ x , z ⁢ ⁢ xv ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ v ⁡ ( x , y , z ) ( 8 ) z _ ⁡ ( y ) = ∑ n ⁢ ⁢ z n ⁢ v n ∑ n ⁢ v n = ∑ x , z ⁢ ⁢ zv ⁡ ( x , y , z ) ∑ x , z ⁢ ⁢ v ⁡ ( x , y , z ) ( 9 ) since v is merely the radial component of velocity , it is desirable to calculate s is the magnitude of the vector v , the vector of true velocity in the direction of fluid flow 28 at the centerline 14 . let n represent a voxel number ( the n th voxel in or on the ellipse 36 ). the measured mean doppler frequency , f n , at each voxel is proportional to v = v z , the z component of the mean velocity , v n , in that resolution cell . the flow center can be defined as the locus of centers of the elipses as y varies ( i . e ., along the centerline 14 ). to derive v and s from v n which is itself derived from f n using the autocorrelation method mentioned above , let us obtain the complex output of the wall filter in each bin n , or u nj . if n s ultrasound pulses are used ( n s ≦ 32 ) with an n f tap wall filter ( n f ≦ 11 ), there will be j = n s − n f + 1 values of j . ignoring the voxel identifier , n ( to simplify notation ), let the autocorrelation vector u 1 =( u 1 , u 2 . . . u j - 1 ) t and let u 2 =( u 2 , u 3 . . . u j ) t where u 1 is autocorrelated with u 2 , u 2 is autocorrelated with u 3 , etc . let f = u 1 * u 2 ( the complex inner product , where * is the conjugate transpose ), then angle ( f )= a tan 2 [ im ( f )/ re ( f )] ( 12 ) where prf is the ultrasound pulse repetition frequency . put another way , the quantity f is the autocorrelation function of the complex wall filter output at a lag of one . the 3 - d orientation of the centerline 14 and hence the direction of the vector velocity v can be computed , for example , by using two consecutive values of y , forming the vector v =( v x , v y , v z )∝( { overscore ( x )} ( y 2 )− { overscore ( x )} ( y 1 ), y 2 − y 1 , { overscore ( z )} ( y 2 )− { overscore ( z )} ( y 1 ) ( 13 ) which can be transformed into a unit vector by dividing by the square root of the sum of the squares of the three coordinate differences . the magnitude of the velocity is then obtained by dividing the measured radial velocity by the cosine of the 3 - doppler angle θ to determine the speed s n at each voxel . thus if f n ( x , y , z ) is the doppler frequency calculated above and s n = s ( x , y , z ) is the blood speed , then s n ⁡ ( x , y , z ) = c 2 ⁢ f 0 ⁢ ( x - a ) 2 + ( y - b ) 2 + z 2 ( x - a ) ⁢ v x + ( y - b ) ⁢ v y + z ⁢ ⁢ v z ⁢ f n ⁡ ( x , y , z ) ( 14 ) where ( a , b , 0 ) is the center of the sub - array of the ultrasound probe currently active to observe the point ( x , y , z ). the constant c is the speed of sound in soft tissue , about 1540 meters / second or mm / millisecond , and f 0 is the center frequency or carrier frequency of the ultrasound energy being used . a more convenient way to express this formula is to choose two points on the vessel centerline 14 , near where f n was measured , and let the coordinates of one with respect to the other be ( x c , y c , z c ). the true speed s n of a voxel is then given by s n = c 2 ⁢ f 0 ⁢ f n cos ⁢ ⁢ θ = cf n 2 ⁢ ⁢ f 0 ⁢ x c 2 + y c 2 + z c 2 z c ( 15 ) to obtain a centerline 14 from threshold flow data , the equations listed above for obtaining the mean , median , or mode , and particularly the x and z dimensions of the mean centers of the centerline 14 would apply to values of v or p above a certain threshold value . with reference to fig1 , another parameter of interest is to obtain the volume of fluid 42 passing through the plane 24 per unit of time . this quantity is defined as the volume flow . obtaining this quantity is facilitated by calculating the centerline 14 of the fluid flow . the volume flow can be obtained by at least two methods : an n - point fast fourier transform ( fft ) or via “ 4 - d true velocity flow ” color - doppler image data . to obtain the volume flow using an n - point fft , reference is made now to fig8 - 10 . the fft samples 42 for each bin of frequencies i from an n - point fft , where | i |& lt ; n / 2 leads to a discrete power spectrum p i , the area under the output spectrum 44 after the wall filter , whose output appears as pseudo - bar graph elements 46 . for a given voxel element n , the power spectrum in the voxel n in the frequency bin i is given by p n , i , and the power spectrum per bin , pi is obtained by summing the per - voxel power spectrum over all voxels at a given y . the power in each frequency bin is p i = ∑ n ⁢ ⁢ p n , i ; ( 16 ) v i = c 2 ⁢ ⁢ f 0 ⁢ f i = prf n ⁢ c 2 ⁢ f 0 ⁢ i ; ( 18 ) f 1 = ∑ - n 2 - 1 + n 2 - 1 ⁢ ⁢ i × p i ( 19 ) q . = kf 1 / p 0 ⁢ ⁢ where ⁢ ⁢ k = prf n ⁢ c 2 ⁢ f 0 ⁢ δ ⁢ ⁢ x ⁢ ⁢ δ ⁢ ⁢ z , ( 20 ) where p 0 is the total power out of the wall filter in a single central voxel about the centerline 14 , and δx , δz are the lengths of the dimensions of each voxel ( n ) in the summation . the result is independent of cos θ , provided that θ is not close to 90 °. alternatively , volume flow can be estimated directly from “ 4 - d true velocity flow ” color - doppler image data . referring again to fig3 , the direct approach is to choose the plane 24 ( the plane that cuts though the vessel 16 orthogonal to the centerline 14 ), sum the s n &# 39 ; s for every non - zero pixel in the plane 24 , and multiply by the pixel area . an approximate way to estimate the volume flow from raw color doppler data is to sum the autocorrelation doppler values over all the pixels in the vessel 16 at a fixed y , and use the slope of the centerline 14 in the y - z plane as a correction factor . the result is q . = ( c 2 ⁢ f 0 ⁢ ⁢ δ ⁢ ⁢ x ⁢ ⁢ δ ⁢ ⁢ z ) ⁢ y c z c ⁢ ∑ n ⁢ ⁢ f n . ( 21 ) the simple y c / z c slope simultaneously corrects for both the doppler angle θ and the orientation angle of the x - z image plane φ without having to compute the square root of the sum of the squares that is needed to determine s n . to determine the lumen area from either power doppler , color doppler , or true velocity flow ( p n , f n , or s n ), select the plane 24 ( the plane that cuts though the vessel 16 orthogonal to the centerline 14 ), count the number of pixels in the vessel 16 , and multiply by the pixel area . pixels on vessel boundaries can be given a reduced weight for a more precise measurement . additional parameters can be obtained or imaged once the centerline and true vector velocity is known . referring now to fig1 - 14 , the location of a stenosis 48 can be found as the point of highest peak true ( systolic ) velocity along the centerline 14 of a vessel 16 . one can model the true velocity as a function of distance from the centerline to the walls 50 of the vessel 16 . since velocity is likely to be higher in the area 52 near the centerline 14 than the area 54 closer to the walls 50 of the vessel 16 , a three dimensional image displaying the degree of translucency of a vessel 16 can be generated by imaging software within ultrasound equipment . that same imaging software can map the entire vessel along the entire field of view and keep track of that vessel despite the movement of a patient by beam tracking software that focuses on the location of the centerline 14 . the coordinates of the endpoints 56 of several centerlines 14 can be aligned so as to “ stitch ” together several fields of view 58 and thus display the entire length of the vessel 16 , no matter how tortuous its path . once the centerline 14 is calculated in the field of view 60 throughout the vessel 16 , a bisection 62 of the vessel 16 can be obtained from a plane 62 that slices though the centerline 14 . with reference to fig1 , a block diagram of a system 64 that implements the method of obtaining a centerline in accordance with an exemplary embodiment of the present invention is depicted . the system 64 includes the ultrasound probe 66 , coaxial cables 68 , a connector panel 70 , an analog processor 72 , a digital interface processor 74 , a digital processor 76 , an image processor 78 , controls 80 , a display 82 , and data storage ( memory ) 84 , interconnected as shown through a system bus 86 . the ultrasound probe 66 contains a number of piezoelectric acoustic transducers ( not shown ) arranged as an array of elements . for 3 - d or 4 - d imaging , a two dimensional arrangement of elements is necessary . for 2 - d imaging , a one dimensional array of 1 × n elements is needed . the transducer elements can both send and receive , but the elements that transmit ultrasound pulses do not necessarily have to be the same elements of the array that receive reflections from a vessel 16 . the cables 68 transmit and receive electrical impulses and are generally coaxial cables . the analog processor 72 contains circuitry for amplification , gain management , and analog - to - digital ( a / d ) conversion of the ultrasound pulses to be transmitted and the received reflections from the transducer elements . between the transmitting and receiving circuitry ( not shown ) is an electrical protection circuit , since the signals emanating from the transducer elements require voltages in the neighborhood of 100 v , while the received reflected signals are on the order of microvolts . since the dynamic range of the received signal is very high , there is a need for a circuit for performing time gain control . since reflected signals are received from different locations in the body , these signals may be out of phase with each other , so that gain for each transducer received signal is adjusted dynamically in time to line up received signals . an anti - aliasing filter is located between the receiving amplifier and the a / d converter . the a / d converter can be of a type that outputs the signal in a parallel array of bits or can output the digital data serially . a digital interface processor ( dip ) 74 receives the digital version of the received signal from the analog processor 72 . the dip 74 organizes the sampled data to put it in a proper format so that the digital processor 76 can form a beam . if the data from the a / d converter of the analog processor 72 is processed serially , then the dip 74 can also packetize and time compress the data . the digital processor ( dp ) 76 takes packetized ( in the case of serial processing ) or time division multiplexed ( in the case of parallel processing ) data and forms a beam representing the array of transduced elements in the ultrasound probe . 66 . for each transduced element , a time delay is added to cause all elements of the combined wavefront to be in phase . after beam forming , the combined beam contains the wavefronts represented by the frequency shifted doppler signal . at this point , the doppler information is separated from the non - doppler information using a wall filter as previously discussed with reference to fig7 - 9 . the imaginary part , i , and the real part , q , from the autocorrelation functions of the data as previously discussed are extracted . the doppler information is separated from the non - doppler information by taking the arctangent of i / q from which the angle is proportional to the radial component of the true velocity of the blood flow . the image processor 78 takes this output , organizes the data into volumes and generates the centerline 14 , and from the centerline 14 the true vector velocity , blood volume flow , lumen area , and other parameters of interest . the image processor 78 then puts these parameters in a format for displaying on the display 82 . the controls hardware / software 80 provides the man - machine interface to a user , so that a user can use an input device such as a joy stick to highlight portions of the centerline and display measurements . the data storage 84 , which can include ram , rom , floppy disks , hard disks , and / or optical media , provides the memory necessary for the dip 74 , the digital processor 76 , and the image processor 78 to carry out their specific functions . it will be understood that the embodiments described herein are merely exemplary and that a person skilled in the art may make many variations and modifications without departing from the spirit and scope of the invention . all such variations and modifications are intended to be included within the scope of the invention .
a method and associated apparatus are disclosed for determining the location of an effective center of fluid flow in a vessel using an ultrasound apparatus . ultrasound energy is propagated along an axis of propagation and projects upon the vessel . a doppler - shifted signal reflected from the fluid in the vessel is received and a set of quantities expressed as a density is derived from the doppler shifted signal for each of a set of coordinates , the density being a function of the doppler shift in frequency associated with each of the coordinates . one of a mean , mode or median is calculated for each of the dimensions of the set of coordinates in conjunction with the density associated therewith . this calculation is repeated throughout the field of view of the vessel to define a centerline .