Abstract:
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.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Application Ser. No. 60/515,350 filed Oct. 29, 2003, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to ultrasound data processing, and more particularly, to finding the attributes of fluid flow in a living body, such as ascertaining the speed, direction, and volume of a fluid flow in a vessel using ultrasound. 
     BACKGROUND OF THE INVENTION 
     Several techniques exist for locating an object using wave-propagation. In the fields of sonar, radar, ultrasound, and telecommunications, transmitting/receiving elements are placed in an array. Some or all of the elements of the array emit pulses of electromagnetic radiation or sound toward a target, and reflections of the wave pattern from the target are received at some or all of the elements. To receive the maximum amplitude (strongest signal) possible, the received signals from all the elements are focused into a beam. 
     To determine blood flow velocity from a beam, techniques from Doppler radar may be adapted for use in ultrasound imaging. With reference to  FIG. 1 , acoustical energy from an ultrasound probe  2  is aimed at a region  4  of a blood vessel  6  through which blood  8  is flowing with a certain velocity. Wavefronts  10  of acoustical energy impinge on the region  4  with a frequency f 0 . The wavefronts  12  returning from region  4  of the blood vessel  6  are shifted in frequency to a value of f 0 +f c , the change in frequency f c  being proportional to double the velocity of the flow of blood  8 . The frequency f 0  of the carrier wavefronts  10  is on the order of megahertz, while the frequency of the Doppler shift f c  is on the order of kilohertz. The greater the velocity of the blood  8  the greater the frequency shift f c . The frequency shift f c  and the blood flow velocity are related to the speed of sound in soft tissue, c, which is nearly a constant of about 1540 meters/second. Known ultrasound equipment may be used to measure the radial component of blood flow, i.e., the component parallel to the direction of sonic propagation, rather than the true velocity v. 
     Known ultrasound imaging equipment displays the radial component of blood flow (or the power associated therewith) by translation into a color scale. Given this colorized display, the direction of flow is estimated by a skilled sonographer and input into a 2-D display in order to enable the approximate calculation of actual velocity (as opposed to its radial component) at one point in the vessel. 
     A drawback of this manual approach is that even for a skilled sonographer, the resultant true velocity is only approximate. Another drawback is that the sonographer needs to use both hands and eyes to obtain a single measurement. The sonographer manipulates an ultrasound probe with one hand and manipulates a joy stick or track ball with the other hand, all while observing the ultrasound image on a screen. The sonographer uses the joy stick or track ball to “draw” a line segment parallel to the blood flow on the screen and then have the ultrasound equipment compute an approximate “true” velocity from the measured radial velocity. The computation is made by utilizing the relationship between the true velocity at a point in a blood vessel to the radial component of velocity by s=v cos θ where s is the magnitude of the true velocity and θ is the angle (2-dimensional for 2-D ultrasound imaging or 3-dimensional for 3-D or 4-D ultrasound imaging) between the radial velocity measured by the probe and the actual direction of flow, which is approximated by the line drawn on the screen by the sonographer. 
     It is difficult to get a good approximation of the angle θ using this two hand manual approach. Traditionally, peak systolic blood velocity at one point has been obtained with this method. However, it is difficult, if not impossible, to obtain other desirable parameters such as volume flow (the amount of blood flowing through a given cross-sectional area of the blood vessel) and lumen area (the total area of a cross section perpendicular to the blood vessel at a given point) with the use of this method. Nor can true velocity be obtained at more than one point, such as the full field of view of the blood vessel  6 . To calculate values accurately, it is necessary to find the true vector velocity of blood flow, including magnitude and direction, over the entire field of view. 
     SUMMARY OF THE INVENTION 
     The disadvantages and limitations of prior art ultrasound apparatus and methods are overcome by the present invention which includes, a method for determining the location of an effective center of a fluid flow in a vessel using an ultrasound apparatus with a transducer array for propagating and receiving ultrasound energy. Ultrasound energy is propagated along an axis of propagation Z, which can be described by a spacial coordinate system (x, y, z) in which the dimension z is in the same direction as the axis of propagation Z. The ultrasound energy projects upon the vessel defining a set of coordinates in the spacial coordinate system where the ultrasound energy impinges upon fluid in the vessel at a given value of the dimension y. A Doppler-shifted signal reflected from the fluid in the vessel at a plurality of the set of coordinates is received and a set of quantities expressed as a density a is derived from the Doppler shifted signal for each of the set of coordinates, the density being a function of the Doppler shift in frequency associated with each of the coordinates, the density being indicative of the movement of the fluid. One of a mean, mode or median is calculated of each of the dimensions of the set of coordinates in conjunction with the density associated therewith. 
     The steps above are repeated after changing the set of coordinates to a second set of coordinates to determine another center in the fluid flow at a different point along the length of the vessel and then determining a vector v which connects the two centers and indicates the approximate direction of flow and the approximate centerline. In a similar manner, a plurality of center points and vectors can be determined using the method just described to ascertain a centerline of the vessel over an entire field of view. 
     Further features and advantages of the invention are described in the following detailed description of an exemplary embodiment of the invention, by way of example with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, reference is made to the following detailed description of an exemplary embodiment considered in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a diagrammatic view of an ultrasound probe transmitting ultrasound waves to and receiving reflected waves from a blood vessel as is known in the prior art; 
         FIG. 2  is a diagrammatic view of a centerline of a vessel determined in accordance with an exemplary embodiment of the present invention; 
         FIG. 3  is a diagrammatic view of the vessel of  FIG. 2 , showing a first surface defined by the intersection of the wavefronts of an ultrasound probe with the vessel and a second surface defined by the cross-sectional area of the vessel perpendicular to the centerline of the vessel at a line intersecting the first surface; 
         FIG. 4  is a perspective view of the planes associated with the first and second surfaces depicted in  FIG. 3 , along with vectors parallel to the centerline and parallel to the direction of propagation of the ultrasound wave and the angles between the respective vectors and planes; 
         FIG. 5  is a schematic view of two rectangular coordinate systems imposed on a vessel and its associated centerline in three-on-two dimensions looking into the lumen of the vessel; 
         FIG. 6  is a schematic view of the projections of the vessel and centerline onto the coordinate planes of  FIG. 5 ; 
         FIG. 7  is a frequency spectrum of the Doppler output power of the received signal vs. frequency both before and after a Wall filter; 
         FIG. 8  is a frequency spectrum of the Doppler output power of the received signal vs. frequency after a Wall filter along with a graph depicting FFT sampling in the frequency range of the Doppler output power; 
         FIG. 9  is a frequency spectrum of the Doppler output power of the received signal vs. frequency after a Wall filter which intersects the FFT samples of  FIG. 8 ; 
         FIG. 10  is a diagrammatic view of the vessel of  FIG. 2  with a superimposed diagrammatic representation of volume flow within the vessel in the vicinity of the centerline; 
         FIG. 11  is a diagrammatic view of a blood vessel with a stenosis; 
         FIG. 12  is a diagrammatic view of the vessel of  FIG. 2  with a superimposed diagrammatic representation of a measure of “translucency” within the vessel; 
         FIG. 13  is a diagrammatic view of an image of a vessel composed of multiple subsections; 
         FIG. 14  is a diagrammatic view showing how a centerline can be used to bisect or divide a vessel in two; and 
         FIG. 15  depicts a block diagram of a system that implements the method in accordance with an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     With reference to  FIGS. 2 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           ,         
and the mode is the value x p  for which
 
     
       
         
           
             
               
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     Now referring to  FIGS. 3 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  FIGS. 5 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 00/72756 (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 
               v   =       c     2   ⁢     f   0         ⁢   f       ,         
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  FIGS. 3 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: 
     
       
         
           
             
               
                 
                   
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     With reference to  FIGS. 7 , as is customary in Modern Doppler ultrasound, p plotted vs. frequency in  FIG. 7 , 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  FIG. 7 ), the resulting plot of p vs. frequency is shown in  FIG. 8 , 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: 
     
       
         
           
             
               
                 
                   
                     
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     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: 
     
       
         
           
             
               
                 
                   
                     
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     Since v is merely the radial component of velocity, it is desirable to calculate
 
s(x,y,z,t) “4-D True Velocity Flow”  (10)
 
     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
 
 f   n =( PRF/ 2π)angle( F )   (11)
 
and
 
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  FIG. 10 , 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  FIGS. 8–10 . 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, p i  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 
                   ) 
                 
               
             
           
         
       
     
     the Doppler frequency per frequency bin is
 
 f   i   =PRF×i/N;    (17)
 
     and the velocity in a frequency bin is 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       i 
                     
                     = 
                     
                       
                         
                           c 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               0 
                             
                           
                         
                         ⁢ 
                         
                           f 
                           i 
                         
                       
                       = 
                       
                         
                           PRF 
                           N 
                         
                         ⁢ 
                         
                           c 
                           
                             2 
                             ⁢ 
                             
                               f 
                               0 
                             
                           
                         
                         ⁢ 
                         i 
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     The power-velocity integral is computed as 
     
       
         
           
             
               
                 
                   
                     F 
                     1 
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           - 
                           
                             N 
                             2 
                           
                         
                         - 
                         1 
                       
                       
                         
                           + 
                           
                             N 
                             2 
                           
                         
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       i 
                       × 
                       
                         p 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     and i≠0. The volume flow is then 
     
       
         
           
             
               
                 
                   
                     
                       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  FIG. 3 , 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  FIGS. 11–14 , 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  FIG. 15 , 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  FIGS. 7–9 . 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.