Ultrasonic system and method for measurement of fluid flow

A system and methods for measuring the volume flow of fluid in an enclosed structure with an ultrasound system is provided. Manual designation of flow angles and areas may not be necessary. Velocities along two or more different scan lines in a first scan plane are obtained to determine an angle of flow within the enclosed structure. A Doppler spectrum parameter is measured from a transmission in a second scan plane substantially perpendicular to the first scan plane. Volume flow is calculated from the flow angle and the parameter. The scan planes are associated with rotating a linear array transducer or holding a multi-dimensional transducer in place. A C-scan method with a linear transducer may also be used.

BACKGROUND OF THE INVENTION
 This invention relates in general to ultrasound systems, and in particular
 to an ultrasound system for measuring fluid volume flow.
 Volume flow measurements may be important for various medical diagnosis.
 Volume flow indicates blockage in blood vessels and the performance of
 diseased or transplanted organs. For example, changes in the blood flow
 out of a kidney over time may be determined. Other examples of clinical
 application of volume flow measurements include: blood flow through
 shunts, blood flow to or from transplanted or diseased organs, umbilical
 cord and uterine artery flow, flow through various arteries and vessels,
 the blood flow in the brachial artery before and after artificially
 induced ischemia, flow through mitral aortic tricuspid and pulmonic
 valves, and others.
 Ultrasound systems have been used to estimate volume flow. For example, a
 mean velocity estimate for a small sample volume inside a vessel is
 obtained from spectral Doppler information. An angle of flow is estimated
 from a user input angle. The user also manually outlines the vessel's
 cross section to obtain an estimate of area. The mean velocity, area and
 the appropriate trigonometric function of the Doppler angle are multiplied
 to obtain a flow estimate. However, the various manual tracings and
 estimations are laborious and prone to inaccuracies due to human error.
 Furthermore, obtaining the mean velocity from one sample volume may not
 accurately represent the true mean velocity across the entire vessel.
 In another ultrasound technique for measuring volume flow, a high spatial
 resolution image is used to measure the flow profile across a vessel. The
 individual estimates of flow from each volume cell within a vessel are
 summed together to obtain the total volume flow. However, due to non-ideal
 ultrasound beam profiles, the information from one volume cell may
 duplicate, in part, another volume cell. Furthermore, this technique
 assumes that flow is parallel to the vessel or requires user estimation of
 the flow angle.
 In yet another ultrasound technique to obtain volume flow, the velocity
 profile across a vessel is assumed to correspond to a particular function,
 such as a parabolic or plug profile. A single velocity estimate is
 obtained at the center of the vessel and used to estimate volume flow. The
 area of the vessel is calculated either manually or assumed to be
 circular. However, the area measurement is prone to human or estimation
 errors, and the actual flow profiles of fluids within a vessel may not
 match the parabolic or plug functions. Furthermore, as discussed above,
 the flow angle is manually entered, making the volume flow calculation
 laborious and error prone.
 In yet another ultrasound technique for measuring volume flow, a cross
 section of a vessel located within a sample volume is insonified using a
 C-scan. See Hottinger U.S. Pat. No. 4,067,236. Therefore, ultrasound
 information is obtained from a plane parallel to the face of the
 transducer. In order to obtain the C-scan information, a fixed one or
 two-element transducer or a two-dimensional array transducer is used. The
 first moment of the C-scan information is calculated, eliminating the need
 to measure the area of the vessel. Measuring data in a plane parallel to
 the face of the transducer also eliminates the need to measure the flow
 direction. However, this technique does not accurately estimate volume
 flow in vessels that run parallel to the face of the transducer.
 Additionally, specialized transducers are required.
 SUMMARY
 The present systems and methods may avoid many of the problems of the prior
 art. The present invention is defined by the following claims, and nothing
 in this section should be taken as a limitation on those claims. By way of
 introduction, the preferred embodiment described below includes a system
 and method for measuring the volume flow of fluid in an enclosed structure
 with an ultrasound system. Velocities along two different scan lines in a
 first scan plane are obtained to determine an angle of flow within the
 enclosed structure. A Doppler spectrum parameter is measured from a
 transmission in a second scan plane substantially perpendicular to the
 first scan plane. Volume flow is calculated from the flow angle and the
 parameter. Some examples of the various aspects of this invention are
 summarized below.
 According to a first embodiment, a first area of the enclosed structure is
 uniformly insonified. A first parameter of a Doppler spectrum responsive
 to the insonification is measured. An angle associated with a direction of
 flow in the enclosed structure is obtained. Volume flow is determined as a
 function of the first parameter and the angle.
 According to a second embodiment, a first parameter of a first Doppler
 spectrum is measured. First and second velocities associated with a first
 area and first and second scan lines at first and second angles,
 respectively, are also measured. A flow angle associated with flow in the
 enclosed structure is determined as a function of the first and second
 velocities and first and second angles. Volume flow is determined as a
 function of the first parameter and the flow angle.
 According to a third embodiment, axial or azimuthal uniform insonification
 of a longitudinal section of the enclosed structure is used to determine
 volume flow. Scatterer calibration and normalization values associated
 with a cross-section of the enclosed structure are determined. The
 enclosed structure associated with a longitudinal cross-section is
 uniformly insonified either axially or azimuthally with a linear
 transducer. Volume flow is determined as a function of the scatter
 calibration and normalization values and the uniform insonification
 information.
 Other embodiments are possible. Further aspects and advantages of the
 invention are discussed below in conjunction with the preferred
 embodiments.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
 The volume flow, as calculated by the preferred embodiments discussed
 below, is graphically represented in FIG. 1. An enclosed structure 20,
 such as an artery, vessel, shunt, chamber, or other bodily structure, is
 shown. An arbitrary surface, S, 22 is shown inside the enclosed structure
 20. An area element, dS, 24 is shown on the arbitrary surface 22. A vector
 26 normal to the arbitrary surface 22 at the area element 24 is also
 shown. The velocity of scatters, u(r), at any location on the arbitrary
 surface 22, such as the area element 24, is shown as vectors 28. The
 cross-sectional area of the enclosed structure 20 perpendicular to the
 axis of the enclosed structure 20 is designated as A.sub.O. The volume
 flow, Q, through the arbitrary surface 22 is given by:
EQU Q=.intg..sub.S u(r).multidot.dS=A.sub.0 u.sub.0, (1)
 where u.sub.0 is the mean velocity of scatters in a plane perpendicular to
 the axis of the enclosed structure 20, such as the plane defined by the
 smallest cross sectional area. Equation (1) is based on the assumption
 that there is no flow through the walls of the enclosed structure, and the
 flow passing through the arbitrary surface 22 exits through the cross
 sectional area A.sub.0.
 The preferred embodiments described below are designed to provide accurate
 measurements of volume flow. The measurements are based on the
 three-dimensional orientation of the vessel in relation to a transducer.
 Velocities associated with two scan lines at different angles in a first
 scan plane are obtained. A first moment (a parameter) of a Doppler
 spectrum associated with uniform insonification in a second scan plane are
 also obtained. The first scan plane is oriented to maximize the displayed
 area of the enclosed structure in the longitudinal view, and the second
 scan plane is oriented to minimize the width of the displayed area of the
 enclosed structure in the lateral view (the first scan plane is
 substantially perpendicular to the second scan plane). An angle of flow in
 the enclosed structure is determined as a function of the velocities.
 Volume flow is determined from the angle of flow and the parameter
 associated with the second scan plane.
 A. Systems
 Various ultrasound systems are capable of calculating the flow measurement
 as described above and detailed below. For example, an ultrasound system
 capable of obtaining Doppler velocity data along non-colinear scan lines,
 obtaining Doppler spectrum parameters and processing the data below may be
 used.
 One embodiment of an ultrasound system for calculating volume flow is shown
 generally at 100 in FIG. 2. The system 100 includes a data path comprising
 a transducer 102, a beamformer 104, a signal processor (estimator) 106, a
 scan converter 108 and a display device 110. A processor 112 is connected
 to the data path, preferably at least to the signal processor 106.
 The transducer 102 is any of various transducers, such as a linear or
 multi-dimensional array of piezoelectric elements. The beamformer 104 is
 constructed as known in the art. The beamformer 104 may comprise separate
 transmit and receive beamformers. The beamformer 104 produces excitation
 signals for each or a subset (i.e. a sub-aperture) of the elements of the
 transducer 102. The excitation signals are processed, such as by applying
 a relative delay or amplitude, to focus ultrasonic waveforms along one or
 more scan lines 114, 116. The scan lines may be at any of various angles
 relative to the transducer 102 and originate at various locations along
 the transducer 102. The plane defined by two or more scan lines or any
 linear combination of transducer elements comprises a scan plane.
 The acoustic waveforms are reflected off of structures within a body,
 including moving fluid within an enclosed structure, as echoes. The echoes
 are detected by the elements of transducer 102 and provided as voltage
 signals to the beamformer 104. The beamformer 104 sums the voltage signals
 and outputs ultrasound data representative of structures along the one or
 more scan lines.
 The signal processor (estimator) 106 is a construction known in the art,
 such as a Doppler digital signal processor or filtering device for
 providing Doppler estimates from the representative ultrasound data. The
 signal processor 106 may also include a parallel B-mode processor or
 spectral Doppler processor. A clutter filter may also be included. The
 signal processor 106 estimates the Doppler velocity, energy, and/or
 variance for each of various points or ranges along each scan line. The
 estimates and any B-mode information may be stored in a memory, such as a
 CINE memory.
 The estimates, such as Doppler velocity, and/or any B-mode information
 representing areas in the scan plane or along a scan line are provided to
 the scan converter 108. The scan converter 108 is a processor or dedicated
 hardware for formatting the estimates into a Cartesian coordinate system
 for display.
 The display device 110 is a monitor, such as a color monitor. The scan
 converted ultrasound data representing the scan plane is displayed on the
 display device 110 as a B-mode intensity, Doppler velocity, Doppler
 energy, Doppler variance or combination image.
 The processor 112 is a digital signal processor or multi-purpose processor
 for calculating the volume flow from the Doppler velocity estimates.
 Alternatively, other hardware, such as an accumulator, summer and buffer
 data path, may calculate the volume flow. The processor 112 obtains
 information, such as Doppler velocities and Doppler spectrum parameters.
 The processor 112 also obtains or stores orientation information
 corresponding to the various scan lines. The information includes values
 for calculating volume flow as discussed below.
 The calculated volume flow quantity, other quantities, waveform and/or
 waveforms are provided to the display device 110. The calculated
 information is displayed with or separate from the B-mode or Doppler
 image. Preferably, the calculated information is displayed in real-time.
 The processor 112 may also provide control instructions to various
 components of the system 100. For example, the processor 112 controls the
 beamformer 104 to generate acoustic waveforms along scan lines 112, 114 in
 certain directions and scan formats. Alternatively, a separate processor
 provides control of the system 100.
 The processor 112 or another processor may also coordinate user input.
 Thus, the user designates a region of interest on a displayed ultrasound
 image. The region of interest corresponds to pixels associated with the
 enclosed structure for calculation of volume flow. Alternatively, the
 region of interest is identified by the system 100 by applying one or more
 thresholds to the Doppler estimates or B-mode information as discussed
 below. The identified regions, regardless of the process of
 identification, are stored in the processor 112, another processor or a
 memory separate from the processor 112. Alternatively, the user configures
 the scan plane and associated image to be associated with only the region
 of interest.
 B. Volume Flow Determination
 Using one of the systems described above or another ultrasound system, the
 volume flow is determined. Referring to FIG. 3(a), a portion of the above
 described method for determining volume flow is graphically represented. A
 transducer 30 is positioned so that the azimuthal axis is perpendicular to
 an axis 36 of an enclosed structure 32, such as a vessel. For this
 arrangement, the instantaneous volume flow is given by:
 ##EQU1##
 where c is the speed of sound, f.sub.c is the center frequency, .DELTA. is
 the thickness of the intersection 38, .sigma. is the density of moving
 scatterers, K includes a scattering coefficient and the path attenuation
 effects, M.sup.1 is the first moment of the Doppler spectrum and .DELTA.
 is the Doppler angle (i.e. the angle between the vessel axis 36 and an
 intersection 38 or a scan plane 40). M.sup.1 may be measured; f.sub.c is
 known or determined from the transmission of the ultrasonic waveform for
 measuring M.sup.1 ; and .sigma., K, .DELTA. and .alpha. are determined
 from other measurements. The discussion below details obtaining
 information for these variables.
 1. Angle of Flow(.alpha.)
 One of multiple techniques determine the angle of flow or Doppler angle
 .alpha.. For example, the angle is manually determined. A user may place
 calipers or other markers to designate the axis 36 on a B-mode, Doppler or
 other image associated with a scan plane. The angle is calculated from the
 axis designation and the scan plane position.
 In a preferred example, the angle is determined automatically from
 measurements.
 Automatic determination may be more accurate than manual determination. For
 automatic determination, the user places the transducer 102 on a patient's
 skin and images an enclosed structure. Preferably, a Doppler mode is used
 for imaging but other modes, such as B-mode, may be used.
 Referring to FIGS. 3(b) and 5, a method of one embodiment for automatically
 determining the angle or direction of volume flow is graphically
 represented. The transducer 30 is oriented to image an enclosed structure
 32. A B-mode, Doppler or other image is displayed to the user. Preferably,
 the user maximizes the longitudinal cross section of the displayed
 enclosed structure 32. By positioning the transducer 30, the user orients
 a scan plane 34 associated with the displayed image to be generally
 parallel with an axis 36 of the enclosed structure 32. Preferably, the
 scan plane 34 intersects the axis 36. For curving enclosed structures 32,
 the longitudinal cross-section is maximized for the relevant section (ie.
 near the desired measurement position).
 After positioning the transducer 30, the user selects an area 39 within the
 enclosed structure 32. Preferably, the user places a marker or cursor on
 the image. Other techniques for selecting the area 38 may be used, such as
 automatic system selection, such as based on thresholds. After placing the
 marker, the user activates transmissions of ultrasonic waves for flow
 angle determination associated with the volume flow calculation. For
 example, the user depresses a button on a keyboard or touch screen.
 In response to activation, the system 100 (FIG. 2) determines the flow
 angle or angle representing the direction of flow within the enclosed
 structure 32. Echo data along at least two scan lines 42 and 44 and
 associated with the area 39 (ie. the range or ranges along each scan line
 42 and 44 throughout the enclosed structure 32) is obtained.
 The scan lines 42 and 44 are at different angles, .beta..sub.1 and
 .beta..sub.2, from the face of the transducer 30 (see FIG. 5). To provide
 the different angles, the transducer 30 is divided into subapertures A and
 B. More subapertures may be used. The subapertures may overlap (i.e. use
 some or all of the same transducer elements).
 Using Doppler velocity processing, Doppler velocities (ie. mean velocities)
 .nu..sub.1 and .nu..sub.2 of the echo data at the area 39 along each scan
 line 42 and 44 are measured. In alternative embodiments, the mean
 velocities are calculated using autocorrelation estimation, fast-Fourier
 transform or cross correlation algorithms.
 The Doppler velocities and scan line angles determine the flow angle. For
 example, simultaneous pulse-chasing is used. This multiple pulse chasing
 technique is disclosed in U.S. Pat. No. 5,522,393. One ultrasonic wave is
 transmitted from one of the subapertures A or B or another aperture.
 Reception processing is performed substantially simultaneously for echoes
 associated with each scan line 42 and 44 (i.e. subapertures A and B are
 used to receive echoes at the same time). The Doppler velocities of moving
 scatterers at the area 39 are equated as represented by:
 ##EQU2##
 Solving for the flow angle, .alpha., equation (3) becomes:
 ##EQU3##
 The flow angle is determined by measuring the Doppler velocities along at
 least the scan lines 42 and 44 using equations (4) and (5). The scan lines
 are associated with known angles relative to the transducer 30. The
 Doppler velocities may be measured and the flow angle determined by
 multiple acquisitions and averaged.
 In another example, sequential firing is used to determine the flow angle.
 The subapertures, such as subapertures A and B, are each used to
 sequentially transmit ultrasound waves and receive echoes. For example,
 transmission and reception events associated with each subaperture are
 interleaved. The Doppler velocities are equated as represented by:
 ##EQU4##
 Solving for the flow angle, equation (6) becomes:
 ##EQU5##
 The flow angle is determined by measuring the Doppler velocities along at
 least the scan lines 42 and 44 using equations (7) and (8). The Doppler
 velocities may be measured or the flow angle determined multiple times and
 averaged (e.g. measurements taken over a period of time, such as a
 fraction of a second, one or more seconds, or one or more heart cycles).
 As yet another alternative, a plurality of ultrasound beams are transmitted
 substantially simultaneously. A method and system for such transmissions
 is described in U.S. Pat. No. 5, 675,554. The echo signals are received
 substantially simultaneously along a plurality of scan lines associated
 with the transmitted beams.
 Simultaneous pulse-chasing May be substantially faster for determining
 volume flow than sequential firing. Only one transmit event is used for
 simultaneous pulse-chasing as compared to one transmit event for each scan
 line for sequential firing. Simultaneous pulse-chasing is more likely to
 avoid misregistration or other problems associated with movement as a
 function of time.
 2. Density of Scatterers and Scatter/Coefficients/Path Attenuation Effects
 (.sigma. and K)
 .sigma. and K are determined from at least one transmission associated with
 a different transducer position than the position for determining the flow
 angle. Referring to FIGS. 3(a), 4(a) and 4(b), the transducer 30 is
 rotated substantially 90 degrees. The scan plane 40 is substantially
 perpendicular to the scan plane 34 used for determining the flow angle.
 For rotation of the transducer 30, the cross hair of the shaded region
 (intersection 38) in FIG. 3(a) preferably corresponds to the area 39 of
 FIG. 3(b). The amount of compression applied by the transducer 30 for both
 longitudinal and transversal views is preferably the same. To provide
 similar compression, the user places a cursor to designate a particular
 point in the imaged structure, such as the center or a near-field portion
 of the enclosed structure 32. The distances from the transducer 30 to the
 cursors are kept constant throughout continued imaging, such as between
 rotations of the transducer 30.
 The transducer 30 is positioned transverse to the enclosed structure 32 as
 discussed above, but the width of the area displayed for the enclosed
 structure 32 is minimized on a displayed image. Minimization may result in
 a rotation of less than 90 degrees, and the term substantially
 perpendicular covers both minimization or rotation close to 90 degrees,
 without minimization. For minimization, the width of the displayed area of
 the enclosed structure 32 is minimized by the user or the system 100 (FIG.
 2). An automated calculation of area based on border detection may be
 displayed or used by the system 100 to aid minimization or maximization as
 discussed above.
 After minimization or rotation of the transducer 30, the user designates
 the enclosed structure 32 as discussed above. For example, the user
 designates an area, A.sub.c, completely within the enclosed structure 32.
 After designation, the user activates determination of volume flow.
 In response to the activation, the system 100 (FIG. 2) calibrates for
 .sigma. and K. As shown in FIG. 4(b), a beam 50 with a known width and
 spatial extent is transmitted, and corresponding echoes are received. The
 area of beam 50 is not necessarily small, but is preferably enclosed by
 the enclosed structure 32. The echoes are processed to isolate information
 associated with the area, A.sub.c, 52 (e.g. one range gate). A zeroth
 moment, M.sup.0.sub.c, of a Doppler spectrum associated with the isolated
 echo information (i.e. area 52) is calculated. If the area 52 is
 completely within the enclosed structure 32, then:
 ##EQU6##
 Combining equations (9) and (2), the volume flow is calculated as:
 ##EQU7##
 In summary, .sigma. and K are calibrated or accounted for by measuring the
 zeroth moment (i.e. a Doppler parameter) of the known area 52. This
 measurement may be obtained over different time intervals to account for
 vessel and flow plusitility.
 3. First Moment Parameter (M.sup.1)
 After calibration and determination of the flow angle, instantaneous volume
 flow is calculated by measuring the first moment (i.e. a Doppler
 parameter). To determine the first moment, the enclosed structure 32 is
 uniformly insonified. Echo information is received. The first moment is
 measured from the Doppler spectrum of the echo information associated with
 a range substantially covering the enclosed structure 32.
 As represented by FIG. 4(a), a beam 54 associated with a wide beam profile
 in the scan plane is transmitted. Preferably, the beam 54 substantially
 covers the enclosed structure 32. For example, points of the beam profile
 -6 dB from the peak (the dashed beam boarders) lay outside of the enclosed
 structure 32. Substantially the entire enclosed structure 32 is uniformly
 insonified. Preferably, for ranges corresponding to the enclosed structure
 32, the beam 54 does not intersect any moving fluids or structures not
 associated with the enclosed structure 32.
 The width and range of the ultrasound beam for uniform insonification is
 determined as a function of user input or by automatic methods. Either the
 user designated a width or designates a point in the enclosed structure
 32. If the user designates a point, the system 100 (FIG. 2) determines an
 area for insonification associated with fluid flow. The processor 112
 (FIG. 2) applies selection criteria to determine whether there is valid
 fluid flow data associated with each pixel or sample volume. Doppler or
 B-mode values only or in combination are used to determine valid fluid
 flow. For example, if the amplitude of the B-mode signal associated with a
 pixel is high, a Doppler value for such pixel may not be a reliable
 indication of fluid flow. A low B-mode value and a high Doppler value
 indicates fluid flow. If the information corresponds to fluid flow, then
 the pixel is included in the area to be uniformly insonified. The width is
 determined from the area.
 The profile of the beam 54 is widened using various methods, such that the
 enclosed structure is uniformly insonified. For example, (1) a sinc
 apodization function is used to provide a wide rectangular beam profile
 pattern; (2) the aperture width associated with the beam 54 is
 appropriately adjusted; (3) low frequencies are used with the beam 54; or
 (4) the beam 54 is defocused, such as using appropriate delays or moving
 the focus nearer or beyond the enclosed structure 32. All four methods may
 be used together, and other methods for providing a wide beam profile may
 be used.
 The Doppler spectrum associated with the echo information is computed. The
 power returned by scatterers having Doppler shifts between a first
 frequency f.sub.d and a second frequency, f.sub.d +df.sub.d, is
 represented by the function P(f.sub.d)df.sub.d. M.sup.0 and M.sup.1, the
 zeroth and first moments of the Doppler spectrum, are represented by:
EQU M.sup.0 =.intg.P(f.sub.d)df.sub.d, and (11)
EQU M.sup.1 =.intg.f.sub.d P(f.sub.d)df.sub.d, respectively. (12)
 Using the first moment associated with the beam 54, the zeroth moment and
 area associated with the calibration beam 50, and the flow angle, volume
 flow is calculated.
 After determining the instantaneous volume flow as discussed above, the
 quantity is displayed in real-time to the user or used to generate a
 waveform of volume flow as a function of time. The instantaneous volume
 flow calculation may be repeated in real time. The flow angle and
 calibration information (i.e. .alpha., A.sub.c and M.sup.0.sub.c) are
 preferably used for each volume flow calculation during each imaging
 sequence, but may be measured for each or a subset of all the volume flow
 calculations. Using the same flow angle and calibration information, the
 enclosed structure is repetitively uniformly insonified and new first
 moments are calculated. The new first moments are used to calculate new
 volume flow quantities. An average of the instantaneous volume flow
 quantities may also be displayed. Other quantities such as the area,
 Doppler moments or angle may be displayed.
 C. Multi-Dimensional Transducers
 In alternative embodiments, multi-dimensional transducers are used. For
 example, I beam, T beam, + beam, 1.5 or 2 dimensional transducers are
 used. These transducers include elements arrayed on a plane (i e. arrayed
 in two dimensions). For a description of an I beam transducer, see U.S.
 application Ser. No. 08/916,163, filed Aug. 21, 1997. The I beam
 transducer generally includes elements in the plane arrayed in an I
 pattern. As shown in FIG. 6(a), three scan planes 70, 72, and 74
 associated with the I pattern may be generated. As shown in FIGS. 6(b) and
 6(c), two scan planes 76 and 78 associated with the T and + patterns,
 respectively, may be generated. Transducers with other element patterns
 may be used. For 1.5 or 2 dimensional transducers, any of the various scan
 plane formats or patterns may be generated.
 Using multi-dimensional transducers, the user holds the transducer in one
 position for calculating volume flow. One scan plane, such as scan planes
 72 or 76, is used for determining the flow angle as discussed above. For
 example, the user rotates the multi-dimensional transducer so that the
 longitudinal view of the enclosed structure 32 associated with one scan
 plane 72 or 76 is maximized (e.g. view B). Once positioned, another scan
 plane (e.g. view A), such as one of scan planes 70, 74 or 78, is
 substantially perpendicular to the scan plane 72 or 76 associated with
 maximization. Alternatively, the user rotates the multi-dimensional
 transducer so that the width of the transversal view of the enclosed
 structure 32 in one scan plane 70, 74 or 78 is minimized (e.g. view B).
 Without rotating the transducer, the scan plane 70, 74 or 78 associated
 with view A is used to calibrate and measure the first moment as discussed
 above. For the I beam transducer, one or both of the scan planes 70 and 74
 associated with view A are used to calculate volume flow. If both are
 used, then the resulting quantities may be averaged or displayed
 separately.
 Using a two-dimensional transducer, the scan planes associated with views A
 and B may be independently minimized or maximized, respectively.
 Therefore, the scan plane associated with view A may be at an angle less
 than 90 degrees to the scan plane associated with view B.
 Using a multi-dimensional transducer, the volume flow may be calculated
 without minimization or maximization. Preferably, a two-dimensional
 transducer 80 is used as shown in FIG. 7. The transducer is positioned to
 image an arbitrary cross-section of the enclosed structure 32. The
 multi-dimensional transducers allow measurement of the orientation of the
 axis 36 in three-dimensions.
 The orientation is determined by transmissions along three or more scan
 lines 82. The three scan lines 82 are associated with different positions
 or three-dimensional orientations. The scan lines 82 intersect at an
 volume 86 within the enclosed structure. For example, three subapertures
 84 on the two-dimensional transducer 80 are used to generate the
 ultrasonic waves along the scan lines 82 in response to user designation
 of the volume 86. The system 100 (FIG. 2) determines appropriate
 subapertures and scan line orientations in response to the designation of
 the volume 86. For I beam, T beam and + beam transducers, the transducer
 is positioned so that volume 86 is located along an intersection of
 perpendicular scan planes.
 Volume flow is calculated as a function of the flow orientation in
 three-dimensions and uniform insonification of the enclosed structure as
 discussed above. The flow orientation or angle in three-dimensions is
 calculated as a function of the orientation of the scan lines 82 and mean
 velocities associated with each of the scan lines 82. In the case of three
 scan lines 82, w.sub.0, w.sub.1, and w.sub.2 represent unit vectors
 defining the orientation of the scan lines 82, and u represents a unit
 vector defining the orientation of the axis 36. For simultaneous pulse
 chasing (i.e. transmitting along scan line A0 and receiving along scan
 lines A0, A1, and A2), the dot product, h.sub.i, of w.sub.i.multidot.u,
 where i=0, 1 . . N (the number of scan lines minus 1) is used to represent
 the relationship between the scan lines and velocities:
 ##EQU8##
 where .nu..sub.0, .nu..sub.1, .nu..sub.2 and are the mean velocities
 measured along the scan lines 82 for the volume 86. The mean velocities
 are obtained using either simultaneous or sequential transmissions as
 discussed above. Defining:
 ##EQU9##
 the enclosed structure 32 orientation is given by:
 ##EQU10##
 where,
EQU g=A
 Using equations (18) and (19), the vessel orientation u is determined. The
 Doppler angle or flow angle is given by:
EQU cos.alpha.=u.multidot.w (20)
 where w is the orientation of a scan line, such as one of scan lines 82, a
 different scan line or a combination of scan lines (ie. average). Based on
 the Doppler angle and at least one uniform insonification of the enclosed
 structure, the volume flow is determined.
 D. Alternate Volume Flow Determination
 Using the system 100 (FIG. 2) and many of the techniques discussed above,
 volume flow as defined in FIG. 1 may be calculated in an alternate method.
 The method described above includes determining an angle of the enclosed
 structure 32 associated with a longitudinal image and then determining
 volume flow from data associated with a cross-sectional image. In the
 alternate method, calibration and normalization steps are first performed
 and are associated with a cross-sectional image, and then volume flow is
 calculated from data associated with a longitudinal image.
 Referring to FIG. 8, volume flow is calculated from data associated with
 the longitudinal image using axial insonification (FIG. 8(a)), azimuthal
 insonification (FIG. 8(b)) or a combination thereof. Uniform
 insonification is preferably used for both axial and azimuthal
 insonification. For axial insonification, a linear transducer 200
 transmits a beam 202 with a narrow beam width and receives echo signals.
 The echo signals are associated with a range gate size large enough to
 include the entire enclosed structure 32. Data representing the area 204,
 A.sub.y, with a width .DELTA. is obtained. For azimuthal insonification,
 the linear transducer 200 transmits a beam 206 with a wide beam width
 substantially covering the enclosed structure 32. The echo signals are
 associated with a small range gate, such as .DELTA.. Data representing the
 area 208, A.sub.x, is obtained.
 The volume flow is determined from the axial and azimuthal insonification
 data from the following equations:
 ##EQU11##
 respectively. Equation 22 is independent of the flow angle, .alpha.. For
 equation 21, the flow angle is determined as discussed above. .sigma. and
 K are determined as discussed below. All other quantities in equations 21
 and 22 are known as discussed above.
 If the enclosed structure 32 is or is close to parallel to the linear
 transducer 200, the axial volume flow calculation (i.e. equation 21)
 provides accurate estimations, and the azimuthal volume flow calculation
 (i.e. equation 22) provides less accurate estimations. Conversely, if the
 enclosed structure 32 is or is close to perpendicular to the linear
 transducer 200, the azimuthal volume flow calculation provides accurate
 estimations, and the axial volume flow calculation provides less accurate
 estimations. Less accurate estimations include values associated with
 noise. Preferably, the system 100 automatically selects the insonification
 technique associated with the highest accuracy estimates. For example, the
 multiple sub-aperture simultaneous pulse chasing method or the sequential
 firing method described above is used to determine the orientation of the
 enclosed structure 32. If the enclosed structure 32 is oriented closer to
 parallel than perpendicular to the transducer 100, axial insonification is
 used. If the enclosed structure 32 is oriented closer to perpendicular
 than parallel to the transducer 100, azimuthal insonification is used.
 Alternatively, the user manually tilts the transducer 100 to avoid
 parallel or perpendicular imaging, such as rotating the transducer 100
 around the azimuthal axis while imaging the cross-section of the enclosed
 structure 32.
 To further improve accuracy of the volume flow estimates, the system 100
 makes multiple measurements. Referring to FIG. 9, the multiple
 measurements are preferably associated with different angles of
 insonification. For example, the beams are transmitted along scan lines
 210 at different angles, .beta., to the line normal to the transducer 200.
 For azimuthal volume flow estimation, equation 22 is used. For axial
 volume flow estimation, equation 21 becomes:
 ##EQU12##
 The angle .beta. is changed and a corresponding number of estimates are
 obtained. Simultaneous pulse chasing may be used for measuring the first
 moment at different angles .beta.. The estimates are combined to determine
 volume flow. For example, the estimates are averaged or weighted and
 averaged. Furthermore, estimates associated with axial estimation may be
 combined with estimates associated with azimuthal estimation.
 Before measuring the first moment as discussed above and for improved
 accuracy, a normalization factor, .kappa., is determined. The transducer
 is first positioned to image the cross-section of the enclosed structure
 32 (i.e. transverse to the enclosed structure 32) as shown in FIGS. 4 and
 10(a). Preferably, the user positions a region of interest or box 212
 around the enclosed structure. The box 212 is preferably sized to be as
 small as possible and include all of the enclosed structure 32. In
 alternative embodiments, the region of interest is determined
 automatically. The user or the system 100 also may place a icon or cursor
 214 at the center of the enclosed structure 32 for guiding the beams as
 discussed below.
 The normalization factor, .kappa., compensates for axial and azimuthal
 insonification where the elevation thickness of the beam pattern does not
 completely cover the enclosed structure 32. The elevation thickness is
 represented as the portion of area 204 or 208 along the z dimension in
 FIG. 8. Referring to FIG. 4(a), the beam 54 with a width encompassing the
 enclosed structure 32 is generated. The range gate size preferably also
 encompasses the enclosed structure 32. The first moment, M.sup.1.sub.w, of
 the wide beam 54 is calculated. Referring to FIG. 4(b), the beam 50 with
 an azimuthal width the same as the elevation thickness throughout the
 enclosed structure 32 is generated. The range gate size preferably also
 encompasses the enclosed structure 32. The first moment, M.sup.1.sub.n, of
 the narrow beam 50 is calculated. Assuming that the flow through the
 enclosed structure 32 represented by FIG. 4 is the same as the flow
 through A.sub.y or A.sub.x of FIG. 8, the normalization factor is:
 ##EQU13##
 Using the normalization factor, equations 21 and 22 are represented as:
 ##EQU14##
 respectively.
 While the transducer is in the cross-sectional image position, .sigma. and
 .kappa. are also calibrated. Referring to FIG. 4(b), the beam 50 with a
 known width is transmitted, and corresponding echoes are received. The
 echoes are processed to isolate information associated with the area 52,
 A.sub.c, (e.g. one range gate). The zeroth moment, M.sup.0.sub.c, of a
 Doppler spectrum associated with area 52 is calculated. If the area 52 is
 completely within the enclosed structure 32, then:
 ##EQU15##
 where .DELTA..sub.c is the elevation thickness associated with the beam 50.
 The zeroth moment may be calculated from echoes associated with the narrow
 beam used for determining the normalization factor, but with a different
 range gate size.
 Using equations 25, 26 and 27:
 ##EQU16##
 The quantities in equations 28 and 29 are known or measurable. After
 measuring quantities associated with the normalization factor and .sigma.
 and K, measurements associated with the axial and/or azimuthal
 insonification are made and volume flow is estimated.
 For estimating volume flow with axial or azimuthal insonification, the
 transducer 200 is rotated approximately 90.degree. around the y-axis (see
 FIG. 8). Referring to FIG. 10, the image associated with the transducer
 position changes from the cross-section shown in FIG. 10(a) to the
 longitudinal view shown in FIG. 10(b). Volume flow is then estimated as
 discussed above.
 In one embodiment, the user presses a button or indicates that the
 transducer 200 has been rotated. A horizontal line 240 is placed in the
 image 242 by the system 100 and is at the same depth as the cursor 214.
 The user maximizes the size of the enclosed structure 32 by moving the
 transducer 200 in the elevation dimension. The user then presses a button
 or indicates completion of the placement of the transducer 200. The system
 100 generates a cursor 244 on the image 242. The user positions the cursor
 244 approximately at the center of the enclosed structure 32 along the
 horizontal line 240. Completion of placement of the cursor 244 is
 indicated by the user. The system 100 then determines the angle of flow at
 the cursor 244 and determines which insonification technique, axial or
 azimuthal, may provide the most accurate estimates of volume flow. The
 system 100 generates a vertical line 246 for axial insonification or
 highlights the horizontal line 244 for azimuthal insonification. The user
 then sizes the vertical or horizontal line 244 or 246 to extend just
 beyond the enclosed structure 32 and presses a button to begin axial or
 azimuthal insonification. Based on the vertical or horizontal line 244 or
 246, the system 100 generates one or more uniform transmit beams for axial
 or azimuthal insonification, and estimates volume flow.
 Instantaneous volume flow through many enclosed structures 32 varies in a
 periodic fashion with the cardiac cycle. Furthermore, the cross-section
 dimensions of the enclosed structure 32 may change throughout the cardiac
 cycle. The normalization factor, .sigma., and K estimated at one instant
 in time may not be suitable for estimation of volume flow at all times
 throughout the cardiac cycle. Preferably, each of these factors is
 determined at a number of different times during a cardiac cycle. Each
 different factor and corresponding estimates of volume flow are registered
 with a triggered time stamp, such as from an ECG trigger. Alternatively, a
 waveform of M.sup.1.sub.n, M.sup.1.sub.w, M.sup.1, a combination thereof
 or other measured parameters that vary as a function of the cardiac cycle
 is used to designate different times throughout the cardiac cycle. Volume
 flow is estimated using the normalization factor associated with the same
 or similar portions of the cardiac cycle.
 A waveform representing volume flow is preferably generated as shown in
 FIG. 10(e). Other parameters, such as stroke volume, heart rate, vessel
 area, Doppler moments and average volume flow, are also preferably
 displayed.
 While the invention has been described above by reference to various
 embodiments, it will be understood that different changes and
 modifications can be made without departing from the scope of the
 invention. For example, dedicated hardware or multi-processors may be used
 for any of the various calculations. Additionally, differing formulas may
 be used to obtain the same or similar quantities.
 It is therefore intended that the foregoing detailed description be
 understood as an illustration of the presently preferred embodiments of
 the invention, and not as a definition of the invention. It is only the
 following claims, including all equivalents, that are intended to define
 the scope of the invention.