# Patent

## Title
Method and system for analyzing cardiovascular sounds

## Abstract

A method and system for analyzing sounds originating in at least a portion of an individual's cardiovascular system. N transducers, where N is an integer, are fixed on a surface of the individual over the thorax. The ith transducer is fixed at a location xi and generates an initial signal P(xi,i) indicative of pressure waves at the location xi, for i=1 to N. the signals P(xi,t) are processed so as to generate filtered signals in which at least one component of the signals P(xi,t)not arising from cardiovascular sounds has been removed. The filtered signals may be used for generating an image of the at least portion of the cardiovascular system.

## Background
This application claims the benefit of prior U.S. provisional patent application No. 60/474,595 filed Jun. 2, 2003, the contents of which are hereby incorporated by reference in their entirety.


FIELD OF THE INVENTION
This invention relates to medical devices and methods, and more particularly to such devices and methods for analyzing body sounds.
BACKGROUND OF THE INVENTION
Body sounds are routinely used by physicians in the diagnosis of various disorders. A physician may place a stethoscope on a person's chest or back and monitor the patient's breathing or heartbeat in order to detect adventitious (i.e. abnormal or unexpected) lung or heartsounds. The identification and classification of adventitious lung or heart sounds often provides important information about pulmonary or cardiac abnormalities.
It is also known to fix one or more microphones onto a subject's chest or back and to record lung sounds. U.S. Pat. No. 6,139,505 discloses a system in which a plurality of microphones are placed around a patient's chest. The recordings of the microphones during inhalation and expiration are displayed on a screen, or printed on paper. The recordings are then visually examined by a physician in order to detect a pulmonary disorder in the patent. Kompis et al. (Chest, 120(4), 2001) disclose a system in which M microphones are placed on a patient's chest, and lung sounds are recorded. The recordings generate M linear equations that are solved using a least-squares fit. The solution of the system is used to determine the location in the lungs of the source of a sound detected in the recordings.
U.S. Pat. No. 5,285,788 discloses an ultrasound tissue imaging system having an acoustic transducer, and imaging means for producing an image of tissue. The system also includes Doppler imaging means to produce a scanned acoustic image of moving tissue that is displayed superimposed on the ultrasound image.
SUMMARY OF THE INVENTION
In the following description and set of claims, two explicitly described, calculable, or measurable variables are considered equivalent to each other when the two variables are proportional to one another.
The present invention provides, in one of its embodiments, a system and method for recording and analyzing cardiovascular sounds produced in the cardiovascular system. The system includes a plurality of N transducers (microphones) configured to be attached to an essentially planar region R of the individual's back or chest over the individual's thorax. Positions in the region R are indicated by two-dimensional position vectors x=(x1,x2) in a two-dimensional coordinate system defined in the planar region R. The ith transducer, for i=1 to N, is fixed at a position xi in the region R and generates a signal, denoted herein by P(xi,t), indicative of pressure waves in the body arriving at xi.
The transducers are typically embedded in a matrix that permits to affix them easily onto the individual's skin. Such a matrix may typically be in the form of a vest or garment for easily placing over the individual's thorax. As may be appreciated, different matrices may be used for differently sized individuals, for different ages, sexes, etc.
The N signals P(xi,t) are processed by signal processing circuitry. In accordance with the invention, the signals are filtered so as to remove one or more components of the signals not arising from cardiovascular sounds (e.g. respiratory tract signals). Cardiovascular sounds are typically in the range of 6 to 45 Hz, while respiratory tract sounds are typically in the range of 100 to 400 Hz. Thus, respiratory sounds may be removed from the signals by filtering the signals, for example, with a band pass filter passing between 15 to 45 Hz.
The N filtered signals (also indicated herein by P(xi,t)) may be processed in order to diagnose the state of the individual's cardiovascular system. This may be via an automatic differential diagnosis in which the results of the processing are compared to functions or parameters previously stored in a database that are known to be indicative of various disorders in the body region.
The filtered signals may also be processed to generate an image of the individual's cardiovascular system. The results of this processing are displayed on a display device, for example using a gray level scale, as demonstrated in the examples below. In the image, anatomic features of the heart such as the atria, ventricles, septal walls, can be observed. The image may be visually or automatically analyzed for the detection of a disorder in the cardiovascular system similar to the analysis of images obtained by other imaging methods such as X-ray (scintigraphy) or ultrasound imaging (echocardiography).
A region or regions of the heart or cardiovascular system in a displayed image that are suspected of including a pathological condition, may be identified in the image, and this may be in a number of ways, for example, by different colors, by different patterns, by way of a written text, and many other ways. The term “pathological condition” refers to any deviation from the normal, healthy condition of the cardiovascular system. This includes murmurs and other hemodynamic irregularities, cardiac effusion, narrowing of blood vessel, and other space containing lesions in the cardiovascular system, etc.
Additionally, a time interval can be divided into a plurality of sub intervals, and each subinterval processed separately. An image of the cardiovascular system for each of these subintervals may then be determined and displayed sequentially on the display device. This generates a movie showing dynamic changes occurring in the cardiovascular system over the time interval. This allows viewing of the systoles and diastoles of the different parts of the heart during the heartbeat.
In a preferred embodiment, the processing involves determining from the N signals an average acoustic energy arising from cardiovascular sounds, denoted herein by {tilde over (P)}(x,t1,t2), at at least one position x in the region R over a time interval from t1 to t2. The term “acoustic energy” at a location is used herein to refer to a parameter indicative of or approximating the product of the pressure and the mass propagation velocity at that location.
In one embodiment, an average acoustic energy over a time interval from t1 to t2 is obtained at a position of one of the microphones using the algebraic expression




  
    
      
        
          
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where xi is the position of the microphone.
In a more preferred embodiment, the processing involves obtaining an average acoustic energy {tilde over (P)}(xi,t1,t2) over a time interval from t1 to t2 at a plurality of positions xi of the microphones, for example using Equation (1), and then calculating {tilde over (P)}(x,t1,t2) at other locations x by interpolation of the {tilde over (P)}(xi,t1,t2) using any known interpolation method.
In a most preferred embodiment, the interpolation is performed to obtain an average acoustic energy {tilde over (P)}(x,t1,t2) at a position x=(x1,x2) in the surface R using the algebraic expression:




  
    
      
        
          
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where g(x, xi,σ) is a kernel satisfying





  
    
      
        
          
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and where xi=(xi1, xi2) is the position of the ith microphone and σ is a selectable parameter.

For example, the kernel




  
    
      
        
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may be used.

The system may optionally contain a display device for displaying the function {tilde over (P)}. The function {tilde over (P)} may be displayed on the display, for example using a gray level scale, as demonstrated in the examples below. A two dimensional graphical representation of the function {tilde over (P)} produces an image of the cardiovascular system. In the image anatomic features of the heart such as the atria, ventricles, septal walls, can be observed. The image may be analyzed for the detection of a disorder in the cardiovascular system similar to the analysis of images obtained by other imaging methods such as X-ray (scintigraphy) or ultrasound imaging (echocardiography).
A region or regions of the heart or cardiovascular system in a displayed image that are suspected of including a pathological condition, may de identified in the image, and this may be in a number of ways, for example, by different colors, by different patterns, by way of a written text, and many other ways. The term “pathological condition” refers to any deviation from the normal, healthy condition of the cardiovascular system. This includes murmurs and other hemodynamic irregularities, cardiac effusion, narrowing of blood vessel, and other space containing lesions in the cardiovascular system, etc.
Additionally, a time interval can be divided into a plurality of sub intervals, and an average acoustic energy {tilde over (P)} determined over the region R for two or more of the sub intervals. An image of {tilde over (P)} for each of these sub intervals may then be determined and displayed sequentially on the display device. This generates a movie showing dynamic changes occurring in the acoustic energy in the body region, over the time interval. For example, transducers may be placed on a person's chest or back and an average acoustic energy {tilde over (P)} determined in accordance with the invention for a plurality of sub intervals over one or more heartbeats. An image can be obtained for each of these sub intervals and displayed sequentially so as to generate a movie showing changes in the acoustic energy of the heart over the heartbeat. This allows viewing of the systoles and diastoles of the different parts of the hear during the heartbeat.
The signals P(xi,t) may also be subjected to additional analysis to detect abnormal heart sounds.
The present invention also provides a program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for determining for at least one time interval, an average acoustic energy function {tilde over (P)} arising from cardiovascular sounds using an algorithm involving at least one signal P(xi,t) indicative of pressure waves at a location xi on a body surface.
The present invention still further provides a computer program product comprising a computer useable medium having computer readable program code embodied therein analyzing sounds in at least a portion of an individual's cardiovascular system, the computer program product comprising:
computer readable program code for causing the computer to determine, for at least one time interval, an acoustic energy function {tilde over (P)} arising from the portion of the cardiovascular system, {tilde over (P)} being determined in algorithm involving at least one signal P(xi,t) indicative of pressure waves at a location xi on a body surface.
The invention thus provides a system for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:

    (One) N transducers, where N is an integer, each transducer configured to be fixed on a surface of the individual over the thorax, the ith transducer being fixed at a location xi and generating an initial signal P(xi,t) indicative of pressure waves at the location xi; for i=1 to N; and
    (Two) a processor configured to receive the signals P(xi,t) and to filter the signals P(xi,t) so as to generate filtered signals in which at least one component of the signals P(xi,t)not arising from cardiovascular sounds has been removed.


The invention thus further provides a system for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:

    (a) N transducers, where N is an integer, each transducer configured to be fixed on a surface of the individual over the thorax, the ith transducer being fixed at a location xi and generating an initial signal P(xi,t) indicative of pressure waves at the location xi; for i=1 to N; and
    (Two) a processor configured to receive the signals P(xi,t) and to generate therefrom an image of the at least portion of the cardiovascular system.


The invention thus further provides a method for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:

    (One) fixing on a surface of the individual over the thorax, N transducers, where N is an integer, the ith transducer being fixed at a location xi and generating an initial signal P(xi,t) indicative of pressure waves at the location xi; for i=1 to N; and
    (Two) processing the signals P(xi,t) so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed.


The invention thus further provides a method for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:

    (One) fixing on a surface of the individual over the thorax, N transducers, where N is an integer, the ith transducer being fixed at a location xi and generating an initial signal P(xi,t) indicative of pressure waves at the location xi; for i=1 to N; and
    (Two) processing the signals P(xi,t) so as to generate therefrom an image of the at least portion of the cardiovascular system.


The invention thus further provides a program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for analyzing sounds originating in at least a portion of an individual's cardiovascular system, comprising: processing N initial signals P(xi,t), where N is an integer, the initial signals being indicative of pressure waves at a location xi; for i=1 to N, so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed.
The invention thus further provides a computer program product comprising a computer useable medium having computer readable program code embodied therein for analyzing sounds originating in at least a portion of an individual's cardiovascular system, comprising: processing N initial signals P(xi,t), where N is an integer, the initial signals being indicative of pressure waves at a location xi; for i=1 to N, so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed.



BRIEF DESCRIPTION OF THE DRAWINGS
In order to understand the invention and to see how it may be carried out in practice, a preferred embodiment will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:
FIG. 1 shows a system for obtaining an analyzing cardiovascular sounds in accordance with one embodiment of the invention;
FIG. 2 shows a flow chart for carrying out a method of analyzing cardiovascular sounds in accordance with one embodiment of the invention;
FIG. 3 shows the locations of transducers on an individual's back for analyzing cardiovascular sounds;
FIG. 4 shows successive frames from a movie of the heart of a healthy individual over one heart beat;
FIGS. 5A and 5A1 show successive frames from a movie of the heart and lungs of an individual over one respiratory cycle.



DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 shows a system generally indicated by 100 for analyzing body sounds in a three-dimensional region of an individual's body in accordance with one embodiment of the invention. A plurality of N sound transducers 105, of which four are shown, are applied to a planar region of the chest or back skin of individual 110. The transducers 105 may be any type of sound transducer, such as a microphone or a Doppler shift detector. The transducers 105 may be applied to the subject by any means known in the art, for example using an adhesive, suction, or fastening straps. Each transducer 105 produces an analog voltage signal 115 indicative of pressure waves arriving to the transducer. The analog signals 115 are digitized by a multichannel analog to digital converter 120. The digital data signals P(xi,t) 125, represent the pressure wave at the location xi of the ith transducer (i=1 to N) at time t. The data signals 125 are input to a memory 130. Data input to the memory 130 are accessed by a processor 135 configured to process the data signals 125. The signals 125 may be denoised by filtering components having frequencies outside of the range of body sounds in the body region, for example, vibrations due to movement of the individual. Each signal 125 may also be subject to band pass filtering so that only components in the signal within the range of cardiovascular sounds are analyzed. The signal may be divided into frequency bands, and each band analyzed separately.
An input device such as a computer keyboard 140 or mouse 145 is used to input relevant information relating to the examination such as personal details of the individual 110. The input device 140 may also be used to input values of the times t1 and t2. Alternatively, the times t1 and t2 may be determined automatically in a respiratory phase analysis of the signals P(xi,t) performed by the processor 135. The processor 135 determines an average acoustic energy {tilde over (P)}(x,t1,t2) over the time interval from t1 to t2 at least one location x in the region R in a calculation involving at least one of the signals P(xi,t).
The average acoustic energies are stored in the memory 130 and may be displayed on a display device 150 such as a CRT screen for diagnosis by a physician.
The processor 135 may also perform an automatic differential diagnosis by comparing the function {tilde over (P)} to functions stored in the memory and known to be indicative of various disorders in the body region.
FIG. 2 shows a flow chart diagram for carrying out the method of the invention in accordance with one embodiment. In step 200 the signals P(xi,t) are obtained from N transducers placed at predetermined locations xi for i from 1 to N in a region R on the body surface. In step 205 values of t1 and t2 are either input to the processor 135 using the input devices 140 or 145, or are determined by the processor. In step 210, an average acoustic energy {tilde over (P)}(x,t1,t2) is determined at least one location x in the region R over the time interval t1 to t2. In step 220 the average acoustic energy is displayed on the display 150 for at least one value of x. In step 230, it is determined whether a function {tilde over (P)} is to be determined over another time interval. If yes, the process returns to step 205. If not, the process terminates.
It will also be understood that the system according to the invention may be a suitably programmed computer. Likewise, the invention contemplates a computer program being readable by a computer for executing the method of the invention. The invention further contemplates a machine-readable memory tangibly embodying a program of instructions executable by the machine for executing the method of the invention.
EXAMPLES
The system and method of the invention were used to analyze cardiovascular sounds in an individual.
Example 1
FIG. 3 shows recording of signals over one heartbeat in an individual. A two-dimensional coordinate system was defined on the individual's back. As shown in FIG. 3, 48 transducers were placed on the individual's back over the thorax, at the locations indicated by the circles 300. The curves 305 show the presumed contours of the lungs, and the curve 306 shows the presumed contour of the heart. As can be seen, the transducers were arranged in a regular orthogonal lattice with spacing between the transducers in the horizontal and vertical directions of 2.5 cm. The signals P(xi,t) from each transducer were then recorded over one heartbeat. Each signal was filtered using a 6-45 Hz band pass filter, in order to remove respiratory tract sounds. The heartbeat was divided into intervals of 0.1 sec duration, and for each interval, {tilde over (P)}(x,t1,t2) was obtained using Equations (1) and (2) above with the kernel g of Equation (5) with σ=36 pixels. FIG. 4 shows the images obtained by representing the obtained functions {tilde over (P)}(x,t1,t2) by gray level shading. The images may be displayed on the display device 150 in rapid succession so as to produce a movie of the heart over a heartbeat. The movie can be analyzed to determine the values of basic parameters of heart function, such as left ventricular end diastolic (LVED) volume, left ventricular end systolic (LVES) volume, right ventricular end diastolic (RVED) volume, right ventricular end systolic (RVES), volume, left atrium end diastolic (LAED) diameter, right atrium end diastolic (LAES) diameter, wall thickness of the inter-ventricular septum (systolic and diastolic), and parameters derivable from these parameters such as left ventricle stroke volume, left ventricular cardiac output, ejection fraction, left ventricular fractional shortening, inter-ventricular septal thickening. The movie can also be analyzed in order to detect heart defects such as valve dysfunction and cardiac arrhythmia.
Example 2
The signals P(xi,t) were obtained from each transducer as described in Example 1, and were then recorded over one respiratory cycle which includes about 5 heartbeats. Each signal was divided into two sub-signals P1(xi,t) and P2(xi,t) of different frequency bands. The sub-signal P1(xi,t) was obtained by filtering the signal using a 6-40 Hz band pass filter. The sub-signal P2(xi,t) was obtained by filtering the signal using a 100-150 band pass filter. The sub-signal P1(xi,t) consists primarily of heart sounds, while the sub-signal P2(xi,t) consists primarily of lung sounds. The P1(xi,t) sub-signal was analyzed by the method of the invention, and the sub-signal P2(xi,t) was analyzed as disclosed in Applicant's co-pending U.S. patent application Ser. No. 10/338,742 filed on Jan. 9, 2003. The signal P2(xi,t) was divided into intervals of 0.25 sec duration, and the signal P1(xi,t) was divided into intervals of 0.1 sec duration. For each interval, functions {tilde over (P)}(x,t1,t2) and {tilde over (P)}(x,t1,t2) were obtained from P1(xi,t) and P2(xi,t), respectively, using Equations (1) and (2) above with the kernel g of Equation (5) with σ=36 pixels. The two functions are preferably displayed simultaneously on a display device by intensity shading, using a different color for each function. FIG. 5 shows the images obtained by representing the obtained functions {tilde over (P)}(x,t1,t2) and {tilde over (P)}(x,t1,t2) simultaneously by gray level shading. The images may be displayed on the display device 150 in rapid succession so as to produce a movie of the heart over a heartbeat. The movie can be analyzed to determine the values of parameters of heart function, such as cardiac output and blood ejection fraction. The movie can also be analyzed in order to detect hear defects such as valve dysfunction and cardiac arrhythmia.

## Claims

1. A system for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:
(One) N transducers, where N is an integer, each transducer configured to be fixed on a surface of the individual over the thorax, the ith transducer being fixed at a location xi and generating an initial signal P(xi,t) indicative of pressure waves at the location xi, for i=1 to N; and
(Two) a processor configured to receive the signals P(xi,t) and to filter the signals P(xi,t) so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed
wherein respiratory tract sounds have been removed, and
wherein the processor is further configured to determine an average acoustic energy {tilde over (P)} (x,t1,t2) arising from the cardiovascular system at at least one position x over a time interval from a first time t1 to a second time t2, {tilde over (P)} being determined in an algorithm involving at least one of the processed signals,
wherein the function {tilde over (P)} is determined at one or more locations x in an algorithm comprising:
(One) determining an average acoustic energy {tilde over (P)} (xi,t1,t2) over a time interval from t1 to t2 at a plurality of locations xi of transducers; and
(Two) determining an average acoustic energy {tilde over (P)} (x,t1, t2) at at least one location x by interpolation of the determined {tilde over (P)} (xi,t1, t2).

2. The method according to claim 1 wherein the initial signals are filtered by a band pass filter passing between 15 to 45 Hz.

3. The system according to claim 1 wherein the processor is further configured to generate an image of the at least portion of the cardiovascular system from at least one of the filtered signals.

4. The system according to claim 3 wherein the processor is further configured to display an image of the at least portion of the cardiovascular system on a display device.

5. The system according to claim 1 wherein the processor is configured to generate an image of the at least portion of the cardiovascular system at a plurality of times or over a plurality of successive time intervals, and to display the images successively on a display device.

6. The system according to claim 1 further comprising a two-dimensional display device.

7. The system according to claim 1 wherein the processor is further configured to compare the average acoustic energy {tilde over (P)} to one or more predetermined functions {tilde over (F)} and determine a function {tilde over (F)}0 from among the functions {tilde over (F)} most similar to {tilde over (P)}.

8. The system according to claim 7 wherein the processor is further configured to make a diagnosis based upon the determined function.

9. The system according to claim 1 wherein the average acoustic energy {tilde over (P)} over a time interval from t1 to t2 is determined at a location xi of a transducer using the algebraic expression:




  
    
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10. The system according to claim 1 wherein the average acoustic energy is determined at at least one location x by interpolation of the determined {tilde over (P)} (xi,t1,t2) using the algebraic expression:




  
    
      
        
          
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where g(x,xi,σ) is a kernel satisfying




  
    
      
        
          
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11. The system according to claim 10 wherein g(x,νi,σ) is the kernel




  
    
      
        
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                      -
                      
                        
                          x
                          i
                          2
                        
                        ⁢
                        
                          σ
                        
                      
                    
                    )
                  
                  2
                
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  σ
                
              
              )
            
            .
          
        
      
    
    
      
        (
        5
        )

12. The system according to claim 8 wherein the processor is further configured to display the average acoustic energy {tilde over (P)} (x,t1,t2) on a display device.

13. The system according to claim 1 wherein the processor is configured to determine an average acoustic energy over a plurality of successive time intervals, each average acoustic energy being determined using an algorithm involving at least one of the signals P(xi,t).

14. The system according to claim 13 wherein the processor is configured to sequentially display on a display device a representation of each determined average acoustic energy.

15. The system according to claim 1, wherein the processor is further configured to
subject the signals P(xi,t1,t2) to band pass filtering in each of one or more frequency bands; and
determine the average acoustic energy function for each frequency band based upon at least one of the filter signals.

16. The system according to claim 15 wherein the processor is configured to display one or more of the average acoustic energy functions determined for a frequency band on a display device.

17. A method for analyzing sounds originating in at least a portion of an individual's cardiovascular system comprising:
(One) fixing on a surface of the individual over the thorax, N transducers, where N is an integer, and for i=1 to N, the ith transducer being fixed at a location xi and generating an initial signal P(xi, t) indicative of pressure waves at the location xi;
(Two) processing the signals P(xi,t) so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed and
(Three) determining an average acoustic energy {tilde over (P)} (x,t1,t2) arising from the cardiovascular system at at least one position x over a time interval from a first time t1 to a second time t2, {tilde over (P)} being determined in an algorithm involving at least one of the processed signals,
wherein the function {tilde over (P)} is determined at one or more locations x in an algorithm comprising:
(One) determining an average acoustic energy {tilde over (P)} (xi,t1,t2) over a time interval from t1 to t2 at a plurality of locations xi of transducers; and
(Two) determining an average acoustic energy {tilde over (P)} (x,t1,t2) at at least one location x by interpolation of the determined {tilde over (P)} (xi,t1,t2).

18. The method according to claim 17 wherein respiratory tract sounds are filtered from the initial signals.

19. The method according to claim 17 wherein the initial signals are filtered by a band pass filter passing between 15 to 45 Hz.

20. The method according to claim 17 further comprising generating an image of the at least portion of the cardiovascular method from at least one of the filtered signals.

21. The method according to claim 20 further comprising displaying an image of the at least portion of the cardiovascular system on a display device.

22. The method according to claim 17 further comprising generating an image of the at least portion of the cardiovascular method at a plurality of times or over a plurality of successive time intervals, and displaying the images successively on a display device.

23. The method according to claim 17 further comprising comparing the average acoustic energy {tilde over (P)} to one or more predetermined functions {tilde over (F)} and determining a function {tilde over (F)}0 from among the functions {tilde over (F)} most similar to {tilde over (P)}.

24. The method according to claim 23 wherein the processor is further configured to make a diagnosis based upon the determined function.

25. The method according to claim 17 wherein the average acoustic energy {tilde over (P)} (xi,t1,t2) is determined over a time interval from t1 to t2 at a plurality of locations xi of transducers using the algebraic expression:




  
    
      P
      ~
    
    ⁡
    
      (
      
        
          x
          i
        
        ,
        
          t
          1
        
        ,
        
          t
          2
        
      
      )
    
  
  =
  
    
      ∫
      
        t
        2
      
      
        t
        2
      
    
    ⁢
    
      
        
          P
          2
        
        ⁡
        
          (
          
            
              x
              i
            
            ,
            t
          
          )
        
      
      ⁢
      
        
          d
          t
        
        .

26. The method according to claim 17 wherein the average acoustic energy is determined at at least one location x by interpolation of the determined {tilde over (P)} (xi,t1,t2) using the algebraic expression:




  
    
      
        
          
            P
            ~
          
          ⁡
          
            (
            
              
                x
                i
              
              ,
              
                t
                1
              
              ,
              
                t
                2
              
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              1
            
            N
          
          ⁢
          
            
              
                P
                ~
              
              ⁡
              
                (
                
                  
                    x
                    i
                  
                  ,
                  
                    t
                    1
                  
                  ,
                  
                    t
                    2
                  
                
                )
              
            
            ⁢
            
              g
              ⁡
              
                (
                
                  x
                  ,
                  
                    x
                    i
                  
                  ,
                  σ
                
                )
              
            
          
        
      
    
    
      
        (
        2
        )
      
    
  




where g(x,xi,σ) is a kernel satisfying




  
    
      
        
          
            ∇
            2
          
          ⁢
          g
        
        =
        
          
            ∂
            g
          
          
            ∂
            σ
          
        
      
    
    
      
        (
        3
        )
      
    
  
  
    
      
        
          ∑
          
            i
            =
            1
          
          N
        
        ⁢
        
          
            g
            ⁡
            
              (
              
                x
                ,
                
                  x
                  i
                
                ,
                σ
              
              )
            
          
          ⁢
          
            
          
          ⁢
          is
          ⁢
          
            
          
          ⁢
          approximately
          ⁢
          
            
          
          ⁢
          equal
          ⁢
          
            
          
          ⁢
          to
          ⁢
          
            
          
          ⁢
          1.
        
      
    
    
      
        (
        4
        )

27. The method according to claim 26 wherein g(x,νi,σ) is the kernel




  
    
      
        
          g
          ⁡
          
            (
            
              x
              ,
              
                x
                i
              
              ,
              σ
            
            )
          
        
        =
        
          Exp
          -
          
            
              (
              
                
                  
                    (
                    
                      
                        x
                        1
                      
                      -
                      
                        
                          x
                          i
                          1
                        
                        ⁢
                        
                          σ
                        
                      
                    
                    )
                  
                  2
                
                
                  2
                  ⁢
                  σ
                
              
              )
            
            ·
            Exp
          
          -
          
            
              (
              
                
                  
                    (
                    
                      
                        x
                        2
                      
                      -
                      
                        
                          x
                          i
                          2
                        
                        ⁢
                        
                          σ
                        
                      
                    
                    )
                  
                  2
                
                
                  2
                  ⁢
                  σ
                
              
              )
            
            .
          
        
      
    
    
      
        (
        5
        )

28. The method according to claim 17 further comprising displaying the average acoustic energy {tilde over (P)} (x,t1,t2) on a display device.

29. The method according to claim 17 further comprising determining an average acoustic energy over a plurality of successive time intervals, each average acoustic energy being determined using an algorithm involving at least one of the signals P(xi,t).

30. The method according to claim 29 further comprising sequentially displaying on a display device a representation of each determined average acoustic energy.

31. The method according to claim 17 further comprising determining an average acoustic energy over a plurality of successive time intervals, each average acoustic energy being determined using an algorithm involving at least one of the signals P(xi,t).

32. The method according to claim 17 further comprising:
subjecting the signals P(xi,t1,t2) to band pass filtering in each of one or more frequency bands; and
determining the average acoustic energy function for each frequency band based upon at least one of the filter signals.

33. The method according to claim 32 further comprising displaying one or more of the average acoustic energy functions determined for a frequency band on a display device.

34. A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for analyzing sounds originating in at least a portion of an individual's cardiovascular system, comprising:
processing N initial signals P(xi,t), where N is an integer, the initial signals being indicative of pressure waves at a location xi; for i=1 to N, so as to generate filtered signals in which at least one component of the signals P(xi,t) not arising from cardiovascular sounds has been removed and
determining an average acoustic energy {tilde over (P)} (x,t1,t2) arising from the cardiovascular system at at least one position x over a time interval from a first time t1 to a second time t2, {tilde over (P)} being determined in an algorithm involving at least one of the processed signals,
wherein the average acoustic energy {tilde over (P)} over a time interval from t1 to t2 is determined at a location xi of a transducer using the algebraic expression:





  
    
      P
      ~
    
    ⁡
    
      (
      
        
          x
          i
        
        ,
        
          t
          1
        
        ,
        
          t
          2
        
      
      )
    
  
  =
  
    
      ∫
      t1
      t2
    
    ⁢
    
      
        
          P
          2
        
        ⁡
        
          (
          
            
              x
              i
            
            ,
            t
          
          )
        
      
      ⁢
      
        
          d
          t
        
        .

35. A computer program product comprising a computer useable medium having computer readable program code embodied therein for analyzing sounds originating in at least a portion of an individual's cardiovascular system, comprising:
processing N initial signals {tilde over (P)}(xi, t), where N is an integer, the initial signals being indicative of pressure waves at a location xi, for i=1 to N, so as to generate filtered signals in which at least one component of the signals P(xi, t) not arising from cardiovascular sounds has been removed and
determining an average acoustic energy {tilde over (P)} (x,t1,t2) arising from the cardiovascular system at at least one position x over a time interval from a first time t1 to a second time t2, {tilde over (P)} being determined in an algorithm involving at least one of the processed signals,
wherein the average acoustic energy {tilde over (P)} over a time interval from t1 to t2 is determined at a location xi, of a transducer using the algebraic expression:





  
    
      P
      ~
    
    ⁡
    
      (
      
        
          x
          i
        
        ,
        
          t
          1
        
        ,
        
          t
          2
        
      
      )
    
  
  =
  
    
      ∫
      
        t
        ⁢
        
          
        
        ⁢
        1
      
      
        t
        ⁢
        
          
        
        ⁢
        2
      
    
    ⁢
    
      
        
          P
          2
        
        ⁡
        
          (
          
            
              x
              i
            
            ,
            t
          
          )
        
      
      ⁢
      
        
      
      ⁢
      
        
          d
          t
        
        .