Systems and methods for obtaining pulsation modes

Abstract

The invention relates to measurement systems and methods comprising at least one first transducer for generating measurement signals of a state variable representing a blood flow rate or pressure in an artery, an electrocardiograph for recording an electrocardiogram to allow for synchronization of multiple of said measurement signals, a software comprising an input comprising multiple of said measurement signals, each of said measurement signals contains a time domain signal of at least one state variable representing a blood flow rate or pressure within an artery at a single measurement point of multiple measurement points distributed throughout an arterial tree, wherein the software is capable of performing at least a first signal processing step and a second signal processing step on the measurement signals including the approximation or identification of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree.

Description

[0001] Systems and methods for obtaining pulsation modes

[0002] The present invention relates to systems for measurement and computer-implemented methods for signal processing to obtain pulsation modes of a state variable throughout an arterial tree .

[0003] The arterial tree is a complex network of vessels that transport blood from the heart aorta to the capillaries . The vessels conduct a pulsating flow excited by the heart . They can be regarded as acoustic ducts whose dynamic behavior depends on their physical properties . These properties will be changed by aneurysms and stenoses , which are abnormal dilations and narrowings of the arteries , respectively .

[0004] With current methods , aneurysms and stenoses are monitored by measurements at the location where the abnormal dilation or narrowing occurs , which sometimes requires computed tomography or magnetic resonance imaging, for example for arteries located in the thoracic area or in the abdominal area of adipose sub j ects .

[0005] The theory that led to the present invention states that local changes in physical properties will influence the global dynamic behavior of the arterial tree and change natural pulsation frequencies and pulsation mode shapes . This suggests an attempt for acoustic health monitoring similar to structural health monitoring of civil structures based on experimental modal analysis .

[0006] The obj ect of the invention is to perform or approximate an experimental modal analysis for obtaining natural pulsation modes of the arterial tree from single point measurements . The present disclosure provides measurement systems and signal processing methods for identi fying or approximating natural pulsation modes of a state variable throughout an arterial tree .

[0007] A measurement system is proposed comprising : at least one first transducer for generating measurement signals of a state variable representing a blood flow rate or pressure in an artery, an electrocardiograph for recording an electrocardiogram to allow for synchroni zation of multiple of said measurement signals , a software , comprising an input comprising multiple of said measurement signals , each of said measurement signals contains a time domain signal of at least one state variable representing a blood flow rate or pressure within the artery at a single measurement point of multiple measurement points di stributed throughout an arterial tree , wherein the software is capable of performing at least a first signal processing step and a second signal processing step on the measurement signals including the approximation or identi fication of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree .

[0008] A measurement method is proposed comprising : measuring with at least one first transducer measurement signals of a state variable representing a blood flow rate or pressure at multiple measurement points distributed throughout an arterial tree , recording with an electrocardiograph an electrocardiogram to allow for synchroni zation of multiple of said measurement signals , inputting to a software multiple of said measurement signals , each of said measurement signals contains a time domain signal of at least one state variable representing a blood flow rate or pressure within the artery at a single measurement point of said multiple measurement points , performing at least a first signal processing step and a second signal processing step on the measurement signals for approximating or identi fying of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree .

[0009] In an embodiment a measurement system is provided which consists of a transducer for measuring an excitation state variable representing a blood flow rate in the heart aorta, at least one transducer for measuring a state variable representing a blood flow rate or pressure in an artery, an electrocardiograph, and an experimental modal analysis software package .

[0010] In the same embodiment , a computer-implemented method for signal processing is provided, wherein the time domain signal of the excitation state variable and multiple measurement signals obtained on an arterial tree are used as input , each of said measurement signals contains a time domain signal o f at least one state variable representing a blood flow rate or pressure within the artery at a single measurement point of multiple measurement points distributed throughout the arterial tree , wherein the method comprises : a first signal processing step that is applied to each measurement signal on the arterial tree and comprises the determination of a frequency response function between an excitation state variable in the heart aorta and a state variable in an artery for a single heartbeat at each measurement point ; a second signal processing step comprising the identification of at least one natural pulsation frequency and one pulsation mode shape of a state variable throughout the arterial tree using an experimental modal analysis software package .

[0011] Preferably, the measurement system contains at least one linear array ultrasound transducer for measuring a state variable representing a blood flow rate in an artery .

[0012] Preferably, the measurement system contains at least one curved array ultrasound transducer for measuring a state variable representing a blood flow rate in an artery . Preferably, the measurement system contains a sector ultrasound transducer for measuring an excitation state variable representing a blood flow rate in the heart aorta .

[0013] Preferably, a blood flow rate at a measurement point at an instant of time is determined by multiplying the mean blood flow velocity at the measurement point at the instant of time by the cross-sectional area of the artery at the measurement point , which is determined from the ultrasound image of the artery at the measurement point .

[0014] Preferably, the mean blood flow velocity at a measurement point at an instant of time is determined by averaging al l blood flow velocities measured by an ultrasound transducer over the entire cross-section of the artery at the measurement point at the instant of time .

[0015] Alternatively, the mean blood flow velocity at a measurement point at an instant of time is determined by the brightest pixel in the velocity signal display at the instant of time .

[0016] Alternatively, the mean blood flow velocity at a measurement point at an instant of time is determined by the pixel representing the maximum absolute value in the velocity signal display at the instant of time .

[0017] Preferably, a frequency response function between an excitation state variable in the heart aorta and a state variable in an artery is calculated by dividing the Fourier trans formation of the state variable in the artery by the Fourier transformation of the excitation state variable in the heart aorta .

[0018] Preferably, frequency response functions between blood flow rate in the heart aorta and blood flow rates on the arterial tree are divided by the square of the angular frequency and processed by the experimental modal analysis software package .

[0019] Alternatively, the measurement system contains at least one non- invasive blood pressure transducer for measuring a state variable representing a blood pressure in an artery . Preferably, frequency response functions between blood flow rate in the heart aorta and blood pressures in the arterial tree are divided by the angular frequency and processed by the experimental modal analysis software package .

[0020] In another embodiment a measurement system is provided which consists of at least one transducer for measuring a blood flow rate or pressure in an artery, an electrocardiograph, and an experimental modal analysis software package .

[0021] In the same embodiment , a computer-implemented method for signal processing is provided, wherein multiple measurement signals obtained on an arterial tree are used as input , each of said measurement signals contains a time domain signal o f at least one state variable representing a blood flow rate or pressure within the artery in a single measurement point of multiple measurement points distributed throughout the arterial tree , wherein the method comprises : a first signal processing step that is applied to each measurement signal and comprises at least a Fourier trans formation to calculate a frequency spectrum representing a single heartbeat at each measurement point ; a second signal processing step comprising the approximation of at least one natural pulsation frequency and one pulsation mode shape of the measured state variable throughout the arterial tree by using an experimental modal analysis software package .

[0022] Preferably, the frequency spectra of the measurement signals are processed by the experimental modal analysis software package .

[0023] In another embodiment a measurement system is provided which consists of at least one transducer for measuring a blood flow rate or pressure in an artery and an electrocardiograph . In the same embodiment , a computer-implemented method for signal processing is provided, wherein multiple measurement signals obtained on an arterial tree are used as input , each of said measurement signals contains a time domain signal o f at least one state variable representing a blood flow rate or pressure within the artery in a single measurement point of multiple measurement points distributed throughout the arterial tree , wherein the method comprises : a first signal processing step that is applied to each measurement signal and comprises at least a Fourier trans formation to calculate a frequency spectrum representing a single heartbeat at each measurement point ; a second signal processing step comprising the approximation of at least one natural pulsation frequency and one pulsation mode shape of the measured state variable throughout the arterial tree by the identi fication of amplitude maxima in the frequency spectra, whereby natural pulsation frequencies are approximated as the frequency values at which the amplitude maxima occur, and pulsation mode shapes are approximated by combining the values of the frequency spectra at the respective amplitude maximum throughout the arterial tree .

[0024] Preferably, each of the multiple measurement signal s contains multiple heartbeats wherein the first signal proces sing step is applied to each of multiple heartbeats of the measurement signal of each measurement point and wherein the frequency response function or frequency spectrum representing a single heartbeat of a single measurement point is obtained by averaging the frequency response functions or frequency spectra o f multiple heartbeats .

[0025] Preferably, the second signal processing step comprises the identi fication or approximation of pulsation mode shapes of the measured state variable throughout the arterial tree for at least two natural pulsation frequencies . For example , a first natural pulsation frequency can be at 2 . 3 Hz and a second natural pulsation frequency can be at 5 . 7 Hz .

[0026] Preferably, the first step comprises a synchroni zation of the single heartbeat signals such that each single heartbeat signal refers to the same section of a heartbeat . Preferably, the signal of an electrocardiogram that was simultaneously recorded for each measurement signal is used as a trigger to define the sections of the measurement s ignal that are used as single heartbeat signals .

[0027] Preferably, the first step comprises a windowing procedure by subtracting linear functions to set the first and last value of each single heartbeat signal to zero .

[0028] Preferably, the method comprises outputting the identi fied or approximated pulsation mode shapes of the measured state variable .

[0029] Preferably, the method comprises comparing of the identi fied or approximated pulsation mode shapes of the measured state variable to a reference mode shape model and highlighting dif ferences in the models .

[0030] Preferably, the method comprises comparing the identified or approximated natural pulsation frequencies with reference frequencies of the modes and outputting di f ferences in the frequencies .

[0031] Preferably, the method comprises using characteristics of the investigated subj ect to calculate a reference mode shape model based on a stored mathematical model of the arterial tree of a healthy subj ect .

[0032] The identi fied or approximated pulsation mode shapes of the measured state variable can be compared to a reference model . The reference model can be a theoretical modal model resembling a healthy subj ect with similar characteristics as the test person . A theoretical modal model can be obtained from an eigenvalue analysis of a lineari zed autonomous dynamic model of the arterial tree with a comparable boundary condition in the heart aorta . For example , weight , si ze and age can be entered as parameters for the theoretical modal model . The reference model can be a historic model already obtained for the same person or another person with similar characteristics as the test person.

[0033] The identified or approximated natural pulsation frequencies obtained can be compared to theoretical natural pulsation frequencies of a healthy person or premeasured natural pulsation frequencies of the same person. A shift of the natural pulsation frequencies to higher frequencies may indicate stiffening of the arteries .

[0034] In one embodiment, other quantities such as average blood pressure, temperature or pulse can be measured and included in the reference model. It is also possible to keep one or more of these parameters constant or as much as possible constant for different measurements on several persons or on the same person at different times.

[0035] The invention is illustrated by way of example by reference to the accompanying drawings .

[0036] Fig. 1: Shows a theoretical flow rate pulsation mode shape of a healthy subject with open boundary in the heart aorta at a natural pulsation frequency of 2.37 Hz.

[0037] Fig. 2: shows an approximated flow rate pulsation mode shape of a test subject with open boundary in the heart aorta at an approximated natural pulsation frequency of 1.47 Hz.

[0038] Fig. 3: shows a theoretical flow rate pulsation mode shape of a healthy subject with closed boundary in the heart aorta at a natural pulsation frequency of 3.11 Hz.

[0039] Fig. 4: shows an identified flow rate pulsation mode shape of a test subject with closed boundary in the heart aorta at an identified natural pulsation frequency of 1.88 Hz.

[0040] Fig. 5: shows a theoretical flow rate pulsation mode shape of a healthy subject with closed boundary in the heart aorta at a natural pulsation frequency of 5.02 Hz. Fig . 6 : shows an identi fied flow rate pulsation mode shape of a test subj ect with closed boundary in the heart aorta at an identi fied natural pulsation frequency of 4 . 45 Hz .

[0041] Fig . 7 : shows possible measurement points for ultrasound transducers with an exemplary measurement result in measurement point 11 .

[0042] For mechanical applications , it is known that the input of an experimental modal analysis software package can consist of frequency response functions between force excitation and displacement response . The software package provides the required identi fication procedure to determine natural vibration frequencies and vibration mode shapes in terms of displacement . Natural frequencies and mode shapes are obtained for a free boundary at the excitation location .

[0043] According to the duality between mechanical and acoustic systems , natural pulsation frequencies and pressure pulsation mode shapes of an acoustic system can be identi fied by an experimental modal analysis software for mechanical systems i f frequency response functions between the time derivative of flow rate excitation and pressure response are used as input instead of frequency response functions between force excitation and displacement response . In this case , pressure pulsation mode shapes are obtained for a closed boundary at the excitation location . This situation is encountered i f blood flow rate in the heart aorta and blood pressures on the arterial tree are measured .

[0044] In some known mechanical applications , the system i s excited by a known displacement in a single degree of freedom, which is called base excitation . Instead of frequency response functions between force excitation and displacement response , frequency response functions between the second time derivative of the base excitation and displacements relative to the base degree of freedom can be used as input for an experimental modal analysis software package to obtain natural frequencies and mode shapes for a fixed boundary at the base degree of freedom .

[0045] According to the analogy between mechanical and acoustic systems , this situation is encountered i f blood flow rate in the heart aorta and blood flow rates on the arterial tree are measured . The respective flow rate pulsation mode shapes comply with a closed boundary in the heart aorta . Relative flow rates can be replaced by absolute flow rates i f zero frequency modes are not considered .

[0046] In Figures 1 to 6 , the absolute value of flow rate is indicated by the line width, and the arrows indicate the direction . The procedure of the previous paragraph has been applied to obtain the mode shape in Figure 4 , which can be compared to the theoretical mode shape in Figure 3 , and to obtain the mode shape in Figure 6 , which can be compared to the theoretical mode shape in Figure 5 . Fig . 4 and 6 refer to a closed boundary in the heart aorta which corresponds to the embodiment in which a second transducer for measuring an excitation state variable representing a blood flow rate in the heart aorta i s used . This second transducer measures at location 23 . The other exemplary locations 1 to 10 and 12 to 15 and 17 to 22 represent the multiple measurement points distributed throughout an arterial tree , at which measurements with at least one first transducer for generating measurement signals of a state variable representing a blood flow rate are made .

[0047] Figure 2 has been obtained by using frequency spectra of blood flow rates in the arterial tree as input for an experimental modal analysis software package . For frequencies up to the approximated natural pulsation frequency of 1 . 47 Hz , the time derivative of blood pressure in the heart aorta can be approximated by a dirac delta function, which means that the frequency spectra of blood flow rates on the arterial tree approximate the respective frequency response functions between the time derivative of blood pressure in the heart aorta and blood flow rates on the arterial tree . According to the analogy between mechanical and acoustic systems , these frequency response functions can be used as input for an experimental modal analysis software package to obtain natural pulsation frequencies and flow rate pulsation mode shapes with an open boundary in the heart aorta . Therefore , the flow rate pulsation mode shape in Figure 2 can be compared to the theoretical mode shape in Figure 1 .

[0048] For higher frequencies , the second time derivative of the blood flow rate in the heart aorta can be approximated by a dirac delta function . I f only first transducers are used to make measurements at measurement points , flow rate pulsation mode shapes with a closed boundary in the heart aorta wi ll be approximated at higher natural pulsation frequencies .

[0049] I f the natural pulsation frequencies of an arterial tree are well separated from each other, the use of an experimental modal analysis software package can be replaced by the identi fication of amplitude maxima in the frequency spectra, whereby natural pulsation frequencies are approximated as the frequency values at which the amplitude maxima occur, and pulsation mode shapes are approximated by combining the values of the frequency spectra at the respective amplitude maximum throughout the arterial tree .

[0050] Fig . 7 illustrates an example of how measurement signals can be obtained, which can be used as input for the present method .

[0051] In an experiment an ultrasound measuring device was used to record and subsequently evaluate the blood velocities of a test person . Measurements were taken one after the other at eighteen dif ferent points , which are shown in Figure 7 . The measurement points were selected at locations 1 to 18 that are commonly used in medicine and are easy to sonicate .

[0052] In an experiment data from the ultrasound device was exported as video files and then analyzed by stitching the individual images together to create a large panoramic image . An individual image is shown on the right side of Figure 7 . The blood velocity profile of multiple heart beats is shown in the upper signal . Simultaneously, an electrocardiogram (ECG) was recorded, which appears in the curve below . The ECG was then used as a trigger signal to define individual sections of the panoramic image with a fixed si ze of pixels . The images were used to create a function consisting of the brightest pixels in each column of the image . As a windowing procedure , linear functions were subtracted to set the first and last value to zero . Finally, the spectrum was calculated using a Fourier trans formation . This process was repeated for eight pulses at each measurement point , and the spectra were averaged . This procedure was carried out for all eighteen measurement points .

[0053] It should be noted that in this example the starting point for the data processing steps are video files of the ultrasound device . Therefore , it was necessary to obtain the velocity profiles by image processing . I f the data of the velocity profiles is provided directly from the measurement signal , the image processing steps can be omitted .

Claims

Claims1 . A measurement system comprising : at least one first transducer for generating measurement signals of a state variable representing a blood flow rate or pressure in an artery, an electrocardiograph for recording an electrocardiogram to allow for synchroni zation of multiple of said measurement signals , a software , comprising an input comprising multiple of said measurement signals , each of said measurement signals contains a time domain signal of at least one state variable representing a blood flow rate or pressure within the artery at a single measurement point of multiple measurement points distributed throughout an arterial tree , wherein the software is capable of performing at least a first signal processing step and a second signal processing step on the measurement signals including the approximation or identi fication of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree .2 . The measurement system as claimed in claim 1 , wherein the software is an experimental modal analysis software package .3 . The measurement system as claimed in claim 2 , further comprising a second transducer for measuring an excitation state variable representing a blood flow rate in the heart aorta, said input further comprising a time domain signal of the excitation state variable .4 . The measurement system as claimed in claim 3 , wherein the second transducer is a sector ultrasound transducer .5 . The measurement system as claimed in any one of claims 1 to 4 , wherein the at least one first transducer is one of a linear array ultrasound transducer or a curved array ultrasound transducer .6 . The measurement system of any one of claims 1 to 4 , wherein the at least one first transducer is a non-invasive blood pressure transducer measuring the state variable representing the blood pressure in the artery .7 . A measurement method comprising : measuring with at least one first transducer measurement signals of a state variable representing a blood flow rate or pressure at multiple measurement points distributed throughout an arterial tree , recording with an electrocardiograph an electrocardiogram to allow for synchroni zation of multiple of said measurement signals , inputting to a software multiple of said measurement signals , each of said measurement signals contains a time domain signal of at least one state variable representing a blood flow rate or pressure within the artery at a single measurement point of said multiple measurement points , performing at least a first signal processing step and a second signal processing step on the measurement signals for approximating or identi fying of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree .8 . The measurement method of claim 7 further comprising : applying the first signal processing step to each measurement signal comprising at least a Fourier trans formation to calculate frequency spectra, each frequency spectrum representing a single heartbeat at each measurement point and the second signal processing step comprising the approximation of at least one natural pulsation frequency and one pulsation mode shape of the measured state variable throughout the arterial tree by identi fication of amplitude maxima in said frequency spectra, whereby natural pulsation frequencies are approximated as frequency values at which the amplitude maxima occur, and pulsation mode shapes are approximated by combining the values of the frequency spectraat the respective amplitude maximum throughout the arterial tree .9 . The measurement method of claim 7 further comprising : applying the first signal processing step to each measurement signal comprising at least a Fourier trans formation to calculate frequency spectra, each frequency spectrum representing a single heartbeat at each measurement point and the second signal processing step comprising the approximation of at least one natural pulsation frequency and one pulsation mode shape of the measured state variable throughout the arterial tree using an experimental modal analysis software package .10 . The measurement method of claim 9 further comprising : processing the frequency spectra of the measurement signals by the experimental modal analysis software package .11 . The measurement method of claim 7 further comprising : measuring with a second transducer an excitation state variable representing a blood flow rate in the heart aorta, and inputting to the software a time domain signal of the excitation state variable , applying the first signal processing step to each measurement signal comprising the determination of a frequency response function between the excitation state variable in the heart aorta and the measured state variable in the artery for a single heartbeat at each measurement point and the second signal processing step comprising the identi fication of at least one natural pulsation frequency and one pulsation mode shape of the state variable throughout the arterial tree using an experimental modal analysis software package .12 . The measurement method of claim 11 further comprising : calculating the frequency response function between the excitation state variable in the heart aorta and the state variable in the artery by dividing a Fourier trans formationof the state variable in the artery by a Fourier trans formation of the excitation state variable in the heart aorta .13 . The measurement method of claim 12 further comprising : dividing the frequency response functions between blood flow rate in the heart aorta and blood flow rates on the arterial tree by the square of an angular frequency and processing the result by the experimental modal analysis software package .14 . The measurement method of any one of claims 7 to 13 further comprising : determining the blood flow rate at each measurement point at an instant of time by multiplying a measured mean blood flow velocity at the measurement point at the instant of time by the cross-sectional area of the artery at the measurement point , which is determined from the ultrasound image of the artery at the measurement point .15 . The measurement method of claim 14 further comprising one of : a ) determining the mean blood flow velocity at a measurement point at an instant of time by averaging all blood flow velocities measured by the ultrasound transducer over the entire cross-section of the artery at the measurement point at the instant of time , or b ) determining the mean blood flow velocity at a measurement point at an instant of time by the brightest pixel in the velocity signal display at the instant of time , or c ) determining the mean blood flow velocity at a measurement point at an instant of time by the pixel representing the maximum absolute value in the velocity signal display at the instant of time .16 . The measurement method of any one of claims 7 to 12 further comprising : measuring with at least one non-invasive blood pres sure transducer the state variable representing the blood pressure in an artery .17 . The measurement method of claim 16 further comprising : dividing a frequency response functions between blood flow rate in the heart aorta and blood pressures in the arterial tree by an angular frequency and processing the result by an experimental modal analysis software package .18 . The measurement method of any one of claims 7 to 17 , wherein each of the multiple measurement signals contains multiple heartbeats wherein the first signal processing step is applied to each of multiple heartbeats of the measurement signal of each measurement point and wherein the frequency response function or frequency spectrum representing a single heartbeat of a single measurement point is obtained by averaging the frequency response functions or frequency spectra of multiple heartbeats .

19. The measurement method of claim 18 , wherein the first step comprises a synchroni zation of the single heartbeat signals such that each single heartbeat signal refers to the same section of a heartbeat .20 . The measurement method of any one of claims 18 to 19 , wherein the signal of the electrocardiogram that was simultaneously recorded for each measurement signal is used as a trigger to define the sections of the measurement signal that are used as single heartbeat signals .21 . The measurement method of any one of claims 18 to 20 , wherein the first step comprises a windowing procedure by subtracting linear functions to set the first and last value of each single heartbeat signal to zero .22 . The measurement method of any one of claims 7 to 21 , wherein the second signal processing step comprises the identi fication or approximation of pulsation mode shapes of the measured state variable throughout the arterial tree for at least two natural pulsation frequencies .23 . The measurement method of any one of claims 7 to 22 , wherein the method comprises outputting the identi fied orapproximated pulsation mode shapes of the measured state variable .24 . The measurement method of any one of claims 7 to 23 , wherein the method comprises comparing of the identi fied or approximated pulsation mode shapes of the measured state variable to a reference mode shape model and highlighting dif ferences in the models .

25. The measurement method of any one of claims 7 to 24 , wherein the method comprises comparing the identi fied or approximated natural pulsation frequencies with reference frequencies of the modes and outputting di f ferences in the frequencies .26 . The measurement method of claims 24 or 25 , wherein the method comprises using characteristics of an investigated subj ect to calculate the reference mode shape model based on a stored mathematical model of the arterial tree of a healthy subj ect .

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