WO2022190006A1

WO2022190006A1 - Central blood pressure estimation based on photoplethysmography data

Info

Publication number: WO2022190006A1
Application number: PCT/IB2022/052116
Authority: WO
Inventors: Taous Meriem LALEG; Peihao LI
Original assignee: King Abdullah University Of Science And Technology
Priority date: 2021-03-10
Filing date: 2022-03-09
Publication date: 2022-09-15

Abstract

A method for estimating blood pressure related quantities associated with a patient includes receiving (1300) a photoplethysmography, PPG, signal (132), wherein the PPG signal (132) is collected with a single PPG sensor; extracting (1302) plural semi-classical signal analysis, SCSA, features (128) from the PPG signal (132), by using a Schrodinger operator; processing (1304) the plural SCSA features (128) at processor (122) with a machine learning algorithm module (130), to calculate negative eigenvalues (k_n) and associated eigenfunctions (ψ_n ) of the Schrodinger operator, wherein n varies between 1 and N _h , N _h is a total number of negative eigenvalues (k_n ), and h is a semi-classical constant; and calculating (1306) the blood pressure related quantities (132, 134) based on (1) the calculated negative eigenvalues (k_n) and (2) the associated eigenfunctions (ψ_n) of the Schrodinger operator.

Description

CENTRAL BLOOD PRESSURE ESTIMATION

BASED ON PHOTOPLETHYSMOGRAPHY DATA

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63/159,047, filed on March 10, 2021, entitled “CENTRAL BLOOD PRESSURE ESTIMATION FROM DISTAL PPG MEASUREMENT,” the disclosure of which is incorporated herein by reference in its entirety.

BACKGROUND

TECHNICAL FIELD

[0002] Embodiments of the subject matter disclosed herein generally relate to a system and method for continuously being able to calculate/estimate the blood pressure in a patient, without using a cuff, and more particularly, estimating the blood pressure from photoplethysmography measurements using semiclassical signal analysis features.

DISCUSSION OF THE BACKGROUND

[0003] Blood pressure (BP) is what drives the flow of blood through the blood vessels in humans, thus playing an important role in the dynamics of blood flow in each heartbeat interval. Abnormal blood pressure is currently being considered as a crucial risk factor for cardiovascular diseases. Hypertension is one of the major aspects leading to the evolution of cardiovascular diseases (CVDs) while the CVDs are the leading cause in deaths. Hypertension silently harms internal body organs such as the brain, eyes and kidneys, which can also cause strokes, heart attacks, and kidney failure. The negative cardiovascular effects of hypertension have been reported to be largely dependent on the absolute BP values and increased blood pressure variability (BPV).

[0004] Thus, accurate BP measurement and estimation are vital for prevention, diagnosis, and treatment of hypertension and related CVDs. Depending on the clinical situation, either continuous or intermittent blood pressure monitoring is employed. There are two types of approaches for BP measurement known as invasive and noninvasive measurements. Invasive BP measurement is a highly accurate method available for measuring continuous BP, but it causes potential health issues to patients, such as bleeding and infection risks, while damages at the vascular tissues cause arterial obstruction. Also, in specific clinical situations, there are cases where the invasive BP monitoring may be not feasible if safety conditions are not met properly.

[0005] Korotkoff sounds may be used to estimate Systolic BP (SBP) and Diastolic BP (DBP), which is another accurate and reliable way of BP measurement, but it requires trained professionals and it prevents ambulatory blood pressure measurement (ABPM). Cuff-based BP measurement equipment is widely used in hospitals and home settings to detect abnormal BP. However, limitations due to its discontinuous nature and the discomfort caused by the repeated cuff inflations prevent continuous BP monitoring.

[0006] Because the traditional methods for measuring BP waveforms are not convenient for continuous measurement and ABPM applications, recently, there has been an increase in research for cuffless BP estimation algorithms to enable continuous BP monitoring in an easy way, by mapping signals that are easy to measure, to individual’s beat to beat BPs. In terms of method simplicity, Gesche et al. and Mase et al. have attempted to develop algorithms for cuffless ABP estimation. Although their studies have achieved acceptable accuracy using MLR algorithms, their methods are limited due to practical issues, i.e. , the need to place two sensors on the patient, which will cause movement inconvenience for the users. In fact, most researchers use more than two sensors in their research of cuff-less ABP estimation. There are works that utilize only one signal, such as [1], however, multiple magnetic sensors need to be placed on the patient in order to obtain pulse wave velocity (PWV) signal, hindering their simplicity to use.

[0007] To address these issues, photoplethysmography (PPG) technology has gained considerable interest by being widely applied to wearable sensors [2] The non-invasive estimation of blood pressure (BP) using the PPG method has become a hot topic nowadays. The PPG signal can be separated into systolic and diastolic parts. The systolic part of the signal related to the process of contraction of the heart while the diastolic part of the signal is related to the process of cardiac expansion. One of the challenges for this technique is that, at the intersection of the two parts, there is a split between the systolic and diastolic parts called “dicrotic notch.” In the recorded samples of some individuals (typically in a patient), the dicrotic notch is not detectable, thus casting doubt on studies where inappropriate PPG signals are recorded. Such signals might result in high errors with unknown effects.

[0008] One group [3] developed a new method for estimating the BP regardless of the form and shape (appropriate and inappropriate) of the PPG signal. However, their results do not fall into the required accuracy range for manufacturing a corresponding device. Another challenge for the existing methods, such as [3], is that the results slightly exceeds the error boundary of the systolic blood pressure (SBP) requirement stated in the American National Standard for Electronic or Automated Sphygmomanometers, document PANSI/AAMI SP 102002, Association for the Advancement Instrumentation, Arlington, VA, USA, 2002. Also, after implementing the method of [4] in the MIMIC II database, the inventors found the algorithm’s accuracy slightly decreases. Therefore, increasing the SBP estimation accuracy of the existing methods is desired.

[0009] Thus, there is a need for a new system and method that is capable of continuously and non-intrusively monitoring the BP of a patient, while the accuracy of the method does not negatively affect the actual BP.

BRIEF SUMMARY OF THE INVENTION

[0010] According to an embodiment, there is a method for estimating blood pressure related quantities associated with a patient. The method includes receiving a photoplethysmography, PPG, signal, wherein the PPG signal is collected with a single PPG sensor, extracting plural semi-classical signal analysis, SCSA, features from the PPG signal, by using a Schrodinger operator, processing the plural SCSA features at processor with a machine learning algorithm module, to calculate negative eigenvalues ( k_n ) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, wherein n varies between 1 and N , N_h is a total number of negative eigenvalues ( k_n), and h is a semi-classical constant, and calculating the blood pressure related quantities based on (1) the calculated negative eigenvalues ( k_n ) and (2) the associated eigenfunctions (Ψ_h) of the Schrodinger operator.

[0011] According to another embodiment, there is a system for estimating blood pressure related quantities associated with a patient. The system includes an interface configured to receive a photoplethysmography, PPG, signal, wherein the PPG signal is collected with a single PPG sensor, and a processor connected to the interface. The processor is configured to extract plural semi-classical signal analysis, SCSA, features from the PPG signal, by using a Schrodinger operator, process the plural SCSA features with a machine learning algorithm module to calculate negative eigenvalues (k_n) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, wherein n varies between 1 and N_h, N_h is a total number of negative eigenvalues (k_n), and h is a semi-classical constant, and calculate the blood pressure related quantities based on (1) the calculated negative eigenvalues ( k_n ) and (2) the associated eigenfunctions (Ψ_h) of the Schrodinger operator.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

[0013] Figure 1 is a schematic diagram of a central blood pressure estimation system that uses a PPH signal;

[0014] Figures 2A and 2B are histograms of a database parameters for systolic blood pressure and diastolic blood pressure that are used for training the system of Figure 1 ;

[0015] Figure 3 illustrates blood pressure ranges for the database illustrated in Figures 2A and 2B;

[0016] Figures 4A to 4D illustrate PPH signals constructed based on semi- classical signal analysis features generated from various combinations of eigenvalues;

[0017] Figure 5 illustrates an estimated systolic signal versus a measured systolic signal;

[0018] Figure 6 illustrates an estimated diastolic signal versus a measured diastolic signal;

[0019] Figure 7 schematically illustrates a system that estimates the blood pressure of a patient based on a PPH signal and ECG signal by applying a regression algorithm; [0020] Figure 8 illustrates a PPG waveform and associated features;

[0021] Figure 9 illustrates a PPG waveform containing undetectable dicrotic notch;

[0022] Figure 10 schematically illustrates a multiple linear regression algorithm used to estimate the blood pressure of a patient based on SCSA features; [0023] Figure 11 schematically illustrates a support vector machine algorithm used to estimate the blood pressure of a patient based on SCSA features;

[0024] Figure 12 schematically illustrates a decision tree algorithm used to estimate the blood pressure of a patient based on SCSA features;

[0025] Figure 13 is a flow chart of a method for calculating the blood pressure of a patient based on a machine learning algorithm that uses SCSA features as discussed above;

[0026] Figure 14 is a table that presents the results of the method illustrated in Figure 13 for various machine learning algorithms;

[0027] Figure 15 is a table that presents errors associated with the results of the method illustrated in Figure 13 versus medical standard requirements;

[0028] Figure 16 is a table that present results of the method illustrated in Figure 13 versus various traditional methods; and

[0029] Figure 17 is a schematic diagram of a neural network architecture that is used for the method illustrated in Figure 13. DETAILED DESCRIPTION OF THE INVENTION

[0030] The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to a PPH sensor that can be attached to the finger of a patient and the PPH sensor communicates with a processing device that process the acquired signals and estimates the BP. However, the embodiments to be discussed next are not limited to a PPH sensor placed on the finger, but may be used with sensors placed on other parts of the body or with a different type of sensor.

[0031] Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

[0032] According to an embodiment, a novel method and system 100 (see Figure 1) for measuring the BP of a patient in a non-invasive way, without the need of a cuff, and continuously, includes a PPH sensor 110 and a processing device 120. The PPH signals 112 acquired by the PPH sensor 110 are transferred (in a wired or wireless manner) to the processing device 120, for example, through an input/output interface 114, and the processing device 120 includes, at a minimum, a processor 122 and a memory 124 for processing these signals. The system may be located in a hospital or in the patient’s home. The memory stores instructions for extracting plural features (to be discussed later) from the PPH sensor, and also instructions for running a machine learning algorithm so that the extracted plural features are used to estimate the BP. Further, the memory 124 may store reference values of the BP and associated quantities, like SBP and DBP, so that the machine learning algorithm can be trained. Details of the plural features and their implementation in the machine learning algorithm are now discussed.

[0033] A semi-classical signal analysis (SCSA) method has been proposed for pulse-shaped signal analysis by one of the inventors in [5] Application of SCSA to BP waveform has been shown in previous studies [6], by one of the inventors. A soliton based method was developed by [7]-[9] and used herein as insight. A potential in the soliton-based method is given by the solution of the Korteweg-de Vries (KdV) equation, where each negative eigenvalue is correlated to one soliton [7] A soliton is the solution of some nonlinear partial differential equations like the KdV equation proposed in Crepeau and co-workers. These eigenvalues describe solitons in terms of soliton velocities with the largest eigenvalues describing fast solitons [7] Therefore, they have been utilized as features for the ABP signal. Moreover, it has been shown that there is a similarity between the PPG and ABP morphologies, suggesting PPG holds informative features that exist in ABP. [0034] Based on all these observations, the inventors propose herein two frameworks for beat-to-beat BP estimation based on extracted PPG features. BP regression analysis has been extensively studied in different research, and this body of research indicated that there is a correlation between the PPG signal and the actual BP of a patient. However, when the PPG shapes are inappropriate, as is the case with most patients from intensive care units (ICU) affected by drugs, several important features of the PPH signal can be difficult to localize and extract.

[0035] Thus, the inventors propose in the first BP estimation framework, a new algorithm for estimating the DBP, the Mean Arterial Pressure (MAP), and the SBP, based on the PPG signal with both appropriate and inappropriate shapes. For this first approach, the SCSA method is used to decompose the systolic and diastolic phases, regardless of its appropriateness. The PPG waveform segments are decomposed by SCSA and used as features for supervised machine learning. To further increase the accuracy of the SBP estimation, it was suggested in the field that artificial neural networks (AN Ns) have better performance compared to traditional regression analysis techniques using pulse arrival time (PTT). Based on this observation, a second framework is developed that uses the PPG features as ANN input, which solved the SBP estimation boundary issue. These two frameworks are now discussed in more detail.

[0036] The first framework is discussed with regard to the system 100, which is being configured to predict blood pressure using supervised machine learning algorithms. The process implemented in the system 100 for estimating the MAP,

SBP, and DBP has been validated based on the Physionet’s multiparameter Intelligent monitoring in intensive Care (MIMIC) II online waveform database, which is illustrated in Figures 2A and 2B, and also in Table 1 in Figure 3. Figures 2A and 2B show histograms of the datasets parameters for the SBP and DBP, respectively, while Table 1 shows the BP ranges in the MIMIC II database. This database is used for accuracy analysis and comparison with the existing methods. Simultaneous PPG and ABP signals have been recorded for many patients in various intensive care units (ICU), with part of them used in this study.

[0037] The ABP signal is used for the extraction of reference BP values (see Table 1 in Figure 3 and also the memory 124 in Figure 1 storing these values), while the PPG signal 112 (see Figure 1) is used for extraction of the SCSA features. Over 8,000 instances were used in the database of Figures 2A and 2B with signals sampled at 125Hz and precision of 8 bits. The ABP signal has been recorded invasively from the aorta for patients around the globe and the PPG signal 112 is recorded, continuously and non-invasively, from the fingertip, with the PPG sensor 110. In one application, an interval of 40 seconds was used to estimate the BP from the ABP signal. Other values may be used. In each signal segment, the minimum and maximum values are considered as the DBP and SBP values. Accordingly, the MAP parameter is calculated as MAP = (2 ^c SBP + DBP)/3. The database of Figures 2A and 2B includes 707,567 signal segments which belong to 8,000 individual records. In order to remove the adverse influence of noise and artifacts from the raw signals, existing technologies are used regarding the preprocessing of the individual records. This step is implemented in block 124 as shown in Figure 1. [0038] The features 128 that are extracted from the PPH signal 112 are generated in block 126, based on the SCSA method. More specifically, the SCSA method assumes that a real positive signal y(t) can be decomposed into a set of squared eigenfunctions by using the discrete spectrum of the Schr'dinger operator (introduced in left hand side of equation (2)). Thus, a reconstructed signal y_h(t ) is given by equation:

where are the negative eigenvalues ), and

a^re the corresponding -normalized eigenfunctions (n =

1, 2, ...,N_h) such that the following equation is true:

[0039] In this equation, N_h is the total number of negative eigenfunctions K_nh for the Schrodinger equation (2) and h is a positive parameter, known as the semi- classical constant. N_h is the index that is manipulated when reconstructing the PPH signal. When N_h is relatively large ( h tends to zero), the reconstructed spectrum y_h converges to the true spectrum y. This observation is consistent with the semi- classical properties of the Schrodinger operator where N_h increases when h decreases. One of the important consequences of equations (1) and (2) is that the eigenfunctions Ψ (t), which correspond to large eigenvalues K_nh represent the profiles of the peaks, whereas the remaining functions characterize the noise details of these profiles. In the specific case of the PPG signal feature extraction, the inventors have tested a range of N_h s and selected N_h for each individual case which properly reconstructs the PPG signal given the similarities in morphology between them.

[0040] In this regard, Figures 4A to 4D show the measured PPG signal 400 versus the estimated PPG signal 410 for several values of the parameter h and thus N_h. It is noted that the PPG signal is properly reconstructed when N_h varies in the range [5, 12] for individual cases.

[0041] With this mathematical processing as the background, it is now possible to extract various features 128 of the PPH signal 112, to be fed to the machine learning algorithm module 130 in Figure 1. More specifically, each PPG signal waveform 112 can be divided into two parts. The first part P_s of the signal 112 is related to the contraction of the heart or the systole while the second part P_d is related to cardiac expansion or diastole. Therefore, in this embodiment, the processor 122 of the system 100 is configured to decompose the PPG signal or waveform 112 into two partial sums: the first sum P_s is composed of the N_s ( N_s =

1, 2, ...min largest k_nh and the second sum P_d is composed of the

remaining K_nh components. The first partial sum P_s is used in this embodiment to describe rapid phenomena of the systolic phase and the second partial sum P_d is used to describe slow phenomena of the diastolic phase. These sums P_s and P_d are illustrated in Figures 5 and 6, respectively, and compared to the PPH signal 112. [0042] The mathematical expressions of the sums P_s and P_d are given by

[0043] Several SCSA based features 128 are extracted from the sums described by equations (3) and (4), based on the PPH segments. One such feature is the SCSA eigenvalues

where i takes the values 1, 2, ...,N_h - 1 ,N_h, and the SCSA eigenvalues may be written as:

Note that the number of SCSA eigenvalues may be 5 or more.

[0044] Other SCSA related features 128 are the SCSA systolic invariants, one of which is given by:

and another one being given by:

[0045] Yet other SCSA features 128 are the SCSA diastolic invariants, one of which is given by:

and another one being given by:

[0046] Still another SCSA feature 128 is the SCSA eigenvalue summation, which is given by:

which is the sum of all the eigenvalues.

[0047] It is noted that the maximum total number of features 128 that may be used in the present embodiments is N_h + 5, i.e., N_h SCSA eigenvalues, two systolic invariants, two diastolic invariants, and one eigenvalue summation. Note that not all the features need to be used when estimating the BP. In other words, any number of the SCSA features 128, up to N_h + 5, may be used in any embodiment. One or more of these features are fed to the supervised machine learning algorithm module 130 for estimating the SBP value 132 and the DBP value 134, as schematically illustrated in Figure 1. These values are then either displayed on a monitor 136 or are printed on a medium so that the doctor can provide an adequate treatment to the patient. [0048] In one embodiment, only the features 128 from the PPG signal waveform 112 are fed to the supervised machine learning algorithm module 130, for generating the SBP and DBP values, i.e., no other information is used to calculate the BP values. However, in another embodiment, it is possible to fed, in addition to the features 128 discussed above, an electrocardiogram (ECG) signal waveform 710 and/or associated features 712, and to use all these features for generating the SBP and DBP values, as schematically shown in Figure 7. This last approach is called pulse arrival time (PAT)-included features approach and is discussed later. For the ECG signal 710, a corresponding 714 sensor needs to be placed on the patient for collecting this information.

[0049] Other features may be collected and supplied to the supervised machine learning algorithm module 130. In one application, it is possible to use the heart rate HR as a feature. The HR is measured by the interval length L between R peaks of ECG signals, as also shown in Figure 7. Given the sampling frequency of the ECG signal 710, the HR can be calculated by using the formula:

[0050] Another feature may be the inflection point area (I PA) ratio and width. Past studies have shown that I PAR is strongly correlated to the total peripheral resistance (TPR), which is then selected to extract features for ABP estimation. The I PR ratio is the ratio of the four pulse areas between selected points in the PPG signal waveform 112 shown in Figure 8, which are denotated as S1 to S4. In one application, the sum of these areas S_ns can be used to calculate the peak widths and they can be selected as a feature for SBP and DBP estimation.

[0051] Another feature is related to the large artery stiffness index (LASI), which is an indicator of the arterial stiffness. LASI is inversely related to the time interval 802 between the inflection point 804 and systolic peak 806 immediately before it, as illustrated in Figure 8. Another possible feature is the augmentation index (Al). Al is a measure of the wave reflection on the arteries wall, which is contributing on systolic arterial pressure. It is calculated as the ratio of X and Y, both of which are illustrated in Figure 8. The value of X corresponds to the amplitude of the inflection point 804 while the value of Y corresponds to the amplitude of the systolic peak 806.

[0052] The PAT features are calculated as the distance between the ECG R- peak and the I PA characteristic point on the PPG signal, as shown in Figure 7. More specifically, the PATp is defined as the distance between the ECG R peak and the PPG systolic peak immediately after it, the PATd is defined as the distance between the ECG R peak and the PPG diastolic peak immediately after it, and the PATf is defined as the distance between the ECG R peak and the point at which the maximum value of the PPG signal first derivative occurs. Each of these distances is shown in Figure 7.

[0053] In the PPG signal 112, there is a splitting point in the time scale, which is between systolic and diastolic cardiac phases, which is called the dicrotic notch, which corresponds to the inflection point 804 in Figure 8. In the MIMIC II database illustrated in Figures 2A and 2B, many recorded samples of the PPG signal waveforms 112 from patients are affected by drugs or hypertension, and thus, the dicrotic notch is not easy to be localized, and in some cases, it is simply not detectable, as illustrated in Figure 9. However, the system 100 is capable to determine the SBP and DBP as now discussed.

[0054] To create the training and testing dataset for supervised machine learning module 130, the periodic ABP signal was divided into separate interval segments, to obtain the reference SBP and DBP as the target, which corresponds to the maximum and minimum values of the segments. Training features are extracted from simultaneously obtained PPG segments. The proposed methodology can continuously estimate the ABP (SBP and DBP) with the estimation frequency that depends on the subject’s heart rate (HR), normally in an order of seconds. The estimation process is considered as continuous in contrast to sensor measurement frequency (in milliseconds) depending on specific sensor types and sampling and measurement frequency settings. While same feature vectors (with each element containing one SCSA extracted feature) are used for the prediction of the SBP, DBP, different machine learning models are trained to estimate the targets. The models are now discussed.

[0055] A machine learning algorithm that can used in the module 130 is the multiple linear regression (MLR). The MLR fits a linear equation to the observed data, which models the relationship between two or more multiple variables and one target variable. The MLR has been previously used by researchers for cuffless ABP estimation. This algorithm selects correlation coefficients θ₁, θ₂, ... , θ_h. As shown in Figure 10, each input feature 128 is associated with a corresponding correlation coefficient θ_i, which gets iteratively updated with the least square algorithm 1010 in the module 130, to minimize a regression error (R_error). The result of this process is the estimated SBP and DBP values 132, 134. In one implementation, the regression error is described by the following equation:

with

where m is the number of training samples in the datasets, e is a bias coefficient plus some random error, are the coefficients of the MLR algorithm are the SCSA

eigenvalues, and N_h is the total number of eigenvalues. More or less features may be used for this method, where the features are selected from any of the features discussed above.

[0056] Another algorithm that may be implemented in the module 130 is the Support Vector Machine (SVM), which is schematically illustrated in Figure 11. The SVM can be used as a regression method, maintaining all the main features that characterize the algorithm by using a kernel function, as discussed, for example, in [4] SVM regression has a similar working principle as the least square method of the MLR, i.e. , tries to minimize an error function 1110 (e.g., squared error between the predicted and reference SBP and DBP values), with different approaches of minimizing the error function. The SVM approach tries to maximize the margin between the closest support vectors, which helps pushing the limitations subjected to distributional properties of underlying variables, geometry of the data and the common problem of overfitting. Figure 11 shows that the features 128 are used as the input for this approach. At 1102, the input data set is split into subsets and these subsets are fed to the least square error module 1110. Then, at 1114, a decision tree is pruned, so that a size of the decision tree is reduced, i.e. , data compression is achieved. The non-critical and redundant sections of the tree are removed in this step. As the SVM algorithm is well known in the art, its detailed description is omitted herein.

[0057] Yet another algorithm that may be implemented in the module 130 is the Decision Tree algorithm, which is a faster algorithm for the training process when compared to the SVM algorithm. In addition, this algorithm does not need to normalize and scale data, thus requiring less effort in data preparation. It follows the same approach as used by the humans when generally making decisions, which propagates decisions from the root nodes to the leaf nodes in numeric form. It splits the dataset with the best optimization criteria. The process includes a step 1210 of splitting input data into subsets based on a hyperplane 1220 and pruning the data to reduce the size of decision trees by removing branches and leaves of the tree that provide little power to classify instances, as schematically illustrated in Figure 12. As the Decision Tree algorithm is well known in the art, its detailed description is omitted herein.

[0058] Based on the above observations and innovations, a method for continuous estimation of the blood pressure in a patient, in a non-invasive way, based only on PPH data, has been developed, as now discussed with regard to Figure 13. The method includes a step 1300 of receiving a photoplethysmography, PPG, signal, wherein the PPG signal is collected with a single PPG sensor, a step 1302 of extracting plural semi-classical signal analysis, SCSA, features from the PPG signal, by using a Schrodinger operator, a step 1304 of processing the plural SCSA features at a processor with a machine learning algorithm module to calculate negative eigenvalues ( k_n ) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, where n varies between 1 and N_h, N is a total number of negative eigenvalues (k_n), and h is a semi-classical constant, and a step 1306 of calculating the blood pressure related quantities based on (1) the calculated negative eigenvalues ( k_n ) and (2) the associated eigenfunctions (Ψ_h) of the Schrodinger operator.

[0059] The method may further include a step of estimating a heart’s health status of a patient from which the PPH signal was collected, based on the calculated blood pressure related quantities. The blood pressure related quantities include a systolic blood pressure and a diastolic blood pressure. In one application, the blood pressure related quantities are calculated without using an electrocardiogram, ECG, signal. The method may further include selecting largest N_s negative eigenvalues (k_n) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, calculating a systolic blood pressure, SBP, as a sum of the largest N_s negative eigenvalues (k_n), each multiplied by a corresponding eigenfunctions (Ψ_h) of the Schrodinger operator, and calculating a diastolic blood pressure, DBP, as a sum of the remaining negative eigenvalues (k_n), each multiplied by a corresponding eigenfunctions (Ψ_h) of the Schrodinger operator, where N_s is smaller than N_h. [0060] In one embodiment, the plural SCSA features includes one or more of the negative eigenvalues ( k_n ). In this or another embodiment, the plural SCSA features further include a first systolic invariant, which includes a sum of largest N_s negative eigenvalues ( k_n ) of the Schrodinger operator. In this or another embodiment, the plural SCSA features further include a second systolic invariant, which includes a sum of largest N_s negative eigenvalues ( k_n ) of the Schrodinger operator, at power three. In this or another embodiment, the plural SCSA features further include a first diastolic invariant, which includes a sum of a remainder of the negative eigenvalues ( k_n ) of the Schrodinger operator. In this or another embodiment, the plural SCSA features further include a second diastolic invariant, which includes a sum of the remainder of the negative eigenvalues (k_n) of the Schrodinger operator, at power three. In this or another embodiment, the plural SCSA features further include an eigenvalue summation that includes a sum of all the negative eigenvalues (k_n) of the Schrodinger operator. In this or another embodiment, the machine learning algorithm module uses a multiple linear regression to calculate the negative eigenvalues (k_n) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, or a support vector machine, or a decision tree algorithm, or a feed forward neural network, as discussed later in more detail.

[0061] The system 100 shown in Figure 1 was run on selected data from the MIMIC II database to test the capabilities of the method discussed above with regard to Figure 13. The data associated with about 8,000 individuals from the database has been used for feature extraction and prediction evaluation. The algorithm performance was evaluated by averaging MAE and STD out of records, each records containing 40 seconds sampling time. MLR, SVM and regression tree algorithms were used in the machine learning algorithm module 130 and each of them was evaluated in terms of overall ABP estimation accuracy. The system 100 was trained using 70% of the signal segments from the selected 8,000 patients records from the MIMIC II database. The remaining 30% of the data was used to predict the BP. Each tested case contains reference ABPs (mmHg), estimated ABPs (mmHg), and the error (mmHg) given by the absolute difference between reference and estimated ABPs. The ABPs (including both reference and estimated ABPs) are calculated for each case based on a certain segment in that case. In comparison, all the methods show acceptable prediction accuracy by training with the SCSA features.

[0062] Table 2 in Figure 14 shows the MAE and STD of the estimated ABPs being calculated for the three machine learning algorithms discussed above, based on estimation cases as an overall ABP estimation evaluation. These results show that the SVM achieves the smallest mean average error of SBP (7.44 mmHg difference between reference and predicted SBP) while also achieving the smallest STD (7.37 mmHg) when compared with the regression tree and SVM algorithms.

The same is true when analyzing the estimated DBP. Similarly, the decision tree has shown an acceptable MAE and STD (by not exceeding 10 mmHg). It is also observed that the SVM performance is leading in the three algorithms by providing better estimation in terms of SBP and DBP. It can be seen from Table 2 that the STD of SBP is larger than the STD of DBP. [0063] The estimates shown in Figure 14 need to be viewed in the context of the standard set up by the Association for the Advancement of Medical Instrumentation Standard (AAMI) as any system that implements such measurements and estimations need to meet these standards. In this regard, Table 3 in Figure 15 compares the results of the novel ABP estimation methodology illustrated in Figure 13 to the AAMI standard. The AAMI requires the BP measurement devices to have an ME less than 5 mmHg and STD less than 8 mmHg. According to Table 3, the proposed method has the ME values close to zero, which is much lower than the ME maximum standard margin proposed by the standard. Further, regarding the STD criterion, the DBP and MAP values are within the 8 mmHg STD standard margin, while the STD value of the SBP estimation is slightly exceeding the standard’s limit (10.22 mmHg out of 8 mmHg).

[0064] It is also worth mentioning that the AAMI standard requires medical devices to be evaluated on a sample of at least 85 different subjects. This condition has been met as the ABP estimation methodology of Figure 13 was tested on a population of 6,760 subjects selected from the MIMIC II database, which guarantees a considerably stronger statistical reliability and robustness than the AAMI standard. Note that the SVM method was chosen during the evaluation because the SVM outperforms the multiple linear regression and decision tree methods, by showing lower MAE and STD at the same time, in both the SBP and DBP estimates.

[0065] The estimates of the method presented in Figure 13 have also been compared to estimates obtained using the existing methods, based on the same number of individuals and type of database. Most cuffless ABP estimation methods directly utilize the PPG or ECG signal waveforms when analyzing the ABP values. In comparison, the method of Figure 13 extracts more information from the PPG signal, and thus, it presents better results than the existing methods. Table 4 in Figure 16 summarize the estimates of the novel method of Figure 13 and the existing methods (listed based on the features/signals that are used for determining the BP, for example, pulse transit time, PTT) and the results in these tables indicate that the novel method performs better by showing a better accuracy in terms of DBP and MAP estimates.

[0066] Compared to other literature works, an advantage of the method of Figure 13 is that only one PPG sensor is required. The sensor can be easily placed at the finger level, which pushes the limit of easy implementation of cuff-less BP estimation. The current method presents promising results, in terms of MAE and STD, comparable with the existing method [10] that comprehensively combine PPG features and ECG PAT features. While combining PPG and ECG features presents the best performance, the significance of the method of Figure 13 lies in the fact that only PPG signals are used, which is far more convenient then simultaneously using ECG and PPG as in [10].

[0067] The SCSA features 128 discussed above may also be implemented as a neural network (NN) in the machine learning algorithm module 130. There are various artificial neural network (ANN) architectures for fitting the input data to a target, such as counter propagation, learning vector quantization, and radial basis function. Despite their good performances, these architectures require large numbers of neurons and cannot be applied in the case of a large training set, due to their substantial memory requirements.

[0068] Thus, in this embodiment, the PPG features 128 are fed to a multilayer feed forward neural network (FFNN) architecture, which has a given number (for example, 14) of input neurons (equal to or less than the total number of SCSA features 128) and 3 output neurons, to simultaneously estimate SBP, DBP and MAP. One possible architecture of the FNNN 1700 is shown in Figure 17 and has one hidden layer 1702. A loss function L of the neural network is defined as:

where m is the number of samples, y is the expected output, and y is reference output. Considering that this NN architecture is for small and middle scale problems such as BP regression, the Levenberg-Marquardt (LM) algorithms are utilized in the network back-propagation training process. The approximated Hessian H used in the hidden layer 1702 for estimating the expected output y is given by:

where μ > 0 and J denotes the Jacobian matrix of the loss function L of equation (14). The Levenberg-Marquardt algorithm uses this approximated Hessian matrix to iteratively update the hidden layer 1702’s weights W, in a Newton like way, as described by:

[0069] The obtained histograms of errors for the differences between the real SBP and DBP and the output of the FFNN indicate that the mean difference and standard deviation between the estimated BP and measured BP are -0.0252 ± 4.8569 mmHg for DBP and 0.0349 ± 6.4477 mmHg for SBP, which meets the ISO standards.

[0070] The method discussed in [10] has the problem of its SBP estimate not meeting the AAMI standard. The FFNN structure discussed above solves this problem by increasing the SBP estimation accuracy. Similarly, to the algorithms previously used in the method of Figure 13, the AAMI standard has been used to evaluate the results of the NN based method. The inventors found that the proposed ABP estimation algorithm works properly, with estimation accuracy meeting the ISO standard.

[0071] The various implementations of the method presented in Figure 13 solved the problem of continuous ABP estimation by utilizing a single noninvasive PPG sensor. A noninvasive, cuffless, calibration-free, and continuous BP estimation approach was developed based on the semi-classical signal analysis. These methods present a completely new way of PPG signal feature extraction using SCSA. The proposed methods were tested based on the MIMC II database, which contains a large volume of samples, and the tests demonstrated robustness and statistical reliability. In one embodiment, the proposed methodology includes signal preprocessing, feature extraction, and regression stages. It was shown that the proposed ABP estimation algorithm works properly, with estimation accuracy meeting the ISO standard.

[0072] The disclosed embodiments provide methods and systems for estimating the blood pressure in a patient in a non-invasive and continuous way, using just a sensor, and producing accurate results. It should be understood that this description is not intended to limit the invention. On the contrary, the embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details.

[0073] Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. [0074] This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.

References

The entire content of all the publications listed herein is incorporated by reference in this patent application.

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Claims

WHAT IS CLAIMED IS:

1. A method for estimating blood pressure related quantities associated with a patient, the method comprising: receiving (1300) a photoplethysmography, PPG, signal (132), wherein the PPG signal (132) is collected with a single PPG sensor; extracting (1302) plural semi-classical signal analysis, SCSA, features (128) from the PPG signal (132), by using a Schrodinger operator; processing (1304) the plural SCSA features (128) at processor (122) with a machine learning algorithm module (130), to calculate negative eigenvalues ( k_n ) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, wherein n varies between 1 and N_h, N_h is a total number of negative eigenvalues (k_n), and h is a semi-classical constant; and calculating (1306) the blood pressure related quantities (132, 134) based on (1) the calculated negative eigenvalues ( k_n ) and (2) the associated eigenfunctions (Ψ_h) of the Schrodinger operator.

2. The method of Claim 1, further comprising: estimating a heart health status of a patient from which the PPH signal was collected, based on the calculated blood pressure related quantities.

3. The method of Claim 1, wherein the blood pressure related quantities includes a systolic blood pressure and a diastolic blood pressure.

4. The method of Claim 1, wherein the blood pressure related quantities are calculated without using an electrocardiogram, ECG, signal.

5. The method of Claim 1, further comprising: selecting largest N_s negative eigenvalues ( k_n ) and associated eigenfunctions ( Ψ _n ) of the Schrodinger operator; calculating a systolic blood pressure, SBP, as a sum of the largest N_s negative eigenvalues ( k_n ), each multiplied by a corresponding eigenfunctions ( Ψ_h ) of the Schrodinger operator; and calculating a diastolic blood pressure, DBP, as a sum of the remaining negative eigenvalues ( k_n ), each multiplied by a corresponding eigenfunctions ( Ψ_h ) of the Schrodinger operator, wherein N_s is smaller than N_h.

6. The method of Claim 1, wherein the plural SCSA features includes one or more of the negative eigenvalues ( k_n ).

7. The method of Claim 6, wherein the plural SCSA features further include a first systolic invariant, which includes a sum of largest N_s negative eigenvalues ( k_n ) of the Schrodinger operator.

8. The method of Claim 7, wherein the plural SCSA features further include a second systolic invariant, which includes a sum of largest N_s negative eigenvalues

( k_n ) of the Schrodinger operator, each at power three.

9. The method of Claim 8, wherein the plural SCSA features further include a first diastolic invariant, which includes a sum of a remainder of the negative eigenvalues ( k_n ) of the Schrodinger operator.

10. The method of Claim 9, wherein the plural SCSA features further include a second diastolic invariant, which includes a sum of the remainder of the negative eigenvalues ( k_n ) of the Schrodinger operator, each at power three.

11. The method of Claim 10, wherein the plural SCSA features further include an eigenvalue summation that includes a sum of all the negative eigenvalues ( k_n ) of the Schrodinger operator.

12. The method of Claim 1, wherein the machine learning algorithm module uses a multiple linear regression to calculate the negative eigenvalues ( k_n ) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, or a support vector machine, or a decision tree algorithm, or a feed forward neural network.

13. A system (100) for estimating blood pressure related quantities associated with a patient, the system (100) comprising: an interface (114) configured to receive (1300) a photoplethysmography,

PPG, signal (132), wherein the PPG signal (132) is collected with a single PPG sensor; and a processor (122) connected to the interface (114) and configured to, extract (1302) plural semi-classical signal analysis, SCSA, features (128) from the PPG signal (132), by using a Schrodinger operator, process (1304) the plural SCSA features (128) with a machine learning algorithm module (130) to calculate negative eigenvalues ( k_n ) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, wherein n varies between 1 and N_h, N_h is a total number of negative eigenvalues (k_n), and h is a semi-classical constant, and calculate (1306) the blood pressure related quantities (132, 134) based on (1) the calculated negative eigenvalues ( k_n ) and (2) the associated eigenfunctions (Ψ_h) of the Schrodinger operator.

14. The system of Claim 13, wherein the processor is further configured to: estimate a heart health status of a patient from which the PPH signal was collected, based on the calculated blood pressure related quantities.

15. The system of Claim 13, wherein the blood pressure related quantities includes a systolic blood pressure and a diastolic blood pressure.

16. The system of Claim 13, further comprising: only the PPG sensor, wherein the blood pressure related quantities are calculated without using an electrocardiogram, ECG, signal.

17. The system of Claim 13, wherein the processor is further configured to: select largest N_s negative eigenvalues ( k_n ) and associated eigenfunctions

(Ψ_h) of the Schrodinger operator; calculate a systolic blood pressure, SBP, as a sum of the largest N_s negative eigenvalues (k_n), each multiplied by a corresponding eigenfunctions (Ψ_h) of the Schrodinger operator; and calculate a diastolic blood pressure, DBP, as a sum of the remaining negative eigenvalues (k_n), each multiplied by a corresponding eigenfunctions (Ψ_h) of the Schrodinger operator, wherein N_s is smaller than N_h.

18. The system of Claim 13, wherein the plural SCSA features includes one or more of the negative eigenvalues ( k_n ).

19. The system of Claim 18, wherein the plural SCSA features further include one or more of a first systolic invariant, which includes a sum of largest N_s negative eigenvalues ( k_n ) of the Schrodinger operator, a second systolic invariant, which includes a sum of largest N_s negative eigenvalues ( k_n ) of the Schrodinger operator, each at power three, a first diastolic invariant, which includes a sum of a remainder of the negative eigenvalues ( k_n ) of the Schrodinger operator, a second diastolic invariant, which includes a sum of the remainder of the negative eigenvalues ( k_n ) of the Schrodinger operator, at power three; and an eigenvalue summation that includes a sum of all the negative eigenvalues (k_n) of the Schrodinger operator.

20. The system of Claim 13, wherein the machine learning algorithm module uses a multiple linear regression to calculate the negative eigenvalues (k_n) and associated eigenfunctions (Ψ_h) of the Schrodinger operator, or a support vector machine, or a decision tree algorithm, or a feed forward neural network.