Patent Description:
<CIT> relates to determining vital signs of a subject.

<NPL> highlights the PPG morphological analysis based on pressure-flow relationship and correlation analysis between blood pressure and derived parameter.

<CIT> relates to a method to estimate the blood pressure and the arterial stiffness based on photoplethysmographic (PPG) signals.

Blood pressure (BP) is an important indicator of health in a person/subject. In the US it is estimated about <NUM>% of the adult population has high blood pressure. Hypertension is a common health problem which has no obvious outward symptoms. Blood pressure generally rises with aging and the risk of becoming hypertensive in later life is considerable. Persistent hypertension is one of the key risk factors for strokes, heart failure and increased mortality. The condition of a subject can be improved by lifestyle changes, healthy dietary choices and medication. Particularly for high risk patients, continuous <NUM>-hour blood pressure monitoring is very important by means of systems which do not impede ordinary daily life activities. Continuous monitoring of blood pressure can also be useful for patients in a healthcare environment, such as a hospital e.g. in the operating room (OR) or the Intensive Care Unit (ICU). A low blood pressure can lead to a poor oxygenation of important organs and could result in organ damage. A too high blood pressure can cause bleeding which should be prevented especially during and after surgical procedures, specifically in brain surgeries.

In some cases, absolute measurements of blood pressure can be obtained, and in other cases relative measurements of blood pressure can be obtained, for example a measurement of a change in blood pressure. In particular, blood pressure can change over short time windows, e.g. of the order of a few minutes, and these changes can be relevant for further medical examination and possibly medical intervention.

There are a number of different techniques available for measuring blood pressure, and/or changes in blood pressure. Some of these techniques measure blood pressure itself, while other techniques measure other physiological characteristics of the subject and use these as surrogates for blood pressure, for example by relating changes or values of the physiological characteristic to changes or values of blood pressure. Some of the techniques for directly measuring blood pressure require invasive access to the arteries of the subject, or the use of bulky/inconvenient equipment such as inflatable cuffs. However, some of the physiological characteristics used as surrogates for blood pressure can be measured using simple and/or unobtrusive sensors applied to the body of the subject.

Tonometry uses an externally placed force or pressure sensor to measure arterial distension (i.e. a waveform representing the distension of the artery) as pressure is applied to the artery. Alternatively, one or more photoplethysmography (PPG) sensors can be placed on a part of the body to obtain one or more PPG signals that represent the changes in volume of the blood flow in the body part during a number of heart cycles (cardiac cycles). Both of these techniques obtain a pulse wave signal (PWS) from the subject that covers a number of cardiac cycles of the subject. This pulse waveform/signal can be analysed to determine one or more physiological characteristics that are used as surrogate blood pressure measurements.

One physiological characteristic that can be used as a surrogate blood pressure measurement is pulse wave velocity (PWV). When the heart beats, a pulse wave is generated through the blood of the aorta and the further arterial system. The speed of the pulse wave (called pulse wave velocity) is influenced by blood (fluid) properties and some arterial properties (like diameter and compliance). These blood properties and arterial properties are also influenced by blood pressure, and so changes in PWV can be linked to changes in blood pressure.

Some techniques for measuring PWV use a two-spot or dual-spot approach. This requires two sensors (e.g. PPG sensors) in order to capture two signals simultaneously. The signal from the first sensor is used to detect the onset of the pulse wave at a proximal location, e.g. close to the heart. The signal from the second signal is used to detect the arrival of the pulse wave at a distal location, e.g. at the femoral artery of the finger of the patient.

However, to minimise the inconvenience for the subject due to the measurement equipment, single-spot techniques for measuring PWV are being developed. These techniques make use of pulse wave reflections in the arterial tree. There is a direct pulse wave traveling from the aorta to, for example, the finger, and there is an indirect pulse wave that first travels from the aorta to the renal bifurcation and then travels from the renal bifurcation to the finger. In this way, the indirect (reflected) pulse wave arrives later at the finger location than the direct pulse wave. When the arrival times of the direct and indirect pulse waves are measured at the finger, a subtraction of these arrival times gives the time required to travel from the aortic arch to the renal bifurcation and back. With knowledge (or an approximation) of this extra travel distance of the reflected pulse wave, it is possible to estimate the pulse wave velocity of the reflected wave according to Equation (<NUM>) below: <MAT> where Lhr is the distance between the aortic arch and the renal bifurcation and PRT is the so-called pulse reflection time, which is defined as the time between the start (up-flank) of the direct pulse wave until the time of the start (up-flank) of the indirect pulse wave. The times tc and ta required to compute the PRT can be determined via the so-called "acceleration waveform" of the PPG measurement, that is obtained via, e.g. double-differentiation of the PPG waveform with respect to time.

Typically, it is assumed that the acceleration waveform consists of five 'fiducial points' or 'reference points', as shown in <FIG> shows an exemplary PPG signal covering a <NUM> second period with the dicrotic notch indicated. <FIG> shows a first derivative of the PGG signal of <FIG> with respect to time, and <FIG> shows a second derivative of the PGG signal of <FIG> with respect to time. The first derivative is denoted v-PPG and the second derivative (acceleration waveform) is denoted a-PPG. The five reference points are shown in the acceleration waveform, <FIG>. The a point marks the start of the direct pulse wave and the b point marks the end of the direct pulse wave. The e point marks the end of the systolic period (aortic valve closure), and for the purposes of this disclosure it is assumed that the c point marks the start of the reflected wave and the d point marks the end of the reflected wave.

<FIG> shows an example of a single-spot PPG measurement and PWV derivation according to Equation (<NUM>). The graph in <FIG> shows the mean arterial pressure (MAP) in mmHg over a period of <NUM> hours of an ICU patient. The graph in <FIG> shows PWV in m/s calculated from a PPG signal according to Equation (<NUM>), with an estimation of <NUM>Lhr (twice the heart to the renal bifurcation distance) as <NUM>.

It can be seen in <FIG> that there is a strong positive correlation between the MAP and the pulse wave velocity from the single-spot measurement. However, the robustness of the pulse wave velocity measurement can be questioned since there are a lot of outliers in the pulse wave velocity values, particularly when compared to pulse wave velocity derived from a two-spot measurement approach.

Part of the problem with the single-spot pulse wave velocity measurement is that the fiducial points of the reflected pulse waves are not always easy to detect. This can be seen from the a-PPG plot in <FIG>. Computing a second derivative of this PPG signal leads to a very poor signal because of the quantization and noise in the original PPG signal. Signal smoothing (either temporal or over multiple cardiac cycles) can be applied in order to obtain improved fiducial point detections. After such smoothing, it becomes possible to robustly detect the fiducial points. However, for a good detection of the c and d points (which relate to the reflected wave) quite substantial smoothing needs to be applied before the fiducial points can be robustly detected. Too much temporal smoothing leads to loss in the high-frequency fiducial points, whereas too much averaging over multiple cardiac cycles gives problems under time varying conditions).

Therefore, there is a need for improvements in the averaging of cardiac cycle waveforms.

The techniques described herein apply averaging over multiple cardiac cycles to reduce or remove the noise in the resulting average to enable an improved analysis of reflected pulse waves and/or other characteristics of the cardiac cycle waveform. As noted above, analysis of reflected pulse waves can be used as a surrogate blood pressure measurement, but it will be appreciated that analysis of an averaged cardiac cycle waveform can be used for monitoring other aspects of the health of the subject, e.g. trends of arterial compliance of a patient during a full hospital stay.

According to a first specific aspect, there is provided a computer-implemented method for analysing a pulse wave signal (PWS) obtained from a subject. The PWS comprises pulse wave measurements for a plurality of cardiac cycles of the subject during a first time period. The method comprises (i) analysing the PWS to identify a plurality of cardiac cycles and a respective reference point for each identified cardiac cycle; (ii) determining 2PWS as a second derivative with respect to time of the PWS; (iii) determining a normalised 2PWS by, for each part of the 2PWS corresponding to a respective identified cardiac cycle, normalising said part of the 2PWS with respect to the amplitude of the 2PWS at the identified reference point for said cardiac cycle; (iv) for a first lag time value, determining an n-th order polynomial fit for a first set of values of the normalised 2PWS, wherein the first set of values of the normalised 2PWS comprises the values of the normalised 2PWS occurring the first lag time value from the reference point of each identified cardiac cycle, wherein n is equal to or greater than <NUM>; (v) performing one or more further iterations of step (iv) for one or more further lag time values to determine respective further n-th order polynomial fits for respective sets of values of the normalised 2PWS, wherein a respective set of values of the normalised 2PWS comprises the values of the normalised 2PWS that occur the respective further lag time value from the reference point of each identified cardiac cycle; and (vi) forming a first average cardiac cycle waveform for a first time point in the first time period, wherein the first average cardiac cycle waveform is formed from values of the plurality of n-th order polynomial fits at the first time point. Therefore, this aspect provides an improved average cardiac cycle waveform that takes into account a trend in the PWS over the first time period, and that allows for improved analysis of a PWS obtained using, for example, a single-spot measurement technique.

In some embodiments, the method further comprises forming a second average cardiac cycle waveform for a second time point in the first time period, wherein the second average cardiac cycle waveform is formed from values of the plurality of n-th order polynomial fits at the second time point.

In these embodiments, the method can further comprise comparing the first average cardiac cycle waveform and the second average cardiac cycle waveform to determine a change in the average cardiac cycle waveform between the first time point and the second time point. These embodiments provide that changes in the average cardiac cycle waveform over the first time period can be evaluated, for example to evaluate how a property related to the cardiac cycle has changed.

In these embodiments, the method can further comprise determining a measure of the blood pressure of the subject, or a measure of a change in blood pressure of the subject, from the first average cardiac cycle waveform and the second average cardiac cycle waveform.

In some embodiments, the method further comprises processing the first average cardiac cycle waveform to determine a measure of the blood pressure of the subject.

In some embodiments, each of the first lag time value and the one or more further lag time values are equal to or less than a duration of a cardiac cycle of the subject.

In some embodiments, the reference point for each identified cardiac cycle is an onset of a pulse wave of the subject. This reference point is useful as it is relatively easy to detect in first or second derivative of the PWS with respect to time.

In some embodiments, step (ii) is performed prior to, or as part of, step (i), and step (i) can comprise identifying the plurality of cardiac cycles and the respective reference point for each identified cardiac cycle as local maxima in the 2PWS.

In alternative embodiments, step (ii) is performed prior to, or as part of, step (i), and step (i) can comprise detecting peaks in a first derivative with respect to time of the PWS (1PWS); and identifying the plurality of cardiac cycles and the respective reference point for each identified cardiac cycle as local maxima in the 2PWS within respective search windows defined by the detected peaks in the 1PWS.

In some embodiments, n is <NUM>. In other embodiments, n is <NUM>. In some embodiments, the PWS is a photoplethysmogram (PPG) signal.

According to a second aspect, there is provided an apparatus for analysing a pulse wave signal (PWS) obtained from a subject. The PWS comprises pulse wave measurements for a plurality of cardiac cycles of the subject during a first time period. The apparatus is configured to: (i) analyse the PWS to identify a plurality of cardiac cycles and a respective reference point for each identified cardiac cycle; (ii) determine 2PWS as a second derivative with respect to time of the PWS; (iii) determine a normalised 2PWS by, for each part of the 2PWS corresponding to a respective identified cardiac cycle, normalising said part of the 2PWS with respect to the amplitude of the 2PWS at the identified reference point for said cardiac cycle; (iv) for a first lag time value, determine an n-th order polynomial fit for a first set of values of the normalised 2PWS, wherein the first set of values of the normalised 2PWS comprises the values of the normalised 2PWS occurring the first lag time value from the reference point of each identified cardiac cycle, wherein n is equal to or greater than <NUM>; (v) perform one or more further iterations of operation (iv) for one or more further lag time values to determine respective further n-th order polynomial fits for respective sets of values of the normalised 2PWS, wherein a respective set of values of the normalised 2PWS comprises the values of the normalised 2PWS that occur the respective further lag time value from the reference point of each identified cardiac cycle; and (vi) form a first average cardiac cycle waveform for a first time point in the first time period, wherein the first average cardiac cycle waveform is formed from values of the plurality of n-th order polynomial fits at the first time point. Therefore, this aspect provides an improved average cardiac cycle waveform that takes into account a trend in the PWS over the first time period, and that allows for improved analysis of a PWS obtained using, for example, a single-spot measurement technique.

In some embodiments, the apparatus is further configured to form a second average cardiac cycle waveform for a second time point in the first time period, wherein the second average cardiac cycle waveform is formed from values of the plurality of n-th order polynomial fits at the second time point.

In these embodiments, the apparatus can be further configured to compare the first average cardiac cycle waveform and the second average cardiac cycle waveform to determine a change in the average cardiac cycle waveform between the first time point and the second time point. These embodiments provide that changes in the average cardiac cycle waveform over the first time period can be evaluated, for example to evaluate how a property related to the cardiac cycle has changed.

In these embodiments, the apparatus can be further configured to determine a measure of the blood pressure of the subject, or a measure of a change in blood pressure of the subject, from the first average cardiac cycle waveform and the second average cardiac cycle waveform.

In some embodiments, the apparatus can be further configured to process the first average cardiac cycle waveform to determine a measure of the blood pressure of the subject.

In some embodiments, operation (ii) is performed prior to, or as part of, operation (i), and operation (i) can comprise identifying the plurality of cardiac cycles and the respective reference point for each identified cardiac cycle as local maxima in the 2PWS.

In alternative embodiments, operation (ii) is performed prior to, or as part of, operation (i), and operation (i) can comprise detecting peaks in a first derivative with respect to time of the PWS (1PWS); and identifying the plurality of cardiac cycles and the respective reference point for each identified cardiac cycle as local maxima in the 2PWS within respective search windows defined by the detected peaks in the 1PWS.

In some embodiments, n is <NUM>. In other embodiments, n is <NUM>.

In some embodiments, the PWS is a photoplethysmogram (PPG) signal.

In some embodiments, the apparatus further comprises a pulse wave sensor for obtaining the PWS from the subject. In alternative embodiments, the apparatus is configured to receive the PWS from a pulse wave sensor.

According to a third aspect, there is provided a computer program product comprising a computer readable medium having computer readable code embodied therein, the computer readable code being configured such that, on execution by a suitable computer or processor, the computer or processor is caused to perform the method according to the first aspect or any embodiment thereof.

The techniques described herein apply averaging over multiple cardiac cycles to reduce or remove the noise in the resulting average to enable an improved analysis of reflected pulse waves and/or other characteristics of the cardiac cycle waveform. Analysis of reflected pulse waves can be used as a surrogate blood pressure measurement, but it will be appreciated that analysis of an averaged cardiac cycle waveform can provide information about other aspects of the health of the subject. The described techniques are particularly useful for the so-called single-spot measurement techniques where a single sensor is applied to a subject.

For a pulse wave signal (PWS) that includes information about pulse changes/pulse waves at a measurement point on a body of a subject, reference points for each of the cardiac cycles to be smoothed are identified in the PWS. The PWS can be, e.g., a PPG signal or a pulse wave signal obtained using tonometry. The reference point to be identified preferably relates to the initial up-flank of the pulse wave, which should be free of influences of reflections and hence should be a stable reference point (i.e. not dependent on blood pressure changes). However it will be appreciated that a different reference point can be used if desired. Next, the times and amplitudes of the various occurrences of the reference points are used in order to compute an average cardiac cycle waveform. Normal averaging of all cardiac cycle waveforms across the time window does not allow for time-varying circumstances. Such normal averaging is described in <CIT>. The averaging technique described herein extends the averaging to allow for (linear) variation in time for each lag in the averaging procedure (where the lag, or lag time, is a time relative to the identified reference point for each cardiac cycle, e.g. the time relative to the identified a reference point for each cardiac cycle).

<FIG> is a block diagram of an apparatus <NUM> for analysing a PWS according to various embodiments of the techniques described herein. A pulse wave sensor <NUM> is shown in <FIG> that is used to measure pressure waves at a single point on the body of a subject and to output a PWS. The pulse wave sensor <NUM> can be a PPG sensor, a tonometry-based sensor or a hydraulic sensor pad that can be applied with some application pressure to the (upper) arm of the subject and using a pressure sensor of any type, e.g. the MPXV6115 Series Integrated Silicon Pressure Sensor from NXP Semiconductors. In some embodiments, the pulse wave sensor <NUM> can be part of, or integral with, the apparatus <NUM>. In other embodiments, the apparatus <NUM> can be connected to the pulse wave sensor <NUM>, either directly (e.g. wired) or indirectly (e.g. using a wireless communication technology such as Bluetooth, WiFi, a cellular communication protocol, etc.). In alternative embodiments, the apparatus <NUM> may not be connected to the pulse wave sensor <NUM>, and instead the apparatus <NUM> can obtain the PWS from another device or apparatus, such as a server or database.

As is known, a PPG sensor <NUM> can be placed on the body of the subject, for example on an arm, leg, earlobe, finger, etc., can provide an output signal (a 'PPG signal') that is related to the volume of blood passing through that part of the body. The volume of blood passing through that part of the body is related to the pressure of the blood in that part of the body. A PPG sensor <NUM> typically comprises a light sensor, and one or more light sources. The PPG signal output by the PPG sensor <NUM> may be a raw measurement signal from the light sensor (e.g. the PPG signal can be a signal representing light intensity over time). Alternatively, the PPG sensor <NUM> may perform some pre-processing of the light intensity signal, for example to reduce noise and/or compensate for motion artefacts, but it will be appreciated that this pre-processing is not required for the implementation of the techniques described herein.

The apparatus <NUM> may be in the form of, or be part of, a computing device, such as a server, desktop computer, laptop, tablet computer, smartphone, smartwatch, etc., or a type of device typically found in a clinical environment, such as a patient monitoring device (e.g. a monitoring device located at the bedside of a patient in a clinical environment) that is used to monitor (and optionally display) various physiological characteristics of a subject/patient.

The apparatus <NUM> includes a processing unit <NUM> that controls the operation of the apparatus <NUM> and that can be configured to execute or perform the methods described herein to analyse the PWS. The processing unit <NUM> can be implemented in numerous ways, with software and/or hardware, to perform the various functions described herein. The processing unit <NUM> may comprise one or more microprocessors or digital signal processors (DSPs) that may be programmed using software or computer program code to perform the required functions and/or to control components of the processing unit <NUM> to effect the required functions. The processing unit <NUM> may be implemented as a combination of dedicated hardware to perform some functions (e.g. amplifiers, pre-amplifiers, analog-to-digital convertors (ADCs) and/or digital-to-analog convertors (DACs)) and a processor (e.g., one or more programmed microprocessors, controllers, DSPs and associated circuitry) to perform other functions. Examples of components that may be employed in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, DSPs, application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), hardware for implementing a neural network and/or so-called artificial intelligence (AI) hardware accelerators (i.e. a processor(s) or other hardware specifically designed for AI applications that can be used alongside a main processor).

The processing unit <NUM> is connected to a memory unit <NUM> that can store data, information and/or signals for use by the processing unit <NUM> in controlling the operation of the apparatus <NUM> and/or in executing or performing the methods described herein. In some implementations the memory unit <NUM> stores computer-readable code that can be executed by the processing unit <NUM> so that the processing unit <NUM> performs one or more functions, including the methods described herein. In particular embodiments, the program code can be in the form of an application for a smartwatch, smartphone, tablet, laptop or computer. The memory unit <NUM> can comprise any type of non-transitory machine-readable medium, such as cache or system memory including volatile and non-volatile computer memory such as random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM) and electrically erasable PROM (EEPROM), and the memory unit <NUM> can be implemented in the form of a memory chip, an optical disk (such as a compact disc (CD), a digital versatile disc (DVD) or a Blu-Ray disc), a hard disk, a tape storage solution, or a solid state device, including a memory stick, a solid state drive (SSD), a memory card, etc..

In some embodiments, the apparatus <NUM> comprises a user interface <NUM> that includes one or more components that enables a user of apparatus <NUM> to input information, data and/or commands into the apparatus <NUM>, and/or enables the apparatus <NUM> to output information or data to the user of the apparatus <NUM>. Information that can be output by the user interface <NUM> can include an indication or illustration of an averaged cardiac cycle waveform for one or more time points, and/or information derived from an averaged cardiac cycle waveform. The user interface <NUM> can comprise any suitable input component(s), including but not limited to a keyboard, keypad, one or more buttons, switches or dials, a mouse, a track pad, a touchscreen, a stylus, a camera, a microphone, etc., and/or the user interface <NUM> can comprise any suitable output component(s), including but not limited to a display screen, one or more lights or light elements, one or more loudspeakers, a vibrating element, etc..

It will be appreciated that a practical implementation of an apparatus <NUM> may include additional components to those shown in <FIG>. For example the apparatus <NUM> may also include a power supply, such as a battery, or components for enabling the apparatus <NUM> to be connected to a mains power supply. The apparatus <NUM> may also include interface circuitry for enabling a data connection to and/or data exchange with other devices, including the pulse wave sensor <NUM> (in embodiments where the pulse wave sensor <NUM> is separate from the apparatus <NUM>), servers, databases, user devices and/or other sensors.

The flow chart in <FIG> shows an exemplary method for analysing a PWS obtained from a subject according to various embodiments. In some embodiments, the processing unit <NUM> in the apparatus <NUM> can be configured to implement the method in <FIG>. In other embodiments computer readable code can be provided that causes a computer or the processing unit <NUM> to perform the method of <FIG> when the computer or processing unit <NUM> executes the code.

The PWS is received from a pulse wave sensor <NUM> located at a single measurement point on the subject and the PWS represents pulse wave measurements for a plurality of cardiac cycles (i.e. heart beats) of the subject. The PWS is obtained with a sampling rate Fs. The method in <FIG> is described below with reference to a PWS in the form of a PPG signal, but it will be appreciated that the method can be applied to other forms of PWS. In some embodiments, the method in <FIG> can be performed periodically or continuously on a PWS as it is received or measured from the subject. In some embodiments, the method of <FIG> can operate on a windowed portion of a longer PWS, for example a <NUM>-minute window of a PWS covering a time period of <NUM> hour. However, it should be appreciated that the method can be applied to a PWS having any desired length that covers any number of cardiac cycles. In the following description, references to operations or steps being performed on the PWS relates to performing those operations or steps on the part of the PWS of interest, e.g. a part corresponding to a <NUM>-minute time period.

In a first step of the method, step <NUM>, the PWS is analysed to identify cardiac cycles, and a respective reference point is identified for each cardiac cycle. The reference point is a point in each cardiac cycle that can be used in subsequent steps to 'align' the cardiac cycles and enable an average to be determined.

As described above with reference to <FIG>, each cardiac cycle in an 'acceleration waveform' (the second derivative of the PWS with respect to time) can be considered to comprise five 'fiducial points' or 'reference points'. The a reference point marks the start of the direct pulse wave, which is the onset of the pulse wave (i.e. the pulse of blood caused by the beat of the heart) and the b point marks the end of the direct pulse wave. The e point marks the end of the systolic period (aortic valve closure), and for the purposes of this disclosure it is assumed that the c point marks the start of the reflected wave and the d point marks the end of the reflected wave. Preferably, in step <NUM> the reference point for each cardiac cycle is the onset of the pulse wave (the direct part of the pulse wave) which can be seen as the start of the systole phase - i.e. reference point a. However, it will be appreciated that in other embodiments, other ones of the reference points can be identified in step <NUM>, or indeed a different reference point to reference points a to e shown in <FIG>.

In the following, the signal corresponding to the first derivative of the PWS with respect to time is denoted '1PWS' and the signal corresponding to the second derivative of the PWS with respect to time is denoted '2PWS'. When described with reference to the specific example of a PPG signal, the 1PWS is also referred to as a 'velocity waveform' (v-PPG) and the 2PWS is also referred to as an 'acceleration waveform' (a-PPG).

Some embodiments of step <NUM> provide for the detection of the onsets of the pulse wave by detecting the local maxima in each cardiac cycle represented in the 2PWS. However, it can be seen in <FIG> that a double-differentiated PPG signal can be of low quality because of noise or quantization in the original PPG signal.

Therefore, in a more preferred embodiment, the onset of the pulse wave is detected using a two stage process. <FIG> shows the same <NUM>-second segment of the PPG signal shown in <FIG>. <FIG> shows the first derivative of the PPG signal with respect to time (v-PPG), and <FIG> shows the second derivative of the PPG signal with respect to time (a-PPG). In <FIG>, the onset of the pulse wave for the two cardiac cycles is indicated by the points labelled <NUM>, and the aim of this embodiment is to identify these points. In the first stage, peak detection is performed on the first derivative of the PWS with respect to time (1PWS). It can be seen in <FIG> that the peaks in the v-PPG signal will correspond roughly to the steepest flank in the original PPG waveform (shown in <FIG>). The peaks detected in the v-PPG signal are labelled <NUM>.

After detecting the maximum velocity peaks <NUM> in the 1PWS, then in the second stage narrowed (local) search windows are applied to the 2PWS (e.g. the a-PPG shown in <FIG>) based on the timing of each of the maximum velocity peaks <NUM>, and the maximum peaks in those narrowed search windows on the 2PWS are detected. The narrowed search window can have a duration of <NUM>-<NUM>. These maximum peaks correspond to the desired a reference points, i.e. the onset of the pulse wave corresponding to the up-flank in the PWS signal. In the a-PPG waveform shown in <FIG>, the narrowed search windows are indicated by the horizontal lines <NUM> that end at the timing of the detected velocity peaks <NUM>. The maximum peaks identified in those narrowed search windows on the a-PPG waveform are labelled <NUM>, and correspond to the desired a reference points.

Since the 2PWS can be noisy in case of poorly quantized signals, it can be beneficial to perform some smoothing prior to detection of the peaks in the 1PWS. This smoothing can be applied to the PWS before differentiation, or applied to the 1PWS before peak detection is performed. In some embodiments the smoothing can be achieved using by filtering, e.g. Savitzky-Golay filtering. The result of the smoothing process and differentiating a smoothed PWS/1PWS to determine the 2PWS can be seen by the smoothed line in <FIG>.

In <FIG> the maxima/minima of the b, c, d and e waves are also shown for the first cardiac cycle. It can be seen that the c and d waves are very small (even in this best case situation) and will typically be very difficult to detect robustly. This illustrates the preference for the detection of the a reference point, but as noted above it would be possible to target the detection of other reference points in step <NUM>. In the following, the detected a reference points for multiple cardiac cycles are used to perform an averaging of multiple cardiac cycles in order to determine an average cardiac cycle waveform.

Next, in steps <NUM>, <NUM> and <NUM>, an averaging technique is applied to the PWS to determine an average cardiac cycle waveform for one or more time points Y in the time period covered by the PWS. Steps <NUM>, <NUM> and <NUM> are described below with reference to the exemplary 2PWS (in the form of an a-PPG) shown in <FIG>. The 2PWS in <FIG> is derived from a PPG signal covering a <NUM>-minute time period for a particular subject. This <NUM>-minute time period covers <NUM> cardiac cycles of the subject. The respective reference points identified in step <NUM> for each cardiac cycle in the a-PPG waveform are marked in <FIG> shows measurements of the arterial blood pressure (ABP - the thin line) and mean arterial pressure (MAP - the thicker line) for the same subject and same time period that the a-PPG signal in <FIG> relates to. The ABP measurements are shown in <FIG> to provide context for the a-PPG waveform in <FIG>, and it will be appreciated that an ABP measurement will typically not be available for a subject for which a single-spot PWS measurement is being obtained. It can be seen in <FIG> that there is an increase in the mean arterial pressure of the order of <NUM> mmHg between <NUM> and <NUM> seconds. In the a-PPG waveform (<FIG>) there is some visible change at around <NUM> seconds (e.g. high respiratory modulation of the a reference points from <NUM>-<NUM> seconds and low respiratory modulation of the a reference points from <NUM>-<NUM> seconds), and the averaging technique described herein can be used to identify and/or analyse the changes in the morphology of the a-PPG waveform over and/or throughout the <NUM>-second window.

To show how the morphology of the a-PPG changes over the <NUM>-second duration, <FIG> is a graph showing seven cardiac cycles from the a-PPG waveform of <FIG> overlaid with each other. The seven cardiac cycles included in <FIG> are labelled <NUM> to <NUM> in <FIG>, and they are relatively evenly spaced through the <NUM>-minute time window. It should be noted that these <NUM> cardiac cycles have been arbitrarily chosen from the cardiac cycles identified in <FIG> simply to provide a representation of how the cardiac cycle can change. In <FIG> the a-PPG waveforms for the <NUM> selected cardiac cycles are overlaid with the a reference points of each a-PPG waveform aligned, and the respective a-PPG waveforms are normalised so that the amplitude of each a-PPG waveform at the aligned a reference points are the same (amplitude = <NUM>), and at other times the a-PPG waveforms have respective amplitudes that are usually in the range of -<NUM> to <NUM>. The time measured from the aligned reference points is referred to as the "lag time" or "lag time value", and is denoted TΔk, with the aligned reference points corresponding to lag time TΔk = <NUM> seconds. Each of the <NUM> waveforms shown in <FIG> are referred to as 'normalised' a-PPG waveforms herein, i.e. they are normalised around a common part of the cardiac cycle (e.g. reference point 'a' of each cardiac cycle in this example), with the amplitudes of the a-PPG waveforms matched at that reference point.

It can be seen in <FIG> that the complete morphology (after the a reference point) changes over time because of the blood pressure change. It can also be seen that it is very difficult to identify or analyse the waveforms separately, in part due to the noise in the second-derivative computation.

Since the pulse wave morphology can be constantly changing, as shown in the example of <FIG>, simply applying an averaging to the multiple waveforms would lose the high-frequency information that is relevant for the analysis of the reflected pulse wave. Therefore, an averaging method is required where a linear change can be taken into account. The averaging technique disclosed herein is based on the technique in <CIT> with an extension to accommodate the linear change.

For describing the algorithm hereafter, a vector x is defined as the a-PPG data in a time window with a duration of Nx/Fs seconds. The reference points (which in the following worked example are the peak locations, the a reference points) of the waveform selection x are listed as a vector p that has a length Np, where Np is the number of cardiac cycles/identified reference points. In the example of <FIG> and <FIG>, Np is <NUM>. The waveform values at the detected peak locations are denoted by x(p)j where j = <NUM>,. , Np-<NUM> is the index of the peak in each heart cycle. The values from the peak locations will be denoted in short format later on as <MAT> where j = <NUM>,. , Np-<NUM> is the index of the peak. The next step in the averaging process is to analyse the Np neighbouring samples (towards the left and right with respect to the initial peaks (the a reference points) and compute the average change (decrease) compared to the initial peak level. Similar to the peaks, the neighbouring locations with respect to the peak locations are defined in short format as: <MAT> where Δk is the lag index with respect to the peak locations, which can be either positive or negative valued. The lag index Δk relates to the lag time TΔk via: <MAT>.

For all neighbouring locations with respect to the peak locations which are inside the <NUM>-minute window, the average level change (drop) is computed as: <MAT> where N equals the number of averaged values that are in the region [<NUM>.

This means that N in the averaging procedure is not necessarily equal to the number of peaks Np, and will be <NUM> or <NUM> smaller depending on whether some of the values (p)j + Δk are outside the window with length Nx.

The computation of the model is done for several negative and positive values of Δk, called iterations or repetitions. All the average values in the average model can be independently computed. Since only the average model values in the systole phase of the heart-cycle are of interest, bounds for the negative and positive values of Δk can be applied. For the negative values of Δk only negative values that are part of the start of the systole phase can be included. Since the peak location is very close to this start of the systole, the negative values of Δk can be limited to be equivalent to e.g. -<NUM> seconds. For the positive values of Δk, lag times that are part of the remainder of the systole are included. Typical maximum positive values for Δk can be chosen to be equivalent to lag times TΔk of e.g. <NUM> seconds. The average normalised waveform w can now be computed for all lag indices Δk as: <MAT> with ψΔk as computed by Equation (<NUM>).

<FIG> shows the average normalised waveform (the thicker line <NUM>) overlaid on the seven cardiac cycles from the normalised a-PPG waveforms shown in <FIG>. In effect, the average normalised waveform <NUM> from the above process is obtained by taking the average (mean) of each normalised cardiac cycle at each lag time value (TΔk). For example, the value (i.e. normalised amplitude) of the average waveform <NUM> at lag time TΔk = +<NUM> is given by the average (mean) of the values of the individual normalised a-PPG waveforms at lag time TΔk = +<NUM> (i.e. normalised in time and amplitude relative to the identified a reference point for each cardiac cycle). This average waveform <NUM> can also be described as a <NUM>-th order polynomial fit for the normalised a-PPG cardiac cycles.

However, as shown in <FIG>, this average over the full <NUM>-minute window is not a good fit for all of the normalised cardiac cycles in the full <NUM>-minute window since the morphology of the waveform is varying over time.

Therefore, the above averaging procedure is generalised to accommodate time-varying situations by not simply computing the <NUM>-th order average of the Np values at lag time TΔk, but a <NUM>st order or higher polynomial fit of the Np values at lag time TΔk. Since this polynomial fit, having order n (where n is equal to or greater than <NUM>) will have (lag) time on the x-axis and the level drop values on the y-axis, the averaged (or curve fitted) level drop will also have a dependency on time for polynomial orders larger than <NUM>. For each of the lag times Δk, m (m ≤ n) polynomial curve fit coefficients can be computed. These coefficients a<NUM>,. ,am can be computed in such a way to obtain a minimisation in the least-squares sense: <MAT> where <MAT> is the linear fitting model: <MAT>.

Next, based on the polynomial coefficients a<NUM>(Δk),. , am(Δk), the average level change (drop) can be computed directly via the linear fitting model <MAT> as: <MAT>.

It can be seen that for n = <NUM>, we obtain the average level change (drop) as given by Equation (<NUM>) and via using Equation (<NUM>) we get the average fitting model as described in <CIT> and shown in <FIG>, which will not depend on the actual location within the time window (e.g. the <NUM>-minute window in this example). However, for n > <NUM>, the average fitting model will depend on the actual location within the time window. This is illustrated in <FIG>, which shows the normalised a-PPG waveform values at a lag time of +<NUM> with respect to the identified a reference points for the <NUM> cardiac cycles in the above example. The normalised a-PPG waveform values are indicated by line <NUM>. Thus, each value in line <NUM> corresponds to the value of a normalised a-PPG waveform at lag time +<NUM> for one of the cardiac cycles within the time window. For example, the value of line <NUM> for the <NUM>th cardiac cycle is the value of the normalised a-PPG waveform of the <NUM>th cardiac cycle at +<NUM> lag time from the a reference point, the value of line <NUM> for the <NUM>th cardiac cycle is the value of the normalised a-PPG waveform of the <NUM>th cardiac cycle at +<NUM> lag time from the a reference point, and so on. Thus, line <NUM> in <FIG> shows how the values of the normalised a-PPG waveforms at +<NUM> after the a reference point change within the time window across the cardiac cycles in the PWS.

<FIG> also shows the <NUM>-th order average of the normalised a-PPG waveform values at lag time +<NUM> (line <NUM> - which corresponds to the conventional approach to just average (derive the mean) of all values at that lag time), the <NUM>st order average of the normalised a-PPG waveform values at lag time +<NUM> (line <NUM>), and the <NUM>nd order average of the normalised a-PPG waveform values at lag time +<NUM> (line <NUM>).

Respective versions of <FIG> (i.e. respective fitted models) are determined for a range of lag time values. That is, respective versions of <FIG> are formed from the values of the normalised a-PPG waveforms at respective lag times. For example, there can be a respective version of <FIG> for each of lag times <NUM>, <NUM>, <NUM>, etc. These versions of <FIG> will show how the values of the normalised a-PPG waveforms at the respective lag time value change with time across the cardiac cycles in the PWS. For each respective version of <FIG>, a respective <NUM>th, <NUM>st and/or subsequent order average is determined.

The graph in <FIG> shows average normalised cardiac cycle waveforms for several time points Y in the a-PPG signal in <FIG> using the average (time-varying) fitted models for the range of lag time values (TΔk) for n = <NUM>. Thus, <FIG> shows the average waveform resulting from determining the <NUM>st order averages of the normalised a-PPG waveform values for the range of lag time (TΔk) values between -<NUM> and +<NUM>. Merely as an example, <FIG> shows the average waveform for time point Y = <NUM> sec (labelled <NUM>), time point Y = <NUM> minute (labelled <NUM>), and the average waveforms for the time points corresponding to waveforms <NUM>-<NUM> labelled in <FIG>. Time point Y = <NUM> sec corresponds to the start of the <NUM>-second time period covered by the PWS in <FIG>, and time point Y = <NUM> sec corresponds to the end of the time period covered by the PWS in <FIG>.

The average normalised cardiac cycle waveform is derived for the range of lag time values TΔk, e.g. between -<NUM> and +<NUM> in the example in <FIG>. The values that form the average normalised cardiac cycle waveform are taken from the set of average (time-varying) fitted models (for a desired value of n) for the range of lag time values TΔk. In other words, for a selected time point Y for which an average normalised cardiac cycle waveform is required, the values that form that average normalised cardiac cycle waveform in the range -<NUM> to +<NUM> are the values at time point Y in the fitted models (e.g. <FIG> line <NUM>, <NUM>) for that range of lag times TΔk.

As an example, consider <FIG> for lag time +<NUM>, and consider there to be corresponding versions of <FIG> for other lag time values in the range -<NUM> to +<NUM>. The desired value for n is <NUM>, and the average normalised cardiac cycle waveform (which is shortened to "averaged waveform" herein) is to be derived for time point Y = <NUM> sec (i.e. at the start of the time period covered by the PWS). The value of the average waveform at lag time +<NUM> is the value of line <NUM> in <FIG> at time point Y = <NUM> (or at the cardiac cycle index corresponding to Y = <NUM>). It can be seen from a comparison of <FIG> to the values of the average cardiac cycle waveform in <FIG> at a lag value of +<NUM> that the value at lag time +<NUM> for the averaged waveform for time point Y = <NUM> is -<NUM> (i.e. the <NUM>st order polynomial fit <NUM> has a value of -<NUM> for Y = <NUM> (or the cardiac cycle with index <NUM>)), whereas the value at +<NUM> for the averaged waveform for time point Y = <NUM> minute is approximately <NUM> (i.e. the <NUM>st order polynomial fit <NUM> has an approximate value of <NUM> for time point Y = <NUM> minute (or the cardiac cycle with index <NUM>)). This is repeated for the other lag time values (i.e. using the other versions of <FIG>) to derive the full averaged waveform in the range -<NUM> to +<NUM>. Thus, the value of the averaged waveform for Y = <NUM> at lag time TΔk = -<NUM> is the value of the corresponding line <NUM> (for lag time TΔk = -<NUM>) at Y = <NUM> (or the cardiac cycle with index <NUM>), the value of the averaged waveform for Y = <NUM> at lag time TΔk = +<NUM> is the value of the corresponding line <NUM> for lag time TΔk = +<NUM> at Y = <NUM>, etc..

The average cardiac cycle waveform for a selected time in the <NUM>-minute time window can therefore be derived from the respective polynomial fit at each of the lag time values. In addition, it can be seen that all intermediate average waveform results (for the times corresponding to the normalised a-PPG waveforms labelled <NUM> to <NUM> in <FIG>) at the different timings within the <NUM>-minute window can also be derived. Therefore, by using an order n ≥ <NUM>, time-varying changes are accommodated in the averaging procedure. It should be noted that although n can be any integer value equal to or greater than <NUM>, n = <NUM> already gives good results in practice for a PWS representing a cardiac cycle in which the PWS is analysed over a relatively short time period and the underlying changes in the waveform are straightforward. If there are expected to be more substantial changes in the morphology over time, then n can be set to a value higher than <NUM>.

Steps <NUM>, <NUM> and <NUM> in <FIG> implement the above averaging technique as follows. In line with the above averaging technique, steps <NUM>, <NUM> and <NUM> operate on a 'normalised 2PWS'. The normalised 2PWS is obtained by separately normalising each part of the 2PWS corresponding to a respective cardiac cycle identified in step <NUM> with respect to the amplitude of the 2PWS at the identified reference point for that cardiac cycle. That is, for a particular cardiac cycle identified in step <NUM>, the amplitude of the 2PWS corresponding to that cardiac cycle is normalised around the amplitude of the 2PWS at the identified reference point for that cardiac cycle.

In step <NUM>, for a first lag time value, TΔk, that is measured with reference to the identified reference points, an n-th order polynomial fit is determined for a first set of values of the normalised 2PWS. As noted above, n is equal to or greater than <NUM>. The first set of values of the normalised 2PWS comprises the values of the 2PWS occurring the first lag time value from the reference point of each identified cardiac cycle. That is, in step <NUM>, for a lag time value of X ms, the first set of values is the values of the normalised 2PWS that are X ms from each of the reference points identified in step <NUM>. In the example shown in <FIG>, the first set of values corresponds to the line <NUM>. So, for example, for a lag time value TΔk of <NUM>, the value for, say, the <NUM>th identified cardiac cycle in <FIG> is the value of the normalised 2PWS for the <NUM>th identified cardiac cycle at <NUM>. The line <NUM> is formed from the values of the normalised 2PWS at <NUM> for each of the identified cardiac cycles. The n-th polynomial fit (with n ≥ <NUM>) determined in step <NUM> corresponds to line <NUM> for n = <NUM> and line <NUM> for n = <NUM>.

In step <NUM>, step <NUM> is repeated one or more times for one or more further lag time values. Thus, in step <NUM> one or more further iterations of step <NUM> are performed for one or more further lag time values to determine respective further n-th order polynomial fits <NUM>, <NUM> for respective sets of values of the normalised 2PWS. Each of the respective sets of values of the normalised 2PWS comprises the values of the normalised 2PWS that occur the respective further lag time value from the reference point of each identified cardiac cycle. Thus, step <NUM> results in one or more respective versions of <FIG> being derived for the respective lag time value TΔk.

As noted below with reference to step <NUM>, the number of times that step <NUM> is repeated determines the time-resolution of the averaged cardiac cycle waveform determined in step <NUM>. The higher the number of times that step <NUM> is repeated, the higher the smoothness and resolution of the resulting average cardiac cycle waveform. In some embodiments, step <NUM> can be repeated for lag time values in the range -<NUM> to +<NUM>. It will be appreciated that an upper limit on the size of the lag time value range can be imposed by the heart rate of the subject (with higher heart rates shortening the range of lag time values, and lower heart rates enabling the range of lag time values to be wider). The lag time value range should cover one cardiac cycle or less (but enough of the cardiac cycle for pulse wave features such as the reflected pulse wave to be observed in the resulting average cardiac cycle waveform).

Next, in step <NUM>, a first average cardiac cycle waveform is formed for a first time point Y in the time period covered by the PWS. For example, for the PPG signal covering the <NUM>-minute time period from which the 2PWS in <FIG> was derived, the first time point Y could be any of: <NUM> seconds (i.e. at the start of the <NUM>-minute time period), <NUM> seconds (i.e. part way through the <NUM>-minute time period), <NUM> seconds/<NUM> minute (i.e. at the end of the <NUM>-minute time period), etc..

In step <NUM>, rather than evaluate Equation (<NUM>) above, the coefficients a<NUM>(Δk),. , am(Δk) are evaluated at a time point Y: <MAT> where the parameter Fs denotes the sampling-rate of the PWS signal to translate the time point Y into a sample-number, similar to Equation (<NUM>).

The first average cardiac cycle waveform is formed from (normalised amplitude) values of the plurality of n-th order polynomial fits <NUM>, <NUM> at the first time point. Thus, for a time point Y in the time period covered by the PWS, the value of the average cardiac cycle waveform for time point Y is given by the (normalised average) value at time point Y of the n-th order polynomial fit <NUM>, <NUM> for the first set of values determined in step <NUM> (i.e. the value at time point Y of the n-th order polynomial fit <NUM>, <NUM> for the first lag time value), and the respective values at time point Y of each of the further n-th order polynomial fits <NUM>, <NUM> determined in step <NUM> (i.e. the values at time point Y of the n-th order polynomial fit <NUM>, <NUM> for the further lag time values).

In a specific example for a time point Y = <NUM> and n = <NUM>, the average cardiac cycle waveform is formed from the (normalised amplitude) values at time point Y in the <NUM>st order polynomial fits <NUM> for each lag time value. Step <NUM> can result in, for example, an average cardiac cycle waveform <NUM>, <NUM> as shown in <FIG>. More generally, step <NUM> is implemented as described above with reference to <FIG> and <FIG>.

In some embodiments, the average cardiac cycle waveform formed in step <NUM> can be analysed to determine information about a health status of the subject. In some embodiments, the information about the health status is a measurement or indication of the blood pressure of the subject and/or a measurement or indication of a change in the blood pressure of the subject.

In some embodiments, a second average cardiac cycle waveform can be formed for a second time point in the time period covered by the PWS. The second average cardiac cycle waveform can be formed in the same way as the first average cardiac cycle waveform determined in step <NUM>. As an example, one of the first time point and the second time point can be at or near to the start of the PWS, and the other one of the first time point and the second time point can be at or near to the end of the PWS. In further embodiments, one or more further average cardiac cycle waveforms can be determined for respective time points in the time period covered by the PWS.

In embodiments where a second average cardiac cycle waveform is formed, the method can further comprise comparing the first average cardiac cycle waveform and the second average cardiac cycle waveform to determine or identify a change in the average cardiac cycle waveform between the first time point and the second time point. This step can comprise determining a difference signal representing the difference between the two average cardiac cycle waveforms for all lag time values, and/or determining a difference between a specific part or parts of the average cardiac cycle waveforms. For example, a difference can be determined between the magnitude of the minimum in the average cardiac cycle waveforms following the identified a reference point. As another example, a difference can be determined between the timing of different reference points in the two average cardiac cycle waveforms. reference point e could be identified in each average cardiac cycle waveform, and the time between the respective a and e reference points for each average cardiac cycle waveform can be compared.

In some embodiments, a measure of the blood pressure of the subject, or a measure of a change in blood pressure of the subject can be determined from the first average cardiac cycle waveform and the second average cardiac cycle waveform. In some embodiments, the measure of the blood pressure or change in blood pressure can be determined from the comparison of the first and second average cardiac cycle waveforms. In particular embodiments, a blood pressure surrogate measurement can be determined from the time between the a reference point and the c reference point, which corresponds to the pulse reflection time (PRT).

<FIG> is a functional block diagram illustrating various operations in analysing a PWS according to various exemplary embodiments. A PWS <NUM> (e.g. a PPG signal) with a duration Nx / Fs is received by a Derivative Computation block <NUM> and a Peak Finding block <NUM>. The Derivative Computation block <NUM> determines the first order derivative of the PWS with respect to time (1PWS) and the second order derivative of the PWS with respect to time (2PWS). The 1PWS and/or 2PWS signals can be provided to the Peak Finding block <NUM>. The Peak Finding block <NUM> evaluates the input signals to identify cardiac cycles and the reference points corresponding to a part of the cardiac cycle in the 2PWS (e.g. the early systole/up-flank a reference point). The operations of the Derivative Computation block <NUM> and the Peak Finding block <NUM> correspond generally to step <NUM> described above.

The 2PWS and the identified reference points are input to an Averaging block <NUM>. A desired value <NUM> of n for the polynomial fit is input to the Averaging block <NUM>. Alternatively the desired value of n can be predetermined or preset in the Averaging block <NUM>. The Averaging block <NUM> implements the waveform averaging process described above in steps <NUM>, <NUM> and <NUM> based on the input 2PWS and the identified reference points. The Averaging block <NUM> outputs at least one average cardiac cycle waveform for a particular time point. In <FIG> the Averaging block <NUM> is shown as outputting an average cardiac cycle waveform for Y = <NUM> and Y = -Nx / Fs (e.g. <NUM> minute prior to t = <NUM>).

In optional embodiments, the average cardiac cycle waveform can be input to an Analysis block <NUM> that can perform some analysis of the average cardiac cycle waveform to determine information about the health status of the subject. In some embodiments, the Analysis block <NUM> can determine a surrogate blood pressure measurement. As an example, the Analysis block <NUM> could subtract the two averaged cardiac cycle waveforms as follows: <MAT> where: <MAT> is the first average cardiac cycle waveform for a time point Y = <NUM> and <MAT> is the second average cardiac cycle waveform for a time point Y = <NUM> seconds.

The value of <MAT> is indicative of the changes of energy in the pulse wave in the course of the window length (e.g. <NUM> minute) at a specific lag-time TΔk. Since blood pressure changes will lead to changes of the energy in the pulse wave at lag times where reflections are to be expected (e.g. reflections from renal bifurcations), the value of <MAT> can be exploited to estimate the amount of blood pressure change in the course of the window length.

Claim 1:
A computer-implemented method for analysing a pulse wave signal (PWS), obtained from a subject, wherein the pulse wave signal (PWS) comprises pulse wave measurements for a plurality of cardiac cycles of the subject during a first time period, the method comprising:
(i) analysing (<NUM>) the pulse wave signal (PWS) to identify a plurality of cardiac cycles and a respective reference point for each identified cardiac cycle;
characterized in that the method further comprises:
(ii) determining a second derivative with respect to time of the pulse wave signal (PWS);
(iii) determining a normalised second derivative by, for each part of the second derivative corresponding to a respective identified cardiac cycle, normalising said part of the second derivative with respect to the amplitude of the second derivative at the identified reference point for said cardiac cycle;
(iv) for a first lag time value, determining (<NUM>) an n-th order polynomial fit for a first set of values of the normalised second derivative, wherein the first set of values of the normalised second derivative comprises the values of the normalised second derivative occurring the first lag time value from the reference point of each identified cardiac cycle, wherein n is equal to or greater than <NUM>;
(v) performing (<NUM>) one or more further iterations of step (iv) for one or more further lag time values to determine respective further n-th order polynomial fits for respective sets of values of the normalised second derivative, wherein a respective set of values of the normalised second derivative comprises the values of the normalised second derivative that occur the respective further lag time value from the reference point of each identified cardiac cycle; and
(vi) forming (<NUM>) a first average cardiac cycle waveform for a first time point in the first time period, wherein the first average cardiac cycle waveform is formed from values of the plurality of n-th order polynomial fits at the first time point.