CN117279562A

CN117279562A - System and method for estimating a value of a target cardiac parameter

Info

Publication number: CN117279562A
Application number: CN202280031451.4A
Authority: CN
Inventors: Z·托库齐; F·C·内尔特曼; V·拉韦佐; K·D·S·H·楼; R·T·H·梅森
Original assignee: Koninklijke Philips NV
Current assignee: Koninklijke Philips NV
Priority date: 2021-04-27
Filing date: 2022-04-18
Publication date: 2023-12-22

Abstract

A method for determining a set of one or more values of a target cardiac parameter of a subject. The cardiovascular model generates at least one set of output values (for the respective at least one property of the heart function) by processing the model parameters. One or more sets of measurements corresponding to non-invasively measurable properties of cardiac function are processed with the corresponding sets of output values to modify model parameters. This modification continues until some predetermined criteria are met, such that the model more closely matches the true representation of the heart function of the subject. A set of one or more values is then derived from the output of the cardiovascular model and/or model parameters of the cardiovascular model.

Description

System and method for estimating a value of a target cardiac parameter

Technical Field

The present invention relates to the field of cardiac parameters, and in particular to estimating a value of a target cardiac parameter.

Background

Cardiac parameters such as cardiac filling pressure are important measurements for both diagnostic (e.g., heart failure for ejection fraction retention, HFpEF) and monitoring purposes, providing information about left and right heart function and cardiovascular and cardiopulmonary interactions. High cardiac filling pressures are associated with myocardial dysfunction and/or high blood volume, and subjects with high cardiac filling pressures tend to have poor long-term survival.

Cardiac filling pressure measurements are typically obtained by left heart catheterization for left ventricular pressure or left ventricular filling pressure LVFP and right heart catheterization for pulmonary capillary wedge pressure PCWP. Invasive means that conventional methods for obtaining these measurements are uncomfortable, expensive, time consuming, and present additional risks to the patient. Scheduling the taking of these measurements during heart failure diagnosis may also be logically difficult. Because of these drawbacks, cardiac filling pressure has historically been used for diagnosis of heart failure only in cases where there is ambiguity in diagnosis.

Various studies have explored the relationship of noninvasive measurements to such cardiac filling pressure measurements. However, the reproducibility of relationships identified in the literature has proven elusive, such that the reliability, robustness or validity of any statistical model that utilizes any such relationship has been questioned. It is believed that any such existing statistical model is heavily dependent on patient population and user/measurement accuracy.

Accordingly, there is a need for an improved method for estimating a value of a target cardiac parameter, such as left ventricular filling pressure.

Disclosure of Invention

The invention is defined by the claims.

According to an example of an aspect of the invention, a processing system for estimating a set of one or more values of a target cardiac parameter of a subject is provided.

The processing system is configured to: obtaining a model of a cardiovascular system, the model using a plurality of model parameters to generate output data comprising a plurality of sets of output values, each set of output values being associated with a different non-invasively measurable property of cardiac function, wherein: each output value set contains at least one value of an associated non-invasively measurable property of cardiac function; and the plurality of model parameters comprises the target cardiac parameter and/or the output data comprises a further set of output values of the target cardiac parameter; obtaining cardiac data comprising a plurality of sets of measurements, wherein each set of measurements is associated with a different set of output values and comprises one or more measurements of the non-invasively measurable property associated with the associated set of output values; iteratively modifying values of the plurality of model parameters of the model, thereby modifying differences between the plurality of sets of output values of the output data and corresponding sets of measured values in the cardiac data until one or more predetermined criteria are met; and after iterative modification: if the plurality of model parameters includes the target cardiac parameter, defining a set of the one or more values of the modified target cardiac parameter as an estimated set of one or more values of the target cardiac parameter; or if the output data comprises the further set of output values, defining the further set of output values as an estimated set of one or more values of the target cardiac parameter.

The inventors have realized that a model of the cardiovascular system (CVS) may be used to non-invasively estimate one or more values of a target cardiac parameter. The model is personalized to the heart function of the subject by fitting model parameters based on non-invasively acquired measurements of the subject. This avoids the need for cardiac catheterization, thereby reducing the risk, cost, and time of acquiring left ventricular filling pressure.

The CVS model is a biophysical model of the function of (parts of) the heart and circulatory system. For any defined set of values for each of a plurality of model parameters, the CVS model outputs a solution (i.e., output data) comprising a set of output values for a plurality of non-invasive measurement parameters. The values of the plurality of model parameters are modified until the set of output values matches (e.g., within a predetermined error or certainty) a set of measured values contained in the cardiac data of the subject.

A non-invasive measurement index representing cardiac function is a parameter representing cardiac function that can be measured using non-invasive methods (e.g., echocardiography, cardiac MRI, cuff pressure measurement, etc.). Methods for non-invasively acquiring such measurements are well known and established in the art.

After the iterative modification, the modified value sets of each model parameter are thereby personalized or customized towards the object under investigation, i.e. object specific values. This means that a set of values of the target cardiac parameter can be obtained. The set of values may be included in output data provided by the CVS model and/or in model parameters of the CVS model.

The target cardiac parameter may be left ventricular pressure. This embodiment provides a particularly useful scenario for using the proposed method, since the existing method of determining left ventricular pressure relies on invasive measurements, and it would be preferable to generate an accurate measure of this value (for improved assessment of the subject) without surgical intervention.

The plurality of non-invasively measurable properties may include left ventricular volume and at least one peripheral pressure property. Only these parameters may be sufficient to determine the values of the model parameters that most closely correspond to the cardiac data of the subject.

For example, left ventricular volume may be measured based on 2D echocardiography (using a disk method), 3D echocardiography, or cardiac MRI.

For example, peripheral pressure may be measured by taking cuff pressure measurements (e.g., to measure brachial artery, finger, neck toe, ankle, and/or leg pressure) or using ultrasound (e.g., to measure aortic pressure) during diastole and systole.

The at least one peripheral pressure measurement may comprise a pressure measurement from an arm, leg, wrist, neck, foot, finger or toe of the subject. In one example, the peripheral pressure measurement may be, for example, a brachial artery cuff pressure (e.g., measured at an arm of the subject). As another example, the peripheral pressure measurement may be a measurement taken at the neck of the subject, such as carotid artery pressure.

In some examples, the peripheral pressure measurements may be converted to aortic pressure, for example using one or more transfer functions.

The plurality of non-invasively measurable metrics may include at least one of: aortic valve flow, mitral valve flow, and/or timing of cardiac cycle events.

These measurements may be used to improve the accuracy of the estimation, for example compared to the left ventricular volume alone and the at least one peripheral pressure measurement.

Aortic and/or mitral valve flow measurements can be determined, for example, using cardiovascular MRI or based on doppler measurements and orifice area.

The timing of the cardiac cycle event may include, for example, timing of the opening of the mitral valve, timing of the closing of the mitral valve, timing of the opening of the aortic valve, timing of the closing of the aortic valve, and/or timing of the onset of left ventricular systole. Such measurements may be determined from the ECG data.

The processing system may be configured to iteratively modify the plurality of model parameters by: defining a solution vector comprising a plurality of sets of output values of a model of the cardiovascular system; defining a measurement data vector comprising the plurality of measurement value sets; defining a cost function quantifying the difference between the solution vector and the measurement data vector; and iteratively determining a value of the cost function and modifying the plurality of model parameters based on the value of the cost function until the one or more predetermined criteria are met.

The value of the model parameter for which the cost function is minimized is the value at which the output of the CVS model most closely matches the heart data of the subject.

The processing system may be configured to iteratively determine values of the cost function and modify the plurality of model parameters by: setting an initial value set of each model parameter of the plurality of model parameters; determining the plurality of sets of output values for the model of the cardiovascular system based on a current set of values for each of the plurality of model parameters; calculating a value of the cost function based on the determined plurality of output values; modifying the set of values for each model parameter of the plurality of model parameters based on the calculated values for the cost function; and iteratively repeating the steps of: determining the plurality of sets of output values, calculating the value of the cost function, and modifying the set of values for each of the plurality of model parameters until the one or more predetermined criteria are met. In other words, a simultaneous approach may be used to minimize the cost function. This allows the object-specific value to be effectively identified.

For example, the values of the model parameters may be adjusted using a gradient-based minimization method (e.g., BFGS method) or a non-gradient-based method (e.g., particle swarm or bayesian optimization).

In some examples, the processing system is configured to iteratively modify the values of the plurality of model parameters of the model by: dividing the plurality of model parameters into a plurality of sets of one or more model parameters; setting an initial value set of each model parameter of the plurality of model parameters; for each set of one or more model parameters in turn, the following iterative steps are performed: determining one or more sets of output values of the model of the cardiovascular system based on at least a current set of values of the set of model parameters; calculating a value of a cost function based on the determined one or more sets of output values and the set of measured values associated with the one or more sets of output values; and adjusting the set of values of each model parameter of the set of model parameters based on the calculated values of the cost function, wherein the iterating step is repeated until a predefined convergence condition is met.

The overall process of iteratively modifying each set of one or more model parameters may then be iteratively repeated until one or more predetermined criteria are met.

The processing system may be configured to: dividing the plurality of model parameters into a plurality of sets of one or more model parameters by dividing the plurality of model parameters into a first set of model parameters and a second set of model parameters; modifying the set of values for each model parameter in the first set of model parameters by: determining the plurality of sets of output values for the model of the cardiovascular system based on a current set of values for each of the plurality of model parameters; calculating a value of the cost function based on the determined plurality of sets of output values; adjusting a set of values for each model parameter in the first set of model parameters based on the calculated values of the cost function; and iteratively repeating the steps of: determining the plurality of sets of output values, calculating the values of the cost function, and adjusting the set of values for each model parameter in the first set of model parameters until a first predefined convergence condition is met; modifying the set of values for each model parameter in the second set of model parameters by: determining the plurality of sets of output values for the model of the cardiovascular system based on a current set of values for each of the plurality of model parameters; calculating a value of the cost function based on the determined plurality of sets of output values; adjusting the set of values for each model parameter in the second set of model parameters based on the calculated values of the cost function; and iteratively repeating the steps of: determining the plurality of sets of output values, calculating the values of the cost function, and adjusting the set of values for each model parameter in the second set of model parameters until a second predefined convergence condition is met; and iteratively repeating the steps of: modifying the set of values for each of the first set of model parameters and modifying the set of values for each of the second set of model parameters until the one or more predetermined criteria are met.

In other words, a two-layer optimization method of optimizing different parameter sets independently of each other may be used to minimize the cost function. The use of a two-layer optimization algorithm reduces the likelihood that the optimization process will sink to a local minimum on the cost function hypersurface and thus cannot identify a global minimum.

The plurality of model parameters may include the target cardiac parameter, and the processing system is configured to divide the plurality of model parameters into a first set of model parameters and a second set of model parameters by: defining the first set of model parameters to include only the target cardiac parameter; and defining the second set of model parameters to include the remaining model parameters. In this way, the target cardiac parameter is optimized independently of the other model parameters.

The processing system may be configured to divide the plurality of model parameters into a first set of model parameters and a second set of model parameters by: performing a sensitivity analysis on the model of the cardiovascular system; and dividing the plurality of model parameters into the first set and the second set based on the sensitivity analysis.

The results of the sensitivity analysis may be used to distinguish model parameters having a strong influence on the cost function from model parameters having a weak influence. For example, the first set of model parameters may include model parameters having strong influence, and the second set of model parameters may include model parameters having weak influence.

The one or more predetermined criteria may include at least one of: determining that a difference in a set of values for each of the plurality of model parameters between a current iteration and an immediately preceding iteration is below a predetermined threshold; a determination that a difference in the value of the cost function between a current iteration and an immediately preceding iteration is below a predetermined threshold; determining that the number of iterations has exceeded a predetermined threshold; a determination that an amount of time spent performing the iterative modification exceeds a predetermined amount of time and/or a determination that a difference between each of the plurality of sets of output values of the model of the cardiovascular system and the corresponding set of measurement values is lower than an uncertainty of the corresponding set of measurement values.

Each of these conditions may be used to identify values of the plurality of model parameters for which the cost function may be considered to be minimized.

The processing system may be configured to iteratively modify the plurality of model parameters by: defining a plurality of quantities of interest, wherein a quantity of interest is a set of output values of the model of the cardiovascular system corresponding to a predetermined characteristic; identifying a set of measurements in the cardiac data corresponding to the volume of interest; and iteratively modifying the plurality of model parameters of the model, thereby modifying differences between the quantity of interest and the identified set of measurements until the one or more predetermined criteria are met.

The model of the cardiovascular system may be a zero-dimensional or one-dimensional model. Low-dimensional CVS models such as these effectively model cardiac function while having a relatively small number of model parameters, which allows them to be solved efficiently.

The processing system may be further configured to, after the iterative modification: determining the plurality of sets of output values of the model of the cardiovascular system based on the modified set of values for each of the plurality of model parameters; and generating one or more cardiac function curves based on the determined plurality of sets of output values. Cardiac function curves, such as time traces of pressure, volume and flow, and pressure-volume cycling, provide additional clinically useful information.

A computer-implemented method for estimating left ventricular filling pressure of a subject is presented. The computer-implemented method includes: obtaining a model of a cardiovascular system, the model using a plurality of model parameters to generate output data comprising a plurality of sets of output values, each set of output values being associated with a different non-invasively measurable property of cardiac function, wherein: each output value set contains at least one value of an associated non-invasively measurable property of cardiac function; and the plurality of model parameters comprises a target cardiac parameter and/or the output data comprises a further set of output values of the target cardiac parameter; obtaining cardiac data comprising a plurality of sets of measurements, wherein each set of measurements is associated with a different set of output values and comprises one or more measurements of the non-invasively measurable property associated with the associated set of output values; iteratively modifying values of the plurality of model parameters of the model, thereby modifying differences between the plurality of sets of output values of the output data and corresponding sets of measured values in the cardiac data until one or more predetermined criteria are met; and after iterative modification: if the plurality of model parameters includes the target cardiac parameter, defining a set of one or more values of the modified target cardiac parameter as an estimated set of one or more values of the target cardiac parameter; or if the output data comprises the further set of output values, defining the further set of output values as an estimated set of one or more values of the target cardiac parameter.

Any of the processing systems described herein may be adapted to perform any variation of any of the methods described herein, and vice versa.

A computer program product comprising computer program code means is also presented which, when run on a computing device having a processing system, causes said processing system to perform all the steps of any of the methods described herein.

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

Drawings

For a better understanding of the invention and to show more clearly how it may be carried into effect, reference will now be made, by way of example only, to the accompanying drawings, in which:

FIG. 1 illustrates a system for estimating left ventricular filling pressure of a subject in accordance with an embodiment of the invention;

FIG. 2 illustrates a graphical representation of an example model of the cardiovascular system that may be used with the present invention;

FIG. 3 illustrates an example cost function as a weighted sum of areas between curves for each of a plurality of non-invasively measurable metrics;

FIG. 4 illustrates the point-by-point difference between the measured and output values of the CVS model of cuff pressure at systolic and diastolic;

FIG. 5 illustrates a method for iteratively determining values of a cost function and modifying a plurality of model parameters according to an embodiment of the invention;

FIG. 6 illustrates an alternative method for iteratively determining the value of the cost function CF and modifying a plurality of model parameters in accordance with another embodiment of the present invention;

FIG. 7 illustrates example results of a Sobol sensitivity analysis;

FIG. 8 illustrates a sub-step of step 630 of the method of FIG. 6;

FIG. 9 illustrates a sub-step of step 640 of the method of FIG. 6;

FIG. 10 illustrates an alternative method for iteratively determining the value of the cost function CF and modifying a plurality of model parameters in accordance with another embodiment of the present invention; and is also provided with

FIG. 11 illustrates a computer-implemented method for estimating left ventricular filling pressure of a subject in accordance with an embodiment of the invention.

Detailed Description

The present invention will be described with reference to the accompanying drawings.

It should be understood that the detailed description and specific examples, while indicating exemplary embodiments of the apparatus, system, and method, are intended for purposes of illustration only and are not intended to limit the scope of the invention. These and other features, aspects, and advantages of the apparatus, system, and method of the present invention will become better understood from the following description, claims, and accompanying drawings. It should be understood that the drawings are merely schematic and are not drawn to scale. It should also be understood that the same reference numerals are used throughout the figures to indicate the same or similar parts.

In accordance with the inventive concept, a method for determining a set of one or more values of a target cardiac parameter of a subject is presented. The cardiovascular model generates at least one set of output values (for the respective at least one property of the heart function) by processing the model parameters. One or more sets of measured values corresponding to non-invasively measurable properties of cardiac function are processed with the corresponding sets of output values to modify model parameters. The modification continues until some predetermined criteria are met such that the model more closely matches the true representation of the heart function of the subject. A set of one or more values is then derived from the output of the cardiovascular model and/or from model parameters of the cardiovascular model.

Embodiments are based, at least in part, on the recognition that: the cardiovascular model may be adapted to more closely model the real cardiovascular system of the subject by modifying the model based solely on data that can be measured non-invasively. This effectively means that the values of certain cardiac parameters that were previously only accurately measured with invasive measurements can be predicted using more accurate models than were previously available.

For example, the illustrative embodiments may be used in any clinical setting in which non-invasive measurements of a subject's cardiac function may be obtained, such as in a clinic, hospital, or even in the subject's home setting.

Fig. 1 illustrates a system 100 for estimating left ventricular filling pressure of a subject in accordance with an embodiment of the invention. The system 100 includes a processing system 110 and a memory unit 120. The processing system itself is an embodiment of the present invention.

The processing system 110 obtains a model 130 of the cardiovascular system from the memory unit 120. The model of the cardiovascular system (CVS model) is a biophysical model of (at least part of) the function of the heart and circulatory system. The plurality of model parameters are used to generate output data comprising a plurality of sets of output values. Model parameters are defined inputs or intermediate variables or coefficients of the CVS model. Each set of output values is associated with a different property of cardiac function and comprises one or more output values representing a (predicted) value of that property of cardiac function. Models of the cardiovascular system are well known and suitable CVS models for carrying out the present invention will be apparent to the skilled person. Examples of suitable CVS models are described in more detail below.

More specifically, the CVS model 130 obtained by the processing system 110 is a model of the cardiovascular system that provides output data including sets of output values, each set of output values representing a different non-invasively measurable property of cardiac function.

The plurality of model parameters of the CVS model comprises at least the target cardiac parameter and/or the output data further comprises a further set of output values of the target cardiac parameter. Thus, the target cardiac parameter may be represented in input, intermediate or output data for the CVS model.

The non-invasively measurable property of the cardiac function may be any property indicative of the cardiac function and its value may be determined or derived (preferably directly) from non-invasively acquired measurements (e.g. ultrasound cardiographic measurements, cardiac or cardiovascular MRI, peripheral pressure measurements, etc.). For example, the non-invasively measurable properties may include one or more of left ventricular volume, aortic pressure, cuff pressure, aortic valve flow, and/or mitral valve flow. Methods for non-invasively measuring these properties have been established in the art.

In some examples, the CVS model 130 may be a low-dimensional model of the cardiovascular system (i.e., a zero-dimensional or one-dimensional CVS model). The low-dimensional CVS model effectively models cardiac function using a relatively small number of model parameters (i.e., a smaller number than the higher-dimensional model) and can be solved more effectively than the higher-dimensional model. However, the invention is not limited to the use of a low-dimensional CVS model, and the use of a higher-dimensional model of the cardiovascular system is also contemplated.

FIG. 2 provides a graphical representation of an example model 230 of the cardiovascular system that may be used with the present invention. The CVS model 230 is a simple open loop zero-dimensional model of the left heart. The open loop CVS model is a CVS model in which the circulation loop is not closed.

In general, a model may define a variety of relationships between different possible parameters of the cardiovascular system. These relationships may be expressed in formulated terms, examples of which are described below.

In the example model 230, left atrial pressure P _la Modeled as a constant throughout the cardiac cycle:

P _la (t)＝P _la (1)

inflow of blood Q in the left ventricle _mv Is modeled as being derived from left atrial pressure P _la And left ventricular pressure P _lv Difference between them and resistance R of mitral valve _mv And (3) driving:

modeling left ventricular pressure-volume relationship using elastic function:

P _lv ＝E _lv (V _lv -V _lv,0 ) (3)

wherein E is _lv Is left ventricular elasticity, V _lv Is left ventricular volume, and V _lv,0 Is the left ventricular dead volume. At End Diastole (ED), this results in:

P _lv (t＝ED)＝P _la ＝LVEDP (4)

wherein LVEDP is left ventricular end-diastole filling pressure which is the left ventricular filling pressure at end-diastole.

Left ventricular volume V _lv Variation dV of (2) _lv Dt is modeled as the difference between inflow and outflow of the left ventricle:

wherein H is _mv And H _av States of mitral valve and aortic valve, respectively (i.e. whether the valve is open or closed), and And Q is _av Is the outflow of blood from the left ventricle into the aorta, i.e. aortic valve flow.

Outflow of blood from left ventricle into aorta Q _av (i.e., aortic valve flow) is modeled as measured by left ventricular pressure P _lv With aortic pressure P _AO Difference between them and resistance R of aortic valve _p And (3) driving:

aortic pressure P _AO Modeling was performed using a lumped ternary Windkessel model:

wherein Z is _c 、R _d And C are the lumped impedance, resistance and compliance of the arterial system, respectively.

The CVS model 230 may be numerically solved by solving a system of ordinary differential equations. In particular, the use includes left atrial pressure P _la As input to a model which gives an output solution containing the left ventricular pressure P as a function of time _lv Aortic pressure P _AO Left ventricular volume V _lv Inflow of blood Q in left ventricle _mv And flow out Q _av (i.e., flow through the mitral valve and aortic valve, respectively).

This can be expressed more clearly or more vividly by introducing model parameter vectors:

μ＝[P _la ,p ₁ ,p ₂ ,…] (8)

wherein p is ₁ 、p ₂ … except for left atrium pressure P _la A plurality of model parameters in addition. For left ventricular volume V _lv Left ventricular pressure P _lv Aortic pressure P _AO Mitral and aortic flow Q _mv And Q _av The model solution of (2) can be expressed as:

V _lv ＝V _lv (t,μ),P _lv ＝P _lv (t,μ),P _AO ＝P _AO (t,μ),Q _mv ＝Q _mv (t,μ),Q _av ＝Q _av (t,μ) (9)

in other words, the CVS model 230 may be considered to be the input left atrial pressure P _la And other model parameters p ₁ 、p ₂ Mapping … to output cardiovascular function curves (i.e. time traces of pressure, volume and flow). This can also be expressed by assembling a model solution in solution vector F (t, μ). The model may be considered as a mapping of model parameter vector μ to solution vector F:

μ→F(t,μ)＝[V _lv (t,μ),P _lv (t,μ),P _AO (t,μ),Q _mv (t,μ),Q _av (t,μ)] (10)

it will be appreciated that the plurality of elements in the solution vector F represent non-invasively measurable properties of cardiac function. Thus, at least some of the elements of the solution vector can represent a set of output values associated with non-invasively measurable properties of cardiac function. Other elements of the solution vector F represent additional sets of output values (which represent, for example, properties or parameters of cardiac function that have historically only been able to be measured using invasive techniques).

Thus, the set of values in the output data can be effectively split into an output data set (which represents only the non-invasively measurable property of cardiac function) and a further output data set (which can represent the invasively measurable property of cardiac function).

For the purposes of the disclosed embodiments, one of the parameters represented by the additional set of output values (if present) may serve as the target cardiac parameter. For example, left ventricular pressure P _lv May serve as the target cardiac parameter. Other target cardiac parameters may be envisaged for examples of CVS models or for different types of CVS models.

In other examples, the target cardiac parameter is one of the model parameters. In the previously described example CVS model, left ventricular pressure P _lv Also serves as a model parameter because it is used to calculate the blood inflow Q _mv And blood outflow Q _av Such as, for example, etcThe formulae (2) and (6).

Thus, for the example CVS model, the plurality of model parameters includes a target cardiac parameter and the output data includes a further set of output values for the target cardiac parameter.

The present invention will be further described with reference to this example CVS model 230; however, the invention is not limited to the use of this model, and any suitable model of the cardiovascular system may be used, including closed loop models, models with more realistic valve behavior, models with non-constant left atrial pressure (e.g., models including atrial elastic function), and models with expanded arterial system.

Returning to fig. 1, the processing system 110 obtains cardiac data 140 of the subject. The cardiac data includes a set of measurements for each set of output values. Thus, each set of measurements is associated with a respective non-invasively measurable property.

The cardiac data 140 may be obtained from the memory unit 120 and/or from a cardiac monitoring system (not shown).

In some examples, cardiac data 140 may include a set of measured values of all properties or parameters provided by CVS model 130 as a set of output values. Of course, the CVS model may provide an additional set of output values that do not have a corresponding set of measurement values in the cardiac data 140. In other words, the plurality of non-invasively measurable properties represented by the set of measurements in the cardiac data may include only a portion of the solution of the CVS model.

In some examples, each measurement set may include multiple values measured at different points in the cardiac cycle (specific noninvasive measurable properties for cardiac function).

For example, the plurality of non-invasively measurable properties (represented by the respective sets of output values) may include left ventricular volume and at least one peripheral pressure parameter. It has been determined that, for example, in the case of the example model 230 described above, these measured values of properties are sufficient to determine an estimate of certain target cardiac parameters, such as left ventricular filling pressure.

In other words, the cardiac data 140 may include a set of measurements of left ventricular volume and a set of measurements of each of one or more peripheral pressure parameters. The one or more peripheral pressure parameters may include diastolic and/or systolic pressure.

Left ventricular volume may be measured, for example, by 2D echocardiography (e.g., using a disk method), 3D echocardiography (e.g., philips dynamic heart model), and/or by cardiac MRI. Non-invasive methods of measuring left ventricular volume will be apparent to the skilled artisan.

Non-invasive methods of measuring peripheral pressure will also be apparent to the skilled artisan. For example, peripheral pressure may be measured by taking cuff systolic and diastolic pressure measurements (e.g., measuring brachial artery pressure, finger pressure, neck pressure, toe pressure, ankle pressure, and/or leg pressure). In another example, an ultrasound device may be used to measure continuous arterial blood pressure measurements. See, for example, wang et al (2018), "Monitoring of the central blood pressure waveform via a conformal ultrasonic device", nat Biomed Eng,2:687-695.

One or more transfer functions may be used to convert the peripheral pressure to aortic pressure P _AO The converted measurement(s) may form part of a set of measurements.

In some examples, the plurality of non-invasively measurable properties (representative of the output data set in the output data) may also include aortic valve flow and/or mitral valve flow. In other words, the cardiac data 140 may also include one or more sets of measurements that contain at least one aortic valve flow measurement or one or more mitral valve flow measurements.

Non-invasive methods of measuring aortic and/or mitral valve flow will be apparent to the skilled artisan and may include cardiovascular MRI flow measurements, doppler measurements, and orifice area measurements.

In some examples, the plurality of non-invasively measurable properties (representative of the set of output data in the output data) may also include timing of cardiac cycle events. For example, the cardiac data 140 may also include at least one set of measurements comprising: timing of the opening of the mitral valve, timing of the closing of the mitral valve, timing of the opening of the aortic valve, timing of the closing of the aortic valve, and/or timing of the onset of left ventricular systole.

Non-invasive methods of measuring the timing of cardiac cycle events will be apparent to the skilled artisan. For example, ECG data may be used to determine the timing or occurrence of cardiac cycle events.

Having obtained the CVS model 130 and the cardiac data 140, the processing system 110 iteratively modifies a plurality of model parameters of the model, thereby modifying differences between the set of output values of the model and the set of measured values of the cardiac data until one or more predetermined criteria are met. Suitable working examples of the one or more predetermined criteria are described in more detail below.

The processing system then identifies a set of one or more values of the target cardiac parameter (i.e., the value at the end of the iterative process) as an estimated set of one or more values of the target cardiac parameter.

This may include identifying a set of one or more values of a further set of output values representing the target cardiac parameter (e.g., as compared to other sets of output values representing non-invasively measurable properties of cardiac function). This approach may be employed if the output of the CVS model 130 includes a further set of output values of the target heart parameter.

Alternatively, this may include identifying a set of one or more values defined for model parameters of the CVS model, which are used in processing performed by the CVS model to generate output data. This approach may be employed if the model parameters of the CVS model 130 include the target heart parameter and thus include a set of values of the target heart parameter.

In other words, the processing system 110 estimates a set of one or more values of the target cardiac parameter of the subject by fitting the model parameters to the measured values in the cardiac data 140. In other words, the processing system 110 identifies a set of values of the model parameters for which the solution or output of the model 130 corresponds substantially (i.e., according to a predetermined criterion) to the cardiac data of the subject.

In this way, the obtained cardiac data effectively acts as boundary conditions or boundary values for the CVS model 130.

In some examples, processing system 110 iteratively modifies the plurality of model parameters by defining solution vectors including a plurality of sets of output values of CVS model 130 and measurement data vectors containing corresponding sets of measurement data. The solution vector may be defined in the same manner as the solution vector of the example model 230 described above: according to the model parameter vector mu containing the model parameters.

The processing system 110 may then define a cost function that quantifies (a part of) the difference between the solution vector and the measurement data vector. For example, at discrete time points t in each of the solution vector and the measurement data vector ^k In the case of calculation or measurement at the collection of (c), the cost function CF can be expressed as:

wherein F (t) ^k μ) is a solution vector, and F _d (t ^k ) Is a measurement data vector.

It will be appreciated that for the purpose of equation (11), the solution vector used contains only the cardiac properties equivalently represented in the measured data vector. Thus, the cardiac properties defined or represented by the measured data vector define the properties used in the cost function.

In some embodiments, the cost function is defined using only a subset of the sets of measurements in the cardiac data and corresponding sets of output values of the output data and/or using only the values of any of the sets of measurements and the selection of corresponding ones of the sets of output values.

For example, a quantity of interest (e.g., a particular value or set of values) may be identified in a set of measured values and a corresponding set of output values produced by the CVS model. The quantity of interest may correspond to a particular or predetermined property (e.g., end diastole left ventricular volume and/or end systole left ventricular volume). Only these quantities of interest may be used to define the cost function.

Thus, the cost function may be a function that uses only the quantities of interest (i.e. a subset of all possible measured and model-determined parameter values) to define the difference between the solution vector (i.e. the set of output values) and the measurement data vector (i.e. the set of measurement data).

The processing system 110 may iteratively determine the value of the cost function CF and modify the plurality of model parameters based on the value of the cost function until one or more predetermined criteria are met. The objective is to find a model parameter vector μ (i.e. the value of the model parameter) for which the cost function is minimized.

If the model parameters include a target cardiac parameter, such as left ventricular pressure, the method facilitates identifying one or more values of the target cardiac parameter from the model parameter vector μ.

If the output data generated by the CVS model includes an additional set of output values for the target heart parameter, such as left ventricular pressure, the method facilitates identifying one or more values for the target heart parameter from the output data (or solution vector) generated by the CVS model.

This concept is represented in fig. 3, fig. 3 illustrating an example cost function CF as a weighted sum of areas (shaded portions of fig. 3) between curves for each of a plurality of non-invasively measurable properties.

In the example shown in FIG. 3, the plurality of non-invasively measurable properties includes left ventricular volume V _LV Aortic pressure P _AO Aortic valve flow rate Q _av And mitral valve flow Q _mv . The tag of fig. 3 identifies the associated region illustrated by the figure.

The cost function can be expressed as:

CF＝Δ _rel V _LV +Δ _rel P _AO +Δ _rel Q _av +Δ _rel Q _mv (12)

the shaded area of each graph represents the difference between a data curve (i.e., a curve based on measurements in cardiac data) and a solution curve (i.e., a curve based on the current output of the CVS model 130) of a property that can be measured non-invasively. The process of minimizing the example cost function CF corresponds to minimizing the size of the shadow area.

For some non-invasive measurable properties, there may not be enough measurements (in the corresponding set of measurements) to construct the data curve, e.g., for a particular non-invasive measurable property, there may be only one or two measurements. In such an example, instead of the area between the curves of one or more of the plurality of non-invasively measurable properties, one or more point-wise differences between the measured value(s) and the current output value(s) of the CVS model 130 may be used in the cost function.

For example, FIG. 4 illustrates the cuff pressure P for systolic and diastolic blood pressure _{Sleeve belt} Point-by-point differences (Δp, respectively) between measured and output values of the CVS model 130 _sys And DeltaP _dia ). This may be used instead of the area between the aortic pressure curves in the example cost function of fig. 3, where the aortic pressure data curves are not available. In this case, the cost function can be expressed as:

CF＝Δ _rel V _LV +Δ _rel P _cuff +Δ _rel Q _av +Δ _rel Q _mv (13)

several methods are contemplated for iteratively determining the value of the cost function CF and modifying the plurality of model parameters based on the value of the cost function (i.e., to minimize the cost function), and further suitable methods will be apparent to the skilled person. In particular, simultaneous optimization methods (e.g., gradient-based minimization methods such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, or non-gradient-based methods such as particle swarm and Bayesian optimization) and multi-level (e.g., bi-level) optimization methods may be used.

Fig. 5 illustrates a method 500 for iteratively determining the value of the cost function CF and modifying a plurality of model parameters according to an embodiment of the invention. The method 500 uses a simultaneous approach to minimize the cost function, where the cost function is modified simultaneously as a function of all elements in the model parameter vector μ (i.e., all model parameters).

The method 500 begins at step 510, where a set of initial values is set for each of a plurality of model parameters of the CVS model 130. The initial value set may be a randomly assigned value, a predefined value, or a value obtained by user input. For example, the initial value may be defined as an average of its possible ranges. For some model parameters, initial values may be estimated from the cardiac data 140.

At step 520, a plurality of sets of output values of the CVS model 130 are determined based on the current set of values for each of the plurality of model parameters. In other words, the CVS model is solved using the current value set of each of the plurality of model parameters. For the first iteration of the method, the current set of values is the initial set of values at step 510. For later iterations, the current value set is a modified value set, as described below.

At step 530, a value of the cost function is calculated based on the determined plurality of sets of output values and corresponding sets of measured values of the non-invasively measurable property in the cardiac data 140. In a particular example, differences between a solution of the CVS model (generated using current values of model parameters) and data of the object are determined.

At step 540, the processing system 110 determines whether one or more predetermined criteria are met. In response to a determination that one or more predetermined criteria are not met, the method 500 proceeds to step 550.

At step 550, a set of values for each of the plurality of model parameters is modified based on the calculated values of the cost function. The modification may be performed using a gradient descent method or any other suitable modification method for minimizing or reducing the cost function, as will be readily apparent to those skilled in the art.

Steps 520 through 550 are iteratively repeated until it is determined that one or more predetermined criteria are met. In response to a determination that one or more predetermined criteria are met, the method 500 proceeds to step 560.

At step 560, the processing system 110 estimates a set of one or more values of a target cardiac parameter of the subject.

Step 560 may be performed by identifying a modified set of values of the target heart parameter (i.e., the current set of values of the target heart parameter at the most recent iteration) as a set of one or more values of the estimated target heart parameter of the subject if the plurality of model parameters includes the target heart parameter.

Alternatively, step 560 may be performed, if the output data of the CVS model contains a further set of output values of the target heart parameter, identifying the further set of output values as a set of one or more values of the estimated target heart parameter of the subject.

Fig. 6 illustrates an alternative method 600 for iteratively determining the value of the cost function CF and modifying a plurality of model parameters according to another embodiment of the invention. The method 600 uses a two-layer optimization method to minimize the cost function, wherein different parameter sets are modified independently of each other.

The method 600 begins at step 610, where a plurality of model parameters are partitioned into a first set of model parameters and a second set of model parameters.

In some examples, a first set of model parameters may be defined such that the first set includes only the target cardiac parameter, and a second set of model parameters may be defined such that the second set includes the remaining model parameters (i.e., all of the plurality of model parameters except the target cardiac parameter). Of course, in this scenario, the model parameters include at least the target cardiac parameters. The method allows modification of the target cardiac parameter independent of other model parameters. In other words, the target cardiac parameter may be interpreted as a control input that is different from the remaining model parameters.

In other examples, processing system 110 may divide the plurality of module parameters into a first set and a second set by performing a sensitivity analysis on CVS model 130 and dividing the plurality of model parameters into the first set and the second set based on the sensitivity analysis.

Any suitable sensitivity analysis, such as the Morris method or the Sobol method, may be used to divide the plurality of model parameters into a first set and a second set. In some examples, more than one sensitivity analysis may be performed. For example, the Morris method can be used for the first screening and the Sobol method can be used for more detailed analysis.

The results of the sensitivity analysis may for example be used to distinguish model parameters having a strong influence on the cost function CF from model parameters having a weak influence on the cost function. The first set of model parameters may be defined to include model parameters having a stronger effect and the second set of model parameters may be defined to include model parameters having a weaker effect.

For example, the first set of model parameters may be defined as comprising model parameters having a Sobol index above a predetermined threshold, or comprising N model parameters having the highest Sobol index, where N is a predetermined number. The second set of model parameters may be defined as comprising model parameters having a Sobol index not higher than a predetermined threshold value, or comprising all model parameters except the N model parameters having the highest Sobol index.

FIG. 7 illustrates example results 700 of a Sobol sensitivity analysis performed on a CVS model with aortic valve resistance r _p Arterial resistance r _d Arterial resistance c, mitral valve resistance r _mv Left atrial pressure P _la Elasticity e _min Elasticity e _max 、m ₁ 、m ₂ 、τ ₁ 、τ ₂ And left ventricular dead volume V _lv,0 As model parameters.

In example result 700, left atrial pressure P _la Is the main model parameter with the strongest influence on the cost function (S1) and the most pronounced interaction with the other model parameters (ST), followed by the elasticity e _min And aortic valve resistance r _p . The Sobol index of the remaining model parameters is very small.

Based on the example result 700, the left atrial pressure P may be determined, for example, by _la Assigning the first set and the remaining model parameters to the second set or by assigning left atrial pressure P _la Elasticity e _min And aortic valve resistance r _p The model parameters are assigned to the first set and the remaining model parameters are assigned to the second set to divide the model parameters into the first set and the second set. In another example, model parameters may be divided into three sets: a first set comprising only left atrial pressure; a second set comprising elasticity and aortaResistance to valve movement; and a third set comprising the remaining model parameters. The skilled person will be able to easily adapt the method 600 to a method with three sets of model parameters.

Returning to FIG. 6, at step 620, initial values are set or defined for each of a plurality of model parameters. The initial value may be a randomly assigned value, a predefined value, or a value obtained through user input.

In some examples, at least some of the initial values may be estimated from available measurements (e.g., from a set of measurement data) in step 620. The method may utilize existing statistical models to define or predict parameter values from non-invasively measurable data (which may not be accurate enough for a particular object, but may prove to be a good starting point for tuning model parameters to a particular object).

At step 630, the processing system 110 iteratively modifies the value set of each of the first set of the plurality of model parameters until a first predefined convergence condition is satisfied.

Step 630 will be described in more detail with reference to fig. 8, fig. 8 illustrating sub-steps of step 630.

At sub-step 631, a plurality of sets of output values of the CVS model 130 are determined based on the current values of each of the plurality of model parameters.

At sub-step 632, a value of a cost function is calculated based on the determined plurality of output values.

At sub-step 633, the processing system determines whether a first predefined convergence condition is met. This may be achieved, for example, when the value of the cost function falls below a certain first predetermined threshold. Other examples are provided later in this disclosure.

In response to a determination that the first predefined convergence condition is not met, method 630 proceeds to sub-step 634.

At sub-step 634, a set of values for each of the first set of model parameters is adjusted based on the calculated values of the cost function. During sub-step 634, the set of values of the model parameters in the second set are not adjusted.

Sub-steps 631 to 634 are iteratively repeated until it is determined that the first predefined convergence condition is met. In response to determining that the first predefined convergence condition is met, the method 600 proceeds to step 640.

Returning to FIG. 6, at step 640, the processing system 110 iteratively modifies the value sets of each of the second set of the plurality of model parameters until a second predefined convergence condition is satisfied.

Step 640 will be described in more detail with reference to fig. 9, fig. 9 illustrating sub-steps of step 640.

At sub-step 641, a plurality of sets of output values of the CVS model 130 are determined based on the current set of values for each of the plurality of model parameters.

At sub-step 642, a value of the cost function is calculated based on the determined plurality of sets of output values (and sets of measured values).

At sub-step 643, the processing system determines whether a second predefined convergence condition is met. This may be achieved, for example, when the value of the cost function falls below a certain second predetermined threshold. Other examples are provided later in this disclosure.

In response to a determination that the second predefined convergence condition is not met, the method 640 proceeds to sub-step 644.

At sub-step 644, a set of values for each of the second set of model parameters is adjusted based on the calculated values of the cost function. The set of values of any model parameter in the first set is not adjusted during sub-step 644.

Sub-steps 641 to 644 are iteratively repeated until it is determined that the second predefined convergence condition is met. In response to determining that the second predefined convergence condition is met, method 600 proceeds to step 650.

Steps 630 and 640 may be better understood by considering step 610 of dividing the model parameters into a first set and a second set in terms of splitting the model parameter vector μ into two components. For example, in the case of dividing a plurality of model parameters according to the result of sensitivity analysis, the model parameter vector μmay be expressed as being split into two components:

μ＝[μ ^{strong strength} ,μ ^{Weak and weak} ] (14)

Wherein mu ^{Strong strength} Is a vector containing a first set of model parameters (i.e., model parameters with a strong influence), and μ ^{Weak and weak} Is a vector containing a second set of model parameters (i.e., model parameters with weaker influence).

At step 630, the purpose is to find the vector μ ^{Strong ×} Wherein:

μ ^{strong ×} ＝argminCF(μ ^{Strong strength} ,μ ^{Weak and weak} ) (15)

At step 640, the purpose is to find the vector μ ^{Weak x} Wherein:

μ ^{weak x} ＝argminCF(μ ^{Strong ×} ,μ ^{Weak and weak} ) (16)

At step 650, the processing system 110 determines whether one or more predetermined criteria are met.

In response to a determination that one or more predetermined criteria are not met, steps 630 through 650 are iteratively repeated until it is determined that one or more predetermined criteria are met. In some examples, the predetermined criterion may be met if both the first convergence condition and the second convergence condition are met and supported.

In response to a determination that one or more determination criteria are met, the method 600 proceeds to step 660.

At step 660, the processing system 110 estimates a target cardiac parameter of the subject by identifying the modified set of values of the target cardiac parameter model parameter as the estimated target cardiac parameter of the subject.

The embodiments described with reference to fig. 6-9 effectively divide the model parameters into two sets and perform an iterative modification process on each set of model parameters. The method may be extended to include dividing the model parameters into N sets (N > 1) and performing iterative modification on each set of parameters.

This generalized method is illustrated by fig. 10, fig. 10 illustrating a method 1000 for iteratively determining the values of the cost function CF and modifying a plurality of model parameters.

The method 1000 includes a step 1010 of partitioning the model parameters into a plurality of N sets, where N is any positive integer greater than 1. The method 1000 further includes a step 1020 of setting one or more initial values for the model parameters.

Each set of model parameters is iteratively modified in turn until some predetermined (termination) criteria are met for each instance of the iterative modification. This is illustrated by steps 1030 through 1050 of fig. 10.

In step 1030, the Z-th set of parameters is modified (where Z is initially 1).

In step 1040, the method determines whether some predetermined criteria have been met, e.g., whether the cost function for the Z-th set of parameters meets some predetermined criteria. The cost function may be different for each set of parameters. Of course, the same cost function may be shared between two or more sets of parameters.

If the result of step 1040 is negative, the method returns to step 1030. If the result of step 1040 is affirmative, the method determines (in step 1050) whether all sets have been processed. If all sets have been processed, the method moves to step 1060 where the value(s) of the target cardiac parameter are estimated. Otherwise, step 1030 is performed on the next set of parameters (e.g., by adding 1 to the value of Z in step 1055, and then returning to step 1030).

In some examples, if all sets have been processed, the method may return to step 1030 for the first set of processed model parameters instead of moving to step 1060. Thus, Z can effectively be reset to 1. This is because modifications to the subsequent set may already affect the accuracy of the model. This repetition of modifying the set of model parameters may be performed until some predetermined criteria have been met, examples of which will be described later.

Suitable methods for modifying the parameters have been described previously.

The partitioning of the model parameters into N sets may be performed, for example, based on sensitivity analysis of the model parameters.

A particularly advantageous method of setting the model parameters of the example model described with reference to fig. 2 will be described below.

The proposed method combines the results of sensitivity analysis of an example model of the CV system, based on assumptions of understanding of physiology and cardiac function, and the relationship and interactions between model parameters. The method described below may thus generate model parameters that more accurately or correctly represent the actual process occurring in the object.

In the method, the first set of model parameters includes an unknown parameter Z _c 、R _d And C, which are lumped impedance, resistance, and compliance of the arterial system, respectively (see equation (7)). These three parameters may be referred to as Windkessel (WK) parameters because they form part of the Windkesser model.

In the method, the second set of model parameters includes only the filling pressure P _la And left ventricular dead volume V _lv,0 . From the sensitivity analysis, the second set has been identified as being particularly effective in modifying the solution vector generated by the example model.

In the method, the third set of model parameters includes all remaining parameters of the example model. The third set may effectively fine tune the example model based on coarser modifications performed using the first set and the second set.

As previously explained, the cost function used in iteratively modifying each set of model parameters may be different for the set of model parameters being processed.

As an example, for the first set of model parameters, the cost function may be a predicted aortic pressure (e.g., in a solution vector or output data and/or processing the aortic flow Q by using equation (7) _av ) And true aortic pressure P _AO (in the cardiac data or measurement data vector). Aortic flow Q _av May be available in the cardiac data or may be derived from another parameter available in the measured data vector.

For the second and third sets of model parameters, the cost function may be a quantization difference (e.g., a sum error, an average error, or a mean square error) between all model parameters shared by the solution vector and the measured data vector. Other suitable examples will be apparent.

To process the first set of model parameters, the flow rate Q is measured at the aorta _av In cases where no measurement data vector is available (e.g. when operating under the assumption that there is no regurgitation through the mitral valve during systole), the aortic flow Q may be determined _av The LV volume is estimated to vary in time such that Qav (t) =dvlv (t)/dt.

In some examples, the measurement data vector contains peripheral pressure measurements, such as brachial artery cuff measurements P _{Sleeve belt} . The measurement may be converted to aortic pressure P using one or more transfer functions _AO Is a similar value to (a) in the above. Suitable transfer functions will be readily apparent to the skilled person.

The various iterative modification processes performed in such iterative processes may be performed using any known modification process, such as common gradient-based minimization methods, non-gradient-based and global optimization methods (particle swarm, genetic algorithm, bayesian optimization, etc.).

In one example, the iterative modification process may include generating a set of output values for each of a plurality of different sets of values for a set of model parameters being modified, determining a cost function for each set of output values, and selecting a value for the set of model parameters associated with the lowest cost function. For example, the plurality of different values may include a plurality of value sets, each value set representing a value of each of the plurality of parameters to be modified. In some examples, there may be a maximum and minimum value for each parameter, which may be defined based on a known range for the parameter. Each set of values may represent samples within these maximum and minimum boundaries. The plurality of value sets need not contain all possible values for each parameter, but rather sample selection of possible values for each parameter may be used.

In any of the above-described embodiments, one or more boundaries or constraints for one or more model parameters are defined by processing the determined values of other model parameters. In particular, values of model parameters that are part of a subsequent set of model parameters may be bound (at an upper and/or lower limit) to previously processed model parameters based on the determined values of model parameters determined in the previous process. In this context, the subsequent set is the set that the model parameters have.

Consider a scenario in which a certain set of model parameters includes filling pressure P _la And left ventricular dead volume V _lv,0 And the later set of model parameters (i.e., the set of model parameters modified after a certain set) contains left ventricular elasticity Elv.

In this scenario, constraint E for left ventricular elasticity Elv is defined using the following equation _min It is possible to:

EDV is the end diastole volume that can be identified in the cardiac data.

It is possible to define the left ventricular elasticity Elv (used in equation (3)) using the following equation:

wherein,is a normalized elastic function that can be expressed in different formulas. Suitable examples are the so-called Double-Hill representations, but others will be apparent to the skilled person and a combination of sinusoidal and exponential functions may be employed. E (E) _min And E is _max Thereby indicating elasticity E to the left ventricle _lv Is a constraint of (a).

This example illustrates how it is possible to set constraints on one or more other model parameters based on one or more previously determined values of the parameters.

As previously mentioned, the processing system iteratively modifies the plurality of model parameters, thereby modifying the difference between the output value and the measured value, until one or more predefined criteria or convergence condition(s) are met. Termination criteria for the optimization process are well known and suitable criteria for use as one or more predefined criteria will be apparent to the skilled person.

For example, the one or more predetermined criteria or convergence conditions may include at least one of: determining that a difference in value of each of a plurality of model parameters between a current iteration and an immediately preceding iteration is below a predetermined threshold; determining that a difference in value of a cost function between a current iteration and an immediately preceding iteration is below a predetermined threshold; determining that the number of iterations has exceeded a predetermined threshold; and/or a determination that a difference between each of the plurality of output values of the CVS model 130 and a corresponding measurement value in the cardiac data 140 is less than an uncertainty of the measurement value. Suitable values for the predetermined threshold will be apparent to the skilled person. In some examples, the one or more predetermined criteria may include at least one criterion related to a history of model parameter values to terminate the process when the solution oscillates between the two values.

In the event that the one or more predetermined criteria or convergence conditions include a number of predetermined criteria, the processing system may iteratively modify the model parameters until all of the predetermined criteria are met or until at least one of the predetermined criteria has been met.

In some examples, the output data of the CVS model 130 may be used to generate a cardiac function curve of the subject. Processing system 110 may determine a plurality of sets of output values (and optionally any additional sets of output values, if any) of the CVS model based on the modified sets of values for each of the model parameters (i.e., the sets of values at the end of the iterative process once one or more predetermined criteria are met), and generate one or more cardiac function curves based on the determined sets of output values and any additional sets of output values, if any.

The one or more cardiac function curves may include one or more of the following: a time trace of pressure (e.g., left ventricular and/or aortic pressure) over one or more cardiac cycles, a time trace of volume (e.g., left ventricular volume) over one or more cardiac cycles, a time trace of flow (e.g., flow through the mitral valve and/or aortic valve) over one or more cardiac cycles, and/or a pressure-volume loop.

Fig. 11 illustrates a computer-implemented method 1100 for estimating a target cardiac parameter of a subject, according to an embodiment of the invention.

Method 1100 begins at step 1110, where a model of the cardiovascular system is obtained. A model of the cardiovascular system uses a plurality of model parameters to generate output data comprising a plurality of sets of output values, each set of output values being associated with a different non-invasively measurable property of cardiac function. Each set of output values contains at least one value representing a value of an associated non-invasively measurable property of cardiac function. The plurality of model parameters comprises a target heart parameter and/or the output data comprises a further set of output values of the target heart parameter.

At step 1120, cardiac data for the subject is obtained. The cardiac data includes a plurality of sets of measurements, wherein each set of measurements is associated with a different set of output values and includes one or more measurements of a non-invasive measurable property associated with the associated set of output values.

At step 1130, the method iteratively modifies the value sets of the plurality of model parameters of the CVS, thereby modifying differences between the plurality of output value sets of the output data and corresponding measurement value sets in the cardiac data until one or more predetermined criteria are met.

Step 1140 is performed after the iterative modification and a set of one or more values of the target cardiac parameter is established or defined. Step 1140 includes: if the plurality of model parameters includes the target heart parameter, a set of one or more values of the modified target heart parameter is defined as an estimated set of one or more values of the target heart parameter. Alternatively, step 1140 may comprise: if the output data comprises a further set of output values, the further set of output values is defined as an estimated set of one or more values of the target cardiac parameter.

The method 1100 may further include the following step 1150: at the output interface, a user-perceptible output is provided in response to the estimated set of one or more values of the target cardiac parameter. The user-perceivable output may be a visual representation of the set of estimates (e.g., in the form of a display of a curve or any value).

It will be appreciated that the disclosed method is a computer-implemented method. Thus, a concept of a computer program is also presented, comprising code means for implementing any of the described methods when said program is run on a processing system.

The skilled person will be readily able to develop a processor for performing any of the methods described herein. Accordingly, each step of the flowchart may represent a different action performed by the processor and may be performed by a corresponding module of the processor.

As discussed above, the system utilizes a processor to perform data processing. A processor may be implemented in numerous ways, using software and/or hardware, to perform the various functions required. A processor typically employs one or more microprocessors that may be programmed using software (e.g., microcode) to perform the required functions. A processor may be implemented as a combination of dedicated hardware performing some functions and one or more programmable microprocessors and associated circuitry performing other functions.

Examples of circuitry that may be employed in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, application Specific Integrated Circuits (ASICs), and Field Programmable Gate Arrays (FPGAs).

In various implementations, the processor may be associated with one or more storage media, such as volatile and non-volatile computer memory, such as RAM, PROM, EPROM and EEPROM. The storage medium may be encoded with one or more programs that, when executed on one or more processors, perform the required functions. Various storage media may be fixed within the processor or the controller may be transportable such that the program or programs stored thereon can be loaded into the processor.

Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the word "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. Although specific measures are recited in mutually different dependent claims, this does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the internet or other wired or wireless telecommunication systems. If the term "adapted to" is used in the claims or specification, it should be noted that the term "adapted to" is intended to be equivalent to the term "configured to". Any reference signs in the claims shall not be construed as limiting the scope.

Claims

1. A processing system for estimating a set of one or more values of a target cardiac parameter of a subject, the processing system configured to:

obtaining a model of a cardiovascular system, the model using a plurality of model parameters to generate output data comprising a plurality of sets of output values, each set of output values being associated with a different non-invasively measurable property of cardiac function, wherein:

each output value set contains at least one value of an associated non-invasively measurable property of cardiac function; and is also provided with

The plurality of model parameters comprises the target cardiac parameter and/or the output data comprises a further set of output values of the target cardiac parameter;

obtaining cardiac data comprising a plurality of sets of measurements, wherein each set of measurements is associated with a different set of output values and comprises one or more measurements of the non-invasively measurable property associated with the associated set of output values;

iteratively modifying values of the plurality of model parameters of the model, thereby modifying differences between the plurality of sets of output values of the output data and corresponding sets of measured values in the cardiac data until one or more predetermined criteria are met; and is also provided with

After iterative modification:

if the plurality of model parameters includes the target cardiac parameter, defining a set of the one or more values of the modified target cardiac parameter as an estimated set of one or more values of the target cardiac parameter; or alternatively

If the output data comprises the further set of output values, the further set of output values is defined as an estimated set of one or more values of the target cardiac parameter.

2. The processing system of claim 1, wherein the target cardiac parameter is left ventricular pressure.

3. The processing system of claim 1 or 2, wherein a plurality of the non-invasively measurable properties include left ventricular volume and at least one peripheral pressure property.

4. A processing system according to any of claims 1 to 3, wherein the plurality of non-invasively measurable metrics comprises at least one of: aortic valve flow, mitral valve flow, and/or timing of cardiac cycle events.

5. The processing system of any of claims 1 to 4, wherein the processing system is configured to iteratively modify the plurality of model parameters by:

Defining a solution vector comprising the plurality of sets of output values of the model of the cardiovascular system;

defining a measurement data vector comprising the plurality of measurement value sets;

defining a cost function quantifying the difference between the solution vector and the measurement data vector; and is also provided with

Iteratively determining a value of the cost function and modifying the plurality of model parameters based on the value of the cost function until the one or more predetermined criteria are met.

6. The processing system of claim 5, wherein the processing system is configured to iteratively determine the value of the cost function and modify the plurality of model parameters by:

setting an initial value set of each model parameter of the plurality of model parameters;

determining the plurality of sets of output values for the model of the cardiovascular system based on a current set of values for each of the plurality of model parameters;

calculating a value of the cost function based on the determined plurality of output values;

modifying the set of values for each model parameter of the plurality of model parameters based on the calculated values for the cost function; and is also provided with

The following steps are repeated iteratively: determining the plurality of sets of output values, calculating the value of the cost function, and modifying the set of values for each of the plurality of model parameters until the one or more predetermined criteria are met.

7. The processing system of any of claims 1 to 4, wherein the processing system is configured to iteratively modify the values of the plurality of model parameters of the model by:

dividing the plurality of model parameters into a plurality of sets of one or more model parameters;

for each set of one or more model parameters in turn, the following iterative steps are performed:

determining one or more sets of output values of the model of the cardiovascular system based on at least a current set of values of the set of model parameters;

calculating a value of a cost function based on the determined one or more sets of output values and the set of measured values associated with the one or more sets of output values; and is also provided with

Adjusting the set of values of each model parameter of the set of model parameters based on the calculated values of the cost function,

Wherein the iterative step is repeated until a predefined convergence condition is met.

8. The processing system of claim 7, wherein the processing system is configured to:

dividing the plurality of model parameters into a plurality of sets of one or more model parameters by dividing the plurality of model parameters into a first set of model parameters and a second set of model parameters;

modifying the set of values for each model parameter in the first set of model parameters by:

calculating a value of the cost function based on the determined plurality of sets of output values;

adjusting a set of values for each model parameter in the first set of model parameters based on the calculated values of the cost function; and is also provided with

The following steps are repeated iteratively: determining the plurality of sets of output values, calculating the values of the cost function, and adjusting the set of values for each model parameter in the first set of model parameters until a first predefined convergence condition is met;

Modifying the set of values for each model parameter in the second set of model parameters by:

adjusting the set of values for each model parameter in the second set of model parameters based on the calculated values of the cost function; and is also provided with

The following steps are repeated iteratively: determining the plurality of sets of output values, calculating the values of the cost function, and adjusting the set of values for each model parameter in the second set of model parameters until a second predefined convergence condition is met; and is also provided with

The following steps are repeated iteratively: modifying the set of values for each of the first set of model parameters and modifying the set of values for each of the second set of model parameters until the one or more predetermined criteria are met.

9. The processing system of claim 8, wherein the plurality of model parameters includes the target cardiac parameter, and the processing system is configured to divide the plurality of model parameters into a first set of model parameters and a second set of model parameters by:

Defining the first set of model parameters to include only the target cardiac parameter; and is also provided with

The second set of model parameters is defined to include the remaining model parameters.

10. The processing system of any of claims 7 to 9, wherein the processing system is configured to divide the plurality of model parameters into a plurality of sets of one or more model parameters:

performing a sensitivity analysis on the model of the cardiovascular system; and is also provided with

The plurality of model parameters is partitioned into a plurality of sets of the one or more model parameters based on the sensitivity analysis.

11. The processing system of any of claims 5 to 10, wherein the one or more predetermined criteria include at least one of: determining that a difference in a set of values for each of the plurality of model parameters between a current iteration and an immediately preceding iteration is below a predetermined threshold; a determination that a difference in the value of the cost function between a current iteration and an immediately preceding iteration is below a predetermined threshold; determining that the number of iterations has exceeded a predetermined threshold; a determination that an amount of time spent performing the iterative modification exceeds a predetermined amount of time and/or a determination that a difference between each of the plurality of sets of output values of the model of the cardiovascular system and the corresponding set of measurement values is lower than an uncertainty of the corresponding set of measurement values.

12. The processing system of any of claims 1 to 4, wherein the processing system is configured to iteratively modify the plurality of model parameters by:

defining a plurality of quantities of interest, wherein a quantity of interest is a set of output values of the model of the cardiovascular system corresponding to a predetermined characteristic;

identifying a set of measurements in the cardiac data corresponding to the volume of interest; and is also provided with

Iteratively modifying the plurality of model parameters of the model, thereby modifying differences between the quantity of interest and the identified set of measurements until the one or more predetermined criteria are met.

13. The processing system of any of claims 1 to 12, wherein the processing system is further configured to, after the iterative modification:

determining the plurality of sets of output values of the model of the cardiovascular system based on the modified set of values for each of the plurality of model parameters; and is also provided with

One or more cardiac function curves are generated based on the determined plurality of sets of output values.

14. A computer-implemented method for estimating left ventricular filling pressure of a subject, the computer-implemented method comprising:

The plurality of model parameters comprises a target cardiac parameter and/or the output data comprises a further set of output values of the target cardiac parameter;

After iterative modification:

if the plurality of model parameters includes the target cardiac parameter, defining a set of one or more values of the modified target cardiac parameter as an estimated set of one or more values of the target cardiac parameter; or alternatively

15. A computer program product comprising code means which when run on a computer having a processing system causes said processing system to perform all the steps of the method according to claim 14.