# Imaging-based method to quantify left ventricular diastolic pressures

Otto A Smiseth, Joao F Fernandes, Nobuyuki Ohte, Kazuaki Wakami, Erwan

Donal, Espen W Remme, Pablo Lamata

► To cite this version:

Otto A Smiseth, Joao F Fernandes, Nobuyuki Ohte, Kazuaki Wakami, Erwan Donal, et al.. Imaging-based method to quantify left ventricular diastolic pressures. European Heart Journal - Cardiovascular Imaging, 2025, 26 (7), pp.1184-1194. 10.1093/ehjci/jeaf017. hal-04926365

HAL Id: hal-04926365

https://hal.science/hal-04926365v1

Submitted on 8 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Imaging-based method to quantify left ventricular diastolic pressures

Otto A. Smiseth ID¹*†, Joao F. Fernandes ID²*†, Nobuyuki Ohte ID³, Kazuaki Wakami³, Erwan Donal ID⁴, Espen W. Remme ID⁵,⁶, and Pablo Lamata ID²

¹Institute for Surgical Research, Division of Cardiovascular and Pulmonary Diseases, Oslo University Hospital, Rikshospitalet and University of Oslo, Sognsvannsveien 20, NO-0372 Oslo, Norway; ²School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK; ³Department of Cardiology, Nagoya City University Graduate School of Medical Sciences, Nagoya, Japan; ⁴Department of Cardiology, CHU Rennes and Inserm, LTSI, University of Rennes, Rennes, France; ⁵Institute for Surgical Research, Oslo University Hospital, Rikshospitalet, Oslo, Norway; and ⁶The Intervention Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway

Received 29 October 2024; revised 21 December 2024; accepted 11 January 2025; online publish-ahead-of-print 16 January 2025

See the editorial comment for this article 'Predicting the diastolic left ventricular pressure curve non-invasively: how far can echo go?', by F.A. Flachskampf and J.D. Thomas, https://doi.org/10.1093/ehjci/jeaf088.

## Aims

To establish an imaging-based method to quantify left ventricular (LV) diastolic pressures.

## Methods and results

In 115 patients suspected of coronary artery disease, LV pressure was measured by micromanometers and images by echo-cardiography. LV filling pressure was measured as LV pre-atrial contraction pressure (pre-A $P_{LV}$). Based on previous observations, we hypothesized that pre-A $P_{LV}$ approximates the sum of minimum $P_{LV}$ and maximum transmitral pressure difference. Parameters used for pressure estimates included LV volumes and strain, left atrial strain, mitral flow velocities, systolic arterial cuff pressure, and body mass index. Minimum $P_{LV}$ was estimated by predictors identified in a derivative cohort ($n = 81$). Mitral pressure difference was calculated by a simplified Navier-Stokes equation. Accuracy of estimates of minimum $P_{LV}$, pre-A $P_{LV}$, and end-diastolic $P_{LV}$ was investigated in a testing cohort ($n = 19$). Patient-specific LV diastolic pressure curves were constructed by adjusting a reference curve according to pressure estimates at key diastolic events. There was good agreement between estimated and measured pre-A $P_{LV}$: bias 0.0, limits of agreement < 3.1 mmHg (±1.96 SD). Estimated minimum $P_{LV}$ and end-diastolic $P_{LV}$ also showed good agreement with measured pressures. Furthermore, there was good agreement between measured and estimated LV diastolic pressure curves, quantified as mean LV diastolic pressure: bias 0.2, limits of agreement < 3.2 mmHg.

## Conclusion

The proposed non-invasive method provided estimates of minimum $P_{LV}$, pre-A $P_{LV}$, and end-diastolic $P_{LV}$, each reflecting different features of diastolic function. Additionally, it provided an estimate of the LV diastolic pressure curve. Validation in larger populations with different phenotypes is necessary to determine the validity of the method in clinical practice.

<footnote>* Corresponding authors. E-mail: otto.smiseth@gmail.com and jf.fernandes@kcl.ac.uk</footnote>

<footnote>† These authors are shared first authors.</footnote>

<footnote>© The Author(s) 2025. Published by Oxford University Press on behalf of the European Society of Cardiology. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.</footnote>
## Graphical Abstract

### Imaging-based method to quantify left ventricular diastolic pressures

**Key question:** Can cardiac imaging provide quantitative estimates of left ventricular (LV) diastolic pressures?

**Key findings:** ☐ In a patient population suspected of coronary artery disease, LV filling pressure, measured as LV pre-atrial contraction pressure, was estimated with good accuracy.

☐ The method also provided estimates of minimum LV pressure and end-diastolic LV pressure.

☐ The method has potential to provide an estimate of the LV diastolic pressure curve.

**Take home message:** This study shows feasibility of a quantitative estimate of LV filling pressure and the LV diastolic pressure curve by imaging.

**Population:** A retrospective study in 115 patients referred for suspected coronary artery disease

**Measurements:** Echocardiography and LV pressure by micromanometer-tipped catheters

### INPUTS

Imaging parameters:

<figure><img src="image_3.png" /></figure>

LV volume

<figure><img src="image_4.png" /></figure>

Left atrial (LA) reservoir strain

<figure><img src="image_5.png" /></figure>

LV global longitudinal strain

<figure><img src="image_6.png" /></figure>

Mitral flow velocities

Clinical parameters:

Systolic arterial pressure

<figure><img src="image_7.png" /></figure>

Body mass index

LV diastolic pressures to be estimated

<figure><img src="image_8.png" /></figure>

### OUTPUTS

#### Pre-A LV pressure

Surrogate of mean LA pressure

Estimated as sum of min $P_{LV}$ and max $\Delta P_{MV}$

<figure><img src="image_9.png" /></figure>

Pre-A $P_{LV}$ was estimated with high accuracy:
Bias: 0 mmHg. Limits of agreement: <3.1 mmHg

#### Minimum LV pressure

Marker of myocardial relaxation

Estimated from a set of predictors which included a non-invasive time constant of LV relaxation and LA reservoir strain.

Was estimated with high accuracy:

Bias: -0.6 mmHg. Limits of agreement: <2.2 mmHg

#### End-diastolic LV pressure

Measure of preload

Estimated as sum of pre-A $P_{LV}$ and atrial contraction-induced pressure rise.

Was estimated with moderate accuracy:

Bias: -1.8 mmHg. Limits of agreement: <6.8 mmHg

Estimation of LV diastolic pressure curve

A pressure curve was constructed based on pressure estimates at key diastolic events as indicated by the orange symbols.

MVO = mitral valve opening
MVC = mitral valve closure

<figure><img src="image_10.png" /></figure>

A representative example

**Conclusions:** The proposed non-invasive method estimated LV filling pressure measured as LV pre-A pressure with good accuracy. The method also provided an accurate estimate of minimum $P_{LV}$ which is a marker of LV relaxation and restoring forces. The method also has potential to provide an estimate of LV end-diastolic pressure and the LV diastolic pressure curve. Future studies in larger populations and different phenotypes are needed to define the clinical potential of the proposed method.

### Keywords

echocardiography • diastole • diastolic pressure • filling pressure • heart failure • left ventricle • isovolumic relaxation time

## Introduction

Left ventricular (LV) filling pressure is important as a diagnostic marker when evaluating patients for suspected heart failure and as a therapeutic target in patients with established heart failure and pulmonary vascular congestion. In clinical routine, echocardiography is the most widely used method for evaluating LV filling pressure, and a combination of several parameters can differentiate between normal and elevated LV filling pressure with good accuracy.¹⁻³ Echocardiography, however, does not provide a quantitative estimate of LV filling pressure and does not differentiate between mean left atrial pressure ($P_{LA}$) and end-diastolic LV pressure ($P_{LV}$), which are used clinically as alternative parameters of filling pressure. This differentiation can be important in certain patients, as mean $P_{LA}$ is a key factor in pulmonary vascular congestion, while LV end-diastolic pressure indicates preload and influences stroke volume. Furthermore, echocardiography does not provide an estimate of minimum $P_{LV}$ that is an interesting parameter as it is related to LV relaxation and restoring forces.⁴ In the present study,

we propose a method with potential to estimate the different components of LV diastolic pressure.

In 2012, we introduced a method to construct the LV systolic pressure curve and estimate myocardial work based on echocardiography.⁵ That method, however, does not provide an estimate of LV diastolic pressures, which is the focus of the present study. The main objective of the study was to develop a non-invasive method to provide quantitative estimates of LV diastolic pressures, and as a secondary objective, to investigate feasibility of constructing the LV diastolic pressure curve by an imaging approach. To ensure high accuracy in the pressure measurements, the study was conducted in patients investigated with high-fidelity LV pressure catheters.

## Methods

This study is divided into two parts: (i) estimation of LV filling pressure, and (ii) estimation of the LV diastolic pressure curve.
Clinical data originated from two studies previously published by the authors of this article (O.A.S., N.O., and K.W.).⁶,⁷ Both studies had approval from ethics committees and patient informed consent. The study included a total of 115 patients: 100 patients were used in the development of method to estimate LV diastolic pressure and 15 patients for development of method to construct a LV pressure curve (eight for defining a reference curve and seven for testing accuracy). Patients with acute coronary syndrome, primary valvular heart disease, atrial fibrillation, or intraventricular conduction disturbance were excluded.

## Part 1: non-invasive LV diastolic pressure

Part 1 of the study considered 100 patients who underwent cardiac catheterization due to suspected coronary artery disease (CAD).⁶ In all patients, LV pressures were measured by high-fidelity pressure sensors using micromanometer-tipped catheters. Table 1 shows the characteristics of the patients. We used 81 patients as a derivative cohort and 19 patients as a testing cohort. As explained in more detail in Supplementary data online, Data B, subjects were assigned to each group sorted in sequential order of data acquisition, with the first 81 allocated to the derivative cohort and the last 19 to the testing cohort.

Input data used for estimating LV diastolic pressures were echocardiographic measurements of LV end-diastolic and end-systolic volumes, LV and LA strain traces, mitral flow velocities, systolic brachial artery pressure by the cuff method, and body mass index (BMI).

### Echocardiography

Echocardiography was performed within 2 h before catheterization using Aplio-80 or Aplio Artida SSH-880A (Toshiba Medical Co., Tokyo, Japan), with patients in left decubitus position.

Two-dimensional echocardiography was performed in the three apical views. Measurements of LV and LA dimensions were performed according to existing guidelines. LV global longitudinal strain (GLS) and LA reservoir and pump strains were measured by speckle tracking echocardiography using frame rates from 40 to 80 Hz. A maximum of two segments could be rejected due to suboptimal tracking when calculating GLS. LA reservoir and pump strains (LARS and LAPS, respectively) were calculated from recordings in apical four-chamber view. The measurements also included mitral early-diastolic (E) and atrial contraction-induced (A) mitral flow

velocities, and early-diastolic mitral annular velocity (e') as the average of velocities at the septal and lateral corners of the mitral annulus by pulsed Doppler echocardiography.

### Measurement of LV pressure

LV pressure was measured with micromanometer-tipped catheters with a lumen for contrast injection (SPC-454D, Millar Instrument Co., Houston, TX, USA) and via the same lumen absolute LV pressure was measured by an external conventional manometer. All pressure transducers were calibrated with a mercury manometer. Pressure-zero was set at mid-chest level. To adjust for electronic drifting and hydrostatic effects on pressure as result of changes in catheter position, the micromanometer was zero-referenced at the end of diastasis against pressure recorded via the fluid-lumen inside the pressure catheter. Measurements were done before injection of contrast material.

LV pressure ($P_{LV}$) measurements included minimum $P_{LV}$, pre-A $P_{LV}$, and end-diastolic $P_{LV}$ (Figure 1). As parameter of LV relaxation, we calculated the time constant of LV isovolumic pressure decay ($\tau$) according to Weiss et al.⁸ The values of minimum $P_{LV}$, pre-A $P_{LV}$, and end-diastolic $P_{LV}$ were calculated as an average from 10 consecutive heart cycles in each patient, whereas all the remaining pressure and echocardiography metrics were obtained as the median of 3 consecutive beats, recorded during breath holding at end-expiration. In the derivative cohort, systolic pressure was measured as peak LV pressure and in the testing cohort as systolic brachial artery pressure using the cuff method. Supplementary data online, Data F shows how errors in estimates of LV systolic pressure influence our diastolic pressure estimates. We found that the estimates were reasonably robust to 20% error in measurements in systolic pressure.

The analysis of echocardiographic data was performed blindly to the measured pressures.

### Definition of LV filling pressure

In the present study, the term LV filling pressure refers to mean $P_{LA}$ that was approximated as pre-A $P_{LV}$.¹ The validity of this approximation was confirmed in previous studies.⁹,¹⁰ Figure 1 illustrates the different LV diastolic pressure components.

### Method for estimating LV filling pressure

The method is built on three principles, as explained next.

The first principle is that mean pressure in the left atrium ($P_{LA}$) can be approximated as the sum of minimum $P_{LV}$ and maximum early-diastolic transmitral pressure difference ($\max \Delta P_{MV}$), as illustrated in Figure 1. This principle is supported by several studies in conscious and anaesthetized dogs under a wide range of haemodynamic conditions, including congestive heart failure (HF), as summarized in Supplementary data online, Data A, which also explains the physical rationale for the principle. We used LV pre-A pressure as a substitute for mean LA pressure as described in Eq. (1).

<table><caption>**Table 1** Clinical characteristics (n = 100)</caption><thead><tr><th></th><th>Preserved systolic function (EF ≥ 50%)</th><th>Systolic dysfunction (EF &lt; 50%)</th></tr></thead><tbody><tr><td>Male/female</td><td>80/20</td><td></td></tr><tr><td>Age (years)</td><td>66 ± 9</td><td></td></tr><tr><td>HR (beats/min)</td><td>65 ± 12</td><td></td></tr><tr><td>MAP (mmHg)</td><td>89 ± 10</td><td></td></tr></tbody></table><table><thead><tr><th></th><th>Preserved systolic function (EF ≥ 50%)</th><th>Systolic dysfunction (EF &lt; 50%)</th></tr></thead><tbody><tr><td>Number of patients</td><td>83</td><td>17</td></tr><tr><td>Atypical chest pain</td><td>10</td><td>0</td></tr><tr><td>CAD without MI</td><td>36</td><td>0</td></tr><tr><td>CAD with MI</td><td></td><td></td></tr><tr><td>Anterior</td><td>28</td><td>8</td></tr><tr><td>Inferior</td><td>8</td><td>3</td></tr><tr><td>Combined</td><td>1</td><td>6</td></tr></tbody></table>

CAD, coronary artery disease; HR, heart rate; MAP, mean arterial pressure; MI, myocardial infarction.

<figure><img src="image_11.png" /><figcaption>**Figure 1** Schematic illustration of the principle that LV pre-atrial contraction pressure (pre-A $P_{LV}$) was estimated as the sum of minimum LV pressure (min $P_{LV}$) and the maximum early-diastolic atrioventricular pressure difference ($\max \Delta P_{MV}$). The horizontal, dashed line represents mean left atrial pressure (mean $P_{LA}$).</figcaption></figure>
$$ \text{LV filling pressure} = \text{pre-A} P_{\text{LV}} \approx \min P_{\text{LV}} + \max P_{\text{MV}} \quad (1) $$

The second principle used in the estimation of LV filling pressure is that minimum $P_{LV}$ can be estimated by a linear model from a set of biomarkers learned from analysis of the derivative cohort. A total of 10 candidate variables were explored (presented in Supplementary data online, Data B), and the final optimized model consisted of four independent predictors of minimum $P_{LV}$ (see Table 2). These four predictors of minimum $P_{LV}$ were incorporated in a multivariable linear regression model [Eq. (2)]:

$$ \min P_{\text{LV}} \approx -6.885 + 0.025 \cdot P_{\text{sys}} + 0.243 \cdot \text{BMI} - 0.097 \cdot \text{LARS} + 0.158 \cdot \tau \quad (2) $$

The strongest predictors of minimum $P_{LV}$ were the time constant of LV isovolumic relaxation ($\tau$) and LA reservoir strain (LARS) (Figure 2 and Table 2). Systolic pressure ($P_{sys}$) and BMI were weaker, but statistically significant predictors (see Supplementary data online, Data B). A sensitivity analysis on errors of inputs for estimation of minimum $P_{LV}$ is presented in Supplementary data online, Data F.

The third and last principle is that maximum $\Delta P_{MV}$ can be computed by a simplification of the Navier-Stokes momentum conservation equation. As such, the peak early-diastolic transmitral pressure difference is computed as:

$$ P_{\text{MV}} \approx \frac{P}{2} \left( v_{\text{MV}}^2 + \frac{Q v_{\text{MV}}^2}{\Delta Q} \right) \quad (3) $$

using the transmitral flow velocity ($v_{MV}$), the flow rate ($Q$), and its increment in time ($\Delta Q$). The LV volume trace was obtained by fitting the GLS trace to the peak ESV and EDV, assuming that the LV volume curve mirrors the GLS curve. Mitral flow rate was calculated as the time derivative of the volume trace (dV/dt). This is explained in Supplementary data online, Data E. It is

referred to Table 3C for inputs. Supplementary data online, Data D explains details and includes an example case (see Supplementary data online, Figure S5) showing how the transmitral pressure difference was calculated.

### Method to estimate the time constant $\tau$ of LV pressure decay

The time constant of LV pressure decay during isovolumic relaxation ($\tau$) is defined according to an exponential decay model of diastolic pressure as proposed by Weiss et al.⁸:

$$ P_{\text{LV}}(t) = P_0 * e^{-\frac{t}{\tau}} \quad (4) $$

where $e$ is the natural logarithmic base, $t$ is time, and $P_0$ is LV pressure at time of peak negative LV dP/dt. Our method to estimate $\tau$ non-invasively is based on the principles proposed by JD Thomas and co-workers.¹¹,¹²

In the 81 patients of the derivative cohort, we found $P_0$ to be 65 ± 7% [mean ± standard deviation (SD)] of peak LV pressure from invasive measurements. For the non-invasive estimate of $\tau$, we assumed $P_0$ to be a fixed fraction of 65% of peak LV pressure ($P_{sys}$). Based on observations in previous studies,⁷,¹²⁻¹⁴ $P_{MVO}$ was assumed to be 5 mmHg higher than mean $P_{LA}$. Thus, $P_{MVO}$ becomes dependent on Eqs. (1) and (2), resulting in a coupled system of equations that is solved by an iterative algorithm (where 10 iterations were enough to obtain a precise convergence of minimum $P_{LV}$, $\tau$, pre-A $P_{LV}$, and $P_{MVO}$). Consistent with the Weiss study,⁸ our estimated time of aortic valve closure (AVC) occurred slightly before peak negative dP/dt. Therefore, we used 85% of isovolumic relaxation time (IVRT) in our $\tau$ estimate. For details in measurement of IVRT, it is referred to Supplementary data online, Data E.

With these assumptions, $\tau$ can be estimated as:

$$ \tau = \frac{0.85 \cdot \text{IVRT}}{\ln(0.65 \cdot P_{\text{sys}}) - \ln(P_{\text{MVO}})} \quad (5) $$

The estimation of $\tau$ in Eq. (5) depends on the accuracy of the two estimated pressures in the denominator as well as IVRT in the nominator. We investigated the sensitivity of the estimated $\tau$ to errors in $P_{sys}$, $P_{MVO}$, and IVRT (see Supplementary data online, Data C).

### Method to estimate end-diastolic $P_{LV}$

Building on the same principles as above, the end-diastolic $P_{LV}$ is computed by adding to pre-A $P_{LV}$ the maximum $\Delta P_{MV}$ during the A-wave, and the pressure increase due to passive filling as detailed in Supplementary data online, Data E.

<table><caption>**Table 2** Independent predictors of minimum $P_{LV}$</caption><thead><tr><th colspan="2">Independent predictors of minimum P<sub>LV</sub></th></tr></thead><tbody><tr><td>Time constant τ of LV relaxation:<br/>r = 0.71</td><td>Left atrial reservoir strain:<br/>r = 0.65</td></tr><tr><td>Body mass index: r = 0.37</td><td>Systolic pressure: r = 0.23</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Figure 2** Association between measured minimum $P_{LV}$ (min $P_{LV}$) and LV isovolumic relaxation time constant ($\tau$; left) and LA reservoir strain (LARS; right). Data from the full cohort of 100 patients are shown (derivative cohort, n = 81, and testing cohort, n = 19). Regression data for the derivative cohort are indicated.</figcaption></figure>
Validation of pressure estimates

The coefficients in Eqs. (2) and (5) were found from the derivation cohort of 81 patients using invasive data. In the 19 patients used as a testing cohort, the estimated values for minimum $P_{LV}$, $\tau$, pre-A $P_{LV}$, and end-diastolic $P_{LV}$ were compared with their invasive reference values.

<table><caption>**Table 3** Input variables used for calculating (A) the minimum LV pressure, (B) the time constant ($\tau$) of LV pressure decay, and (C) the maximum atrio-ventricular pressure difference</caption><thead><tr><th></th><th>Symbol</th><th>Description</th><th>Units</th></tr></thead><tbody><tr><td rowspan="4">A</td><td>P<sub>sys</sub></td><td>Systolic aortic pressure</td><td>mmHg</td></tr><tr><td>BMI</td><td>Body mass index</td><td>kg/m<sup>2</sup></td></tr><tr><td>LARS</td><td>LA reservoir strain</td><td>%</td></tr><tr><td>τ</td><td>Time constant of LV pressure decay</td><td>ms</td></tr><tr><td rowspan="3">B</td><td>t<sub>AVC</sub></td><td>Time of aortic valve closure</td><td>s</td></tr><tr><td>t<sub>MVO</sub></td><td>Time of mitral valve opening</td><td>s</td></tr><tr><td>P<sub>MVO</sub></td><td>P<sub>LV</sub> at mitral valve opening</td><td>mmHg</td></tr><tr><td rowspan="3">C</td><td>P<sub>sys</sub></td><td>Systolic LV pressure</td><td>mmHg</td></tr><tr><td>v<sub>MV</sub></td><td>Velocity across the mitral valve</td><td>m/s</td></tr><tr><td>Q</td><td>Flow rate trace across mitral valve</td><td>mL/s</td></tr><tr><td></td><td>ΔQ</td><td>Change of flow rate</td><td>mL/s</td></tr></tbody></table>

## Part 2: non-invasive LV diastolic pressure curve

The second aim of the study was non-invasive generation of a patient-specific LV diastolic pressure curve. As illustrated in Figure 3A and B, the first step was construction of a time-normalized reference curve with several diastolic events indicated. The second step, which is illustrated in Figure 3C and D, was to estimate pressure at each diastolic event and to convert the normalized time scale to an absolute time scale. The curve estimates were validated by comparison with invasively measured pressure curves. This approach is somewhat similar to the principle we used in the study by Russell et al.⁵ for imaging-based estimation of the LV systolic pressure curve.

### Reference LV pressure curve

A previously published dataset from Smiseth et al.⁷ was used to define a diastolic pressure reference curve. The reference cohort consists of a dataset with eight stable patients referred for evaluation of suspected CAD. Pressures were recorded by micromanometers using dual-sensor 7 F catheters (model no. SSO-654, Millar Instruments, Houston, TX), with one sensor located near the LV base, in the LV outflow tract and one more distally in the ventricle. For construction of the reference pressure curve, we used pressure measured by the distal sensor.

Each individual $P_{LV}$ curve from the reference cohort was first annotated with the occurrence of the key diastolic events: mitral valve opening (MVO), minimum $P_{LV}$, peak E-wave, start and peak A-wave, and mitral valve closure (MVC). Then, the temporal duration between these events was normalized before calculating an averaged pressure curve (panels A and B).

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 3** Left ventricular (LV) reference curve and pressure estimates to define patient-specific curves. (A) Single patient recordings of LV pressure ($P_{LV}$) from the cohort used to define an averaged diastolic $P_{LV}$ curve. The symbols on the curves indicate key diastolic events. (B) Same data as in A, showing time-normalized single LV pressure curves and the averaged curve (solid black line). (C) Starting with the averaged $P_{LV}$ curve, a patient-specific $P_{LV}$ curve was constructed by shifting pressure at key diastolic events vertically according to the pressure estimate at each event. (D) Conversion of the time-normalized $P_{LV}$ curve to a curve with absolute time units involved use of the GLS trace to define the phases of diastole, as illustrated in Figure 4.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 4** Estimation of isovolumic relaxation time (IVRT) and timing of diastolic events. The LV volume curve and its derivative were used to estimate timing of key diastolic events (cf. Figure 3 for illustration of time-normalized diastolic pressure curve). The estimated pressure curve was compared with the measured LV pressure curve. t0: start of exponential pressure decay during isovolumic relaxation time (IVRT); AVC, aortic valve closure; MVO, mitral valve opening; MVC, mitral valve closure; a, b, c, and d represent, respectively, minimum P<sub>LV</sub>, peak early-diastolic mitral flow velocity, atrial contraction start, and peak atrial-induced mitral flow velocity.</figcaption></figure>

## Estimated LV pressure curve

The ability to generate patient-specific diastolic LV pressure curves was validated in an independent group of seven patients. They were selected because echocardiography was done while the patients were on the catheterization table that allowed pressures and images to be recorded simultaneously. Echocardiography and LV pressure were recorded from the same series of beats and recordings were done during breath-hold at end-expiration.

Figures 3 and 4 illustrate the principle for estimation of the patient-specific P<sub>LV</sub> curve by key diastolic events. As illustrated in Figure 3C, the value of each pressure point was shifted vertically according to the estimated pressure at each diastolic event. Then, correct timing in the heart cycle of each diastolic event was obtained by using the GLS trace and its derivatives, as illustrated in Figure 4. The key diastolic events included the following: MVO, minimum P<sub>LV</sub>, peak mitral E-velocity, pre-A P<sub>LV</sub>, peak mitral A velocity, and MVC. Details of the method to estimate the pressures and timings of these diastolic events are explained in Supplementary data online, Data E.

A LV volume trace was inferred by scaling the LV GLS trace to measured end-systolic and end-diastolic volumes, and subsequently computing the corresponding temporal transients of transmitral flow rate [Eq. (6)] and flow acceleration and deceleration [Eq. (7)], as illustrated in Figure 4:

$$Q = \frac{dV}{dt} \qquad (6)$$

$$\frac{dQ}{dt} = \frac{d^2V}{dt^2} \qquad (7)$$

where V is LV volume (mL), Q is flow rate (mL/s), and t is time (s). Details in calculation of dV/dt are explained in Supplementary data online, Data E.

To evaluate this method, the estimated pressure curves were plotted together with the invasively measured curves and compared. Furthermore, the mean pressure from MVO to MVC was computed and compared with the respective measured value.

## Statistical analysis

Values are presented as mean ± SD. Univariate and multivariable linear regression analysis were used to identify predictors of minimum LV pressure and τ.

To evaluate the agreement between estimated and measured LV diastolic pressure key markers and τ, linear correlation and Bland-Altman plots were considered. Correlation based on the linear least squares regression was performed and respective linear equation and R² are provided in plots. Bland-Altman plot with 95% limits of agreement was used for comparison
between estimated and measured pressures, with the limits of agreement given as 1.96 * SD of the difference. For statistical testing, a value of P < 0.05 was considered significant.

# Results

## Estimated LV diastolic pressures

Figure 5 shows agreements between estimated and measured LV diastolic pressures and between estimated and measured $\tau$ in the 19 patients in the testing cohort. The estimated minimum $P_{LV}$ had a bias of -0.6 mmHg and limits of agreement < 2.2 mmHg (±1.96 * SD) when compared with invasively measured minimum $P_{LV}$ (Figure 5A). The estimated pre-A $P_{LV}$ also had good agreement with its invasive reference value with a bias of 0.0 mmHg and limits of agreement < 3.1 mmHg (Figure 5C). The estimates of end-diastolic $P_{LV}$ had a bias of -1.8 mmHg and limits of agreement < 6.8 mmHg when compared with invasively measured end-diastolic $P_{LV}$.

The intermediate variable $\tau$ that was required in the estimation of minimum $P_{LV}$ corresponded well with its invasive reference: estimated $\tau$ had a bias of -6.8 ms and limits of agreement < 19.5 ms when compared with invasively measured $\tau$ (Figure 5B). The sensitivity analysis of $\tau$ estimation to errors in $P_{SYS}$ and $P_{MVO}$ showed that errors of 15 and 5 mmHg, respectively, resulted in errors in $\tau$ of 7.3 and 8.6 ms, respectively (see Supplementary data online, Data C). For perspective, such can be related to the range of $\tau$ from 28 to 71 ms in our population (Figure 5B). An error in $\tau$ of 8.6 ms will alter the estimated minimum $P_{LV}$ by 1.35 mmHg [via Eq. (2)].

## Estimated LV diastolic pressure curve

The non-invasive estimate of the diastolic segment of the $P_{LV}$ curve showed good agreement with invasive pressure recordings, both visually and quantitatively by comparing the mean diastolic $P_{LV}$ from $t_{MVO}$ to $t_{MVC}$ (Figures 6 and 7). Estimated mean diastolic $P_{LV}$ showed a bias of 0.2 mmHg and limits of agreement < 3.2 mmHg. A sensitivity analysis to the core inputs of the methodology (LV systolic pressure, IVRT, and mitral E-velocity) reported robust results to changes up to 20% (see Supplementary data online, Data F).

# Discussion

In the present study, we propose an innovative imaging-based method to estimate LV diastolic pressures non-invasively. The method estimated pre-A $P_{LV}$ as a surrogate for mean $P_{LA}$ with high accuracy when validated against invasively measured pre-A $P_{LV}$. The method also provided estimates of minimum $P_{LV}$, a parameter that reflects LV relaxation and restoring forces, and end-diastolic $P_{LV}$ as measure of preload. Therefore, the method has potential to provide LV functional data that are not accessible with current non-invasive approaches. Additionally, the method offers an estimate of the complete LV diastolic pressure curve, demonstrating good accuracy when validated in a subset of independent patients.

The imaging parameters required for the method are recorded routinely when performing clinical echocardiography, and each parameter has high measurement feasibility. Calculation of the different pressure outputs require data processing that needs to be semiautomated to make the method time efficient as a clinical tool. Since the study included exclusively patients evaluated for CAD and had a relatively small sample size, it should be regarded as a proof-of-principle study for application of the novel method. Ultimately, the utility of the method in clinical practice depends on its accuracy when tested in diverse phenotypes beyond CAD and in larger populations, and such studies are planned.

# Principles behind the method

The proposed method to estimate LV filling pressure used pre-A $P_{LV}$ as a surrogate for mean $P_{LA}$ that is consistent with previous studies and current recommendations.¹,⁹,¹⁰ In patients with mitral stenosis or severe mitral regurgitation, however, mean $P_{LA}$ may markedly exceed pre-A $P_{LV}$. With these limitations in mind, we consider pre-A $P_{LV}$ to be a valid surrogate for mean $P_{LA}$.

A central assumption in our method is that mean $P_{LA}$ can be estimated as the sum of minimum $P_{LV}$ and maximum $\Delta P_{MV}$. The validity of this assumption comes from observations in several experimental studies under a wide range of haemodynamic conditions, including studies in failing hearts.¹³,¹⁵⁻¹⁷ The physical rationale for the assumption is that end of diastasis (pre-A) represents an equilibrium pressure point between the LV and LA chambers, and that early filling is driven by the difference in pressure when this equilibrium is not reached yet. Details of this proposed mechanism are presented in Supplementary data online, Data A.

Minimum $P_{LV}$ was estimated based on a linear regression model using $\tau$, LA reservoir strain, systolic blood pressure, and BMI as predictors. Among them, and considering the physiological range of each, $\tau$ was the largest contributor, and was estimated non-invasively using principles similar to Scalia et al.¹² Our estimate of $\tau$ was derived from a formula that incorporated measurement of IVRT from the LV strain signal. This approach enables single-beat analysis, which paves the way for future automation of the method. The conventional approach for measuring IVRT, however, is by measuring LV outflow velocities by continuous wave or pulsed Doppler echocardiography.¹ Whether the LV strain-based method is comparable to the Doppler methods remains to be studied.

The observation that LA reservoir strain, in addition to $\tau$, is a strong predictor of minimum $P_{LV}$ represents a novel finding in this study. It may reflect dependency of LA reservoir strain on minimum $P_{LA}$, which closely approximates minimum $P_{LV}$, rather than a specific association between LA reservoir strain and minimum $P_{LV}$.¹⁸ An association between LA reservoir strain and minimum $P_{LA}$ is expected due to the important role of suction for LA filling and reservoir function.¹⁹ The suction is generated as a combined effect of LA relaxation and LV longitudinal shortening and is reflected in the reduction in $P_{LA}$ in early systole. Furthermore, as shown by Hunderi et al.,²⁰ the LA pressure-volume curve is curvilinear with shallow slope (high reservoir capacity) at low pressures and steeper slope (low reservoir capacity) at higher pressures. Therefore, when minimum $P_{LA}$ is in the lower range at onset LA filling, LA reservoir capacity is high. We suggest that these mechanisms contribute to the correlation between LA reservoir strain and minimum $P_{LV}$.

The finding that systolic blood pressure was an additional, but weak, independent predictor of minimum $P_{LV}$ is consistent with known effects of afterload on LV early-diastolic pressures.²¹ The association between BMI and minimum $P_{LV}$ may reflect an impact of conditions commonly associated with overweight and obesity.

Finally, note that there was no significant independent contribution to infer minimum $P_{LV}$ from $e'$ that is often used as marker of relaxation, probably because the impact of relaxation on minimum $P_{LV}$ was reflected in the estimated $\tau$.

The early-diastolic transmitral pressure difference, maximum $\Delta P_{MV}$, the second summand to estimate mean $P_{LA}$ in Eq. (1), was calculated by a simplification of the Navier-Stokes equation of conservation of mass, i.e. of momentum conservation. As shown by JD Thomas and co-workers, inertial forces represent a substantial fraction of the early-diastolic pressure difference across a normal mitral valve and therefore need to be incorporated when estimating transmitral pressure differences for unrestricted mitral flow.²²⁻²⁴ This is explained in more detail in Supplementary data online, Data D. In mitral stenosis, however, there is dominance of advective forces (i.e. those to create the spatial acceleration into a narrow filling jet) over inertial forces, which justifies using the simplified Bernoulli's equation²⁵ and its correction²⁶ to determine severity of the stenosis.
<figure><img src="image_18.png" /><figcaption>**Figure 5** Correlation and agreement between estimated and invasively measured LV diastolic pressures and τ. Correlation and Bland–Altman plots between estimated and invasive measurements in the *n* = 19 patients in the testing cohort: (A) minimum left ventricular pressure (min P<sub>LV</sub>); (B) isovolumic relaxation time constant τ; (C) pre-A P<sub>LV</sub>; (D) end-diastolic P<sub>LV</sub>.</figcaption></figure>
## Alternative methods to estimate LV filling pressure

Recent innovations in artificial intelligence (AI) make use of 'black box' approaches, with promising examples in HF diagnostics based on raw echocardiographic data or electrocardiograms.²⁷,²⁸ These approaches provide the likelihood of a given HF diagnostic, but do not provide mechanistic insights or clinical interpretation. On the contrary, our method addresses the need for LV diastolic pressures by a synergetic combination of statistic [a linear regression, Eq. (2)] and mechanistic [for relaxation and transmitral pressure differences, Eqs. (3) and (5)] models, a strength in the use of digital twin technologies.²⁹

A number of qualitative or semiquantitative echocardiographic methods for evaluating LV diastolic function and filling pressure are available,¹⁻³ but none of them can differentiate between mean LA pressure and LV end-diastolic pressure. Furthermore, they do not provide estimates of minimum LV pressure that is a marker of LV relaxation and restoring forces. The same limitations apply to pulmonary capillary

wedge pressure that is used as an indirect measure of mean LA pressure. Therefore, potentially our method may provide new insights into diastolic function beyond just providing an estimate of mean LA pressure.

## Uncontrolled factors in the definition of LV filling pressure

A potential challenge with defining and measuring LV diastolic pressure is the existence of intraventricular pressure differences.³⁰ In the patient population used to define the reference curve, which included patients with apparently normal LV systolic function, we used a catheter with two pressure sensors. The average difference between the location with lowest and highest minimum $P_{LV}$ was circa 2 mmHg and peak pressure difference occurred during early rapid filling and with lowest pressure in the LV outflow tract.⁷ This would have a small impact on the measured LV minimum pressure. In that study, there was no measurable intraventricular pressure differences in pre-A pressure,⁷ which is as expected in late diastasis when there are low intraventricular flow velocities. Furthermore, as we have shown previously, intraventricular pressure differences are reduced in ventricles with systolic dysfunction.³¹ Therefore, we do not consider regional differences in minimum $P_{LV}$ to be an important limitation in the present study or in hearts with reduced LV systolic function.

However, variations in the RR intervals may influence degree of filling that is a challenge when comparing methods for measuring diastolic pressure. To minimize this influence in the subgroup used for validation of the diastolic pressure curve, echocardiography and pressure measurements were done simultaneously. In the other patients, echocardiography and pressure measurements were performed no more than two hours apart.

Considering these adverse factors of intracardiac variability (both over space and time) the obtained filling pressure limits of agreement (±1.96 * SD) of <3.1 mmHg is a noteworthy outcome of the present study.

## Defining the LV diastolic pressure curve

The solution presented is inspired by our previously published non-invasive methodology to estimate the LV systolic pressure curve and myocardial work.⁵,³² In the present study, a similar approach was used to define a reference diastolic pressure curve and pressures were estimated at several diastolic events. Furthermore, timing of

<figure><img src="image_19.png" /></figure>

**Figure 6** Patient-specific diastolic left ventricular (LV) pressure curve. A representative patient showing a non-invasive estimate of the diastolic LV pressure curve (blue thicker line) and diastolic events (orange dots) in comparison with the measured pressure curve (black thinner line). These diastolic LV pressure events (estimates in orange) include the following: aortic valve closure (AVC), mitral valve opening (MVO), minimum LV pressure (min $P_{LV}$), peak E-wave, end-diastasis (A-wave$_{start}$), peak A-wave (A-wave$_{peak}$), and end-diastole corresponding to mitral valve closure (MVC).

<figure><img src="image_20.png" /></figure>

**Figure 7** Correlation and agreement between estimated and measured mean diastolic $P_{LV}$ calculated from mitral valve opening to mitral valve closure.
diastolic events in the heart cycle was defined by using GLS to define IVRT and phases of diastolic filling.

Since the pressure curve validation was done in only a small number of patients, this part of the protocol should be considered just a testing of the principle, which should be explored in future studies. Nonetheless, the present findings suggest that the diastolic pressure curved can be estimated by echocardiography.

## Clinical applications

Elevated LV filling pressure is a diagnostic hallmark of HF, and the novel method could play a role in the diagnostics and management of this large group of patients. The method may also be of value in patients with established HF when considering adjustment of medical therapy to prevent or treat pulmonary vascular congestion.

Furthermore, our method provides an estimate of minimum $P_{LV}$ that is a parameter of LV early-diastolic function and is an interesting variable since it reflects LV relaxation and LV restoring forces (elastic recoil).33,34 There is limited knowledge, however, about a potential diagnostic value of minimum $P_{LV}$ since it has not been feasible to measure in clinical diagnostics when using conventional (fluid-filled) catheters due to their poor frequency response causing artefacts in the pressure trace in early diastole when LV pressure changes rapidly.33,35,36 Low value of minimum $P_{LV}$ is important for efficient LV filling at rest and even more during exercise when reduction in minimum $P_{LV}$ allows increase in transmitral flow rate in normal hearts with little or no increase in LA pressure.4 Therefore, minimum $P_{LV}$ reflects an important feature of diastolic function. Potentially, demonstration of elevated minimum $P_{LV}$ as sign of impaired LV relaxation, may be used to identify diastolic dysfunction in patients with normal LA pressure at rest.

Currently, algorithms that combine several echocardiographic parameters are used to differentiate between normal and elevated LV filling pressure but have limited ability to quantify filling pressure. Furthermore, none of these approaches differentiates between mean LA pressure and LV end-diastolic pressure, which represent two different physiological variables. In heart failure patients, mean LA pressure is an important parameter as it determines pulmonary vascular congestion, whereas LV end-diastolic pressure is a more direct reflector of LV preload, which determines stroke volume. The novel method has potential to differentiate between these two physiological variables.

Clinical implementation of the novel method requires development of software that allows rapid calculation and reporting of the estimated pressures, ideally online during an imaging study or as an off-line analysis tool. Such an automatization of the filling pressure and pressure curve generation will become possible by incorporating machine learning approaches that will increase processing speed and robustness of the input data and hence the results. The echocardiographic variables needed to estimate LV filling pressure with the novel method are part of clinical routine, except for LA strain that is not yet widely implemented.

Furthermore, future studies should also investigate if the proposed method for estimating LV diastolic pressures may be combined with LV volumes to calculate LV diastolic stiffness as a diagnostic parameter when evaluating patients suspected of heart failure or other disorders with LV dysfunction. Moreover, in principle the presented methodology may be adapted for imaging with cardiac magnetic resonance that should be investigated in future studies.

## Study limitations

The study is based on analysis in populations that were included in previous publications from the authors of this study (O.A.S., N.O., and K.W.).6,7 We consider the retrospective approach justified due to the uniqueness of the database that includes patients studied by echocardiography and LV pressure using micromanometer-tipped catheters combined with simultaneous pressure via a fluid line that is needed to ensure correct absolute pressure.33,35 Whereas micromanometers are

excellent for measuring pressure waveforms and pressure amplitudes, they tend to drift, which in some cases may cause several mmHg errors in absolute LV diastolic pressure. In the patients in our database, this was adjusted for by simultaneously recording pressure via a fluid line.

In clinical routine, LV pressure is measured via fluid-filled catheters, which is just fine for pre-A $P_{LV}$ and in most cases for end-diastolic pressure, but do not provide the accuracy needed to measure minimum $P_{LV}$ and $\tau$,33,35 which were fundamental parameters for development of our method. For ethical reasons, we preferred utilizing our existing database rather than subjecting new patients to a complex invasive protocol with dual pressure recordings to test the novel concept.

The estimation of the LV volume curve was derived from echocardiographic measurements of end-diastolic and end-systolic volumes in combination with GLS, under the assumption that the LV GLS curve closely mirrors the LV volume curve. However, the relationship between LV volume and GLS is not perfectly linear, which may have introduced some degree of error into the volume estimates. Ideally, LV volume assessments should be performed using high-frame-rate 3D imaging, which was not available in our database. Since imaging quality is both patient and operator dependent, the robustness of the method should be further explored and potentially improved by use of AI and semiautomated measurements.

Whereas our dataset was limited by its size, the variabilities in the estimates of LV filling pressure and minimum $P_{LV}$ were small, supporting the validity of the proposed methodology. The accuracy of the estimated LV end-diastolic pressure, however, tended to be lower than for the other LV pressure parameters. We are currently planning a prospective multicentre study for testing the method in a larger population and in different cardiac phenotypes. Potentially, other predictors of minimum $P_{LV}$ could be considered in specific cardiac diseases. Nevertheless, the variables we used to estimate minimum $P_{LV}$, with $\tau$ and LA reservoir strain as the unique determinants, are expected to be disturbed in most cardiac diseases with LV dysfunction. Furthermore, the principles used to estimate $\Delta P_{MV}$ by Navier-Stokes equation are expected to be valid regardless of phenotype.

## Conclusions

In the present study, we introduce a novel method based on cardiac imaging and fluid mechanics analysis for estimation of LV diastolic pressures. The method estimated LV filling pressure measured as pre-A $P_{LV}$ with good accuracy and provided an accurate estimate of minimum $P_{LV}$ that is a marker of LV relaxation and restoring forces. The method also provided an approximation of the LV diastolic pressure curve. Furthermore, the method has potential to differentiate between LA mean pressure, which is closely related to pulmonary vascular congestion, and LV end-diastolic pressure that determines preload and stroke volume. To determine the clinical utility of the method, validation in larger populations with different phenotypes is needed and is being prepared.

## Acknowledgements

Dr John M. Aalen and Dr Ole J. Sletten are thanked for technical assistance during the initial phase of the project.

## Supplementary data

Supplementary data are available at *European Heart Journal - Cardiovascular Imaging* online.

## Funding

European Union's Horizon 2020 research and Innovation program. Marie Skłodowska-Curie Grant agreement no. 764738 (J.F.F.); Wellcome Trust,
Senior Fellowship 209450/Z/17/Z (P.L.) and Centre for Medical Engineering
WT203148/Z/16/Z (P.L. and J.F.F.).

**Conflict of interest:** O.A.S. is co-inventor of 'Method for myocardial segment work analysis'. O.A.S. is patent inventor of 'Estimation of blood pressure in the heart', which was used in this study. O.A.S. has received one speaker honorarium from GE Healthcare. O.A.S. is a member of the European Heart Journal Cardiovascular Imaging Editorial Board. J.F.F. is patent inventor of 'Estimation of blood pressure in the heart', which was used in this study. N.O. is collaborator on the innovation 'Estimation of blood pressure in the heart'. P.L. is collaborator on the innovation 'Estimation of blood pressure in the heart'. E.D. is a member of the European Heart Journal Cardiovascular Imaging Editorial Board.

## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## References

1. Nagueh SF, Smiseth OA, Appleton CP, Byrd BF, Dokainish H, Edvardsen T et al. Recommendations for the evaluation of left ventricular diastolic function by echocardiography: an update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging. *Eur Heart J Cardiovasc Imaging*. 2016; **17**: 1321–60.

2. Smiseth OA, Morris DA, Cardim N, Cikes M, Delgado V, Donal E et al. Multimodality imaging in patients with heart failure and preserved ejection fraction: an expert consensus document of the European Association of Cardiovascular Imaging. *Eur Heart J Cardiovasc Imaging* 2022; **23**:e34–61.

3. Chubuchny V, Pugliese NR, Taddei C, Poggianti E, Spini V, Barison A et al. A novel echocardiographic method for estimation of pulmonary artery wedge pressure and pulmonary vascular resistance. *ESC Heart Fail* 2021; **8**:1216–29.

4. Smiseth OA, Donal E, Boe E, Ha J-W, Fernandes JF, Lamata P. Phenotyping heart failure by echocardiography: imaging of ventricular function and haemodynamics at rest and exercise. *Eur Heart J Cardiovasc Imaging* 2023; **24**:1329–42.

5. Russell K, Eriksen M, Aaberge L, Wilhelmsen N, Skulstad H, Remme EW et al. A novel clinical method for quantification of regional left ventricular pressure-strain loop area: a non-invasive index of myocardial work. *Eur Heart J* 2012; **33**:724–33.

6. Yoshida T, Ohte N, Narita H, Sakata S, Wakami K, Asada K et al. Lack of inertia force of late systolic aortic flow is a cause of left ventricular isolated diastolic dysfunction in patients with coronary artery disease. *J Am Coll Cardiol* 2006; **48**:983–91.

7. Smiseth OA, Steine K, Sandbaek G, Stugaard M, Gjolberg T. Mechanics of intraventricular filling: study of LV early diastolic pressure gradients and flow velocities. *Am J Physiol* 1998; **275**:H1062–9.

8. Weiss JL, Frederiksen JW, Weisfeldt ML. Hemodynamic determinants of the time-course of fall in canine left ventricular pressure. *J Clin Invest* 1976; **58**:751–60.

9. Rahimtoola SH, Loeb HS, Ehsani A, Sinno MZ, Chuquimia R, Lal R et al. Relationship of pulmonary artery to left ventricular diastolic pressures in acute myocardial infarction. *Circulation* 1972; **46**:283–90.

10. Yamamoto K, Nishimura RA, Redfield MM. Assessment of mean left atrial pressure from the left ventricular pressure tracing in patients with cardiomyopathies. *Am J Cardiol* 1996; **78**:107–10.

11. Thomas JD, Flachskampf FA, Chen C, Guererro JL, Picard MH, Levine RA et al. Isovolumic relaxation time varies predictably with its time constant and aortic and left atrial pressures: implications for the noninvasive evaluation of ventricular relaxation. *Am Heart J* 1992; **124**:1305–13.

12. Scalia GM, Greenberg NL, McCarthy PM, Thomas JD, Vandervoort PM. Noninvasive assessment of the ventricular relaxation time constant (τ) in humans by Doppler echocardiography. *Circulation* 1997; **95**:151–5.

13. Yamamoto K, Masuyama T, Tanouchi J, Uematsu M, Doi Y, Naito J et al. Importance of left ventricular minimal pressure as a determinant of transmitral flow velocity pattern in the presence of left ventricular systolic dysfunction. *J Am Coll Cardiol* 1993; **21**:662–72.

14. Cheng CP, Igarashi Y, Little WC. Mechanism of augmented rate of left ventricular filling during exercise. *Circ Res* 1992; **70**:9–19.

15. Hasegawa H, Little WC, Ohno M, Brucks S, Morimoto A, Cheng HJ et al. Diastolic mitral annular velocity during the development of heart failure. *J Am Coll Cardiol* 2003; **41**:1590–7.

16. Ishida Y, Meisner JS, Tsujioka K, Gallo JI, Yoran C, Frater RW et al. Left ventricular filling dynamics: influence of left ventricular relaxation and left atrial pressure. *Circulation* 1986; **74**:187–96.

17. Yellin EL, Nikolic S, Frater RWM. Left ventricular filling dynamics and diastolic function. *Prog Cardiovasc Dis* 1990; **32**:247–71.

18. Little WC, Ohno M, Kitzman DW, Thomas JD, Cheng CP. Determination of left ventricular chamber stiffness from the time for deceleration of early left ventricular filling. *Circulation* 1995; **92**:1933–9.

19. Smiseth OA, Thompson CR, Lohavanichbutr K, Ling H, Abel JG, Miyagishima RT et al. The pulmonary venous systolic flow pulse–its origin and relationship to left atrial pressure. *J Am Coll Cardiol* 1999; **34**:802–9.

20. Hunderi JO, Thompson CR, Smiseth OA. Deceleration time of systolic pulmonary venous flow: a new clinical marker of left atrial pressure and compliance. *J Appl Physiol* 2006; **100**:685–9.

21. Gillebert TC, Leite-Moreira AF, De Hert SG. Relaxation–systolic pressure relation: a load-independent assessment of left ventricular contractility. *Circulation* 1997; **95**:745–52.

22. Flachskampf FA, Rodriguez L, Chen C, Guerrero JL, Weyman AE, Thomas JD. Analysis of mitral inertia: a factor critical for early transmitral filling. *J Am Soc Echocardiogr* 1993; **6**:422–32.

23. Greenberg NL, Vandervoort PM, Thomas JD. Instantaneous diastolic transmitral pressure differences from color Doppler M mode echocardiography. *Am J Physiol* 1996; **271**: H1267–76.

24. Firstenberg MS, Vandervoort PM, Greenberg NL, Smedira NG, McCarthy PM, Garcia MJ et al. Noninvasive estimation of transmitral pressure drop across the normal mitral valve in humans: importance of convective and inertial forces during left ventricular filling. *J Am Coll Cardiol* 2000; **36**:1942–9.

25. Holen J, Aaslid R, Landmark K, Simonsen S. Determination of pressure gradient in mitral stenosis with a non-invasive ultrasound Doppler technique. *Acta Med Scand* 1976; **199**: 455–60.

26. Donati F, Myerson S, Bissell MM, Smith NP, Neubauer S, Monaghan MJ et al. Beyond Bernoulli: improving the accuracy and precision of noninvasive estimation of peak pressure drops. *Circ Cardiovasc Imaging* 2017; **10**:e005207.

27. Akerman AP, Porumb M, Scott CG, Beqiri A, Chartsias A, Ryu AJ et al. Automated echocardiographic detection of heart failure with preserved ejection fraction using artificial intelligence. *JACC Adv* 2023; **2**:100452.

28. Lee E, Ito S, Margara F, Marciniak M, Rodero C, Loncaric F, Feng Y et al. The 'Digital Twin' to enable the vision of precision cardiology. *Eur Heart J* 2020; **41**:4556–64.

29. Corral-Acero J, Margara F, Marciniak M, Rodero C, Loncaric F, Feng Y et al. The 'Digital Twin' to enable the vision of precision cardiology. *Eur Heart J* 2020; **41**:4556–64.

30. Courtois MA, Sandor J, Kovacs J, Ludbrook PA. Physiological early diastolic intraventricular gradient is lost during acute myocardial ischemia. *Circulation* 1990; **81**:1688–96.

31. Steine K, Stugaard M, Smiseth OA. Mechanisms of retarded apical filling in acute ischemic left ventricular failure. *Circulation* 1999; **99**:2048–54.

32. Ribic D, Remme EW, Smiseth OA, Massey RJ, Eek CH, Kvitting J-PE et al. Non-invasive myocardial work in aortic stenosis–validation and improvement of left ventricular pressure estimation. *Eur Heart J Cardiovasc Imaging* 2024; **25**:201–12.

33. Udelson JE, Bacharach SL, Cannon RO III, Bonow RO. Minimum left ventricular pressure during beta-adrenergic stimulation in human subjects. Evidence for elastic recoil and diastolic "suction" in the normal heart. *Circulation* 1990; **82**:1174–82.

34. Opdahl A, Remme EW, Helle-Valle T, Lyseggen E, Vartdal T, Pettersen E et al. Determinants of left ventricular early-diastolic lengthening velocity: independent contributions from left ventricular relaxation, restoring forces, and lengthening load. *Circulation* 2009; **119**:2578–86.

35. Courtois M, Fattal PG, Kovacs SJ Jr, Tiefenbrunn AJ, Ludbrook PA. Anatomically and physiologically based reference level for measurement of intracardiac pressures. *Circulation* 1995; **92**:1994–2000.

36. Grossmann W. Pressure measurement. In: Grossmann W, Baim DS, eds. *Cardiac Catheterization, Angiography and Intervention (4th Edition)*. Philadelphia: Lea & Febiger; 1991. p123–42.