Introduction

Hemodynamic forces (HDF) analysis has been proposed as a promising approach for the study of blood flow within the ventricular chambers through the evaluation of intraventricular pressure gradients (IVPG) [1]. In fact, the blood flow is driven by IVPG, which in turn are determined by the functional interplay of the myocardium, valves, and large vessels. Previous attempts to explore HDF (which represents the forces exchanged between blood and surrounding tissues and corresponds to the global value of IVPG integrated over the ventricular volume) were based on echocardiographic particle image velocimetry and 4-D flow magnetic resonance imaging, which gained limited popularity for various reasons: the former needs contrast agent infusion and present limited accuracy, the latter is the reference standard but presents high cost, low availability, and the procedure is complex and time-consuming. Recently, a new approach using a mathematical model based on the first principle of fluid dynamics and mass conservation principles has been proposed [2]. This model is based on the detection and tracking of endocardial tissue velocities (using the same speckle tracking technique used for strain and strain rate analysis), and on the blood velocity across the valves (which is calculated from the volumetric changes of the left ventricle and the valve area, using the conservation of mass principle). By integrating knowledge of left ventricular (LV) geometry, endocardial tissue movement, and the dimensions of the aortic and mitral orifices, the need for direct measurements of blood velocities within the left ventricle is eliminated (Figure 1). Therefore, the force associated with a fluid volume can be evaluated from measurements performed at the boundaries of the volume regardless of flow phenomena developing in the cavity.

Display full size

Figure 1. Flow chart of the steps required for HDF analysis. Images are acquired using routine 2-D echocardiography or non-contrast CMR. Three apical views are selected and the endocardial border is detected. Tracking of the endocardial motion provides strain assessment. Aortic and mitral valve areas are calculated from the relative valve diameters. Finally, a mathematical model based on the first principle of fluid dynamics and mass conservation principles allows for HDF curve assessment and display. AV: aortic valve; CMR: cardiac magnetic resonance; HDF: hemodynamic forces; MV: mitral valve. Adapted with permission from the Figure previously published by the author of this article [11], © 2024 the authors (CC BY NC ND)

In this article, we describe the pattern of a normal HDF curve, the morphology of the discrete parts of the cardiac cycle, and the parameters that can be derived. In addition, studies on HDF are reported in terms of parameters that have been used and clinical findings.

Image acquisition

HDF analysis can be performed from cine cardiac magnetic resonance (CMR) or 2-D echocardiography. The CMR scanning protocol includes standard cardiac sequences (long axis 2-, 3-, and 4-chamber views) recommended by international associations. Echocardiography is similarly focused on the acquisition of good quality apical views (2-, 3-, and 4-chamber). A parasternal long-axis view is recommended for accurate measurement of the aortic valve (AV) diameter. The acquired images are stored in an archive for offline analysis using dedicated software.

Image analysis

End-diastolic and end-systolic frames in the acquired images are selected. Then, the LV endocardial border is automatically detected by the software and the operator has the freedom to manually adjust the endocardial border if needed. The endocardial border is tracked over the cardiac cycle to derive a calculation of the standard volumetric parameters. The calculation of HDF requires measurements of the aortic and mitral valve area, which can be derived from the measurements of the respective valve diameters. Figure 2 represents a schematic drawing of the time course of the parameters derived from image analysis.

Display full size

Figure 2. Longitudinal HDF (green) and hemodynamic power (orange) curves in relation to LV volume (blue), instantaneous LV volume changes over time (dV/dt) (red), mitral and aortic valve opening and closure, and ECG. By convention, an IVPG directed from the apex to the base (apical pressure higher than basal pressure) is represented by a positive HDF value (above the zero line); when the IVPG is directed from the base to the apex it is displayed as negative (below the zero line). The different phases of the cardiac cycle considered for measurements of HDF parameters are labeled with letters (S = systolic ejection; S/D = systo-diastolic transition; D = diastole) and numbers. S1: initial impulse; S2: force decline; S3: elastic rebound; D1: suction; D2: early filling of the left ventricle; D3: diastasis; D4: late filling of the left ventricle. In this diagram, the time interval of each phase is set up from the HDF curve (light blue dots); the area under the curve on the corresponding time interval of the HDF curve represents the impulse (change of momentum, Δp) of the selected cardiac phases. AVC: aortic valve closure; AVO: aortic valve opening; ECG: electrical activity; HDF: hemodynamic forces; IVPG: intraventricular pressure gradients; LV: left ventricular; MVC: mitral valve closure; MVO: mitral valve opening. Adapted with permission from the Figure previously published by the author of this article [11], © 2024 the authors (CC BY NC ND)

The HDF curve represents the integral over the LV blood volume of the force per unit volume (pressure gradient), and the result is a force measurable in Newton (N). Positive values indicate gradients with an apex-to-base vector, while negative values indicate gradients with a base-to-apex vector. For easy comparison between subjects with different LV sizes, values are normalized with the LV volume and expressed as a percentage of gravity acceleration. Thus, units are dimensionless (%). It is important to understand the difference between the direction of the HDF (pressure gradients within the ventricle) and the direction of blood flow (pressure gradients between cardiac chambers). In fact, the vectors of the two gradients are dissociated (opposite directions) during selected parts of the cardiac cycle (see below, HDF during discrete parts of the systole).

Similarly, the hemodynamic power (HDP) curve represents the integral of the mechanical power per unit volume (that is the product of pressure gradient and blood velocity) and the result is the mechanical power measured in Watt (J/s) [3]. Although interesting from a theoretical point of view, the HDP suffers from practical drawbacks (complexity of the formula, noise, and extreme sensitivity to the measurement of valve dimensions) and does not provide robust data, therefore its use is still under investigation. The LV volume curve represents the changes in the LV volume over time. Units are mL. Finally, the dV/dt curve represents the rate at which the LV volume changes over time. Units are mL/s.

HDF parameters

Phantom validation of HDF showed good accuracy [4], and force reproducibility in humans has been proven to be strong [5, 6]. Normal values of HDF have been reported [7–9] and the method has been applied to several clinical models including athletes [10, 11], hypertensive patients [11], heart failure [12–15], dilated and non-ischemic cardiomyopathies [16–18], post-CRT (cardiac resynchronization therapy) [19–22], post-myocardial infarction [23], post-aortic coarctation repair [24], post-transcatheter AV implantation [25], evaluation of diastolic dysfunction [26], and to evaluate the effect of medical therapy [27, 28], however, several parameters have been proposed including HDF values throughout the cardiac cycle which provides information on the overall myocardial function. Selected HDF parameters have also been proposed with the aim of understanding the IVPG behavior during a specific time interval of the cardiac cycle [29, 30], however, there is a lack of consistency in the definition of the cardiac phases and how to set the time interval for HDF measurements. Table 1 summarizes the HDF parameters that have been reported in previous studies.

Clearly, different parameters are calculated in different phases of the cardiac cycle. More importantly, the terminology is sometimes confusing. For instance, the definition of the systolic phase varies according to the time limits (encompassing or not the negative wave of the elastic recoil). Furthermore, the term “impulse” can be ambiguous according to the context where it is used. In physics, the impulse is a vector quantity defined as the time integral of the force or as the change in momentum (Δp) and is equivalent to the area under a force-time curve. However, from a physiological and semantic point of view, the term impulse implies a thrust related to acceleration. Thus, to avoid confusion and misinterpretation, we suggest using the term “impulse” for the intervals including an ascending HDF curve (acceleration) and reserving the term “change in momentum” when the waves are downsloping (deceleration). Finally, the AUC (area under the curve) can be measured either in the HDF or in the HDP curve. In the first case, the AUC represents an impulse (change in momentum) and once normalized by the time interval it is the averaged or normalized AUC (nAUC). When the AUC is computed from the HDP curve, it represents a hemodynamic work. A glossary of physics terms with a technical meaning is reported in Table 2.

Based on our experience, we describe the main parameters that can be derived from the HDF curve with the aim of providing a guide for a uniform assessment and easy comparison among different studies.

HDF throughout the entire cardiac cycle

This analysis includes the whole cardiac cycle from the beginning to the end of the curve. It corresponds to the mean amplitude of the forces throughout the entire cardiac cycle. Longitudinal and latero-medial HDF are expressed as root mean squared (RMS), also called quadratic mean, which is the arithmetic mean of the squares of a group of values. Thus, both positive and negative values of the curve are included in the analysis. Accordingly, the following parameters can be derived:

• a.

  Longitudinal (apex-to-base) HDF (%)

• b.

  Latero-medial HDF (%)

• c.

  Latero-medial/longitudinal HDF ratio

In addition, the average angle of the HDF vector (which represents the dominant direction of HDFs) can be measured using a polar coordinate system, with values ranging from 90° (when the force is perfectly along the base-apex direction) to 0°. In normal subjects, HDF are predominantly oriented in a longitudinal direction, with a small component aligned in a lateral direction. Although these measurements are widely used, they include both systole and diastole, thus the contribution of the specific phases of the cardiac cycle cannot be differentiated.

HDF during discrete parts of the cardiac cycle

Analysis of a given event during the cardiac cycle can be easily performed by selecting appropriate time intervals on the curves. At this aim, the dV/dt curve is theoretically ideal, because it represents the rate at which volume changes over time, which can be crucial for understanding the behavior of systems whose volume is not constant. However, in practice, the dV/dt curve is often noisy (this usually happens when the quality of wall tracking is poor and the volume curve itself is irregular, which is uncommon in CMR studies), which may hamper the accuracy of the selection of proper time intervals. Alternatively, the HDF curve can be used, with the intercept of the curve with the zero line (zero-crossing) as a reliable marker for the selection of most of the time intervals. It should be noted that when one event fades into another without crossing the zero line (as the transition from the elastic recoil into suction), the time setting from the HDF curve is misleading.

Systolic ejection

This phase is defined from the rise of the HDF curve [in patients with delayed ventricular contraction, the R wave in the ECG (electrical activity) is preferred] until the next zero-crossing, which corresponds to the minimum value on the volume curve. The systolic ejection includes two components.

Systo-diastolic transition

This phase consists of two components, the elastic rebound and the suction.

Diastole

Practical tips

The separation between elastic rebound and suction is not always clear. In this case, a single interval including both events (S3 + D1) is recommended as a measure of the systo-diastolic transition.

Spectral Doppler recording of the aortic and mitral flow can be used as an additional marker for time setting of the intervals of the cardiac phases in case of HDF curve ambiguity.

Aortic and mitral valve areas affect the morphology of the HDF curve. Therefore, care must be taken for the acquisition of high-quality images (in particular with echocardiogram) and standardization of diameter measurements. For follow-up studies, the same values of valve areas are recommended in the same subject.

There are no data on the feasibility of echocardiography and CMR for HDF analysis. Reliable HDF curves are based on high-quality endocardial border tracking, thus higher feasibility with CMR can be anticipated.

Clinical relevance

Given the profound impact of various clinical conditions on the magnitude, spatial distribution, and temporal trend of both segmental and global myocardial mechanics, the great diagnostic potential of HDF analysis becomes evident. In fact, this approach translates complex myocardial dynamics into a concise set of clinically relevant parameters which facilitates diagnostic accuracy.

Thanks to the application of advanced mathematical models, HDF analysis can be currently applied to routinely acquired echocardiographic or CMR images independent from the brands of equipment. This approach offers advantages compared to LVEF (left ventricular ejection fraction) and deformation imaging and is able to resolve the changes in cardiac mechanics that occur during selected phases of the cardiac cycle. The main findings of the studies on HDF are reported in Table 1 based on the conclusions of the authors. The available experience indicates the clinical utility of HDF in the early detection and follow-up of patients with cardiomyopathy/heart failure, assessment of patients with dyssynchrony, and evaluation of the athlete’s heart. However, the most relevant parameters in these clinical scenarios have not been defined yet. Finally, comparative studies between echocardiography and CMR in the same group of normal subjects are needed to assess differences in values due to the imaging methods applied.

Conclusions

HDF is a physical property that provides a spatial-temporal representation of the pressure gradients induced by cyclic interaction between blood and tissue boundaries. Its analysis represents a useful novel tool to detect early impairment of LV function and might provide an opportunity for medical intervention at an early stage. The definition of cardiac events, both in terms of timing and terminology, is of paramount importance for comparing the results of different studies. The HDF parameters reported in this article might represent an effort toward standardization for most clinical studies. Additional parameters during different phases of the cardiac cycle could be considered to answer specific questions.