Jerk Analysis Facilitates Automated LVEDP Extraction from Catheter Measurements and Offers Valve Actuation Functions as New CHF Markers

Jerk Analysis Facilitates Automated LVEDP Extraction from Catheter Measurements and Offers Valve Actuation Functions as New CHF Markers. Biomed J Sci & Tech Res 39(5)-2021. BJSTR. MS.ID.006354. Left Ventricle End-Diastolic Pressure (LVEDP) is an accepted marker for Congestive Heart Failure (CHF). Right Ventricle End-Diastolic Pressure (RVEDP) is a marker for Right Heart Failure (RHF). Despite the wide usage of L/RVEDP in heart catheterization, the exact definition presuming fully automated calculation of L/RVEDP without human intervention with the monitor display has not yet been fully implemented. We fill this gap by exploiting kinetic features revealed when the pressure variation is measured with high resolution, namely, by tracing the third derivative of the pressure with respect to time (jerk analysis). In Physics, the notion of jerk means the rate of change of acceleration with respect to time. The ventricular pressures exhibit largest changes in their jerk during isovolumetric contraction and relaxation responding to the valves opening and closing. Observed regularities in the pattern of jerk behavior on these time intervals enable a precise determination of L/RVEDP and are correlated with CHF progression. This observation leads to a new independent CHF marker we call

Left Ventricle End-Diastolic Pressure (LVEDP) is an accepted marker for Congestive Heart Failure (CHF). Right Ventricle End-Diastolic Pressure (RVEDP) is a marker for Right Heart Failure (RHF). Despite the wide usage of L/RVEDP in heart catheterization, the exact definition presuming fully automated calculation of L/RVEDP without human intervention with the monitor display has not yet been fully implemented. We fill this gap by exploiting kinetic features revealed when the pressure variation is measured with high resolution, namely, by tracing the third derivative of the pressure with respect to time (jerk analysis). In Physics, the notion of jerk means the rate of change of acceleration with respect to time. The ventricular pressures exhibit largest changes in their jerk during isovolumetric contraction and relaxation responding to the valves opening and closing. Observed regularities in the pattern of jerk behavior on these time intervals enable a precise determination of L/RVEDP and are correlated with CHF progression. This observation leads to a new independent CHF marker we call "Mitral Valve Actuation", the average number of the third derivative local maxima points in the time interval between ECG R-peak and the end of isovolumetric contraction of the Left Ventricle (LV) bounded by an inflection point: the time moment when ventricular pressure rise max, / L dP dt is achieved. This number characterizes the non-uniformity and therefore loss or gain in quality of the ventricular preload and isovolumetric contraction. We further define "Valve Actuation" (VA) for each of four heart valves closure processes denoted as TVA, MVA, AVA and PVA following the valves' names. The Valve Actuation functions, MVA and TVA, as time series, are found to be statistically uncorrelated with ventricular pressure rise functions max, / / L R dP dt which are classical quality markers of LV and RV systolic functions [1]. Further analysis of time intervals where "Valve Actuation" is calculated leads to new numerical characteristics of myocardial behaviour and new markers of heart failure, such as Mitral/Tricuspid Valve Actuation Triangular Index (MVATI/TVATI), and in the same way Aortic/ Pulmonary Valve Actuation Triangular Index (AVATI/PVATI). The new values of TVA, MVA, AVA, PVA, MVATI, TVATI, AVATI, PVATI are changing according to the patients' hemodynamic and clinical status. While the Actuation group is generally increasing in the course of CHF progress, the Index group is respectively decreasing.

Introduction and Definitions
Heart diseases including CHF are a major cause of death according to the American Heart Association [2]. Left Ventricle End-Diastolic Pressure (LVEDP) is an acknowledged prognostic marker of congestive heart failure [3]. Measuring PAP and LAP (or it's proxy PCWP) directly with micro-manometer catheters (pressure transducers), or implantable devices as CardioMEMS (Atlanta, GA) and Vectorious (Tel Aviv, Israel) helps to predict CHF, as pulmonary hypertension is a major chronic disease associated with CHF [4]. LAP and/or PCWP could serve as marker for left ventricle diastolic dysfunction, which is highly connected to CHF, however, it is not exactly an equivalent to LVEDP being the exact marker for left ventricle diastolic dysfunction [5,6] and thus the further algorithmic extraction of LVEDP from LAP/LVP is needed. The first modern paper where the deeper mathematical investigation of left ventricular pressure (LVP) rise time interval was achieved by D. Adler, et al. [1]. In that pioneering study the time from the onset of contraction (which with the technology available then was corresponding generally to R-peak of ECG) to the ventricular pressure rise max, / L dP dt is suggested as an index of contractility and denoted as t_d. The analysis in this work shows that t d at any given heart rate (HR), is a reliable index of contractility. The shifted regression function ( ) d t HR serves as the indicator boundary for myocardial dysfunction. In the present work we go deeper and exploit "higher order" kinetic characteristics of the heart contraction during the t d time interval. We use a consistent feature of these kinetics for the determination of LVEDP. We further introduce and calculate "Mitral Valve Actuation" (MVA), a measure of extra nonlinearity of the heart contraction on t d time interval as a marker of dysfunction. A similar calculation is provided for each of the other three heart valves and is actually motivated by the work of Kenichi, et al. [7], where RV relaxation period (τ ), peak change in minimum Such definition also does not offer algorithmic, fully automated acquisition of LVEDP. We fill this gap by defining and presenting an algorithm for fully automated calculation of L/RVEDP by jerk (third derivative) analysis. The need for a fully automated calculation of L/RVEDP was raised in the context of calibration process of a non-invasive intra-cardiac pressure measurement system (ICPM) discussed in [9].
In the current work we show that LVEDP (and RVEDP) can be accurately and consistently determined using automated jerk analysis. Remind that in Physics, the notion of jerk means the rate proportional to the absolute peak ratio of the jerk maxima. This means, for example, that the LVEDP time point is 5 times closer to the right jerk maximum point than to the left one, if the right jerk maximum point peak is 5 times higher than the left one ( Figure   2). In dynamics such pair of points is called attractive-repulsive pairs. Physiologically this means that the largest myocardial muscle contraction force change indicates the most visible start of the isovolumetric contraction visually taken as LVEDP point.  The working hypothesis is that an ideal healthy subject has MVA = 1, meaning that the closer MVA is to 1, the better appears to be myocardial performance -matching with improved LVEDP values.
( Figures 3 & 4) for the MVA dynamics of the NSTEMI myocardial infarction patients before and after stent deployment.
In the same manner as LVEDP and MVA we define the RVEDP and TVA.

Definition 1R
RVEDP is defined as the Right Ventricular Pressure (RVP)    for an ideal healthy subject AVA = 1, meaning that the closer is AVA to 1, the better is the myocardial functional state.
In the same manner, as AVA is defined while investigating the descending slope of LVP, we further define PVA when considering the descending slope of RVP. We

Description of Equipment and the Experiment Setup
The underwent hemodynamic diagnostic catheterization (out of them 6 with known CAD). All the above patients were undergoing a planned catheterization procedure. During the procedure several recordings of the patients' intra-cardiac pressure were taken using the above described setup. The acquired data was post-processed by the following algorithm.

Description of the Algorithm
I. The Monitor pressure data channels are synchronized with ECG data channel at 1 msec level.

II.
The moving window averaging is applied to all channels to smoothen the functions and enable to calculate numerical derivatives.

III. Identifying L/RVEDP time points:
• Finding R -peak times T 1 on ECG (or S-peaks if R-peaks are unavailable or insufficiently manifested).
• Finding max, / / L R dP dt times T 2 on the cycle after ECG peak.

Results
We measure stability of measured L/RVEDP in several ways:

III.
Relative Standard Deviation is only 17% for LVEDP and 5% for RVEDP over all subjects and times supporting the stability of the method ( Figure 5). Tables 1 and 2 • Left jerk maxima count Table 3.
• Right jerk maxima count Table 4.  patients with preserved and reduced ejection fraction: (Table 5). MVATI and AVATI can be the further markers differentiating NSTEMI Myocardial infarction with preserved and reduced ejection fraction: (Table 7).

Discussion
We The Indexes are generally decreasing, while "Valve Actuation" are generally increasing in the course of CHF progress. Being capable to measure independent behaviour characteristics of all 4 heart valves enables to obtain a full clinical picture of the patient heart condition. Implementation of these new parameters in advanced and automated cardiac monitoring systems will enhance the efficacy of cardiac performance evaluation and the quality of therapy.